In Situ Uncrewed Aircraft Measurements of Turbulent Kinetic Energy over Heterogeneous Terrain
1. Introduction
One of the most crucial quantities to consider when studying phenomena such as convection and wind shear in the atmospheric boundary layer (ABL) is turbulent kinetic energy (TKE). It is defined as the mean kinetic energy that stems from the variances of the three wind velocity components; it is physically related to the kinetic energy of the turbulent eddies and directly connected to the transport of momentum, heat, and moisture (Stull 1988). Over the decades, several studies have focused on characterizing and modeling its budget equation (Wyngaard and Coté 1971; Lenschow 1974; Caughey and Wyngaard 1979). This attention arises from the fact that certain components of the TKE budget are directly related to commonly used atmospheric stability parameters. The objective of these studies has been to identify similarities or scaling parameters under specific atmospheric conditions, with the ultimate goal of facilitating the development of simplified analytical models (Wyngaard 1992).
The exponential growth in computing capabilities over recent decades has led to the widespread use of large-eddy simulation (LES) models and high-resolution numerical weather forecast models (Andren et al. 1994; Stoll et al. 2020). TKE is a key parameter in various turbulence models used in LES, as it provides a quantitative measure of the turbulence intensity and dynamics, particularly at scales that are not directly resolved in the simulations. These tools, created by various research groups, often yield similar outcomes (Hodgson et al. 2023), but, as for any numerical simulation, validation through experimental results is still crucial (El Bahlouli et al. 2020; Platis et al. 2021; zum Berge et al. 2021). Moreover, obtaining input parameters closely aligned with realistic conditions becomes essential for enhancing the model’s ability to accurately simulate real-world turbulent flows and, therefore, to provide reliable forecasting results (Bielli and Roux 1999; Xu et al. 2009; Wang et al. 2010; Auerswald et al. 2012; Brilouet et al. 2020).
For these reasons, there is a significant demand for in situ measurements of turbulent quantities (Wilczak et al. 2019), particularly in areas where simulations deal with distinctive topography, heterogeneous terrain, or natural obstacles; essentially, regions where the characteristics deviate from the conventional flat and homogeneous terrain (Risanto et al. 2023). This is because over such terrains, simplified models such as similarity constants cannot be used reliably (Foken 2006), given that different terrain surfaces facilitate the development and interaction of boundary layers with profoundly different characteristics (Kalthoff et al. 1998; Kossmann et al. 1998; Bou-Zeid et al. 2020).
In the atmosphere, TKE can be determined with high-resolution measurements of the three-dimensional wind vector (Foken and Bange 2021). For ground-based meteorological stations or towers, sonic anemometers provide such detailed measurements. However, these sensors provide fixed-point measurements that are generally limited to altitudes close to the ground or up to heights of 300 m at a very few instrumented tall towers. Measurements at higher levels or based on more flexible measurement strategies can only be obtained by using crewed (Lenschow 1970, 1974; Pennell and LeMone 1974; Nicholls and Readings 1979; Tjernström and Smedman 1993; Lohou et al. 1998; Brooks et al. 2003; Saïd et al. 2010; Cook and Renfrew 2015; Brilouet et al. 2020; Siedersleben et al. 2020; Syed et al. 2022; Platis et al. 2022, 2023) or uncrewed aircrafts systems (UASs) (Reuder et al. 2012; Platis et al. 2016; Alaoui-Sosse et al. 2019; Lampert et al. 2020; zum Berge et al. 2021; Chechin et al. 2021; Wildmann and Wetz 2022; zum Berge et al. 2022; Shelekhov et al. 2022).
As mentioned by Bange et al. (2021), smaller research UAS can provide accurate data on temperature, humidity, and wind, comparable to larger crewed aircraft and can fly at lower altitudes. Even though these UAS have smaller payloads and less endurance, they come with cost and logistical advantages that make them suitable tools for capturing detailed small-scale patterns of atmospheric wind, temperature, and moisture fields (Platis et al. 2016; Rautenberg et al. 2019b; zum Berge et al. 2021; Schön et al. 2022; de Boer et al. 2024). Moreover, the application of small UAS for remote sensing validation has been established in previous studies (Martin et al. 2011). For a comprehensive overview of meteorological UAS and research aircraft in general, readers are directed to Bange et al. (2013).
In our study, fixed-wing UASs of type multipurpose airborne sensor carrier (MASC-3) (Rautenberg et al. 2019b) were employed by the Environmental Physics Group of the University of Tübingen, Germany, to collect in situ turbulent wind-vector measurements during three intensive observation periods (IOPs) in 2020, 2021, and 2022, in the frame of the validation of numerical simulations and remote sensing using UAS (VALUAS) project. One of the objectives of the project was to utilize UAS-derived data as a reference for evaluating the accuracy and precision of TKE retrievals between 100 m and 500 m above ground level (AGL) obtained by Doppler wind lidars (DWLs) operated by the German Weather Service [Deutscher Wetterdienst (DWD)].
However, turbulence-related in situ measurements and remote sensing devices validation using fixed-wing UAS have rarely been practiced, and a few existing studies note the importance of terrain homogeneity on the results (Beyrich et al. 2012; Sun et al. 2023). As highlighted by Rautenberg et al. (2019b), the ability to accurately compare data obtained from a flying fixed-wing UAS with a stationary sensor depends on the validity of the Taylor hypothesis of frozen turbulence. Therefore, it becomes crucial to examine carefully whether this hypothesis holds true and if terrain heterogeneity plays a role in its validity.
The primary objective of this initial phase of the study is to evaluate the accuracy and precision of the UAS system itself in measuring TKE. This is achieved by comparing its measurements with those obtained from an ultrasonic anemometer mounted on a meteorological tower. A similar investigation was previously conducted, wherein the MASC-3 system flew over a flat, homogeneous ice surface under strong stable conditions in Finland. The results, presented by Rautenberg et al. (2019b), showcased a high level of agreement between the flying system and a sonic anemometer installed on a meteorological tower and demonstrated the capabilities of the MASC-3 to measure statistical moments up to second order. However, for the region where the VALUAS IOPs took place, previous studies (Bange et al. 2002; Beyrich et al. 2006; Platis et al. 2017a,b) on low-altitude flights for momentum and sensible heat fluxes indicated that the results were highly dependent on the roughness of the surface below, and flights over a forested area resulted in larger fluxes. These results were also in alignment with direct measurements from ground stations at the same location. Furthermore, the effect of land use and vegetation type on resulting turbulent flux calculations has been shown to be significant between classes of different surface characteristics such as water, or a forest (Beyrich et al. 2002a,b, 2006). Building on these premises, this study addresses the following questions:
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How can data from a UAS be compared accurately with that from a stationary sensor?
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Is it feasible to compare turbulence measurements obtained by a stationary sensor and a UAS over heterogeneous terrain, such as that encountered during the VALUAS IOPs? Does the Taylor hypothesis of frozen turbulence remain valid?
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How is the quality of the comparison, and are there any flight-specific factors influencing it?
The manuscript is structured as follows: section 2 introduces the measurement site, outlines the three field campaigns, and discusses the two systems considered for the comparison. Special attention is given to data handling, as there is currently no established method for processing and comparing datasets from stationary and moving sensors, requiring careful consideration and clarification. The turbulent quantity under analysis (TKE) is defined, along with the quality metrics employed to assess the precision and accuracy of one sensor compared to the other. In section 3, the results of the three IOPs are presented in an overall plot, proving the advantages of the data-handling algorithm. Subsequently, the influence of different parameters on the quality of the comparison is studied in detail. Finally, section 4 summarizes the key findings of the study and provides an assessment of the feasibility of the potential next validation of the DWLs by using the UAS dataset.
2. Materials and methods
a. Measurement site and campaigns
The boundary layer field site Falkenberg [in German, Grenzschicht-Messfeld (GM) Falkenberg] of the DWD, about 60 km southeast of Berlin, Germany, hosted all the measurement campaigns for this study.
The DWD operates this site to study the ABL in the area around the Meteorological Observatory Lindenberg–Richard Aßmann Observatory (MOL-RAO), aiming to provide comprehensive measurements of the entire tropospheric reference profile known as the “Lindenberg column” (Neisser et al. 2002). The field site is situated upon a low grass meadow and surrounded closely by agricultural fields on which mostly rye, triticale, rape, maize, and sunflowers are grown as typical vegetation. The small village of Falkenberg is located approximately 600 m to the southeast, while forest patches grow in the western and northwestern areas approximately 1.5 km distant. The results of the Lindenberg Inhomogeneous Terrain—Fluxes between Atmosphere and Surface: A Long-Term Study project (LITFASS) (Beyrich et al. 2002a) demonstrate within an area of 20 × 20 km2 surrounding the GM Falkenberg, how the turbulent fluxes, and in particular vertical momentum and heat fluxes, are extremely dependent on the local surface properties (Bange et al. 2002; Beyrich et al. 2006; Platis et al. 2017a,b). Moreover, it was also noted how even above the same surface (forest, meadow, or agricultural field), there can be very high variability of the turbulent quantities and fluxes mostly due to inhomogeneities in the soil moisture content (Mengelkamp et al. 2006). Therefore, the terrain surrounding the measurement site is considered heterogeneous.
In the framework of the VALUAS project, three IOPs were conducted at the GM Falkenberg. Details about the three measurement campaigns are reported in Table 1, while more in-depth details of the flights are presented in appendix A.
Details of the three measurement campaigns carried out at GM Falkenberg by the Eberhard Karls Universität Tübingen Umweltphysik group in the framework of the VALUAS project including the number of flights and the number of legs (see section 2b) considered for this study.
b. MASC-3 uncrewed aircraft system
The well-established UAS platform MASC-3 was utilized to collect in situ measurements of atmospheric quantities during the three IOPs (Fig. 1). MASC-3 has demonstrated its reliability across a diverse range of studies, establishing itself as a dependable platform for sampling the lower atmospheric boundary layer (Wildmann et al. 2017; zum Berge et al. 2021; Schön et al. 2022; zum Berge et al. 2022). High-resolution measurements of the three-dimensional wind vector are achieved by outfitting the system with a five-hole probe (5HP), an inertial measurement unit (IMU), and a fast thin-wire resistance thermometer (van den Kroonenberg et al. 2008; Wildmann et al. 2014a,b).
The UAS platform MASC-3 and launching catapult before takeoff. The standard turbulence instrumentation is mounted at the very front of the aircraft. Additional (electrical charge and particle—not topic of this study) sensors are mounted on the wings. The pusher engine with two rotor blades is at the tail of the UAS.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
A comprehensive description of the UAS system, including the scientific payload and data postprocessing algorithms, is provided in Rautenberg et al. (2019b). Operating at a constant airspeed (AS) of 19.5 m s−1, the UAS gathers valuable data along so-called “legs,” which denote straight and leveled flight sections. Due to challenges in accurately postprocessing the wind vector during turns, only the legs are considered in the subsequent analysis. Mission planning ensured that the aircraft traveled both forward and backward along the same path, with adjustments made to align with the prevailing wind direction as closely as possible. Table 2 outlines the characteristics of the MASC-3 measurement outputs.
Basic measurement characteristics of the MASC-3 (Rautenberg et al. 2019a,b) and the Metek USA-1 sonic anemometer mounted at 90-m height on the meteorological tower.
c. Sonic anemometer
Two Metek USA-1 ultrasonic anemometers are mounted on the DWD’s meteorological tower at heights of 50 and 90 m AGL (see Table 2). These anemometers operate continuously, providing three-dimensional wind vector measurements at a sampling frequency of 20 Hz.
Situated on horizontal booms extending southward from the main tower structure, these anemometers encounter limitations in specific wind directions due to interference from the tower itself. For this study, we focused on the ultrasonic anemometer mounted at 90 m AGL (Fig. 2).
View on the upper part of the 99-m tower at GM Falkenberg toward WSW, the sonic is mounted on the boom pointing to the left (S) at a height of 90 m. From Boventer et al. (2024).
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
d. Data processing
1) Data filtering
As mentioned in section 2c, the highest ultrasonic anemometer installed at Falkenberg is positioned at a height of 90 m AGL. Consequently, among all the UAS flight legs, only those with an average altitude below 105 m and above 80 m AGL were selected.
Additionally, the permanent sensor has limitations in certain wind directions, as its data should not be used for comparison due to the tower’s structure standing on the one side of the ultrasonic anemometer. This creates artificial disturbances when the wind blows from between 0° and 50°. A second filter is then applied to the entire set of legs to remove cases where this condition is met. Approximately 6% of the flight legs fall into this category and were consequently excluded from further analysis.
The analysis outlined in Boventer et al. (2024) underscores the significance of maintaining a low angle between the ground trajectory of the aircraft and the mean atmospheric wind direction. This is crucial to ensure that the tower-mounted sensor and the airborne platform measure the same air mass. Further details about this parameter, referred to as the fetch angle, can be found in the aforementioned study.
Thus, in a third and final filtering step, the flight legs were precisely assessed for the fetch angle. Similar to Boventer et al. (2024), only legs with a fetch angle smaller than 40° were considered for further comparison. This additional criterion resulted in the removal of another 35% of the remaining legs.
2) Upwind and downwind legs
As detailed in Rautenberg et al. (2019b) and emphasized in section 2b, the MASC-3 flight controller is programmed to maintain a constant AS during flight, irrespective of the atmospheric wind, by using propulsion and pitch in order to regulate the speed. The flight strategy involves flying continuously straight legs between two waypoints, resulting in legs of equal length in space but changing duration in time in case the atmospheric wind is not zero. In the presence of nonzero wind and given the low fetch angle values resulting from the filtering, the UAS flies against the wind on one leg (headwind) and with the wind on the other leg (tailwind). These two conditions are commonly referred to as upwind and downwind legs. It is straightforward that during upwind legs, the ground speed of the aircraft is lower, while it is higher for downwind legs. With legs of equal length, this effect results in time series of different durations, where the time difference between upwind and downwind sections is merely a function of the magnitude of the meteorological horizontal wind speed. Figure 3 illustrates a clear example of the difference between upwind and downwind legs during flight number 118. In accordance with Lenschow et al. (1994), a single, longer data series provides a lower systematic statistical error over turbulent quantity measurements compared to averaging multiple shorter series. Therefore, only the upwind legs are considered for the comparison with the ultrasonic anemometer.
Example of time difference between upwind (light green) and downwind (dark green) legs. The variable h represents the fluctuating part of the horizontal wind speed. Time series from flight 118 (2 Jul 2021): the mean horizontal wind speed is 7.0 m s−1, the upwind leg duration is around 244 s, while the downwind leg lasts only 116 s.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
3) Time series versus space series
The histogram in Fig. 4 shows the distribution of the spatial length of the 120 legs that passed the aforementioned filters.
Distribution of leg length for the data used in the analysis. The black line represents the median value.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
Although a direct comparison between the UAS leg data and the ultrasonic anemometer data from the beginning to the end of the leg may appear to be a straightforward approach, a closer examination reveals that it is, in fact, flawed and would inevitably yield misleading results. This discrepancy can be attributed to the fundamentally different measurement methods employed by the two sensors. The anemometer, which is mounted on a tower, samples the air mass that is advected through it, whereas the UAS maintains a fixed AS as it flies through the air. Provided that the wind speed does not exceed the target AS maintained by the autopilot, it will consistently sample a greater volume of air than a stationary sensor in the same period of time. To overcome this difference when comparing high-resolution UAS and ground-based sonic data, both time series must be converted into space series, thus ensuring that the same air masses are being compared.
This assumption is valid only if we consider no crosswind along the flight leg and if the Taylor hypothesis of frozen turbulence holds.
The leg-space series is obtained by integrating the instantaneous true AS (TAS) measured by the sensor payload over the logging time of the leg. The same procedure is applied to the sonic anemometer, using the horizontal wind speed and considering a wider start and end time, given that it always takes longer for the sonic anemometer to sample the same air mass as the UAS. The challenge arises in determining the correct position for the smaller UAS-space series within the wider sonic-space series. In other words, the objective is to identify the identical air mass for both sensors. This procedure is not straightforward, as the overlap of the two data series depends on the relative position in space of the beginning and end of the legs with respect to the tower and the direction of the mean wind.
A mathematical method for obtaining this information is to perform a cross correlation of the two series and identify the maximum value in the cross-correlation coefficient, which indicates the point of greatest similarity between the two series. This procedure facilitates the identification of the spatial lag between MASC-3 and the ultrasonic anemometer data. The aforementioned correction has been applied to the upwind leg of Fig. 3, as depicted in Fig. 5. This information enables the determination of the start and end timestamps for the sonic data, thus ensuring their complete representativeness of the air mass sampled by the UAS during each leg.
Example of space-series conversion and synchronization. Here, the two space series are overlapped to obtain the maximum of the cross correlation between them as explained in section 2d(3). The variable h represents the fluctuating part of the horizontal wind speed. Space series from flight 118 (2 Jul 2021): the mean horizontal wind speed is 7.0 m s−1. The leg shown here corresponds to the upwind leg of Fig. 3.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
Figure 6 displays the distribution of the UAS time series duration (Fig. 6a) together with the distribution of the respective duration of the sonic anemometer time series (Fig. 6b) and the horizontal length of the air volume sampled by the two sensors (Fig. 6c): it can be noted, as previously explained, that the sonic anemometer takes longer than the UAS to sample the same length of the air volume. Only after applying this filtering and these corrections, the two datasets, which differ in duration but sample an equal amount of air, can be used for calculating turbulent quantities that can be meaningfully compared.
Distribution of (a) MASC-3 time series duration, namely, the length in time of each UAS leg; (b) sonic anemometer time series duration after the space-series conversion synchronization with the UAS signal; and (c) horizontal length of the air volume sampled by the two sensors.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
It is important to remember that this algorithm is based on two assumptions that are linked to each other. These are the Taylor hypothesis of frozen turbulence and the assumption that the trajectory of the UAS during its mission is perfectly aligned with the wind direction. In the case of our dataset, it is not possible to verify both hypotheses, so it would be unwise to expect to have eliminated all uncertainties simply by this procedure. Taylor’s hypothesis is the subject of one scientific question of the present study. Therefore, it is not yet possible to consider it valid. Moreover, in order to maintain a significant number of legs in our analysis, it is necessary to relax the condition on the crosswind. However, as will be shown in the following sections, the application of this method to the present dataset provides a significant improvement in the process of comparison between the UAS and the sonic anemometer.
e. Turbulent quantities
TKE
f. Quality metrics
To compare the two datasets, one coming from the meteorological tower and the other one from the UAS, we define the following statistical quantities:
1) Bias difference and mean bias difference
2) RMSD
3. Results and discussion
a. TKE comparison
Figure 7 presents a direct comparison of the TKE measurements acquired using the sonic anemometer and the UAS. Figure 7a illustrates the outcome of our data postprocessing, following the method detailed in section 2d(3). In contrast, Fig. 7b displays same values obtained using the same UAS data series, but the sonic data series are simply confined within the start and end of each leg.
Comparison between TKE measured by the sonic anemometer on the meteorological tower and the UAS system. Each of the scatter points corresponds to one UAS leg. (a) Comparison performed over shifted space series; (b) comparison performed by simply considering the sonic and UAS time series cut with the start and end time of each leg.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
These two graphs prove that the comparison performed in this last way is inherently flawed. The comparison of two equally long time series results in a different amount of air sampled by the two systems, with the sonic sensor consistently sampling less air. It is evident that, although the validity of the frozen turbulence hypothesis remains so far unverified and despite a permitted crosswind angle of up to 40°, the simple act of comparing an equivalent amount of air reduces the overestimation of TKE by a factor of 3 or more.
Nevertheless, even when the appropriate postprocessing method is employed, the MBD between the UAS and the reference is still 64%, indicating a systematic overestimation in measurements obtained from the uncrewed aircraft in comparison to the tower reference. Furthermore, the RMSD stands at 105%. This overestimation and scatter appear to be consistent for all the three components of the TKE (appendix B), suggesting that there is no systematic measurement error along any particular direction. This discrepancy demands further investigation to ascertain whether factors pertaining to the UAS or atmospheric conditions exert a substantial influence or whether the two hypotheses that are not entirely fulfilled are the sources of this residual bias.
b. Spatial influence
Given the comparatively poorer statistical performance compared to the mean wind analysis conducted in Boventer et al. (2024) (MBD: 1.8%, RMSD: 19.4% for leg-cup anemometer comparison), initial interest was placed on whether further filtering of the results by using the relative distance to the reference sensor would improve the statistics. As elucidated in section 2d, the two measurement devices operate on inherently different principles and methodologies. Despite the meticulous postprocessing corrections described in section 2d(3), statistical disparities may persist owing to the fundamental difference that the two sensors do not measure at the same location. As a result, the UAS legs underwent a progressive filtering process, taking into account circular regions around the meteorological tower. The minimum radius around the tower was established at 300 m, while the maximum radius (where all data are encompassed) was set at 1800 m. An additional criterion was implemented, stating that any new leg entering the subsequent circular region must sample at least 100 m of air. Figure 8a visually illustrates the various circular regions around the meteorological tower.
(a) Map of all the legs used for the analysis with the corresponding increasing cut circles around the meteorological tower. (b) Behavior of the TKE statistics (MBD and RMSD expressed in percentage) with increasing cut radius, increasing the number of legs but not their space extent. (c) Behavior of the TKE statistics (MBD and RMSD expressed in percentage) with increasing cut radius, increasing the leg’s space extent but not their number.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
As we gradually expand the area around the meteorological tower, two distinct factors can influence the TKE comparison statistics. First, in the smallest area (only 300 m around the tower), approximately 50% of the legs fall within this range; as we increase the radius, more legs are encompassed in the analysis, with all legs included once the 800-m radius circle around the tower is reached. Second, as the area considered expands, a larger fraction of each leg is included in the analysis. Consequently, the length of the space series used to calculate TKE progressively increases.
In an attempt to discern between these two effects, two distinct analyses were conducted. The first, depicted in Fig. 8b, involved calculating TKE quality metrics for each leg solely at the moment it entered the analysis area, without updating the values at subsequent iterations. This approach involved generally shorter space series than the ones available from each leg; however, it allowed visualizing the influence of the increasing number of legs within our statistical sample. Initially, just over 50% of the legs (66) are included in the calculation of MBD and RMSD, with 100% of the legs being reached at a radius of 800 m. It can be observed that both MBD and RMSD do not vary significantly as the sample population increases: MBD starts at 82% and stabilizes at 73% when all legs are considered, while RMSD fluctuates but consistently remains around 135%.
On the other hand, Fig. 8c illustrates an analysis where only the 66 legs within the circle of radius 300 m were utilized for calculating quality metrics, ignoring any leg that would enter the area of interest in further iterations. As the area considered around the meteorological tower expands, the length of each leg increases, consequently increasing the space series length and the amount of air utilized for TKE statistics computation. Initially, only about 25% of the total air is utilized to compute MBD and RMSD, with 100% being utilized only in the area with a radius greater than 1800 m.
Once again, MBD initiates at 82% and decreases to approximately the value depicted in Fig. 7c (around 64%), confirming the adequacy of our statistical sample while also indicating the bias’s independence of the leg length. Conversely, RMSD decreases from an initial value of 135%–105%, meaning that considering the legs in their completeness leads to an uncertainty reduction of the measurement although it means flying further from the tower.
c. Influence of environmental and UAS-related variables
Our UAS was primarily programmed to execute flight paths aligned either in the north–south (NS) or east–west (EW) directions based on the prevailing wind direction each day. Due to the terrain characteristics, it appears of interest to investigate whether one direction yields better outcomes when comparing the TKE measurements of the two sensors. The parameter indicating the precise direction toward which the UAS is flying is denoted as ground course ψ, typically ranging from 0° to 360° (starting from north in a clockwise direction). However, at this point, it is irrelevant toward where exactly the UAS is flying: what matters is just the orientation of the leg on the map; therefore, wrapping the ground course between 0° and 180° makes the analysis and the plotting of the results simpler and easier. A ground course of 0° or 180° signifies a perfect NS leg, whereas 90° represents a perfect EW orientation.
As depicted in Fig. 9, the flights at approximately 90 m exhibit a distinct grouping into two primary ground course directions. However, in order to accurately classify the legs as either NS or EW, it is essential to allow for some margin around 90° as well as around 0° or 180°. We chose to keep a margin of ±30° around the exact NS and EW directions, in a way described in Table 3.
Map including all the legs considered for the TKE analysis. The red dot represents the meteorological tower at the GM Falkenberg. The legs plotted in red belong to the NS ground course group, while the ones in green belong to the EW ground course group. The black lines do not belong to either of the two groups and were excluded from further analysis.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
NS and EW leg group splitting according to the ground course ψ.
Figure 10 presents a scatterplot comparison of the TKE for the two distinct ground course groups. The number of legs is almost evenly divided between the NS and EW groups. However, the statistics do not appear to be dependent on the specific ground course: the MBD remains just above 60%, while the RMSD is 114% for the NS direction and 100% for the EW direction.
Comparison between TKE measured by the sonic anemometer and the UAS system. (a) NS ground course and (b) EW ground course.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
However, even within these two ground course groups, there is a substantial difference due to the wind direction, which determines the direction of the upwind legs used for the analysis. Thus, we decided to further split the two ground course groups based on the main wind direction. The EW group was divided into two subgroups representing winds coming from the east (E) and west-northwest (WNW), while the NS group was split into winds coming from the south (S) and north-northwest (NNW). The details of the splitting are summarized in Table 4.
Subgroup division of the ground course NS and EW groups. The different subgroups are generated according to the mean wind direction.
The four subgroups encompass all legs where the wind originated from the regions visualized in Fig. 11: S and E correspond to the purple sector, while WNW and NNW correspond to the red sector. In the S and E group, the wind blows from an area predominantly characterized by flatland and cultivated ground, whereas in the other two groups, the wind comes from an area where forest patches of different sizes are present.
Map including all the legs and the two main wind direction sectors considered for the analysis. The purple sector spans from 140° to 220° (flat land), while the red sector spans from 240° to 360° (forest).
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
The TKE comparison for the four subgroups is depicted in Fig. 12, while the MBD and RMSD for all the TKE components are reported in Table 5. Unfortunately, the E group comprises only six legs which makes the statistics more uncertain than for the other groups. This analysis reveals that during the NS ground course legs with wind coming from a southern direction (S, flat land), the MBD is 3 times smaller than in cases where the wind blows from WNW (forest): around 21% against 68%. Additionally, the data scatter is 2 times less for the S group. Moreover, it can be noticed in Table 5 that when flying north–south legs with wind coming from the south, the variance of the main wind component, in this case υ, agrees almost perfectly (only 4% difference) with what is recorded by the sonic anemometer. A similar behavior can be seen for the E subgroup, where the lowest MBD and scatter are recorded for the variance of the u component; however, as already mentioned, this group is probably not big enough to be taken as a valid reference. The same tendency also appears when comparing S with NNW with even higher MBD (97%) and RMSD (151%). This suggests that even for NS ground course legs, when the wind blows from the forest region, the statistics considerably worsen.
Comparison between TKE measured by the sonic anemometer and the UAS system. (a) Subgroup of the EW ground course legs, wind blows from E; (b) subgroup of the NS ground course legs, wind blows from south; (c) subgroup of the EW ground course legs, wind blows from WNW; (d) subgroup of the NS ground course legs, wind blows from NNW.
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
MBD and RMSD between UAS measurements and sonic anemometer measurements for the different ground course subgroups.
The reasons for this poorer comparison observed for the two wind directions WNW and NNW (hereafter abbreviated as NW) are difficult to pinpoint, as the variables involved are numerous and can act in opposite directions, masking the effects of each other. In the following sections, the data available in terms of TKE have been analyzed by separating the two wind directions mentioned above and trying to find a correlation in the TKE BD as a function of some important variables related to both the environmental conditions and the UAS itself.
d. Average altitude
As depicted in Fig. 13a, the average altitude of each leg can exhibit variations of up to 15 m around the target altitude of 90 m. This is due to the fact that some of the legs were not programmed to be flown exactly at 90 m, and also because of the many thermals that the UAS can encounter on its way, especially during the summer flights. The Pearson correlation coefficient (Benesty et al. 2009) of the BD with the flight altitude is remarkably weak for the NW direction, revealing that this specific parameter has no discernible influence on the quality of the comparison between the two sensors when the wind blows from this specific direction. On the other hand, it is interesting to see that when analyzing the legs with south wind direction (the dark purple ones), there is a slight tendency to improve the BD, with the smallest values being around 90 m as expected. The correlation is still quite low, but a dependency is definitely discernible when compared to the other wind direction.
Influence of six different variables on the BD between UAS and sonic anemometer. (a) Average leg altitude, (b) fetch angle, (c) bulk Richardson number, (d) TKE recorded by the sonic anemometer, (e) UAS TAS standard deviation, and (f) mean horizontal wind recorded by the sonic anemometer. Each point in the plot represents one flight leg, while ρ represents the Pearson correlation coefficient (Benesty et al. 2009).
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
e. Fetch angle
As elucidated in section 2d(1) and in Boventer et al. (2024), the fetch angle holds substantial significance in this analysis, and a threshold of 40° was previously implemented to enhance the quality of comparisons. Hence, it is essential to reevaluate whether there persists a discernible dependency of the bias difference on this variable.
Figure 13b indicates a weak, if not entirely nonexistent, correlation. Therefore, it appears that this variable does not exert significant influence at this point on the quality of comparison between the sonic anemometer and a mobile UAS platform.
f. Bulk Richardson number
The Rib values above 0.25 signify thermally and dynamically stable conditions, 0 < Rib < 0.25 indicates solely thermally stable conditions, and Rib < 0 suggests a thermally unstable lower ABL. Figure 13c illustrates the relationship between the BD and Rib for all legs. Again, the correlation coefficient is exceptionally weak for the NW wind direction, suggesting that atmospheric stability does not significantly affect the quality of the comparison between the UAS and sonic anemometers. For the south wind direction group, the correlation coefficient is slightly higher, but it is difficult to find a clear dependency, at least for Rib > 0, and there is only one point with stable atmospheric conditions, so it is difficult to draw any conclusions.
g. TKE
Exploring whether the discrepancy between the two measurements of TKE correlates with the TKE value itself is an intriguing aspect to investigate. As depicted in Fig. 13d, the correlation between bias and TKE appears relatively weak for both wind directions. However, in both cases, it is negative, and it is noteworthy that the largest bias tends to occur for relatively low TKE values.
This can be due to the inherent uncertainty in the measurements with both systems but also to the fact that under conditions where the turbulence level is relatively low (e.g., lower than 1 m2 s−2), local effects—such as the terrain footprint—might still be present but not dissipating rapidly enough. Consequently, these effects could potentially corrupt the measurement over a span of several hundred meters, contributing to the observed discrepancies and underlining the influence of surface heterogeneity on the observations. Although this is only speculation, it may be a reasonable explanation for this weak dependence.
h. TAS standard deviation
As described in section 2b, the UAS is programmed to maintain a constant TAS. Clearly, this is possible on average, but instantaneously, the system will be subject to acceleration and deceleration caused by various factors including vertical wind, turbulent eddies, and thermal currents. No matter how robust the flight control system is, it will take some time for it to adapt to the new flight conditions. To try to describe, and take into account this phenomenon, the parameter considered here is the standard deviation of the TAS. Figure 13e shows the BD of the TKE as a function of this flight system parameter. Clearly, higher values of the standard deviation represent legs where the UAS had more difficulty in keeping the TAS value constant. In any case, no clearly defined BD dependence can be observed for this parameter either for the wind direction coming from flat terrain or for the wind direction sector coming from the forest.
i. Mean horizontal wind speed
The last variable analyzed here is the mean horizontal wind measured by our reference sensor, the sonic anemometer. Again, the BD shows no dependence on increasing wind speed, and the correlation coefficient for both wind direction groups only confirms what is clear from a visual inspection of Fig. 13f.
j. Terrain characteristics
The only conclusion that can be drawn from the analysis of all these variables is that there must be something else influencing the distribution of BDs between the UAS and the sonic anemometer, especially for the NW wind direction. As indicated by numerous preceding studies (Bange et al. 2002; Platis et al. 2017b), the terrain heterogeneity surrounding GM Falkenberg bears significant importance. It is well known that turbulent fluxes are generally higher over forested regions. The presence of trees increases the roughness length, and a shear layer forms in the downwind region: both factors increase the mechanical turbulence (Bange et al. 2002; Mengelkamp et al. 2006; zum Berge et al. 2022). Although we cannot provide incontrovertible evidence for the following statements, we suspect that the reasons for the poorer comparison observed in the NW directions are due to the flight path crossing areas of forest and a wind blowing from the direction of forest. In addition, looking at the elevation contours in Fig. 11, it can be seen that the northwest area also has a slightly higher elevation than the south area. The forest area is at an elevation of around 85–90 m AGL, while the tower site is at 73 m AGL. This difference, although small, must be added to the height of the trees, and since the MASC flies by maintaining the same altitude with respect to the starting point, this means that the distance between the UAS and the top of the trees is even smaller. It is the authors’ opinion that these two effects together result in a high inhomogeneity of atmospheric turbulence. Of course, these factors are not the only ones that cause such high TKE scatter between their systems, but they seem to be the ones that have the largest influence, somewhat overriding other variables to which TKE seems to be less sensitive (e.g., exact flight altitude). The even higher MBD (97%) and RMSD (151%) of the NNW subgroup might also be a consequence of the disturbance of the tower structure on the sonic signal, still present despite filtering wind directions between 0° and 50°.
4. Conclusions and outlook
As part of the VALUAS project, three intensive observation periods were conducted near GM Falkenberg, over a heterogeneous rural landscape southeast of Berlin. The UAS of type MASC-3, operated by the University of Tübingen, was deployed to collect more than 43 h of flight data at various altitudes. This dataset were intended for use in validating new DWL systems employed by the German Weather Service (DWD). In a prior study by Boventer et al. (2024), the validity of utilizing UASs to provide a reference for these systems was demonstrated, specifically focusing on mean wind speed and direction.
In the initial phase of this study, the analysis of flight data is expanded to encompass atmospheric wind fluctuation components through turbulent kinetic energy (TKE). The specific focus on this variable arises from the fact that the DWL systems slated for validation provide an estimate of TKE over a 30-min time average.
The primary objective of this analysis is to evaluate the capabilities of a fixed-wing UAS system in delivering accurate TKE measurements above a distinctly heterogeneous terrain and to assess whether Taylor’s hypothesis of frozen turbulence holds true under these conditions.
The current study builds upon concepts explained in Boventer et al. (2024), such as the fetch angle, and establishes a detailed and systematic method for filtering and synchronizing measurements obtained from the UAS and a sonic anemometer operated as a reference sensor on a meteorological tower at 90 m above ground level. This data processing step is crucial due to the intrinsic differences in measurement methods between the two compared sensors: one captures measurements along a straight line traversing the lower atmospheric boundary layer, while the other functions as a static sensor.
In the text, the correctness of the postprocessing algorithm is demonstrated, which reduces the bias and scatter between UAS and sonic anemometer measurements by 3/4. Additionally, the influence of the total number of legs and their length on the quality metrics is examined. It is found that increasing the leg length significantly reduces the scatter but only slightly affects the bias between the two systems. However, considering all flight legs under analysis together, there remains a noticeable bias between the two systems of 64% and a scatter of 105%.
A subsequent analysis indicates improved agreement between the UAS and the sonic anemometer (MBD: 21%, RMSD: 53%) when the flight path is directed from north to south and the wind originates from the south, encompassing predominantly flat and cultivated land. In contrast, when the wind blows from the west-northwest, characterized by forest-covered land, the quality metrics more than double (MBD: 68%, RMSD: 103%).
In light of these results, it is evident that the frozen turbulence hypothesis is not verified. It is the authors’ opinion that in this specific case, the terrain heterogeneity plays a predominant role when comparing a stationary and a moving sensor as it has been shown that other variables have little or even no influence on the UAS–sonic anemometer comparison.
These findings present new challenges in validating lidars using the MASC-3 dataset within the VALUAS project. While it is reasonable to restrict the dataset to wind directions from the south, this results in a significant reduction in the available legs. Furthermore, at higher altitudes, the effect of the terrain may be less pronounced than at the 90 m AGL of the data considered in this analysis. In light of the current situation, where the comparison results are already predominantly dependent on the wind direction, the additional dependence on flight altitude introduces a further variable that cannot be compared with any reference sensor.
Given the particular test site and flight strategy in question, it is not possible to ascertain the accuracy of the UAS TKE estimate with sufficient confidence. It is important to note that this issue is not inherently related to the accuracy of the UAS data acquisition capabilities, which have been previously validated in other studies. Rather, it is a consequence of the fact that one sensor is stationary while the other is moving in space.
The optimal methodology for conducting comparative experiments at the Falkenberg site with regard to turbulent quantities would be the utilization of rotary-wing UAS, which are capable of maintaining a fixed spatial position while measuring atmospheric flow conditions.
Acknowledgments.
The authors thank the German Weather Service (DWD) for funding and supporting this research under Grant Agreement with a reference: 4819EMF01. The authors declare no conflict of interest.
Data availability statement.
The data of the 2021 IOP are publicly available at Jung et al. (2023). The rest of the data can become available from the corresponding author upon reasonable request.
APPENDIX A
Flights Overview
The flights used in this study (Table A1) are approximately the same as those used in Boventer et al. (2024) where the UAS is validated against the tower and subsequently the two DWLs are validated against the UAS in terms of mean wind speed. For this purpose, the missions were designed to fly at different altitudes for at least 10 min. This strategy provides an average of two legs per altitude, and therefore, we only have two legs around 90 m, after which the UAS would climb to the next predefined altitude. For the next part of this work, the comparison between the UAS and DWL in terms of TKE, the MASC-3 had to fly for at least 30 min at each altitude, as the DWL TKE estimates are given with a frequency of one every 30 min. As a result, some of the flights (e.g., 110, 111, 115, 119, 131) have several legs around 90 m.
List of all MASC-3 measurement legs used in this analysis of IOP-1, IOP-2, and IOP-3 in the years 2020, 2021, and 2022 at the MOL-RAO.
APPENDIX B
TKE Components
In this appendix, the comparison of the individual components of the TKE variable is plotted together with the TKE of the horizontal wind (Fig. B1). They consist of the variance of the three components of the wind vector. The data shown in these plots consist of the same legs of Fig. 7 before the application of any filtering on the ground course or wind direction.
Comparison between variables measured by the sonic anemometer on the meteorological tower and the UAS system. Each of the scatter points corresponds to one UAS leg. (a) Var(u), (b) Var(υ), (c) TKEH, and (d) Var(w).
Citation: Journal of Atmospheric and Oceanic Technology 42, 3; 10.1175/JTECH-D-24-0026.1
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