Influence of Complex Terrain on Near-Surface Turbulence Structures over Loess Plateau

To study the influence of complex terrain with different scales on the structure of near-surface turbulence, the turbulence observational data from Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) were analyzed. SACOL is located in typical Loess Plateau topography. The terrain around the site varies greatly with the direction. Representative data from the Northeast, Southeast, Southwest, and Northwest were selected to study the structure characteristics of the near surface turbulence. The complex topography within the flux footprint enhances the vertical scale of turbulence σw and thereby increases the vertical–longitudinal ratio of turbulence Ar. While the turbulent horizontal scale σu is also significantly affected by the distant terrain beyond the flux footprint. The upwind terrain undulation increases σu and reduces Ar. Affected by the complex terrain, the ratio of the spectrum of the vertical velocity to that of the longitudinal velocity, Sw(n)/Su(n), is far less than 4/3 in the southwest direction, and the turbulence is significantly anisotropic.


Introduction
Boundary layer turbulence connects the surface thermal, hydrology, and biochemical processes with atmospheric motions, thus affecting the global atmospheric circulation and climate system. It is a crucial concern to research regional responses and feedback to climate change, as well as the impact of human activities on the environment and climate [1,2]. Atmospheric turbulence is also an important process that affects extreme weather and climate disasters such as heavy rain, sand, and hail. Near-surface turbulent fluxes are the most important indicators in the study of land-atmosphere interaction, which is one of the core issues for developing atmospheric models and improving the accuracy of the simulation, and they are also key input parameters for studying the carbon cycle of the earth-atmosphere system and estimating crop yields. In addition, to understand the diffusion of atmospheric pollutants [3] and the utilization of wind energy [4], it is necessary to understand the structure and motion characteristics of boundary layer turbulence.
The concepts that relate to the turbulence of the atmospheric boundary layer (ABL), such as the Monin-Obukhov similarity theory (MOST), were usually developed over a horizontally homogeneous surface [5]. However, the turbulence in the ABL is directly affected by the underlying surface [6]. As a result, the laws that describe the average field and turbulent field established under the condition of flat and uniform underlying surface are not completely applicable to the ABL on the inhomogeneous underlying surface. However, since it is affected by factors such as topographic fluctuations, soil types, and surface vegetation differences, the actual underlying surface is ever-changing and often inhomogeneous. Data from TRACT (TRansport of Air pollutants over Complex Terrain) showed that the terrain had a significant impact on the structure of the boundary layer, and the topography-induced secondary circulation affected

Site Description
The Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) is located on the top of Cuiying Mountain (35.946° N, 104.137° E) at Yuzhong Campus of Lanzhou University. SACOL was established in 2005 to fill in the gaps in long-term observations of landatmosphere interaction on the Loess Plateau, to study the effects of atmospheric aerosols on the surface water cycle and climate change and to understand the impact of human activities on climate change in this semi-arid region.
From a mesoscale perspective, SACOL is located on a loess mesa, Cuiying Mountain, which is roughly north-south trending with a 1965.8 m elevation (Figure 1 Figure  1 (a) is drawn using ASTER GDEM v2 data [25].
The flux observation field is basically flat, about 200 m in the east-west direction, and about 400 m in the north-south direction, evenly covered with Stipa bungeana, Artemisia frigida, and Leymus secalinus. The height of the vegetation is about 0.24 m in summer and 0.10 m in winter. Except for a long and narrow area west to the south of the observation field, the periphery of the observation field in other directions is a hillside, and the terrain height decreases rapidly. The vegetation is basically in its native state, with a height of about 0.10 m in winter and 0.24 m in summer. For more information about SACOL, please refer to Huang et al. [26]. The area surrounded by the yellow line is the observation field, and circles filled with yellow and blue represent the locations of the boundary layer meteorological tower (BLM tower) and the eddy covariance system (EC). The topographic map in Figure 1 (a) is drawn using ASTER GDEM v2 data [25].
The flux observation field is basically flat, about 200 m in the east-west direction, and about 400 m in the north-south direction, evenly covered with Stipa bungeana, Artemisia frigida, and Leymus secalinus. The height of the vegetation is about 0.24 m in summer and 0.10 m in winter. Except for a long and narrow area west to the south of the observation field, the periphery of the observation field in other directions is a hillside, and the terrain height decreases rapidly. The vegetation is basically in its native state, with a height of about 0.10 m in winter and 0.24 m in summer. For more information about SACOL, please refer to Huang et al. [26].

Instruments
SACOL has accumulated a large amount of data for long-term continuous observation in the semi-arid region of the Loess Plateau, which has provided a basis for studying the characteristics of land-atmosphere interactions on the complex terrain in the semi-arid region of the Loess Plateau. The observations used in this study include the boundary layer meteorological observing tower (BLM tower) and the eddy covariance system (EC). The BLM tower is 32.5 m high, with wind speed, temperature, and humidity sensors installed at the heights of 1, 2, 4, 8, 12, 16, and 32 m, respectively, and a wind direction sensor at 8 m. Moreover, a CS105 barometric pressure sensor and a TE525MM-L rain gauge are used to detect and record the atmospheric pressure and snow. The BLM tower data are automatically collected and recorded every half hour. The EC consists of a three-axis sonic anemometer (CSAT3) and an open-path infrared CO 2 and H 2 O analyzer with a sampling frequency of 10 Hz, which are placed 3.0 m above the surface and are calibrated in May every year. The orientation of the CSAT3 is 15 • east by north. The main observation instruments, observation items, and installation locations are presented in Table 1. The time involved in this study is in Beijing time (BJT) unless otherwise specified. BJT is 8 h earlier than universal time and 1 h earlier than the local time of SACOL.

Data and Methods
Observation data of the EC and BLM tower of SACOL in 2008 were selected to analyze the characteristics of near-surface turbulence on complex terrain. Figure 2 shows the wind direction and velocity distribution of SACOL in 2008. Located in a southeast-northwest valley, the dominant wind directions of SACOL are southeast and northwest winds. Blocked by the mountains on both sides, the northeast and southwest winds are rare and weak. To compare the turbulence characteristics over different terrains, the turbulence data of the EC were filtered according to the wind direction: observations with wind directions of 0 • -60 • , 90 • -150 • , 180 • -240 • , and 270 • -330 • and the standard deviation of the wind direction within 30 min being less than 30 • were selected, and then, they were run through the following quality controls: (1) Runs when the instrument's warning signals arose or when precipitation occurred were rejected.
(2) Runs with more than 10 consecutive observed values that did not meet the physical threshold of the instrument were rejected. (3) Spikes were removed following the algorithm from Vickers and Mahrt [27].
Then, we obtained 400, 6546, 422, and 3112 records (here and after, a 30-min time series of the EC is called a record), respectively, as the representative data of the northeast (NE), southeast (SE), southwest (SW) and northwest (NW) direction.
To eliminate the influence caused by the slope of the terrain or the installation tilt of the instrument, double coordinate rotation was performed for each record, in such a way that the x-axis is along the average airflow direction, and the z-axis is perpendicular to the ground. After the double rotation, the wind speeds in the x, y, and z directions are, respectively, denoted as u, v, w, which in turn represent the longitudinal wind, lateral wind and vertical velocity. Then, the turbulence statistics in the four directions of NE, SE, SW, and NW were calculated, and the characteristics of the turbulence in different directions were compared, subsequently the influence of the terrain on the turbulence structure was analyzed. Then, we obtained 400, 6546, 422, and 3112 records (here and after, a 30-min time series of the EC is called a record), respectively, as the representative data of the northeast (NE), southeast (SE), southwest (SW) and northwest (NW) direction.
To eliminate the influence caused by the slope of the terrain or the installation tilt of the instrument, double coordinate rotation was performed for each record, in such a way that the x-axis is along the average airflow direction, and the z-axis is perpendicular to the ground. After the double rotation, the wind speeds in the x, y, and z directions are, respectively, denoted as u, v, w, which in turn represent the longitudinal wind, lateral wind and vertical velocity. Then, the turbulence statistics in the four directions of NE, SE, SW, and NW were calculated, and the characteristics of the turbulence in different directions were compared, subsequently the influence of the terrain on the turbulence structure was analyzed.
The gradient Richardson Number Ri was used as a stability parameter instead of ζ to avoid the self-correlation caused by the shared use of the same turbulent fluctuation in both the independent and dependent variables.
where U and θ are the average of wind speed and potential temperature, respectively, and g is the gravitational acceleration. Ri was evaluated based on local scaling from the BLM tower data measured at 2 m and 4 m. The flux footprints of the representative data in each direction were calculated by Kljun's model [28] (Figure 3), which is suitable for application to long time series and has been used and confirmed in many studies [29,30]. In the NE and SW directions, 80% of the turbulence came from the flat surface of the flux observation field, while in the NW and SE directions, a larger part of the turbulence observed by the EC came from the surrounding undulating surface outside the observation field. It should be noted that although the observed turbulence comes from the observation field, it is still very different from that recorded over a uniform surface, because of the airflow distortion caused by the complex terrain outside the flux footprint. The gradient Richardson Number Ri was used as a stability parameter instead of ζ to avoid the self-correlation caused by the shared use of the same turbulent fluctuation in both the independent and dependent variables.
where U and θ are the average of wind speed and potential temperature, respectively, and g is the gravitational acceleration. Ri was evaluated based on local scaling from the BLM tower data measured at 2 m and 4 m. The flux footprints of the representative data in each direction were calculated by Kljun's model [28] (Figure 3), which is suitable for application to long time series and has been used and confirmed in many studies [29,30]. In the NE and SW directions, 80% of the turbulence came from the flat surface of the flux observation field, while in the NW and SE directions, a larger part of the turbulence observed by the EC came from the surrounding undulating surface outside the observation field. It should be noted that although the observed turbulence comes from the observation field, it is still very different from that recorded over a uniform surface, because of the airflow distortion caused by the complex terrain outside the flux footprint.

The Mean Flow
In the direction of NW, NE, SE and SW, the strong stratification with |Ri| > 1 accounted for 14.3%, 4.8%, 5.1% and 6.8%, respectively ( Figure 4). Complex terrain, on the one hand, changes the structure of airflow to inhibit the development of stratification [7], and on the other hand, it generates

The Mean Flow
In the direction of NW, NE, SE and SW, the strong stratification with |Ri| > 1 accounted for 14.3%, 4.8%, 5.1% and 6.8%, respectively ( Figure 4). Complex terrain, on the one hand, changes the structure of airflow to inhibit the development of stratification [7], and on the other hand, it generates turbulence through surface friction, which increases the momentum and heat exchange between the upper and lower layers and weakens the stability of the stratification.  [28]. The red and blue coverage areas are flux footprints for unstable and stable conditions, respectively, and the two contours of each footprint indicate 80% and 90% flux of the contributing source area. (a) NW direction; (b) NE direction; (c) SW direction; (d) SE direction.

The Mean Flow
In the direction of NW, NE, SE and SW, the strong stratification with |Ri| > 1 accounted for 14.3%, 4.8%, 5.1% and 6.8%, respectively ( Figure 4). Complex terrain, on the one hand, changes the structure of airflow to inhibit the development of stratification [7], and on the other hand, it generates turbulence through surface friction, which increases the momentum and heat exchange between the upper and lower layers and weakens the stability of the stratification. According to the distribution of Ri, we divided the stratification stability into several categories: strongly unstable (Ri < −1), moderately unstable (−1 ≤ Ri < −0.5), weakly unstable (−0.5 ≤ Ri < −0.02), neutral/near-neutral (−0.01 ≤ Ri < 0.01), weakly stable (0.02 ≤ Ri < 0.25), moderately stable (0.25 ≤ Ri < 1), and strongly stable (Ri ≥ 1). It was dominated by unstable stratification in the direction of NW, which was mainly of weak and moderate instability, while it was dominated by stable stratification in the SW direction. Figure 5 is the average value of the longitudinal wind speed, u, in different stable ranges. To reduce the random error of the data, samples with less than 15 records were not counted. Except for the neutral/near-neutral condition in the SE direction, the mean value of the u component of the wind According to the distribution of Ri, we divided the stratification stability into several categories: strongly unstable (Ri < −1), moderately unstable (−1 ≤ Ri < −0.5), weakly unstable (−0.5 ≤ Ri < −0.02), neutral/near-neutral (−0.01 ≤ Ri < 0.01), weakly stable (0.02 ≤ Ri < 0.25), moderately stable (0.25 ≤ Ri < 1), and strongly stable (Ri ≥ 1). It was dominated by unstable stratification in the direction of NW, which was mainly of weak and moderate instability, while it was dominated by stable stratification in the SW direction. Figure 5 is the average value of the longitudinal wind speed, u, in different stable ranges. To reduce the random error of the data, samples with less than 15 records were not counted. Except for the neutral/near-neutral condition in the SE direction, the mean value of the u component of the wind speed was less than 3.0 m/s in the NW, NE, and SW directions. Because the valley SACOL location is northwest-southeast, and at the same time is affected by the weather-scale movements in the region, the airflow mainly runs along the valley. Due to the blocking and fragmentation of the western mesa, the northwest wind is weak. The distant terrain in the southeast direction is flat, having a small blocking effect on the airflow in such a way that winds with a u component greater than 3 m/s are mainly concentrated in this direction, and they are usually accompanied by weak stratification of −0.5 ≤ Ri < 0.25 (conditions of weakly unstable, neutral/near-neutral, and weakly stable). The southeast wind decreased with the increase in the stratification. Under strong stratification (strongly stable, strongly unstable), u decreased to less than 2.0 m/s, which was not significantly different from the wind speed during the stratification in the northwest direction.
blocking effect on the airflow in such a way that winds with a u component greater than 3 m/s are mainly concentrated in this direction, and they are usually accompanied by weak stratification of -0.5 ≤ Ri < 0.25 (conditions of weakly unstable, neutral/near-neutral, and weakly stable). The southeast wind decreased with the increase in the stratification. Under strong stratification (strongly stable, strongly unstable), u decreased to less than 2.0 m/s, which was not significantly different from the wind speed during the stratification in the northwest direction.

Turbulence Scale
To analyze the turbulence scale, we chose the standard deviations of the longitudinal and vertical wind σu and σw as the research objects, without using the friction velocity u* to normalize them. The purpose of this choice was to pay attention to the absolute mean scale of the turbulence directly and to avoid the false instability caused by a small denominator during stable stratification. Figure 6 shows the distribution of σu in different wind directions with Ri. For the specific direction, σu was the largest at the neutral/near-neutral condition and decreased while the stratification increased. In a stable stratification, σu was smaller than in an unstable condition and decreases faster with stability. It was basically consistent with the change of u with Ri in the corresponding direction. Comparing σu in the NW and SE directions, at neutral/near neutral, the much stronger wind in the SE direction resulted in σu being greater than in the NW direction, while under moderately strong stratification, it was greater than the latter, although the wind speed in the SE direction was stronger or comparable to the NW direction. This finding reflects the "memory" of horizontal turbulence to distant terrain, in other words, affected by the undulating terrain; the scale of horizontal turbulence blowing from the northwest is larger. Compared with running along the valley, excluding the significant difference in the wind speed, σu in the NE was greater under the same stability. Under weak stratification, σu in the NE was between that in the NW and SE, but it was somewhat smaller under the strong stratification. The wind in the NE is related to the local circulation of the mountain-valley breezes, and the special landform makes the valley wind circulation extremely complicated by many factors, which results in larger horizontal scales of turbulence. For the same reason, although the winds in the SW are much weaker than those in the NW and SE in the stable boundary layer, σu was similar to these two directions.

Turbulence Scale
To analyze the turbulence scale, we chose the standard deviations of the longitudinal and vertical wind σ u and σ w as the research objects, without using the friction velocity u * to normalize them. The purpose of this choice was to pay attention to the absolute mean scale of the turbulence directly and to avoid the false instability caused by a small denominator during stable stratification. Figure 6 shows the distribution of σ u in different wind directions with Ri. For the specific direction, σ u was the largest at the neutral/near-neutral condition and decreased while the stratification increased. In a stable stratification, σ u was smaller than in an unstable condition and decreases faster with stability. It was basically consistent with the change of u with Ri in the corresponding direction. Comparing σ u in the NW and SE directions, at neutral/near neutral, the much stronger wind in the SE direction resulted in σ u being greater than in the NW direction, while under moderately strong stratification, it was greater than the latter, although the wind speed in the SE direction was stronger or comparable to the NW direction. This finding reflects the "memory" of horizontal turbulence to distant terrain, in other words, affected by the undulating terrain; the scale of horizontal turbulence blowing from the northwest is larger. Compared with running along the valley, excluding the significant difference in the wind speed, σ u in the NE was greater under the same stability. Under weak stratification, σ u in the NE was between that in the NW and SE, but it was somewhat smaller under the strong stratification. The wind in the NE is related to the local circulation of the mountain-valley breezes, and the special landform makes the valley wind circulation extremely complicated by many factors, which results in larger horizontal scales of turbulence. For the same reason, although the winds in the SW are much weaker than those in the NW and SE in the stable boundary layer, σ u was similar to these two directions. Figure 7 is the variation of σ w in different wind directions with Ri. For the near-neutral stratification, due to the high wind speed and strong shear in the SE, σ w was the largest, at 0.53 m s −1 . From weakly stable/unstable to strongly stable/unstable stratification, although there were significant differences in the wind speeds in the NW, NE, and SE, there was no significant difference in σ w under the same stability conditions, and the vertical scale of the turbulence was approximately the same. Turbulence in the vertical direction was mainly small-scale and can quickly adapt to surface changes, that is, σ w was mainly affected by the surface of the flux footprint area. The surface features in the flux footprint area in the NW and SE were similar, and thus the vertical scale of the turbulence was close. In the NE, σ u was larger, and the shear of the horizontal airflow in the vertical direction was stronger. However, the turbulence was more from the flat surface near the observation field and the surface friction was small, which weakened the shear generation of the airflow. As a result, σ w was almost the same as the directions along the valley. In the SW, most of the fluxes came from the flat surface, and the wind speed itself was small, which caused the σ w to be significantly smaller than in other directions.  From weakly stable/unstable to strongly stable/unstable stratification, although there were significant differences in the wind speeds in the NW, NE, and SE, there was no significant difference in σw under the same stability conditions, and the vertical scale of the turbulence was approximately the same. Turbulence in the vertical direction was mainly small-scale and can quickly adapt to surface changes, that is, σw was mainly affected by the surface of the flux footprint area. The surface features in the flux footprint area in the NW and SE were similar, and thus the vertical scale of the turbulence was close. In the NE, σu was larger, and the shear of the horizontal airflow in the vertical direction was stronger. However, the turbulence was more from the flat surface near the observation field and the surface friction was small, which weakened the shear generation of the airflow. As a result, σw was almost the same as the directions along the valley. In the SW, most of the fluxes came from the flat surface, and the wind speed itself was small, which caused the σw to be significantly smaller than in other directions.   From weakly stable/unstable to strongly stable/unstable stratification, although there were significant differences in the wind speeds in the NW, NE, and SE, there was no significant difference in σw under the same stability conditions, and the vertical scale of the turbulence was approximately the same. Turbulence in the vertical direction was mainly small-scale and can quickly adapt to surface changes, that is, σw was mainly affected by the surface of the flux footprint area. The surface features in the flux footprint area in the NW and SE were similar, and thus the vertical scale of the turbulence was close. In the NE, σu was larger, and the shear of the horizontal airflow in the vertical direction was stronger. However, the turbulence was more from the flat surface near the observation field and the surface friction was small, which weakened the shear generation of the airflow. As a result, σw was almost the same as the directions along the valley. In the SW, most of the fluxes came from the flat surface, and the wind speed itself was small, which caused the σw to be significantly smaller than in other directions.  It can be concluded from this section that the vertical scale of the turbulence is related to the surface characteristics in the flux footprint area, while the turbulent horizontal scale is also significantly affected by the distant terrain at the same time, because of the influence of the upstream terrain on the airflow. The more the terrain undulates in the flux footprint area, the larger the vertical scale of the turbulence is, and the greater the upwind terrain undulation, the larger the turbulent horizontal scale is. In addition, we noticed that under strongly unstable stratification, where the thermal convection develops to the strongest, σw decreases significantly. The reason for this phenomenon is not well explained by the current data, and further research is needed.

Vertical-Longitudinal Ratio of the Turbulence
Our previous study on the stable boundary layer turbulence at SACOL showed that topographyinduced nonstationary motions, on the time scales of minutes or tens of minutes leading to abrupt variability in the wind direction or wind speed, are important for the condition of u < 3.0 m/s. The nonstationary motions are anisotropic with strong horizontal fluctuations and weak vertical fluctuations, and they affect the structure of the local turbulence generated by the local shear, resulting in a weakened σw/σu. To describe the spatial structure of turbulence, we defined the verticallongitudinal ratio of the turbulence, which is the ratio of the vertical scale to the horizontal scale of the turbulence, that is, Ar = σw/σu. Ar can reflect the combined influence of undulating terrain at different scales on the turbulence scale (Figure 8). From a comparison of the different directions, under the same stratification conditions, Ar in the four directions was SE > NW > NE > SW in turn, which is consistent with the terrain in the corresponding direction. In the NW and SE, the turbulent footprint covered more undulating surfaces, with Ar being the largest; in the SW, the turbulence mainly came from a flat surface, with Ar being the smallest, even less than 0.3 under stable stratification; and the NE was in the middle. In the NW and SE, the topographic features in the turbulent flux footprint were similar, while the upwind topography was much more undulating in the NW, causing Ar in the NW to be smaller than SE under any stability conditions. The complex topography within the flux footprint increased Ar, and the distant topographic relief reduced Ar. It can be concluded from this section that the vertical scale of the turbulence is related to the surface characteristics in the flux footprint area, while the turbulent horizontal scale is also significantly affected by the distant terrain at the same time, because of the influence of the upstream terrain on the airflow. The more the terrain undulates in the flux footprint area, the larger the vertical scale of the turbulence is, and the greater the upwind terrain undulation, the larger the turbulent horizontal scale is. In addition, we noticed that under strongly unstable stratification, where the thermal convection develops to the strongest, σ w decreases significantly. The reason for this phenomenon is not well explained by the current data, and further research is needed.

Vertical-Longitudinal Ratio of the Turbulence
Our previous study on the stable boundary layer turbulence at SACOL showed that topographyinduced nonstationary motions, on the time scales of minutes or tens of minutes leading to abrupt variability in the wind direction or wind speed, are important for the condition of u < 3.0 m/s. The nonstationary motions are anisotropic with strong horizontal fluctuations and weak vertical fluctuations, and they affect the structure of the local turbulence generated by the local shear, resulting in a weakened σ w /σ u . To describe the spatial structure of turbulence, we defined the vertical-longitudinal ratio of the turbulence, which is the ratio of the vertical scale to the horizontal scale of the turbulence, that is, A r = σ w /σ u . A r can reflect the combined influence of undulating terrain at different scales on the turbulence scale (Figure 8). From a comparison of the different directions, under the same stratification conditions, A r in the four directions was SE > NW > NE > SW in turn, which is consistent with the terrain in the corresponding direction. In the NW and SE, the turbulent footprint covered more undulating surfaces, with A r being the largest; in the SW, the turbulence mainly came from a flat surface, with A r being the smallest, even less than 0.3 under stable stratification; and the NE was in the middle. In the NW and SE, the topographic features in the turbulent flux footprint were similar, while the upwind topography was much more undulating in the NW, causing A r in the NW to be smaller than SE under any stability conditions. The complex topography within the flux footprint increased A r , and the distant topographic relief reduced A r . In the same direction, the SE, Ar varied with the stability. In the neutral condition, Ar was approximately 0.45, which is close to the observation results of Martins et al. [14] on a 400 m hillside, and lower than the ideal surface (σw/u*= 1.25, σu/u*= 2.39, Ar = 0.52). The rapid decrease in Ar in the stable boundary layer indicates that the friction of the surface on the turbulence is mainly in the horizontal direction, and the turbulence is quasi-two-dimensional. Under unstable conditions, the addition of thermal turbulence did not change the spatial structure of the turbulence, and Ar was equal to or even slightly reduced from the neutral layer structure. It shows that the terrain has a large influence on the turbulence, even in the strongly unstable boundary layer. The friction of the complex terrain produces strong dynamic turbulence, which increases the vertical mixing and weakens the thermal stratification.

Turbulence Spectra
To compare the effect of the terrain scale on the turbulent structure, the power spectral densities of the longitudinal Su(n) and vertical velocity Sw(n) in the NW and SE were analyzed, with n being the frequency. The power spectra densities were multiplied by the frequency n, and thus the area under the spectral function curve can represent the total variance. At the same time, to visually reflect the turbulence variance at different degrees of stability in each direction, we have not normalized the spectra. The longitudinal/vertical velocity spectra classified by the stability are shown in Figure 9. Note that the protrusions at the high-frequency ends of the spectra are mainly caused by white noise and aliasing, having no significant effect on the turbulent fluxes [31], so we calculated the turbulence statistics without filtering.
(a) (b) In the same direction, the SE, A r varied with the stability. In the neutral condition, A r was approximately 0.45, which is close to the observation results of Martins et al. [14] on a 400 m hillside, and lower than the ideal surface (σ w /u * = 1.25, σ u /u * = 2.39, A r = 0.52). The rapid decrease in A r in the stable boundary layer indicates that the friction of the surface on the turbulence is mainly in the horizontal direction, and the turbulence is quasi-two-dimensional. Under unstable conditions, the addition of thermal turbulence did not change the spatial structure of the turbulence, and A r was equal to or even slightly reduced from the neutral layer structure. It shows that the terrain has a large influence on the turbulence, even in the strongly unstable boundary layer. The friction of the complex terrain produces strong dynamic turbulence, which increases the vertical mixing and weakens the thermal stratification.

Turbulence Spectra
To compare the effect of the terrain scale on the turbulent structure, the power spectral densities of the longitudinal S u (n) and vertical velocity S w (n) in the NW and SE were analyzed, with n being the frequency. The power spectra densities were multiplied by the frequency n, and thus the area under the spectral function curve can represent the total variance. At the same time, to visually reflect the turbulence variance at different degrees of stability in each direction, we have not normalized the spectra. The longitudinal/vertical velocity spectra classified by the stability are shown in Figure 9. Note that the protrusions at the high-frequency ends of the spectra are mainly caused by white noise and aliasing, having no significant effect on the turbulent fluxes [31], so we calculated the turbulence statistics without filtering.
under the spectral function curve can represent the total variance. At the same time, to visually reflect the turbulence variance at different degrees of stability in each direction, we have not normalized the spectra. The longitudinal/vertical velocity spectra classified by the stability are shown in Figure 9. Note that the protrusions at the high-frequency ends of the spectra are mainly caused by white noise and aliasing, having no significant effect on the turbulent fluxes [31], so we calculated the turbulence statistics without filtering.

Turbulence Spectra
The longitudinal velocity u spectra do not comply with the −2/3 law in the high-frequency range, and the spectral curves are smoother, following a −2/5 law (Figure 9a,b). The friction of the complex terrain causes small-scale turbulence to increase and contribute to the flux. In the SE, there were sharp peaks in the spectra from neutral to stable stratification, which was approximately 0.05 Hz under neutral conditions and decreased with increasing stability. There were no clear spectral peaks in the unstable boundary layer, and the spectra did not change much at the low-frequency end. In the NW, the spectral peak at neutral stratification was around 0.1 Hz, but the shape is rather flat, and there is no peak in the u spectra in stable and unstable stabilities. The more complicated surface friction in the NW made the turbulence horizontal scale larger, that is, low-frequency turbulence contributed a large amount to the total variance, especially in stable boundary layers.
In the SE, from stable to neutral stratification, the low-frequency bands of the u spectra are upturned. The more stable the boundary layer is, the steeper the spectral curve is, and the inflection points decrease with decreased stability. Moreover, this phenomenon disappears in the unstable boundary layer. The observation data in Antarctica also found that the u spectra were upturned at the low-frequency end, and this was attributed to the disturbance caused by the terrain [32]. Högström et al. [33] also found the same phenomenon and thought it was the result of mesoscale atmospheric waves. However, in the NW, no buoyancy subrange appears in the stable stratification. The possible reasons for this difference are: (1)There is a series of hills with different scales along with the airflow in the NW. The complicated terrain has a severe crushing effect on the airflow and, as a result, it is difficult to form stable mesoscale atmospheric waves.
(2)The scale of the atmospheric wave in the NW is large and cannot be observed within an average time of 30 min.
In the NW and SE, the shapes of the vertical velocity w spectra were almost the same under various stability conditions (Figure 9c,d), that is, under the same stability conditions, the vertical turbulent scale components in the two directions were the same. This further confirms the point in

Turbulence Spectra
The longitudinal velocity u spectra do not comply with the −2/3 law in the high-frequency range, and the spectral curves are smoother, following a −2/5 law (Figure 9a,b). The friction of the complex terrain causes small-scale turbulence to increase and contribute to the flux. In the SE, there were sharp peaks in the spectra from neutral to stable stratification, which was approximately 0.05 Hz under neutral conditions and decreased with increasing stability. There were no clear spectral peaks in the unstable boundary layer, and the spectra did not change much at the low-frequency end. In the NW, the spectral peak at neutral stratification was around 0.1 Hz, but the shape is rather flat, and there is no peak in the u spectra in stable and unstable stabilities. The more complicated surface friction in the NW made the turbulence horizontal scale larger, that is, low-frequency turbulence contributed a large amount to the total variance, especially in stable boundary layers.
In the SE, from stable to neutral stratification, the low-frequency bands of the u spectra are upturned. The more stable the boundary layer is, the steeper the spectral curve is, and the inflection points decrease with decreased stability. Moreover, this phenomenon disappears in the unstable boundary layer. The observation data in Antarctica also found that the u spectra were upturned at the low-frequency end, and this was attributed to the disturbance caused by the terrain [32]. Högström et al. [33] also found the same phenomenon and thought it was the result of mesoscale atmospheric waves. However, in the NW, no buoyancy subrange appears in the stable stratification. The possible reasons for this difference are: (1) There is a series of hills with different scales along with the airflow in the NW. The complicated terrain has a severe crushing effect on the airflow and, as a result, it is difficult to form stable mesoscale atmospheric waves.
(2) The scale of the atmospheric wave in the NW is large and cannot be observed within an average time of 30 min.
In the NW and SE, the shapes of the vertical velocity w spectra were almost the same under various stability conditions (Figure 9c,d), that is, under the same stability conditions, the vertical turbulent scale components in the two directions were the same. This further confirms the point in Section 3.2. From weakly stable/unstable to strongly stable/unstable conditions, the vertical scale of the turbulence is about the same under the same stability conditions. Additionally, the turbulence in the vertical direction is mainly affected by the surface of the flux footprint, while the distant complex terrain has little effect on it.

Local Anisotropy of the Turbulence
According to Kolmogorov's turbulence theory, if the spectral densities of longitudinal velocity S u (n), the lateral velocity S v (n), and the vertical velocity S w (n) in the inertial subrange satisfy the relationship of S v (n)/S u (n) = S w (n)/S u (n) = 4/3, then the turbulence is isotropic. In the NW of SACOL, the w spectra were smaller than the corresponding u spectra under all the stability stratifications ( Figure 10). The phenomenon that S w (n)/S u (n) is less than 4/3 has been found in many previous studies [34][35][36][37]. Chamecki and Dias [38] tested the applicability of the local isotropy hypothesis to surface-layer turbulent flow. They concluded that sonic anemometry, at the currently available measurement frequencies and sensor path lengths, was unable to resolve the full inertial range of the velocity spectra. Even in some cases, whether the turbulence can reach isotropy outside the resolution limit of the sensor remains an unidentifiable question.
Atmosphere 2020, 11, x FOR PEER REVIEW 12 of 15 relationship of Sv(n)/Su(n) = Sw(n)/Su(n) = 4/3, then the turbulence is isotropic. In the NW of SACOL, the w spectra were smaller than the corresponding u spectra under all the stability stratifications ( Figure  10). The phenomenon that Sw(n)/Su(n) is less than 4/3 has been found in many previous studies [34][35][36][37]. Chamecki and Dias [38] tested the applicability of the local isotropy hypothesis to surface-layer turbulent flow. They concluded that sonic anemometry, at the currently available measurement frequencies and sensor path lengths, was unable to resolve the full inertial range of the velocity spectra. Even in some cases, whether the turbulence can reach isotropy outside the resolution limit of the sensor remains an unidentifiable question.
(a) (b) Figure 10. Ratio of vertical velocity spectral density Sw(n) to longitudinal velocity spectral density Su(n) for different stability ranges the directions of northwest (a) and southeast (b).
In the SE, however, when the stratification was relatively strong (Ri < −0.5 or Ri > 0.25), the vertical-to-longitudinal velocity component spectra tended to converge towards a 4/3 value at the high-frequency range, which is an indicator of local isotropy. In the SE, the ratio Sw(n)/Su(n) changed significantly with Ri, while it was almost not related to the stability in the NW. The upwind terrain undulation caused the turbulence, which was more anisotropic with a strong horizontal fluctuation and a weak vertical fluctuation. On a sufficiently complex surface, the dynamic effects of topography have greater influence on the turbulence anisotropic than thermal stratification.

Summary
The Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) is in a very complex terrain environment, and the terrain in each direction is different, which provides valuable data for studying the impact of the terrain scale on the turbulence scale. Using the observational data of SACOL in the year 2008, the characteristics of the near-surface turbulence on the complex terrain of the Loess Plateau were analyzed, and the influence of the terrain scale on the turbulence scale was discussed. The data with wind directions of 0-60°, 90-150°, 180-240°, and 270-330°, and the standard deviations of the wind directions within 30 min less than 30°, were taken as representative data for the directions of northeast, southeast, southwest, and northwest respectively. The main results are as follows: Figure 10. Ratio of vertical velocity spectral density S w (n) to longitudinal velocity spectral density S u (n) for different stability ranges the directions of northwest (a) and southeast (b).
In the SE, however, when the stratification was relatively strong (Ri < −0.5 or Ri > 0.25), the vertical-to-longitudinal velocity component spectra tended to converge towards a 4/3 value at the high-frequency range, which is an indicator of local isotropy. In the SE, the ratio S w (n)/S u (n) changed significantly with Ri, while it was almost not related to the stability in the NW. The upwind terrain undulation caused the turbulence, which was more anisotropic with a strong horizontal fluctuation and a weak vertical fluctuation. On a sufficiently complex surface, the dynamic effects of topography have greater influence on the turbulence anisotropic than thermal stratification.

Summary
The Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) is in a very complex terrain environment, and the terrain in each direction is different, which provides valuable data for studying the impact of the terrain scale on the turbulence scale. Using the observational data of SACOL in the year 2008, the characteristics of the near-surface turbulence on the complex terrain of the Loess Plateau were analyzed, and the influence of the terrain scale on the turbulence scale was discussed. The data with wind directions of 0-60 • , 90-150 • , 180-240 • , and 270-330 • , and the standard deviations of the wind directions within 30 min less than 30 • , were taken as representative data for the directions of northeast, southeast, southwest, and northwest respectively. The main results are as follows: (1) The undulations of the terrain in the flux footprint were in the order of Southeast ≈ Northwest > Northeast >Southwest. Except for the flat terrain in the southeast direction, the distant terrain outside the footprint area was very complicated. The complex terrain resulted in weak stratification stability. Ri was mainly distributed between −1 and 1, and it was even more concentrated in the range of −0.2-0.2 in the directions of the northeast and southeast. Except for the northwest direction, the records with strong stratification, where Ri was greater than 1 or smaller than −1, accounted for fewer than 10% of the total records. (2) The vertical scale of the turbulence is related to the surface characteristics in the flux footprint area, while the turbulent horizontal scale is also significantly affected by the distant terrain. The more the terrain undulates in the flux footprint area, the larger the vertical scale of the turbulence is; the greater the upwind terrain undulation, the larger the turbulent horizontal scale is. (3) The vertical-longitudinal ratio, A r = σ w /σ u , is used to indicate the influence of the topographic scale on the turbulent structure in different directions. Under the same stratification conditions, A r was in the order of Southeast > Northwest > Northeast > Southwest. The complex topography within the flux footprint increased A r , and the distant topographic fluctuations reduced A r . In the southeast direction, A r was about 0.45 in the neutral/near-neutral stratification, and it decreased in the unstable stratification with an average value of above 0.4. In the northwest, northeast, and southwest directions, from unstable to neutral/near-neutral stratification, A r changed slightly, fluctuating around 0.4, 0.35, and 0.3, respectively. In the stable boundary layer, A r decreased rapidly with increasing stability, and the turbulence was quasi-two-dimensional. (4) In the southeast direction, there was a buoyancy subrange in the u spectrum of the stable boundary layer, and the inflection point was of the order of 10 −3 Hz, which increased with increasing stability; in the northwest direction, affected by the distant complex terrain, there was no buoyant subzone observed in the records of 30 min. Affected by the complex terrain in the Northwest, S w (n)/S u (n) was far less than 4/3, and the turbulence was significantly anisotropic.
Author Contributions: Conceptualization, methodology, and writing-original draft preparation, J.L.; validation, J.L., Q.G., and Z.Z.; writing-review and editing, M.Z., P.T., and L.Z. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China, grant number 41605005, 41475008.