COCAP measures carbon dioxide using a sensor from SenseAir AB based on their HPP (High Performance Platform) family of gas sensors . It is a nondispersive infrared sensor operating at a wavelength of 4.26 µm. The optical path has a length of 128 cm, which is obtained by 16 passes in an 8 cm long White cell . The total internal volume of the cell is 48 cm3. The mirrors are fabricated using plastic moulding which lowers the production cost. Heating elements and temperature sensors that enable temperature stabilisation of the optics are moulded into the mirrors. The sensor's mass is 80 g, including electronics.

Air that is drawn into COCAP's sample line is chemically dried as a first step. We use magnesium perchlorate (105873, Merck KGaA, Germany) in cartridges built in-house from aluminium (Fig. S4 in the Supplement). For improved drying performance we sieve the magnesium perchlorate and use only particles smaller than 2 mm. A single drying cartridge holds 1.5 g of magnesium perchlorate, which is sufficient to dry nearly saturated air at a temperature of 24 ∘C and a flow rate of 300 mL min-1 to a water mole fraction of less than 200 µmol mol-1 for 1 h.

Downstream of the drying cartridge a 0.2 µm filter (CM-0118, CO2Meter.com, USA) protects the pump, flow regulator and CO2 sensor from particles. The air flow through the gas line is driven by a diaphragm pump (NMS 020 B, KNF Neuberger GmbH, Germany) and throttled to a flow rate of 300 mL min-1 by the mechanical flow controller (PCFCDH-1N1-V, Beswick Engineering Inc., USA). At this flow rate the pump reaches a differential pressure of 350 hPa, whereas the flow controller is preset at the factory to a higher pressure difference of 700 hPa. We lowered the setting of the flow controller, but tests indicate that in the current configuration the flow rate is directly proportional to ambient pressure, i.e. the flow controller behaves like a needle valve. In future designs we recommend to better tune the flow controller for performance at low pressure differences or to reduce mass by replacing it with a needle valve.

The temperature of sample air is measured inside the inlet and the outlet of the CO2 sensor with miniature thermistors (NCP15XH103F03RC, Murata Ltd., Japan) that are suspended from 0.2 mm diameter wire (Figs. S2 and S3 in the Supplement). Pressure is measured with a compact piezoresistive pressure sensor (LPS331AP, STMicroelectronics, Switzerland). This model was chosen for its small physical size, high resolution and digital interface. As it lacks a connection port, we glued a 3-D-printed cap with a turned stainless steel port connector to the PCB so that it forms an airtight enclosure around the pressure sensor (Fig. S5 in the Supplement). The sample pressure is measured downstream of the CO2 sensor close to its outlet. As the flow between the measurement cell and this point is virtually unrestricted, we assume equal pressure; i.e. we treat the reading of the pressure sensor as the pressure of the air inside the CO2 sensor's measurement cell.

Finally, the mass flow rate of the sample air is measured with an analogue sensor (AWM3300V, Honeywell, USA). Downstream of the mass flow sensor the sample air is released from the gas line into COCAP's housing.

The measurement of features in temperature and humidity on the scale of tens of metres with UASs that can move several metres per second requires fast measurements with time constants on the order of 1 s. This calls for unrestricted or even forced ventilation of the sensing elements. To this end we designed a small (60 mm × 35 mm) printed circuit board (PCB) that can be mounted in the most suitable location for any UAS (Fig. S6 in the Supplement). Temperature is measured with a platinum resistance thermometer (Platinum 600 ∘C MiniSens Pt1000, IST AG, Switzerland), humidity is measured with a capacitive humidity sensor (P14 rapid in wired configuration, IST AG, Switzerland). Both sensors protrude over the edge of the PCB, which minimises thermal mass and improves ventilation. They are protected from mechanical damage and contamination by an aluminium tube (length 30 mm, inner diameter 12 mm). The tube is polished on the outside to prevent heating by the sun and anodised matte black on the inside which avoids reflection and focussing of sunlight onto the sensors. On fixed-wing UASs we mount the PCB facing forward, while on rotary-wing UASs we mount it facing upward in the downwash of the rotors.

The data from all sensors are recorded to a memory card by a data logger. For this purpose we modified an electronics board designed for the operation with SenseAir's HPP gas sensors (Hök Instruments AB, Sweden) by adding connectors that provide an interface for the GPS receiver and different digital sensors. The board runs firmware written for COCAP at the MPI for Biogeochemistry . Sensor data are recorded at 1 Hz. If a sensor samples at a higher rate, the measurements are averaged over 1 s. Data are continuously output via a serial interface and can be transmitted to a computer by means of an adaptor cable or a pair of radio modules (XBee 868, Digi International Inc., USA), allowing for real-time data visualisation and analysis. In addition, the data logger controls the built-in heaters of the CO2 sensor to a user-adjustable temperature.

The temperature inside and outside COCAP influences the measurement of carbon dioxide in different ways. First, the density of the sample air and therefore the number of absorbing molecules in the measurement cell is inversely proportional to absolute temperature (ideal gas law; ). Secondly, electronic components and the optical bandpass filter in the CO2 sensor exhibit drift with temperature . Thirdly, the intensity of the absorption lines of any gas depends on temperature, which makes the optical depth of the sample air temperature dependent . Fourthly, changes in temperature influence the emission strength of the IR source. Fifthly, thermal expansion may cause mechanical deformations of the optical assembly. We correct the xCO2 readings for drift with temperature (see Sect. ), but experience with earlier setups shows that for best possible precision an active stabilisation of temperature is needed.

The HPP CO2 sensor has built-in heaters and temperature sensors that are thermally coupled to the optical surfaces, the IR source and the optical detector. In an earlier version of COCAP we covered the CO2 sensor with isolating material and preheated the air stream with a heated tube that was connected to the sensor inlet. In this setup, the temperature at three points could be precisely controlled to 50 ∘C, but the distribution of temperature was inhomogeneous and varying with ambient conditions. Although a total of nine temperature sensors were present at different locations in COCAP, the uneven temperature distribution made it impossible to fully determine the system's thermal state and a satisfactory temperature correction could not be established.

Consequently, we redesigned the stabilisation system to minimise temperature differences around the CO2 sensor. This goal requires a setup where the heat exchange between different parts of the sensor happens much faster than dissipation of heat from the sensor to the changing environment. In many instruments this is achieved by means of massive bodies of copper or aluminium, which are characterised by high thermal diffusivity. However, as the mass of large metal parts is unacceptable for our application, we use air to transport heat inside COCAP. The lower thermal diffusivity of air is compensated for by forced convection driven by a fan. A heater, a temperature sensor and a custom PCB are connected and programmed as a control loop that stabilises the air temperature at 50 ∘C. The warm air stream circulates throughout COCAP's housing (Fig. S1 in the Supplement) so that the CO2 sensor is not only decoupled from changes in ambient temperature but all electronics boards benefit from the stabilisation as well.

While being flown on a UAS the temperature around COCAP can change by several degrees within seconds. Compensation for these changes requires a fast control loop, which calls for a heating element and a temperature sensor with low thermal mass. We built the heating element (Fig. ) from 38 surface-mount technology resistors (nominal resistance 360 Ω, length × width 2 mm × 1.25 mm, rated power 0.5 W) which are connected in parallel and provide a maximum heating power of 15 W at 12 V.

We installed the heating element just above the air inlet of the fan (RLF 35-8/12 N, ebm-papst Mulfingen GmbH & Co. KG, Germany). Placing the heating element at the outlet of the fan would reduce the response time, but would likely result in a less homogeneous temperature distribution across the air stream.

The temperature sensor (“air stream sensor”, Fig. ) in the control loop is a miniature thermistor (NCP15XH103F03RC, Murata Ltd., Japan). It is placed close to the detector of the CO2 sensor and oriented perpendicular to the flow of circulating air to minimise flow resistance.

Fan, heating element and air stream sensor are connected to an in-house-built control board (Figs. S7 and S8 in the Supplement) that runs a PID (proportional–integral–derivative) controller implemented in software. The temperature-dependent resistance of the air stream sensor is measured in a Wheatstone bridge configuration with a resolution of 1 mK at 50 ∘C. A trimmer potentiometer allows calibration of the temperature measurement. The control board detects whether the thermistor is shorted or disconnected and disables heating in such cases.

The power dissipation of the heating element is controlled by pulse-width modulation with 16 bit resolution. The control board monitors the current drawn by the fan and powers the heating element only if the fan is operating normally. This protection prevents damage to the heating element, which would overheat if the fan is disconnected or broken.

The performance of the temperature stabilisation under flight conditions is discussed in Sects.  and .

COCAP requires a source of electrical power with a voltage in the range 10.2–14.0 V. We use a single lithium polymer battery with a nominal voltage of 11.1 V. The battery life time depends on the ambient temperature, but generally we can operate COCAP for more than 1 h from a 2200 mAh battery weighing 200 g. By choosing a different battery size the package can be optimised for lower mass or longer run time.

Multicopters are rotorcraft with more than two rotors. They are generally easier to handle than fixed-wing aircraft due to their hovering ability and their built-in electronic control systems. Multicopters feature vertical take-off and landing as well as arbitrarily low vertical and horizontal flight speed. However, for aerodynamic reasons they typically have a lower endurance than fixed-wing aircraft of similar mass. Moreover, the strong mixing around and below the rotors gives rise to an uncertainty of the origin of a measured air sample. We alleviate this problem by sampling air through a carbon fibre tube with the inlet placed sideways or above the rotors.

So far we have flown COCAP on two different multicopters. One is an octocopter (S1000, DJI Ltd., China) with a total take-off mass of 9.2 kg. The other one is a quadcopter (custom-built, Sensomotion UG, Germany, and Ostwestfalen-Lippe University of Applied Sciences, Germany, Fig. S10 in the Supplement) weighing 4.8 kg with COCAP mounted. Both multicopters are electrically powered and provide at least 10 min of flight time.

Fixed-wing aircraft require a minimum air speed to fly and generally depend on an airstrip or additional equipment like bungees and nets for take-off and landing. However, they tend to have higher endurance and longer reach than multicopters. We carried out successful flight tests with an electrically powered fixed-wing aircraft (X8, Skywalker Technology Ltd., China) using a dummy that has the same mass and size as COCAP. The complete system weighed approximately 3.6 kg.

The influence of white noise on a measurement can be reduced by averaging over several samples. However, the precision achievable by averaging is limited by drift of the instrument over time; i.e. over long averaging periods the imprecision caused by drift becomes larger than the imprecision caused by noise. Allan or two-sample variance σy2(τ) is a measure commonly used to analyse these two sources of error. It is defined as σy2(τ)=12(Δy)2, where Δy is the difference between two consecutive averages over a period of τ and the angle brackets denote the expected value. The square root of the Allan variance is called Allan deviation σy.

To characterise noise and drift of COCAP we connected the analyser in an open-split configuration to a cylinder containing natural air with a CO2 dry air mole fraction of 384.3 µmol mol-1. This air sample was measured in a lab environment over a period of 24 h. The Allan deviation of this dataset (Fig. ) reaches a minimum of approximately 0.2 µmol mol-1 at an averaging period of 230 s.

For averaging periods shorter than 100 s the curve has a slope of -12 in the log–log plot, which is characteristic of white noise. At τC=1800 s, the typical time between field calibrations, the Allan deviation is approximately 0.7 µmol mol-1 and dominated by drift. Our correction scheme (see Sect. ) removes offset and gain errors at the point in time when the field calibrations were carried out and uses linear interpolation between the calibrations. Therefore, the largest uncorrected drift is expected to be lower than 0.4 µmol mol-1, the Allan deviation for 12τC=900 s. Figure  also shows the Allan deviation of COCAP's xCO2 measurements during the simulated flights described in Sect. . Forced ventilation and substantial changes in ambient pressure and temperature during the simulated flights lead to an increased Allan deviation compared to the measurements in a lab environment. Estimation of the expected drift for 12τC=900 s is not feasible due to artefacts that become visible at averaging periods beyond 400 s.

An instrument that is flown on a small UAS can be exposed to rapid changes in temperature and pressure, especially if the flight pattern covers a large range in altitude. To assess the measurement error caused by such changes, we simulated three consecutive flights between 0 and 1000 m above sea level (Fig. a, b) in an environmental chamber (CH3030, SIEMENS AG, Germany).

Temperature and pressures were controlled to approximately resemble the International Civil Aviation Organization Standard Atmosphere . Each simulated flight had a duration of 20 min with 5 min ascent and 15 min descent. After a 20 min break without changes in temperature and pressure this pattern was repeated. Only dry air samples from cylinders were supplied to COCAP; hence no drying cartridge was necessary. Otherwise, the analyser was operated in standard configuration, including pump and flow control. An open split with overflow upstream of the analyser's inlet ensured that air was sampled at the pressure of the environmental chamber at all times. First we measured two gas standards with CO2 dry air mole fractions of 397.5 and 447.4 µmol mol-1 for 5 min each at 15 ∘C and 100 kPa. Afterwards, air with 418.6 µmol mol-1 CO2 was supplied over a period of 2 h while the environmental chamber was simulating three flights as detailed above. Finally, we sampled the two gas standards again for 5 min each at 15 ∘C and 100 kPa. The xCO2 measurement by COCAP is affected by different sources of error: random noise, drift over time, calibration errors and drift with temperature and pressure. We reduced the noise by convoluting the time series with a Gauss window of 200 s full width at half maximum (Fig. c). A two-point calibration was derived from the standard measurements at the beginning and end of the test and applied to the full time series using linear interpolation in time. This cancelled out linear drift over time, but due to the influence of noise on the measurement of the gas standards and non-linearity in the instrument response, a calibration error remains. Drift with temperature and pressure is corrected for with the calibration curve described in Sect. , but this correction does not completely eliminate the effect of these parameters on the measurement result. The xCO2 time series in Fig. c exhibits a local minimum whenever pressure and temperature are minimal, with a maximum deviation from the assigned value of the cylinder (418.6 µmol mol-1) of -1.2 µmol mol-1 at 02:10 h. The bias of the mean over the whole test, representing the combined effect of the calibration error and drift with temperature and pressure, was -0.03 µmol mol-1. The standard deviation of the 1 Hz time series before convolution with a Gauss window was 2.7 µmol mol-1; the standard deviation after convolution was 0.41 µmol mol-1.

Figure  shows time series of temperatures measured at different points inside COCAP during the simulated flights.

Statistics of these time series are given in Table .

The differences in the observed patterns result from the air circulation inside COCAP's housing: first, heated air from the fan streams along the inlet tube of the CO2 sensor. Next, it passes the air stream sensor (see Sect ). Finally, it reaches the outlet tube and the detector of the CO2 sensor.

The air stream sensor is part of the control loop and therefore its temperature stays close to the set point of 50 ∘C. The inlet and outlet temperature sensors measure the temperature of the sample gas, which indirectly reflects the temperature of the air circulation because heat is exchanged through the walls of the inlet and outlet tubes. The temperatures of the outlet exhibit minima whenever the ambient temperature is reduced. This is caused by increased heat transfer from the circulating air to outside COCAP's housing. The inlet shows the inverse behaviour, i.e. increasing temperature under reduced ambient temperature, because it is located between fan and air stream sensor. In a colder environment the air has to be heated more to keep the temperature at the air stream sensor constant, so the temperature at the inlet rises.

The temperature of the detector varied qualitatively similarly to that of the outlet because detector and outlet are located close to each other. However, the temperature of the detector is approximately 5 K higher and the amplitude of the temperature variations is roughly 3 times lower than at the outlet. This is due to the detector's thermal coupling to the component block, which is temperature-controlled to 55 ∘C. Overall, the temperature stabilisation reduces the variability in the internal temperatures by 2 orders of magnitude compared to the changes in ambient temperature (see Table ).

Testing COCAP under realistic conditions requires the measurement of xCO2 in ambient air with varying composition. Specifically, changes in humidity are desirable to reveal potential problems with the drying of the sample gas and changes in CO₂ content allow validation of COCAP's calibration curve. To this end, a reference instrument must simultaneously sample the same air as COCAP. Laser-based instruments are widely used for high-accuracy measurements of greenhouse gases (e.g. ) and therefore suitable to be used as a reference, but at a mass of more than 10 kg they are too large to fly on any UAS available for this work. As an intermediate step between stationary indoor testing and UAS flights we integrated COCAP into the “Mobile Lab” , an instrumented van equipped with a CRDS analyser for carbon dioxide, carbon monoxide, methane and water (G2401-m, Picarro Inc., USA). Air was sampled at 3.5 m above street level. Field calibrations (see Sect. ) were carried out by injecting air from cylinders with slightly higher-than-ambient pressure into the sampling line at regular intervals.

As COCAP and the CRDS analyser were connected to the same sampling line, delay and mixing caused by tubing and inlet filter affected them equally. However, the flushing time for the analyser's measurement cells is different, which makes direct comparison of their readings inappropriate. In the following we explain how we handled this issue mathematically.

The flushing process can be described as a convolution of the CO2 dry air mole fraction at the inlet of the sampling line, xInlet(t), with an analyser-specific instrument function f(t): x(t)=(xInlet∗f)(t),=∫-∞∞xInlet(t-t′)⋅f(t′)dt′. The response x(t) of the analyser is the reported CO2 dry air mole fraction. Due to causality, x(t) cannot depend on future CO2 dry air mole fractions at the inlet. Hence, the lower limit of the integration can be set to zero: x(t)=∫0∞xInlet(t-t′)⋅f(t′)dt′. The instrument function f(t) is not known a priori, but it can be estimated from the response to a step change in xInlet(t). Such step changes occurred at the end of calibration measurements when the supply of gas standard into the sampling line was shut off. From the data we found that for both analysers the response xSC(t) to a step change can be modelled by an exponential decay of the form xSC(t)=(x0-x∞)⋅e-t/τ+x∞, where x0 and x∞ are the CO2 dry air mole fractions before and after the step change, respectively, and τ is the characteristic time constant of the flushing process. We determined time constants of 13 s for COCAP and 25 s for the CRDS analyser. To find the function f(t) we differentiate Eq. : ddtx(t)=ddt∫0∞xInlet(t-t′)⋅f(t′)dt′,=∫0∞f(t′)⋅ddtxInlet(t-t′)dt′ In the case of a step change at the inlet, the differentiation yields the Dirac delta function δ, scaled by the height of the step (x∞-x0): ddtxSC(t)=∫0∞f(t′)⋅(x∞-x0)⋅δ(t-t′)dt′,=(x∞-x0)⋅f(t). Rearranging and applying Eq. , f(t)=ddtxSC(t)x∞-x0,=(x∞-x0)⋅e-t/τ(x∞-x0)⋅τ,=e-t/ττ. This means that the instrument function of either analyser can be described with an exponential decay which has the same time constant as the analyser's step response. For practical reasons, we treat f(t) as equal to zero outside 0≤t≤5τ. Because no carbon dioxide is created or removed inside the analysers, the time integral over f(t) must be equal to one, necessitating normalisation of the truncated response function: f′(t)=0ift<0f(t)1-e-5if0≤t≤5τ0ift>5τ. Through the measurement process both analysers effectively convolute the xCO2 signal present at the inlet of the sampling line with their respective instrument function. To make the results comparable, we convolute the measurements of each analyser with the instrument function of the other analyser. If both measurements were perfect, this would yield identical results because convolution is commutative: xCOCAP⋅fCRDS=(xInlet⋅fCOCAP)⋅fCRDS,=(xInlet⋅fCRDS)⋅fCOCAP,=xCRDS⋅fCOCAP. Here xCOCAP and xCRDS are the CO2 dry air mole fractions measured by COCAP and the CRDS analysers, respectively. Convoluting each analyser's measurement with the instrument function of the other analyser can therefore be viewed as an equalisation of the flushing times of both analysers.

We carried out the experiment with the Mobile Lab in Boulder, Colorado, USA, on 15 October 2015. We drove up and down a road that covers 700 m in elevation (1650–2360 m above sea level), exposing COCAP to the same pressure changes that would occur during a flight at these altitudes. The temperature inside the van increased from 14 ∘C to 20 ∘C during the drive. Despite the substantial changes in ambient conditions, the measurements from both analysers agree to within 2 µmol mol-1 during most of the experiments (Fig. ).

Differences are mainly caused by limitations of the simple model for the instrument functions, which become apparent during fast changes in xCO2, and by sensor noise. They are reduced to less than 1 µmol mol-1 when high-frequency variations are filtered out. The negative bias of about -0.8 µmol mol-1 observed between 09:55 and 10:15 LT might be the effect of sunlight exposure. At the time of the experiment, the temperature stabilisation described in Sect.  had not yet been implemented, which is why COCAP was sensitive to changes in ambient conditions.

The so far highest flight of COCAP on a UAS was carried out in Lannemezan, France, on 20 May 2016 at 15:30 UTC (17:30 local time). COCAP was mounted under a custom-built multicopter (Sensomotion UG, Germany, and Ostwestfalen-Lippe University of Applied Sciences, Germany, Fig. S10 in the Supplement). Starting from an elevation of 600 m above sea level a maximum height of 430 m above ground level was reached. The flight took place under clear sky in a light breeze (2 m s-1 wind speed). It served as a real-world test of COCAP's temperature stabilisation (Fig. ).

While ambient pressure p changed by 5 kPa and ambient temperature TAmbient by 4.5 ∘C during the flight, the temperature of the air stream at the CO2 sensor's outlet TOutlet varied by only 0.13 ∘C and the temperature of the optical detector TDetector by only 0.02 ∘C.

In order to verify COCAP's in-flight measurements of ambient CO2 dry air mole fraction, we made a comparison to the atmospheric observatory Lindenberg. The Lindenberg observatory is part of the Integrated Carbon Observation System (ICOS, http://www.icos-ri.eu) and meets the World Meteorological Organization (WMO) Global Atmosphere Watch (GAW) recommendations for high-accuracy atmospheric trace gas measurements . The Lindenberg observatory (ICOS short name: LIN) is located in the eastern part of Germany (52∘10′ N, 14∘07′ E) in a flat, rural area. At LIN a 99 m mast is equipped with inlets at 2.5, 10, 40 and 98 m above ground level. Air is drawn from all inlets continuously, but only one sampling line is analysed at a time. The gas analyser is switched to a different sampling line every 5 min (“quasi-continuous sampling”). It measures carbon dioxide and methane dry air mole fraction.

We mounted COCAP on the same multicopter that was used in Lannemezan (see Sect. ) and carried out a total of 21 flights close to the mast (distance less than 150 m) on 18 and 27 October 2016, using the same setup on both days. During each flight, the multicopter ascended vertically to 100 m above ground level at a climb rate of 0.5 m s-1, followed by a descent at a rate of 2 m s-1. The same pattern was then repeated at approximately 70 m distance from the first ascent. Each flight lasted 9 min and the two ascents were separated in time by 4 min. The only exception was flight 7, which we had to abort after the first ascent due to a technical problem with the multicopter.

In flight, the multicopter mixes the air around it. To avoid artefacts in our measurements caused by this mixing, we sampled air from 70 cm above the rotors. Furthermore, for the analysis detailed below we used only the data collected during the ascents, i.e. when the UAS was flying into and sampling undisturbed air. In each flight, we carried out the second ascent upwind of the first ascent, which ensured that the mixing caused by the first ascent did not degrade the measurements during the second ascent.

On the evening of 18 October, the sky was cloudy with occasional drizzle, the wind speed was low (1.5 m s-1), and the lowest 100 m of the atmosphere was weakly stable. On the early evening of 27 October, conditions were similar, but without precipitation. After 21:00 LT on 27 October, the sky cleared up, followed by the formation of radiation fog.

At the mast's 2.5 and 10 m inlets, the variability of the CO2 dry air mole fraction was larger than above due to respiration fluxes from soil and vegetation that were intermittently mixed upwards by turbulence. This high variability makes these levels less suitable for comparison to COCAP, as our flights were not synchronised with the sampling at the mast. We were not allowed to fly higher than 100 m; hence the 98 m inlet was not well covered by the flight pattern. We therefore focus our comparison on the 40 m inlet of the mast.

After applying the calibration curve to the measurements of COCAP's CO2 sensor, we corrected for its temporal response by deconvolution. For each ascent, we then calculated the arithmetic mean of the measurements taken between a height of 30 and 50 m. Figure  shows these means together with the LIN measurements at 40 m plotted against time. Overall, there is good agreement between COCAP and LIN. The variability in COCAP's data is higher, likely caused by a low-pass effect of the mast's sampling system. Further differences are due to the measurements being taken 100–150 m apart and at different times. Finally, instrument noise leads to discrepancies. All these factors should have a zero mean effect, whereas a consistent bias between COCAP and the Lindenberg observatory would indicate a problem with the calibration. A change in bias over time would suggest instrument drift.

To better assess the presence of bias, we averaged the measurements from the mast's 40 m inlet over a period starting 20 min before and ending 20 min after the respective flight (Fig. a).

We then calculated the difference between the measurements by COCAP and LIN (Fig. b). Additionally, we estimated the noise level of COCAP's CO2 sensor. The correction for COCAP's finite time response by deconvolution has the side effect of amplifying high-frequency electronic noise. Therefore, we did not use the Allan deviation of the data described in Sect  but calculated the Allan deviation of the deconvoluted time series. During each ascent, the multicopter climbed from 30 to 50 m height in approximately 40 s. In analysing a period during which a standard gas was measured, we found an Allan deviation of 1 µmol mol-1 for τ=40 s. This number is represented as error bars in Fig. b.

Table  contains the mean difference between the measurements by COCAP and LIN. A bias of zero lies within 1 standard error of the mean difference. This is also true for both nights considered individually and for both ascents of all flights considered individually. Table  lists the results of statistical tests of three hypotheses: (1) no bias between COCAP and LIN, (2) no change in the mean difference between COCAP and LIN from 18 October to 27 October and (3) no change in the mean difference between COCAP and LIN from the first to the second ascends. None of the hypotheses was rejected (p>0.7 in all cases).

The physical connection between COCAP and the multicopter did not include a dedicated shock absorber (see Fig. S10 in the Supplement). Although COCAP's plastic foam housing and the flexibility of the mounting straps provided limited mechanical isolation, sudden movements and vibrations of the multicopter due to turbulence, rotor unbalance and flight manoeuvres have been partially transmitted to the measurement system. In theory, these mechanical disturbances could deteriorate the accuracy of the xCO2 measurements, e.g. by causing misalignment of the optical bench of the CO2 sensor. The data collected during the flights at LIN, however, do not exhibit increased noise levels or instrument drift compared to data collected on the ground, suggesting that the movements and vibrations did not degrade COCAP's performance.

We conclude that the measurements gave no indication of (1) calibration problems, (2) uncorrected drift of COCAP between 18 and 27 October, (3) drift of COCAP during flight or (4) degradation of COCAP's accuracy due to vibrations and sudden movements of the multicopter.