1 Introduction

With a share of 23.7% in 2020, wind energy is one of the main contributors to German electricity production (BMWi 2020). This 23.7% of wind energy in Germany is produced by a total power of 54.4 GW (87.6%) from onshore wind turbines and 7.75 GW (12.4%) from offshore wind turbines (BMWi 2020). With the ongoing change towards more renewable energies, additional sites are to be developed. Accordingly, not only flat terrain but also complex terrain is coming to the attention of the government and wind turbine operators for fulfilling the needs of renewable energy.

With their 1970s studies, Taylor and Gent (1974) and Jackson and Hunt (1975) initiated a larger interest in boundary-layer flows over hills, where the hill height is much smaller than the hill length. They used numerical and analytical linear modelling approaches to determine the flow regimes over low hills. Taylor and Gent (1974) and Jackson and Hunt (1975) extended and improved their own theories over the following years. Within the last 20 years, the development of models and the corresponding computing power has increased greatly. This allows for the simulation of the flow field over more complex structures. However, the underlying theories and models of Taylor et al. (1974, 1987) and Finnigan (1988) still prove to be a strong base for an analytical comparison to measured data.

Finnigan and Brunet (1995) were among the first to look into boundary-layer flows within and above a canopy on low hills. Later studies used their findings in more precise and detailed large-eddy simulations (LESs) for more complex terrain (Dupont et al. 2008; Ross 2008; Wang et al. 2015; Liu et al. 2019). However, research on possible influences of the canopy on the local wind field for the WINSENT (“Wind Science and Engineering in Complex Terrain”) test site has not yet been performed sufficiently. El-Bahlouli et al. (2019) and Berge zum et al. (2021) suggested a large impact by the deciduous forest onto the flow field in the lowest 60 m above ground. What was not considered in earlier studies is the variation during seasons of the leaf area index (LAI) and the resulting effect on the wind field, the turbulence in the lee of the trees, and speed-up over the crest. The impacts of complex terrain on wind speed, turbulence, inclination angle, and wind direction are relevant for the assessment of possible wind energy sites, as they have an influence on the power output, fatigue, and financial and energetic amortization time of wind turbines (Maeda et al. 2004; Schulz et al. 2016a, b; Lutz et al. 2017; El-Bahlouli et al. 2020).

The measurement and characterization of a flow in complex terrain are more challenging compared to flat terrain. The flow is behaves less predictably with rapid changes close to the ground, which makes an evaluation with remote sensing devices like lidar and sodar difficult. Due to their large averaging volumes and the heterogeneity of the orography, sodar and lidar are not able to spot small and fast changes in the wind profile. Sonic measurements on towers give a high temporal resolution of the wind speed and direction, but are fixed to one location and are not representative for the immediate vicinity (Ayotte et al. 2001). Fixed wing UASs (uncrewed aircraft system) are able to measure a two-dimensional field of wind, temperature, and humidity with a high spatial and temporal resolution, covering a large area vertically and/or horizontally. This ensures that small phenomena, like turbulent structures, and larger effects, like the speed-up over the crest or recirculation zones downstream of an escarpment, are picked up. With their high resolution data acquisition applied over a large area in multiple heights, UASs are closing the gap between static but high temporal resolution instrumentation on the ground or on towers and remote sensing with its coarser temporal resolution but capabilities of covering large areas.

Where remote sensing requires multiple devices or specialized algorithms (Wildmann et al. 2020) to measure all three wind components or the turbulence kinetic energy (TKE), the UAS does this with a higher temporal resolution over a large area and additionally measures the temperature and humidity at the same time in the same area. This makes a UAS a good tool for measurements in complex terrain.

Considering the trend towards building more wind energy turbines in complex terrain in combination with the effects of this terrain on wind energy production, the project WINSENT was established. WINSENT is a research project by the wind energy research cluster WindForS with several southern German research institutions. The main goals of WINSENT are the characterization of the micro-climate and meteorology at the test site in the Swabian Alps, the preparation and modification of wind energy converters, and the construction and operation of the test site (WindForS 2018).

In the course of the WINSENT project and previous projects, multiple measurements and simulations (Wildmann et al. 2014a, 2017; Knaus et al. 2018; El-Bahlouli et al. 2019, 2020; Letzgus et al. 2018, 2020; Berge zum et al. 2021) were performed at the location of the test site to investigate the influences of complex terrain on the wind field and wind turbines, including the role of the forest. Measurements and simulations showed an accelerated flow over the escarpment with westerly winds.

According to the findings by El-Bahlouli et al. (2019) and Berge zum et al. (2021), the forest at that particular site has a large impact on the turbulence kinetic energy k in the lee of the trees. Blades of modern wind turbines reach into the boundary layer above and behind the tree canopy, an area with increased turbulence. Knaus et al. (2018) found similar results by using Reynolds-averaged Navier-Stokes (RANS) simulations, modelling the flow over the escarpment, where the trees had a significant impact on the turbulence kinetic energy in the lowest 50 m above ground. Thus, this study aims at answering the following questions:

  • How strong is the difference in speed-up above the crest and the turbulence kinetic energy k with changing LAI?

  • Are the analytical models from past research applicable for the forested escarpment at the WINSENT test site?

This study compares eight measurement flights in the same area above the escarpment from July–September (summer, high LAI) and six measurement flights between October–March (winter, low LAI) from 2018 to 2021.

2 History of Analytical Flow Models

Over the last decades, a variety of models and approaches have been developed for modelling airflows in complex terrain. The works by Jackson and Hunt (1975) and Finnigan (1988) developed and improved analytical models to describe the flow over (low) hills. A speed-up above the crest of a hill occurs, and this speed-up is dependent on the hill shape and its roughness. The core principle of the model by Jackson and Hunt (1975) was to linearize the equations of motion with a logarithmic background wind profile (Fig. 1). This profile is assumed in a flat and undisturbed area upstream of the hill.

Fig. 1
figure 1

Ideal hill with its flow features on the findings by Jackson and Hunt (1975). \(U_{\mathrm {B}}(z)\) is the undisturbed approaching wind profile

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The result of the analysis by Jackson and Hunt (1975) is that the speed-up is much greater than the slope of the hill would suggest (Finnigan et al. 2020). This speed-up is based on the conventional formula for the fractional speed-up \({\Delta } S\) by Jackson and Hunt (1975),

$$\begin{aligned} {\Delta } S(x,z) = \frac{U(x,z)-U_{\mathrm {B}}(z)}{U_{\mathrm {B}}(z)}, \end{aligned}$$
(1)

where U(x, z) is the wind profile at a location x, which is the lateral distance between the profile and the crest and \(U_{\mathrm {B}}\), the undisturbed approaching wind profile (Fig. 1).

Figure 1 also shows the influence onto the mean flow over a hill incorporating the characteristic mean stream-wise velocity scale \(U_{0} = U_{\mathrm {B}}(z)\). Above the crest in Fig. 1 a speed-up is expected when compared to the undisturbed upwind profile. This maximum in the mean horizontal wind speed is not visible in the downwind profile. According to Finnigan (1988) this downwind profile is somewhat influenced by the forming of a separation bubble in the lee of the hill (Fig. 1). Based on the findings of Jackson and Hunt (1975) and Taylor and Lee (1984) formulated assumptions for wind-speed changes over low hills. For three-dimensional axially symmetric hills they concluded \({\Delta } S_{\text {max}}=1.6\{\frac{H}{L}\}\), for two-dimensional escarpments, \({\Delta } S_{\text {max}}=0.8\{\frac{H}{L}\}\) and over two-dimensional ridges, \({\Delta } S_{\text {max}}=2\{\frac{H}{L}\}\), where H is the hill height and L is the hill length at the half-height point H/2 (Fig. 1). The analytical model by Jackson and Hunt (1975) was later improved by Sykes (1980), Hunt et al. (1988) and Finnigan (1988). The first numerical model by Taylor and Gent (1974) was developed even before the results from Jackson and Hunt (1975) were published. The upcoming numerical models to simulate hill flows adopted the analytical basics from Jackson and Hunt (1975). This led to numerical models like WAsP (Wind energy industry-standard software; Troen and Petersen 1989) that are still used in wind energy site assessment nowadays. With always growing capacities in computing power, existing models by Jackson and Hunt (1975) and Hunt et al. (1988) were improved and new RANS and LES models (Letzgus et al. 2018) were developed but are still using the analytical and numerical basics published by Taylor and Gent (1974) and Jackson and Hunt (1975) in the 1970s (Finnigan et al. 2020). However, these theories only consider low hills with a very small roughness length \(z_{0}\) and only under neutral thermal stratification.

The first steps towards understanding the impact of a hill covered by canopy onto the flow field were taken in the 1990s with a wind-tunnel experiment by Finnigan and Brunet (1995). They placed a well-studied model canopy on a 2D ridge in a wind tunnel to analyze the impact of the added roughness into the flow field over the low hill. Within the last two decades various other studies on the impact of canopy covered complex terrain onto the flow field above and around hills were performed. However, there is still a lack of real-world experimental datasets. Big field experiments have been carried out in the past, eg., Black Mountain (Bradley 1980), Askervein (Taylor and Teunissen 1987), and Perdig\(\tilde{\text {a}}\)o (Fernando et al. 2019). Most of the experiments only utilized stationary measurements at certain points like the crest and the undisturbed inflow. This set-up can give an insight on the speed-up directly above the crest (but not the full 2D or 3D flow field) and is limited in height.

3 Methods

3.1 Measurement System

For data acquisition the airborne measurement platform MASC-3 (Multi-Purpose Airborne Sensor Carrier) was used. The MASC-3 (Fig. 2) is an UAS that allows for turbulent wind, humidity, and temperature measurements with constant air speed and direction along previously defined flight paths with specific altitudes (Rautenberg et al. 2019). The electrically powered UAS has a wingspan of 4 m and a takeoff weight of 7–8 kg, depending on the battery load. The speed, direction, and altitude is controlled by the autopilot system (Pixhawk 2.1 Cube) via changing the angle of attack and throttle (Rautenberg et al. 2019).

Fig. 2
figure 2

The MASC-3 UAS equipped with sensor compartment after take-off

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The sensor compartment consists of a five-hole probe for measuring the wind vector, a fine wire platinum resistance thermometer (Wildmann et al. 2013), two hygrometers (Wildmann et al. 2014b; Mauz et al. 2020), and an inertial measurement unit (IMU) for exact position information. MASC-3 samples the sensors with 100 Hz to measure the three-dimensional wind vector and air temperature with up to 30 Hz (Wildmann et al. 2014a). More detailed information on the MASC-3 and the measurement system were published by Rautenberg et al. (2019).

3.2 Measurement Site and Strategy

The WINSENT test site is located near Geislingen an der Steige on the Swabian Alb (48.664\(^\circ \)N, 9.836\(^\circ \)E). The area is characterized by its complex terrain, containing a steep escarpment with a flat plateau (665 m a.s.l.) to the east and a small hill about 1.5 km west of the escarpment (Fig. 3). The escarpment has a slope of up to 40\(^\circ \) and a height of approximately 200 m with respect to the valley. The upper 100 m of the escarpment is covered with a dense and mostly deciduous forest (Schulz et al. 2016a; Wildmann et al. 2017). The mean wind direction with approximately 295\(^\circ \) is perpendicular to the crest of the escarpment, which makes this area interesting for building the test site. For a more detailed view of height differences in the wider area around the test site, Berge zum et al. (2021) showed a map derived from a digital elevation model.

Fig. 3
figure 3

Satellite picture of the WINSENT test site (48.664\(^\circ \)N, 9.836\(^\circ \)E) in southern Germany. The site is east of a forested escarpment (1) with a height of 200 m in respect to the valley. A hill (2) is around 1.5 km west of the escarpment. The blue arrow shows the mean wind direction of all flights combined. The red circle shows the location of the test site. Sources: Satellite image: ©2020 Microsoft Corporation ©2020 Maxar ©CNES (2020) Distribution Airbus DS; OSM Standard: ©OpenStreetMap contributors, CC-BY-SA. https://www.openstreetmap.org/copyright. https://www.openstreetmap.org. https://www.opendatacommons.org

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Figure 4 shows a more detailed view of the escarpment at the test site. Using the analytical model by Hunt et al. (1988) (see Fig. 1) we can estimate \({\Delta } S_{\text {max}}\) using the hill length L and the hill height H. The hill length L is taken as length of the hill at half of the hill height (Hunt et al. 1988). The darker areas of the contour show the trees with a mean height of 23 m. We assume the forest with no foliage in winter to be sparse enough to let the air flow through more freely, while in summer the full foliage cover acts as a vertical extension of the hill shape (red dashed line in Fig. 4). Because we are now using the highest point of the crest itself (blue line) instead of the treetop (red line) the effective hill height from summer to winter is reduced by about 16 m.

Fig. 4
figure 4

Cut through the escarpment. The canopy is dark grey. Hill length L and hill height H are displayed following the model of Hunt et al. (1988). Red lines for summer (high LAI) and blue lines for winter (low LAI). The red dashed line shows the assumed hill shape with full foliage in summer

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To analyze the magnitude of effect of the LAI on the flow field above a forested escarpment, flight legs (i.e., straight and level flight paths) perpendicular to the slope were performed. In total, 14 measurement flights at heights between 30 and 200 m during different seasons and westerly winds are considered here. The wind speeds during the measurement flights range from 2 m s\(^{-1}\) to more than 10 m s\(^{-1}\) (Table 1). The height difference between flown altitudes is small close to the ground and increases towards the highest flight altitudes. This measurement strategy ensures that the most decisive area behind the forest is covered by a denser grid of data. For statistical significance, each flight level consists of 2–4 straight flight legs on the same track in opposing directions. The raw data are sampled with 100 Hz which yields 5–6 data points per metre flight path.

To compare measurements from flights with a low LAI to flights with a high LAI, the data are visualized by using line plots on a cross-section (Fig. 5) of the mean vertical velocity component U, the turbulence kinetic energy k, and the inclination angle \(\alpha \), for each flown altitude. The inclination, a proxy for the vertical velocity component w, is defined as the vertical deviation of the flow from the x-axis:

$$\begin{aligned} \alpha = \text {tan}^{-1} \left( \frac{w}{u}\right) , \end{aligned}$$
(2)

with w and u being the velocity components in z and x directions. Due to the fact that some earlier flights (14 August 2018, 21 September 2018, and 22 September 2018) are not covering the same heights later flights did, some altitudes are derived by interpolation. Because the flown altitudes are not evenly distributed, this was done by using the inverse distance interpolation (Lu and Wong 2008). The data for U and k were normalized using their mean values from all flight legs combined at 200 m altitude for each of the 14 measurement flights. Values for U, k, and \(\alpha \) were extracted at certain heights (30 m, 40 m, 60 m, 80 m, 100 m, 120 m, 160 m, and 200 m) for each flight. These datasets were then combined and a mean was calculated for each corresponding point on the flight leg along the escarpment and the plateau.

For calculation of the fractional speed-up \({\Delta } S_{\text {max}}\), an idealized logarithmic wind profile based on the mean wind speed in 200 m above ground was extrapolated downwards using:

$$\begin{aligned} {U}_{2} = {U}_{1}\frac{\text {ln}\left( \frac{h_{2}}{z_{0}}\right) }{\text {ln}(\frac{h_{1}}{z_{0}})}, \end{aligned}$$
(3)

with the known wind speed \({U}_{1}\) in 200 m (\(h_{1}\)), the height \(h_{2}\) of the wind speed \({\textbf {U}}_{2}\), and the roughness length \(z_{0}\) with a value of 0.4 (small villages, agricultural land, forests, rough terrain).

Fig. 5
figure 5

Flight paths between 30 and 200 m above the plateau. The escarpment is facing west. Source of the satellite image: Google

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For more details on the measurement strategy, the measurement principle, the data structure, and the interpolation method refer to Van den Kroonenberg et al. (2008), Rautenberg et al. (2018), and Berge zum et al. (2021).

Table 1 Lapse rate and bulk Richardson number calculated from flight data for heights between 30 and 200 m, calculated using the equations in Sect. 3.3
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3.3 Averaging and Second-Order Moments

The results presented in Sect. 4 are averages of the 14 flights from Table 1. The process starts with single flights that have measured data on altitudes between 30 and 200 m a.g.l. Each of those altitudes consists of multiple legs, typically four. To obtain data for each altitude step within a single flight, the flight data from the flight legs on the same altitude is spatially averaged along the flight path. This results in the 14 flights with data on the discrete heights of 30, 40, 60, 80, 100, 120, 160, and 200 m. To compare the results between the seasons, the data of the six flights in winter and the eight flights in summer is again spatially averaged, e.g., the data at 30 m of the six flights during winter. The standard deviation \(\sigma \) used in Sect. 4.1 was calculated before the first step of averaging took place to make sure no error is introduced by calculating \(\sigma \) from already averaged data. For more information refer to Berge zum et al. (2021).

The mean horizontal wind U and the TKE k in Sect. 4 are normalized. The horizontal wind is normalized using an idealized logarithmic wind profile (Eq. 3) where each measurement altitude was normalized with the corresponding altitude from the logarithmic wind profile. The TKE was normalized using the mean TKE from the measurement in 200 m a.g.l.

To determine the atmospheric stability during the time of flight, the lapse rate,

$$\begin{aligned} {\gamma } = \frac{{\Delta } \theta _{v}}{{\Delta } z}, \end{aligned}$$
(4)

with the difference in virtual potential temperature \({\Delta } \theta _{v}\) over the height \({\Delta } z\) and the bulk Richardson number,

$$\begin{aligned} \text {Ri}_{\mathrm {B}} = \frac{(\frac{g}{T_{v}}) {\Delta } \theta _{v} {\Delta } z}{({\Delta } u)^2 + ({\Delta } v)^2}, \end{aligned}$$
(5)

with the the acceleration due to gravity g, the absolute virtual temperature \(T_{v}\), the virtual potential temperature \(\theta _{v}\), the difference across a layer \({\Delta } z\) and the changes in the horizontal wind components \({\Delta } u\) and \({\Delta } v\) were calculated. The results of the stability estimation are presented in Table 1.

3.4 Leaf Area Index Estimates

The leaf area index (LAI) is a measure for the one-sided leaf area per ground area (Tian et al. 2004). It varies with forest type, time of the year, and latitude (Tian et al. 2004). The value of LAI of a forest with height h is derived by calculating the parameter integral of the leaf area density (LAD) over height z (Shaw and Schumann 1992):

$$\begin{aligned} LAI = \int _0^h \! LAD(z) \, \mathrm {d}z. \end{aligned}$$
(6)

It is important to note that in its definition, the LAI only considers the leaf area. While this is useful for application in agriculture or climatology, it is insufficient for simulating or measuring the flow components within a forest and above. For this task the branches and the tree trunks are also increasing the drag within and above the forest and therefore need to be considered. Measurements, either from the ground using cameras or from above by satellite imaging are incorporating branches at lower levels within the forest (Verger and Descals 2021).

The forest at the WINSENT test site consists mainly of deciduous trees. Figure 6 shows the LAD distribution with height in a deciduous forest with a value of LAI of 2 and 5. The variations in LAD with height are lower for a smaller LAI, which is due to most foliage being apparent in the canopy of the forest. This illustration by Shaw and Schumann (1992) was not made for a certain kind of tree but for deciduous trees in general. There are large differences between different kinds of trees. Maple or Oak have branches with a lot of leaves starting much lower a.g.l. than for example Alder or Pine trees. When using the LAD or LAI this has to be considered.

Fig. 6
figure 6

Distribution of LAD with height within a deciduous forest for a LAI of 2 and a LAI of 5. Source: Shaw and Schumann (1992)

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The difference in foliage density results in different drag within the forest (Kaimal and Finnigan 1994; Lalic et al. 2003). A high LAI results in lower wind speeds within the forest and in the transition zone directly above it (Lalic et al. 2003).

In deciduous forests, changes in LAI can be seen in the course of the year. The LAI for the forest covering the escarpment was estimated according to the method described by Baret et al. (2010), Confalonieri et al. (2013), and Martin (2015), using vegetation images that are automatically processed and the LAI calculated by using the so called ‘gap fraction’ (Confalonieri et al. 2013; Martin 2015):

$$\begin{aligned} \mathrm {Gap \ fraction} = \frac{\mathrm {Sky \ area}}{\mathrm {Total \ area}}. \end{aligned}$$
(7)

The pictures were taken from the ground (upward directed photo), using the sky area for the gap fraction in Baret et al. (2010).

Before calculating the gap fraction, the picture is binarized, so sky pixels are assigned the value zero and vegetation pixels the value one by using the ‘histogram-based unimodal threshold method’ (Martin 2015). The LAI calculation with the method of Martin (2015) is based on:

$$\begin{aligned} LAI = - \left( \dfrac{\cos (\theta _v)}{G(\theta _v,\phi _v)} \right) \log (P_0(\theta _v,\phi _v)). \end{aligned}$$
(8)

The equation uses the gap fraction \(P_0(\theta _v,\phi _v)\), zenith angle \(\theta _v\), azimuth angle \(\phi _v\), and projection function \(G(\theta _v,\phi _v)\), which is the fraction of foliage in direction of the view angle (Bréda 2003; Confalonieri et al. 2013). The value of G is set to 0.5 and the value of \((\theta _v,\phi _v)\) to \(57.5^\circ \), as the angle of the leaves is then negligible according to Weiss et al. (2004).

The values of LAI for winter and summer were calculated from spherical photos at 17 different locations along the escarpment transect made at a single representative day in July (summer) and February (winter). For winter, the value of LAI in those locations ranged from 0.1 to 1.1, with an overall mean of 0.6 (marked with ‘low LAI’ in Table 1). The same locations during summer resulted in a LAI ranging from 1.8 to 2.2 and a mean of 2.07 (high LAI in Table 1). These results are lower than found by Tian et al. (2004) and Tillack et al. (2014), but are close to the satellite derived data from Copernicus with a LAI of 0.6 for winter (low LAI) and 3 for summer (high LAI) (Copernicus Service information 2021).

4 Results

The atmospheric stability has a strong influence on turbulence production close to the ground. An unstable atmosphere generates buoyancy, which causes turbulence additional to the turbulent shear stress induced by the orographic effect. Table 1 shows the calculated lapse rate \(\gamma \) (Eq. 4), which is a measure of thermal stability, for the times of each flight between 30 and 200 m a.g.l. The lapse rate is negative for four flights with high LAI and one flight with low LAI. However, they are still very close to zero with a maximum decrease in virtual potential temperature \(\theta _{v}\) of − 0.71 K over 100 m altitude. The lapse rate during the first flight on 10 March 2021 was clearly larger than zero, meaning the atmosphere was slightly stably stratified. A stable thermal stratification is dampens turbulence, but this had a negligible effect on the measured data. Therefore the flight was also included in the analysis. All other flights are considered with a near neutral thermal stratification.

The bulk Richardson number (\(\text {Ri}_{\mathrm {B}}\)) was also calculated using flight data, similar to the method used in Platis et al. (2021). It is a measure to distinguish between turbulence driven by buoyancy and turbulence driven by vertical shear stress due to the surroundings (mechanically driven). Values above 0 and especially above 0.25, the critical Richardson Number, are considered stable and most of the turbulence is mechanically driven. For negative values the part of buoyancy-driven turbulence is equal or even higher than from mechanical sources like the orographic effect. The data shown in Table 1 evince that during three measurements (14 August 2018, 10 December 2019, and 29 July 2021), the value of \(\text {Ri}_{\mathrm {B}}\) was significantly below 0 and therefore buoyancy was dominating. The \(\text {Ri}_{\mathrm {B}}\) values (Eq. 5) where calculated for each altitude segment of the flight data. Table 1 shows \(\text {Ri}_{\mathrm {B}}\) between the lowest altitude at 30 m and the highest altitude at 200 m. Calculations of the bulk Richardson number indicate that, due to the warm surface, most of the buoyancy-driven turbulence is introduced in the altitudes closest to the ground (not shown), but influences the results for \(\text {Ri}_{\mathrm {B}}\) over the whole altitude range.

The mean wind speed and wind direction for each flight is shown in Table 1. The wind speed ranges from 2 to 8.5 m s\(^{-1}\) with most of the measurements done at 3–6 m s\(^{-1}\), which is the most common wind speed range for this area. Wind direction was limited to flights with westerly components (Table 1). Complexity to the terrain profile is added by the small hill upstream of the test area, well within the range of accepted wind directions for this analysis (Fig. 3).

4.1 Mean Wind Speed

Figure 7 shows the normalized wind speed for eight heights between 30 and 200 m a.g.l. with the height reference (ground level) on the plateau at a distance of 600 m (Sect. 3.2). Especially at heights below 60 m, a pronounced speed-up over the crest is visible. At heights of 30 m and 40 m a.g.l. right above the escarpment edge, the wind speed in summer (red line) increases to a factor of 1.61 in relation to an idealized logarithmic wind profile (Eq. 3), based on the mean wind speed in 200 m, in a flat area upstream of the crest. In winter (blue line), this factor peaks at 1.13, meaning a speed-up over the crest of 13% compared to the logarithmic wind profile upstream.

Fig. 7
figure 7

The mean wind speed calculated from UAS wind data for summer (red) and winter (blue) for altitudes between 30 and 200 m above the plateau and normalized with an idealized logarithmic wind profile upstream of the escarpment (solid lines). The shaded areas are the standard deviation between those flights

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The speed-up in winter (blue line) is not as strong in altitudes close to the ground, but still visible when compared to the flow speed further downstream or upstream of the crest. The difference between summer and winter and a speed-up is still visible in 40 m, but already less pronounced.

Fig. 8
figure 8

Vertical profiles off all flights for summer and winter. The first column shows the standard deviation of the u-component of the wind. The middle and right column show the standard deviation of the v- and w-component, respectively. The data have not been normalized

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Due to the consideration of the hill to be lower in height during winter without the thick foliage and therefore larger parts of the air flowing through the forest instead of being deflected upwards, the maximum speed-up in winter might be lower than 30 m altitude, where the UAS was not able to measure, and thus not visible in the data. The different hill shape due to the forest might also explain the difference in wind speed at the lowest altitudes of 30 m and 40 m between the seasons. In summer, the now steeper hill with the forest acting as a vertical extension (Fig. 4) causes an increased speed-up above the crest compared to winter, where larger amounts of air can flow through the forest instead of above it.

At 80 m and above, no distinctive speed-up over the crest is visible (Fig. 7). At altitudes of 100 m and 160 m the measurements show higher values in normalized wind speeds for summer and winter, respectively. This might also be another speed-up effect caused by the upstream hill (labelled with No. 2 in Fig. 3) and shifted up in altitude with distance over the valley. This effect of accelerated winds in 100–140 m was already visible in a case study done with UAS at the same site by Berge zum et al. (2021). Here the numerical models and the measurements showed an additional layer in those altitudes with faster flowing air masses when compared with neighbouring streamlines above and below.

The standard deviation between flights, plotted as shaded areas, also decreases with height. The trailing edge of the forest, but also the orography itself are causing perturbations in the wind components in altitudes of up to 80 m a.g.l. These perturbations are also in accordance with the measurements by Berge zum et al. (2021) and simulations by Knaus and Dürr (2015) and Knaus et al. (2018).

The vertical profiles in Fig. 8 shows the three meteorological wind components u, v, and w. The vertical profiles in Fig. 8, extracted from the horizontal legs in Fig. 7 are plotted for the three wind components during both seasons at three locations to reference the locations of theoretical data in Fig. 1. Due to not having the wind components, the upwind location is not the idealized logarithmic wind profile (Eq. 3), but the furthest flight data available to the west. The downwind data originates from the flight measurements furthest to the east. Already above the slope (upwind) in the lowest altitudes smaller perturbations are visible, especially for u and v. They are more pronounced over the crest and the plateau. The speed-up over the crest is mostly visible in the u-component. During winter, the flow speed of the v-component is much higher above the plateau. Also visible here is the second flow maxima at heights of 100 m a.g.l.

Figure 9 shows the standard deviation for more locations along the escarpment and the plateau. Each graph consists of data points within ± 15 m around the points at 200, 300, 400, 500, 600, 700, and 800 m distance (x axis) along the slope and the plateau. The lowest altitude with measurement data is 30 m. We can see stronger perturbations for the lowest three altitudes at 30, 40, and 60 m. The escarpment influences especially the horizontal components u and v, while the vertical component w shows smaller fluctuations due to smaller values of w. Directly above the slope, the deviation in the signal is stronger for w compared to the area above the plateau. This can also be seen in the inclination angle \(\alpha \), a proxy for the vertical velocity w, which is discussed in Sect. 4.3.

Simulations and wind-tunnel experiments by Liu et al. (2019) showed a very similar behaviour for the horizontal components u and v over a model hill with stronger perturbations in the lowest data points above the crest. Figure 7 also indicates the earlier mentioned second speed-up in altitudes above 100 m, especially in winter. The standard deviations observed for v in Fig. 9 at the altitudes of 30–60 m are more pronounced when compared with u and therefore have a larger impact on the seasonal differences. This is contrary to the findings by Hunt et al. (1988), where the v-component is causing less perturbation when compared with u. These differences can be explained with the non-ideal terrain, a 3D environment and the canopy. Especially for wind directions with a northern component, the wind is deflected by the escarpment towards the measurement site (Fig. 3) causing stronger perturbations in the v component.

Fig. 9
figure 9

Vertical profiles of all flights for summer and winter. The lowest row shows the standard deviation of the u-component of the wind. The middle and top row show the standard deviation of the v- and w-component, respectively. The data have not been normalized

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Fig. 10
figure 10

Turbulence kinetic energy calculated from UAS wind data for summer (red) and winter (blue) for altitudes between 30 and 200 m above the plateau and normalized with the 200 m altitude data. The solid lines show the mean of all flights for each season and the shaded areas are the standard deviation between those flights

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4.2 Turbulence Kinetic Energy

The turbulence kinetic energy per mass, k, was calculated separately for each measurement height within each flight and then the individual flights were averaged the same way as the standard deviation \(\sigma \) of the wind components in Sect. 4.1. Values of \(\sigma \) (shaded areas) reaching into negative plot regions in altitudes at 100 m and above in Fig. 10 are caused by the always positive standard deviation in some locations being larger than the TKE base value.

The TKE displayed in Fig. 10 shows a strong dependence on the height a.g.l. At 30 m and 40 m above the plateau, in the lee of the forest edge, strong turbulence develops, five times higher in summer and three times higher in winter compared to the undisturbed flow at 200 m altitude. To a certain degree the slightly unstable thermal stratification on some days in summer will have an impact onto the turbulence production on the plateau, but the fact that the largest TKE is measured directly at the crest in the lee of the forest shows that the main contributor is the orography and the canopy. Above 60 m altitude, the TKE in both seasons is nearly equal and no second peak is visible at heights where there was another speed-up in the horizontal wind measured. The orographic effect on the TKE is to be expected in the lowest altitudes above the crest (Liu et al. 2019). This can be seen in the UAS measurements as well, but especially in summer the turbulence production by the foliage seems to superimpose the orographic effect. In winter this superimposition is less pronounced and more of the actual orographic effect can be measured when the flow can move through the canopy more easily.

Figure 11 shows the difference in TKE for the summer (left) and winter (right) measurements. The higher production in summer due to the high LAI and a longer and thicker wake over the plateau is clearly visible. Berg et al. (2011) and Lange et al. (2016) found an enhancement of the turbulence of up to 300% for the Bolund test site in Denmark. Since the Bolund test site has no forested slope, this supports the assumption that the forest at the WINSENT test site has little influence on TKE production in winter, and therefore low LAI, and that most of the turbulence is generated by the orography through shear stresses between the decreased wind speed in the lee of the crest and the speed-up above it.

Fig. 11
figure 11

Contour plots of the turbulence kinetic energy of all flights for summer (left) and winter (right). The darker shaded areas on the hill slope is the canopy

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4.3 Inclination Angle

The inclination angle \(\alpha \) (Eq. 2), the inclination of the horizontal wind caused by the vertical wind component w, is typically positive above the hill slope and negative or neutral on the hill’s lee side. The escarpment at the WINSENT test site does not have a lee side, but a long plateau. Figure 12 presents the measured data for summer and winter. The difference in \(\alpha \) is strongest at the lowest altitudes with 10\(^\circ \) over the slope and 0 to \(-\,8^\circ \) over the plateau. In altitudes above 120 m, the difference in inclination between slope and plateau has decreased.

The values 30 m above the plateau especially indicate a strong variation between the single flights in summer and winter. The lowest altitudes are still strongly influenced by the canopy causing larger variations in vertical wind w (Liu et al. 2019). In general the inclination angle does not depict a strong dependence on the seasons and therefore the LAI. Above the slope and the crest, the values for summer are higher at 30 m, 60 m, and 80 m when compared to the data from winter. Only at an altitude of 120 m the \(\alpha \) in winter is constantly higher. It is not clear why there is an offset between summer and winter in that altitude. The data shows larger variations in 120 m possibly caused by single flights with significantly lower inclination angles in summer.

Fig. 12
figure 12

Inclination angle \(\alpha \) calculated from UAS wind data for summer (red) and winter (blue) for altitudes between 30 and 200 m above the plateau. The solid lines show the mean of all flights for each season and the shaded areas are the standard deviation between those flights

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4.4 Comparison to Past Literature

Theories and past experiments predict a speed-up effect close to the ground over the crest of a hill (Bradley 1980; Taylor et al. 1987) when compared with the undisturbed flow higher up or upwind of the crest. This effect is also visible in Fig. 7. The increased wind speed in low altitudes in summer fits well to measurements done with a single tower at the crest of Black Mountain by Bradley (1980), with a maximum speed-up found in a height of 28 m above the canopy and a displacement height of 7 m.

For the WINSENT test site the calculated \({\Delta } S_{\text {max}}\), using the equation for a 2D escarpment by Taylor and Lee (1984), reaches a value of 0.58 for summer and 0.39 for winter meaning the maximum wind speed above the crest is 58% and 39% higher in summer and winter, respectively. Table 2 shows the calculated values for the site specific terrain for all equations suggested by Taylor and Lee (1984). The measured values for the escarpment at the WINSENT test site are written in brackets behind the calculated values from theory.

Table 2 Calculated \({\Delta } S_{\text {max}}\) using the suggested equations for certain hill shapes by Taylor and Lee (1984) with the defined hill length L from Hunt et al. (1988)
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The fractional speed-up \({\Delta } S_{\text {max}}\) derived from the measurements (Fig. 7) for the WINSENT test site is 0.61 (red line) for summer and 0.13 (blue line) for winter, using the idealized undisturbed wind profile upstream of the crest for each altitude. The fractional speed-up for the measurements during summer above the crest in the heights listed in Table 3 fits well in the ranges for 2D escarpments proposed by Taylor and Lee (1984) in Table 2. With the modification to the hill shape in Fig. 4, the calculated \({\Delta } S_{\text {max}}\) for winter is at a maximum value of 0.39 and thus three times higher than the measured value of 0.13.

The analysis by Taylor and Lee (1984) was done for hills without a canopy and for idealized terrain. Such idealized topography is of course very rare in the real world. In this case a more complex terrain and a large canopy on the escarpment play major roles in the formation of the wind field. Despite these limitations our results fit well with the theoretical foundations by Taylor and Lee (1984). The results by Bradley (1980) for Black Mountain with its similar hill length L and hill height H predict the speed-up in the same range of altitude above the crest, but resulted in a much higher \({\Delta } S_{\text {max}}\) of 1.07, a 107% higher wind speed compared to the undisturbed measurement (Table 3). Because Black Mountain is not an escarpment, but a ridge, the speed-up is higher according to the theories and models.

Table 3 \({\Delta } S_{\text {max}}\) for the WINSENT test site and the Black Mountain experiment Bradley (1980) describing the maximal speed-up close to the ground above the crest when using the idealized logarithmic wind profile
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5 Conclusion

The MASC-3 UAS was used to measure the wind field over the WINSENT test site during 14 flights in high and low LAI conditions. Data from those flights were compared to theories and experiments by Jackson and Hunt (1975), Bradley (1980), Taylor et al. (1987), Taylor and Teunissen (1987), and Hunt et al. (1988). Those theories were developed for low hills with more gentle slopes and neutral conditions, but most of the features they predict are evident in the presented dataset by airborne measurements over a more complex terrain with a forested slope. The mean velocity and velocity perturbations above the hill crest are in accordance with the theories by Jackson and Hunt (1975).

These studies often only analyzed the impact of a hill or a hill covered with a canopy on the wind field. However, at least for deciduous forests in a moderate climate a large difference in drag and shear exists between the seasons. This difference is estimated by the leaf area index. The present study aimed at answering the question if there is a difference in the velocity components and the turbulence of the flow field between the seasons in complex terrain and finding a link to the theories and models developed decades ago. Those differences are important for the installation, energy production and interpretation of the data collected with wind energy converters in complex terrain in general and especially with the research wind energy converters that are going to be installed at the WINSENT test site.

A clear difference in wind speed over the WINSENT test site was found between the seasons. The lowest altitudes between 30 and 60 m are strongly influenced by the foliage density. The maximum speed-up \({\Delta } S_{\text {max}}\) measured above the crest in summer was 0.61 or 61% using as reference an idealized logarithmic wind profile upstream. The speed-up in winter was slightly lower with a factor of 0.13. When using the undisturbed logarithmic wind profile upstream, the assumptions by Taylor et al. (1987) for a 2D escarpment using the hill shape for summer (Fig. 4) agree very well. In winter, with the hill having a lower profile due to the low LAI (missing foliage), the calculations with the equations in Table 2 yield a value of 0.39 being three times higher than the measured value of 0.13 or 13%. The differing hill shape during the seasons (Fig. 4) might also be a possible explanation for the stronger winds in heights of 30 m and 40 m during summer. The very sparse forest in winter without any foliage and thus a low LAI lets air flow more freely through the forest and is therefore a smaller obstacle than the forest during summer with its high LAI and a dense foliage acting as a hill extension increasing the speed-up above the crest.

At higher altitudes this difference in speed-up is not visible, except for a band between 120 and 160 m a.g.l. In this area the wind speed picks up again with the data from winter being higher. This might be the influence of the upstream hill (see Fig. 3) disturbing the wind field and causing a speed-up that was advected upwards over the valley before reaching the crest of the escarpment.

The different amplitude in speed-up above the crest during the seasons is explainable with the forest itself. During winter with no foliage and therefore a very low LAI of 0.6, the air can flow more freely through the forest while in summer the dense canopy forces a large part of the flow above it artificially making the escarpment higher. If we consider this in the equations by Hunt et al. (1988) we get a lower \({\Delta } S_{\text {max}}\) for winter.

Same as the wind speed, the turbulence kinetic energy is largely impacted by the LAI. In 30 m and 40 m a.g.l. the measurements in summer showed a 40% higher TKE than in winter. The turbulence decreases with height, but the foliage dependence is clearly visible.

The main results are:

  • A clear difference in speed-up over the crest (up to 61% in summer) and a strong difference in TKE in the lee of the trees on top of the escarpment were found. The highest values were reached close to the ground in altitudes of 40 m and below.

  • Despite the complex terrain and the high canopy, the analytical models and theories from the 1970s and 1980s are still evident. Especially the measurement flights during summer (high LAI) resulted in a good agreement with the theoretical calculations using the equations by Taylor and Lee (1984) done for the WINSENT test site. The measurements during winter resulted in a fractional speed-up that is only one third of the calculated speed-up from the theories. However, it is important to note that the theories and analytical models only covered hills without or a small canopy. Especially the forest edge, which was included in any past model discussed here, has a large influence on turbulence production in the lowest altitudes a.g.l.

This study showcased the influence of the leaf area index (foliage) onto the flow field over an escarpment. The difference in flow features for different seasons have a large impact on life time calculations and power output for wind energy applications in complex terrain. To obtain a better picture of the flow phenomena in complex terrain during different seasons more experiments are needed and model calculations should take into account the different foliage in the corresponding seasons to obtain more reliable results for modelling the wind field in complex terrain. It would also be beneficial to compare future measurements during different thermal stability conditions and compare those results to the analytical models.