The SWUF-3D UAS are commercially available racing drone frames of type Holybro QAV250. They are powered by a Pixhawk 4 Mini autopilot. Depending on the batteries which are used for the specific operation, the QAV250 can reach flight times up to 25 min. In this study, only batteries with a lower capacitiy were available, so that maximum flight times were 15 min and therefore, the hover periods were set to a maximum of 12 min. Further characteristics of the UAS are described in . In a fleet configuration, a multitude of drones can fly pre-defined routes synchronously and automatically. Up to twenty drones were operated during the FESSTVaL campaign . At the research wind park WiValdi, ten drones were operated simultaneously in multiple campaigns before . Through field tests and wind tunnel calibration , the accuracy of wind speed measurement was found to be well below 0.5 m s⁻¹ and mostly below 0.3 m s⁻¹. The fleet of drones was deployed in the past to investigate spatial correlation and coherence in the ABL as well as wind speed deficit, turbulence and distinct vortices in wind turbine wakes .

The implementation of a compact temperature and humidity sensor on a custom UAS requires a design of a sensor carrier that matches the UAS design. We present here what we call the SWUF-T temperature and humidity module. The concept for the SWUF-T module is to provide a robust commercial and factory-calibrated temperature and humidity sensor along-side a fast and self-calibrated fine-wire platinum resistance thermometer (FWPRT). The commercial sensor is of type HYT.R411 (in previous versions HYT271) by Innovative Sensor Technologies (IST AG). The FWPRT consists of a 13 µm platinum wire of approximately 60 mm length, yielding a resistance R≈50Ω. It is connected to an Analog Devices MAX31865 resistance-to-digital converter chip in a four-wire sensor connection setup. The MAX31865 produces a constant current through a reference resistor (here: 100 Ω) and the platinum wire. The voltage difference is a measure for the resistance of the wire and can be directly converted to a temperature value based on the known temperature-dependent properties of platinum. The I2C interface of the HYT sensors as well as the SPI interface of the MAX31865 are made available at the GH connector of the SWUF-T board, but can also be routed to an Arduino Nano Every Board that can be attached on top. If the Arduino Nano Every is attached, the GH connector provides a UART interface to the Arduino through which both, HYT and FWPRT measurements are transmitted e.g. via MAVLink protocol. The latter is the setup which is used in this study to connect SWUF-T measurements to the Pixhawk 4 Mini autopilot board. Figure  shows the principle design (a) and pictures of the board without (b) and with (c) sensor housing. The housing is designed to shield the sensors from incoming radiation, while allowing passive ventilation. showed that already slow airspeeds provide sufficient ventilation for forced convection on the thin wire and thus omit radiation and self-heating effects. The radiation can however strongly effect the HYT sensor, so that a shield is recommended.

and recently showed by means of CFD simulations and field measurements that the best position to place a flow sensor on a multicopter is upstream in front of the rotors. Especially since we are operating with the weather-vane mode that will always point the y-axis of the UAS body-frame into the main wind direction, we place the SWUF-T sensor upstream in the main axis, too. The sensing elements of the sensor in our setup is 50 mm in front of the rotor plane. Recent CFD simulations of the QAV250 airframe showed that at this position, without any inflow wind speed, a flow of approximately 2 m s⁻¹ is induced by the rotors, which means that the sensor will always be ventilated. As soon as an inflow wind speed is present, the downwash of the rotors is pushed back and the sensor is naturally ventilated. Experiments show that relatively small airflow (i.e. <2 m s⁻¹) is sufficient to prevent air being trapped in the housing (see Appendix ).

The research wind farm WiValdi at Krummendeich (https://windenergy-researchfarm.com/, last access: 18 October 2025) in Germany is a facility that is operated by the German Aerospace Center and was instrumented in cooperation with the ForWind universites at Oldenburg, Bremen and Hannover. The meteorological mast array (MMA), which is a set of two 100 m and one 150 m mast in the center, is a suitable infrastructure to validate spatial measurements in the field with UAS and vice versa (i.e. to determine flow disturbance by the masts). Details about the masts are given in Sect. .

The analyses in this study are based on a campaign that was conducted in July 2024, particularly from 22–25 July 2024, when flights were conducted in close proximity to the mast array. During these days, the wind turbines OPUS1 and OPUS2 at the site were not operating. Figure  shows a map with hover positions of the UAS relative to the masts and Table  gives a list of flights that were used for the analyses with the corresponding meteorological conditions. Two different flight pattern “MMA” and “calib” are listed and correspond to the pink and orange dots of UAS positions in Fig.  respectively. The “MMA” pattern was designed to mimic sensor positions of the mast array in a further plane perpendicular to the mast array axis, whereas the “calib” pattern was used to have five UAS as close as possible to each other for cross-calibration of wind and temperature measurements. A comprehensive table of which drones were flown at which position during each flight is provided in Appendix . For all flight periods, an instationarity-test according to was performed based on sonic anemometer measurements and showed that the observational periods can be considered stationary for second-order statistics and sensible heat flux.

The National Test Centre for Unmanned Aircraft Systems at the airport of Cochstedt is a facility operated by the German Aerospace Center, specifically designed to support UAS operations with its infrastructure. An airport traffic zone (ATZ) can be activated up to 3000 feet (∼914 m)) above ground level to mitigate air risk for UAS operation. We used this possibility to conduct vertical profiles with our SWUF-3D drones in June 2024. Most of the flights were conducted using a newer version and frame of a multicopter; however, we also conducted one flight on 25 June 2024, up to 300 m in height with the frame as described in Sect.  which is used in this study.

The meteorological mast array (MMA), conceptualized by the University of Oldenburg, features 51 3D sonic anemometers and 32 cup anemometers to measure distributed wind fields within an area covering the rotor diameter of the installed wind turbine at the WiValdi site. The three masts are separated by 50 m, with the central mast reaching 150 m and the outer masts reaching 100 m. In this study, we use five sonic anemometers as a reference for the drone-based measurements. The position and identification of these sonic anemometers are listed in Table .

The sonic anemometers at 25 m height are installed on 7 m booms pointing towards the central mast; those at 99 m are installed on top of the masts to reach their final height. Each Thies Clima 3D sonic anemometer provides three-dimensional wind information in the anemometer's coordinate system and three readings of sonic temperature (see Sect. ). The raw data of the instruments is available at a frequency of 10 Hz. A cross-wind correction is performed internally by the sonic anemometer according to and we use the median of the three measured temperatures (Tu, Tv and Tw) to obtain a final temperature reading, Ts, as suggested by the manufacturer: 1Ts=median(Tu,Tv,Tw)

For turbulence and heat flux measurements, accurate absolute temperature is not critical. The raw temperature data from the sonic anemometers is not well calibrated and exhibits offsets compared to the drone measurements and the well-calibrated temperature sensor at the WiValdi site's inflow mast, located approximately 600 m to the west (out of scale in Fig. ). For the three days of flights analyzed in this study, we apply a rough bias correction based on the inflow mast measurements. Details of all the used sensors at the WiValdi masts is given in Appendix . For spatial temperature measurements with the MMA, improved corrections will be necessary in future work if high absolute accuracy is required.

The in-flight performance of the temperature sensor requires validation through field experiments. The preferred method is to fly the UAS in close proximity to sonic anemometers. A sonic anemometer provides a temperature reading derived from the speed of sound, the sonic temperature Ts. This value is close to, but not equal to virtual temperature Tv. A common equation to calculate sonic temperature from air temperature T is according to : 2Ts=(T+T0)(1.0+0.51q)-T0, where q is the specific humidity and a conversion to the absolute Kelvin scale with the absolute zero temperature T0=273.15 °C is necessary inside the equation. The SWUF-T sensor also measures humidity, so that measured air temperature by the FWPRT temperature sensor can approximately be converted to a sonic temperature more easily than vice versa. Therefore, all temperature readings from the UAS that are compared with sonic anemometer measurements are converted to sonic temperature according to Eq. ().

Using the eddy covariance method, sensible heat flux, H, can be calculated from variations in temperature and vertical wind speed as 3H=ρCpT′w′‾ where ρ is the air density, Cp is the specific heat capacity of air and T′w′‾ the covariance of temperature and vertical wind speed (the so-called kinematic heat flux). Since the sonic anemometers do not directly measure T′w′‾, but Ts′w′‾ , we calculate the covariance of sonic temperature and vertical wind for both, UAS and sonic anemometer and, assuming that Ts≈Tv, use this kinematic vertical flux of virtual temperature scaled with ρCp to obtain the buoyancy flux 4Hb=ρCpTs′w′‾. Both variables ρ and Cp can be calculated from thermodynamic measurements made by the drone itself, namely temperature, humidity, and pressure. We apply a correction for moisture to the specific heat capacity of dry air, such that 5Cp=1004.67Jkg-1K-11+0.84mh where mh is the water vapor mixing ratio.

We intentionally calculate buoyancy flux using 10 min averages, recognizing that a representative flux may require longer averaging periods to adequately sample the largest turbulent eddies for the eddy covariance method. However, the purpose of this paper is not to study heat flux itself within the atmospheric boundary layer, but rather to determine the capability of drones equipped with fast temperature sensors to derive heat flux values comparable to those from other in situ sensors, especially in the small scales. At the current stage of development in this study, the SWUF-3D fleet was unable to fly for 30 min or longer. The most consistent, extensive and comparable dataset was obtained using 10 min averages.

The HYT sensors come factory-calibrated with a specified accuracy of 0.2 K in the temperature range 0–50 °C. The MAX31865 defines a total accuracy of temperature measurements over all operating conditions of 0.5 K. In our setup, we do not use a standard PT100 or PT1000 element, but use a platinum fine wire as specified in Sect. . From a known base resistance of the wire at 0 °C (R0) the actual resistance Rpt is a function of temperature T according to the Callendar-Van Dusen equation for temperatures above 0 °C: 6Rpt=R01+aT+bT2, where a and b are material specific coefficients.

The length of the wire varies due to manufacturing inaccuracies, so that R0=50±5Ω are possible in the manufacturing process. For best accuracy, we calibrate each sensor individually in an EdgeTech RHCal portable calibration chamber with certified and traceable accuracy of 0.1 °C. We use the device's full temperature range of 10–50 °C with a step size of 5 °C. Figure  shows the calibration curve of five sensors compared to the theoretical curve of a platinum resistance with R0=50Ω.

The curves show a strong linear relationship between temperature and resistance in the calibration range, which corresponds to the theoretical expectations. Applying a linear model to the theoretical platinum curve within the considered temperature range results in a coefficient of determination of R2=1-2.86×10-6, indicating a very low calibration error. Due to the temperature limitations of the EdgeTech RHCal calibration chamber, we cannot measure R0 directly. Instead, we fit the measured resistance values to the known calibration temperatures with a first-order polynomial: 7Tpt=c1⋅Rpt+c0. We obtain two coefficients c0 and c1 for each FWPRT sensor (see Table ). These coefficients are then used to calculate the temperature Tpt based on the measured resistance Rpt of the platinum fine wire. Applying this linear model to the measurement series now produces a median R2=1-6.57×10-6. The coefficients of determination exceed 0.99, indicating a good linear relationship and confirming the suitability of a linear calibration model for our sensors.

Observed deviations are primarily biases, which can be corrected by adjusting resistance values. Figure  shows the errors for the whole calibration range if only a bias correction is applied (red curves) in comparison to the polynomial fit as in Eq. () (black curves). While an individual bias correction (0-D calibration, only modifying c0) provides a reasonable approximation, it shows that the differences in the slopes of the individual curves are too large to achieve the desired precision of less than 0.1 K over the full temperature range. These variations in slope may be attributed to material impurities and production tolerances. Therefore, a slope adjustment by the previously mentioned first-order calibration equation (Eq. ) with a calibration of c1 becomes necessary. Not all temperature sensors, including spares, could readily be calibrated in the calibration chamber for the campaign so that some were only calibrated with the bias correction. We thus expect an average absolute RMSE <0.5K. The calibration coefficients for the calibrated temperature sensors that were used in this study are listed in Appendix  in Table . It can be seen in the table that sensors 1 and 4 showed a significant bias, even though they had been calibrated, which could be caused either by a mistake in calibration or some damage to the sensor changing the platinum wire or reference resistance.

Attempting to calculate fluxes with the eddy covariance method requires synchronous measurements of temperature with vertical flow velocity w. As described in , vertical velocity can be estimated from thrust and lift of the UAS. The force acting on the drone in z-direction Fz in the body frame of the drone is a combination of gravitational force (mg rotated into body frame with roll φ and pitch θ angle), vertical accelerational forces mz¨, thrust T and lift force FL which depends on the drag force Fx: 8Fz=-mgcos⁡(θ)cos⁡(φ)+mz¨+T+FL(Fx) Vertical velocity is derived based on a calibrated curve using the equations 9wb=cz↑Fzbz↑Fz≥0cz↓Fzbz↓Fz<0.

Since the study in 2022, new rotors and new batteries were installed on the SWUF-3D UAS, which changes the thrust and lift behaviour. Parameters were adjusted accordingly. It also showed that it is beneficial to first rotate the forces into the geodetic coordinate system and do the vertical velocity calibration in this frame of reference, so that: 10w=cz↑Fzgz↑Fz≥0cz↓Fzgz↓Fz<0.

From and , we know that the resolution of turbulence by measuring the three-dimensional wind vector with the SWUF-3D fleet is limited to approximately 2 Hz, corresponding to a 2.5 m eddy size at a mean wind speed of 5 m s⁻¹. To demonstrate that the flow at these scales is not significantly disturbed at the temperature sensor's position, we visualized the flow using smoke and flew the drone within the plume. At wind speeds of 2–3 m s⁻¹, recorded during the test, it is clear that the flow is significantly disturbed only by the downwash below and downstream of the UAS. Virtually no disturbance is detected directly in front of the UAS. At higher wind speeds, upstream effects will be even smaller. Figure  shows a snapshot of the flow visualization. Previous studies using CFD and lidar measurements have shown the effects of rotor downwash on sensor position for much larger drones but reached the same conclusion: placement in front of the drone, aligned with the wind direction, is the optimal location. Operating the drone in weather vane mode, i.e., turning the nose into the wind, is essential for good measurement accuracy. A small experiment was also setup to show that the sensor housing alone does not trap the flow at flow velocities as low as 1–2 m s⁻¹ and is described in Appendix .

As typical for such instruments, the sonic anemometers at the met mast array do not provide a precise measurement of the absolute virtual temperature value and were corrected accordingly as described in Sect. . To show that the calibrated SWUF-T sensors provide robust temperature readings, we show the comparison of five UAS that were flown in close proximity (calib_pattern, see Sect. ) in Fig. . In the background, the corrected sonic temperatures at 99 m are shown for the south (solid blue) and center (light blue) mast. It shows that the temperature readings of QAV21 have somewhat smaller variance, which is consistent throughout the experiment and may be due contamination or other issues with the platinum wire that can unfortunately not be traced back.

The mean absolute deviations between the four sensors on the UAS are below 0.1 K for this test. The deviations to the sonic anemometers are larger which can be attributed to the distance of 50 m to the mast. It is evident that the fluctuations within the 10 min period fit better to the south mast anemometer than the center mast which is even further away.

Temperature sensors are known to introduce errors in vertical profiling with UAS (see for fixed-wing and for multicopters), as well as with radiosondes , when slow sensor response times meet temperature gradients during ascent (and descent). These errors can be corrected if the sensor's time constant is well known , but this requires rigid filtering of high-frequency noise, which can also eliminate information about small-scale turbulence. A fast sensor is always preferable for accurate soundings. Unlike radiosonde sensors, our sensor is not exposed to very low temperatures and pressures, which are particularly unfavorable conditions. The SWUF-3D fleet is designed for boundary-layer operation in non-precipitation conditions and can therefore be optimized for these conditions. Figure  shows two examples of vertical profiles measured simultaneously with an HYT sensor and a FWPRT. The hysteresis caused by the HYT sensor's time response is clearly evident in Fig. a and results in a temperature offset of almost 1 °C between ascent and descent. No hysteresis is observed with the FWPRT sensor (red curves). The FWPRT data does indicate that more turbulent fluctuations are observed during ascent, likely due to mixing by rotor downwash during descent. The dotted blue lines show a time-lag-corrected version of the HYT measurements, which shows good agreement in this case with a constant temperature gradient. The time lag corrected temperature is calculated as 11Tcorr=T+τdTdt with a time constant τ of 20 s and filtering data with a 5 s moving average to avoid noise amplification before. It is worth noting that this time constant is much larger than the specified time constant for the sensor (5 s for the HYT271 used in this flight). Figure b provides an example of a more complex boundary layer in the early morning, where a nighttime inversion is still present but is being slowly eroded by surface heating below 100 m. Between ascent and descent, a 10 min hover period is included in this flight during which the temperature at 150 m significantly cools from the bottom. This cooling can be seen in the measurements by the fast sensor, but not by the slow sensor, particularly because the temperature increase during ascent was not accurately measured. Additionally, the vertical profile was interrupted at a height of 100 m for 10 s during ascent and descent, which is clearly reflected in a temperature adjustment for the slow sensor (dark blue line) due to its response time. Time response correction brings the slow sensor's curves significantly closer to the fast sensor's curves but is highly sensitive to the applied time constant and can therefore introduce large errors. Both examples demonstrate the importance of fast temperature sensors for profiling the atmospheric boundary layer with the goal of resolving small-scale structures, accurate inversions, and temperature gradients.

We developed and integrated the SWUF-T module into the SWUF-3D fleet with the primary goal of resolving small-scale turbulent temperature fluctuations and determining second-order statistics with accuracy comparable to that of other in situ instrumentation. This chapter presents the results of in-flight tests of the SWUF-T module, comparing its measurements with those from sonic anemometers at the MMA in the WiValdi research park.