<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">AMT</journal-id><journal-title-group>
    <journal-title>Atmospheric Measurement Techniques</journal-title>
    <abbrev-journal-title abbrev-type="publisher">AMT</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Meas. Tech.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1867-8548</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/amt-16-3739-2023</article-id><title-group><article-title>Drone-based meteorological observations up to<?xmltex \hack{\break}?> the tropopause – a concept study</article-title><alt-title>Drone system for meteorological observations up to the tropopause</alt-title>
      </title-group><?xmltex \runningtitle{Drone system for meteorological observations up to the tropopause}?><?xmltex \runningauthor{K. B. Bärfuss et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Bärfuss</surname><given-names>Konrad B.</given-names></name>
          <email>k.baerfuss@tu-braunschweig.de</email>
        <ext-link>https://orcid.org/0000-0001-5130-5494</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Schmithüsen</surname><given-names>Holger</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5776-6777</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Lampert</surname><given-names>Astrid</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1414-1616</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Institute of Flight Guidance, Technische Universität Braunschweig, 38108 Braunschweig, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Helmholtz Centre for Polar and Marine Research, Alfred Wegener Institute, 27570 Bremerhaven, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Konrad B. Bärfuss (k.baerfuss@tu-braunschweig.de)</corresp></author-notes><pub-date><day>11</day><month>August</month><year>2023</year></pub-date>
      
      <volume>16</volume>
      <issue>15</issue>
      <fpage>3739</fpage><lpage>3765</lpage>
      <history>
        <date date-type="received"><day>15</day><month>August</month><year>2022</year></date>
           <date date-type="rev-request"><day>26</day><month>September</month><year>2022</year></date>
           <date date-type="rev-recd"><day>2</day><month>July</month><year>2023</year></date>
           <date date-type="accepted"><day>4</day><month>July</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 </copyright-statement>
        <copyright-year>2023</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://amt.copernicus.org/articles/.html">This article is available from https://amt.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e107">The main in situ database for numerical weather prediction currently relies on radiosonde and airliner observations, with large systematic data gaps: horizontally in certain countries, above the oceans and in polar regions, and vertically in the rapidly changing atmospheric boundary layer, as well as up to the tropopause in areas with low air traffic.
These gaps might be patched by measurements with drones. They provide a significant improvement towards environment-friendly additional data, avoiding waste and without the need for helium. So far, such systems have not been regarded as a feasible alternative for performing measurements up to the upper troposphere.
In this article, the development of a drone system that is capable of sounding the atmosphere up to an altitude of 10 km with its own propulsion is presented, for which Antarctic and mid-European ambient conditions were taken into account:
after an assessment of the environmental conditions at two exemplary radiosounding sites, the design of the system and the instrumentation are presented. Further, the process to get permissions for such flight tests even in the densely populated continent of Europe is discussed, and methods to compare drone and radiosonde data for quality assessment are presented.
The main result is the technical achievement of demonstrating the feasibility of reaching an altitude of 10 km with a small meteorologically equipped drone using its own propulsion. The first data are compared to radiosonde measurements, demonstrating an accuracy comparable to other aircraft-based observations, despite the simplistic sensor package deployed. A detailed error discussion is given.
The article closes with an outlook on the potential use of drones for filling data gaps in the troposphere.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Bundesministerium für Verkehr und Digitale Infrastruktur</funding-source>
<award-id>19F2072A</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e119">Accurate weather predictions are of high importance for humankind, considering aspects from agriculture via air traffic and warning of severe weather events like storm and heavy rain to the personal activities of individuals. With increasing computational power, there have been significant improvements in operational weather models <xref ref-type="bibr" rid="bib1.bibx11" id="paren.1"/>.
However, these global and mesoscale models require measurement data as input to tie the short-term forecast to observations <xref ref-type="bibr" rid="bib1.bibx123" id="paren.2"/>. In this computing-intensive process, data can be assimilated continuously, with high flexibility regarding spatial and temporal resolution and trajectories <xref ref-type="bibr" rid="bib1.bibx12" id="paren.3"/>.
The data to be assimilated originate from the World Meteorological Organization (WMO) Global Observing System <xref ref-type="bibr" rid="bib1.bibx116 bib1.bibx127 bib1.bibx129" id="paren.4"/>, consisting of measurements using both in situ and remote sensing techniques. Atmospheric measurements of pressure, temperature, humidity, wind speed and wind direction are crucial to numerical weather prediction (NWP). These measurements can partially be provided by ground-based remote sensing techniques <xref ref-type="bibr" rid="bib1.bibx85 bib1.bibx76" id="paren.5"/>, satellite-based remote sensing techniques <xref ref-type="bibr" rid="bib1.bibx112 bib1.bibx71 bib1.bibx105" id="paren.6"/>, radiosondes <xref ref-type="bibr" rid="bib1.bibx57" id="paren.7"/>, aircraft <xref ref-type="bibr" rid="bib1.bibx39" id="paren.8"/> and dropsondes (meteorological sensor packets dropped from high-altitude platforms; <xref ref-type="bibr" rid="bib1.bibx52" id="altparen.9"/>). Each of these observing system types has its own peculiarities which have to be considered for implementing in weather models, and each has a different impact on the forecast quality.</p>
      <?pagebreak page3740?><p id="d1e150"><?xmltex \hack{\newpage}?>Ground-based remote sensing instruments need significant financial effort to be deployed and operated. Their use around the globe is therefore quite limited. Satellite-based remote sensing measurements provide superior global coverage and have a high impact in NWP <xref ref-type="bibr" rid="bib1.bibx16" id="paren.10"/>, especially over data-poor areas <xref ref-type="bibr" rid="bib1.bibx14" id="paren.11"/>. For calibration and validation of these satellite sensors and data products, satellite-based observing systems (and in general remote sensing measurements) rely on in situ data for calibration and validation <xref ref-type="bibr" rid="bib1.bibx44 bib1.bibx19 bib1.bibx15 bib1.bibx18" id="paren.12"/>. An increasing challenge (and also a potential opportunity; <xref ref-type="bibr" rid="bib1.bibx94" id="altparen.13"/>) for retrieving meteorological observations from satellite microwave instruments (e.g. <xref ref-type="bibr" rid="bib1.bibx71" id="altparen.14"/>) is the “society’s insatiable need for the radio spectrum” <xref ref-type="bibr" rid="bib1.bibx94" id="paren.15"/>, potentially harming future measurements. Space-based Doppler wind lidar measurements are regarded as essential data for weather models, addressing the urgent need to provide wind profiles at all latitudes and altitudes <xref ref-type="bibr" rid="bib1.bibx3" id="paren.16"/>.</p>
      <p id="d1e176">Of major importance regarding in situ observations are vertical profiles measured by radiosondes. They are launched at specific stations and at fixed launch times, from typically daily frequency to four times per day. The measurement data are transferred to the ground via telemetry and are sent to the Global Telecommunication System (GTS) network to be accessed by weather services in a specific data format <xref ref-type="bibr" rid="bib1.bibx56" id="paren.17"/>. Typical state-of-the-art sounding systems provide measurements of altitude, pressure, temperature, humidity, wind speed and wind direction once per second. Depending on the sounding system and balloon sizes used, radiosondes typically measure atmospheric profiles up to an altitude of 35 km or even 40 km, covering the entire troposphere and most of the stratosphere. Usually, radiosondes are not collected and re-used but remain in the landscape as litter. The around 800 radiosonde launch sites worldwide are not evenly distributed around the globe. There are large areas with only few regular launches, in particular above the oceans and in the polar regions.</p>
      <p id="d1e182">Another important source of in situ data originates from AMDAR (Aircraft Meteorological DAta Relay) and the US-related TAMDAR (Tropospheric Airborne Meteorological Data Reporting) programme <xref ref-type="bibr" rid="bib1.bibx90 bib1.bibx98 bib1.bibx99 bib1.bibx97" id="paren.18"/>. In the vicinity of large cities, vertical profiles of temperature, wind speed and wind direction (and partly humidity) are measured frequently through commercial aircraft equipped with the AMDAR-specific meteorological sensor package <xref ref-type="bibr" rid="bib1.bibx126" id="paren.19"/>, with additional observations at flight level provided during cruising. For this airborne method, careful calibration and processing of the data are required <xref ref-type="bibr" rid="bib1.bibx27" id="paren.20"/>. Due to less coverage because of fewer en route flights and especially fewer airports, regions like the Arctic and Antarctic as well as mid-Africa suffer from a lower data density regarding the AMDAR system.</p>
      <p id="d1e195">Data comparable to aircraft and radiosonde measurements can be gathered using sondes dropped by aircraft – either crewed <xref ref-type="bibr" rid="bib1.bibx82" id="paren.21"/> or uncrewed <xref ref-type="bibr" rid="bib1.bibx78" id="paren.22"/> – and balloons <xref ref-type="bibr" rid="bib1.bibx124" id="paren.23"/> from altitudes close to the ground up to 30 km <xref ref-type="bibr" rid="bib1.bibx23" id="paren.24"/>. Data from dropsonde measurements have recently been used for intense observation periods <xref ref-type="bibr" rid="bib1.bibx103 bib1.bibx101 bib1.bibx78 bib1.bibx108 bib1.bibx102 bib1.bibx135" id="paren.25"/>, but as they are used for specific target areas and specific purposes only, they do not play a significant role in global observations.</p>
      <p id="d1e213">To assess their impact on forecast quality and subsequently the importance of these different observing systems (single observation systems) in order to further develop the Global Observing System, observing system experiments <xref ref-type="bibr" rid="bib1.bibx13" id="paren.26"/>, sensitivity-to-observation experiments <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx81" id="paren.27"/> and similar experiments <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx93" id="paren.28"/> can be carried out. As new observing systems are deployed, their impact on weather models (including the assimilation system) is evaluated and reviewed using these techniques <xref ref-type="bibr" rid="bib1.bibx105 bib1.bibx97 bib1.bibx99 bib1.bibx14 bib1.bibx13 bib1.bibx106" id="paren.29"/>.
For example, space-based Doppler wind lidar measurements are regarded as essential for numerical weather prediction <xref ref-type="bibr" rid="bib1.bibx3" id="paren.30"/>. The examination of including wind retrievals using the first spaceborne wind lidar showed a positive impact on forecasting quality <xref ref-type="bibr" rid="bib1.bibx105" id="paren.31"/>. Aircraft meteorological measurements complement radiosonde measurements when radiosonde data were not used in the forecast experiments <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx86 bib1.bibx72" id="paren.32"/>.
Aircraft wind and temperature reports show a significant improvement of model results at pressure levels between 700–400 hPa (around 3–7 km altitude) <xref ref-type="bibr" rid="bib1.bibx97" id="paren.33"/>. The availability of additional aircraft humidity data has the highest impact between 1000–400 hPa (around 0.5–7 km altitude) <xref ref-type="bibr" rid="bib1.bibx99" id="paren.34"/>, whereas additional radiosonde in situ humidity data have the highest influence on weather models at 700–600 hPa (around 3–4 km altitude) <xref ref-type="bibr" rid="bib1.bibx93" id="paren.35"/>. In comparison with temperature and wind, the impact of aircraft humidity data showed lower influence on the results of weather models <xref ref-type="bibr" rid="bib1.bibx59" id="paren.36"/>.</p>
      <p id="d1e250">Summing up the components of the Global Observation System, in situ data gaps of important observations are obvious, as radiosonde- and aircraft-based soundings are sparsely distributed over remote areas and oceans, associated with the increased impact of additional radiosonde observations <xref ref-type="bibr" rid="bib1.bibx93" id="paren.37"/>. The density of observations is not well balanced with user requirements for observations. Breakthrough requirements as defined in <xref ref-type="bibr" rid="bib1.bibx133" id="text.38"/> from data users exceed today's capabilities of the Global Observation System in terms of temporal and spatial resolution for the use case of global and high-resolution numerical weather prediction. These requirements differ between their application<?pagebreak page3741?> area and the variable of interest; e.g. for global NWP, the breakthrough requirement for the spatial resolution of temperature measurements is 100 km horizontally and 1 km vertically with an observation cycle of 6 h and a timeliness of 30 min <xref ref-type="bibr" rid="bib1.bibx84" id="paren.39"/>. Generally speaking, more and higher-resolution data lead to improved numerical simulations of both local and regional weather forecasts <xref ref-type="bibr" rid="bib1.bibx36" id="paren.40"/>. Numerical weather prediction models perform best with observations of similar temporal and spatial resolution to those in the model <xref ref-type="bibr" rid="bib1.bibx25" id="paren.41"/>.</p>
      <p id="d1e268">Besides regional data gaps <xref ref-type="bibr" rid="bib1.bibx58 bib1.bibx131" id="paren.42"/> and general data gaps <xref ref-type="bibr" rid="bib1.bibx54" id="paren.43"/>, there is a data gap in the lower troposphere in atmospheric observing systems <xref ref-type="bibr" rid="bib1.bibx84 bib1.bibx100" id="paren.44"/>, and the potential of drones to fill the gap is currently being discussed. Drones (also called remotely piloted aircraft systems, RPASs, or unmanned aircraft systems or uncrewed aircraft systems as a gender-neutral term, UASs – <xref ref-type="bibr" rid="bib1.bibx68" id="altparen.45"/>) provide a flexible tool for atmospheric sensing. The use of small drones as a platform for meteorological sensors dates back to the early 1960s <xref ref-type="bibr" rid="bib1.bibx75" id="paren.46"/>. Far from being mature at that time, their use was limited to augmented line-of-sight operations using binoculars to monitor the aircraft's attitude and therefore to the lower troposphere. A comprehensive review of the historical and recent use of fixed-wing drones for meteorological sensing can be found in <xref ref-type="bibr" rid="bib1.bibx32" id="text.47"/>. In consequence of the emergence of commercial off-the-shelf drones (both fixed-wing and multicopter), the use of drones in different fields of research has rapidly increased during the last decade.</p>
      <p id="d1e290">The atmospheric boundary layer experiences high temporal changes, and as it is closely connected to the spatially variable Earth surface, the boundary layer plays a key role in initiating or hindering weather events like convection or cloud and fog formation. Therefore, drone measurements in the boundary layer have high potential for providing data of added value to weather forecasts <xref ref-type="bibr" rid="bib1.bibx62" id="paren.48"/>, for example by determining the boundary layer altitude capped by a temperature inversion <xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx38" id="paren.49"/>.</p>
      <p id="d1e299">The improvement of assimilating drone measurements of the atmospheric boundary layer into numerical weather predictions during intensive meteorological campaigns has been demonstrated <xref ref-type="bibr" rid="bib1.bibx26" id="paren.50"/>, with improvements of modelling results for a distance of up to 300 km <xref ref-type="bibr" rid="bib1.bibx114" id="paren.51"/>. Significant benefit from regular drone soundings even to limited altitudes of 1 km or 3 km has been demonstrated for precipitation <xref ref-type="bibr" rid="bib1.bibx20" id="paren.52"/> and cloud coverage <xref ref-type="bibr" rid="bib1.bibx84" id="paren.53"/>, and a reduction of over 40 % has been observed for the root-mean-square error and bias in the 15 min forecasts of temperature, wind and humidity between the benchmark run and a model run with assimilated data of a coordinated fleet of drones <xref ref-type="bibr" rid="bib1.bibx65 bib1.bibx66" id="paren.54"/>, despite the challenges of data assimilation in mountainous environments <xref ref-type="bibr" rid="bib1.bibx45" id="paren.55"/>. However, drone measurements up to higher altitudes would be more beneficial <xref ref-type="bibr" rid="bib1.bibx114" id="paren.56"/>. It must be noted here that the deployment of drone systems for operational meteorology only has benefits if data can be transferred and distributed in near real time, which has not been demonstrated within most of the above-mentioned studies.</p>
      <p id="d1e325">For obtaining additional data similar to the classical radiosondes, balloon-launched drones that are carried up to a certain altitude, which can be around 20–40 km, have been developed. Upon reaching the target altitude, the systems are released from the balloons and then return to the starting location in restricted airspace <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx77 bib1.bibx109" id="paren.57"/> – at least for low-wind-speed conditions. These drones further provide the advantage of controlling the direction of flight. In comparison to radiosondes, it is therefore possible to deploy more sophisticated instrumentation, as it can be used multiple times, and sensors can be calibrated before and after a sounding for quality checks. High data quality enables further use of the measurements, such as in climate applications <xref ref-type="bibr" rid="bib1.bibx130" id="paren.58"><named-content content-type="pre">see Annex 12.B in</named-content></xref>. However, balloon-launched systems require the availability of helium and a certain launching infrastructure, like for classical radiosonde launches, and are barely able to glide back to their starting location for wind speed exceeding 15 m s<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e348">For increasing the flexibility of the launching site, it is beneficial to deploy systems with their own propulsion. Regular soundings of multicopter drones to improve weather forecast for airports have been established in Switzerland <xref ref-type="bibr" rid="bib1.bibx84" id="paren.59"/>. Other studies to improve weather prediction include fixed-wing drones as well <xref ref-type="bibr" rid="bib1.bibx73" id="paren.60"/>. Further, no waste is left from such a drone ascent, which is of high importance in particular in the Antarctic, where the Antarctic Treaty requires environmental impact assessments to be developed for all activities and which sets rules for waste disposal and management <xref ref-type="bibr" rid="bib1.bibx110" id="paren.61"/>. Nevertheless, systems with their own propulsion normally do not reach the altitudes of radiosondes and therefore can be compared more easily to aircraft (e.g. AMDAR–TAMDAR). The main technical challenges of drone operations up to high altitudes compared to observations from commercial aircraft are high wind speed, low temperatures, potential icing and extremely low specific humidities regarding measurement techniques. Individual systems and concepts have been developed for applications in high wind speeds, such as for in situ measurements of hurricanes and tornadic supercells <xref ref-type="bibr" rid="bib1.bibx22 bib1.bibx33" id="paren.62"/> and for measurements up to and within the stratosphere <xref ref-type="bibr" rid="bib1.bibx107" id="paren.63"/>.</p>
      <?pagebreak page3742?><p id="d1e366">Nowadays, the status of small drones for weather sensing in the lower troposphere is quite mature <xref ref-type="bibr" rid="bib1.bibx100" id="paren.64"/> and close to being ready for operational applications in meteorology.
As an experiment to collect experience on both the drone operation and the NWP aspect, the WMO is preparing a coordinated worldwide demonstration campaign in 2024 <xref ref-type="bibr" rid="bib1.bibx132" id="paren.65"/>. There is broad agreement that drones are becoming an increasingly important tool for all sorts of meteorological tasks <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx120" id="paren.66"/>. Interestingly, drones which are capable of reaching the upper troposphere and even lower stratosphere are viewed as a future alternative to current in situ observing systems and enable the community to address important scientific issues, but these drone systems have not received much attention in scientific discussion – the road to inexpensive high-flying drones seems to have remained unpaved.</p>
      <p id="d1e378">The importance of aircraft measurements in the troposphere concomitant with in situ data gaps in the troposphere and over remote areas was the starting point for a research project at the Technische Universität Braunschweig (Germany), in which a drone was developed to augment in situ data in Antarctica. The drone represents a fairly unusual class <xref ref-type="bibr" rid="bib1.bibx125" id="paren.67"><named-content content-type="pre">medium altitude, short endurance;</named-content></xref>. The propelled drone technique presented here provides the capability of sounding the entire troposphere vertically or performing level legs at designated altitudes while measuring pressure, temperature, humidity, wind speed, wind direction and turbulence, and it flexibly addresses data needs <xref ref-type="bibr" rid="bib1.bibx54" id="paren.68"/>.
Regarding data assimilation, drone data transferred to the GTS are similar to aircraft data (this is especially true for regional aircraft observations; <xref ref-type="bibr" rid="bib1.bibx91" id="altparen.69"/>) and radiosonde data (ascent and descent).</p>
      <p id="d1e392">This feasibility study presents the concept, design and first applications of the system LUCA (Lightweight Unmanned high-Ceiling Aerial system), which was developed to provide complementary in situ data up to an altitude of 10 km at flexible locations. Simultaneous radiosonde ascents are used to validate the quality of the meteorological observations acquired during the first flights.</p>
      <p id="d1e395">Please be aware of Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>–<xref ref-type="sec" rid="App1.Ch1.S4"/>, to which the authors paid particular attention. Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/> contains a detailed description of the data processing, Appendix <xref ref-type="sec" rid="App1.Ch1.S2"/> introduces generally valid calibration techniques, Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/> theoretically estimates measurement errors and Appendix <xref ref-type="sec" rid="App1.Ch1.S4"/> presents a note on the variability of the atmosphere.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e414">Analysis of environmental constraints at the radiosonde stations Lindenberg in Germany <bold>(a, b)</bold> and Neumayer in the Antarctic <bold>(c, d)</bold>. Panels <bold>(a)</bold> and <bold>(c)</bold> show the probability distribution function (PDF) of air temperature with altitude in greyscale and panels <bold>(b)</bold> and <bold>(d)</bold> the PDF of wind speed with altitude. The median is indicated in blue and the minimum and maximum values as dotted black lines, and the percentiles including 90 % (light blue), 95 % (magenta) and 99 % (red) of the data are indicated. The plot is based on the time period from 2016 to 2018, including all radiosonde launches at Neumayer around 12:00 UTC and all launches around 00:00 UTC as well as 12:00 UTC at Lindenberg.</p></caption>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f01.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d1e450">In the following, the process towards the design of the LUCA-type drone is presented briefly. Requirements for the system are derived from the environmental conditions to be expected to obtain high availability of measurements. Based on the environmental conditions for two sites, the design of the mission and of the drone is introduced. The simplistic sensor package that was used for the demonstration flights is described, including uncertainty aspects. The process of obtaining flight permissions for such altitudes is presented. The methods for data post-processing are presented, and the data quality obtained is assessed. The section closes with a note on the variability of the atmosphere.</p><?xmltex \hack{\newpage}?>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Environmental conditions</title>
      <p id="d1e461">LUCA was designed to operate in mid-latitude and polar conditions. Therefore, the expected environmental constraints were evaluated from the radiosonde stations Neumayer in Antarctica and Lindenberg in Germany (Fig. <xref ref-type="fig" rid="Ch1.F1"/>) episodically over 3 years (2016–2018). The temperature range covering 90 % of the operating conditions of the ascents at Lindenberg is between <inline-formula><mml:math id="M2" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>60 and 20 <inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and at Neumayer is between <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula>  and <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. For the Lindenberg station, the median wind speed is up to 20 m s<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and the wind speed that is encountered in 90 % of the cases (90th percentile) is up to 42 m s<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for the altitude of the jet stream (7–15 km) <xref ref-type="bibr" rid="bib1.bibx96" id="paren.70"/>.
For the Neumayer station, the median wind speed is up to 14 m s<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and the wind speed that can be expected in 90 % of the cases is up to 28 m s<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e563">Operational challenges at Neumayer arise from the surface wind speed, which is generally higher than in Europe. The most frequent surface wind conditions are either from the east due to cyclonic activities near the polar front, with a typical wind speed of 20 m s<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, or from the south due to katabatic flow, with a typical wind speed of 10 m s<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx74" id="paren.71"/>.
High wind speed values are further reached at the altitude of the tropopause, around 9–13 km <xref ref-type="bibr" rid="bib1.bibx34" id="paren.72"/> in the polar jet stream <xref ref-type="bibr" rid="bib1.bibx1" id="paren.73"/>.</p>
      <p id="d1e599">The LUCA system was designed for operation in the temperature range between <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and for a wind speed of less than 28 m s<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> over the whole vertical profile to limit the maximum vector displacement of the drone from its launch site. Assuming the system is capable of operating in conditions exceeding the design temperature and nominal wind speed by 15 %, this would allow ascents in 87 % of the radiosonde days at Neumayer in the Antarctic and 72 % at Lindenberg.
Restricting wind speed conditions such that the drone does not have to stay above the launch point but must be able to return to the base, the mean wind speed over the atmospheric profile to be observed by the drone should not exceed the nominal horizontal airspeed component of 28 m s<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Despite the limited applicability of this approach when using the drone in a reserved airspace and ignoring possible environmental threats such as heavy precipitation or in-flight icing, the system is capable of covering 94 % of the measurements in Lindenberg and 98 % at the Neumayer station. Adding a margin of 15 %, the availability increases to 97 % for Lindenberg and 100 % for Neumayer.
At the Neumayer station, on 96 % of the days, radiosondes can typically be launched. Lindenberg has a temporal coverage of 99 % of all days. In addition, the development of the drone addresses measurements during rainfall, snow and heavy turbulence and within clouds, but these capabilities have yet to be proven in upcoming measurement campaigns.</p>
      <p id="d1e655">Particular attention was paid to takeoff and landing under high-surface-wind conditions, which are accompanied at the Neumayer station by low visibility due to drifting and blowing snow. The probability of 23 % to operate under<?pagebreak page3743?> conditions with a visibility below 500 m requires a highly automated takeoff and landing procedure that does not rely on visual contact of the operator with the system, similarly to operations shown by <xref ref-type="bibr" rid="bib1.bibx104" id="text.74"/>.</p>
      <p id="d1e662">A possible threat for drone measurements comprises in-flight icing conditions, which depend on temperature, humidity and droplet size <xref ref-type="bibr" rid="bib1.bibx64" id="paren.75"/>.
An idea of the frequency of icing conditions might be available from icing forecast data using ADWICE (Advanced Diagnosis and Warning System for Aircraft Icing Environments; <xref ref-type="bibr" rid="bib1.bibx115" id="altparen.76"/>) along with validation studies using PIREPs (pilot reports). Such comparisons exist for regions with dense air traffic, e.g. Europe <xref ref-type="bibr" rid="bib1.bibx69" id="paren.77"/>,
but no validation studies are found for the Antarctic.
In addition, icing differs strongly between crewed aircraft (what ADWICE is made for) and drones <xref ref-type="bibr" rid="bib1.bibx47" id="paren.78"/>.
A report for Norway and its surrounding regions explicitly focused on icing for drones using meteorological reanalysis data (ECMWF ERA5; <xref ref-type="bibr" rid="bib1.bibx51" id="altparen.79"/>) and an ice accretion model (ICE3D; <xref ref-type="bibr" rid="bib1.bibx111" id="altparen.80"/>), and it found theoretical icing frequencies of 45 % at an altitude between 1–1.5 km between September and May and a lower risk with the highest frequency of 30 % peaking at 2.5 km altitude in June to August.
These values are not directly applicable to the Antarctic, but the process to determine the likelihood of icing might be used to preliminarily estimate icing frequency and icing risk for drones in the Antarctic.</p>
      <p id="d1e684">Drones are usually operated without sophisticated anti-icing and de-icing concepts like in crewed aviation, in particular as most drones are operated in visual line of sight. However, icing is a threat that may lead to a complete loss of the system. Icing protection for drones has been demonstrated <xref ref-type="bibr" rid="bib1.bibx48" id="paren.81"/> but requires additional substantial energy for heating, even if combined with specific ice-phobic coatings or liquids <xref ref-type="bibr" rid="bib1.bibx55" id="paren.82"/>.</p>
      <p id="d1e693">For the demonstration flights shown here, the LUCA drone was prepared to be equipped with an icing sensor to measure in situations with a substantial risk of meeting icing conditions during the flight, but the sensor was not installed during the demonstration flights as zero risk of icing was present. Together with monitoring performance parameters, this allows for estimating the severity of icing and supports the decision of abandoning the mission in icing cases. More details about the all-weather strategy can be found in <xref ref-type="bibr" rid="bib1.bibx8" id="text.83"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>System design</title>
      <p id="d1e707">Before designing the physical aircraft system, the mission to be accomplished by the drone was defined. Although data assimilation is nowadays highly flexible regarding time, the mission was designed according to radiosonde observations to hypothetically surpass the 100 hPa surface at 12:00 UTC <xref ref-type="bibr" rid="bib1.bibx61" id="paren.84"/> and ensure timeliness in anticipation<?pagebreak page3744?> of future in-flight reporting analogue to radiosonde reporting, where a first dataset is sent to the GTS when the sonde reaches the 100 hPa level <xref ref-type="bibr" rid="bib1.bibx56" id="paren.85"/>. With a targeted climb rate of 10 m s<inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> arbitrarily chosen from simple analytical estimates, the drone has to be launched around 11:33 UTC, and it reaches the design ceiling of 10 km at 11:50 UTC. During the flight, 1 Hz real-time data are available.
After descending with a vertical rate similar to the climb rate, an approach procedure is flown in the vicinity of the landing site to determine wind direction and wind speed, and subsequently the approach trajectory is calculated automatically on the onboard computer. After the “splashdown” into a horizontal landing net, the drone can be recovered, and data processing including quality checks and transcoding begins. The observations of the complete flight are finally transferred into the GTS around 13:00 UTC. Thus, there is a target of making post-processed data from the descent profile available within an hour of the measurements being taken. Figure <xref ref-type="fig" rid="Ch1.F2"/> illustrates the mission design.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e732">Mission design for the LUCA drone. In order to be able to provide a first observation dataset for assimilation at 12:00 UTC, the drone is launched from the catapult at 11:33 UTC (as shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>a) and starts with the vertical sounding in the form of spirals at 11:35 UTC, hypothetically reaching the 100 hPa level at 12:00 UTC. After reaching its target altitude of 10 km at 11:50 UTC, the drone descends with a sink rate equal to the rate of climb (10 m s<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) until it arrives at the designated approach altitude around 12:05 UTC. After circles to determine the speed and direction of the near-surface wind, LUCA begins with the approach and lands in a horizontal landing net. Data processing, quality checks and transcoding into the WMO BUFR data format start directly after landing to enable data transfer of the complete flight to the GTS at around 13:00 UTC.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f02.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e757"><bold>(a)</bold> The LUCA drone mounted on the catapult to get airborne for measurements over the Baltic Sea. <bold>(b)</bold> A picture from the LUCA drone 10 km above the Lübeck Bight, the Baltic Sea, on 28 October 2021.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f03.jpg"/>

        </fig>

      <p id="d1e772">As key design driving parameters, the ability to fly against high-speed winds, an efficient electric propulsion chain and a highly flight-state-independent position for the sensor package are essential. These requirements led to the development of a tailless fixed-wing configuration with a pusher propeller. As the result of a multi-variant optimisation for profiling the atmosphere vertically up to 10 km, the design weighs 5–6 kg, depending on the deployed sensor package; has a wingspan of less than 2 m; and operates at a constant airspeed of 30 m s<inline-formula><mml:math id="M20" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> with a typical ascent rate of 10 m s<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> controlled by the autopilot system.
Thus, the system has a minimum airspeed of 18 m s<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, exceeding the minimum airspeed of crewed ultralight aircraft. Subsequently, it is not feasible to launch the drone by hand, and a dedicated mechanical catapult was adapted and used during the measurement campaign (Fig. <xref ref-type="fig" rid="Ch1.F3"/>a).
As automatic takeoff and landing are required for future operations in zero-visibility conditions, a horizontal landing net has been developed and an appropriate manoeuvre to get the drone safely into the net was implemented in the autopilot firmware (ArduPilot). The manoeuvre itself can be considered an automated vertical dive into the horizontally arranged net. While a belly landing is principally possible, the net-landing technique was preferred as it protects the drone and the sensors from the hostile surface in the Antarctic, and prevents the system from being blown away and lost in low-visibility conditions of drifting and blowing snow in the case of high near-surface wind speed, as occurs frequently in the Antarctic.
For the launch and retrieval system, no specific operation limits are in place regarding wind speed, as long as the launch and the landing is performed against the wind direction. Preliminary operating limits are therefore bound to the nominal airspeed of the drone.
To address the risk of disintegration in turbulence, the airframe was constructed to resist gusts according to EASA Certification Specifications 23.333 <xref ref-type="bibr" rid="bib1.bibx31" id="paren.86"/>.
On the avionics side, the systems on the drone were widely predefined by national regulations (e.g. the redundancy of the command and control link).
<xref ref-type="bibr" rid="bib1.bibx8" id="text.87"/> reveal more technical details of the drone and its ground systems, which are not within the scope of this article.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Simplistic sensor package</title>
      <p id="d1e829">An overview of the sensors and their accuracy according to the data sheet is provided in Table <xref ref-type="table" rid="Ch1.T1"/>. The placement of the sensors is based on experience with similar drone-based systems <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx6 bib1.bibx80" id="paren.88"><named-content content-type="pre">e.g.</named-content></xref>, and the sensor behaviour and possibilities of correcting, for example, sensor response time are well known. The performance of sensors and the data quality are assessed directly from the atmospheric measurements, without including wind tunnel tests for the overall setup.</p>
      <?pagebreak page3745?><p id="d1e839">To enable the autopilot sensors to measure dynamic and static pressure, a total pressure port (pitot tube) and static pressure ports on both sides of the drone were implemented in the nose section of LUCA.
Below the pitot tube, an air inlet for the closed sensing path for the temperature–humidity probe (<inline-formula><mml:math id="M23" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>/RH probe inlet) is installed, as sensor installation is known to influence the measurements <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx62" id="paren.89"/>.
The combined resistance temperature and capacitive humidity sensor HMP110 (Vaisala, Finland), providing measurements of temperature and relative humidity in the closed sensing path, was mounted within the bulkhead, which separates the sensor chamber from the fuselage area. Subsequent to passing by the sensing elements, the air perfuses the measurement chamber and is vented out through apertures in the bottom of the nose section (venting).
This ensures well-defined pressure conditions at the sensor location that are close to total pressure while maintaining ventilation of the sensing element.
The ventilation rate, which is assumed to be still higher than the ventilation rate of radiosonde sensors, minimises the response time of the sensors as the sensor is exposed to an increased amount of air over time compared to radiosondes.
The enclosure furthermore protects the sensors from damage due to ground contact, even during rough landings. An illustration of the sensor installation used for the measurement flights is provided in Fig. <xref ref-type="fig" rid="Ch1.F4"/>a, where the measurement nose of the drone is shown.
As the body of the combined temperature and humidity probe is made of stainless steel and is mounted through the bulkhead between the sensor chamber and the fuselage area, thermal conduction into the sensor chamber which might affect the measurements is expected in the case of temperature differences between the ambient air temperature and the temperature inside the fuselage, as mentioned in, for example, <xref ref-type="bibr" rid="bib1.bibx80" id="text.90"/>. Additionally, the response times of the humidity measurements are expected to increase further, as the “wetted” area inside the sensor chamber is not well vented.
Besides the sensors and pressure ports in the nose section, measurements of static and dynamic pressure, attitude angles, the Earth-related position, and velocities – all taken by the autopilot system (Cube Orange, HexAero, Singapore) – were recorded to derive atmospheric variables. As a drawback, the inertial navigation algorithm running on the autopilot system to calculate attitude angles, the Earth-related position and velocities relies on industrial-grade GNSS (global navigation satellite system), rotation rate, acceleration and magnetic field sensors, which limits the accuracy of the location and attitude estimation and subsequently limits the accuracy of the wind calculation, varying with the flight trajectory.
Particularly, heading information might be adversely affected by electromagnetic interference originating from the power train, which is more pronounced during the ascent. Additionally, the estimation filter in the inertial navigation algorithm is not able to observe sensor (e.g. turn rate sensor) errors well during flight phases with low-trajectory dynamics. Measured parameters including data sheet uncertainties for both the LUCA drone and the radiosonde launched for data intercomparison are summarised in Table <xref ref-type="table" rid="Ch1.T1"/>.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e862">Sensor summary for the radiosonde and the LUCA drone using data sheet values.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Radiosonde</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Sensor uncertainty</oasis:entry>
         <oasis:entry colname="col2">Graw DFM-09</oasis:entry>
         <oasis:entry colname="col3">LUCA</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Position</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">2.5 m<inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Pressure</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> Pa</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> Pa</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Temperature</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M37" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>
         <oasis:entry colname="col3">0.4 <inline-formula><mml:math id="M38" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C<inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Humidity</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> % RH</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> % RH<inline-formula><mml:math id="M42" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">c</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Wind speed</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M44" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">NA<inline-formula><mml:math id="M45" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Wind direction</oasis:entry>
         <oasis:entry colname="col2">NA<inline-formula><mml:math id="M46" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">d</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">NA<inline-formula><mml:math id="M47" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e865"><inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Slightly differing between vertical and horizontal.
<inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> Data sheet measurement range from <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> to 80 <inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C.
<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msup></mml:math></inline-formula> Including non-linearity and repeatability.
<inline-formula><mml:math id="M29" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">d</mml:mi></mml:msup></mml:math></inline-formula> Depending on wind speed.
<inline-formula><mml:math id="M30" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula> Complex error behaviour.
NA: not available.</p></table-wrap-foot><?xmltex \gdef\@currentlabel{1}?></table-wrap>

      <p id="d1e1198">As an example for a flight trajectory, the measurement flight on 28 October 2021 at 07:20 UTC is shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/>b. The trajectory during the measurement flight consists mainly of circular patterns and therefore provides trajectory dynamics to facilitate the calculation of aircraft attitude, velocity and position performed by the inertial navigation algorithm.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e1205"><bold>(a)</bold> The measurement nose section with pressure ports for total pressure (“Pitot tube”) and static pressure (“Static pressure port”) and the installation of the temperature and humidity probe (“<inline-formula><mml:math id="M48" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>/RH probe”, HMP110, Vaisala, Finland). The probe itself is mounted in the bulkhead, which separates the sensor chamber from the general fuselage area. The air enters the air inlet (“<inline-formula><mml:math id="M49" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>/RH probe inlet”), passes the sensing element and is vented out through apertures in the bottom of the nose section (“Venting”).
<bold>(b)</bold> Trajectory of the measurement flight on 28 October 2021 at 07:20 UTC – besides the launch site, the intermediate climb position where the drone climbs up to 3 km and the final climb position where it climbs up to ceiling, as well as the descent funnel, are labelled.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f04.png"/>

        </fig>

      <p id="d1e1233">A cut-out in the left wing is foreseen to be used for an icing sensor as shown in <xref ref-type="bibr" rid="bib1.bibx8" id="text.91"/>, but other instruments can be fitted into it. As the risk of in-flight icing was negligible during the measurements, a camera was installed into the cut-out. The camera captured video and audio during the measurements, see Fig. <xref ref-type="fig" rid="Ch1.F3"/>b, and helped to analyse the behaviour of the flight controller and the motor controller of the drone.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Permissions for operation</title>
      <p id="d1e1249">The most important aspects for drone flights relate to safety.
Operational requirements are different for each region of the world; however, in Europe, there are now unified regulations for drone operation <xref ref-type="bibr" rid="bib1.bibx31" id="paren.92"/>.
The requirements concerning redundancy and the level of integrity of the drone depend on the overall risk analysis. For relatively small and lightweight drones performing flights beyond visual line of sight, which is the case for any system operating up to an altitude of 10 km, the drone falls into the category “specific”, and precautions to avoid damage to a third party have to be met. An operational handbook includes, for example, regular checks and maintenance of vital parts like motors and propellers, redundancy in the electric system, regular training of the crew, independent control links, and many more aspects defined in the so-called operational safety objectives.
The flight tests were therefore done in restricted military areas, in this case close to the Baltic Sea, Germany, and the internationally recognised high-quality portable radiosonde system of Graw, Germany <xref ref-type="bibr" rid="bib1.bibx92" id="paren.93"/>, was deployed from the launching site for direct comparison. In the restricted areas, cooperation with the German Federal Armed Forces is required, and flight permission of the German Federal Supervisory Authority for Air Navigation Services (Bundesaufsichtsamt für Flugsicherung, BAF) is necessary.</p>
      <?pagebreak page3746?><p id="d1e1258">For the operation in the Antarctic, a thorough risk assessment was performed with particular emphasis on safety and redundancy to avoid damage to third parties even in such a sparsely populated area.
Further, for the deployment in the Antarctic, permission of the German Environmental Agency (Umweltbundesamt) is required, ensuring that no material stays in the pristine environment and that the penguin population near the Neumayer station is not disturbed.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Method to assess the data quality of the simplistic sensor setup</title>
      <p id="d1e1269">For a comparison of data obtained by LUCA and radiosonde data, a procedure similar to what is presented in <xref ref-type="bibr" rid="bib1.bibx122" id="text.94"/> is applied to the data.
In a first step, data within pressure bands of 2 hPa are found for drone observations and radiosonde observations. Assuming a constant wind situation at the particular altitude associated with the pressure band, the air parcel measured by the radiosonde is shifted with the wind according to the time difference between the drone measurement and the radiosonde measurement.
For example, if the drone was measuring at 09:20 UTC within the pressure level of 500 hPa and the radiosonde was measuring at 09:30 UTC at the same pressure level, the radiosonde position would be shifted backwards by the distance an air parcel would have been travelling within this 10 min period in constant wind at this particular pressure level. This leads to a “source” position of the air parcel measured by the radiosonde at a specific time – the time when the drone was measuring at the same pressure level (altitude).
These virtual positions are then taken into account to select measurements collocated in space and time. Collocation conditions identical to the conditions used in <xref ref-type="bibr" rid="bib1.bibx122" id="text.95"/> (spatial distance less than 50 km, temporal gap less than 30 min) were then applied, before measurements were intercompared. No explicit filter for outliers was applied, but the drone data were implicitly filtered for outliers by median-filtering the data measured in each particular pressure band of 5 hPa width. Differences were computed for all pressure bands on all six flights.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
      <p id="d1e1287">In the following section, the technical achievements and the resulting potential of drone measurements are presented. Therefore, the data are discussed in a qualitative and a quantitative way.</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><?xmltex \opttitle{Technical achievement: first flight up to 10\,km with a battery-powered meteorological drone}?><title>Technical achievement: first flight up to 10 km with a battery-powered meteorological drone</title>
      <?pagebreak page3747?><p id="d1e1298">LUCA represents a new type of small fixed-wing drone. The combination of a relatively small wingspan below 2 m and a total weight of more than 6 kg leads to a high minimum flight speed of 18 m s<inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> at sea level for obtaining the lift required to fly and therefore complicates the process of getting airborne and landing safely compared to aircraft with larger wing areas related to the total mass.
During the flight test and measurement campaign, the design altitude of 10 km was reached. Ascending to such altitudes can be regarded as unique for an electrically powered fixed-wing drone without solar panels. To the authors' knowledge, it is the first time that a meteorological drone powered only by electrical batteries reached the altitude of 10 km. In addition, the landing manoeuvre has been proven to be repeatable during test flights without manual control. A list of flights performed can be accessed in <xref ref-type="bibr" rid="bib1.bibx8" id="text.96"/>.
During flight tests at sea level, a maximum airspeed of more than 60 m s<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> was reached, indicating that the drone is able to operate in equally high wind speed <xref ref-type="bibr" rid="bib1.bibx100" id="paren.97"/>. For operations, a safety margin has been applied, and the designated horizontal wind speed limit for normal operations was set to 28 m s<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, which equals the nominal horizontal component of the true airspeed during the ascent. Drifting away from the measurement location is prevented by forcing the minimum ground speed to 2 m s<inline-formula><mml:math id="M53" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The flight controller automatically increases the airspeed when the minimum ground speed falls below the threshold because of high wind speed – potentially trading the climb rate for airspeed.
Resisting high wind speed and the corresponding turbulence was demonstrated during the flight on 25 October 2021 starting at 12:12 UTC, where the maximum measured wind speed was 28 m s<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> during ascent and descent at an altitude of 7800 m a.m.s.l. (above mean sea level). Operations in BVLOS (beyond visual line of sight) conditions and in the presence of closed cloud layers have been conducted successfully.</p>
      <p id="d1e1368">The drone measurements can take place starting from any location, up to the altitude of 10 km, if flight permission is obtained. Operations are completely independent of additional infrastructure, like an airport, or the availability of helium. The drone only requires a cylindrical airspace with a radius of about 11 km for the whole mission. The drone ascends and descends at a vertical speed of 10 m s<inline-formula><mml:math id="M55" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and a horizontal speed component of 100 km h<inline-formula><mml:math id="M56" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Therefore, the mission reaching up to 10 km altitude and returning to the landing site takes in total 33 min. The data are available by remote transfer with a temporal resolution of 1 Hz. The full dataset with a resolution of up to 25 Hz can be downloaded after landing and is preprocessed automatically for upload into the GTS. The subsequent launch after landing can be typically performed after a turnaround time of 20 min.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Qualitative comparison of meteorological observations between drone and radiosonde data</title>
      <p id="d1e1403">A measurement campaign with LUCA and radiosondes was performed over the Baltic Sea (54.4<inline-formula><mml:math id="M57" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 10.6<inline-formula><mml:math id="M58" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E) from 25 to 29 October 2021. An overview of the development of the meteorological conditions with altitude is shown in Fig. <xref ref-type="fig" rid="Ch1.F5"/>, based on hourly ERA5 reanalysis data <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx51" id="paren.98"/>. The distribution of relative humidity with time and altitude was highly variable during the measurement period. Also, wind speed and wind direction (indicated with wind barbs) varied with height and time. The temporal distribution of the LUCA flights and parallel additional radiosondes are indicated in the overview (Fig. <xref ref-type="fig" rid="Ch1.F5"/>). LUCA was tested during a time period with high relative humidity, corresponding to cloudy conditions, and with high wind speed of up to 50 m s<inline-formula><mml:math id="M59" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, but the drone was not operated at the time of the maximum wind speed at 9 km altitude.
The overall wind direction was from the west with surface wind speed around 10 m s<inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and an absence of precipitation. Low and high scattered cloud layers were present, and a broad jet stream was forecasted just in the north of Denmark, with the jet core expected at 400 km distance to the north of the measurement campaign location.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1458">Overview of the meteorological situation between 25 and 31 October 2021 (date format: month-day) using ERA5 reanalysis data at the grid point closest to the drone measurements. The background in grey indicates relative humidity (linearly interpolated between times and levels), whereas the coloured isolines indicate air temperature. The measurement times using the LUCA drone are shown in magenta; the measurements with a timely and spatially collocated radiosonde (type DFM-09, Graw, Germany) for comparison with the drone data are marked in blue. The wind barbs as defined in <xref ref-type="bibr" rid="bib1.bibx128" id="text.99"/> indicate the high wind speed during the measurements, which coincides with the high variability in humidity over time.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f05.png"/>

        </fig>

      <p id="d1e1470">Exemplarily, Fig. <xref ref-type="fig" rid="Ch1.F6"/> shows measurements of temperature, relative humidity, wind speed and wind direction recorded by LUCA at up to 10 km. The measurements took place on 26 October 2021 at 08:45 UTC and on 29 October 2021 at 07:22 UTC. The data of the nearly simultaneous radiosonde are shown, as well as ERA5 reanalysis data.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1478">Skew-<inline-formula><mml:math id="M61" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> log-<inline-formula><mml:math id="M62" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> diagrams of the vertical profiles (descent) of temperature (solid lines), dew point temperature (dashed lines) and wind (wind barbs) measured with LUCA data in magenta, the simultaneously launched radiosonde data in blue and ERA5 data in red.
In <bold>(a)</bold>, the launch time of LUCA was 08:45 UTC on 26 October 2021 and the radiosonde was released at 09:11 UTC. The drone profile was measured during the descent from 09:09 to 09:30 UTC.
In <bold>(b)</bold>, the drone was launched at 07:22 UTC on 29 October 2021 and the corresponding radiosonde was released at 08:01 UTC. The drone profile was measured during the descent from 07:47 to 08:12 UTC. Statistics as well as observation uncertainties are shown in Fig. <xref ref-type="fig" rid="Ch1.F8"/> for the profile presented in panel <bold>(b)</bold>.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f06.png"/>

        </fig>

      <p id="d1e1513">Each profile provided by LUCA shows qualitatively the same atmospheric structures as the radiosonde measurements with a similar sensor package to that used on the radiosondes.</p>
      <p id="d1e1516">On 26 October 2021, the strong temperature inversion at 400 m as well as the transition to a different temperature gradient at an altitude of around 6500 m is equally captured by the drone and the radiosonde measurements (Fig. <xref ref-type="fig" rid="Ch1.F6"/>a).
On 29 October 2021, the temperature inversion at the top of the boundary layer at 400 m altitude is captured by the drone and the radiosonde, as well as ERA5 analyses.</p>
      <p id="d1e1521">Humidity was generally moderately variable during the observation period. The drone and radiosonde measurements, as well as ERA5 data, agree that there was high relative humidity (small differences between dew point temperature and temperature) up to the temperature inversion at around 400 m altitude on 26 October 2021 (Fig. <xref ref-type="fig" rid="Ch1.F6"/>a). On both days, there were layers of lower and higher humidity. On 26 October 2021, in the lower troposphere up to an altitude of around 4 km, the individual layers of different humidities are identically resolved by the drone in terms of altitude and magnitude (Fig. <xref ref-type="fig" rid="Ch1.F6"/>a). On 29 October 2021, humidity measurements using the drone are in good agreement with radiosonde data up to 500 hPa (around 5 km altitude, Fig. <xref ref-type="fig" rid="Ch1.F6"/>b). Above 500 hPa, an increasing deviation between radiosonde and drone measurements can be observed in humidity for<?pagebreak page3748?> both days. This is likely caused by the dramatically increasing response time of the humidity sensor at lower temperatures <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx87" id="paren.100"/> in addition to the delaying effect of the implemented closed-path sensor setup. Moisture is a critical parameter to measure in the upper troposphere <xref ref-type="bibr" rid="bib1.bibx92 bib1.bibx30" id="paren.101"/>.</p>
      <p id="d1e1536">Wind measurements agree well between the drone and the radiosonde measurements. When comparing the measurements directly, one has to take into account that the radiosonde was launched 53 min after the drone. A systematic deviation can be expected for higher altitudes due to the drifting of the radiosonde with the wind, towards the north-east, which resulted in a spatial distance of 40 km from the launch point when reaching the altitude of 10 km.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Case study: quantitative intercomparison of the simplistic sensor setup and radiosonde data</title>
      <p id="d1e1547">Despite the simplistic sensor setup, data measured on board the platform LUCA have been shown to compare at least qualitatively with radiosonde data.
To assess quantitative measures, the methods presented in Sect. <xref ref-type="sec" rid="Ch1.S2.SS5"/> are applied to the data of all six vertical profiles (upwards and downwards) post-processed according to Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>.
These techniques were applied for ascents as well as descents, as data during the ascent are expected to suffer from electromagnetic interference as well as other factors such as thrust line misalignment. The collocated dataset for the pressure bands of 2 hPa width from 1000 to 250 hPa consists of 694 data points for the ascent and 1323 data points for the descent of the drone. Figure <xref ref-type="fig" rid="Ch1.F7"/> shows histograms of the differences between the radiosonde observations and the drone observations for the variables temperature, relative humidity, specific humidity, wind speed, wind direction as well as the norm of the wind vector difference for the descending profiles. Within the histograms, average differences as well as the standard deviation of the intercompared observations are provided.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e1558">Histograms (probability density over observation difference) of the differences between collocated LUCA drone and radiosonde observations for various atmospheric variables. Collocation was assumed for the probed air parcels' virtual spatial distance of less than 50 km and an observation time difference of less than 30 min. The virtual air parcel position was determined by virtually back-shifting the probed air parcel with the negative mean wind vector at the observation level multiplied with the time difference between the drone and the radiosonde measurements within the same pressure level band.
All histograms suffer from the sparse database but indicate a Gaussian-like distribution of observation differences, except the difference in the wind vectors, which follows a Rayleigh distribution as expected from theory. Therefore, the root-mean-square deviation (RMSD) is shown in the histogram for the wind vector difference rather than standard deviation as for the other parameters.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f07.png"/>

        </fig>

      <p id="d1e1567">Despite the sparse database consisting of six vertical descent profiles, the distributions of the differences for the variables of temperature, relative humidity, specific humidity, wind speed and wind direction are similar to Gaussian distributions. The histogram for the norm of the wind vector difference follows a Rayleigh distribution, as is expected for the norm of a two-dimensional vector whose components are stochastically independent Gaussian processes.
For the<?pagebreak page3749?> distribution of the observation differences, the average deviation and the standard deviation (root-mean-square deviation for the Rayleigh distribution) were calculated and are shown in the histogram plots (Fig. <xref ref-type="fig" rid="Ch1.F7"/>). These values were retrieved for both the ascent and the descent and are shown in Table <xref ref-type="table" rid="Ch1.T2"/>.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1578">Statistical measures for the differences in the collocated observation of temperature, humidity and wind between drone measurements and radiosonde measurements. Collocation was assumed when an air parcel, virtually reverse-shifted by the mean wind and the time difference, was within a spatial distance of 50 km and a temporal difference of 30 min.
The statistical measures are shown for both the descent and the ascent profile compared to radiosonde data. During the six ascent profiles, an increased variation in wind observations, particularly the wind direction, can be found compared to the six descent profiles.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center" colsep="1">Descent </oasis:entry>
         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center">Ascent </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Variable</oasis:entry>
         <oasis:entry colname="col2">Average</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">Average</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Temperature</oasis:entry>
         <oasis:entry colname="col2">0.20 K</oasis:entry>
         <oasis:entry colname="col3">0.67 K</oasis:entry>
         <oasis:entry colname="col4">0.00 K</oasis:entry>
         <oasis:entry colname="col5">0.86 K</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Relative humidity</oasis:entry>
         <oasis:entry colname="col2">2.73 %</oasis:entry>
         <oasis:entry colname="col3">8.67 %</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.64</mml:mn></mml:mrow></mml:math></inline-formula> %</oasis:entry>
         <oasis:entry colname="col5">8.16 %</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Specific humidity</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula> g kg<inline-formula><mml:math id="M69" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">0.43 g kg<inline-formula><mml:math id="M70" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.30</mml:mn></mml:mrow></mml:math></inline-formula> g kg<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">0.53 g kg<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Wind speed</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.39</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M75" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.15 m s<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.40</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">2.66 m s<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Wind direction</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.62</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">5.06<inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.77</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M84" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula><inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">21.88<inline-formula><mml:math id="M86" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula><inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Wind vector</oasis:entry>
         <oasis:entry colname="col2">NA</oasis:entry>
         <oasis:entry colname="col3">0.97 m s<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">NA<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">2.66 m s<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Database info</oasis:entry>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1">1323 data points (68 % of dataset) </oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center">694 data points (35 % of dataset) </oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e1581"><inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> RMSD for the wind vector difference. <inline-formula><mml:math id="M64" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> Wind observations during ascent are regarded as invalid due to electromagnetic interferences. NA: not available.</p></table-wrap-foot><?xmltex \gdef\@currentlabel{2}?></table-wrap>

      <p id="d1e2034">Comparing the statistical measures between ascent and descent data, increased differences between the radiosonde and the drone observations are revealed. This is most likely associated with a magnetic deterioration or a possibly induced sideslip angle when the thrust line is not aligned with the drone's body (see Sect. <xref ref-type="sec" rid="Ch1.S2.SS3"/> and Appendix <xref ref-type="sec" rid="App1.Ch1.S1.SS3"/>).
For the descent profile, the average differences as well as the standard deviation of the differences between drone observations and radiosonde observations are in the range of (or even below) statistical measures shown in the study of <xref ref-type="bibr" rid="bib1.bibx122" id="text.102"/>, which includes a comparison of radiosonde data with observation data from the AMDAR–TAMDAR programme. The statistics furthermore support the values of the theoretical error estimation in Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>.
For the humidity measurement, the average of the differences between radiosonde and LUCA measurements differs significantly between ascent and descent, indicating the possible need for further calibration and tuning of the post-processing parameters using a broader database in the future.</p>
      <p id="d1e2046">The overall uncertainties for the measured profile in Fig. <xref ref-type="fig" rid="Ch1.F6"/>b are shown in Fig. <xref ref-type="fig" rid="Ch1.F8"/>. As the contribution of the time lag correction and the wind calculation to the total uncertainty depends on the vertical profile itself, the total uncertainty for the variables of air temperature, relative humidity, wind speed and wind direction is shown as a grey area around the measurements.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e2055">Measurements and associated uncertainties in the LUCA drone during the descent on 29 October 2021 from 07:47 to 08:12 UTC and the radiosonde (“Raso”) launched on the same day at 07:22 UTC, i.e. the same measurements as shown in Fig. <xref ref-type="fig" rid="Ch1.F6"/>b. For the vertical profiles of static air temperature <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in <bold>(a)</bold>, relative humidity RH in <bold>(b)</bold>, wind speed FF in <bold>(c)</bold> and wind direction DD in <bold>(d)</bold>, the corresponding radiosonde profile is plotted. The grey areas surrounding the profiles depict the estimated uncertainties in the measured variables according to Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>. Intercomparison statistics for the profile are added in each of the panels. The time constant for the smoothing filter for the temperature in <bold>(a)</bold> is 4.2 s (roughly comparable to centred average smoothing across 120 m altitude), whereas the lilac curve in <bold>(b)</bold> indicates the variable “time constant” <inline-formula><mml:math id="M92" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M93" display="inline"><mml:mo lspace="0mm">≠</mml:mo></mml:math></inline-formula> time span) for the phase-neutral smoothing filter applied to the humidity measurements, for which no accessible replacement value for a centred average exists.</p></caption>
          <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f08.png"/>

        </fig>

      <p id="d1e2112">For the air temperature <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F8"/>a, the radiosonde observations deviate significantly in the lower boundary layer, likely caused by the temperature sensor being heated up by solar irradiance without venting on the ground before the launch. No particular uncertainty source dominates the total uncertainty for the measurements.
For humidity observations in Fig. <xref ref-type="fig" rid="Ch1.F8"/>b, increased uncertainty around rapid changes in humidity is visible, originating in the uncertainty caused by the time lag correction. The data sheet uncertainty dominates the total uncertainty, in which the calibration drift (up to <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> % per year according to the data sheet) is not yet included. Radiosonde observations lie partly outside the uncertainty area (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> plus systematic errors) for the drone measurements, potentially pointing to the need for further measurements and investigations.
Wind observations in Fig. <xref ref-type="fig" rid="Ch1.F8"/>c and d compared to the radiosonde measurements are within reason regarding the uncertainty and taking into account turbulence as well as the spatio-temporal distance between the radiosonde and the drone.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Discussion and conclusion</title>
      <p id="d1e2162">The in situ data gap in the Global Observing System was reviewed in the Introduction. Experiments on the impact of additional vertical profiles on NWP suggest that in situ observations of the complete tropospheric column in remote areas improve forecast quality, which more frequent sampling<?pagebreak page3750?> of the atmosphere also would. Besides the effort in filling the observation gap in the near-surface boundary layer with drones <xref ref-type="bibr" rid="bib1.bibx84 bib1.bibx100 bib1.bibx62" id="paren.103"/>, the data gap with drone measurements in the free troposphere and the lower stratosphere has not been addressed – the technology of small drones has not been ready for observations at such high altitudes <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx100" id="paren.104"/>.</p>
      <p id="d1e2171">The drone measurements presented here show the potential for covering data gaps as the drone has the capability of measuring frequently, e.g. hourly, with moderate cost and effort. More frequent observations increase the forecast quality <xref ref-type="bibr" rid="bib1.bibx25 bib1.bibx36" id="paren.105"/>, as special atmospheric features like the diurnal cycle can be resolved. The required frequency of measurements strongly depends on the temporal variability of the atmosphere, which is highly variable for different altitude ranges and different for each meteorological parameter, as shown in Fig. <xref ref-type="fig" rid="App1.Ch1.S4.F11"/>.
The atmospheric boundary layer experiences high temporal changes in temperature, wind speed and humidity. Besides these diurnal variations in the lowermost region, temporal changes in temperature and wind speed are seen in the upper<?pagebreak page3751?> troposphere and the lower stratosphere. Processes in this layer <inline-formula><mml:math id="M97" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 5 km around the tropopause <xref ref-type="bibr" rid="bib1.bibx43" id="paren.106"><named-content content-type="pre">the virtual boundary between the troposphere and the stratosphere, e.g.</named-content></xref> are known as being important for global (mass) exchange <xref ref-type="bibr" rid="bib1.bibx53" id="paren.107"/>. Humidity, in contrast, varies highly from the ground up to the lower stratosphere with no preference in terms of timescales, representing a chaotic system.
Interestingly, temperature variability at six cycles per day is low below 5 km altitude (besides the high variability in the boundary layer), emphasising the importance of profiling the atmosphere to higher altitudes.
In NWP, physical processes are modelled to predict a future atmospheric state. The modelling of these processes performs quite well on distinct timescales to reproduce the variability of the atmosphere. The need for observations therefore not only can be defined by the atmospheric variability to avoid undersampling, but also has to be seen as complementary to the stability of the modelled physical processes and regional data gaps. Specified by data users, the WMO provides data requirements for observation spacing and uncertainty <xref ref-type="bibr" rid="bib1.bibx133 bib1.bibx84" id="paren.108"/>, which interestingly differ only little between the boundary layer and the free troposphere for both global and high-resolution NWP, emphasising the benefits of profiling the atmosphere vertically with a drone up to approximately 10 km and above. Filling the in situ observation gap in both the atmospheric boundary layer and the free troposphere will result in better forecast quality and even has the potential to further adjust and develop the modelling of the underlying physical processes.</p>
      <p id="d1e2198">This article presents atmospheric soundings up to 10 km altitude using an electrically powered fixed-wing drone. The developed system represents a milestone, demonstrating the capability of fixed-wing drones to perform tropospheric soundings. Measurements with a basic atmospheric sensor package were conducted. The drone measurements of temperature, humidity and wind reported here generally agree with temporally and spatially coinciding radiosonde measurements. Minor drawbacks in the measurements occurred as expected due to the simple sensor setup.</p>
      <p id="d1e2201">Moisture is generally the most challenging parameter of in-flight atmospheric observations, which demands significant post-processing. This is also a known issue for standard radiosonde systems, where various corrections need to be applied as well <xref ref-type="bibr" rid="bib1.bibx28" id="paren.109"/>. By design, the drone technology bears the pivotal advantages of re-using sensors and the possibility of pre- and post-flight calibration.</p>
      <p id="d1e2208">More advanced sensor techniques that are available could be integrated into the platform. This would enable us to extend the measured parameters or focus on high-quality measurements of basic atmospheric parameters, e.g. by using dew point mirrors for humidity <xref ref-type="bibr" rid="bib1.bibx40" id="paren.110"/> or fine wire temperature sensors with suitable shielding and protection <xref ref-type="bibr" rid="bib1.bibx113 bib1.bibx5" id="paren.111"/>. As an outlook, standard radiosonde accuracy is expected to be reached or even surpassed using a more sophisticated measurement package instead of the simplistic sensor integration used within this study. Sensor limitations and challenges are known; the needs regarding data management <xref ref-type="bibr" rid="bib1.bibx134" id="paren.112"/> are not addressed within this article.</p>
      <p id="d1e2220">The LUCA system was designed to reach its target altitude (10 km) in conditions with average wind speeds of up to 28 m s<inline-formula><mml:math id="M98" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, which results in a minimum flight speed of 18 m s<inline-formula><mml:math id="M99" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The limitations concerning wind speed are related to the current maximum airspeed of 50 m s<inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. In order to ensure the aforementioned operability, LUCA was constructed with suitable ground systems for takeoff and landing. The mechanical start catapult enables robust starts, even in challenging conditions of high wind speed and virtually zero horizontal visibility. The landing net was designed for an automated landing manoeuvre, which allows for landings during high-surface-wind and low-visibility conditions.</p>
      <p id="d1e2259">As for now, LUCA does not incorporate measures to actually prevent icing but features a dedicated sensor to detect icing. This enables safe operation of flights but limits operability significantly. In future developments, this issue needs further attention.</p>
      <p id="d1e2262">The reported flights that were carried out demonstrate the general suitability of the technology for the envisaged purpose, explicitly covering rather challenging environmental conditions. However, systematic and extensive tests in adverse weather still need to be performed in the future. Nevertheless, the LUCA system was successfully operated above the design wind speed and through closed cloud layers.</p>
      <p id="d1e2265">Data quality assessed within a case study using a simple sensor package indicates observation accuracy comparable to AMDAR and TAMDAR observations, but further studies have to be carried out, as the observations within the case study cover only limited atmospheric conditions.</p>
      <p id="d1e2268">Receiving permissions for drone operations beyond visual line of sight is a demanding prerequisite for atmospheric measurement systems like LUCA. With its design mass of 5–6 kg, LUCA is fairly light compared to crewed aircraft but significantly heavier than typical radiosondes. Hence, the operational risk is an issue. By further miniaturisation of the system, both air and ground risk can be reduced and hence is expected to simplify the process of granting permissions.</p>
      <p id="d1e2272">Compared to existing in situ observing systems, the vertical profiles are similar to radiosonde ascents and descents (in some NWP centres, radiosonde descents have already been assimilated; <xref ref-type="bibr" rid="bib1.bibx61" id="altparen.113"/>) and aircraft-based observations close to airports. The assimilation of drone data into the BUFR format <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx61" id="paren.114"/> should therefore be quite straightforward compared to new and complex assimilation processes of, for example, radio occultation data <xref ref-type="bibr" rid="bib1.bibx35" id="paren.115"/>.
In comparison with observations from crewed aircraft, drones typically operate at a lower airspeed, which tends to result in an increased wind observation accuracy <xref ref-type="bibr" rid="bib1.bibx95" id="paren.116"/>.
Even though reaching 10 km can never replace the well-established radiosonde network, the system has the chance to augment radio soundings<?pagebreak page3752?> with more frequent drone measurements. Furthermore, in the future, it might be feasible to set up atmospheric in situ monitoring programmes by combining profiling drones such as the one presented here with solar-powered semi-permanent systems in the stratosphere.</p>
      <p id="d1e2287">There are several possible applications and opportunities for the use of small drones measuring the complete tropospheric column and potentially the lower stratosphere – sampling the atmosphere with an increased number of observations per day with re-usable individual sensors has to be highlighted here. Re-using sensors inevitably leads to substantial knowledge about the stability, strengths and flaws of an individual sensor and has the chance of increasing the ability to precisely specify the uncertainty in observations, which is substantial for data assimilation. This effect is regularly observed regarding satellite sensor assessments <xref ref-type="bibr" rid="bib1.bibx105" id="paren.117"/>.</p>
      <p id="d1e2293">The use of reference radiosondes to characterise the uncertainty in NWP models to improve satellite validation and calibration is another future application <xref ref-type="bibr" rid="bib1.bibx18" id="paren.118"/> to which drone measurements potentially can contribute. The quality of drone observations for sampling the complete troposphere is of superior importance and could possibly contribute to climate applications. Regarding the variables involved, one finds that climate users tend to focus on temperature and humidity data <xref ref-type="bibr" rid="bib1.bibx61" id="paren.119"/>.</p>
      <p id="d1e2302">For NWP applications, wind observations have arguably more than twice the impact on the quality of short-range forecasts compared to temperature observations <xref ref-type="bibr" rid="bib1.bibx60" id="paren.120"/>.
In order to augment and compete with the well-established vertical profile observations (radiosondes, airliner-borne) and be used operationally, a drone must be operable by station staff of existing atmospheric observatories.
Furthermore, the system needs to cope with a variety of challenging environmental conditions, including high wind speed, poor surface visibility or icing during the flight.</p>
      <p id="d1e2308">Upcoming implementations of such systems in the GTS will likely depend on investment cost as well as cost generated by the effort for station staff in respect to operations and maintenance. A generic approach to assessing the economical benefit for drone-based observations is presented in <xref ref-type="bibr" rid="bib1.bibx8" id="text.121"/>, but acquisition and operational costs are widely unclear for the system presented here, in particular regarding system failures and hardware issues.</p>
      <p id="d1e2314">Targeted observations were discussed controversially, as their impact strongly depends on the assimilation scheme and the NWP system <xref ref-type="bibr" rid="bib1.bibx108" id="paren.122"/>. Unquestionable are the use of drone measurements in contributing to scientific campaigns and the resulting reduction in cost and waste when used to replace frequent radio soundings during intense observation periods.</p>
      <p id="d1e2321">Although this study demonstrates the feasibility of using small drones up to the troposphere as carrier systems for atmospheric observations, envisaged extensive test campaigns (like the WMO UAS Demonstration Campaign; <xref ref-type="bibr" rid="bib1.bibx132" id="altparen.123"/>) are needed to assess the impact of drones on forecast skills and will increase and demonstrate the reliability of LUCA in performing successful and safe tropospheric profiling.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Post-processing and calculi applied to data</title>
      <p id="d1e2339">As a fundamental principle, every sensor reading a physical quantity involves a transfer function <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> from the physical quantity to the sensing element. A transfer function, utilising techniques from the field of control theory, can be noted in the complex frequency domain as
          <disp-formula id="App1.Ch1.S1.E1" content-type="numbered"><label>A1</label><mml:math id="M102" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>X</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        with the input signal <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the output signal <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the complex frequency domain parameter <inline-formula><mml:math id="M105" display="inline"><mml:mi>s</mml:mi></mml:math></inline-formula>. Besides the trivial proportional transfer function <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:mi>H</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>P</mml:mi></mml:mrow></mml:math></inline-formula>, which denotes <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mo>⋅</mml:mo><mml:mi>X</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, a common transfer function describing physical processes is the first-order lag function:
          <disp-formula id="App1.Ch1.S1.E2" content-type="numbered"><label>A2</label><mml:math id="M108" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M109" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> is the so-called time constant. In the time domain, such a system has an output rate of change <inline-formula><mml:math id="M110" display="inline"><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover></mml:math></inline-formula> proportional to the difference between the input <inline-formula><mml:math id="M111" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> and the output <inline-formula><mml:math id="M112" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>, scaled with the time constant <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">τ</mml:mi></mml:mfrac></mml:mstyle><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e2566">An example of a sensor with an inherent first-order lag transfer function is a thermistor air temperature sensor, where the heat transfer between the sensor head and the ambient air drives the rate of temperature change of the sensor head and therefore the temperature readings.</p>
<sec id="App1.Ch1.S1.SS1">
  <label>A1</label><title>Temperature corrections</title>
      <p id="d1e2576">The temperature sensor head on board the drone presented here is a thermistor element of specification Pt1000. This type of sensor naturally involves a non-uniform time lag represented by a first-order lag transfer function. This implies spectral errors and an input-signal-dependent time lag in the temperature time series, which are in theory fully recovered using the signal reconstruction (also called inverse filtering) method.
The basic idea is to apply the inverted transfer function to the measured sensor output, taking advantage of a priori knowledge during the post-processing.</p>
      <p id="d1e2579">Expressed by a linear differential equation, the measurement process for the thermistor sensor is defined with
            <disp-formula id="App1.Ch1.S1.E3" content-type="numbered"><label>A3</label><mml:math id="M114" display="block"><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>⋅</mml:mo><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>y</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where the quantity to measure is denoted by <inline-formula><mml:math id="M115" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>, the measurement by <inline-formula><mml:math id="M116" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> (both as a function of time <inline-formula><mml:math id="M117" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>) and a time constant by <inline-formula><mml:math id="M118" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula>. <inline-formula><mml:math id="M119" display="inline"><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover></mml:math></inline-formula> is the derivative of <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> with respect to the time <inline-formula><mml:math id="M121" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>.
Assuming a step change on the input side and solving the<?pagebreak page3753?> differential equation, the time constant represents the sensor response time in the way that the measurement will reach 63 % of the input state within the time span <inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula>.
Having identified the time constant for the sensor response, the signal reconstruction of the measurement time series <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> can be applied to determine the quantity to measure <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by applying Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E3"/>). As the derivative of the measurements <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is needed for signal reconstruction, measurement noise will be amplified in the recovered signal and is phase-neutrally low-pass-filtered by filtering the recovered signal forwards and backwards (e.g. <xref ref-type="bibr" rid="bib1.bibx5" id="altparen.124"/>).</p>
      <p id="d1e2744">The spectrally corrected temperature measurements then represent the actual temperature at the stagnation point at the sensor position. In aviation, this is called “total air temperature” <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and can be transferred into the static air temperature <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, i.e. the temperature of the undisturbed air around the aircraft, with
            <disp-formula id="App1.Ch1.S1.E4" content-type="numbered"><label>A4</label><mml:math id="M128" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:msup><mml:mi mathvariant="italic">Ma</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mi>k</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> is the adiabatic index of air and <italic>Ma</italic> the Mach number. The temperature difference between <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is caused by energy conversion from kinetic to thermal energy in the air, but as the air at the sensed area with the temperature <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is not subject to a complete adiabatic process, an additional recovery factor <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>/</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> in the range of about 0.6–0.95 has to be applied to the temperature rise <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> when using Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E4"/>) (e.g. <xref ref-type="bibr" rid="bib1.bibx83 bib1.bibx4" id="altparen.125"/>).</p>
      <p id="d1e2926">The aforementioned correction for the temperature rise is not applied to the measurements presented here, as the error is expected to be small.</p>
      <p id="d1e2930">An error correction rather specific to the sensor installation in the LUCA drone is the correction for heat transfer through the metal sensor housing between the fuselage area and the sensor chamber, as is visible in the sensor package sketch in Fig. <xref ref-type="fig" rid="Ch1.F4"/>a.
The corrected temperature <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be assumed to behave as
            <disp-formula id="App1.Ch1.S1.E5" content-type="numbered"><label>A5</label><mml:math id="M136" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with the recovered temperature signal <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the temperature <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> measured inside the fuselage and a dimensionless coefficient <inline-formula><mml:math id="M139" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> for the magnitude of the heat transfer. The coefficient <inline-formula><mml:math id="M140" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>, which expresses the heat transfer rate from the fuselage to the sensor, is regarded as independent of environmental conditions and universal for all temperature measurements with the drone LUCA.</p>
</sec>
<sec id="App1.Ch1.S1.SS2">
  <label>A2</label><title>Humidity corrections</title>
      <p id="d1e3034">Similarly to resistive temperature measurements, capacitive moisture measurements suffer from a time lag which can be described by using a first-order lag transfer function <xref ref-type="bibr" rid="bib1.bibx89 bib1.bibx28 bib1.bibx5 bib1.bibx117" id="paren.126"/>. In contrast to temperature sensor transfer functions, the time constant of humidity observations is heavily affected by the ambient temperature, as the diffusion process acting on the sensing element is slowed down in low temperatures (e.g. <xref ref-type="bibr" rid="bib1.bibx89 bib1.bibx21 bib1.bibx87" id="altparen.127"/>).
The so-called “time constant” is therefore not constant anymore and has to be applied as a variable to the signal reconstruction of the humidity measurements.
A power law was found to be appropriate to describe the time constant as a function of altitude (intrinsically representing temperature) and, using the method of comparing ascent and descent profiles, the supporting points for the function
            <disp-formula id="App1.Ch1.S1.E6" content-type="numbered"><label>A6</label><mml:math id="M141" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">humi</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mo>⋅</mml:mo><mml:msup><mml:mi>H</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          which expresses the variable time constant <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">humi</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for the humidity signal as a function of altitude <inline-formula><mml:math id="M143" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> in metres.
The humidity measurements are then corrected with the same recovery algorithm as applied to temperature measurements. For the subsequent low-pass filter, the cut-off frequency was chosen to be 3 times higher than the cut-off frequency of the sensor transfer function.</p>
</sec>
<sec id="App1.Ch1.S1.SS3">
  <label>A3</label><title>Wind calculation</title>
      <p id="d1e3098">The basic equation to calculate the wind vector in the geodetic coordinate system noted as <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> with the wind components north, east and down defined as positive is
            <disp-formula id="App1.Ch1.S1.E7" content-type="numbered"><label>A7</label><mml:math id="M145" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          using the difference between the velocity vector of the aircraft above ground <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the true airspeed vector <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of the aircraft relative to the moving air, both in the geodetic coordinate system. Although this technique has been state of the art for decades – see, for example, <xref ref-type="bibr" rid="bib1.bibx2" id="text.128"/> and <xref ref-type="bibr" rid="bib1.bibx4" id="text.129"/> – some key information is recapped in the following, and errors subject to the simplifications made herein are described in Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>.</p>
      <p id="d1e3208">For the case that the airflow sensor is not located at the chosen reference point of the aircraft, for example, for inertial navigation where <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is determined, the measured airflow includes induced velocities from the rotational speed of the aircraft body <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold">Ω</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, with <inline-formula><mml:math id="M150" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M151" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M152" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> as rotational rates around the roll, pitch and yaw axes, scaled with the lever arm vector <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (here in body-fixed coordinates). This results in
            <disp-formula id="App1.Ch1.S1.E8" content-type="numbered"><label>A8</label><mml:math id="M154" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="bold">Ω</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>
          as the basic equation for wind measurements, including lever-arm-induced velocities. This can be prevented by calculating <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at the airflow sensor position within the inertial navigation system or during post-processing.
Equation (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E8"/>) is usually deployed for research aircraft to enable high-frequency wind and turbulence measurements.</p>
      <?pagebreak page3754?><p id="d1e3335">The geodetic velocity vector
<inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">N</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>
of an aircraft above ground used for wind measurements usually originates directly from the differentiation of position measurements using a GNSS (global navigation satellite system) receiver and velocity measurements of a GNSS receiver (using Doppler shift measurements for each tracked satellite). Before the deployment of GNSS, velocities were determined using an inertial navigation platform, which nowadays is optionally used to complement GNSS measurements, as GNSS data are commonly only available with a frequency of 10 Hz.</p>
      <p id="d1e3375">The true airspeed vector <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (here in aircraft body coordinates) by contrast is measured in two steps. Its measured magnitude <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:mfenced close="|" open="|"><mml:mi mathvariant="bold-italic">u</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> multiplied by the unit vector <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the true airspeed vector in the aerodynamic coordinate system <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="|" close="|"><mml:mi mathvariant="bold-italic">u</mml:mi></mml:mfenced><mml:mo>⋅</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>.
Measurements of the angle of attack and the angle of sideslip with wind vanes and multi-hole probes are then used to transform the true airspeed vector from the aerodynamic coordinate system into the aircraft's body-fixed coordinate system (subscript <inline-formula><mml:math id="M161" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>) with the rotation matrix:
            <disp-formula id="App1.Ch1.S1.E9" content-type="numbered"><label>A9</label><mml:math id="M162" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="bold">M</mml:mi><mml:mi mathvariant="normal">ba</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mtable class="array" columnalign="center center center"><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mn mathvariant="normal">0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M163" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> denotes the angle of attack and <inline-formula><mml:math id="M164" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> denotes the angle of sideslip. An illustration of the angles commonly used for wind calculation is found in, for example, <xref ref-type="bibr" rid="bib1.bibx118" id="text.130"/> or any flight mechanics textbook.</p>
      <p id="d1e3565">Finally, applying the rotational transformation <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold">M</mml:mi><mml:mi mathvariant="normal">gb</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from the aircraft body to the geodetic coordinate system gives
            <disp-formula id="App1.Ch1.S1.E10" content-type="numbered"><label>A10</label><mml:math id="M166" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="bold">M</mml:mi><mml:mi mathvariant="normal">gb</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{7.1}{7.1}\selectfont$\displaystyle}?><mml:mfenced close=")" open="("><mml:mtable class="matrix" columnalign="center center center" framespacing="0em"><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>-</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>+</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>+</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>-</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          with the roll angle <inline-formula><mml:math id="M167" display="inline"><mml:mi mathvariant="normal">Φ</mml:mi></mml:math></inline-formula>, pitch angle <inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> and yaw angle <inline-formula><mml:math id="M169" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula>. This enables us to use the basic equation, Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E7"/>), for airborne wind measurements in the form of
            <disp-formula id="App1.Ch1.S1.E11" content-type="numbered"><label>A11</label><mml:math id="M170" display="block"><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="bold">M</mml:mi><mml:mi mathvariant="normal">gb</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="bold">M</mml:mi><mml:mi mathvariant="normal">ba</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="2em"/><mml:mo mathsize="2.5em">|</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msub><mml:mi mathvariant="bold">Ω</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          neglecting lever arm effects.</p>
      <p id="d1e3839">Assuming <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, which is motivated by the directional stability of an aircraft, and further assuming that <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> as the direction of the body <inline-formula><mml:math id="M173" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis can be freely adjusted to achieve this value, further simplifications follow, which are valid for either calm conditions or ensemble observations to be averaged:
            <disp-formula id="App1.Ch1.S1.E12" content-type="numbered"><label>A12</label><mml:math id="M174" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mfenced close="|" open="|"><mml:mi mathvariant="bold-italic">u</mml:mi></mml:mfenced></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>⋅</mml:mo><mml:mfenced open="(" close=")"><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>-</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo mathsize="2.5em">|</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>and</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e3965">To get rid of the angle <inline-formula><mml:math id="M175" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>, which was adjusted to result in <inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, the mean vertical wind speed is assumed to be zero. Upon this, it follows that
            <disp-formula id="App1.Ch1.S1.E13" content-type="numbered"><label>A13</label><mml:math id="M177" display="block"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mfenced close="|" open="|"><mml:mi mathvariant="bold-italic">u</mml:mi></mml:mfenced><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          which can be used to substitute the dependency on <inline-formula><mml:math id="M178" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> in Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E12"/>), leading to
            <disp-formula id="App1.Ch1.S1.E14" content-type="numbered"><label>A14</label><mml:math id="M179" display="block"><mml:mrow><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">N</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn mathvariant="normal">0</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn mathvariant="normal">0</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msqrt><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo mathsize="2.5em">|</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>and</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          wherein
            <disp-formula id="App1.Ch1.S1.E15" content-type="numbered"><label>A15</label><mml:math id="M180" display="block"><mml:msqrt><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:math></disp-formula>
          can be regarded as the horizontally projected true airspeed of the aircraft.</p>
      <p id="d1e4171">The additional simplification using <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> (which can be assumed during level flight) results in
            <disp-formula id="App1.Ch1.S1.E16" content-type="numbered"><label>A16</label><mml:math id="M182" display="block"><mml:mrow><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">w</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">N</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn mathvariant="normal">0</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn mathvariant="normal">0</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced close="|" open="|"><mml:mi>u</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo mathsize="2.5em">|</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>and</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          for the north and the east wind vector components (<inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) in the geodetic coordinate system.</p>
      <p id="d1e4340">The simplified equation, Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E16"/>), is identical to the formulas given in the “Aircraft Meteorological Data Relay (AMDAR) Reference Manual”, <xref ref-type="bibr" rid="bib1.bibx126" id="text.131"/>, Appendix I, part 4, implying a potentially systematic error in AMDAR–TAMDAR measurements during ascents and descents, which is theoretically quantified during the error discussion in Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>.</p>
      <p id="d1e4350">The calculus for the true airspeed magnitude <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mfenced open="|" close="|"><mml:mi>u</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> used for wind calculation
            <disp-formula id="App1.Ch1.S1.E17" content-type="numbered"><label>A17</label><mml:math id="M185" display="block"><mml:mrow><mml:msup><mml:mfenced close="|" open="|"><mml:mi>u</mml:mi></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mfrac></mml:mstyle><mml:mfenced close="]" open="["><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>k</mml:mi></mml:mfrac></mml:mstyle></mml:msup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          as found in, for example, <xref ref-type="bibr" rid="bib1.bibx83" id="text.132"/>, is derived using Bernoulli's principle, the equation for the ideal gas and an adiabatic process. The adiabatic index of air is <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mi>k</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> and static pressure is denoted by <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the total pressure by <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the calibrated difference between the static air pressure and total air pressure. <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the specific gas constant for humid air, which is assumed to equal approximately the specific gas constant for dry air with <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">287</mml:mn></mml:mrow></mml:math></inline-formula> J kg<inline-formula><mml:math id="M192" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M193" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <?pagebreak page3755?><p id="d1e4550">Regarding air as an incompressible fluid, the calculation of the true airspeed magnitude can be simplified to
            <disp-formula id="App1.Ch1.S1.E18" content-type="numbered"><label>A18</label><mml:math id="M194" display="block"><mml:mrow><mml:msup><mml:mfenced open="|" close="|"><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi></mml:mfrac></mml:mstyle><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo mathsize="2.5em">|</mml:mo><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">ρ</mml:mi></mml:mfrac></mml:mstyle><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:mi mathvariant="italic">ρ</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with the air density <inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e4650">The LUCA drone measures the airspeed with a single pitot probe, leading to the simplification that the airspeed of the drone is aligned with the drone body – in other words, the sideslip angle and angle of attack are assumed to be zero. Therefore, Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E14"/>) using <inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> was applied to the measurements for the calculation of the wind, and Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E18"/>) was applied for the calculation of the true airspeed magnitude within this study.
As the measured pressure difference equals <inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the raw dynamic pressure suffers from pressure port errors, and a calibration factor <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is introduced.</p>
      <p id="d1e4735">Besides the dynamic pressure and air density derived from the meteorological sensors, the velocity vector <inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the yaw angle <inline-formula><mml:math id="M200" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> of the drone are extracted from the autopilot system. Here, a specific filter (an extended Kalman–Bucy–Stratonovich filter; <xref ref-type="bibr" rid="bib1.bibx70" id="altparen.133"/>) fuses measurements of inertial acceleration, inertial rotation, magnetic measurements of the Earth's magnetic field, GNSS position and velocity as well as pressure data into the calculation of the aircraft state.</p>
      <p id="d1e4759">The processed wind measurements with a data rate of 25 Hz are finally averaged over a time span of about 5 s (data are averaged within pressure bands of 2 hPa and without excluding any wind observations, e.g. during aircraft bank angles) to increase the validity of the <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> assumption, as this assures averaging over multiple sequences of <inline-formula><mml:math id="M202" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M203" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> oscillations.</p>
</sec>
</app>

<app id="App1.Ch1.S2">
  <?xmltex \currentcnt{B}?><label>Appendix B</label><title>Calibration technique</title>
      <p id="d1e4801"><disp-quote>
  <p id="d1e4804">While the actual sensors can be calibrated in a laboratory, the corrections needed due to flow distortion by the aircraft body require an in-flight calibration of each instrumented aircraft. <xref ref-type="bibr" rid="bib1.bibx29" id="paren.134"/></p>
</disp-quote></p>
      <p id="d1e4810">This is not limited to atmospheric measurements and flow distortion.
In-flight validation denotes the gold standard in measurements, as there is no “friendly” laboratory environment and no simplifying assumptions can be made.
If any problem or unknown error source in the data is detected, a measurement system can be evaluated in a wind tunnel to identify the error source. Inversely, using simulations and wind tunnel tests can assist in designing a system, but the whole system has to be validated in flight.
As the sensors and installation approaches used in this study were derived from previously built and validated research aircraft, e.g. <xref ref-type="bibr" rid="bib1.bibx5" id="text.135"/> and <xref ref-type="bibr" rid="bib1.bibx80" id="text.136"/>, no wind tunnel tests were conducted initially and no unexpected error in the data during the first measurements was detected that would justify wind tunnel tests or even flow simulations.</p>
      <p id="d1e4819">Whereas crewed research aircraft typically perform well-described calibration and validation manoeuvres <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx29 bib1.bibx4 bib1.bibx24 bib1.bibx88 bib1.bibx49" id="paren.137"/>,
which can also be applied to drone systems, the following techniques freely adopted from <xref ref-type="bibr" rid="bib1.bibx5" id="text.138"/> were used within this study to determine correction parameters:
<list list-type="order"><list-item>
      <p id="d1e4830"><italic>Circles.</italic> During circling at the same altitude, atmospheric variables are not expected to change, and measurements should be independent of the flight direction. This technique can also be used to estimate the error in the dynamic pressure measurements, assuming a constant airspeed of the drone and a constant mean wind field (disregarding underlying turbulence).</p></list-item><list-item>
      <p id="d1e4836"><italic>Ascent and descent.</italic> The resulting profile of a variable over altitude must be independent of the vertical observation direction and speed and must match within the uncorrelated measurement error regimes. Deviations indicate the necessity to apply a time lag correction. Especially around the ceiling of the vertical profile, it can be assumed that atmospheric properties did not change significantly, and the observations obtained during ascent and descent have to agree.</p></list-item><list-item>
      <p id="d1e4842"><italic>Intercomparison.</italic> Using a reference measurement system to observe the same parameters that are spatially and temporally close to the measurement system to be calibrated/validated, independent measurements can be assumed, and the direct intercomparison enables the adjustment of calibration parameters or validates the observations.</p></list-item></list></p>
      <p id="d1e4847">For the true airspeed calibration of the LUCA drone, Technique (1) using circles has been used to obtain the calibration factor <inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which was found to equal <inline-formula><mml:math id="M205" display="inline"><mml:mn mathvariant="normal">0.83</mml:mn></mml:math></inline-formula> (dimensionless).</p>
      <p id="d1e4876">The time constant for the signal reconstruction of the temperature measurements was obtained by comparing ascents with descents, Technique (2), leading to <inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">temp</mml:mi></mml:msub><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">21</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula> for the specific temperature sensor installation.
Assuming a constant lapse rate of <inline-formula><mml:math id="M207" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0065</mml:mn></mml:mrow></mml:math></inline-formula> K m<inline-formula><mml:math id="M208" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and following the fundamentals of control theory, the signal reconstruction would correct for a hypothetical hysteresis of <inline-formula><mml:math id="M209" display="inline"><mml:mn mathvariant="normal">1.38</mml:mn></mml:math></inline-formula> K during the ascent.
The phase-neutral low-pass filter (first-order Butterworth type applied forwards and backwards) to reduce the noise amplified by the signal reconstruction process was set to a cut-off frequency of <inline-formula><mml:math id="M210" display="inline"><mml:mn mathvariant="normal">0.04</mml:mn></mml:math></inline-formula> Hz, which is roughly comparable to a central average over a vertical extent of approximately 120 m.</p>
      <?pagebreak page3756?><p id="d1e4933">Supporting points for the function of the time constant for the humidity sensor signal reconstruction depending on temperature in Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E6"/>) were approached first using the values provided in <xref ref-type="bibr" rid="bib1.bibx89" id="text.139"/> and <xref ref-type="bibr" rid="bib1.bibx28" id="text.140"/> as well as data from recent measurement campaigns in Benin <xref ref-type="bibr" rid="bib1.bibx5" id="paren.141"/> and Svalbard <xref ref-type="bibr" rid="bib1.bibx80" id="paren.142"/>. Combining Techniques (3) and (2), significant humidity layers were identified based on intercomparison with radiosonde data, and comparing ascents with descents led to an estimate of the time constant <inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">humi</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> in specific temperature realms. The function parameters of Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E6"/>) were then fitted to these particular time constants in relation to static air temperature. Expressed over altitude, the supporting points for fitting the function were estimated as <inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">humi</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>= 15 s at 0 km, 60 s at 3 km and 2000 s at 10 km.
The subsequent phase-neutral noise reduction filter was set to a cut-off frequency 3 times higher than the identified low-pass behaviour of the sensor installation.</p>
      <p id="d1e4982">To correct for the heat transfer from the fuselage to the sensing area according to Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E5"/>), the coefficient <inline-formula><mml:math id="M213" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">0.07</mml:mn></mml:mrow></mml:math></inline-formula> was determined by Technique (2), comparing measurements from ascents with measurements from descents.</p>
      <p id="d1e4999">This sums to six relevant calibration and correction parameters, where the noise reduction filters are not counted as relevant. This small number of adjustable calibration and correction parameters ensures that observations are not over-fitted to the expected results.</p>
</app>

<app id="App1.Ch1.S3">
  <?xmltex \currentcnt{C}?><label>Appendix C</label><title>Error estimation of simplifications and measurements</title>
<sec id="App1.Ch1.S3.SS1">
  <label>C1</label><title>Theoretical error estimation of temperature measurements</title>
      <p id="d1e5017">According to <xref ref-type="bibr" rid="bib1.bibx28" id="text.143"/>, systematic and random errors in radiosonde temperature observations include calibration, external radiation, convection of warm air originating from the balloon or the housing, and a time lag following the physical principle presented in Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>. For the calibration error, data sheet values (Table <xref ref-type="table" rid="Ch1.T1"/>) are applied to the drone observations with an uncertainty for the temperature sensor of <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">cal</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn></mml:mrow></mml:math></inline-formula> K (unknown portions of random noise and absolute deviation). External radiation is regarded as negligible, since the sensor is placed within a shielded housing, and the correction for temperature-contaminated air is included in the time lag correction, as the sensor shielding and the fuselage temperature adopts to the air temperature. The prominent error source in temperature is then the uncertainty in the time constant for the time lag correction and the uncertainty in the value for the heat transfer correction from the fuselage to the sensor head.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S3.F9" specific-use="star"><?xmltex \currentcnt{C1}?><?xmltex \def\figurename{Figure}?><label>Figure C1</label><caption><p id="d1e5048"><bold>(a)</bold> A fictional vertical profile of temperature. It is assumed that the drone is moving with a vertical speed of 10 m s<inline-formula><mml:math id="M215" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. In red, the theoretically measured temperature is presented for ascent (dashed line) and descent (solid line), suffering from a time lag with a time constant of 21 s. The blue profile subsequently shows the resulting profile after applying signal reconstruction and subsequently a phase-neutral low-pass filter.
<bold>(b)</bold> The theoretical deviation from the actual profile during ascent (dashed) and descent (solid) for the measured signal and reconstructed signals using the correct time constant <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">temp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as well as erroneous time constants (<inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">temp</mml:mi></mml:msub><mml:mo>±</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></inline-formula>%).</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f09.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S3.F10" specific-use="star"><?xmltex \currentcnt{C2}?><?xmltex \def\figurename{Figure}?><label>Figure C2</label><caption><p id="d1e5103">Error plots for wind observations, depending on the wind speed and wind incident angle with respect to the course over ground. The colour-coded error is further distinguished between the systematic error caused by a hypothetical vertical air movement of 5 m s<inline-formula><mml:math id="M218" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and an error in the airspeed calibration factor (uncertainty in the airspeed of 0.2 m s<inline-formula><mml:math id="M219" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) shown on the left halves of the circles and the random error caused by inertial velocity uncertainty (0.1 m s<inline-formula><mml:math id="M220" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for each component) in addition to an error in the yaw angle <inline-formula><mml:math id="M221" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> with an uncertainty of  5<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> shown on the right halves. Panel <bold>(a)</bold> illustrates the subsequent error for wind speed observations, whereas panel <bold>(b)</bold> reveals systematic as well as random errors in wind direction observations. As the error in the wind direction reaches  180<inline-formula><mml:math id="M223" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for low-wind conditions, uncertainties above 10<inline-formula><mml:math id="M224" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> are whitened out in the plot.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f10.png"/>

        </fig>

      <p id="d1e5190">An illustration of the effect of a time lag on a fictional vertical profile is provided in Fig. <xref ref-type="fig" rid="App1.Ch1.S3.F9"/>.</p>
      <p id="d1e5195">Figure <xref ref-type="fig" rid="App1.Ch1.S3.F9"/>a shows the temperature measured with a sensor that incorporates a significant time constant and its deviation during ascent as well as descent. The minimisation of the difference between the profiles during ascent and descent can then be used to determine the time constant of the sensor according to Technique (2). As an additional line in blue, the reconstructed temperature profile using the inverse transfer function of the sensor behaviour is shown. At the reversal points for the temperature gradient and altitude, a small offset is observed, caused by the low-pass filter applied during the signal reconstruction process to eliminate the noise amplified by the reconstruction filter.
Figure <xref ref-type="fig" rid="App1.Ch1.S3.F9"/>b then shows the correlated errors in temperature observations for the measured temperature, the reconstructed temperature and reconstructed temperatures using an erroneous time constant for the reconstruction filter.
The uncertainty in the time constant <inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">temp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is assumed to be <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula> %. Following Eq. (17) in <xref ref-type="bibr" rid="bib1.bibx28" id="text.144"/>, the correlated uncertainty in the temperature caused by an erroneous time constant for signal reconstruction is
            <disp-formula id="App1.Ch1.S3.E19" content-type="numbered"><label>C1</label><mml:math id="M227" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">rec</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mfenced close="|" open="|"><mml:mrow><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi mathvariant="normal">meas</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">rec</mml:mi></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi mathvariant="normal">meas</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">rec</mml:mi></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:mfenced><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
          with <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi mathvariant="normal">meas</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">rec</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> being the measured signal reconstructed with the time constant <inline-formula><mml:math id="M229" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula>. The additional uncertainty caused by the smoothing filter after the signal reconstruction process <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">smooth</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is roughly estimated as double the magnitude of the error introduced by the time-constant uncertainty <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">rec</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for the reconstruction process based on <xref ref-type="bibr" rid="bib1.bibx28" id="text.145"/>, where smoothing after the signal reconstruction using a different filter type than applied here introduces an uncertainty approximately 1 to 2 times larger than the uncertainty according to Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E19"/>).</p>
      <p id="d1e5361">The maximum error caused by disregarding compressibility (Eq. <xref ref-type="disp-formula" rid="App1.Ch1.S1.E4"/>) is determined by calculating the temperature rise for flight parameters and atmospheric values at sea level and at ceiling (10 km) and leads to a theoretical warm bias of <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">incompress</mml:mi></mml:msub><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> K for the typical flight parameters.</p>
      <p id="d1e5383">Regarding the error incorporated by an erroneous heat transfer correction factor according to Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E5"/>), assumed to deviate with <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula> %, the measured temperature difference between the fuselage area and the sensor head of up to <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> K results in an error of up to <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">transfer</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.45</mml:mn></mml:mrow></mml:math></inline-formula> K.</p>
</sec>
<sec id="App1.Ch1.S3.SS2">
  <label>C2</label><title>Error estimation of humidity measurements</title>
      <p id="d1e5435">As the main error sources affecting humidity profiles, daytime solar heating, a sensor lag and a temperature correction are mentioned in <xref ref-type="bibr" rid="bib1.bibx28" id="text.146"/>. The error introduced by solar heating of the HUMICAP sensor is neglected here, since an enclosure protects the sensor from solar radiation. For the calibration uncertainty, data sheet values are adopted. Regarding the time lag, the error introduced by an erroneous time constant for humidity signal reconstruction is prone to potentially high variability and strong gradients for relative humidity in atmospheric profiles. For the estimation of the error, Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E19"/>) is adopted for humidity measurements and time constants, again using a deviation of <inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> from the assumed correct time constant. Besides the data sheet uncertainty of <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">RH</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> %, the resulting error therefore can only be obtained using observational data.</p>
</sec>
<?pagebreak page3757?><sec id="App1.Ch1.S3.SS3">
  <label>C3</label><title>Error estimation of wind measurements</title>
      <p id="d1e5478">Neglecting lever-arm-induced velocities leads to an error in wind components of magnitude <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mi mathvariant="bold">Ω</mml:mi><mml:mo>×</mml:mo><mml:mi mathvariant="bold-italic">r</mml:mi></mml:mrow></mml:math></inline-formula>.
For typical rotational speeds with <inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">σ</mml:mi><mml:mi mathvariant="bold">Ω</mml:mi></mml:mrow></mml:math></inline-formula> of the LUCA drone and a neglected lever arm of <inline-formula><mml:math id="M240" display="inline"><mml:mn mathvariant="normal">0.3</mml:mn></mml:math></inline-formula> m, the uncertainty from neglecting lever arm effects results in an error of up to <inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M242" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for the vertical and <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M244" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for the horizontal lateral (body-fixed) wind component.</p>
      <p id="d1e5577">The assumption of a zero angle of attack in the first order only influences the vertical wind speed, which will be disregarded in the following, and therefore does not introduce an additional significant error. The assumption of a zero angle of sideslip, however, incorporates an error caused by natural <inline-formula><mml:math id="M245" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> oscillations of the aircraft. For the LUCA drone, the natural oscillation of <inline-formula><mml:math id="M246" display="inline"><mml:mn mathvariant="normal">0.7</mml:mn></mml:math></inline-formula> Hz with an amplitude of around 0.3<inline-formula><mml:math id="M247" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> is irrelevant to the wind and additionally filtered out by averaging the calculated wind in a final step.</p>
      <p id="d1e5603">The error from neglecting the vertical wind speed, in contrast, potentially leads to significant uncorrelated errors. It is similar to the error introduced by neglecting the vertical velocity of the aircraft, as is assumed in Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E16"/>).
Regarding the horizontally projected true airspeed of the aircraft in Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E14"/>), it is evident that the relative error neglecting vertical velocity and the vertical wind speed depends on the ratio of the true airspeed and the vertical velocity/vertical wind speed. Calculating the influence of a neglected vertical speed of 5 m s<inline-formula><mml:math id="M248" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for an airliner and a fixed-wing drone with hypothetical true airspeeds of 280 m s<inline-formula><mml:math id="M249" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 28 m s<inline-formula><mml:math id="M250" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, the deviation from the true airspeed according to Expression (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E15"/>) is 0.05 m s<inline-formula><mml:math id="M251" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for an airliner and 0.45 m s<inline-formula><mml:math id="M252" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for a fixed-wing<?pagebreak page3758?> drone, directly affecting the wind vector. For the error budget of the LUCA drone, this is neglected for normal measurements, but it should be kept in mind for measurements in strong turbulence.</p>
      <p id="d1e5673">Another error source leading to a deviation of the retrieved airspeed from the actual airspeed is the pressure calibration coefficient <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">raw</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. As the pressure calibration is done by an intrinsic in-flight calibration, comparing flight legs in different directions with respect to the wind, the resulting error in the calibration is below 0.2 m s<inline-formula><mml:math id="M254" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e5707">The error for inertial position is complex to assess, as multiple sensors are fused in an estimation filter using aircraft states at different integration levels (e.g. acceleration, velocity and position). One can assume that the uncertainty in the velocities estimated by the inertial navigation system on the drone is less than 0.1 m s<inline-formula><mml:math id="M255" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for each of the three velocity components in <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e5733">This is similar regarding attitude observations, of which only the yaw angle is needed for wind calculation. Attitude observations of LUCA fuse measurements of the Earth's magnetic field among other measurements and therefore suffer significantly from distortions caused by the electrical system. During climb and generally when the motor of the drone is driven, no wind is calculated as magnetic interferences prevent the attitude estimation from working properly.</p>
      <p id="d1e5736">The uncertainty in the yaw angle observation on the drone is assumed to be 5<inline-formula><mml:math id="M257" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. From Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E16"/>) using the small-angle approximation <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>≈</mml:mo><mml:mi mathvariant="normal">Ψ</mml:mi></mml:mrow></mml:math></inline-formula>, yielding <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>≈</mml:mo><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>⋅</mml:mo><mml:mfenced close="|" open="|"><mml:mi>u</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> for the easterly wind component, it can be concluded that the wind observation error for an attitude error equals the product of the attitude error and the true airspeed <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>⋅</mml:mo><mml:mfenced close="|" open="|"><mml:mi>u</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula>.
To reach a comparable uncertainty for the calculated wind, an airliner aircraft (<inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:mi>u</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">280</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M262" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) therefore requires yaw attitude observations that are an order of magnitude lower in uncertainty than the attitude observation uncertainty in a drone with an airspeed of 28 m s<inline-formula><mml:math id="M263" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e5860">Although uncorrelated errors (e.g. originating from the assumption of <inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> in combination with the aircraft's eigen-oscillations) are likely attenuated during the optional averaging of the calculated wind with a raw data rate of  25 Hz, systematic errors persist.
The resulting error for the wind calculation, including systematic errors from neglecting both vertical wind and the airspeed calibration as well as the rather random error sources for inertial velocity and attitude observations, dependent on wind speed and wind direction in relation to aircraft ground course, is presented in Fig. <xref ref-type="fig" rid="App1.Ch1.S3.F10"/>, which can be regarded as a graphical elaboration of the error estimation for wind measurements in <xref ref-type="bibr" rid="bib1.bibx121" id="text.147"/>.</p>
      <p id="d1e5880">For both wind speed and wind direction, the error in the yaw angle is dominant. For the wind speed, the maximum error of 2.7 m s<inline-formula><mml:math id="M265" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is seen when the air is moving laterally to the aircraft's course over ground and is independent of the general wind speed, whereas the error in wind direction is maximum with the wind aligned with the aircraft's longitudinal axis (headwind or tailwind) and generally increases towards low wind speed.
Neglecting knowledge about wind velocity and direction distribution, the averaged uncertainty fields of the wind observations computed for Fig. <xref ref-type="fig" rid="App1.Ch1.S3.F10"/> are 2.1 m s<inline-formula><mml:math id="M266" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in magnitude and  7.5<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in direction.</p>
      <p id="d1e5918">When it comes to peculiarities of different platform types, one can distinguish three types of platforms: aero-static platforms wandering with the wind speed, Earth-fixed systems such as kites or vertically ascending drones, and fixed-wing aircraft of different sizes and speeds. Based on Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S1.E11"/>), aero-static platforms incorporate <inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> with the consequence that only Earth-fixed velocities are needed to calculate wind.
Kites or vertically ascending multicopters per definition incorporate <inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, and all transformations and measurements apply to such platforms. Particularly, errors in the vertical velocity assumptions might introduce substantial errors, as the horizontal true airspeed is low in low-wind-speed conditions for kites, tethered balloons or vertically ascending multicopters.
Fixed-wing platforms, however, suffer from enhanced angular measurement sensitivity regarding the wind calculation as shown before, which increases with the airspeed of this platform type.</p>
</sec>
</app>

<app id="App1.Ch1.S4">
  <?xmltex \currentcnt{D}?><label>Appendix D</label><title>Variability of the atmosphere</title>
      <p id="d1e5988">In the following, the temporal variability of temperature, wind speed and relative humidity up to 35 km is illustrated based on ERA5 reanalyses to enable a discussion of the use of additional data observed with drones.
To describe the variability of the atmosphere at a specific location and altitude for one parameter, time series of the atmospheric variables can be transformed from the time domain into the frequency domain, e.g. by applying a Fourier transformation.
Mapping the results in the frequency domain for every altitude using colours and stacking them over the corresponding altitudes reveal the height-dependent variance of an atmospheric variable on different timescales (herein, the timescale is denoted by cycles per day); e.g. a bright spot for the variable temperature at one cycle per day (period 24 h) close to the surface reveals the diurnal cycle of the temperature in the boundary layer (forced by the sun). Such an analysis of temperature, humidity and wind speed is shown in Fig. <xref ref-type="fig" rid="App1.Ch1.S4.F11"/> for the location of the Lindenberg Meteorological Observatory of the German Weather Service using hourly ERA5 reanalysis data <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx51" id="paren.148"/> for a time span of 1 year.
Similar calculations are found in <xref ref-type="bibr" rid="bib1.bibx119" id="text.149"/> and <xref ref-type="bibr" rid="bib1.bibx37" id="text.150"/>, but in contrast to the study of <xref ref-type="bibr" rid="bib1.bibx119" id="text.151"/>, which focuses on the kinetic energy spectrum in the free troposphere, and the study of <xref ref-type="bibr" rid="bib1.bibx37" id="text.152"/>, which focuses on spectral gaps, the qualitative fields presented here are used to discuss the benefit of sampling the atmosphere frequently (more than twice a day).</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S4.F11" specific-use="star"><?xmltex \currentcnt{D1}?><?xmltex \def\figurename{Figure}?><label>Figure D1</label><caption><p id="d1e6011">Colour-coded mesoscale (periods from 1 to 48 h; <xref ref-type="bibr" rid="bib1.bibx37" id="altparen.153"/>) variance densities of time series of atmospheric variables at specific pressure levels (heights). The variances are representative of the atmospheric variability dependent on height and cycles per day (one cycle per day corresponds to a period of 24 h and two cycles per day to 12 h). The data for this analysis originate from the ERA5 reanalysis product. Bright colours indicate high variance density and hence high variability. Panel <bold>(a)</bold> represents temperature, panel <bold>(b)</bold> represents wind speed and panel <bold>(c)</bold> represents humidity.</p></caption>
        <?xmltex \igopts{width=412.564961pt}?><graphic xlink:href="https://amt.copernicus.org/articles/16/3739/2023/amt-16-3739-2023-f11.png"/>

      </fig>

      <p id="d1e6032">In Fig. <xref ref-type="fig" rid="App1.Ch1.S4.F11"/>a, one can clearly see the diurnal cycle of temperature close to the surface and in the stratosphere through<?pagebreak page3759?> the bright lines at one cycle per day. The bright lines at two cycles per day should not confuse the reader, as the analysis relies on decomposing the time signal in sinusoids with differing frequencies (cycles per day), and higher harmonics (natural products of the fundamental frequency) reveal the non-sinusoidal waveform of the diurnal cycle.
Besides in the atmospheric boundary layer, increased variability can be seen at around 10 km altitude for temperature and, after a dip in activity, at around 20 km. Interestingly, temperature variability at six cycles per day is low below 5 km altitude, emphasising the importance of profiling the atmosphere at higher altitudes.</p>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e6041">The data are published at PANGAEA and available at <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.961200" ext-link-type="DOI">10.1594/PANGAEA.961200</ext-link> <xref ref-type="bibr" rid="bib1.bibx9" id="paren.154"/> and <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.961223" ext-link-type="DOI">10.1594/PANGAEA.961223</ext-link> <xref ref-type="bibr" rid="bib1.bibx10" id="paren.155"/>. Similar datasets obtained with LUCA up to an altitude of 4.5 km are available at
<ext-link xlink:href="https://doi.org/10.1594/PANGAEA.937555" ext-link-type="DOI">10.1594/PANGAEA.937555</ext-link> <xref ref-type="bibr" rid="bib1.bibx6" id="paren.156"/> and  <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.937556" ext-link-type="DOI">10.1594/PANGAEA.937556</ext-link>  <xref ref-type="bibr" rid="bib1.bibx7" id="paren.157"/>.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e6072">AL and HS developed the project idea and acquired funding. HS and KBB performed the analysis of requirements. KBB developed the LUCA system and the instrumentation. KBB performed the data processing and data analysis. All authors contributed to and reviewed the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e6078">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e6084">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e6090">This research has been supported by the Modernity Fund (mFUND) of the German Federal Ministry for Digital and Transport (grant agreement no. 19F2072A).<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>This open-access publication was funded <?xmltex \notforhtml{\newline}?> by Technische Universität Braunschweig.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e6101">This paper was edited by Marc von Hobe and reviewed by Ralph Petersen and one anonymous referee.</p>
  </notes><ref-list>
    <title>References</title>

      <ref id="bib1.bibx1"><?xmltex \def\ref@label{{Archer and Caldeira(2008)}}?><label>Archer and Caldeira(2008)</label><?label archer_historical_2008?><mixed-citation>Archer, C. L. and Caldeira, K.: Historical Trends in the Jet Streams,   Geophys. Res. Lett., 35, L08803, <ext-link xlink:href="https://doi.org/10.1029/2008GL033614" ext-link-type="DOI">10.1029/2008GL033614</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx2"><?xmltex \def\ref@label{{Axford(1968)}}?><label>Axford(1968)</label><?label axfordAccuracyWindMeasurements1968?><mixed-citation>Axford, D. N.: On the Accuracy of Wind Measurements Using an Inertial
Platform in an Aircraft, and an Example of a Measurement of the
Vertical Mesostructure of the Atmosphere, J. Appl.
Meteorol. Climatol., 7, 645–666,
<ext-link xlink:href="https://doi.org/10.1175/1520-0450(1968)007&lt;0645:OTAOWM&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0450(1968)007&lt;0645:OTAOWM&gt;2.0.CO;2</ext-link>, 1968.</mixed-citation></ref>
      <ref id="bib1.bibx3"><?xmltex \def\ref@label{{Baker et al.(2014)}}?><label>Baker et al.(2014)</label><?label baker_lidar-measured_2014?><mixed-citation>Baker, W. E., Atlas, R., Cardinali, C., Clement, A., Emmitt, G. D., Gentry,
B. M., Hardesty, R. M., Källén, E., Kavaya, M. J., Langland, R., Ma,
Z., Masutani, M., McCarty, W., Pierce, R. B., Pu, Z., Riishojgaard, L. P.,
Ryan, J., Tucker, S., Weissmann, M., and Yoe, J. G.: Lidar-Measured Wind
Profiles: The Missing Link in the Global Observing System, B. Am. Meteorol. Soc., 95, 543–564,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-12-00164.1" ext-link-type="DOI">10.1175/BAMS-D-12-00164.1</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx4"><?xmltex \def\ref@label{{Bange et al.(2013)}}?><label>Bange et al.(2013)</label><?label bangeMeasurementAircraftState2013?><mixed-citation>Bange, J., Esposito, M., Lenschow, D. H., Brown, P. R. A., Dreiling, V., Giez,
A., Mahrt, L., Malinowski, S. P., Rodi, A. R., Shaw, R. A., Siebert, H.,
Smit, H., and Zöger, M.: Measurement of Aircraft State and
Thermodynamic and Dynamic Variables, in: Airborne Measurements
for Environmental Research, Chap. 2,  7–75, John Wiley &amp; Sons,
Ltd, <ext-link xlink:href="https://doi.org/10.1002/9783527653218.ch2" ext-link-type="DOI">10.1002/9783527653218.ch2</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx5"><?xmltex \def\ref@label{{B{\"{a}}rfuss et al.(2018)}}?><label>Bärfuss et al.(2018)</label><?label barfuss_new_2018?><mixed-citation>Bärfuss, K., Pätzold, F., Altstädter, B., Kathe, E., Nowak, S.,
Bretschneider, L., Bestmann, U., and Lampert, A<?pagebreak page3760?>.: New Setup of the UAS
ALADINA for Measuring Boundary Layer Properties, Atmospheric
Particles and Solar Radiation, Atmosphere, 9, 28,
<ext-link xlink:href="https://doi.org/10.3390/atmos9010028" ext-link-type="DOI">10.3390/atmos9010028</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx6"><?xmltex \def\ref@label{{B{\"{a}}rfuss et al.(2021a)}}?><label>Bärfuss et al.(2021a)</label><?label barfussAtmosphericProfileMeasurements2021?><mixed-citation>Bärfuss, K., Schmithüsen, H., Dirksen, R., Bretschneider, L.,   Pätzold, F., Bollmann, S., Wickboldt, H., von Unwerth, M., Asmussen,  M., Schwarting, T., and Lampert, A.: Atmospheric Profile Measurements  Conducted by the Unmanned Aerial System LUCA (Panker, Germany, 2020-07-03 and 2021-05-28), PANGAEA [data set], <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.937555" ext-link-type="DOI">10.1594/PANGAEA.937555</ext-link>, 2021a.</mixed-citation></ref>
      <ref id="bib1.bibx7"><?xmltex \def\ref@label{{B{\"{a}}rfuss et al.(2021b)}}?><label>Bärfuss et al.(2021b)</label><?label barfussRadiosondeMeasurementsColocated2021?><mixed-citation>Bärfuss, K., Schmithüsen, H., Dirksen, R., Bretschneider, L.,  Pätzold, F., Bollmann, S., Wickboldt, H., von Unwerth, M., Asmussen,  M., Schwarting, T., and Lampert, A.: Radiosonde Measurements Co-Located with Ascends of the Unmanned Aerial System LUCA (Panker, Germany  2020-07-03 and 2021-05-28), PANGAEA [data set], <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.937556" ext-link-type="DOI">10.1594/PANGAEA.937556</ext-link>, 2021b.</mixed-citation></ref>
      <ref id="bib1.bibx8"><?xmltex \def\ref@label{{B{\"{a}}rfuss et al.(2022)}}?><label>Bärfuss et al.(2022)</label><?label barfuss_drone-based_2022?><mixed-citation>Bärfuss, K. B., Schmithüsen, H., and Lampert, A.: Drone-based meteorological observations up to the tropopause, Atmos. Meas. Tech. Discuss. [preprint], <ext-link xlink:href="https://doi.org/10.5194/amt-2022-236" ext-link-type="DOI">10.5194/amt-2022-236</ext-link>, in review, 2022.</mixed-citation></ref>
      <ref id="bib1.bibx9"><?xmltex \def\ref@label{Bärfuss et al.(2023a)}?><label>Bärfuss et al.(2023a)</label><?label barfuss2023a?><mixed-citation>Bärfuss, K., Wickboldt, H., Schlerf, A., Bollmann, S., Rausch, T., and Lampert, A.: Atmospheric profile measurements conducted by the unmanned aerial system LUCA (Panker, Germany 2021-10-25 to 2021-10-29), PANGAEA [data set], <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.961200" ext-link-type="DOI">10.1594/PANGAEA.961200</ext-link>, 2023a.</mixed-citation></ref>
      <ref id="bib1.bibx10"><?xmltex \def\ref@label{Bärfuss et al.(2023b)}?><label>Bärfuss et al.(2023b)</label><?label barfuss2023b?><mixed-citation>Bärfuss, K., Wickboldt, H., Schlerf, A., Bollmann, S., Rausch, T., and Lampert, A.: Radiosonde measurements co-located with ascends of the unmanned aerial system LUCA (Panker, Germany 2021-10-25 and 2021-10-29), PANGAEA [data set], <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.961223" ext-link-type="DOI">10.1594/PANGAEA.961223</ext-link>, 2023b.</mixed-citation></ref>
      <ref id="bib1.bibx11"><?xmltex \def\ref@label{{Bauer et al.(2015)}}?><label>Bauer et al.(2015)</label><?label bauer_quiet_2015?><mixed-citation>Bauer, P., Thorpe, A., and Brunet, G.: The Quiet Revolution of Numerical
Weather Prediction, Nature, 525, 47–55, <ext-link xlink:href="https://doi.org/10.1038/nature14956" ext-link-type="DOI">10.1038/nature14956</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx12"><?xmltex \def\ref@label{{Bonavita et al.(2016)}}?><label>Bonavita et al.(2016)</label><?label bonavita_evolution_2016?><mixed-citation>Bonavita, M., Hólm, E., Isaksen, L., and Fisher, M.: The Evolution of the
ECMWF Hybrid Data Assimilation System, Q. J. Roy.
Meteorol. Soc., 142, 287–303, <ext-link xlink:href="https://doi.org/10.1002/qj.2652" ext-link-type="DOI">10.1002/qj.2652</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx13"><?xmltex \def\ref@label{{Bormann et al.(2019)}}?><label>Bormann et al.(2019)</label><?label bormann_global_2019?><mixed-citation>Bormann, N., Lawrence, H., Farnan, J., and Farnan, J.: Global Observing System Experiments in the ECMWF Assimilation System, ECMWF, <ext-link xlink:href="https://doi.org/10.21957/sr184iyz" ext-link-type="DOI">10.21957/sr184iyz</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx14"><?xmltex \def\ref@label{{Bouttier and Kelly(2001)}}?><label>Bouttier and Kelly(2001)</label><?label bouttier_observing-system_2001?><mixed-citation>Bouttier, F. and Kelly, G.: Observing-System Experiments in the ECMWF
4D-Var Data Assimilation System, Q. J. Roy.
Meteorol. Soc., 127, 1469–1488, <ext-link xlink:href="https://doi.org/10.1002/qj.49712757419" ext-link-type="DOI">10.1002/qj.49712757419</ext-link>, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx15"><?xmltex \def\ref@label{{Boylan et al.(2015)}}?><label>Boylan et al.(2015)</label><?label boylan_validation_2015?><mixed-citation>Boylan, P., Wang, J., Cohn, S. A., Fetzer, E., Maddy, E. S., and Wong, S.:
Validation of AIRS Version 6 Temperature Profiles and Surface-Based
Inversions over Antarctica Using Concordiasi Dropsonde Data, J. Geophys. Res.-Atmos., 120, 992–1007,
<ext-link xlink:href="https://doi.org/10.1002/2014JD022551" ext-link-type="DOI">10.1002/2014JD022551</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx16"><?xmltex \def\ref@label{{Cardinali(2009)}}?><label>Cardinali(2009)</label><?label cardinali_monitoring_2009?><mixed-citation>Cardinali, C.: Monitoring the Observation Impact on the Short-Range Forecast,
Q. J. Roy. Meteorol. Soc., 135, 239–250,
<ext-link xlink:href="https://doi.org/10.1002/qj.366" ext-link-type="DOI">10.1002/qj.366</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx17"><?xmltex \def\ref@label{{Cardinali(2013)}}?><label>Cardinali(2013)</label><?label cardinali_observation_2013?><mixed-citation>Cardinali, C.: Observation Impact on the Short Range Forecast,
<uri>https://www.ecmwf.int/node/16937</uri> (last access: 1 August 2023), 2013.</mixed-citation></ref>
      <ref id="bib1.bibx18"><?xmltex \def\ref@label{{Carminati et al.(2019)}}?><label>Carminati et al.(2019)</label><?label carminati_using_2019?><mixed-citation>Carminati, F., Migliorini, S., Ingleby, B., Bell, W., Lawrence, H., Newman, S., Hocking, J., and Smith, A.: Using reference radiosondes to characterise NWP model uncertainty for improved satellite calibration and validation, Atmos. Meas. Tech., 12, 83–106, <ext-link xlink:href="https://doi.org/10.5194/amt-12-83-2019" ext-link-type="DOI">10.5194/amt-12-83-2019</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx19"><?xmltex \def\ref@label{{Chander et al.(2013)}}?><label>Chander et al.(2013)</label><?label chander_overview_2013?><mixed-citation>Chander, G., Hewison, T. J., Fox, N., Wu, X., Xiong, X., and Blackwell, W. J.:
Overview of Intercalibration of Satellite Instruments, IEEE
Trans. Geosci. Remote Sens., 51, 1056–1080,
<ext-link xlink:href="https://doi.org/10.1109/TGRS.2012.2228654" ext-link-type="DOI">10.1109/TGRS.2012.2228654</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx20"><?xmltex \def\ref@label{{Chilson et al.(2019)}}?><label>Chilson et al.(2019)</label><?label chilson_moving_2019?><mixed-citation>Chilson, P. B., Bell, T. M., Brewster, K. A., Britto Hupsel de Azevedo, G.,
Carr, F. H., Carson, K., Doyle, W., Fiebrich, C. A., Greene, B. R., Grimsley,
J. L., Kanneganti, S. T., Martin, J., Moore, A., Palmer, R. D.,
Pillar-Little, E. A., Salazar-Cerreno, J. L., Segales, A. R., Weber,
M. E., Yeary, M., and Droegemeier, K. K.: Moving towards a Network of
Autonomous UAS Atmospheric Profiling Stations for Observations in the
Earth's Lower Atmosphere: The 3D Mesonet Concept, Sensors, 19,
2720, <ext-link xlink:href="https://doi.org/10.3390/s19122720" ext-link-type="DOI">10.3390/s19122720</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx21"><?xmltex \def\ref@label{{Choi et al.(2018)}}?><label>Choi et al.(2018)</label><?label choi_evaluation_2018?><mixed-citation>Choi, B. I., Lee, S.-W., Woo, S.-B., Kim, J. C., Kim, Y.-G., and Yang, S. G.: Evaluation of radiosonde humidity sensors at low temperature using ultralow-temperature humidity chamber, Adv. Sci. Res., 15, 207–212, <ext-link xlink:href="https://doi.org/10.5194/asr-15-207-2018" ext-link-type="DOI">10.5194/asr-15-207-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx22"><?xmltex \def\ref@label{{Cione et al.(2020)}}?><label>Cione et al.(2020)</label><?label cione_eye_2020?><mixed-citation>Cione, J. J., Bryan, G. H., Dobosy, R., Zhang, J. A., de Boer, G., Aksoy, A.,
Wadler, J. B., Kalina, E. A., Dahl, B. A., Ryan, K., Neuhaus, J., Dumas, E.,
Marks, F. D., Farber, A. M., Hock, T., and Chen, X.: Eye of the Storm:
Observing Hurricanes with a Small Unmanned Aircraft System, B. Am. Meteorol. Soc., 101, E186–E205,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-19-0169.1" ext-link-type="DOI">10.1175/BAMS-D-19-0169.1</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx23"><?xmltex \def\ref@label{{Cohn et al.(2013)}}?><label>Cohn et al.(2013)</label><?label cohn_driftsondes_2013?><mixed-citation>Cohn, S. A., Hock, T., Cocquerez, P., Wang, J., Rabier, F., Parsons, D., Harr,
P., Wu, C.-C., Drobinski, P., Karbou, F., Vénel, S., Vargas, A.,
Fourrié, N., Saint-Ramond, N., Guidard, V., Doerenbecher, A., Hsu,
H.-H., Lin, P.-H., Chou, M.-D., Redelsperger, J.-L., Martin, C., Fox, J.,
Potts, N., Young, K., and Cole, H.: Driftsondes: Providing In Situ
Long-Duration Dropsonde Observations over Remote Regions, B. Am. Meteorol. Soc., 94, 1661–1674,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-12-00075.1" ext-link-type="DOI">10.1175/BAMS-D-12-00075.1</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx24"><?xmltex \def\ref@label{{Cooper et al.(2014)}}?><label>Cooper et al.(2014)</label><?label cooperCalibratingAirborneMeasurements2014?><mixed-citation>Cooper, W. A., Spuler, S. M., Spowart, M., Lenschow, D. H., and Friesen, R. B.: Calibrating airborne measurements of airspeed, pressure and temperature using a Doppler laser air-motion sensor, Atmos. Meas. Tech., 7, 3215–3231, <ext-link xlink:href="https://doi.org/10.5194/amt-7-3215-2014" ext-link-type="DOI">10.5194/amt-7-3215-2014</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx25"><?xmltex \def\ref@label{{Dabberdt et al.(2005)}}?><label>Dabberdt et al.(2005)</label><?label dabberdt_multifunctional_2005?><mixed-citation>Dabberdt, W. F., Schlatter, T. W., Carr, F. H., Friday, E. W. J., Jorgensen,
D., Koch, S., Pirone, M., Ralph, F. M., Sun, J., Welsh, P., Wilson, J. W.,
and Zou, X.: Multifunctional Mesoscale Observing Networks, B. Am. Meteorol. Soc., 86, 961–982,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-86-7-961" ext-link-type="DOI">10.1175/BAMS-86-7-961</ext-link>, 2005.</mixed-citation></ref>
      <ref id="bib1.bibx26"><?xmltex \def\ref@label{{de~Boer et al.(2020)}}?><label>de Boer et al.(2020)</label><?label boer_development_2020?><mixed-citation>de Boer, G., Diehl, C., Jacob, J., Houston, A., Smith, S. W., Chilson, P.,
Schmale, D. G., Intrieri, J., Pinto, J., Elston, J., Brus, D., Kemppinen, O.,
Clark, A., Lawrence, D., Bailey, S. C. C., Sama, M. P., Frazier, A., Crick,
C., Natalie, V., Pillar-Little, E., Klein, P., Waugh, S., Lundquist, J. K.,
Barbieri, L., Kral, S. T., Jensen, A. A., Dixon, C., Borenstein, S.,
Hesselius, D., Human, K., Hall, P., Argrow, B., Thornberry, T., Wright, R.,
and Kelly, J. T.: Development of Community, Capabilities, and
Understanding through Unmanned Aircraft-Based Atmospheric Research:
The LAPSE-RATE Campaign, B. Am. Meteorol. Soc.,
101, E684–E699, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-19-0050.1" ext-link-type="DOI">10.1175/BAMS-D-19-0050.1</ext-link>, 2020.</mixed-citation></ref>
      <?pagebreak page3761?><ref id="bib1.bibx27"><?xmltex \def\ref@label{{{de Haan} et al.(2022)}}?><label>de Haan et al.(2022)</label><?label de_haan_characterizing_2022?><mixed-citation>de Haan, S., de Jong, P. M. A., and van der Meulen, J.: Characterizing and correcting the warm bias observed in Aircraft Meteorological Data Relay (AMDAR) temperature observations, Atmos. Meas. Tech., 15, 811–818, <ext-link xlink:href="https://doi.org/10.5194/amt-15-811-2022" ext-link-type="DOI">10.5194/amt-15-811-2022</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bibx28"><?xmltex \def\ref@label{{Dirksen et al.(2014)}}?><label>Dirksen et al.(2014)</label><?label dirksen_reference_2014?><mixed-citation>Dirksen, R. J., Sommer, M., Immler, F. J., Hurst, D. F., Kivi, R., and Vömel, H.: Reference quality upper-air measurements: GRUAN data processing for the Vaisala RS92 radiosonde, Atmos. Meas. Tech., 7, 4463–4490, <ext-link xlink:href="https://doi.org/10.5194/amt-7-4463-2014" ext-link-type="DOI">10.5194/amt-7-4463-2014</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx29"><?xmltex \def\ref@label{{Dr{\"{u}}e et al.(2008)}}?><label>Drüe et al.(2008)</label><?label drueAircraftTypespecificErrors2008?><mixed-citation>Drüe, C., Frey, W., Hoff, A., and Hauf, Th.: Aircraft
Type-Specific Errors in AMDAR Weather Reports from Commercial Aircraft,
Q. J. Roy. Meteorol. Soc., 134, 229–239,
<ext-link xlink:href="https://doi.org/10.1002/qj.205" ext-link-type="DOI">10.1002/qj.205</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx30"><?xmltex \def\ref@label{{Dupont et al.(2020)}}?><label>Dupont et al.(2020)</label><?label dupont_characterization_2020?><mixed-citation>Dupont, J.-C., Haeffelin, M., Badosa, J., Clain, G., Raux, C., and Vignelles,
D.: Characterization and Corrections of Relative Humidity Measurement
from Meteomodem M10 Radiosondes at Midlatitude Stations, J.
Atmos. Ocean. Technol., 37, 857–871,
<ext-link xlink:href="https://doi.org/10.1175/JTECH-D-18-0205.1" ext-link-type="DOI">10.1175/JTECH-D-18-0205.1</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx31"><?xmltex \def\ref@label{{EASA(2022)}}?><label>EASA(2022)</label><?label easa_easy_2022?><mixed-citation>EASA: Easy Access Rules for Unmanned Aircraft Systems (Regulation (EU) 2019/947 and Regulation (EU) 2019/945), <uri>https://www.easa.europa.eu/document-library/easy-access-rules/easy-access-rules-unmanned-aircraft-systems-regulation-eu</uri> (last access: 1 August 2023), 2022.</mixed-citation></ref>
      <ref id="bib1.bibx32"><?xmltex \def\ref@label{{Elston et al.(2015)}}?><label>Elston et al.(2015)</label><?label elston_overview_2015?><mixed-citation>Elston, J., Argrow, B., Stachura, M., Weibel, D., Lawrence, D., and Pope, D.:
Overview of Small Fixed-Wing Unmanned Aircraft for Meteorological
Sampling, J. Atmos. Ocean. Technol., 32, 97–115,
<ext-link xlink:href="https://doi.org/10.1175/JTECH-D-13-00236.1" ext-link-type="DOI">10.1175/JTECH-D-13-00236.1</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx33"><?xmltex \def\ref@label{{Elston et al.(2011)}}?><label>Elston et al.(2011)</label><?label elston_tempest_2011?><mixed-citation>Elston, J. S., Roadman, J., Stachura, M., Argrow, B., Houston, A., and Frew,
E.: The Tempest Unmanned Aircraft System for in Situ Observations of Tornadic
Supercells: Design and VORTEX2 Flight Results, J. Field
Robot., 28, 461–483, <ext-link xlink:href="https://doi.org/10.1002/rob.20394" ext-link-type="DOI">10.1002/rob.20394</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx34"><?xmltex \def\ref@label{{Evtushevsky et al.(2008)}}?><label>Evtushevsky et al.(2008)</label><?label evtushevsky_total_2008?><mixed-citation>Evtushevsky, O. M., Grytsai, A. V., Klekociuk, A. R., and Milinevsky, G. P.: Total Ozone and Tropopause Zonal Asymmetry during the Antarctic Spring, J. Geophys. Res.-Atmos., 113, D00B06, <ext-link xlink:href="https://doi.org/10.1029/2008JD009881" ext-link-type="DOI">10.1029/2008JD009881</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx35"><?xmltex \def\ref@label{{Eyre(2008)}}?><label>Eyre(2008)</label><?label eyre_introduction_2008?><mixed-citation>
Eyre, J.: An Introduction to GPS Radio Occultation and Its Use in Numerical
Weather Prediction., in: ECMWF GRAS SAF Workshop on Applications of
GPS Radio Occultation Measurements, 16–18 June 2008, 1–10,
ECMWF, Shinfield Park, Reading, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx36"><?xmltex \def\ref@label{{Faccani et al.(2009)}}?><label>Faccani et al.(2009)</label><?label faccani_impacts_2009?><mixed-citation>Faccani, C., Rabier, F., Fourrié, N., Agusti-Panareda, A., Karbou, F.,
Moll, P., Lafore, J.-P., Nuret, M., Hdidou, F., and Bock, O.: The Impacts
of AMMA Radiosonde Data on the French Global Assimilation and
Forecast System, Weather Forecast., 24, 1268–1286,
<ext-link xlink:href="https://doi.org/10.1175/2009WAF2222237.1" ext-link-type="DOI">10.1175/2009WAF2222237.1</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx37"><?xmltex \def\ref@label{{Fiedler and Panofsky(1970)}}?><label>Fiedler and Panofsky(1970)</label><?label fiedler_atmospheric_1970?><mixed-citation>Fiedler, F. and Panofsky, H. A.: Atmospheric Scales and Spectral Gaps, B. Am. Meteorol. Soc., 51, 1114–1120,
<ext-link xlink:href="https://doi.org/10.1175/1520-0477(1970)051&lt;1114:ASASG&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0477(1970)051&lt;1114:ASASG&gt;2.0.CO;2</ext-link>, 1970.</mixed-citation></ref>
      <ref id="bib1.bibx38"><?xmltex \def\ref@label{{Flagg et al.(2018)}}?><label>Flagg et al.(2018)</label><?label flagg_impact_2018?><mixed-citation>Flagg, D. D., Doyle, J. D., Holt, T. R., Tyndall, D. P., Amerault, C. M.,
Geiszler, D., Haack, T., Moskaitis, J. R., Nachamkin, J., and Eleuterio,
D. P.: On the Impact of Unmanned Aerial System Observations on
Numerical Weather Prediction in the Coastal Zone, Mon. Weather
Rev., 146, 599–622, <ext-link xlink:href="https://doi.org/10.1175/MWR-D-17-0028.1" ext-link-type="DOI">10.1175/MWR-D-17-0028.1</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx39"><?xmltex \def\ref@label{{Fleming(1996)}}?><label>Fleming(1996)</label><?label fleming_use_1996?><mixed-citation>Fleming, R. J.: The Use of Commercial Aircraft as Platforms for
Environmental Measurements, B. Am. Meteorol.
Soc., 77, 2229–2242,
<ext-link xlink:href="https://doi.org/10.1175/1520-0477(1996)077&lt;2229:TUOCAA&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0477(1996)077&lt;2229:TUOCAA&gt;2.0.CO;2</ext-link>, 1996.</mixed-citation></ref>
      <ref id="bib1.bibx40"><?xmltex \def\ref@label{{Fujiwara et al.(2003)}}?><label>Fujiwara et al.(2003)</label><?label fujiwara_performance_2003?><mixed-citation>Fujiwara, M., Shiotani, M., Hasebe, F., Vömel, H., Oltmans, S. J., Ruppert,
P. W., Horinouchi, T., and Tsuda, T.: Performance of the Meteolabor
“Snow White” Chilled-Mirror Hygrometer in the Tropical
Troposphere: Comparisons with the Vaisala RS80 A/H-Humicap
Sensors, J. Atmos. Ocean. Technol., 20, 1534–1542,
<ext-link xlink:href="https://doi.org/10.1175/1520-0426(2003)020&lt;1534:POTMSW&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0426(2003)020&lt;1534:POTMSW&gt;2.0.CO;2</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bibx41"><?xmltex \def\ref@label{{Geerts et al.(2018)}}?><label>Geerts et al.(2018)</label><?label geerts_recommendations_2018?><mixed-citation>Geerts, B., Raymond, D. J., Grubišić, V., Davis, C. A., Barth, M. C.,
Detwiler, A., Klein, P. M., Lee, W.-C., Markowski, P. M., Mullendore, G. L.,
and Moore, J. A.: Recommendations for In Situ and Remote Sensing
Capabilities in Atmospheric Convection and Turbulence, B. Am. Meteorol. Soc., 99, 2463–2470,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-17-0310.1" ext-link-type="DOI">10.1175/BAMS-D-17-0310.1</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx42"><?xmltex \def\ref@label{{Gelaro and Zhu(2009)}}?><label>Gelaro and Zhu(2009)</label><?label gelaro_examination_2009?><mixed-citation>Gelaro, R. and Zhu, Y.: Examination of Observation Impacts Derived from
Observing System Experiments (OSEs) and Adjoint Models, Tellus A, 61, 179–193,
<ext-link xlink:href="https://doi.org/10.1111/j.1600-0870.2008.00388.x" ext-link-type="DOI">10.1111/j.1600-0870.2008.00388.x</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx43"><?xmltex \def\ref@label{{Gettelman et al.(2011)}}?><label>Gettelman et al.(2011)</label><?label gettelman_extratropical_2011?><mixed-citation>Gettelman, A., Hoor, P., Pan, L. L., Randel, W. J., Hegglin, M. I., and Birner,
T.: The Extratropical Upper Troposphere and Lower Stratosphere,
Rev. Geophys., 49, RG3003, <ext-link xlink:href="https://doi.org/10.1029/2011RG000355" ext-link-type="DOI">10.1029/2011RG000355</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx44"><?xmltex \def\ref@label{{Goldberg et al.(2011)}}?><label>Goldberg et al.(2011)</label><?label goldberg_global_2011?><mixed-citation>Goldberg, M., Ohring, G., Butler, J., Cao, C., Datla, R., Doelling, D.,
Gärtner, V., Hewison, T., Iacovazzi, B., Kim, D., Kurino, T., Lafeuille,
J., Minnis, P., Renaut, D., Schmetz, J., Tobin, D., Wang, L., Weng, F., Wu,
X., Yu, F., Zhang, P., and Zhu, T.: The Global Space-Based
Inter-Calibration System, B. Am. Meteorol. Soc.,
92, 467–475, <ext-link xlink:href="https://doi.org/10.1175/2010BAMS2967.1" ext-link-type="DOI">10.1175/2010BAMS2967.1</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx45"><?xmltex \def\ref@label{{Hacker et al.(2018)}}?><label>Hacker et al.(2018)</label><?label hacker_challenges_2018?><mixed-citation>Hacker, J., Draper, C., and Madaus, L.: Challenges and Opportunities for
Data Assimilation in Mountainous Environments, Atmosphere, 9, 127,
<ext-link xlink:href="https://doi.org/10.3390/atmos9040127" ext-link-type="DOI">10.3390/atmos9040127</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx46"><?xmltex \def\ref@label{{Haering(1990)}}?><label>Haering(1990)</label><?label haeringAirdataCalibrationHighperformance1990?><mixed-citation>Haering, E. Jr.: Airdata Calibration of a High-Performance
Aircraft for Measuring Atmospheric Wind Profiles, in: 28th Aerospace
Sciences Meeting, Aerospace Sciences Meetings, American Institute of
Aeronautics and Astronautics, <ext-link xlink:href="https://doi.org/10.2514/6.1990-230" ext-link-type="DOI">10.2514/6.1990-230</ext-link>, 1990.</mixed-citation></ref>
      <ref id="bib1.bibx47"><?xmltex \def\ref@label{{Hann(2020)}}?><label>Hann(2020)</label><?label hann_atmospheric_2020?><mixed-citation>Hann, R.: Atmospheric Ice Accretions, Aerodynamic Icing Penalties, and
Ice Protection Systems on Unmanned Aerial Vehicles, NTNU,
<uri>https://ntnuopen.ntnu.no/ntnu-xmlui/handle/11250/2657638</uri> (last access: 1 August 2023),   2020.</mixed-citation></ref>
      <ref id="bib1.bibx48"><?xmltex \def\ref@label{{Hann et al.(2021)}}?><label>Hann et al.(2021)</label><?label hannExperimentalHeatLoads2021?><mixed-citation>Hann, R., Enache, A., Nielsen, M. C., Stovner, B. N., van Beeck, J.,
Johansen, T. A., and Borup, K. T.: Experimental Heat Loads for
Electrothermal Anti-Icing and De-Icing on UAVs, Aerospace, 8, 83,
<ext-link xlink:href="https://doi.org/10.3390/aerospace8030083" ext-link-type="DOI">10.3390/aerospace8030083</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx49"><?xmltex \def\ref@label{{Hartmann et al.(2018)}}?><label>Hartmann et al.(2018)</label><?label hartmannNewCalibrationProcedures2018?><mixed-citation>Hartmann, J., Gehrmann, M., Kohnert, K., Metzger, S., and Sachs, T.: New calibration procedures for airborne turbulence measurements and accuracy of the methane fluxes during the AirMeth campaigns, Atmos. Meas. Tech., 11, 4567–4581, <ext-link xlink:href="https://doi.org/10.5194/amt-11-4567-2018" ext-link-type="DOI">10.5194/amt-11-4567-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx50"><?xmltex \def\ref@label{{Hersbach et al.(2023)}}?><label>Hersbach et al.(2023)</label><?label hersbachERA5HourlyData2018?><mixed-citation>Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Horányi, A., Muñoz Sabater, J., Nicolas, J., Peubey, C., Radu, R., Rozum, I., Schepers, D., Simmons, A., Soci, C., Dee, D., and Thépaut, J.-N.: ERA5 hourly data on single levels from 1940 to present, Copernicus Climate Change Service (C3S) Climate Data Store (CDS) [data set], <ext-link xlink:href="https://doi.org/10.24381/cds.adbb2d47" ext-link-type="DOI">10.24381/cds.adbb2d47</ext-link>, 2023.</mixed-citation></ref>
      <ref id="bib1.bibx51"><?xmltex \def\ref@label{{Hersbach et al.(2020)}}?><label>Hersbach et al.(2020)</label><?label hersbach_era5_2020-1?><mixed-citation>Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A.,
Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D.,
Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P.,
Biavati, G., Bidlot, J., Bonavita, M., Chiara, G., Dahlgren, P., Dee, D.,
Diamantakis, M., Dragani, R., Flemming, J.<?pagebreak page3762?>, Forbes, R., Fuentes, M., Geer,
A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M.,
Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., Rosnay, P.,
Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.-N.: The ERA5
Global Reanalysis, Q. J. Roy. Meteorol. Soc., 146, 1999–2049,
<ext-link xlink:href="https://doi.org/10.1002/qj.3803" ext-link-type="DOI">10.1002/qj.3803</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx52"><?xmltex \def\ref@label{{Hock and Franklin(1999)}}?><label>Hock and Franklin(1999)</label><?label hock_ncar_1999?><mixed-citation>
Hock, T. F. and Franklin, J. L.: The NCAR GPS Dropwindsonde, B. Am. Meteorol. Soc., 80, 407–420,  1999.</mixed-citation></ref>
      <ref id="bib1.bibx53"><?xmltex \def\ref@label{{Holton et al.(1995)}}?><label>Holton et al.(1995)</label><?label holton_stratosphere-troposphere_1995?><mixed-citation>Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B.,
and Pfister, L.: Stratosphere-Troposphere Exchange, Rev. Geophys.,
33, 403–439, <ext-link xlink:href="https://doi.org/10.1029/95RG02097" ext-link-type="DOI">10.1029/95RG02097</ext-link>, 1995.</mixed-citation></ref>
      <ref id="bib1.bibx54"><?xmltex \def\ref@label{{Houston et al.(2021)}}?><label>Houston et al.(2021)</label><?label houston_national_2021?><mixed-citation>Houston, A. L., PytlikZillig, L. M., and Walther, J. C.: National Weather
Service Data Needs for Short-Term Forecasts and the Role of
Unmanned Aircraft in Filling the Gap: Results from a
Nationwide Survey, B. Am. Meteorol. Soc., 102,
E2106–E2120, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-20-0183.1" ext-link-type="DOI">10.1175/BAMS-D-20-0183.1</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx55"><?xmltex \def\ref@label{{Huang et al.(2019)}}?><label>Huang et al.(2019)</label><?label huang_survey_2019?><mixed-citation>Huang, X., Tepylo, N., Pommier-Budinger, V., Budinger, M., Bonaccurso, E.,
Villedieu, P., and Bennani, L.: A Survey of Icephobic Coatings and Their
Potential Use in a Hybrid Coating/Active Ice Protection System for Aerospace
Applications, Prog. Aerospace Sci., 105, 74–97,
<ext-link xlink:href="https://doi.org/10.1016/j.paerosci.2019.01.002" ext-link-type="DOI">10.1016/j.paerosci.2019.01.002</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx56"><?xmltex \def\ref@label{{Ingleby and Edwards(2015)}}?><label>Ingleby and Edwards(2015)</label><?label ingleby_changes_2015?><mixed-citation>Ingleby, B. and Edwards, D.: Changes to Radiosonde Reports and Their Processing
for Numerical Weather Prediction, Atmos. Sc. Lett., 16, 44–49,
<ext-link xlink:href="https://doi.org/10.1002/asl2.518" ext-link-type="DOI">10.1002/asl2.518</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx57"><?xmltex \def\ref@label{{Ingleby et al.(2016a)}}?><label>Ingleby et al.(2016a)</label><?label ingleby_progress_2016?><mixed-citation>Ingleby, B., Pauley, P., Kats, A., Ator, J., Keyser, D., Doerenbecher, A.,
Fucile, E., Hasegawa, J., Toyoda, E., Kleinert, T., Qu, W., James, J. S.,
Tennant, W., and Weedon, R.: Progress toward High-Resolution, Real-Time
Radiosonde Reports, B. Am. Meteorol. Soc., 97,
2149–2161, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-15-00169.1" ext-link-type="DOI">10.1175/BAMS-D-15-00169.1</ext-link>, 2016a.</mixed-citation></ref>
      <ref id="bib1.bibx58"><?xmltex \def\ref@label{{Ingleby et al.(2016b)}}?><label>Ingleby et al.(2016b)</label><?label ingleby_global_2016?><mixed-citation>Ingleby, B., Rodwell, M., and Isaksen, L.: Global Radiosonde Network under
Pressure, Tech. Rep. 149, ECMWF, <ext-link xlink:href="https://doi.org/10.21957/cblxtg" ext-link-type="DOI">10.21957/cblxtg</ext-link>, 2016b.</mixed-citation></ref>
      <ref id="bib1.bibx59"><?xmltex \def\ref@label{{Ingleby et al.(2020)}}?><label>Ingleby et al.(2020)</label><?label ingleby_evaluation_2020?><mixed-citation>Ingleby, B., Isaksen, L., Kral, T., and Kral, T.: Evaluation and Impact of
Aircraft Humidity Data in ECMWF&amp;#039;s NWP System,
<ext-link xlink:href="https://doi.org/10.21957/4e825dtiy" ext-link-type="DOI">10.21957/4e825dtiy</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx60"><?xmltex \def\ref@label{{Ingleby et al.(2021)}}?><label>Ingleby et al.(2021)</label><?label ingleby_impact_2021?><mixed-citation>Ingleby, B., Candy, B., Eyre, J., Haiden, T., Hill, C., Isaksen, L., Kleist,
D., Smith, F., Steinle, P., Taylor, S., Tennant, W., and Tingwell, C.: The
Impact of COVID-19 on Weather Forecasts: A Balanced View,
Geophys. Res. Lett., 48, e2020GL090699,
<ext-link xlink:href="https://doi.org/10.1029/2020GL090699" ext-link-type="DOI">10.1029/2020GL090699</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx61"><?xmltex \def\ref@label{{Ingleby et al.(2022)}}?><label>Ingleby et al.(2022)</label><?label ingleby_quality_2022?><mixed-citation>Ingleby, B., Motl, M., Marlton, G., Edwards, D., Sommer, M., von Rohden, C., Vömel, H., and Jauhiainen, H.: On the quality of RS41 radiosonde descent data, Atmos. Meas. Tech., 15, 165–183, <ext-link xlink:href="https://doi.org/10.5194/amt-15-165-2022" ext-link-type="DOI">10.5194/amt-15-165-2022</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bibx62"><?xmltex \def\ref@label{{Inoue and Sato(2022)}}?><label>Inoue and Sato(2022)</label><?label inoue_toward_2022?><mixed-citation>Inoue, J. and Sato, K.: Toward Sustainable Meteorological Profiling in Polar
Regions: Case Studies Using an Inexpensive UAS on Measuring Lower
Boundary Layers with Quality of Radiosondes, Environ. Res., 205,
112468, <ext-link xlink:href="https://doi.org/10.1016/j.envres.2021.112468" ext-link-type="DOI">10.1016/j.envres.2021.112468</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bibx63"><?xmltex \def\ref@label{{Jacob et al.(2018)}}?><label>Jacob et al.(2018)</label><?label jacob_considerations_2018-1?><mixed-citation>Jacob, J. D., Chilson, P. B., Houston, A. L., and Smith, S. W.: Considerations
for Atmospheric Measurements with Small Unmanned Aircraft Systems,
Atmosphere, 9, 252, <ext-link xlink:href="https://doi.org/10.3390/atmos9070252" ext-link-type="DOI">10.3390/atmos9070252</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx64"><?xmltex \def\ref@label{{Jeck(2002)}}?><label>Jeck(2002)</label><?label jeck_icing_2002?><mixed-citation>
Jeck, R. K.: Icing Design Envelopes (14 CFR Parts 25 and 29, Appendix C) Converted to a Distance-Based Format, Federal Aviation Administration Report DOT/FAA/AR-00/30, US Department of Transportation, Washington, DC, USA, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx65"><?xmltex \def\ref@label{{Jensen et al.(2021)}}?><label>Jensen et al.(2021)</label><?label jensen_assimilation_2021?><mixed-citation>Jensen, A. A., Pinto, J. O., Bailey, S. C., Sobash, R. A., de Boer, G.,
Houston, A. L., Chilson, P. B., Bell, T., Romine, G., Smith, S. W., Lawrence,
D. A., Dixon, C., Lundquist, J. K., Jacob, J. D., Elston, J., Waugh, S., and
Steiner, M.: Assimilation of a Coordinated Fleet of Uncrewed Aircraft
System Observations in Complex Terrain: EnKF System Design and
Preliminary Assessment, Mon. Weather Rev., 149, 1459–1480,
<ext-link xlink:href="https://doi.org/10.1175/mwr-d-20-0359.1" ext-link-type="DOI">10.1175/mwr-d-20-0359.1</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx66"><?xmltex \def\ref@label{{Jensen et al.(2022)}}?><label>Jensen et al.(2022)</label><?label jensenAssimilationCoordinatedFleet2022?><mixed-citation>Jensen, A. A., Pinto, J. O., Bailey, S. C. C., Sobash, R. A., Romine, G.,
de Boer, G., Houston, A. L., Smith, S. W., Lawrence, D. A., Dixon, C.,
Lundquist, J. K., Jacob, J. D., Elston, J., Waugh, S., Brus, D., and Steiner,
M.: Assimilation of a Coordinated Fleet of Uncrewed Aircraft System
Observations in Complex Terrain: Observing System Experiments,
Mon. Weather Rev., 150, 2737–2763, <ext-link xlink:href="https://doi.org/10.1175/MWR-D-22-0090.1" ext-link-type="DOI">10.1175/MWR-D-22-0090.1</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bibx67"><?xmltex \def\ref@label{{Jonassen et al.(2012)}}?><label>Jonassen et al.(2012)</label><?label jonassen_improving_2012?><mixed-citation>Jonassen, M. O., Ólafsson, H., Ágústsson, H., Rögnvaldsson,
Ó., and Reuder, J.: Improving High-Resolution Numerical Weather
Simulations by Assimilating Data from an Unmanned Aerial System,
Mon. Weather Rev., 140, 3734–3756, <ext-link xlink:href="https://doi.org/10.1175/MWR-D-11-00344.1" ext-link-type="DOI">10.1175/MWR-D-11-00344.1</ext-link>,
2012.</mixed-citation></ref>
      <ref id="bib1.bibx68"><?xmltex \def\ref@label{{Joyce et al.(2021)}}?><label>Joyce et al.(2021)</label><?label joyce_course_2021?><mixed-citation>Joyce, K. E., Anderson, K., and Bartolo, R. E.: Of Course We Fly
Unmanned – We're Women!, Drones, 5, 21,
<ext-link xlink:href="https://doi.org/10.3390/drones5010021" ext-link-type="DOI">10.3390/drones5010021</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx69"><?xmltex \def\ref@label{{Kalinka et al.(2017)}}?><label>Kalinka et al.(2017)</label><?label kalinka_-flight_2017?><mixed-citation>Kalinka, F., Roloff, K., Tendel, J., and Hauf, T.: The In-flight Icing
Warning System ADWICE for European Airspace – Current
Structure, Recent Improvements and Verification Results, Meteorologische
Z., 26, 441–455, <ext-link xlink:href="https://doi.org/10.1127/metz/2017/0756" ext-link-type="DOI">10.1127/metz/2017/0756</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx70"><?xmltex \def\ref@label{{Kalman(1960)}}?><label>Kalman(1960)</label><?label kalmanNewApproachLinear1960?><mixed-citation>Kalman, R. E.: A New Approach to Linear Filtering and Prediction
Problems, J. Basic Eng., 82, 35–45,
<ext-link xlink:href="https://doi.org/10.1115/1.3662552" ext-link-type="DOI">10.1115/1.3662552</ext-link>, 1960.</mixed-citation></ref>
      <ref id="bib1.bibx71"><?xmltex \def\ref@label{{Karbou et al.(2005)}}?><label>Karbou et al.(2005)</label><?label karbou_potential_2005?><mixed-citation>Karbou, F., Aires, F., Prigent, C., and Eymard, L.: Potential of Advanced
Microwave Sounding Unit-A (AMSU-A) and AMSU-B Measurements for
Atmospheric Temperature and Humidity Profiling over Land, J.
Geophys. Res.-Atmos., 110, D07109, <ext-link xlink:href="https://doi.org/10.1029/2004JD005318" ext-link-type="DOI">10.1029/2004JD005318</ext-link>, 2005.</mixed-citation></ref>
      <ref id="bib1.bibx72"><?xmltex \def\ref@label{{Kim and Kim(2019)}}?><label>Kim and Kim(2019)</label><?label kim_forecast_2019?><mixed-citation>Kim, S.-M. and Kim, H. M.: Forecast Sensitivity Observation Impact in the
4DVAR and Hybrid-4DVAR Data Assimilation Systems, J.
Atmos. Ocean. Technol., 36, 1563–1575,
<ext-link xlink:href="https://doi.org/10.1175/JTECH-D-18-0240.1" ext-link-type="DOI">10.1175/JTECH-D-18-0240.1</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx73"><?xmltex \def\ref@label{{Koch et al.(2018)}}?><label>Koch et al.(2018)</label><?label koch_use_2018?><mixed-citation>Koch, S. E., Fengler, M., Chilson, P. B., Elmore, K. L., Argrow, B., Andra,
D. L., and Lindley, T.: On the Use of Unmanned Aircraft for
Sampling Mesoscale Phenomena in the Preconvective Boundary Layer,
J. Atmos. Ocean. Technol., 35, 2265–2288,
<ext-link xlink:href="https://doi.org/10.1175/JTECH-D-18-0101.1" ext-link-type="DOI">10.1175/JTECH-D-18-0101.1</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx74"><?xmltex \def\ref@label{{{K{\"{o}}nig-Langlo} et al.(1998)}}?><label>König-Langlo et al.(1998)</label><?label konig-langlo_climatology_1998?><mixed-citation>König-Langlo, G., King, J. C., and Pettré, P.: Climatology of the
Three Coastal Antarctic Stations Dumont d'Urville, Neumayer,
and Halley, J. Geophys. Res.-Atmos., 103,
10935–10946, <ext-link xlink:href="https://doi.org/10.1029/97JD00527" ext-link-type="DOI">10.1029/97JD00527</ext-link>, 1998.</mixed-citation></ref>
      <ref id="bib1.bibx75"><?xmltex \def\ref@label{{Konrad et al.(1970)}}?><label>Konrad et al.(1970)</label><?label konrad_small_1970?><mixed-citation>
Konrad, T., Hill, M., Rowland, J., and Meyer, J. H.: A Small, Radio-Controlled
Aircraft as a Platform for Meteorological Sensors, Johns Hopkins APL Tech.
Dig., 10, 11–21,   1970.</mixed-citation></ref>
      <ref id="bib1.bibx76"><?xmltex \def\ref@label{{Kotthaus et al.(2023)}}?><label>Kotthaus et al.(2023)</label><?label kotthaus_atmospheric_2022?><mixed-citation>Kotthaus, S., Bravo-Aranda, J. A., Collaud Coen, M., Guerrero-Rascado, J. L., Costa, M. J., Cimini, D., O'Connor, E. J., Hervo, M., Alados-Arboledas, L., Jiménez-Portaz, M., Mona, L., Ruffieux, D., Illingworth, A., and Haeffelin, M.: Atmospheric boundary layer height from ground-based remote sensing: a review of capabilities and limitations, Atmos. Meas. Tech., 16, 433–479, <ext-link xlink:href="https://doi.org/10.5194/amt-16-433-2023" ext-link-type="DOI">10.5194/amt-16-433-2023</ext-link>, 2023.</mixed-citation></ref>
      <?pagebreak page3763?><ref id="bib1.bibx77"><?xmltex \def\ref@label{{Kr{\"{a}}uchi and Philipona(2016)}}?><label>Kräuchi and Philipona(2016)</label><?label krauchi_return_2016?><mixed-citation>Kräuchi, A. and Philipona, R.: Return glider radiosonde for in situ upper-air research measurements, Atmos. Meas. Tech., 9, 2535–2544, <ext-link xlink:href="https://doi.org/10.5194/amt-9-2535-2016" ext-link-type="DOI">10.5194/amt-9-2535-2016</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx78"><?xmltex \def\ref@label{{Kren et al.(2018)}}?><label>Kren et al.(2018)</label><?label kren_impact_2018?><mixed-citation>Kren, A. C., Cucurull, L., and Wang, H.: Impact of UAS Global Hawk Dropsonde
Data on Tropical and Extratropical Cyclone Forecasts in 2016,
Weather  Forecast., 33, 1121–1141, <ext-link xlink:href="https://doi.org/10.1175/WAF-D-18-0029.1" ext-link-type="DOI">10.1175/WAF-D-18-0029.1</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx79"><?xmltex \def\ref@label{{Lafon et al.(2014)}}?><label>Lafon et al.(2014)</label><?label lafon_viable_2014?><mixed-citation>Lafon, T., Fowler, J., Jiménez, J. F., and Cordoba, G. J. T.: A Viable
Alternative for Conducting Cost-Effective Daily Atmospheric Soundings
in Developing Countries, B. Am. Meteorol. Soc.,
95, 837–842, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-13-00125.1" ext-link-type="DOI">10.1175/BAMS-D-13-00125.1</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx80"><?xmltex \def\ref@label{{Lampert et al.(2020)}}?><label>Lampert et al.(2020)</label><?label lampert_unmanned_2020?><mixed-citation>Lampert, A., Altstädter, B., Bärfuss, K., Bretschneider, L., Sandgaard,
J., Michaelis, J., Lobitz, L., Asmussen, M., Damm, E., Käthner, R.,
Krüger, T., Lüpkes, C., Nowak, S., Peuker, A., Rausch, T., Reiser,
F., Scholtz, A., Sotomayor Zakharov, D., Gaus, D., Bansmer, S., Wehner, B.,
and Pätzold, F.: Unmanned Aerial Systems for Investigating the
Polar Atmospheric Boundary Layer – Technical Challenges and
Examples of Applications, Atmosphere, 11, 416,
<ext-link xlink:href="https://doi.org/10.3390/atmos11040416" ext-link-type="DOI">10.3390/atmos11040416</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx81"><?xmltex \def\ref@label{{Langland and Baker(2004)}}?><label>Langland and Baker(2004)</label><?label langland_estimation_2004?><mixed-citation>Langland, R. H. and Baker, N. L.: Estimation of Observation Impact Using the
NRL Atmospheric Variational Data Assimilation Adjoint System, Tellus A. 56, 189–201,
<ext-link xlink:href="https://doi.org/10.3402/tellusa.v56i3.14413" ext-link-type="DOI">10.3402/tellusa.v56i3.14413</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx82"><?xmltex \def\ref@label{{Laursen et al.(2006)}}?><label>Laursen et al.(2006)</label><?label laursen_hiaper_2006?><mixed-citation>
Laursen, K. K., Jorgensen, D. P., Brasseur, G. P., Ustin, S. L., and Huning,
J. R.: HIAPER: THE NEXT GENERATION NSF/NCAR RESEARCH AIRCRAFT,
B. Am. Meteorol. Soc., 87, 896–909, 2006.</mixed-citation></ref>
      <ref id="bib1.bibx83"><?xmltex \def\ref@label{{Lenschow(1972)}}?><label>Lenschow(1972)</label><?label lenschowMeasurementAirVelocity1972?><mixed-citation>Lenschow, H.: The Measurement of Air Velocity and Temperature Using the NCAR
Buffalo Aircraft Measuring System, Technical Report NCAR/TN-74+EDD,
University Corporation for Atmospheric Research,
<uri>https://opensky.ucar.edu/islandora/object/technotes:62/</uri> (last access:  1 August 2023),
1972.</mixed-citation></ref>
      <ref id="bib1.bibx84"><?xmltex \def\ref@label{{Leuenberger et al.(2020)}}?><label>Leuenberger et al.(2020)</label><?label leuenberger_improving_2020?><mixed-citation>Leuenberger, D., Haefele, A., Omanovic, N., Fengler, M., Martucci, G., Calpini,
B., Fuhrer, O., and Rossa, A.: Improving High-Impact Numerical Weather
Prediction with Lidar and Drone Observations, B.
Am. Meteorol. Soc., 101, E1036–E1051,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-19-0119.1" ext-link-type="DOI">10.1175/BAMS-D-19-0119.1</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx85"><?xmltex \def\ref@label{{Lindskog et al.(2004)}}?><label>Lindskog et al.(2004)</label><?label lindskog_doppler_2004?><mixed-citation>Lindskog, M., Salonen, K., Järvinen, H., and Michelson, D. B.: Doppler
Radar Wind Data Assimilation with HIRLAM 3DVAR, Mon. Weather
Rev., 132, 1081–1092,
<ext-link xlink:href="https://doi.org/10.1175/1520-0493(2004)132&lt;1081:DRWDAW&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0493(2004)132&lt;1081:DRWDAW&gt;2.0.CO;2</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx86"><?xmltex \def\ref@label{{Lorenc and Marriott(2014)}}?><label>Lorenc and Marriott(2014)</label><?label lorenc_forecast_2014?><mixed-citation>Lorenc, A. C. and Marriott, R. T.: Forecast Sensitivity to Observations in the
Met Office Global Numerical Weather Prediction System, Q. J. Roy. Meteorol. Soc., 140, 209–224, <ext-link xlink:href="https://doi.org/10.1002/qj.2122" ext-link-type="DOI">10.1002/qj.2122</ext-link>,
2014.</mixed-citation></ref>
      <ref id="bib1.bibx87"><?xmltex \def\ref@label{{Majewski(2020)}}?><label>Majewski(2020)</label><?label majewski_dynamic_2020?><mixed-citation>Majewski, J.: The Dynamic Behaviour of Capacitive Humidity Sensors,
Devices and Methods of Measurements, 11, 53–59,
<ext-link xlink:href="https://doi.org/10.21122/2220-9506-2020-11-1-53-59" ext-link-type="DOI">10.21122/2220-9506-2020-11-1-53-59</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx88"><?xmltex \def\ref@label{{Mallaun et al.(2015)}}?><label>Mallaun et al.(2015)</label><?label mallaunCalibration3DWind2015?><mixed-citation>Mallaun, C., Giez, A., and Baumann, R.: Calibration of 3-D wind measurements on a single-engine research aircraft, Atmos. Meas. Tech., 8, 3177–3196, <ext-link xlink:href="https://doi.org/10.5194/amt-8-3177-2015" ext-link-type="DOI">10.5194/amt-8-3177-2015</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx89"><?xmltex \def\ref@label{{Miloshevich et al.(2004)}}?><label>Miloshevich et al.(2004)</label><?label miloshevich_development_2004?><mixed-citation>Miloshevich, L. M., Paukkunen, A., Vömel, H., and Oltmans, S. J.:
Development and Validation of a Time-Lag Correction for Vaisala
Radiosonde Humidity Measurements, J. Atmos. Ocean.
Technol., 21, 1305–1327,
<ext-link xlink:href="https://doi.org/10.1175/1520-0426(2004)021&lt;1305:DAVOAT&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0426(2004)021&lt;1305:DAVOAT&gt;2.0.CO;2</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx90"><?xmltex \def\ref@label{{Moninger et al.(2003)}}?><label>Moninger et al.(2003)</label><?label moninger_automated_2003?><mixed-citation>Moninger, W. R., Mamrosh, R. D., and Pauley, P. M.: Automated Meteorological
Reports from Commercial Aircraft, B. Am.
Meteorol. Soc., 84, 203–216, <ext-link xlink:href="https://doi.org/10.1175/BAMS-84-2-203" ext-link-type="DOI">10.1175/BAMS-84-2-203</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bibx91"><?xmltex \def\ref@label{{Moninger et al.(2010)}}?><label>Moninger et al.(2010)</label><?label moninger_evaluation_2010?><mixed-citation>Moninger, W. R., Benjamin, S. G., Jamison, B. D., Schlatter, T. W., Smith,
T. L., and Szoke, E. J.: Evaluation of Regional Aircraft Observations Using
TAMDAR, Weather  Forecast., 25, 627–645,
<ext-link xlink:href="https://doi.org/10.1175/2009WAF2222321.1" ext-link-type="DOI">10.1175/2009WAF2222321.1</ext-link>, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx92"><?xmltex \def\ref@label{{Nash et al.(2011)}}?><label>Nash et al.(2011)</label><?label nash_iom_2011?><mixed-citation>Nash, J., Oakley, T., Vömel, H., and Wei, L.: IOM Report, 107. WMO  Intercomparison of High Quality Radiosonde Systems, WMO/TD, World Meteorological Organization, Geneva, 249 pp., <uri>https://library.wmo.int/doc_num.php?explnum_id=9467</uri> (last access:  1 August 2023), 2011.</mixed-citation></ref>
      <ref id="bib1.bibx93"><?xmltex \def\ref@label{{Ota et al.(2013)}}?><label>Ota et al.(2013)</label><?label ota_ensemble-based_2013?><mixed-citation>Ota, Y., Derber, J. C., Kalnay, E., and Miyoshi, T.: Ensemble-Based Observation
Impact Estimates Using the NCEP GFS, Tellus A, 65, 20038, <ext-link xlink:href="https://doi.org/10.3402/tellusa.v65i0.20038" ext-link-type="DOI">10.3402/tellusa.v65i0.20038</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx94"><?xmltex \def\ref@label{{Palmer et al.(2021)}}?><label>Palmer et al.(2021)</label><?label palmer_need_2021?><mixed-citation>Palmer, R., Whelan, D., Bodine, D., Kirstetter, P., Kumjian, M., Metcalf, J.,
Yeary, M., Yu, T.-Y., Rao, R., Cho, J., Draper, D., Durden, S., English, S.,
Kollias, P., Kosiba, K., Wada, M., Wurman, J., Blackwell, W., Bluestein, H.,
Collis, S., Gerth, J., Tuttle, A., Wang, X., and Zrnić, D.: The Need
for Spectrum and the Impact on Weather Observations, B. Am. Meteorol. Soc., 102, E1402–E1407,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-21-0009.1" ext-link-type="DOI">10.1175/BAMS-D-21-0009.1</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx95"><?xmltex \def\ref@label{{P{\"{a}}tzold(2018)}}?><label>Pätzold(2018)</label><?label patzold_windmessung_2018-1?><mixed-citation>Pätzold, F.: Windmessung mittels Segelflugzeug, Forschungsbericht
2018-04, Niedersächsisches Forschungszentrum für Luftfahrt,
Braunschweig, Germany, <ext-link xlink:href="https://doi.org/10.24355/dbbs.084-201805221102-1" ext-link-type="DOI">10.24355/dbbs.084-201805221102-1</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx96"><?xmltex \def\ref@label{{{Pena-Ortiz} et al.(2013){Pena-Ortiz}, Gallego, Ribera, Ordonez, and
{Alvarez-Castro}}}?><label>Pena-Ortiz et al.(2013)Pena-Ortiz, Gallego, Ribera, Ordonez, and
Alvarez-Castro</label><?label pena-ortiz_observed_2013?><mixed-citation>Pena-Ortiz, C., Gallego, D., Ribera, P., Ordonez, P., and Alvarez-Castro,
M. D. C.: Observed Trends in the Global Jet Stream Characteristics during the
Second Half of the 20th Century, J. Geophys. Res.-Atmos., 118, 2702–2713, <ext-link xlink:href="https://doi.org/10.1002/jgrd.50305" ext-link-type="DOI">10.1002/jgrd.50305</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx97"><?xmltex \def\ref@label{{Petersen(2016)}}?><label>Petersen(2016)</label><?label petersen_impact_2016?><mixed-citation>Petersen, R. A.: On the Impact and Benefits of AMDAR Observations
in Operational Forecasting – Part I: A Review of the
Impact of Automated Aircraft Wind and Temperature Reports,
B. Am. Meteorol. Soc., 97, 585–602,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-14-00055.1" ext-link-type="DOI">10.1175/BAMS-D-14-00055.1</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx98"><?xmltex \def\ref@label{{Petersen et al.(2015)}}?><label>Petersen et al.(2015)</label><?label petersen_report_2015?><mixed-citation>Petersen, R. A., Cronce, L., Mamrosh, R., and Baker, R.: A Report to the
World Meteorological Organization on the Impact and Benefits of AMDAR
Temperature, Wind and Moisture Observations in Operational Weather
Forecasting, Tech. rep., University of Wisconsin-Madison, Cooperative
Institute for Meteorological Satellite Studies, Space Science and Engineering
center, <uri>https://search.library.wisc.edu/catalog/9911154629902121</uri> (last access: 1 August 2023),
2015.</mixed-citation></ref>
      <ref id="bib1.bibx99"><?xmltex \def\ref@label{{Petersen et al.(2016)}}?><label>Petersen et al.(2016)</label><?label petersen_impact_2016-1?><mixed-citation>Petersen, R. A., Cronce, L., Mamrosh, R., Baker, R., and Pauley, P.: On the
Impact and Future Benefits of AMDAR Observations in Operational
Forecasting: Part II: Water Vapor Observations, B.
Am. Meteorol. Soc., 97, 2117–2133,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-D-14-00211.1" ext-link-type="DOI">10.1175/BAMS-D-14-00211.1</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx100"><?xmltex \def\ref@label{{Pinto et al.(2021)}}?><label>Pinto et al.(2021)</label><?label pinto_status_2021?><mixed-citation>Pinto, J. O., O'Sullivan, D., Taylor, S., Elston, J., Baker, C. B., Hotz, D.,
Marshall, C., Jacob, J., Barfuss, K., Piguet, B., Roberts, G., Omanovic, N.,
Fengler, M., Jensen, A. A., Steiner, M., and Houston, A. L.: The Status
and Future of Small Uncrewed Aircraft Systems (UAS) in
Operational Meteorology, B. Am. Meteorol. Soc.,
102, E2121–E2136, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-20-0138.1" ext-link-type="DOI">10.1175/BAMS-D-20-0138.1</ext-link>, 2021.</mixed-citation></ref>
      <?pagebreak page3764?><ref id="bib1.bibx101"><?xmltex \def\ref@label{{Rabier et al.(2010)}}?><label>Rabier et al.(2010)</label><?label rabier_concordiasi_2010?><mixed-citation>Rabier, F., Bouchard, A., Brun, E., Doerenbecher, A., Guedj, S., Guidard, V.,
Karbou, F., Peuch, V.-H., Amraoui, L. E., Puech, D., Genthon, C., Picard, G.,
Town, M., Hertzog, A., Vial, F., Cocquerez, P., Cohn, S. A., Hock, T., Fox,
J., Cole, H., Parsons, D., Powers, J., Romberg, K., VanAndel, J., Deshler,
T., Mercer, J., Haase, J. S., Avallone, L., Kalnajs, L., Mechoso, C. R.,
Tangborn, A., Pellegrini, A., Frenot, Y., Thépaut, J.-N., McNally, A.,
Balsamo, G., and Steinle, P.: The Concordiasi Project in Antarctica,
B. Am. Meteorol. Soc., 91, 69–86,
<ext-link xlink:href="https://doi.org/10.1175/2009BAMS2764.1" ext-link-type="DOI">10.1175/2009BAMS2764.1</ext-link>, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx102"><?xmltex \def\ref@label{{Ralph et al.(2020)}}?><label>Ralph et al.(2020)</label><?label ralph_west_2020?><mixed-citation>Ralph, F. M., Cannon, F., Tallapragada, V., Davis, C. A., Doyle, J. D.,
Pappenberger, F., Subramanian, A., Wilson, A. M., Lavers, D. A., Reynolds,
C. A., Haase, J. S., Centurioni, L., Ingleby, B., Rutz, J. J., Cordeira,
J. M., Zheng, M., Hecht, C., Kawzenuk, B., and Monache, L. D.: West Coast
Forecast Challenges and Development of Atmospheric River
Reconnaissance, B. Am. Meteorol. Soc., 101,
E1357–E1377, <ext-link xlink:href="https://doi.org/10.1175/BAMS-D-19-0183.1" ext-link-type="DOI">10.1175/BAMS-D-19-0183.1</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx103"><?xmltex \def\ref@label{{Redelsperger et al.(2006)}}?><label>Redelsperger et al.(2006)</label><?label redelsperger_african_2006?><mixed-citation>Redelsperger, J.-L., Thorncroft, C. D., Diedhiou, A., Lebel, T., Parker, D. J.,
and Polcher, J.: African Monsoon Multidisciplinary Analysis: An
International Research Project and Field Campaign, B.
Am. Meteorol. Soc., 87, 1739–1746,
<ext-link xlink:href="https://doi.org/10.1175/BAMS-87-12-1739" ext-link-type="DOI">10.1175/BAMS-87-12-1739</ext-link>, 2006.</mixed-citation></ref>
      <ref id="bib1.bibx104"><?xmltex \def\ref@label{{Reineman et al.(2016)}}?><label>Reineman et al.(2016)</label><?label reineman_use_2016?><mixed-citation>Reineman, B. D., Lenain, L., and Melville, W. K.: The Use of
Ship-Launched Fixed-Wing UAVs for Measuring the Marine Atmospheric
Boundary Layer and Ocean Surface Processes, J. Atmos.
Ocean. Technol., 33, 2029–2052, <ext-link xlink:href="https://doi.org/10.1175/JTECH-D-15-0019.1" ext-link-type="DOI">10.1175/JTECH-D-15-0019.1</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx105"><?xmltex \def\ref@label{{Rennie et al.(2021)}}?><label>Rennie et al.(2021)</label><?label rennie_impact_2021?><mixed-citation>Rennie, M. P., Isaksen, L., Weiler, F., de Kloe, J., Kanitz, T., and
Reitebuch, O.: The Impact of Aeolus Wind Retrievals on ECMWF Global
Weather Forecasts, Q. J. Roy. Meteorol. Soc.,
147, 3555–3586, <ext-link xlink:href="https://doi.org/10.1002/qj.4142" ext-link-type="DOI">10.1002/qj.4142</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx106"><?xmltex \def\ref@label{{Riishojgaard(2015)}}?><label>Riishojgaard(2015)</label><?label riishojgaardWindMeasurementsWMO2015?><mixed-citation>Riishojgaard, D. L. P.: Wind Measurements in the WMO Global Observing  System, ESA Workshop, p. 31, <uri>https://earth.esa.int/eogateway/documents/20142/37627/Day1_AM_L_P_Riishoigaard.pdf</uri> (last access: 1 August 2023), 2015.</mixed-citation></ref>
      <ref id="bib1.bibx107"><?xmltex \def\ref@label{{Runge et al.(2007)}}?><label>Runge et al.(2007)</label><?label runge_solar-powered_2007-1?><mixed-citation>Runge, H., Rack, W., Alba, R.-L., and Hepperle, M.: A Solar-Powered  HALE-UAV for Arctic Research, in: CEAS Conference 2007, pp. 1–6,  Berlin, <uri>https://elib.dlr.de/51266/</uri> (last access: 1 August 2023), 2007.</mixed-citation></ref>
      <ref id="bib1.bibx108"><?xmltex \def\ref@label{{Schindler et al.(2020)}}?><label>Schindler et al.(2020)</label><?label schindler_impact_2020?><mixed-citation>Schindler, M., Weissmann, M., Schäfler, A., and Radnoti, G.: The Impact
of Dropsonde and Extra Radiosonde Observations during NAWDEX in
Autumn 2016, Mon. Weather Rev., 148, 809–824,
<ext-link xlink:href="https://doi.org/10.1175/MWR-D-19-0126.1" ext-link-type="DOI">10.1175/MWR-D-19-0126.1</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx109"><?xmltex \def\ref@label{{Schuyler et al.(2019)}}?><label>Schuyler et al.(2019)</label><?label schuyler_using_2019?><mixed-citation>Schuyler, T. J., Gohari, S. M. I., Pundsack, G., Berchoff, D., and Guzman,
M. I.: Using a Balloon-Launched Unmanned Glider to Validate Real-Time
WRF Modeling, Sensors, 19, 1914, <ext-link xlink:href="https://doi.org/10.3390/s19081914" ext-link-type="DOI">10.3390/s19081914</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx110"><?xmltex \def\ref@label{{{Secretariat of the Antarctic
Treaty}(2019)}}?><label>Secretariat of the Antarctic
Treaty(2019)</label><?label secretariat_of_the_antarctic_treaty_compilation_2019?><mixed-citation>Secretariat of the Antarctic Treaty: Compilation of Key Documents of the Antarctic Treaty, Secretariat of the Antarctic Treaty, Buenos Aires, 4th edn., <uri>https://documents.ats.aq/atcm42/ww/ATCM42_ww011_e.pdf</uri> (last access: 1 August 2023), 2019.</mixed-citation></ref>
      <ref id="bib1.bibx111"><?xmltex \def\ref@label{{S{\o}rensen et al.(2021)}}?><label>Sørensen et al.(2021)</label><?label sorensen_uav_2021?><mixed-citation>Sørensen, K. L., Borup, K. T., Hann, R., and Hansbø, M.: UAV
Atmospheric Icing Limitations, Climate Report Sor Norway and
Surrounding Regions, Tech. rep., UBIQ Aerospace, 28 pp., <uri>https://www.ubiqaerospace.com/climate-report</uri> (last access: 1 August 2023), 2021.</mixed-citation></ref>
      <ref id="bib1.bibx112"><?xmltex \def\ref@label{{Steiner et al.(2001)}}?><label>Steiner et al.(2001)</label><?label steiner_gnss_2001?><mixed-citation>Steiner, A. K., Kirchengast, G., Foelsche, U., Kornblueh, L., Manzini, E., and
Bengtsson, L.: GNSS Occultation Sounding for Climate Monitoring, Phys. Chem. Earth Pt A, 26, 113–124,
<ext-link xlink:href="https://doi.org/10.1016/S1464-1895(01)00034-5" ext-link-type="DOI">10.1016/S1464-1895(01)00034-5</ext-link>, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx113"><?xmltex \def\ref@label{{Stickney et al.(1994)}}?><label>Stickney et al.(1994)</label><?label stickney_goodrich_1994?><mixed-citation>Stickney, T. M., Shedlov, M. W., and Thompson, D. I.: GOODRICH TOTAL  TEMPERATURE SENSORS, Tech. rep., Goodrich, 32 pp., <uri>https://data.eol.ucar.edu/file/download/53F7B041406B0/TAT-Report.pdf</uri> (last access: 1 August 2023), 1994.</mixed-citation></ref>
      <ref id="bib1.bibx114"><?xmltex \def\ref@label{{Sun et al.(2020)}}?><label>Sun et al.(2020)</label><?label sun_impact_2020?><mixed-citation>Sun, Q., Vihma, T., Jonassen, M. O., and Zhang, Z.: Impact of Assimilation
of Radiosonde and UAV Observations from the Southern Ocean in the
Polar WRF Model, Adv. Atmos. Sci., 37, 441–454,
<ext-link xlink:href="https://doi.org/10.1007/s00376-020-9213-8" ext-link-type="DOI">10.1007/s00376-020-9213-8</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx115"><?xmltex \def\ref@label{{Tafferner et al.(2003)}}?><label>Tafferner et al.(2003)</label><?label tafferner_adwice_2003?><mixed-citation>Tafferner, A., Hauf, T., Leifeld, C., Hafner, T., Leykauf, H., and Voigt, U.:
ADWICE: Advanced Diagnosis and Warning System for Aircraft
Icing Environments, Weather Forecast., 18, 184–203,
<ext-link xlink:href="https://doi.org/10.1175/1520-0434(2003)018&lt;0184:AADAWS&gt;2.0.CO;2" ext-link-type="DOI">10.1175/1520-0434(2003)018&lt;0184:AADAWS&gt;2.0.CO;2</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bibx116"><?xmltex \def\ref@label{{Th{\'{e}}paut and Andersson(2010)}}?><label>Thépaut and Andersson(2010)</label><?label thepaut_global_2010?><mixed-citation>Thépaut, J.-N. and Andersson, E.: The Global Observing System, in: Data
Assimilation: Making Sense of Observations, edited by Lahoz, W.,
Khattatov, B., and Menard, R.,  263–281, Springer, Berlin,
Heidelberg, <ext-link xlink:href="https://doi.org/10.1007/978-3-540-74703-1_10" ext-link-type="DOI">10.1007/978-3-540-74703-1_10</ext-link>, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx117"><?xmltex \def\ref@label{{VAISALA(2021)}}?><label>VAISALA(2021)</label><?label vaisalaResponseTimeHumidity2021?><mixed-citation>VAISALA: Response Time in Humidity Measurement, TECHNICAL NOTE B211803EN-B,   VAISALA, <ext-link xlink:href="https://www.vaisala.com/sites/default/files/documents/Response-time-in-humidity-measurement-Technical-Note-B211803EN.pdf">https://www.vaisala.com/sites/default/files/documents/Response-time-in-humidity</ext-link> (last access: 1 August 2023),
2021.</mixed-citation></ref>
      <ref id="bib1.bibx118"><?xmltex \def\ref@label{{van~den Kroonenberg et al.(2008)}}?><label>van den Kroonenberg et al.(2008)</label><?label kroonenbergMeasuringWindVector2008?><mixed-citation>van den Kroonenberg, A., Martin, T., Buschmann, M., Bange, J., and
Vörsmann, P.: Measuring the Wind Vector Using the Autonomous Mini
Aerial Vehicle M2AV, J. Atmos. Ocean. Technol., 25,
1969–1982, <ext-link xlink:href="https://doi.org/10.1175/2008JTECHA1114.1" ext-link-type="DOI">10.1175/2008JTECHA1114.1</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx119"><?xmltex \def\ref@label{{Vinnichenko(1970)}}?><label>Vinnichenko(1970)</label><?label vinnichenko_kinetic_1970?><mixed-citation>Vinnichenko, N. K.: The Kinetic Energy Spectrum in the Free
Atmosphere – 1 Second to 5 Years, Tellus, 22, 158–166,
<ext-link xlink:href="https://doi.org/10.3402/tellusa.v22i2.10210" ext-link-type="DOI">10.3402/tellusa.v22i2.10210</ext-link>, 1970.</mixed-citation></ref>
      <ref id="bib1.bibx120"><?xmltex \def\ref@label{{V{\"{o}}mel et al.(2018)}}?><label>Vömel et al.(2018)</label><?label h.vomelNCAREOLCommunity2018?><mixed-citation>Vömel, H., Argrow, B. M., Axisa, D., Chilson, P., Ellis, S., Fladeland, M.,
Frew, E. W., Jacob, J., Lord, M., Moore, J., Oncley, S., Roberts, G.,
Schoenung, S., and Wolff, C.: The NCAR/EOL Community Workshop on
Unmanned Aircraft Systems for Atmospheric Research – Final
Report, none, <ext-link xlink:href="https://doi.org/10.5065/D6X9292S" ext-link-type="DOI">10.5065/D6X9292S</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx121"><?xmltex \def\ref@label{{V{\"{o}}rsmann(1984)}}?><label>Vörsmann(1984)</label><?label voersmannBeitragZurBordautonomen1984?><mixed-citation>
Vörsmann, P.: Ein Beitrag zur bordautonomen Windmessung, Dissertation,
TU Braunschweig, 1984.</mixed-citation></ref>
      <ref id="bib1.bibx122"><?xmltex \def\ref@label{{Wagner and Petersen(2021)}}?><label>Wagner and Petersen(2021)</label><?label wagner_performance_2021?><mixed-citation>Wagner, T. J. and Petersen, R. A.: On the Performance of Airborne
Meteorological Observations against Other In Situ Measurements, J. Atmos. Ocean. Technol., 38, 1217–1230,
<ext-link xlink:href="https://doi.org/10.1175/JTECH-D-20-0182.1" ext-link-type="DOI">10.1175/JTECH-D-20-0182.1</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx123"><?xmltex \def\ref@label{{Wang et al.(2000)}}?><label>Wang et al.(2000)</label><?label wang_data_2000?><mixed-citation>Wang, B., Zou, X., and Zhu, J.: Data Assimilation and Its Applications,
P. Natl. Acad. Sci. USA, 97, 11143–11144,
<ext-link xlink:href="https://doi.org/10.1073/pnas.97.21.11143" ext-link-type="DOI">10.1073/pnas.97.21.11143</ext-link>, 2000.</mixed-citation></ref>
      <ref id="bib1.bibx124"><?xmltex \def\ref@label{{Wang et al.(2013)}}?><label>Wang et al.(2013)</label><?label wang_unprecedented_2013?><mixed-citation>Wang, J., Hock, T., Cohn, S. A., Martin, C., Potts, N., Reale, T., Sun, B., and
Tilley, F.: Unprecedented Upper-Air Dropsonde Observations over
Antarctica from the 2010 Concordiasi Experiment: Validation of
Satellite-Retrieved Temperature Profiles, Geophys. Res. Lett., 40,
1231–1236, <ext-link xlink:href="https://doi.org/10.1002/grl.50246" ext-link-type="DOI">10.1002/grl.50246</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx125"><?xmltex \def\ref@label{{Watts et al.(2012)}}?><label>Watts et al.(2012)</label><?label watts_unmanned_2012?><mixed-citation>Watts, A. C., Ambrosia, V. G., and Hinkley, E. A.: Unmanned Aircraft
Systems in Remote Sensing and Scientific Research:
Classification and Considerations of Use, Remote Sens., 4,
1671–1692, <ext-link xlink:href="https://doi.org/10.3390/rs4061671" ext-link-type="DOI">10.3390/rs4061671</ext-link>, 2012.</mixed-citation></ref>
      <?pagebreak page3765?><ref id="bib1.bibx126"><?xmltex \def\ref@label{{WMO(2003)}}?><label>WMO(2003)</label><?label wmo_amdar_2003?><mixed-citation>WMO: AMDAR Reference Manual: Aircraft Meteorological Data Relay, no. 958 in WMO, Secretariat of the World Meteorological Organization, Geneva, 84 pp.,  <uri>https://library.wmo.int/index.php?lvl=notice_display&amp;id=7920</uri> (last access: 1 August 2023), 2003.</mixed-citation></ref>
      <ref id="bib1.bibx127"><?xmltex \def\ref@label{{WMO(2010)}}?><label>WMO(2010)</label><?label wmo_guide_2010?><mixed-citation>WMO: Guide to the Global Observing System, WMO, World Meteorological  Organization, Geneva, 2010th edn. updated in 2017, 228 pp., <uri>https://library.wmo.int/index.php?lvl=notice_display&amp;id=12516</uri> (last access: 1 August 2023),  2010.</mixed-citation></ref>
      <ref id="bib1.bibx128"><?xmltex \def\ref@label{{WMO(2011)}}?><label>WMO(2011)</label><?label wmoManualCodesInternational2011?><mixed-citation>WMO: Manual on Codes - International Codes, Volume I.1, Annex II to the WMO Technical Regulations: Part A – Alphanumeric Codes, WMO, WMO, Geneva, 2011th edn. updated in 2019, 480 pp., <uri>https://library.wmo.int/index.php?lvl=notice_display&amp;id=13617</uri> (last access: 1 August 2023), 2011.</mixed-citation></ref>
      <ref id="bib1.bibx129"><?xmltex \def\ref@label{{WMO(2015)}}?><label>WMO(2015)</label><?label wmo_global_2015?><mixed-citation>WMO: Global Observing System, <uri>https://public.wmo.int/en/programmes/global-observing-system</uri> (last access: 1 August 2023), 2015.</mixed-citation></ref>
      <ref id="bib1.bibx130"><?xmltex \def\ref@label{{WMO(2018)}}?><label>WMO(2018)</label><?label wmo_guide_2018?><mixed-citation>WMO: Guide to Instruments and Methods of Observation, no. 8 in  WMO, Geneva, 2018 edn., 197 pp., <uri>https://library.wmo.int/index.php?lvl=notice_display&amp;id=12407#.XiGSwf5KiUk</uri> (last access: 1 August 2023), 2018.</mixed-citation></ref>
      <ref id="bib1.bibx131"><?xmltex \def\ref@label{{WMO(2020)}}?><label>WMO(2020)</label><?label wmo_gaps_2020?><mixed-citation>WMO: The Gaps in the Global Basic Observing Network (GBON), Tech. rep., WMO Systematic Observations Financing Facility, <uri>https://public.wmo.int/en/resources/library/gaps-global-basic-observing-network-gbon</uri> (last access: 1 August 2023), 2020.
</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bibx132"><?xmltex \def\ref@label{{WMO(2022)}}?><label>WMO(2022)</label><?label wmo_wmo_2022?><mixed-citation>WMO: WMO UAS Demonstration Campaign Description <inline-formula><mml:math id="M270" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> World Meteorological Organization, <uri>https://community.wmo.int/uas-demonstration/description</uri> (last access: 1 August 2023), 2022.</mixed-citation></ref>
      <ref id="bib1.bibx133"><?xmltex \def\ref@label{{WMO OSCAR(2015)}}?><label>WMO OSCAR(2015)</label><?label wmo_oscar_2015?><mixed-citation>WMO OSCAR: User requirements for observation (OSCAR/Requirements), WMO, Geneva, <uri>https://space.oscar.wmo.int/observingrequirements</uri> (last access: 1 August 2023), 2015.</mixed-citation></ref>
      <ref id="bib1.bibx134"><?xmltex \def\ref@label{{Wyngaard et al.(2019)}}?><label>Wyngaard et al.(2019)</label><?label wyngaard_emergent_2019?><mixed-citation>Wyngaard, J., Barbieri, L., Thomer, A., Adams, J., Sullivan, D., Crosby, C.,
Parr, C., Klump, J., Raj Shrestha, S., and Bell, T.: Emergent Challenges
for Science sUAS Data Management: Fairness through Community
Engagement and Best Practices Development, Remote Sens., 11, 1797,
<ext-link xlink:href="https://doi.org/10.3390/rs11151797" ext-link-type="DOI">10.3390/rs11151797</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx135"><?xmltex \def\ref@label{{Zheng et al.(2021)}}?><label>Zheng et al.(2021)</label><?label zheng_improved_2021?><mixed-citation>Zheng, M., Delle Monache, L., Cornuelle, B. D., Ralph, F. M., Tallapragada,
V. S., Subramanian, A., Haase, J. S., Zhang, Z., Wu, X., Murphy, M. J.,
Higgins, T. B., and DeHaan, L.: Improved Forecast Skill Through the
Assimilation of Dropsonde Observations From the Atmospheric River
Reconnaissance Program, J. Geophys. Res.-Atmos., 126,
e2021JD034967, <ext-link xlink:href="https://doi.org/10.1029/2021JD034967" ext-link-type="DOI">10.1029/2021JD034967</ext-link>, 2021.</mixed-citation></ref>

  </ref-list></back>
    <!--<article-title-html>Drone-based meteorological observations up to the tropopause – a concept study</article-title-html>
<abstract-html/>
<ref-html id="bib1.bib1"><label>Archer and Caldeira(2008)</label><mixed-citation>
      
Archer, C. L. and Caldeira, K.: Historical Trends in the Jet Streams,   Geophys. Res. Lett., 35, L08803, <a href="https://doi.org/10.1029/2008GL033614" target="_blank">https://doi.org/10.1029/2008GL033614</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>Axford(1968)</label><mixed-citation>
      
Axford, D. N.: On the Accuracy of Wind Measurements Using an Inertial
Platform in an Aircraft, and an Example of a Measurement of the
Vertical Mesostructure of the Atmosphere, J. Appl.
Meteorol. Climatol., 7, 645–666,
<a href="https://doi.org/10.1175/1520-0450(1968)007&lt;0645:OTAOWM&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0450(1968)007&lt;0645:OTAOWM&gt;2.0.CO;2</a>, 1968.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>Baker et al.(2014)</label><mixed-citation>
      
Baker, W. E., Atlas, R., Cardinali, C., Clement, A., Emmitt, G. D., Gentry,
B. M., Hardesty, R. M., Källén, E., Kavaya, M. J., Langland, R., Ma,
Z., Masutani, M., McCarty, W., Pierce, R. B., Pu, Z., Riishojgaard, L. P.,
Ryan, J., Tucker, S., Weissmann, M., and Yoe, J. G.: Lidar-Measured Wind
Profiles: The Missing Link in the Global Observing System, B. Am. Meteorol. Soc., 95, 543–564,
<a href="https://doi.org/10.1175/BAMS-D-12-00164.1" target="_blank">https://doi.org/10.1175/BAMS-D-12-00164.1</a>, 2014.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>Bange et al.(2013)</label><mixed-citation>
      
Bange, J., Esposito, M., Lenschow, D. H., Brown, P. R. A., Dreiling, V., Giez,
A., Mahrt, L., Malinowski, S. P., Rodi, A. R., Shaw, R. A., Siebert, H.,
Smit, H., and Zöger, M.: Measurement of Aircraft State and
Thermodynamic and Dynamic Variables, in: Airborne Measurements
for Environmental Research, Chap. 2,  7–75, John Wiley &amp; Sons,
Ltd, <a href="https://doi.org/10.1002/9783527653218.ch2" target="_blank">https://doi.org/10.1002/9783527653218.ch2</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>Bärfuss et al.(2018)</label><mixed-citation>
      
Bärfuss, K., Pätzold, F., Altstädter, B., Kathe, E., Nowak, S.,
Bretschneider, L., Bestmann, U., and Lampert, A.: New Setup of the UAS
ALADINA for Measuring Boundary Layer Properties, Atmospheric
Particles and Solar Radiation, Atmosphere, 9, 28,
<a href="https://doi.org/10.3390/atmos9010028" target="_blank">https://doi.org/10.3390/atmos9010028</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>Bärfuss et al.(2021a)</label><mixed-citation>
      
Bärfuss, K., Schmithüsen, H., Dirksen, R., Bretschneider, L.,   Pätzold, F., Bollmann, S., Wickboldt, H., von Unwerth, M., Asmussen,  M., Schwarting, T., and Lampert, A.: Atmospheric Profile Measurements  Conducted by the Unmanned Aerial System LUCA (Panker, Germany, 2020-07-03 and 2021-05-28), PANGAEA [data set], <a href="https://doi.org/10.1594/PANGAEA.937555" target="_blank">https://doi.org/10.1594/PANGAEA.937555</a>, 2021a.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>Bärfuss et al.(2021b)</label><mixed-citation>
      
Bärfuss, K., Schmithüsen, H., Dirksen, R., Bretschneider, L.,  Pätzold, F., Bollmann, S., Wickboldt, H., von Unwerth, M., Asmussen,  M., Schwarting, T., and Lampert, A.: Radiosonde Measurements Co-Located with Ascends of the Unmanned Aerial System LUCA (Panker, Germany  2020-07-03 and 2021-05-28), PANGAEA [data set], <a href="https://doi.org/10.1594/PANGAEA.937556" target="_blank">https://doi.org/10.1594/PANGAEA.937556</a>, 2021b.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>Bärfuss et al.(2022)</label><mixed-citation>
      
Bärfuss, K. B., Schmithüsen, H., and Lampert, A.: Drone-based meteorological observations up to the tropopause, Atmos. Meas. Tech. Discuss. [preprint], <a href="https://doi.org/10.5194/amt-2022-236" target="_blank">https://doi.org/10.5194/amt-2022-236</a>, in review, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>Bärfuss et al.(2023a)</label><mixed-citation>
      
Bärfuss, K., Wickboldt, H., Schlerf, A., Bollmann, S., Rausch, T., and Lampert, A.: Atmospheric profile measurements conducted by the unmanned aerial system LUCA (Panker, Germany 2021-10-25 to 2021-10-29), PANGAEA [data set], <a href="https://doi.org/10.1594/PANGAEA.961200" target="_blank">https://doi.org/10.1594/PANGAEA.961200</a>, 2023a.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>Bärfuss et al.(2023b)</label><mixed-citation>
      
Bärfuss, K., Wickboldt, H., Schlerf, A., Bollmann, S., Rausch, T., and Lampert, A.: Radiosonde measurements co-located with ascends of the unmanned aerial system LUCA (Panker, Germany 2021-10-25 and 2021-10-29), PANGAEA [data set], <a href="https://doi.org/10.1594/PANGAEA.961223" target="_blank">https://doi.org/10.1594/PANGAEA.961223</a>, 2023b.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>Bauer et al.(2015)</label><mixed-citation>
      
Bauer, P., Thorpe, A., and Brunet, G.: The Quiet Revolution of Numerical
Weather Prediction, Nature, 525, 47–55, <a href="https://doi.org/10.1038/nature14956" target="_blank">https://doi.org/10.1038/nature14956</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>Bonavita et al.(2016)</label><mixed-citation>
      
Bonavita, M., Hólm, E., Isaksen, L., and Fisher, M.: The Evolution of the
ECMWF Hybrid Data Assimilation System, Q. J. Roy.
Meteorol. Soc., 142, 287–303, <a href="https://doi.org/10.1002/qj.2652" target="_blank">https://doi.org/10.1002/qj.2652</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>Bormann et al.(2019)</label><mixed-citation>
      
Bormann, N., Lawrence, H., Farnan, J., and Farnan, J.: Global Observing System Experiments in the ECMWF Assimilation System, ECMWF, <a href="https://doi.org/10.21957/sr184iyz" target="_blank">https://doi.org/10.21957/sr184iyz</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>Bouttier and Kelly(2001)</label><mixed-citation>
      
Bouttier, F. and Kelly, G.: Observing-System Experiments in the ECMWF
4D-Var Data Assimilation System, Q. J. Roy.
Meteorol. Soc., 127, 1469–1488, <a href="https://doi.org/10.1002/qj.49712757419" target="_blank">https://doi.org/10.1002/qj.49712757419</a>, 2001.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>Boylan et al.(2015)</label><mixed-citation>
      
Boylan, P., Wang, J., Cohn, S. A., Fetzer, E., Maddy, E. S., and Wong, S.:
Validation of AIRS Version 6 Temperature Profiles and Surface-Based
Inversions over Antarctica Using Concordiasi Dropsonde Data, J. Geophys. Res.-Atmos., 120, 992–1007,
<a href="https://doi.org/10.1002/2014JD022551" target="_blank">https://doi.org/10.1002/2014JD022551</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>Cardinali(2009)</label><mixed-citation>
      
Cardinali, C.: Monitoring the Observation Impact on the Short-Range Forecast,
Q. J. Roy. Meteorol. Soc., 135, 239–250,
<a href="https://doi.org/10.1002/qj.366" target="_blank">https://doi.org/10.1002/qj.366</a>, 2009.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>Cardinali(2013)</label><mixed-citation>
      
Cardinali, C.: Observation Impact on the Short Range Forecast,
<a href="https://www.ecmwf.int/node/16937" target="_blank"/> (last access: 1 August 2023), 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>Carminati et al.(2019)</label><mixed-citation>
      
Carminati, F., Migliorini, S., Ingleby, B., Bell, W., Lawrence, H., Newman, S., Hocking, J., and Smith, A.: Using reference radiosondes to characterise NWP model uncertainty for improved satellite calibration and validation, Atmos. Meas. Tech., 12, 83–106, <a href="https://doi.org/10.5194/amt-12-83-2019" target="_blank">https://doi.org/10.5194/amt-12-83-2019</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>Chander et al.(2013)</label><mixed-citation>
      
Chander, G., Hewison, T. J., Fox, N., Wu, X., Xiong, X., and Blackwell, W. J.:
Overview of Intercalibration of Satellite Instruments, IEEE
Trans. Geosci. Remote Sens., 51, 1056–1080,
<a href="https://doi.org/10.1109/TGRS.2012.2228654" target="_blank">https://doi.org/10.1109/TGRS.2012.2228654</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>Chilson et al.(2019)</label><mixed-citation>
      
Chilson, P. B., Bell, T. M., Brewster, K. A., Britto Hupsel de Azevedo, G.,
Carr, F. H., Carson, K., Doyle, W., Fiebrich, C. A., Greene, B. R., Grimsley,
J. L., Kanneganti, S. T., Martin, J., Moore, A., Palmer, R. D.,
Pillar-Little, E. A., Salazar-Cerreno, J. L., Segales, A. R., Weber,
M. E., Yeary, M., and Droegemeier, K. K.: Moving towards a Network of
Autonomous UAS Atmospheric Profiling Stations for Observations in the
Earth's Lower Atmosphere: The 3D Mesonet Concept, Sensors, 19,
2720, <a href="https://doi.org/10.3390/s19122720" target="_blank">https://doi.org/10.3390/s19122720</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>Choi et al.(2018)</label><mixed-citation>
      
Choi, B. I., Lee, S.-W., Woo, S.-B., Kim, J. C., Kim, Y.-G., and Yang, S. G.: Evaluation of radiosonde humidity sensors at low temperature using ultralow-temperature humidity chamber, Adv. Sci. Res., 15, 207–212, <a href="https://doi.org/10.5194/asr-15-207-2018" target="_blank">https://doi.org/10.5194/asr-15-207-2018</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>Cione et al.(2020)</label><mixed-citation>
      
Cione, J. J., Bryan, G. H., Dobosy, R., Zhang, J. A., de Boer, G., Aksoy, A.,
Wadler, J. B., Kalina, E. A., Dahl, B. A., Ryan, K., Neuhaus, J., Dumas, E.,
Marks, F. D., Farber, A. M., Hock, T., and Chen, X.: Eye of the Storm:
Observing Hurricanes with a Small Unmanned Aircraft System, B. Am. Meteorol. Soc., 101, E186–E205,
<a href="https://doi.org/10.1175/BAMS-D-19-0169.1" target="_blank">https://doi.org/10.1175/BAMS-D-19-0169.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>Cohn et al.(2013)</label><mixed-citation>
      
Cohn, S. A., Hock, T., Cocquerez, P., Wang, J., Rabier, F., Parsons, D., Harr,
P., Wu, C.-C., Drobinski, P., Karbou, F., Vénel, S., Vargas, A.,
Fourrié, N., Saint-Ramond, N., Guidard, V., Doerenbecher, A., Hsu,
H.-H., Lin, P.-H., Chou, M.-D., Redelsperger, J.-L., Martin, C., Fox, J.,
Potts, N., Young, K., and Cole, H.: Driftsondes: Providing In Situ
Long-Duration Dropsonde Observations over Remote Regions, B. Am. Meteorol. Soc., 94, 1661–1674,
<a href="https://doi.org/10.1175/BAMS-D-12-00075.1" target="_blank">https://doi.org/10.1175/BAMS-D-12-00075.1</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>Cooper et al.(2014)</label><mixed-citation>
      
Cooper, W. A., Spuler, S. M., Spowart, M., Lenschow, D. H., and Friesen, R. B.: Calibrating airborne measurements of airspeed, pressure and temperature using a Doppler laser air-motion sensor, Atmos. Meas. Tech., 7, 3215–3231, <a href="https://doi.org/10.5194/amt-7-3215-2014" target="_blank">https://doi.org/10.5194/amt-7-3215-2014</a>, 2014.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>Dabberdt et al.(2005)</label><mixed-citation>
      
Dabberdt, W. F., Schlatter, T. W., Carr, F. H., Friday, E. W. J., Jorgensen,
D., Koch, S., Pirone, M., Ralph, F. M., Sun, J., Welsh, P., Wilson, J. W.,
and Zou, X.: Multifunctional Mesoscale Observing Networks, B. Am. Meteorol. Soc., 86, 961–982,
<a href="https://doi.org/10.1175/BAMS-86-7-961" target="_blank">https://doi.org/10.1175/BAMS-86-7-961</a>, 2005.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>de Boer et al.(2020)</label><mixed-citation>
      
de Boer, G., Diehl, C., Jacob, J., Houston, A., Smith, S. W., Chilson, P.,
Schmale, D. G., Intrieri, J., Pinto, J., Elston, J., Brus, D., Kemppinen, O.,
Clark, A., Lawrence, D., Bailey, S. C. C., Sama, M. P., Frazier, A., Crick,
C., Natalie, V., Pillar-Little, E., Klein, P., Waugh, S., Lundquist, J. K.,
Barbieri, L., Kral, S. T., Jensen, A. A., Dixon, C., Borenstein, S.,
Hesselius, D., Human, K., Hall, P., Argrow, B., Thornberry, T., Wright, R.,
and Kelly, J. T.: Development of Community, Capabilities, and
Understanding through Unmanned Aircraft-Based Atmospheric Research:
The LAPSE-RATE Campaign, B. Am. Meteorol. Soc.,
101, E684–E699, <a href="https://doi.org/10.1175/BAMS-D-19-0050.1" target="_blank">https://doi.org/10.1175/BAMS-D-19-0050.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>de Haan et al.(2022)</label><mixed-citation>
      
de Haan, S., de Jong, P. M. A., and van der Meulen, J.: Characterizing and correcting the warm bias observed in Aircraft Meteorological Data Relay (AMDAR) temperature observations, Atmos. Meas. Tech., 15, 811–818, <a href="https://doi.org/10.5194/amt-15-811-2022" target="_blank">https://doi.org/10.5194/amt-15-811-2022</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>Dirksen et al.(2014)</label><mixed-citation>
      
Dirksen, R. J., Sommer, M., Immler, F. J., Hurst, D. F., Kivi, R., and Vömel, H.: Reference quality upper-air measurements: GRUAN data processing for the Vaisala RS92 radiosonde, Atmos. Meas. Tech., 7, 4463–4490, <a href="https://doi.org/10.5194/amt-7-4463-2014" target="_blank">https://doi.org/10.5194/amt-7-4463-2014</a>, 2014.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>Drüe et al.(2008)</label><mixed-citation>
      
Drüe, C., Frey, W., Hoff, A., and Hauf, Th.: Aircraft
Type-Specific Errors in AMDAR Weather Reports from Commercial Aircraft,
Q. J. Roy. Meteorol. Soc., 134, 229–239,
<a href="https://doi.org/10.1002/qj.205" target="_blank">https://doi.org/10.1002/qj.205</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>Dupont et al.(2020)</label><mixed-citation>
      
Dupont, J.-C., Haeffelin, M., Badosa, J., Clain, G., Raux, C., and Vignelles,
D.: Characterization and Corrections of Relative Humidity Measurement
from Meteomodem M10 Radiosondes at Midlatitude Stations, J.
Atmos. Ocean. Technol., 37, 857–871,
<a href="https://doi.org/10.1175/JTECH-D-18-0205.1" target="_blank">https://doi.org/10.1175/JTECH-D-18-0205.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib31"><label>EASA(2022)</label><mixed-citation>
      
EASA: Easy Access Rules for Unmanned Aircraft Systems (Regulation (EU) 2019/947 and Regulation (EU) 2019/945), <a href="https://www.easa.europa.eu/document-library/easy-access-rules/easy-access-rules-unmanned-aircraft-systems-regulation-eu" target="_blank"/> (last access: 1 August 2023), 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib32"><label>Elston et al.(2015)</label><mixed-citation>
      
Elston, J., Argrow, B., Stachura, M., Weibel, D., Lawrence, D., and Pope, D.:
Overview of Small Fixed-Wing Unmanned Aircraft for Meteorological
Sampling, J. Atmos. Ocean. Technol., 32, 97–115,
<a href="https://doi.org/10.1175/JTECH-D-13-00236.1" target="_blank">https://doi.org/10.1175/JTECH-D-13-00236.1</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib33"><label>Elston et al.(2011)</label><mixed-citation>
      
Elston, J. S., Roadman, J., Stachura, M., Argrow, B., Houston, A., and Frew,
E.: The Tempest Unmanned Aircraft System for in Situ Observations of Tornadic
Supercells: Design and VORTEX2 Flight Results, J. Field
Robot., 28, 461–483, <a href="https://doi.org/10.1002/rob.20394" target="_blank">https://doi.org/10.1002/rob.20394</a>, 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib34"><label>Evtushevsky et al.(2008)</label><mixed-citation>
      
Evtushevsky, O. M., Grytsai, A. V., Klekociuk, A. R., and Milinevsky, G. P.: Total Ozone and Tropopause Zonal Asymmetry during the Antarctic Spring, J. Geophys. Res.-Atmos., 113, D00B06, <a href="https://doi.org/10.1029/2008JD009881" target="_blank">https://doi.org/10.1029/2008JD009881</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib35"><label>Eyre(2008)</label><mixed-citation>
      
Eyre, J.: An Introduction to GPS Radio Occultation and Its Use in Numerical
Weather Prediction., in: ECMWF GRAS SAF Workshop on Applications of
GPS Radio Occultation Measurements, 16–18 June 2008, 1–10,
ECMWF, Shinfield Park, Reading, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib36"><label>Faccani et al.(2009)</label><mixed-citation>
      
Faccani, C., Rabier, F., Fourrié, N., Agusti-Panareda, A., Karbou, F.,
Moll, P., Lafore, J.-P., Nuret, M., Hdidou, F., and Bock, O.: The Impacts
of AMMA Radiosonde Data on the French Global Assimilation and
Forecast System, Weather Forecast., 24, 1268–1286,
<a href="https://doi.org/10.1175/2009WAF2222237.1" target="_blank">https://doi.org/10.1175/2009WAF2222237.1</a>, 2009.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib37"><label>Fiedler and Panofsky(1970)</label><mixed-citation>
      
Fiedler, F. and Panofsky, H. A.: Atmospheric Scales and Spectral Gaps, B. Am. Meteorol. Soc., 51, 1114–1120,
<a href="https://doi.org/10.1175/1520-0477(1970)051&lt;1114:ASASG&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0477(1970)051&lt;1114:ASASG&gt;2.0.CO;2</a>, 1970.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib38"><label>Flagg et al.(2018)</label><mixed-citation>
      
Flagg, D. D., Doyle, J. D., Holt, T. R., Tyndall, D. P., Amerault, C. M.,
Geiszler, D., Haack, T., Moskaitis, J. R., Nachamkin, J., and Eleuterio,
D. P.: On the Impact of Unmanned Aerial System Observations on
Numerical Weather Prediction in the Coastal Zone, Mon. Weather
Rev., 146, 599–622, <a href="https://doi.org/10.1175/MWR-D-17-0028.1" target="_blank">https://doi.org/10.1175/MWR-D-17-0028.1</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib39"><label>Fleming(1996)</label><mixed-citation>
      
Fleming, R. J.: The Use of Commercial Aircraft as Platforms for
Environmental Measurements, B. Am. Meteorol.
Soc., 77, 2229–2242,
<a href="https://doi.org/10.1175/1520-0477(1996)077&lt;2229:TUOCAA&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0477(1996)077&lt;2229:TUOCAA&gt;2.0.CO;2</a>, 1996.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib40"><label>Fujiwara et al.(2003)</label><mixed-citation>
      
Fujiwara, M., Shiotani, M., Hasebe, F., Vömel, H., Oltmans, S. J., Ruppert,
P. W., Horinouchi, T., and Tsuda, T.: Performance of the Meteolabor
“Snow White” Chilled-Mirror Hygrometer in the Tropical
Troposphere: Comparisons with the Vaisala RS80 A/H-Humicap
Sensors, J. Atmos. Ocean. Technol., 20, 1534–1542,
<a href="https://doi.org/10.1175/1520-0426(2003)020&lt;1534:POTMSW&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0426(2003)020&lt;1534:POTMSW&gt;2.0.CO;2</a>, 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib41"><label>Geerts et al.(2018)</label><mixed-citation>
      
Geerts, B., Raymond, D. J., Grubišić, V., Davis, C. A., Barth, M. C.,
Detwiler, A., Klein, P. M., Lee, W.-C., Markowski, P. M., Mullendore, G. L.,
and Moore, J. A.: Recommendations for In Situ and Remote Sensing
Capabilities in Atmospheric Convection and Turbulence, B. Am. Meteorol. Soc., 99, 2463–2470,
<a href="https://doi.org/10.1175/BAMS-D-17-0310.1" target="_blank">https://doi.org/10.1175/BAMS-D-17-0310.1</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib42"><label>Gelaro and Zhu(2009)</label><mixed-citation>
      
Gelaro, R. and Zhu, Y.: Examination of Observation Impacts Derived from
Observing System Experiments (OSEs) and Adjoint Models, Tellus A, 61, 179–193,
<a href="https://doi.org/10.1111/j.1600-0870.2008.00388.x" target="_blank">https://doi.org/10.1111/j.1600-0870.2008.00388.x</a>, 2009.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib43"><label>Gettelman et al.(2011)</label><mixed-citation>
      
Gettelman, A., Hoor, P., Pan, L. L., Randel, W. J., Hegglin, M. I., and Birner,
T.: The Extratropical Upper Troposphere and Lower Stratosphere,
Rev. Geophys., 49, RG3003, <a href="https://doi.org/10.1029/2011RG000355" target="_blank">https://doi.org/10.1029/2011RG000355</a>, 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib44"><label>Goldberg et al.(2011)</label><mixed-citation>
      
Goldberg, M., Ohring, G., Butler, J., Cao, C., Datla, R., Doelling, D.,
Gärtner, V., Hewison, T., Iacovazzi, B., Kim, D., Kurino, T., Lafeuille,
J., Minnis, P., Renaut, D., Schmetz, J., Tobin, D., Wang, L., Weng, F., Wu,
X., Yu, F., Zhang, P., and Zhu, T.: The Global Space-Based
Inter-Calibration System, B. Am. Meteorol. Soc.,
92, 467–475, <a href="https://doi.org/10.1175/2010BAMS2967.1" target="_blank">https://doi.org/10.1175/2010BAMS2967.1</a>, 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib45"><label>Hacker et al.(2018)</label><mixed-citation>
      
Hacker, J., Draper, C., and Madaus, L.: Challenges and Opportunities for
Data Assimilation in Mountainous Environments, Atmosphere, 9, 127,
<a href="https://doi.org/10.3390/atmos9040127" target="_blank">https://doi.org/10.3390/atmos9040127</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib46"><label>Haering(1990)</label><mixed-citation>
      
Haering, E. Jr.: Airdata Calibration of a High-Performance
Aircraft for Measuring Atmospheric Wind Profiles, in: 28th Aerospace
Sciences Meeting, Aerospace Sciences Meetings, American Institute of
Aeronautics and Astronautics, <a href="https://doi.org/10.2514/6.1990-230" target="_blank">https://doi.org/10.2514/6.1990-230</a>, 1990.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib47"><label>Hann(2020)</label><mixed-citation>
      
Hann, R.: Atmospheric Ice Accretions, Aerodynamic Icing Penalties, and
Ice Protection Systems on Unmanned Aerial Vehicles, NTNU,
<a href="https://ntnuopen.ntnu.no/ntnu-xmlui/handle/11250/2657638" target="_blank"/> (last access: 1 August 2023),   2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib48"><label>Hann et al.(2021)</label><mixed-citation>
      
Hann, R., Enache, A., Nielsen, M. C., Stovner, B. N., van Beeck, J.,
Johansen, T. A., and Borup, K. T.: Experimental Heat Loads for
Electrothermal Anti-Icing and De-Icing on UAVs, Aerospace, 8, 83,
<a href="https://doi.org/10.3390/aerospace8030083" target="_blank">https://doi.org/10.3390/aerospace8030083</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib49"><label>Hartmann et al.(2018)</label><mixed-citation>
      
Hartmann, J., Gehrmann, M., Kohnert, K., Metzger, S., and Sachs, T.: New calibration procedures for airborne turbulence measurements and accuracy of the methane fluxes during the AirMeth campaigns, Atmos. Meas. Tech., 11, 4567–4581, <a href="https://doi.org/10.5194/amt-11-4567-2018" target="_blank">https://doi.org/10.5194/amt-11-4567-2018</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib50"><label>Hersbach et al.(2023)</label><mixed-citation>
      
Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Horányi, A., Muñoz Sabater, J., Nicolas, J., Peubey, C., Radu, R., Rozum, I., Schepers, D., Simmons, A., Soci, C., Dee, D., and Thépaut, J.-N.: ERA5 hourly data on single levels from 1940 to present, Copernicus Climate Change Service (C3S) Climate Data Store (CDS) [data set], <a href="https://doi.org/10.24381/cds.adbb2d47" target="_blank">https://doi.org/10.24381/cds.adbb2d47</a>, 2023.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib51"><label>Hersbach et al.(2020)</label><mixed-citation>
      
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A.,
Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D.,
Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P.,
Biavati, G., Bidlot, J., Bonavita, M., Chiara, G., Dahlgren, P., Dee, D.,
Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer,
A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M.,
Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., Rosnay, P.,
Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.-N.: The ERA5
Global Reanalysis, Q. J. Roy. Meteorol. Soc., 146, 1999–2049,
<a href="https://doi.org/10.1002/qj.3803" target="_blank">https://doi.org/10.1002/qj.3803</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib52"><label>Hock and Franklin(1999)</label><mixed-citation>
      
Hock, T. F. and Franklin, J. L.: The NCAR GPS Dropwindsonde, B. Am. Meteorol. Soc., 80, 407–420,  1999.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib53"><label>Holton et al.(1995)</label><mixed-citation>
      
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B.,
and Pfister, L.: Stratosphere-Troposphere Exchange, Rev. Geophys.,
33, 403–439, <a href="https://doi.org/10.1029/95RG02097" target="_blank">https://doi.org/10.1029/95RG02097</a>, 1995.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib54"><label>Houston et al.(2021)</label><mixed-citation>
      
Houston, A. L., PytlikZillig, L. M., and Walther, J. C.: National Weather
Service Data Needs for Short-Term Forecasts and the Role of
Unmanned Aircraft in Filling the Gap: Results from a
Nationwide Survey, B. Am. Meteorol. Soc., 102,
E2106–E2120, <a href="https://doi.org/10.1175/BAMS-D-20-0183.1" target="_blank">https://doi.org/10.1175/BAMS-D-20-0183.1</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib55"><label>Huang et al.(2019)</label><mixed-citation>
      
Huang, X., Tepylo, N., Pommier-Budinger, V., Budinger, M., Bonaccurso, E.,
Villedieu, P., and Bennani, L.: A Survey of Icephobic Coatings and Their
Potential Use in a Hybrid Coating/Active Ice Protection System for Aerospace
Applications, Prog. Aerospace Sci., 105, 74–97,
<a href="https://doi.org/10.1016/j.paerosci.2019.01.002" target="_blank">https://doi.org/10.1016/j.paerosci.2019.01.002</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib56"><label>Ingleby and Edwards(2015)</label><mixed-citation>
      
Ingleby, B. and Edwards, D.: Changes to Radiosonde Reports and Their Processing
for Numerical Weather Prediction, Atmos. Sc. Lett., 16, 44–49,
<a href="https://doi.org/10.1002/asl2.518" target="_blank">https://doi.org/10.1002/asl2.518</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib57"><label>Ingleby et al.(2016a)</label><mixed-citation>
      
Ingleby, B., Pauley, P., Kats, A., Ator, J., Keyser, D., Doerenbecher, A.,
Fucile, E., Hasegawa, J., Toyoda, E., Kleinert, T., Qu, W., James, J. S.,
Tennant, W., and Weedon, R.: Progress toward High-Resolution, Real-Time
Radiosonde Reports, B. Am. Meteorol. Soc., 97,
2149–2161, <a href="https://doi.org/10.1175/BAMS-D-15-00169.1" target="_blank">https://doi.org/10.1175/BAMS-D-15-00169.1</a>, 2016a.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib58"><label>Ingleby et al.(2016b)</label><mixed-citation>
      
Ingleby, B., Rodwell, M., and Isaksen, L.: Global Radiosonde Network under
Pressure, Tech. Rep. 149, ECMWF, <a href="https://doi.org/10.21957/cblxtg" target="_blank">https://doi.org/10.21957/cblxtg</a>, 2016b.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib59"><label>Ingleby et al.(2020)</label><mixed-citation>
      
Ingleby, B., Isaksen, L., Kral, T., and Kral, T.: Evaluation and Impact of
Aircraft Humidity Data in ECMWF&amp;#039;s NWP System,
<a href="https://doi.org/10.21957/4e825dtiy" target="_blank">https://doi.org/10.21957/4e825dtiy</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib60"><label>Ingleby et al.(2021)</label><mixed-citation>
      
Ingleby, B., Candy, B., Eyre, J., Haiden, T., Hill, C., Isaksen, L., Kleist,
D., Smith, F., Steinle, P., Taylor, S., Tennant, W., and Tingwell, C.: The
Impact of COVID-19 on Weather Forecasts: A Balanced View,
Geophys. Res. Lett., 48, e2020GL090699,
<a href="https://doi.org/10.1029/2020GL090699" target="_blank">https://doi.org/10.1029/2020GL090699</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib61"><label>Ingleby et al.(2022)</label><mixed-citation>
      
Ingleby, B., Motl, M., Marlton, G., Edwards, D., Sommer, M., von Rohden, C., Vömel, H., and Jauhiainen, H.: On the quality of RS41 radiosonde descent data, Atmos. Meas. Tech., 15, 165–183, <a href="https://doi.org/10.5194/amt-15-165-2022" target="_blank">https://doi.org/10.5194/amt-15-165-2022</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib62"><label>Inoue and Sato(2022)</label><mixed-citation>
      
Inoue, J. and Sato, K.: Toward Sustainable Meteorological Profiling in Polar
Regions: Case Studies Using an Inexpensive UAS on Measuring Lower
Boundary Layers with Quality of Radiosondes, Environ. Res., 205,
112468, <a href="https://doi.org/10.1016/j.envres.2021.112468" target="_blank">https://doi.org/10.1016/j.envres.2021.112468</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib63"><label>Jacob et al.(2018)</label><mixed-citation>
      
Jacob, J. D., Chilson, P. B., Houston, A. L., and Smith, S. W.: Considerations
for Atmospheric Measurements with Small Unmanned Aircraft Systems,
Atmosphere, 9, 252, <a href="https://doi.org/10.3390/atmos9070252" target="_blank">https://doi.org/10.3390/atmos9070252</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib64"><label>Jeck(2002)</label><mixed-citation>
      
Jeck, R. K.: Icing Design Envelopes (14 CFR Parts 25 and 29, Appendix C) Converted to a Distance-Based Format, Federal Aviation Administration Report DOT/FAA/AR-00/30, US Department of Transportation, Washington, DC, USA, 2002.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib65"><label>Jensen et al.(2021)</label><mixed-citation>
      
Jensen, A. A., Pinto, J. O., Bailey, S. C., Sobash, R. A., de Boer, G.,
Houston, A. L., Chilson, P. B., Bell, T., Romine, G., Smith, S. W., Lawrence,
D. A., Dixon, C., Lundquist, J. K., Jacob, J. D., Elston, J., Waugh, S., and
Steiner, M.: Assimilation of a Coordinated Fleet of Uncrewed Aircraft
System Observations in Complex Terrain: EnKF System Design and
Preliminary Assessment, Mon. Weather Rev., 149, 1459–1480,
<a href="https://doi.org/10.1175/mwr-d-20-0359.1" target="_blank">https://doi.org/10.1175/mwr-d-20-0359.1</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib66"><label>Jensen et al.(2022)</label><mixed-citation>
      
Jensen, A. A., Pinto, J. O., Bailey, S. C. C., Sobash, R. A., Romine, G.,
de Boer, G., Houston, A. L., Smith, S. W., Lawrence, D. A., Dixon, C.,
Lundquist, J. K., Jacob, J. D., Elston, J., Waugh, S., Brus, D., and Steiner,
M.: Assimilation of a Coordinated Fleet of Uncrewed Aircraft System
Observations in Complex Terrain: Observing System Experiments,
Mon. Weather Rev., 150, 2737–2763, <a href="https://doi.org/10.1175/MWR-D-22-0090.1" target="_blank">https://doi.org/10.1175/MWR-D-22-0090.1</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib67"><label>Jonassen et al.(2012)</label><mixed-citation>
      
Jonassen, M. O., Ólafsson, H., Ágústsson, H., Rögnvaldsson,
Ó., and Reuder, J.: Improving High-Resolution Numerical Weather
Simulations by Assimilating Data from an Unmanned Aerial System,
Mon. Weather Rev., 140, 3734–3756, <a href="https://doi.org/10.1175/MWR-D-11-00344.1" target="_blank">https://doi.org/10.1175/MWR-D-11-00344.1</a>,
2012.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib68"><label>Joyce et al.(2021)</label><mixed-citation>
      
Joyce, K. E., Anderson, K., and Bartolo, R. E.: Of Course We Fly
Unmanned – We're Women!, Drones, 5, 21,
<a href="https://doi.org/10.3390/drones5010021" target="_blank">https://doi.org/10.3390/drones5010021</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib69"><label>Kalinka et al.(2017)</label><mixed-citation>
      
Kalinka, F., Roloff, K., Tendel, J., and Hauf, T.: The In-flight Icing
Warning System ADWICE for European Airspace – Current
Structure, Recent Improvements and Verification Results, Meteorologische
Z., 26, 441–455, <a href="https://doi.org/10.1127/metz/2017/0756" target="_blank">https://doi.org/10.1127/metz/2017/0756</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib70"><label>Kalman(1960)</label><mixed-citation>
      
Kalman, R. E.: A New Approach to Linear Filtering and Prediction
Problems, J. Basic Eng., 82, 35–45,
<a href="https://doi.org/10.1115/1.3662552" target="_blank">https://doi.org/10.1115/1.3662552</a>, 1960.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib71"><label>Karbou et al.(2005)</label><mixed-citation>
      
Karbou, F., Aires, F., Prigent, C., and Eymard, L.: Potential of Advanced
Microwave Sounding Unit-A (AMSU-A) and AMSU-B Measurements for
Atmospheric Temperature and Humidity Profiling over Land, J.
Geophys. Res.-Atmos., 110, D07109, <a href="https://doi.org/10.1029/2004JD005318" target="_blank">https://doi.org/10.1029/2004JD005318</a>, 2005.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib72"><label>Kim and Kim(2019)</label><mixed-citation>
      
Kim, S.-M. and Kim, H. M.: Forecast Sensitivity Observation Impact in the
4DVAR and Hybrid-4DVAR Data Assimilation Systems, J.
Atmos. Ocean. Technol., 36, 1563–1575,
<a href="https://doi.org/10.1175/JTECH-D-18-0240.1" target="_blank">https://doi.org/10.1175/JTECH-D-18-0240.1</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib73"><label>Koch et al.(2018)</label><mixed-citation>
      
Koch, S. E., Fengler, M., Chilson, P. B., Elmore, K. L., Argrow, B., Andra,
D. L., and Lindley, T.: On the Use of Unmanned Aircraft for
Sampling Mesoscale Phenomena in the Preconvective Boundary Layer,
J. Atmos. Ocean. Technol., 35, 2265–2288,
<a href="https://doi.org/10.1175/JTECH-D-18-0101.1" target="_blank">https://doi.org/10.1175/JTECH-D-18-0101.1</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib74"><label>König-Langlo et al.(1998)</label><mixed-citation>
      
König-Langlo, G., King, J. C., and Pettré, P.: Climatology of the
Three Coastal Antarctic Stations Dumont d'Urville, Neumayer,
and Halley, J. Geophys. Res.-Atmos., 103,
10935–10946, <a href="https://doi.org/10.1029/97JD00527" target="_blank">https://doi.org/10.1029/97JD00527</a>, 1998.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib75"><label>Konrad et al.(1970)</label><mixed-citation>
      
Konrad, T., Hill, M., Rowland, J., and Meyer, J. H.: A Small, Radio-Controlled
Aircraft as a Platform for Meteorological Sensors, Johns Hopkins APL Tech.
Dig., 10, 11–21,   1970.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib76"><label>Kotthaus et al.(2023)</label><mixed-citation>
      
Kotthaus, S., Bravo-Aranda, J. A., Collaud Coen, M., Guerrero-Rascado, J. L., Costa, M. J., Cimini, D., O'Connor, E. J., Hervo, M., Alados-Arboledas, L., Jiménez-Portaz, M., Mona, L., Ruffieux, D., Illingworth, A., and Haeffelin, M.: Atmospheric boundary layer height from ground-based remote sensing: a review of capabilities and limitations, Atmos. Meas. Tech., 16, 433–479, <a href="https://doi.org/10.5194/amt-16-433-2023" target="_blank">https://doi.org/10.5194/amt-16-433-2023</a>, 2023.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib77"><label>Kräuchi and Philipona(2016)</label><mixed-citation>
      
Kräuchi, A. and Philipona, R.: Return glider radiosonde for in situ upper-air research measurements, Atmos. Meas. Tech., 9, 2535–2544, <a href="https://doi.org/10.5194/amt-9-2535-2016" target="_blank">https://doi.org/10.5194/amt-9-2535-2016</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib78"><label>Kren et al.(2018)</label><mixed-citation>
      
Kren, A. C., Cucurull, L., and Wang, H.: Impact of UAS Global Hawk Dropsonde
Data on Tropical and Extratropical Cyclone Forecasts in 2016,
Weather  Forecast., 33, 1121–1141, <a href="https://doi.org/10.1175/WAF-D-18-0029.1" target="_blank">https://doi.org/10.1175/WAF-D-18-0029.1</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib79"><label>Lafon et al.(2014)</label><mixed-citation>
      
Lafon, T., Fowler, J., Jiménez, J. F., and Cordoba, G. J. T.: A Viable
Alternative for Conducting Cost-Effective Daily Atmospheric Soundings
in Developing Countries, B. Am. Meteorol. Soc.,
95, 837–842, <a href="https://doi.org/10.1175/BAMS-D-13-00125.1" target="_blank">https://doi.org/10.1175/BAMS-D-13-00125.1</a>, 2014.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib80"><label>Lampert et al.(2020)</label><mixed-citation>
      
Lampert, A., Altstädter, B., Bärfuss, K., Bretschneider, L., Sandgaard,
J., Michaelis, J., Lobitz, L., Asmussen, M., Damm, E., Käthner, R.,
Krüger, T., Lüpkes, C., Nowak, S., Peuker, A., Rausch, T., Reiser,
F., Scholtz, A., Sotomayor Zakharov, D., Gaus, D., Bansmer, S., Wehner, B.,
and Pätzold, F.: Unmanned Aerial Systems for Investigating the
Polar Atmospheric Boundary Layer – Technical Challenges and
Examples of Applications, Atmosphere, 11, 416,
<a href="https://doi.org/10.3390/atmos11040416" target="_blank">https://doi.org/10.3390/atmos11040416</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib81"><label>Langland and Baker(2004)</label><mixed-citation>
      
Langland, R. H. and Baker, N. L.: Estimation of Observation Impact Using the
NRL Atmospheric Variational Data Assimilation Adjoint System, Tellus A. 56, 189–201,
<a href="https://doi.org/10.3402/tellusa.v56i3.14413" target="_blank">https://doi.org/10.3402/tellusa.v56i3.14413</a>, 2004.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib82"><label>Laursen et al.(2006)</label><mixed-citation>
      
Laursen, K. K., Jorgensen, D. P., Brasseur, G. P., Ustin, S. L., and Huning,
J. R.: HIAPER: THE NEXT GENERATION NSF/NCAR RESEARCH AIRCRAFT,
B. Am. Meteorol. Soc., 87, 896–909, 2006.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib83"><label>Lenschow(1972)</label><mixed-citation>
      
Lenschow, H.: The Measurement of Air Velocity and Temperature Using the NCAR
Buffalo Aircraft Measuring System, Technical Report NCAR/TN-74+EDD,
University Corporation for Atmospheric Research,
<a href="https://opensky.ucar.edu/islandora/object/technotes:62/" target="_blank"/> (last access:  1 August 2023),
1972.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib84"><label>Leuenberger et al.(2020)</label><mixed-citation>
      
Leuenberger, D., Haefele, A., Omanovic, N., Fengler, M., Martucci, G., Calpini,
B., Fuhrer, O., and Rossa, A.: Improving High-Impact Numerical Weather
Prediction with Lidar and Drone Observations, B.
Am. Meteorol. Soc., 101, E1036–E1051,
<a href="https://doi.org/10.1175/BAMS-D-19-0119.1" target="_blank">https://doi.org/10.1175/BAMS-D-19-0119.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib85"><label>Lindskog et al.(2004)</label><mixed-citation>
      
Lindskog, M., Salonen, K., Järvinen, H., and Michelson, D. B.: Doppler
Radar Wind Data Assimilation with HIRLAM 3DVAR, Mon. Weather
Rev., 132, 1081–1092,
<a href="https://doi.org/10.1175/1520-0493(2004)132&lt;1081:DRWDAW&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0493(2004)132&lt;1081:DRWDAW&gt;2.0.CO;2</a>, 2004.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib86"><label>Lorenc and Marriott(2014)</label><mixed-citation>
      
Lorenc, A. C. and Marriott, R. T.: Forecast Sensitivity to Observations in the
Met Office Global Numerical Weather Prediction System, Q. J. Roy. Meteorol. Soc., 140, 209–224, <a href="https://doi.org/10.1002/qj.2122" target="_blank">https://doi.org/10.1002/qj.2122</a>,
2014.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib87"><label>Majewski(2020)</label><mixed-citation>
      
Majewski, J.: The Dynamic Behaviour of Capacitive Humidity Sensors,
Devices and Methods of Measurements, 11, 53–59,
<a href="https://doi.org/10.21122/2220-9506-2020-11-1-53-59" target="_blank">https://doi.org/10.21122/2220-9506-2020-11-1-53-59</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib88"><label>Mallaun et al.(2015)</label><mixed-citation>
      
Mallaun, C., Giez, A., and Baumann, R.: Calibration of 3-D wind measurements on a single-engine research aircraft, Atmos. Meas. Tech., 8, 3177–3196, <a href="https://doi.org/10.5194/amt-8-3177-2015" target="_blank">https://doi.org/10.5194/amt-8-3177-2015</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib89"><label>Miloshevich et al.(2004)</label><mixed-citation>
      
Miloshevich, L. M., Paukkunen, A., Vömel, H., and Oltmans, S. J.:
Development and Validation of a Time-Lag Correction for Vaisala
Radiosonde Humidity Measurements, J. Atmos. Ocean.
Technol., 21, 1305–1327,
<a href="https://doi.org/10.1175/1520-0426(2004)021&lt;1305:DAVOAT&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0426(2004)021&lt;1305:DAVOAT&gt;2.0.CO;2</a>, 2004.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib90"><label>Moninger et al.(2003)</label><mixed-citation>
      
Moninger, W. R., Mamrosh, R. D., and Pauley, P. M.: Automated Meteorological
Reports from Commercial Aircraft, B. Am.
Meteorol. Soc., 84, 203–216, <a href="https://doi.org/10.1175/BAMS-84-2-203" target="_blank">https://doi.org/10.1175/BAMS-84-2-203</a>, 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib91"><label>Moninger et al.(2010)</label><mixed-citation>
      
Moninger, W. R., Benjamin, S. G., Jamison, B. D., Schlatter, T. W., Smith,
T. L., and Szoke, E. J.: Evaluation of Regional Aircraft Observations Using
TAMDAR, Weather  Forecast., 25, 627–645,
<a href="https://doi.org/10.1175/2009WAF2222321.1" target="_blank">https://doi.org/10.1175/2009WAF2222321.1</a>, 2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib92"><label>Nash et al.(2011)</label><mixed-citation>
      
Nash, J., Oakley, T., Vömel, H., and Wei, L.: IOM Report, 107. WMO  Intercomparison of High Quality Radiosonde Systems, WMO/TD, World Meteorological Organization, Geneva, 249 pp., <a href="https://library.wmo.int/doc_num.php?explnum_id=9467" target="_blank"/> (last access:  1 August 2023), 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib93"><label>Ota et al.(2013)</label><mixed-citation>
      
Ota, Y., Derber, J. C., Kalnay, E., and Miyoshi, T.: Ensemble-Based Observation
Impact Estimates Using the NCEP GFS, Tellus A, 65, 20038, <a href="https://doi.org/10.3402/tellusa.v65i0.20038" target="_blank">https://doi.org/10.3402/tellusa.v65i0.20038</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib94"><label>Palmer et al.(2021)</label><mixed-citation>
      
Palmer, R., Whelan, D., Bodine, D., Kirstetter, P., Kumjian, M., Metcalf, J.,
Yeary, M., Yu, T.-Y., Rao, R., Cho, J., Draper, D., Durden, S., English, S.,
Kollias, P., Kosiba, K., Wada, M., Wurman, J., Blackwell, W., Bluestein, H.,
Collis, S., Gerth, J., Tuttle, A., Wang, X., and Zrnić, D.: The Need
for Spectrum and the Impact on Weather Observations, B. Am. Meteorol. Soc., 102, E1402–E1407,
<a href="https://doi.org/10.1175/BAMS-D-21-0009.1" target="_blank">https://doi.org/10.1175/BAMS-D-21-0009.1</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib95"><label>Pätzold(2018)</label><mixed-citation>
      
Pätzold, F.: Windmessung mittels Segelflugzeug, Forschungsbericht
2018-04, Niedersächsisches Forschungszentrum für Luftfahrt,
Braunschweig, Germany, <a href="https://doi.org/10.24355/dbbs.084-201805221102-1" target="_blank">https://doi.org/10.24355/dbbs.084-201805221102-1</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib96"><label>Pena-Ortiz et al.(2013)Pena-Ortiz, Gallego, Ribera, Ordonez, and
Alvarez-Castro</label><mixed-citation>
      
Pena-Ortiz, C., Gallego, D., Ribera, P., Ordonez, P., and Alvarez-Castro,
M. D. C.: Observed Trends in the Global Jet Stream Characteristics during the
Second Half of the 20th Century, J. Geophys. Res.-Atmos., 118, 2702–2713, <a href="https://doi.org/10.1002/jgrd.50305" target="_blank">https://doi.org/10.1002/jgrd.50305</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib97"><label>Petersen(2016)</label><mixed-citation>
      
Petersen, R. A.: On the Impact and Benefits of AMDAR Observations
in Operational Forecasting – Part I: A Review of the
Impact of Automated Aircraft Wind and Temperature Reports,
B. Am. Meteorol. Soc., 97, 585–602,
<a href="https://doi.org/10.1175/BAMS-D-14-00055.1" target="_blank">https://doi.org/10.1175/BAMS-D-14-00055.1</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib98"><label>Petersen et al.(2015)</label><mixed-citation>
      
Petersen, R. A., Cronce, L., Mamrosh, R., and Baker, R.: A Report to the
World Meteorological Organization on the Impact and Benefits of AMDAR
Temperature, Wind and Moisture Observations in Operational Weather
Forecasting, Tech. rep., University of Wisconsin-Madison, Cooperative
Institute for Meteorological Satellite Studies, Space Science and Engineering
center, <a href="https://search.library.wisc.edu/catalog/9911154629902121" target="_blank"/> (last access: 1 August 2023),
2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib99"><label>Petersen et al.(2016)</label><mixed-citation>
      
Petersen, R. A., Cronce, L., Mamrosh, R., Baker, R., and Pauley, P.: On the
Impact and Future Benefits of AMDAR Observations in Operational
Forecasting: Part II: Water Vapor Observations, B.
Am. Meteorol. Soc., 97, 2117–2133,
<a href="https://doi.org/10.1175/BAMS-D-14-00211.1" target="_blank">https://doi.org/10.1175/BAMS-D-14-00211.1</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib100"><label>Pinto et al.(2021)</label><mixed-citation>
      
Pinto, J. O., O'Sullivan, D., Taylor, S., Elston, J., Baker, C. B., Hotz, D.,
Marshall, C., Jacob, J., Barfuss, K., Piguet, B., Roberts, G., Omanovic, N.,
Fengler, M., Jensen, A. A., Steiner, M., and Houston, A. L.: The Status
and Future of Small Uncrewed Aircraft Systems (UAS) in
Operational Meteorology, B. Am. Meteorol. Soc.,
102, E2121–E2136, <a href="https://doi.org/10.1175/BAMS-D-20-0138.1" target="_blank">https://doi.org/10.1175/BAMS-D-20-0138.1</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib101"><label>Rabier et al.(2010)</label><mixed-citation>
      
Rabier, F., Bouchard, A., Brun, E., Doerenbecher, A., Guedj, S., Guidard, V.,
Karbou, F., Peuch, V.-H., Amraoui, L. E., Puech, D., Genthon, C., Picard, G.,
Town, M., Hertzog, A., Vial, F., Cocquerez, P., Cohn, S. A., Hock, T., Fox,
J., Cole, H., Parsons, D., Powers, J., Romberg, K., VanAndel, J., Deshler,
T., Mercer, J., Haase, J. S., Avallone, L., Kalnajs, L., Mechoso, C. R.,
Tangborn, A., Pellegrini, A., Frenot, Y., Thépaut, J.-N., McNally, A.,
Balsamo, G., and Steinle, P.: The Concordiasi Project in Antarctica,
B. Am. Meteorol. Soc., 91, 69–86,
<a href="https://doi.org/10.1175/2009BAMS2764.1" target="_blank">https://doi.org/10.1175/2009BAMS2764.1</a>, 2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib102"><label>Ralph et al.(2020)</label><mixed-citation>
      
Ralph, F. M., Cannon, F., Tallapragada, V., Davis, C. A., Doyle, J. D.,
Pappenberger, F., Subramanian, A., Wilson, A. M., Lavers, D. A., Reynolds,
C. A., Haase, J. S., Centurioni, L., Ingleby, B., Rutz, J. J., Cordeira,
J. M., Zheng, M., Hecht, C., Kawzenuk, B., and Monache, L. D.: West Coast
Forecast Challenges and Development of Atmospheric River
Reconnaissance, B. Am. Meteorol. Soc., 101,
E1357–E1377, <a href="https://doi.org/10.1175/BAMS-D-19-0183.1" target="_blank">https://doi.org/10.1175/BAMS-D-19-0183.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib103"><label>Redelsperger et al.(2006)</label><mixed-citation>
      
Redelsperger, J.-L., Thorncroft, C. D., Diedhiou, A., Lebel, T., Parker, D. J.,
and Polcher, J.: African Monsoon Multidisciplinary Analysis: An
International Research Project and Field Campaign, B.
Am. Meteorol. Soc., 87, 1739–1746,
<a href="https://doi.org/10.1175/BAMS-87-12-1739" target="_blank">https://doi.org/10.1175/BAMS-87-12-1739</a>, 2006.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib104"><label>Reineman et al.(2016)</label><mixed-citation>
      
Reineman, B. D., Lenain, L., and Melville, W. K.: The Use of
Ship-Launched Fixed-Wing UAVs for Measuring the Marine Atmospheric
Boundary Layer and Ocean Surface Processes, J. Atmos.
Ocean. Technol., 33, 2029–2052, <a href="https://doi.org/10.1175/JTECH-D-15-0019.1" target="_blank">https://doi.org/10.1175/JTECH-D-15-0019.1</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib105"><label>Rennie et al.(2021)</label><mixed-citation>
      
Rennie, M. P., Isaksen, L., Weiler, F., de Kloe, J., Kanitz, T., and
Reitebuch, O.: The Impact of Aeolus Wind Retrievals on ECMWF Global
Weather Forecasts, Q. J. Roy. Meteorol. Soc.,
147, 3555–3586, <a href="https://doi.org/10.1002/qj.4142" target="_blank">https://doi.org/10.1002/qj.4142</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib106"><label>Riishojgaard(2015)</label><mixed-citation>
      
Riishojgaard, D. L. P.: Wind Measurements in the WMO Global Observing  System, ESA Workshop, p. 31, <a href="https://earth.esa.int/eogateway/documents/20142/37627/Day1_AM_L_P_Riishoigaard.pdf" target="_blank"/> (last access: 1 August 2023), 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib107"><label>Runge et al.(2007)</label><mixed-citation>
      
Runge, H., Rack, W., Alba, R.-L., and Hepperle, M.: A Solar-Powered  HALE-UAV for Arctic Research, in: CEAS Conference 2007, pp. 1–6,  Berlin, <a href="https://elib.dlr.de/51266/" target="_blank"/> (last access: 1 August 2023), 2007.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib108"><label>Schindler et al.(2020)</label><mixed-citation>
      
Schindler, M., Weissmann, M., Schäfler, A., and Radnoti, G.: The Impact
of Dropsonde and Extra Radiosonde Observations during NAWDEX in
Autumn 2016, Mon. Weather Rev., 148, 809–824,
<a href="https://doi.org/10.1175/MWR-D-19-0126.1" target="_blank">https://doi.org/10.1175/MWR-D-19-0126.1</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib109"><label>Schuyler et al.(2019)</label><mixed-citation>
      
Schuyler, T. J., Gohari, S. M. I., Pundsack, G., Berchoff, D., and Guzman,
M. I.: Using a Balloon-Launched Unmanned Glider to Validate Real-Time
WRF Modeling, Sensors, 19, 1914, <a href="https://doi.org/10.3390/s19081914" target="_blank">https://doi.org/10.3390/s19081914</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib110"><label>Secretariat of the Antarctic
Treaty(2019)</label><mixed-citation>
      
Secretariat of the Antarctic Treaty: Compilation of Key Documents of the Antarctic Treaty, Secretariat of the Antarctic Treaty, Buenos Aires, 4th edn., <a href="https://documents.ats.aq/atcm42/ww/ATCM42_ww011_e.pdf" target="_blank"/> (last access: 1 August 2023), 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib111"><label>Sørensen et al.(2021)</label><mixed-citation>
      
Sørensen, K. L., Borup, K. T., Hann, R., and Hansbø, M.: UAV
Atmospheric Icing Limitations, Climate Report Sor Norway and
Surrounding Regions, Tech. rep., UBIQ Aerospace, 28 pp., <a href="https://www.ubiqaerospace.com/climate-report" target="_blank"/> (last access: 1 August 2023), 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib112"><label>Steiner et al.(2001)</label><mixed-citation>
      
Steiner, A. K., Kirchengast, G., Foelsche, U., Kornblueh, L., Manzini, E., and
Bengtsson, L.: GNSS Occultation Sounding for Climate Monitoring, Phys. Chem. Earth Pt A, 26, 113–124,
<a href="https://doi.org/10.1016/S1464-1895(01)00034-5" target="_blank">https://doi.org/10.1016/S1464-1895(01)00034-5</a>, 2001.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib113"><label>Stickney et al.(1994)</label><mixed-citation>
      
Stickney, T. M., Shedlov, M. W., and Thompson, D. I.: GOODRICH TOTAL  TEMPERATURE SENSORS, Tech. rep., Goodrich, 32 pp., <a href="https://data.eol.ucar.edu/file/download/53F7B041406B0/TAT-Report.pdf" target="_blank"/> (last access: 1 August 2023), 1994.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib114"><label>Sun et al.(2020)</label><mixed-citation>
      
Sun, Q., Vihma, T., Jonassen, M. O., and Zhang, Z.: Impact of Assimilation
of Radiosonde and UAV Observations from the Southern Ocean in the
Polar WRF Model, Adv. Atmos. Sci., 37, 441–454,
<a href="https://doi.org/10.1007/s00376-020-9213-8" target="_blank">https://doi.org/10.1007/s00376-020-9213-8</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib115"><label>Tafferner et al.(2003)</label><mixed-citation>
      
Tafferner, A., Hauf, T., Leifeld, C., Hafner, T., Leykauf, H., and Voigt, U.:
ADWICE: Advanced Diagnosis and Warning System for Aircraft
Icing Environments, Weather Forecast., 18, 184–203,
<a href="https://doi.org/10.1175/1520-0434(2003)018&lt;0184:AADAWS&gt;2.0.CO;2" target="_blank">https://doi.org/10.1175/1520-0434(2003)018&lt;0184:AADAWS&gt;2.0.CO;2</a>, 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib116"><label>Thépaut and Andersson(2010)</label><mixed-citation>
      
Thépaut, J.-N. and Andersson, E.: The Global Observing System, in: Data
Assimilation: Making Sense of Observations, edited by Lahoz, W.,
Khattatov, B., and Menard, R.,  263–281, Springer, Berlin,
Heidelberg, <a href="https://doi.org/10.1007/978-3-540-74703-1_10" target="_blank">https://doi.org/10.1007/978-3-540-74703-1_10</a>, 2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib117"><label>VAISALA(2021)</label><mixed-citation>
      
VAISALA: Response Time in Humidity Measurement, TECHNICAL NOTE B211803EN-B,   VAISALA, <a href="https://www.vaisala.com/sites/default/files/documents/Response-time-in-humidity-measurement-Technical-Note-B211803EN.pdf" target="_blank">https://www.vaisala.com/sites/default/files/documents/Response-time-in-humidity</a> (last access: 1 August 2023),
2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib118"><label>van den Kroonenberg et al.(2008)</label><mixed-citation>
      
van den Kroonenberg, A., Martin, T., Buschmann, M., Bange, J., and
Vörsmann, P.: Measuring the Wind Vector Using the Autonomous Mini
Aerial Vehicle M2AV, J. Atmos. Ocean. Technol., 25,
1969–1982, <a href="https://doi.org/10.1175/2008JTECHA1114.1" target="_blank">https://doi.org/10.1175/2008JTECHA1114.1</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib119"><label>Vinnichenko(1970)</label><mixed-citation>
      
Vinnichenko, N. K.: The Kinetic Energy Spectrum in the Free
Atmosphere – 1 Second to 5 Years, Tellus, 22, 158–166,
<a href="https://doi.org/10.3402/tellusa.v22i2.10210" target="_blank">https://doi.org/10.3402/tellusa.v22i2.10210</a>, 1970.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib120"><label>Vömel et al.(2018)</label><mixed-citation>
      
Vömel, H., Argrow, B. M., Axisa, D., Chilson, P., Ellis, S., Fladeland, M.,
Frew, E. W., Jacob, J., Lord, M., Moore, J., Oncley, S., Roberts, G.,
Schoenung, S., and Wolff, C.: The NCAR/EOL Community Workshop on
Unmanned Aircraft Systems for Atmospheric Research – Final
Report, none, <a href="https://doi.org/10.5065/D6X9292S" target="_blank">https://doi.org/10.5065/D6X9292S</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib121"><label>Vörsmann(1984)</label><mixed-citation>
      
Vörsmann, P.: Ein Beitrag zur bordautonomen Windmessung, Dissertation,
TU Braunschweig, 1984.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib122"><label>Wagner and Petersen(2021)</label><mixed-citation>
      
Wagner, T. J. and Petersen, R. A.: On the Performance of Airborne
Meteorological Observations against Other In Situ Measurements, J. Atmos. Ocean. Technol., 38, 1217–1230,
<a href="https://doi.org/10.1175/JTECH-D-20-0182.1" target="_blank">https://doi.org/10.1175/JTECH-D-20-0182.1</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib123"><label>Wang et al.(2000)</label><mixed-citation>
      
Wang, B., Zou, X., and Zhu, J.: Data Assimilation and Its Applications,
P. Natl. Acad. Sci. USA, 97, 11143–11144,
<a href="https://doi.org/10.1073/pnas.97.21.11143" target="_blank">https://doi.org/10.1073/pnas.97.21.11143</a>, 2000.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib124"><label>Wang et al.(2013)</label><mixed-citation>
      
Wang, J., Hock, T., Cohn, S. A., Martin, C., Potts, N., Reale, T., Sun, B., and
Tilley, F.: Unprecedented Upper-Air Dropsonde Observations over
Antarctica from the 2010 Concordiasi Experiment: Validation of
Satellite-Retrieved Temperature Profiles, Geophys. Res. Lett., 40,
1231–1236, <a href="https://doi.org/10.1002/grl.50246" target="_blank">https://doi.org/10.1002/grl.50246</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib125"><label>Watts et al.(2012)</label><mixed-citation>
      
Watts, A. C., Ambrosia, V. G., and Hinkley, E. A.: Unmanned Aircraft
Systems in Remote Sensing and Scientific Research:
Classification and Considerations of Use, Remote Sens., 4,
1671–1692, <a href="https://doi.org/10.3390/rs4061671" target="_blank">https://doi.org/10.3390/rs4061671</a>, 2012.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib126"><label>WMO(2003)</label><mixed-citation>
      
WMO: AMDAR Reference Manual: Aircraft Meteorological Data Relay, no. 958 in WMO, Secretariat of the World Meteorological Organization, Geneva, 84 pp.,  <a href="https://library.wmo.int/index.php?lvl=notice_display&amp;id=7920" target="_blank"/> (last access: 1 August 2023), 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib127"><label>WMO(2010)</label><mixed-citation>
      
WMO: Guide to the Global Observing System, WMO, World Meteorological  Organization, Geneva, 2010th edn. updated in 2017, 228 pp., <a href="https://library.wmo.int/index.php?lvl=notice_display&amp;id=12516" target="_blank"/> (last access: 1 August 2023),  2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib128"><label>WMO(2011)</label><mixed-citation>
      
WMO: Manual on Codes - International Codes, Volume I.1, Annex II to the WMO Technical Regulations: Part A – Alphanumeric Codes, WMO, WMO, Geneva, 2011th edn. updated in 2019, 480 pp., <a href="https://library.wmo.int/index.php?lvl=notice_display&amp;id=13617" target="_blank"/> (last access: 1 August 2023), 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib129"><label>WMO(2015)</label><mixed-citation>
      
WMO: Global Observing System, <a href="https://public.wmo.int/en/programmes/global-observing-system" target="_blank"/> (last access: 1 August 2023), 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib130"><label>WMO(2018)</label><mixed-citation>
      
WMO: Guide to Instruments and Methods of Observation, no. 8 in  WMO, Geneva, 2018 edn., 197 pp., <a href="https://library.wmo.int/index.php?lvl=notice_display&amp;id=12407#.XiGSwf5KiUk" target="_blank"/> (last access: 1 August 2023), 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib131"><label>WMO(2020)</label><mixed-citation>
      
WMO: The Gaps in the Global Basic Observing Network (GBON), Tech. rep., WMO Systematic Observations Financing Facility, <a href="https://public.wmo.int/en/resources/library/gaps-global-basic-observing-network-gbon" target="_blank"/> (last access: 1 August 2023), 2020.


    </mixed-citation></ref-html>
<ref-html id="bib1.bib132"><label>WMO(2022)</label><mixed-citation>
      
WMO: WMO UAS Demonstration Campaign Description | World Meteorological Organization, <a href="https://community.wmo.int/uas-demonstration/description" target="_blank"/> (last access: 1 August 2023), 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib133"><label>WMO OSCAR(2015)</label><mixed-citation>
      
WMO OSCAR: User requirements for observation (OSCAR/Requirements), WMO, Geneva, <a href="https://space.oscar.wmo.int/observingrequirements" target="_blank"/> (last access: 1 August 2023), 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib134"><label>Wyngaard et al.(2019)</label><mixed-citation>
      
Wyngaard, J., Barbieri, L., Thomer, A., Adams, J., Sullivan, D., Crosby, C.,
Parr, C., Klump, J., Raj Shrestha, S., and Bell, T.: Emergent Challenges
for Science sUAS Data Management: Fairness through Community
Engagement and Best Practices Development, Remote Sens., 11, 1797,
<a href="https://doi.org/10.3390/rs11151797" target="_blank">https://doi.org/10.3390/rs11151797</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib135"><label>Zheng et al.(2021)</label><mixed-citation>
      
Zheng, M., Delle Monache, L., Cornuelle, B. D., Ralph, F. M., Tallapragada,
V. S., Subramanian, A., Haase, J. S., Zhang, Z., Wu, X., Murphy, M. J.,
Higgins, T. B., and DeHaan, L.: Improved Forecast Skill Through the
Assimilation of Dropsonde Observations From the Atmospheric River
Reconnaissance Program, J. Geophys. Res.-Atmos., 126,
e2021JD034967, <a href="https://doi.org/10.1029/2021JD034967" target="_blank">https://doi.org/10.1029/2021JD034967</a>, 2021.

    </mixed-citation></ref-html>--></article>
