Comparison of Lyman-alpha and LI-COR infrared hygrometers for airborne measurement of turbulent ﬂuctuations of water vapour

. To investigate if the LI-COR humidity sensor can be used as a replacement of the Lyman-alpha sensor for airborne applications, the measurement data of the Lyman-alpha and several LI-COR sensors are analysed in direct intercomparison ﬂights on different airborne platforms. One vibration isolated closed-path and two non-isolated open-path LI-COR sensors were installed on a Dornier 128 twin engine turbo-prop aircraft. The closed-path sensor provided absolute values and ﬂuctuations of the water vapour mixing ratio in good agreement with the Lyman-alpha. The signals of the two open-path sensors showed considerable high-frequency noise, and the absolute value of the mixing ratio was observed to drift with time in this vibrational environment. On the helicopter-towed sensor system Helipod, with very low vibration the open-path LI-COR sensor very the Lyman-alpha sensor over The results show that the LI-COR sensors are well suited for airborne measurements of humidity ﬂuctuations, provided that a vibrationless environment is given, and this turns out to be more important than close sensor spacing.


Introduction
Water vapour and clouds in the atmosphere have a large impact on the energy balance (Ramanathan et al., 1989), the hydrologic cycle (e.g. Chahine, 1992) and on local and global climate (Trenberth et al., 2007;Zhou et al., 2011). Therefore, accurate knowledge of atmospheric water vapour concentration and transport is of high relevance for understanding climate and climate change. A general increase in atmospheric moisture measured at the surface and humidity within the troposphere has been reported (IPCC, 2013). Satellite retrievals of the vertical water vapour distribution provide limited spatial resolution, e.g. 300 m in the vertical and 30 km in horizontal direction (Bender et al., 2011). Turbulence is the most effective way for moisture to be transported from the surface to the atmosphere. Turbulent fluxes are commonly determined with the eddy-covariance method. This technique requires accurate and high-resolution measurements of the fluctuations of the vertical component of wind speed and humidity.
For the quantification of atmospheric processes on local to regional scales, airborne measurements are required to fill the gap between large-scale, low-resolution information from satellites and small-scale measurements at fixed locations, as towers, providing higher vertical and temporal resolution.
For in situ measurements of humidity, the error bars are typically larger than for other atmospheric parameters like temperature and wind. In the troposphere, the water vapour concentration in parts per million varies over 2 orders of magnitude (e.g. Schneider et al., 2010). Since measuring atmospheric water vapour precisely is difficult, the uncertainties of atmospheric water vapour measurements are high. Even with the best systems under well-controlled conditions in the laboratory, there are large discrepancies between different measurement systems; e.g. intercomparison mea-surements of different hygrometers probing the same air simultaneously revealed discrepancies between different measurement systems of around 10 % (Fahey et al., 2014). For cold and dry conditions, as encountered in the upper troposphere and lower stratosphere, the instruments had a variation around the reference value of 20 % (Fahey et al., 2014).
Airborne sensors have to fulfil specific requirements. On the one hand, high temporal resolution is needed in order to obtain high spatial resolution for the moving platforms. On the other hand, long-term stability and high accuracy, if possible without the need for frequent re-calibration, are essential. In practice, as no sensor is available that meets both requirements, this leads to the combination of complementary sensors for both high resolution and long-term accuracy.
In the following, the measurement principles of the different humidity sensors used in this study are shortly summarised.

Material absorption
Capacitive sensors are based on taking up humidity in a porous or hygroscopic material, which changes dielectric properties. An example is the Vaisala Humicap sensor, which is used as the standard for radiosondes. However, the response times for increasing and decreasing humidity may differ significantly due to the different diffusion coefficients into the material and out of the material, and the temporal resolution is limited. For temperatures exceeding 0 • C, and with the help of extensive postprocessing or modelling, the relatively slow polymer-based absorption hygrometers are sometimes used for retrieving humidity fluctuations (Wildmann et al., 2014).
The typical calibration procedure consists of applying saturated salt solutions with different known relative humidities and recording the sensor output, thus creating a calibration curve. The sensor is sensitive to contamination, e.g. by sea salt, which may alter the sensor properties significantly, making regular cleaning and re-calibration necessary.

Atomic absorption
Sensors based on atomic absorption provide the advantage of very fast response time allowing for measurement frequencies exceeding 100 Hz, a sharp absorption line compared to the absorption bands of molecules and a high degree of absorption. This requires measurement cells of only a few millimetres (Buck, 1973). The sensor is based on the emission of ultraviolet (UV) radiation at a wavelength of 121.56 nm (transition of an electron from the first excited state n = 2 to the ground state n = 1 in the hydrogen atom, called Lyman-alpha emission line). As the Lymanalpha wavelength is strongly absorbed by water vapour, the signal in the ion chamber detector is weakened accordingly. The relation is given by the attenuation law of Lambert-Beer. The absorption of the Lyman-alpha line has cross sensitivi-ties with oxygen and ozone molecules. The absorption by oxygen molecules is about 1000 times weaker than by ozone molecules, and can be corrected by taking into account pressure and temperature, as the fractional density is constant. The correction of the absorption by ozone molecules (same order of magnitude with respect to water vapour) is only necessary in the stratosphere (Buck, 1976).
Calibration is done by applying air of known humidities and recording the detector signal as a calibration curve. The aging of the lamp, or degradation of the magnesium fluoride windows, leads to a reduced signal strength with time, which is interpreted as higher absorption, thus higher water content. This (slow) drift makes regular calibration of either the sensor or the retrieved data necessary.
The term "Lyman-alpha" in this paper is used as a synonym for the Buck Research Lyman-alpha absorption hygrometer (Buck, 1973(Buck, , 1976. It has been used as a standard fast humidity sensor on many research aircraft for several decades (Busen and Buck, 1995;Corsmeier et al., 2001;Drüe and Heinemann, 2007;Twohy et al., 1997). However, with the end of the lifetime of the radiation sources (glow discharge lamps) and difficulties in replacing them, other humidity sensors become more important, and a variety of fast-response sensors are now available, e.g. the Krypton hygrometer KH20 (Campbell Scientific, USA), similar to the Lyman-alpha, has cross sensitivity to oxygen as well and therefore, like the Lyman-alpha, has to be calibrated carefully (Foken and Falke, 2012). It is, however, mostly used for ground-based measurements. Furthermore, the instrument is very sensitive to path length, and calibration is difficult even for ground-based application (Foken and Falke, 2010). For NCAR research aircraft, a new Lyman-alpha sensor was built, which has shown promising first results (Beaton and Spowart, 2012).

Molecular absorption
Hygrometers based on molecular absorption can be subdivided into systems based on a laser light source and the simpler and cheaper technique of using a broadband light source combined with interference filters. However, laser sources and fibre optics are now readily available as well due to advances and common use in telecommunications. The disadvantage of molecular absorption is line broadening with pressure, resulting from the impact of other molecules. These measurement systems include the Picarro greenhouse gas analyser (Crosson, 2008) and the Los Gatos Research fast greenhouse gas analyser (Baer et al., 2002), which measure the three most important greenhouse gases water vapour, carbon dioxide and methane simultaneously. For retrieving methane and carbon dioxide with these instruments, the water vapour measurements are necessary to reference the number concentration of methane molecules to the dry mole fraction.
The fast-response LI-COR instruments LI-7500, LI-7500A and LI-7200 for measuring humidity are based on the absorption of near-infrared radiation. They have a longer measurement path of 12.5 cm compared to the few millimetres of the Lyman-alpha. The LI-COR sensors in different forms are used at automated field stations for research networks covering large temporal and spatial scales, and they are therefore well characterised concerning the transfer function of different components (Metzger et al., 2016). The closed-path sensors requiring a gas sampling system can be affected by high-frequency attenuation, so inlets and tubes have to be dimensioned reasonably (Aubinet et al., 2016;Metzger et al., 2016).
Like for the Lyman-alpha, the attenuation of the signal obeys the law of Lambert-Beer relating absorptance to the number density of the absorbing gas, taking into account pressure, and requires correction terms due to crosssensitivities. The calibration procedure consists of applying air with well-defined humidity for two points, and adapting the calibration coefficients accordingly. Zero signal is created by dry, carbon dioxide free gas. The second point can be applied, for example, with the LI-COR dew point generator.
The LI-COR humidity sensors have been used airborne for many years, in addition to or as a replacement for the Lyman-alpha (Beringer et al., 2011;Pillai et al., 2011;Hiller et al., 2014). The sensors have been implemented in various configurations, some with the sensor head forward facing, e.g. on the helicopter-borne sensor system Helipod, and the Airborne Cloud Turbulence Observation System ACTOS (Siebert et al., 2013), some with the sensor head oriented vertically (French Piper Aztec research aircraft), some with open housing (Siebert et al., 2013) and some with a metal grid (Helipod), some with additional purging with synthetic air to keep the detector free of water vapour (Schmitgen et al., 2004).
In the manual, the manufacturer advises that the sensor should not be applied at vibrations around 150 Hz and around the harmonics (Licor, 2014). However, the impact on measurements is not specified or even quantified. As the LI-COR sensor is currently the cheapest fast-response water vapour sensor commercially available, and small enough to be easily integrated into aircraft, its airborne applications will very likely increase. Therefore, knowing the limitations of the LI-COR sensors with respect to vibrations is important, and one of the main aims of this study.
For large research aircraft, some specifically designed hygrometers are implemented: on the National Science Foundation Gulfstream V aircraft, a cavity diode laser hygrometer with two absorption lines in the near-infrared is deployed with a temporal resolution of 25 Hz (Zondlo et al., 2010). On the NASA ER-2 aircraft, a specifically designed near-infrared tunable diode laser spectrometer is deployed for measuring atmospheric water vapour concentration (May, 1998), with a sampling rate of 1 Hz and 10 % accuracy (Herman et al., 2017). On the DLR HALO (High Altitude And Long-Range Research Aircraft), another spectroscopic sensor developed by the Physikalisch-Technische Bundesanstalt (PTB) Braunschweig is deployed (Buchholz et al., 2014). Compared to the LI-COR sensor, this tunable diode laser hygrometer can be operated much faster (up to several kilohertz) and with known accuracy, providing the most precise humidity values available to date (Buchholz et al., 2013(Buchholz et al., , 2014(Buchholz et al., , 2016. However, this hygrometer requires extensive post processing, and as of yet it is not possible to obtain real-time humidity data. The spectroscopic sensors are experimental systems and not commercially available. The aims of this article are (1) to show limitations and provide information on the successful airborne handling of LI-COR humidity sensors, (2) to quantitatively compare fluxes of latent heat obtained with the former "standard" Lymanalpha and with the LI-COR sensors for airborne applications and (3) to determine the required measurement frequency for humidity fluctuations to derive reliable latent heat fluxes for the typical flight altitude of a few hundred metres and airspeed in the range of 35 to 70 m s −1 .

Experimental setup
This section provides a background on the sensors used in the study, including a short overview of the LI-COR sensor working principle, and a description of the airborne platforms and their sensor setup. For the flights, a Lyman-alpha and at least one LI-COR sensor were operated in parallel, and the latent heat fluxes derived from the different humidity sensors and the same wind vector measurements are compared directly.

LI-COR sensors
The working principle of the LI-COR sensor series for water vapour and carbon dioxide (CO 2 ) is the absorption of near-infrared radiation by these molecules. The radiation source is a small lamp with broadband emissions in the nearinfrared (NIR) spectral range. The radiation is focussed on a filter wheel with bandpass filters of different wavelengths, rotating at a speed of 150 Hz. The light at a wavelength of 2590 nm is absorbed by water vapour but not by carbon dioxide; the light at a wavelength of 4260 nm by CO 2 , but not by water vapour; the light at a wavelength of 3950 nm serves as a reference, where neither CO 2 nor water vapour have absorption bands. The narrow band-pass-filtered radiation then passes the 12.5 cm length measurement cell, where the ambient air either passes passively (open-path sensor, LI-7500, and the newer LI-7500A) or is pumped through (closed-path sensor, LI7200), and partly absorbs radiation depending on the number density of the absorbing water molecules and on the CO 2 concentration. The detector on the other side of the measurement cell is a thermopile, additionally cooled by Peltier elements. The system is described in more detail in Licor (2014). The data sampled internally at 150 Hz frequency is processed and provided at a maximum frequency of 20 Hz. The time offset for internal processing is specified for the LI-7500 as 0.185 s, and for both the LI-7500A and LI-7200 as 0.130 s.

Do128 instrumentation
The standard meteorological equipment of the research aircraft Do128 "D-IBUF" of the Institute of Flight Guidance, TU Braunschweig, consists of a five-hole probe and corresponding Setra pressure transducers (static, dynamic and differential pressure), inertial navigation and global navigation satellite system (GNSS) for deriving the 3-D wind vector (see description of methods, e.g. by van den Kroonenberg et al., 2008;Bärfuss et al., 2018), a long-time stable Rosemount DB102 temperature sensor with slow response time of around 1 s and a fast-response (100 Hz) Rosemount EL102 temperature sensor. The temperature sensors are mounted in a sophisticated Rosemount inlet to directly obtain the static air temperature, and can additionally be heated for flights in icing conditions. The humidity channel includes a dew point mirror TP 3-S of Meteolabor (not operational for this study), a capacitive humidity sensor (Vaisala HMP233 Humicap) and a Buck Research Lyman-alpha optical sensor L-6. Further, a surface temperature sensor KT15 is included. Temperature and humidity sensors, as well as the five-hole probe are integrated into the nose boom. More details on the instrumentation can be found in Hankers (1989), Bange et al. (2002) and Corsmeier et al. (2001Corsmeier et al. ( , 2002. The Vaisala Humicap is calibrated before and after each measurement campaign by applying saturated salt solutions and their different known equilibrium relative humidities, and the combined signal of the slow Humicap and the fast Lyman-alpha has been shown to agree well with other independent measurements of humidity (Sodemann et al., 2017).
For the humidity intercomparison flight, three different LI-COR systems were available (open-path LI-7500 with serial number 75H-0775, open-path LI-7500A with serial number 75H-2287 and closed-path LI-7200 with serial number 72H-0584). The two open-path sensors were covered by a metal grid to enforce turbulent mixing and avoid gradients of concentration in the measurement cell. The three LI-COR sensors were installed in addition to the standard equipment at the following locations: on the nose boom (LI-7500A, in the following called Li1), in the cabin directly under the roof (LI-7200, called Li2), with an inlet sampling the air near the LI-7500 (called Li3) on the roof (see Fig. 1). The axis of the optical path of all sensors were oriented along the aircraft longitudinal axis. No purging of the sensors with nitrogen or dried air was applied.
The stainless steel inlet of the Li2 sensor had a length l 1 of 350 mm and an inner diameter of 9.6 mm, resulting in an area of A 1 = 7.24 × 10 −5 m 2 . A volume flow controller provided a flow of Q = 15 L min −1 = 2.5×10 −4 m 3 s −1 . For the tube, the airspeed is therefore v 1 = Q A 1 = 3.45 m s −1 . This results in a time shift t 1 = l 1 v 1 = 0.1 s. Similar calculations are applied for the nylon tube of length l 2 = 400 mm and inner diameter of 8 mm, guiding the air from the inlet to the sensor, which results in an additional time shift of 0.03 s. Additionally, the time for exchanging the air of the measurement cell with an inner diameter of 25 mm and a half length of 125 mm amounts to 0.12 s. Altogether, there is a time shift of 0.25 s caused by the sampling system for the Li2.
For the humidity intercomparison flight, M355B04/03/02 and M356B18 vibration sensors (PCB Piezotronics Inc., USA) were integrated along the x axis (perpendicular to flight path) and z axis (upward directed) of the LI-COR sensors. For the Li2, another vibration sensor in y direction (in flight path along the aircraft and the sensors) was available.

Synchronisation of the Do128 humidity sensors
Before calculating the humidity fluctuations, the four fast humidity sensors (Lyman-alpha, Li1, Li2, Li3) onboard the Do128 located at different places were synchronised. As mentioned in Sect. 2.2, the Lyman-alpha and the Li1 are located on the nose boom, the Li3 on the cabin roof, and the inlet of the Li2 is close to the Li3, also on the cabin roof. First the Lyman-alpha data were shifted in time against the vertical wind speed by maximising the turbulent latent heat flux. The synchronisation was then done by maximising the covariance of the mixing ratio fluctuations of the Lymanalpha and each of the LI-COR sensors for varying temporal offsets. The time step providing the highest correlation was used as the time shift between the sensors. The time signal of the Lyman-alpha was used as reference. The part of the flight used for the synchronisation (shaded in grey in For further calculations, the best fitting time shift correction was applied to all three LI-COR sensors. The correlation between the LI-COR signals and the Lyman-alpha was better than 0.95 for the Li2 and Lyman-alpha, and exceeding 0.8 for the Li1 and Lyman-alpha for the part of the flight considered here. The best correlation between Li3 and Lyman-alpha amounted to 0.6, thus considerably lower (Fig. 9).
The calculations of the best fitting time shift were verified by maximising the coherence spectra of the LI-COR sensors and the Lyman-alpha as a reference, and at the same time minimising the phase between the two signals. This resulted in the same time shift as determined by the method of maximising the correlation.

Helipod instrumentation
Here we analyse the data from a measurement flight with the "Helipod", a meteorological sensor system towed by a helicopter with a rope (e.g. Bange and Roth, 1999;Bange et al., 2002;Martin and Bange, 2014). The Helipod is equipped with different meteorological sensors: humidity measurements are performed with a Lyman-alpha sensor L6 (Buck Research, USA), a capacitive Vaisala Humicap HMP110, a 1011B dew point mirror (General Eastern, USA; not used in this study) and the LI-7500 (same sensor as used for the Do128 flight, there called Li3). Temperature is measured with a Rosemount Pt100 and a Dantec fine wire. A fivehole probe with the same differential pressure sensors as in the Do128 is integrated (D289 for differential pressure and D270 for static pressure, Setra, USA), as well as a GPS system with eight receivers for a full 3-D attitude alignment (GNATTI System, Geo++ GmbH, Germany) and IMU (LCR 88, LITEF, Germany). A KT19 sensor (Heimann, Germany) records the surface temperature. Altitude information is provided by GPS, barometric pressure and a radar altimeter ERT180 (Thomson-CFS, France).

Synchronisation of the Helipod humidity sensors
As the LI-7500 system was calibrated directly before the measurement campaign, and therefore provides reliable absolute values, the Lyman-alpha values of the mixing ratio were calibrated against the LI-COR data using a linear regression method. Before calculating turbulent fluxes of latent heat, the time shift between the LI-COR and the Lymanalpha was corrected by calculating the maximum coherence with minimum phase shift of the two signals. The best correlation was found for a total time shift of 0.315 s. This includes the time shift caused by internal processing of 0.186 s, plus an additional time shift of around 0.13 s. The additional time lag may be attributed to the semi-open housing geometry. This value was confirmed by calculating the best correlation between the time series. The time lag was the same for straight and level flight sections throughout three campaigns in Siberia in April, June and August 2014.  (Fig. 2). The part of the flight that was used for the sensor comparison is displayed in white on the flight track (Fig. 2) and shaded grey in Fig. 3, which fulfills the requirements of Lenschow et al. (1994) for the sampling length for several sub-legs above homogeneous terrain. Such small sub-legs were chosen with different (but homogeneous within the sub-leg) surface conditions and different (but constant within the sub-leg) flight altitudes to see if there are systematic differences in the parameters such as vibration levels.
The flight took place under varying cloud conditions, mostly overcast with a cloud bottom at an altitude of around 1000 m. Above land, a neutrally stratified boundary layer was observed up to an altitude of around 1000 m, with a strong increase of potential temperature of 6 K at 1000 to 1200 m. However, above the North Sea, the atmosphere was stably stratified. Therefore, significant latent heat fluxes were only observed over land.

Helipod flight on 14 August 2014
The overall aim of the Helipod measurements was to study greenhouse gas emissions on a climatically relevant subregional scale of up to 100 km to investigate spatial variability and to analyse how representative the continuous emis-sion measurements on local scales are for this larger scale. During the measurement flight, the Helipod was attached to a Russian Mi8 helicopter with a 30 m rope. The flight was performed at a true airspeed of 40 m s −1 from the Samoylov Island Research Station in the Lena Delta, Siberia.
The Helipod flight analysed here took place on 14 August 2014, when seasonal thawing of the active layer on top of the permafrost was still in progress. The round-trip flight pattern followed a 100 km horizontal leg at 100 m altitude to the north-west with vertical profiles up to 1500 m altitude at both ends of the leg. The atmosphere was neutrally stratified in the lowermost 150 m, then slightly stable up to 1000 m (increase in potential temperature smaller than 1 K from the surface up to that altitude), and the atmospheric boundary layer (ABL) top was evident by an increase of potential temperature at 1000 m altitude.
The flight on 14 August 2014 was done in conditions nearly free of clouds at the beginning with a near-surface air temperature around 17 • C and southerly wind with a speed of 5 m s −1 near ground. The mean wind speed at the altitude of the Helipod transects was 8 m s −1 , and the mean wind direction at that altitude was 180 • . For this instrumental intercomparison, the first long flight transect from Samoylov Station to Arga-Muora is analysed (Fig. 4). On the way back, short rain showers were encountered. The time series of the height, vertical wind speed, mixing ratio, potential temperature and valid data are shown in Fig. 5.

Vibrations during the Do128 flight
The time series of the mixing ratio (Fig. 3) shows the general behaviour of the Li2 sensor, the slow Humicap and the fast Lyman-alpha sensor. The time periods affected by radio communication were excluded from further analyses, as they occasionally induce artificial spikes on the Lyman-alpha sensor. The data used for calculating the spectra are shaded in grey. They were chosen to exclude the flights at higher altitude, where the signal of the Lyman-alpha differs significantly from the other sensors. Under these different pressure conditions, a different sensitivity range would have been necessary, which was not adapted during the flight. For the data of the Li1 and Li3, different effects can be observed: -The signals of the open-path sensors Li1 and Li3 contain a higher level of noise compared to the closed-path Li2 system and the signal of the Lyman-alpha.
-Changes in altitude affect the signals of Li1 and Li3, and the absolute values of the mixing ratio do not follow the behaviour of the Li2 and the Humicap. This might be caused by changing vibration environments due to different power settings.  -There is a general slow drift in the signal of the openpath sensors Li1 and Li3, which does not follow the trend of the closed-path Li2 sensor, the signal of Lymanalpha, and Humicap.
Differences are apparent in the time series of the vibrations (Fig. 6): the amplitude of acceleration in z direction is around 50 m s −2 for the Li3, around 40 m s −2 for the Li1 and around 3 m s −2 for the Li2 sensor. The example shows a small flight section of 3 min, indicated in yellow in Fig. 3, but is representative for sections of this length at constant altitude. The acceleration spectra for all three sensors in y and z directions (along sensor and aircraft axis, and vertically) and x direction (perpendicular to sensor and flight direction) for the Li2 sensor are shown in Fig. 7 for a short flight section of 3 min. Strong and sharp vibration peaks at distinguished frequencies and differences in the broadband features were recorded at the locations of all sensors.
Generally, the acceleration for high frequencies (exceeding 200 Hz) is several orders of magnitude lower for the Li2 sensor compared to the Li1 and Li3 sensors. This feature gets more pronounced for frequencies exceeding 1000 Hz. The strength of vibrations contained within individual peaks is more pronounced for the Li1 and Li3 sensor compared to the Li2 sensor. In Fig. 7, the critical frequencies of 150 Hz and higher harmonics, as specified by the manufacturer, are indicated by vertical black lines. Especially around 450 Hz it can be seen that the vibration level of the Li3 is more than an order of magnitude higher than the vibration level of the Li1. This feature is observed during all flight legs analysed here, and is persistent throughout each flight leg. The high level of vibrations at the critical frequencies and potential impact on    the internal signal processing could be an explanation for the different humidity spectra shown in the following.

Power spectra of humidity fluctuations
The above-mentioned properties of the sensors are reflected in the spectra of the mixing ratio, shown in Fig. 8 for each humidity signal. The sloped lines represent the −5/3 drop-off expected in the inertial subrange. Between 0.003 and 0.3 Hz all sensors follow the Kolmogorov prediction (Kolmogorov, 1941) very well, and those of the Lyman-alpha and Li2 continue for a further decade, while Li1 and Li3 level off indicating a substantial level of white noise superimposed on the humidity signal. The Humicap spectrum gradually decreases slightly faster Overall, the Lyman-alpha spectrum most closely behaves as expected from the theory, and the Li2 spectrum is very similar but drops off marginally faster beyond 1 Hz. This behaviour can be attributed to somewhat increased dampening due to longer inlet tubes in comparison to those for the Lyman-alpha.
At low frequencies the Vaisala Humicap and even more the Li3 sensor show higher variances. It will be shown in the next subsection that this variance is differently correlated with the vertical wind velocity, which has implications for the flux calculation.

Co-spectral analysis
As the Lyman-alpha humidity sensor has been used widely in turbulence studies over decades, it is taken as a reference to compare the behaviour of the other sensors. Cospectra be-tween each of these other sensors and the Lyman-alpha are calculated. Based on the grey-shaded data set of Fig. 3, Fig. 9 shows the coherence and the phase of the different LI-COR sensors with the Lyman-alpha. Li2 provides the best coherence with Lyman-alpha, virtually equal to one over a large frequency range of 3 decades. It only drops off for frequencies beyond 1 Hz due to the spatial separation of the two sensors. No phase difference is observed over the same frequency range. In the phase spectrum the coherence is coded in the thickness of the dots as a phase can only be interpreted if a significant coherence between the signals is present. The marginally positive phase between Li2 and Lyman-alpha is a result of the advancement of the Li2 signal over 0.315 s. This constant shift can only approximate the more complex difference in the high-frequency response behaviour between Li2 and Lyman-alpha due to spacing and tubing. A smaller advancement, however, leads to reduced coherence and a trailing phase shift of Li2 for frequencies below 1 Hz. The other two LI-COR sensors (Li1 and Li3) have far less coherence with the Lyman-alpha. At low frequencies this reflects the drift of both vibration-affected sensors, and at high frequencies the noise masks potential coherence. Note that for all three LI-COR sensors the coherence inversely correlates with the amount of vibration the sensors are exposed to. The response behaviour of the Vaisala Humicap is more complex. At low frequencies (< 0.01 Hz) it agrees reasonably well with the Lyman-alpha. Then the coherence decreases with increasing frequency. The phase shift disappears around 0.4 Hz, but the level of coherence remains lower. To assess the sensor behaviour on the moisture flux calculation, Fig. 9b shows the covariance of the vertical wind speed and the humidity values from the different sensors after correction of the time shift. The spectral estimates are multiplied by the frequency, thus the area below the curves is proportional to the humidity flux. Flux estimates based on Li2 and Lymanalpha reasonably agree, but those calculated by the vibrationaffected LI-COR sensors are too low, most pronounced for Li3. The Humicap shows interesting behaviour: overestimation on a scale of minutes (0.02 Hz) and underestimation for higher frequencies, which compensate for each other to a certain degree. This behaviour seems to be a specific property of the Vaisala Humicap sensor. The latent heat flux determined with the Humicap amounts to 95 % of the reference value determined with the Lyman-alpha. Thus, for moderate conditions (10-20 • C, humidity values typical for mid-latitudes), the Humicap can be used for determining airborne latent heat fluxes with an acceptable error bar. However, the response function of the Humicap is asymmetric, with a different response time for decreasing and increasing humidity, and the response time becomes significantly slower for cold conditions like in the Arctic, where the sensor is not suitable for deriving latent heat fluxes.
Finally the total moisture flux as calculated by the five different moisture signals was compared. In Fig. 10 the integrated covariance spectra (ogives; see e.g. Sievers et al.,  It can be concluded from Fig. 9 that the fluxes for frequencies exceeding 1 Hz are negligible for these specific flight conditions. Therefore, the sampling frequency of 20 Hz is sufficient for airborne turbulent humidity fluxes.
The scale of eddies corresponding to the frequency of 1 Hz and the airspeed of 70 m s −1 is around 70 m. Contributions from eddies smaller than the size of a few tens of metres are negligible. This information is visible in the cospectra and in the ogive functions.
The results emphasise the scales on which turbulent transport of humidity takes place: fluctuations in the frequency range higher than 2 Hz do not contribute significantly to the overall humidity fluxes for these conditions, which are an air speed of 70 m s −1 , altitude of 100 m and the specific surface properties. This is different than flux measurements near ground, where high-resolution sampling and close sensor spacing are essential (Caughey and Palmer, 1979;Kaimal and Finnigan, 1994;Bange et al., 2002). Figure 11a shows the spectra of coherence and phase of the LI7500 signal (time-corrected and uncorrected) against the Lyman-alpha. For a frequency up to 3 Hz, the coherence for the time-corrected signal is higher than 0.8, and the phase shift is around 0 • ; thus the agreement of the two signals is high. The plot on the right represents the humidity flux for both sensors, i.e. the covariance spectra of the humidity and the vertical wind speed component. The areas under the curves are proportional to the humidity fluxes. The Lymanalpha and LI-COR signals agree perfectly in the frequency range up to 2 Hz. For higher frequencies, the humidity flux is negligible anyway. The effect of the time correction for the humidity fluxes can be seen for frequencies exceeding The overall effect is in the range of a few percent. As the LI7500 used on the Helipod flew on the Do128 as well (Li3), the excellent agreement with the Lyman-alpha here demonstrates that the vibrations of the Do128 are the main reason for poor performance there.

Recommendations for airborne applications
For calculating turbulent fluxes, the best temporal correlation of the sensors has to be determined first. The time shifts that were determined are not negligible and have to be taken into account. This is a standard procedure in the flux community (Moore, 1986). Time shifts for the LI-COR sensors are partly caused by internal processing, partly by different locations of the sensors and tube lengths. For the Do128 application, three different LI-COR sensors were subject to different vibration levels. For the Li1 and Li3 sensors, which were not set up to be isolated against vibrations, the correlation with the Lyman-alpha signal was significantly lower than for the Li2 sensor, which was. The different covariance spectra of the vibration-affected humidity measurements of the Li1 and Li3 sensors resulted in larger deviations of the latent heat fluxes compared to the latent heat fluxes based on the Lyman-alpha sensor. The vibrationisolated Li2 sensor showing high correlation with the Lymanalpha sensor resulted in comparable latent heat fluxes. However, the spectral behaviour of the vibrations had no direct linear impact on the humidity spectra of the Li1 and Li3 sen-sors, but the relationship is more complex. This is currently the subject of more detailed investigation.
For the Helipod application with lower vibrations, the humidity fluxes derived from the Lyman-alpha and the openpath LI-COR sensor (Li3) agreed very well after careful sensor calibration to absolute values, and correction of the time lag. Altogether, both open-path and closed-path LI-COR sensors are suitable high-resolution hygrometers for airborne application, if the vibrations are low.
In summary, some precautions have to be taken for employing a LI-COR sensor for airborne turbulent humidity flux measurements. The level of vibrations and its impact on the measurements should be evaluated particularly critically, and the spectra of the measurements should be checked for plausibility. The relative error might be significant, especially for small fluxes. Generally the temporal resolution of the LI-COR sensors of 20 Hz is sufficient for humidity flux calculations, as the contribution of frequencies above approximately 2 Hz is negligible, so 10-fold oversampling for sufficient amplitude retrieval is provided.
Data availability. The data is available upon request from the author.
Author contributions. AL wrote the paper, and FP, JH, AL and LL performed the data processing and analysis for Helipod and the Do128 flight. PH contributed to the analysis. AL, FP and JH planned and conducted the Do128 flight with different LI-COR humidity sensors. TS, EL, KK and AS planned and conducted the He-