The Fendt site is located in southern Germany in the Alpine Foreland (Fig. ) at 47.833∘ N, 11.060∘ E (WGS84), 600 m above mean sea level.

The site lies in a flat valley bordered by a gentle slope to the east and a steep slope leading to a 100 m higher plateau to the west. The valley floor is dominated by pasture and some crops, predominantly maize, which in Germany is typically sown in April or May and harvested between September and November. The slopes to the east and west are covered with coniferous and mixed forest, respectively. Fendt belongs to the district Weilheim–Schongau, which has a population density of 139 km-2 (, 35th percentile of all districts in Germany).

While soil identification at the Fendt site resulted in Stagnosols at three locations, soil organic carbon (SOC) content was determined additionally at 20 locations within a regular grid covering an area of 300 m by 300 m. SOC content at 5 cm depth varied between 4 % and 11 %, while at 50 cm depth, values of up to 23 % were obtained. The highest SOC contents were observed at the eastern side of the regular grid where a peat area is located. According to , organically rich soils (Cambisols and Histosols) prevail within a 20 km radius around the Fendt site (Fig. a). The dominant land cover in this region includes crops, pasture and forest (Fig. b).

About 5 km south-west of the Fendt site lies an isolated, 988 m high mountain, the “Hoher Peißenberg”. Close to its summit the German Weather Service (Deutscher Wetterdienst, DWD) operates the Meteorological Observatory Hohenpeißenberg (MOHP) and the ICOS (Integrated Carbon Observation System) station Hohenpeißenberg (HPB, Fig. ).

Fendt is part of the TERENO (Terrestrial Environmental Observatories) network and is extensively instrumented for the purpose of long-term monitoring of land–atmosphere exchange . Complementary observations were made during the ScaleX 2016 campaign . In the following, we list only those instruments that produced the data presented in this publication.

During the ScaleX 2016 campaign, CO2 dry-air mole fraction at heights of 1, 3 and 9 m above ground level was measured with a cavity ring-down spectrometer by successive sampling of air through three inlets installed at a 9 m high mast. Each inlet was sampled once every 7.5 min, with occasional interruptions due to calibrations and other measurements. An EC system installed at 3.5 m height quantified the turbulent exchange of CO2. Air temperature as well as upward and downward radiation were measured at 2 m height. Two sets of automated chambers were operated to determine the total NEE or respiration flux of grass and soil. One set comprised four LI-8100 long-term chambers (LI-COR, Lincoln, NE, USA), two with a clear enclosure for measuring NEE and two with an opaque enclosure for measuring respiration . All four chambers covered an area of 317.8 cm2 and will be referred to as “small chambers” from here on. The other set consisted of five custom-built opaque chambers covering an area of 2500 cm2, referred to as “big chambers” hereafter. All the instruments mentioned so far were located close to each other, and the horizontal distance between any of the instruments and our UAS was always smaller than 200 m during the flights.

Besides the on-site instruments, we use two more data sources for our analysis. One is the observation of cloudiness at the Meteorological Observatory Hohenpeißenberg, recorded every hour either by a person or an automated instrument. We consider these 5 km distant measurements representative for Fendt, with a potential time lag on the order of 1 h in the case of synoptic events. The second non-local data source is the greenhouse gas monitoring system at the ICOS station Hohenpeißenberg, situated at 934 m above mean sea level. We use its measurements of the CO2 dry-air mole fraction at 131 m height above ground level, i.e. at 460 m above the Fendt site.

For the study presented here, temperature, pressure, relative humidity and CO2 dry-air mole fraction of ambient air were measured using COCAP, the COmpact Carbon dioxide analyser for Airborne Platforms, developed at the Max Planck Institute for Biogeochemistry in Jena (see , for a detailed description). COCAP was mounted below the multicopter. Air samples for the measurement of carbon dioxide dry-air mole fraction were drawn from an inlet placed 30 cm below and 20 cm to the side of the rotors (Fig. ).

The temperature and humidity sensor board, requiring strong ventilation for the fastest response, was placed directly below one of the rotors. The sensor for ambient pressure was located inside COCAP's housing, which was not hermetically sealed and therefore in equilibrium with ambient pressure.

The measurement principles employed by the different sensors as well as their measurement uncertainties are listed in Table . The uncertainty of the calibration is included in the measurement uncertainties reported.

During ScaleX 2016 COCAP was deployed on an S1000 multicopter (SZ DJI Technology, China) controlled by a Pixhawk autopilot (3D Robotics, Berkeley, CA, USA) running the Ardupilot APM:Copter v.3.3.3 firmware. Take-off mass of the whole system was 8 kg. The multicopter was powered by three lithium polymer batteries with a voltage of 22.2 V and a capacity of 5000 mAh each, achieving a maximum flight time of 12 min. Our special flight permit included nighttime flights, but because the take-off mass of our UAS exceeded 5 kg, all flights were limited to a maximum height of 150 m.

A multicopter as a rotary-wing aircraft counterbalances gravity by accelerating air downwards through the movement of its rotors. The resulting displacement of air can interfere with in situ measurements, because air might be sampled at a location where it would normally not reside. In addition, volumes of air originating from different locations can be mixed together. The greater the displacement and mixing caused by the UAS, the greater the potential impact on the measurement of a gradient, for example. Air movement below and above the rotors is not symmetric: below a rotor, air is pushed downwards as a directed stream with high speed. In contrast, the air flow towards the rotor comes from different directions and has a lower speed. The reader can easily confirm this with a fan or a hair dryer: while the outflow of air can be felt metres away, the inflow is hard to sense even near the rotor.

In view of the asymmetric flow pattern, we expect that during ascent of the UAS air parcels are measured with negligible displacement from their undisturbed location. During descent, however, the sensors are moved into a volume that potentially has been flushed with air originating from several metres above. During hovering at a fixed location or during purely horizontal movement, the sensors might reside in a partially closed flow loop that extends below and to the side of the multicopter, effectively measuring a mixture of air from different locations.

For the study presented here, flying near the ground can have a particularly strong influence on the measurements for three reasons. Firstly, downward motion of the air stops at the ground and displaced air must move laterally or upwards, making a fast flow path back to the UAS more likely. Secondly, in our nighttime experiments the air near the ground is stably stratified. Therefore, air pushed downwards by the rotors experiences a restoring upward force, increasing the chance that closed flow loops form. Thirdly, the strongest gradients in temperature and CO2 dry-air mole fraction are present close to the ground, hence even a small displacement of air can have a large effect on the measured values.

In the case of considerable horizontal air speed, due to either wind or horizontal flight, the rotor-induced airflow should have a smaller effect on measurements because the sampling system is moving away from air that has been displaced. We investigated this effect by flying horizontally at different speeds over a homogeneous meadow (see Sect. ).

Based on the considerations above and the data presented in Sect.  and , we determine the NBL budget only from those measurements that were taken during ascent of the multicopter. The sensitivity of the NBL-derived fluxes to inclusion of hover and descent data is discussed in Sect. . Furthermore we discard COCAP's xCO2 data collected below 9 m height for the calculation of the NBL budget. Instead, the lowest part of the xCO2 profile is defined by the stationary measurements at the 9 m mast at 1, 3 and 9 m height. Pressure and temperature at these levels are interpolated from COCAP's measurements. During flight, the horizontal distance between COCAP and the 9 m mast was less than 150 m at any time. Hence, we do not expect pronounced horizontal gradients in xCO2 between the measurement locations. In Sect.  we discuss how the NBL-derived fluxes are affected if the data from the 9 m mast are not used.

On a moving platform the finite response time of sensors can be a source of measurement error, as the response time distorts the attribution of data points to time and location. COCAP's pressure and temperature sensors are fast enough for this effect to be neglected, but both the humidity and the CO2 sensor require correction.

The response of a capacitive humidity sensor can be expressed following : 1dUmdt=k(Ua-Um). Ua and Um are ambient and measured relative humidity, respectively. The coefficient k is inversely related to the sensor's response time and might be temperature-dependent. Solving Eq. () for Ua provides a simple way to compute true humidity from measurements. We use a fourth-order Savitzky–Golay filter with a length of 15 samples to compute dUmdt while keeping high-frequency noise at an acceptable level. The coefficient k=14s was determined by an optimisation that minimises the difference between the corrected humidity profiles for ascent and descent. We tested a linear and quadratic dependence of k on ambient temperature, but we found no improvement that would justify the additional degrees of freedom in the model.

The response of COCAP's CO2 sensor is more complex. Its response to step changes in CO2 dry-air mole fraction can be approximated as 2xSC(t)=x0if t<tda(x0-x∞)e(td-t)/τ1+(1-a)⋅(x0-x∞)e(td-t)/τ2+x∞if t≥td. Here x0 and x∞ denote the CO2 dry-air mole fraction before and infinitely long after the step change, respectively, and td is the sensor's dead time.

We determined the coefficient a, the dead time td, and the time constants τ1 and τ2 from experimental data collected in the field. With COCAP running in flight configuration, i.e. with the inlet tube attached, we connected a tube with gas flowing from a cylinder. We observed a dead time of td=5s between making the connection and the first change of COCAP's reading. The remaining parameters were found by least-squares regression of Eq. () to the data, yielding τ1=27s and τ2=3.2s.

Ignoring noise and calibration error, any CO2 signal xa is reported by COCAP as the convolution of xa with the CO2 sensor's instrument function f (see ): 3xm(t)=(xa⋅f)(t) with 4f=0if t<td1x∞-x0⋅dxSCdtif t≥td. As xSC is known from experiments, f can be calculated. The ambient signal xa can be recovered from the measured signal xm by deconvolution (Fig. ). We carried out the deconvolution in Fourier space where it is equal to a division. In the numerical implementation it is important to discretise f in a way that does not underestimate the slope of f between the time steps td and td+Δt, because doing so would lead to a strong enhancement of the noise during the deconvolution of xm with f. The opposite error, i.e. overestimating the slope between td and td+Δt, is less critical and just results in a slight smoothing.

For a parcel of air in the atmosphere the following continuity equation holds Eq. 6.2: 5σ=∂c∂t+∇⋅(cu),6=∂c∂t+c(∇⋅u)+u∂c∂x+v∂c∂y+w∂c∂z. Here σ is the strength of a volume source (or sink) of carbon dioxide (µmolm-3s-1), c is the concentration of carbon dioxide and t denotes time. The components u, v and w of the wind vector u point towards east (x direction

Only here and in Eq. () x does denote a coordinate in space. Elsewhere in this publication x denotes the dry-air mole fraction of a substance.

The columns of air probed at Fendt at different times had a different history, depending on the wind field and atmospheric stability. Atmospheric transport models can identify the surface areas that have contributed to an observed tracer concentration, i.e. the footprint of an observation. We simulate atmospheric transport with STILT, the Stochastic Time-Inverted Lagrangian Transport model , which is based on NOAA's HYSPLIT particle dispersion model . In our configuration, STILT launches 10 000 air parcels at different heights (see below) at every full hour during the period of our NBL measurements. Driven by meteorological data with a resolution of 0.1∘ × 0.1∘ from the ECMWF IFS (European Centre for Medium-Range Weather Forecasts Integrated Forecast System), STILT calculates the back trajectories of these parcels until 10 h in the past. For each time step of the simulated transport, the model determines the sensitivity of the CO2 concentration in the parcel to the CO2 flux at the surface. To do so, the height up to which mixing occurs is estimated from the meteorological data using a modified Richardson number method . Surface fluxes influence air parcels within a column that extends from the surface to one-half this height in each time step .

The back trajectories calculated by STILT are then aggregated into mole fraction footprints on a regular grid with a resolution of 2km×2km. As explained in the previous section, we assume the xCO2 distribution to be homogeneous in the lateral and horizontal directions at time t0. We therefore restrict the aggregation to that part of each back trajectory that lies between t0 and the time of measurement.

A single STILT run determines the sensitivity of an observation at a specific height to upwind fluxes. Formally, the mole fraction footprint of a measurement taken at the geographic location (l1,l2) at time t and observation height z can be written as f(l1,l2,z,t∣lG1,lG2). As all our measurements were taken at the same horizontal location, the dependency of f on l1 and l2 will be omitted hereafter. The mole fraction footprint is a function whose value is the sensitivity to the surface flux at the grid cell specified by (lG1,lG2) in units of [f]=µmolmol-1µmol-1m2s. To determine the relative contribution of surface fluxes in different areas to our NBL-derived fluxes, we need a different but related function, the flux footprint fF with units [fF]=µmolm-2s-1µmol-1m2s=1. The flux footprint is calculated by integration over an array of mole fraction footprints for different measurement heights, i.e. analogous to Eq. () term A and Eq. (): 14fF(t|lG1,lG2)=∫0ztpd(z,t)RT(z,t)⋅f(z,t|lG1,lG2)dzt-t0. Dry pressure pd and air temperature T at time t and height z are inter- or extrapolated from the measured profiles. The ensemble of mole fraction footprints comprises footprints for 12 different measurement heights between 10 and 120 m in 10 m steps.

The meteorological data we use have a horizontal resolution of 0.1∘ × 0.1∘, corresponding to 11km×8km at the latitude of Fendt. Terrain features that are smaller than a grid cell, like the valley slope to the west of the Fendt site, cannot be represented at these resolutions. The vertical resolution of the meteorological data depends on height above ground. The lowest layer extends from the ground to 10 m height, and the following five layers extend from the top of the previous layer to 31, 55, 80, 108 and 138 m. The temporal resolution of the ECMWF IFS data is 3 h.

The uncertainty of COCAP's xCO2 measurements due to drift and calibration errors is about 1 µmolmol-1 . The additional uncertainty caused by noise is dependent on the data treatment, as can be seen from Fig. . This Allan deviation plot is based on measurements of a gas standard (xCO2=447.44µmol⋅mol-1) over a period of 1.4 h, taken in the field on 6 July 2016.

The curves illustrate that deconvolution amplifies noise in the data by a factor of 7 if no averaging is applied (τ=1s). However, if more than 100 samples are averaged (τ≥100s), the difference between original and deconvoluted data becomes negligible and the uncertainty of the average due to noise is lower than 0.5 µmolmol-1. All our column integrals (see Sect. ) have a sample size larger than 100.

Figure  also shows that the Allan deviation of deconvoluted data that have been smoothed by convolution with a Gaussian function of 10 s full width at half maximum (FWHM) increases between τ=1s and τ=5s. This increase is an artefact caused by the autocorrelation that the smoothing induces. If COCAP were perfectly calibrated and exhibited no drift, any single point in the smoothed data set would have an uncertainty of 2.1 µmolmol-1 (corresponding to τ=5s), not 0.8 µmolmol-1 (corresponding to τ=1s).

From the data collected during ScaleX 2016 we calculate NEE for the nights 6–7 July and 9–10 July. The sun set at 19:15 and 19:14 UTC on 6 and 9 July, respectively, and rose at 03:25 and 03:27 UTC on 7 and 10 July, respectively. Both nights were free of precipitation. Cloud cover was high during the first night (see Fig. a), but the pronounced negative net radiation (Fig. b) indicates that the clouds were mostly transparent for outgoing long-wave radiation.

On the second night the sky was clearer, resulting in a steadier radiation balance. During both nights, strong radiative cooling was observed. Air temperature decreased from 18 to 9 ∘C and from 24 to 11 ∘C over the course of the first and second nights, respectively (Fig. c). In combination with low wind speeds (Fig. d) this led to the development of a pronounced temperature inversion at the surface, i.e. a stable NBL. The change from positive to negative net radiation occurs approximately at t0=18:00 UTC on both nights.

We carried out a total of 27 flights during the ScaleX 2016 campaign. For the calculation of a NBL budget, we analyse those flights that took place after t0=18:00 UTC and reached a height of at least 125 m. Twelve flights fulfil these criteria: flights 4 through 10 (first night, Fig. ) and flights 19 through 23 (second night, Fig. ). For display in panel (b) of Fig.  and the CO2 dry-air mole fraction has been smoothed with a Gaussian filter of 5 s FWHM. To prevent distortion in the vertical direction, the height above ground level z has been filtered the same way. For this reason, the upper end of the profiles in panel (b) is at a slightly lower height than in panel (a). Calculation of the NBL fluxes (see Sect. ) was carried out with unfiltered xCO2 and z.

The times given in Figs.  and are the midtimes of the flights rounded to a full 10 min for readability. The exact times of take-off and landing are provided in Table .

During the first night, a stable NBL can be identified from the UAS profiles for flights 6 through 10. The upper end of the temperature inversion aligns with the top of the CO2 enhancement to within 10–20 m. At the time of flights 6 and 8 through 10, the NBL has a height of 50–70 m, whereas the profile from flight 7 indicates a greater NBL height of ≈100m. We interpret this as an indication that the column measured in flight 7 has been influenced by katabatic inflow of cool, CO2-enriched air at some point during the night, potentially hours before the flight and kilometres away from Fendt. This interpretation is supported by the flux estimates (see Sect. ). The profiles from flight 5, which exhibit virtually no gradient, are discussed below.

During the second night, a stable NBL with a height of 50–70 m is visible in all profiles. The flight pattern had been refined and included two ascents and descents far enough from each other to avoid disturbance of the measurements in the second part by air movements caused during the first part. These redundant measurements give insight into the reliability of the measurement system and the variability of temperature and CO2 dry-air mole fraction on small temporal and spatial scales. The data from flight 21 agree well between each of the two ascents and descents, suggesting that disturbances by the UAS, instrument noise and drift are small compared to the observed signals. Flights 22 and 23 were carried out only 1 and 2 h later, respectively, and followed the same flight track. However, the data from these flights reveal considerable differences between each of the two ascents and descents, especially in xCO2 for heights below 50 m. We interpret this as natural variability on the scale of the flight track, i.e. ≈200m in horizontal distance and ≈3min in time. This small-scale variability is a source of random error in NBL budgets. In our flux calculations multiple ascents during the same flight are effectively averaged, resulting in a reduction of the random error.

The xCO2 profiles measured during flights 20, 22 and 23 all exhibit a non-zero gradient with height in the region above the strong inversion, indicating that some CO2 has escaped the stable NBL. This is supported by the profiles of virtual potential temperature, which are more inclined above the NBL in comparison to the first night. Both features might be the result of intermittent turbulence, a phenomenon often observed at night that can have different causes (see , and references therein). Our budgets include the measurements up to 125 m height, so any CO2 that has been transported higher than this is missing in the budgets. In future campaigns, flights with a greater maximum height could be carried out to quantify the effect this has on the NBL-derived fluxes, or to extend the budget vertically.

The flight pattern used during the second night also included two horizontal transects at 10 m height that were flown at a ground speed of 3 ms-1. Their purpose was to enable measurements of undisturbed air near the ground, but later analysis of flight 14 (see Sect. ) revealed that the ground speed was insufficient to fully reach this goal.

The profiles for flight 5 are close to straight vertical lines, which would indicate a well-mixed atmosphere. However, they were measured under low wind speed 1 full hour after the surface radiation balance became negative, i.e. under conditions favourable for the development of a stable nocturnal boundary layer and accumulation of CO2 near the ground. This apparent contradiction can be explained by comparing COCAP's data to tower-based measurements. Figure a shows the CO2 profile taken by COCAP together with data from the 9 m mast and from HPB (see Sect.  and ).

The diagram includes those measurements from the mast that fall into the time interval from 15 min before take-off to 15 min after landing. They reveal that the CO2 dry-air mole fraction near the ground was increased relative to the upper two-thirds of the profile and fluctuated strongly, e.g. between 450 and 650 µmolmol-1, at 3 m height. These observations are in line with a weakly stable layer near the surface: surface fluxes accumulated in this layer, but weak turbulent events caused by wind shear, for example, occasionally spread them out to higher layers. The disturbance by the multicopter during take-off or landing prevented COCAP from capturing this accumulation. On the other hand, the higher part of COCAP's profile, taken in the residual layer that is left over from the daytime mixed layer, matches the mean CO2 dry-air mole fraction measured at HPB during the time interval from 1 h before take-off to 1 h after landing. This agreement confirms that COCAP was working properly during the flight.

The profile from flight 8, carried out later in the same night, is consistent with the measurements at the 9 m mast (Fig. ). We see two reasons for this difference to flight 5. Firstly, the radiative cooling (see Fig. ) at the time of flight 8 (23:10) was stronger than at the time of flight 5 (19:10). The temperature gradient near the ground was not resolved during flight 5, but the weaker radiative cooling compared to the later flight has likely resulted in a weaker temperature inversion that allowed more vertical displacement of air by the multicopter. Secondly, the thicker NBL at 23:10 with a less steep CO2 gradient close to the ground means that potential sampling of air parcels originating from above or below the multicopter did not affect the measurements during flight 8 as much as during flight 5.

At heights above 70 m the CO2 profile from flight 8 approaches the measurements at HPB, indicating that the stable NBL retains most of the surface-emitted CO2. Likewise, the CO2 profiles of all other flights come near the measurements at HPB above the NBL (not shown). This suggests that any transport of CO2 across the top of the NBL is small in magnitude.

The measurement of continuous profiles of the CO2 dry-air mole fraction up to heights of 100 m or more has been challenging in the past. In some studies, NBL budgets were therefore based on a measurement near the ground and an assumed gradient up to the top of the NBL. However, the complex shape of the profiles displayed in Figs.  and suggests that neither the assumption of a constant (see ) nor a linearly decreasing (see ) CO2 dry-air mole fraction would properly represent the conditions at Fendt. The detailed structures resolved in our measurements also indicate great potential of combined measurements of meteorological parameters and trace gas mole fractions for studying small-scale phenomena in the NBL.

The potential virtual temperature measured at heights between 10 and 60 m is generally higher during descent than during ascent. This effect is more pronounced for flights 19 through 23 (Fig. ), likely due to the stronger temperature gradient compared to flights 5 through 10 (Fig. ). The observed difference supports the reasoning of Sect. : As the multicopter descends, the onboard sensors measure warmer air that was pushed downwards by the rotors. Close to the ground (at heights below 10 m) closed flow loops start to form and colder air from below the multicopter reaches the sensors during descent, as can be seen in the profiles from flights 6, 8, 9, 10 and 23.

Systematic differences between ascent and descent are less visible in the profiles of CO2 dry-air mole fraction, likely due to a larger variability of CO2 within the nocturnal boundary layer. This variability is reflected in the difference in xCO2 between each of the two ascents and descents in the flights 19 through 23, especially flights 20 and 23.

Flight 14 was dedicated to the investigation of vertical mixing during horizontal movement at different air speeds. It was carried out on 7 July at 22:15 UTC. Winds were particularly low that night (on average 0.3 ms-1 between 22:00 and 22:30 UTC), and hence ground speed of the UAS was approximately equal to air speed. A stable nocturnal boundary layer had developed, as can be seen from the profiles of θv and xCO2 measured during an earlier flight at 20:15 UTC (see Fig. a and b).

The UAS flew a spiral pattern at a height of 10 m above ground with decreasing ground speed (Fig. c). Throughout flight 14, COCAP's air inlet faced the direction of movement. The flight took place over a flat, homogeneous meadow. Hence, we assume that terrain and vegetation had caused no heterogeneity in the lateral distribution of temperature and CO2. We analyse three sections of nominal speeds of 5, 3 and 1 ms-1. Figure d shows the median virtual potential temperature and CO2 dry-air mole fraction for each section. The standard error of the median was calculated by bootstrapping with 1000 samples generated from the empirical distribution of the measurements pp. 43 and is depicted as horizontal and vertical bars.

The decrease in virtual potential temperature with decreasing speed in Fig. d suggests that upward mixing of air from lower layers has a stronger influence on the measurements at lower speed. Likewise, the CO2 dry-air mole fraction measured at 1 ms-1 is 20 µmolmol-1 higher than during faster flight. However, we did not observe a significant difference in xCO2 between a ground speed of 3 and 5 ms-1. The sample inlet for the CO2 measurement extends 20 cm to the side of the rotors, while temperature and humidity are measured directly below a rotor (see Fig. ). As the sample inlet was pointing forward throughout the flight, it might have mostly avoided partially closed flow loops during movement at 5 ms-1, while the temperature and humidity sensors were still affected.

In summary, our results suggest that measurements taken during the ascent of the multicopter are more reliable than those taken during descent and hover. Horizontal transects at low heights can yield measurements that are contaminated with air from below the sampling height. This contamination is lower at higher horizontal air speed, because the multicopter moves away from the vortices it has created. Our experiment does not answer the question of whether a horizontal speed of 5 ms-1 at 10 m height is sufficient to avoid the contamination entirely.

The first profiles of the first and second nights were taken at 18:10 UTC (flight 4) and 20:10 UTC (flight 19), respectively. Hence, flight 4 is representative for the xCO2 profile at t0=18:00 UTC, but flight 19 is not. We therefore need an estimate for the profile at t0. Due to the convective mixing that takes place during the day, the CO2 dry-air mole fraction within the boundary layer is nearly independent of height, an assumption that is supported by the profile from flight 4 (see Fig. ). Assuming further that all surface fluxes were trapped in the developing NBL, air parcels above the NBL height should have preserved the CO2 dry-air mole fraction of the column between t0 and the time of the first flight. Consequently, we assume the whole column xCO2(t0,z) to be equal to the mean dry-air mole fraction of the first measured profile between 50 and 125 m height. For consistency we apply this approach to both nights.

The fluxes we calculated from the NBL budgets are listed in Table , given as the amount of CO2 per time and surface area.

The storage flux in Table  corresponds to term (A) in Eq. (), the subsidence flux corresponds to term (B) and the total flux is equal to S‾, i.e. the NEE averaged over the time from t0 to tF. During both nights, horizontal convergence of air masses led to lifting and consequently a negative subsidence flux. However, the subsidence flux was small compared to the storage flux, accounting for about 1 % of the total flux. An important consequence of the low subsidence flux is that errors stemming from the simplified model of the NBL growth (see Sect. ) have only a minor influence on the uncertainty of the total flux.

The plausibility of our results can be checked against EC and chamber measurements taken at Fendt. Both the EC and the chamber measurements observed only the fluxes from the pasture at the site, while the NBL budget has a larger footprint. Even at low wind speeds of 0.5 ms-1 air parcels travel 1.8 km every hour. Therefore, the NBL budget also includes sources that are located several kilometres apart. Given the land cover around Fendt, those sources likely include forests, crop fields and potentially some residential areas (see Figs.  and for exemplary footprints). Nevertheless, as pasture is the dominant land cover in the area, all three methods should agree on the order of magnitude of the CO2 flux at night.

No EC measurements of acceptable quality are available for either of the nights we probed the NBL (Fig. ). Conditions of strong radiative cooling combined with weak wind resulted in stable conditions and a violation of the assumptions underlying the EC technique. As a backup, we calculated the mean diurnal cycle from the EC measurements taken between 4 July 2016, 00:00 UTC, and 11 July 2016, 23:59 UTC, a period that includes all our flights and was reasonably consistent in the diurnal variations in temperature. The result is presented in Fig. . All fluxes calculated from the NBL budget lie within the range of NEE observed by EC between 18:00 and 01:00 UTC (6–16 µmolm-2s-1). The later the flight at Fendt took place, the lower the NBL-based average NEE, indicating a decreasing flux over the course of the night. We interpret this, at least partially, as an effect of the temperature decrease during the night (Fig. ), which reduces respiration. In contrast, NEE measured by the EC station increases during the night. However, an increase in respiration over the course of the night is implausible. Given the small number of EC measurements of acceptable quality, this apparent trend is likely an artefact.

Figure  shows the NBL-derived fluxes in comparison to chamber measurements. Data from the small chambers are available only for the second night. Opaque chambers measure respiration, while clear chambers, the EC station and the NBL budget observe NEE. Therefore, a comparison of the fluxes obtained with these different techniques is only meaningful when photosynthesis is low or absent, i.e. roughly between sunset and sunrise. The convergence of the fluxes of the clear and dark chambers just after 18:00 UTC suggests that photosynthesis has largely ceased as early as t0. Hence, throughout the time span for which we determine the NBL budget NEE is dominated by respiration, and all the different techniques are comparable. Surprisingly, the measurements with the big chambers yield fluxes only one-third as high as obtained with the small chambers, even though all chambers were deployed close to each other on the same meadow. Despite careful investigation, the reason for this discrepancy has not yet been found. The NBL budget agrees in magnitude to the fluxes measured with the small chambers. Similarly to the NBL budget, all chamber measurements exhibit a negative trend in fluxes over the course of both nights.

In addition to in situ measurements at Fendt, the range of nighttime NEE of pasture and forests observed in other studies at central European sites with a climate similar to Fendt (Cfb or Dfb in the Köppen–Geiger classification according to ) provides a plausibility check for the NBL budgets (Table ).

We exclude crop fields from the comparison, as their NEE depends heavily on crop type and time of harvest. Compared to the literature values, NEE for Fendt derived from the NBL budget is on the high end of ranges reported for pasture and higher than most fluxes reported for forests. One explanation is that our measurements took place on two fair weather days in the warmest month of the year 2016, which likely resulted in higher respiration than observed on average over a longer period. Furthermore, Fendt lies in a region with organically rich soils (Fig. a). Soil organic carbon content has been shown to be positively correlated with microbial biomass , suggesting particularly strong respiration under beneficial conditions. This explanation is supported by the measurements at Mooseurach (Table ), a drained peatland forest 20 km to the east of Fendt, where respiration fluxes of up to 15 µmolm-2s-1 have been observed.

Another potential cause for higher fluxes observed with the NBL budget relates to the terrain at Fendt. At night, katabatic flows of cool, CO2-rich air can stream down the steep slope west of the measurement site. Though Fendt is situated in a valley with only a shallow slope to the east, this inflow might lead to localised lifting of air that is not accounted for in the ECMWF IFS data and hence not included in our calculation of subsidence. The increased NBL height and high variability in the lowest 50 m observed during flight 7 as well as the higher flux derived from the NBL budget are an indication of such an inflow event.

The NBL budget is influenced by measurement uncertainty, incomplete knowledge about the state of the atmosphere and data selection. In order to quantitatively assess the influence of these factors on our results, we changed the procedure of calculating fluxes in one of the following ways:

by adding a bias of ±2 m to the altitude measurements;

Example flux footprints of one NBL budget of each night are visualised in Figs.  and .

The footprint depicted in Fig.  was calculated for a column of air passing Fendt on 6 July 2016 at 21:00 UTC, i.e. close to the time of flight 6. The 1 % contour of the footprint encloses an area of 60 km2, which accounts for 60 % of the total sensitivity. The land cover map suggests that the NBL budget represents mainly the respiration of forests, pasture and croplands north of Fendt, with little contribution from urban areas.

The footprint depicted in Fig.  was calculated for a column of air passing Fendt on 9 July 2016 at 21:00 UTC, i.e. close to the time of flight 20. The 1 % contour of the footprint encloses an area of 80 km2, which accounts for 70 % of the total sensitivity. Again, the NBL budget is mainly influenced by forests, pasture and croplands.

The footprints for other times during the two nights are similar in size, i.e. on the order of 100 km2. They mostly cover the sector within 20 km north-west to north-east of Fendt.

We recognise that the relatively low spatial and temporal resolution of the ECMWF IFS meteorological model entails errors in the transport modelling. Variability of the horizontal wind component within a grid cell and on timescales below 3 h is neglected, possibly resulting in an underestimation of the footprint size. Likewise, terrain features that are smaller than a grid cell are not represented in the meteorological model. However, as our NBL budgets cover timescales of 1–7 h and the footprints extend over many grid cells, sub-scale variability should play only a minor role. We are therefore confident that the model results provide a reasonable estimate of the region seen by the NBL budget method.