A multiscale modeling study of a real case has been conducted to explore the capability of the large-eddy simulation version of the Weather Research and Forecasting Model (WRF-LES) over Xiaohaituo Mountain (a game zone for the Beijing, China, 2022 Winter Olympic Games). In comparing WRF-LES results with observations collected during the Mountain Terrain Atmospheric Observations and Modeling (MOUNTAOM) field campaign, it is found that at 37-m resolution with LES settings, the model can reasonably capture both large-scale events and microscale atmospheric circulation characteristics. Employing the Shuttle Radar Topography Mission 1 arc s dataset (SRTM1; ~30 m) high-resolution topographic dataset instead of the traditional USGS_30s (~900 m) dataset effectively improves the model capability for reproducing fluctuations and turbulent features of surface winds. Five sensitivity experiments are conducted to investigate the impact of different PBL treatments, including YSU/Shin and Hong (SH) PBL schemes and LES with 1.5-order turbulence kinetic energy closure model (1.5TKE), Smagorinsky (SMAG), and nonlinear backscatter and anisotropy (NBA) subgrid-scale (SGS) stress models. In this case, at gray-zone scales, differences between YSU and SH are negligible. LES outperform two PBL schemes that generate smaller turbulence kinetic energy and increase the model errors for mean wind speed, energy spectra, and probability density functions of velocity. Another key finding is that wind field features in the boundary layer over complex terrain are more sensitive to the choice of SGS models than above the boundary layer. With the increase of model resolution, the effects of the SGS model become more significant, especially for the statistical characteristics of turbulence. Among these three SGS models, NBA has the best performance. Overall, this study demonstrates that WRF-LES is a promising tool for simulating real weather flows over complex terrain.
High-resolution flow/weather simulations over complex terrain areas are highly needed for mountain outdoor sports, such as alpine skiing, that greatly depend on local wind conditions. Accurate high-resolution modeling requires proper multiscale simulations from the mesoscale (1–20 km) to the microscale (tens of meters). However, various problems may arise when applying numerical weather prediction (NWP) models over complex terrain (Serafin et al. 2018). One major problem is that turbulence parameterizations in the commonly used one-dimensional (1D) planetary boundary layer (PBL) schemes only consider vertical exchange. Numerical artifacts might be produced in areas of complex terrain, where the assumption of horizontal homogeneity is violated (Goger et al. 2018, 2019) while horizontal exchanges and three-dimensional (3D) effects such as horizontal shear production are entirely neglected. 3D PBL schemes (Jiménez and Kosović 2016) should be able to alleviate the effect of complex terrain, yet there exist no robust approaches that have been validated in a wide range of atmospheric conditions. In addition, mesoscale NWP models with relatively coarse resolution cannot capture microscale variabilities driven by atmospheric dynamics (turbulence effects are fully parameterized). Large-eddy simulation (LES) that can explicitly resolve the most energetic turbulent eddies could be an alternative to PBL schemes (Cuxart 2015). Recently, studies targeting to implement LES in mesoscale models for realistic weather situations have emerged. The large-eddy simulation version of the Weather Research and Forecasting Model (WRF-LES) (Skamarock et al. 2008) has been widely applied for various applications, such as wind energy forecasting (Liu et al. 2011, 2012), hydrometeorological prediction (Talbot et al. 2012; Liu et al. 2015), simulation of turbulence characteristics (Rai et al. 2017; Muñoz-Esparza et al. 2017), precipitation simulation (Xue et al. 2016; Gerber et al. 2018), and valley cold-air-pool study (Crosman and Horel 2017). However, the innermost domain in most of these real cases is located at areas with relatively flat terrain. Therefore, the performance of WRF-LES for the simulation of real flow over complex terrain needs to be further evaluated.
In addition to appropriate turbulence parameterization, another critical issue of multiscale simulations in complex terrain is to ensure appropriate PBL treatment in the “gray zone” (Wyngaard 2004; Boutle et al. 2014; Efstathiou and Beare 2015; Honnert et al. 2016; Chow et al. 2019). The gray-zone scale is too fine to apply mesoscale turbulence parameterizations and too coarse for a LES scheme to resolve turbulent eddies. There is a lack of theoretical ground for a perfect solution that works from the mesoscale 1D PBL scheme to the LES 3D subgrid-scale mixing scheme with various grid sizes. Zhou et al. (2014) performed a set of idealized simulations and demonstrated that gray-zone modeling is not only a numerical challenge but also poses dynamical difficulties. The size of initial instability structures is set by the grid spacing rather than the natural state of the flow. Ching et al. (2014) found that this problem is one of the consequences of modeling flows at grid spacings that are too small to justify the application of PBL schemes and yet too large for explicit calculation of turbulent transfer. Meanwhile, scale-aware (Shin and Hong 2015; Zhang et al. 2018; Kurowski and Teixeira 2018) and 3D PBL schemes have been developed to address this issue. In relatively flat terrain, the gray zone can be skipped by using a very large nesting ratio of 11 (Muñoz-Esparza et al. 2017), while in complex terrain, a large mesh refinement ratio would cause significant terrain mismatch at boundaries between the mesoscale and the nested LES domains. Therefore, it is imperative to study the model performance at gray-zone scales over complex terrain.
The validity of LES results depends largely on the assumption that the subgrid-scale (SGS) stress model can provide a correct description of the energy-producing isotropic eddies within the inertial subrange of 3D turbulence (Muñoz-Esparza et al. 2014a,b). One of the most widely used SGS stress models is the Smagorinsky model (Smagorinsky 1963; Lilly 1966), which assumes that SGS stresses are proportional to the product of the strain rate and the subgrid scale, and the equations must be closed via the Smagorinsky coefficient. However, this model still has problems describing complicated nonlocal anisotropic flows. Germano et al. (1991) and Lilly (1992) obtained the Smagorinsky coefficient using a dynamic approach. In an attempt to correct the bias in the predicted eddy viscosity profiles, Sullivan et al. (1994) proposed a new two-part SGS stress model that takes account of the grid dependence of the Smagorinsky-type SGS stress model. However, this type of model assumes that the SGS stress is aligned with the resolved strain, which is incorrect, and fails to capture the backscatter of energy from small scales to resolved eddies. By using a nonlinear relation that includes second-order terms for the deviatoric part of the stress tensor, Kosović (1997) developed the nonlinear backscatter and anisotropy (NBA) model. Recently, the NBA model has been incorporated into WRF and some studies have compared each various SGS stress model in different resolutions for both flat terrain and 2D symmetrical ridge (Mirocha et al. 2010). However, these comparisons are based on an idealized case, and little has been done to evaluate different PBL treatments based on real-case simulations, especially over complex terrain.
In this study, we conduct a full-physics WRF-LES simulation of a 2-day real case over Xiaohaituo Mountain (a game zone of the Beijing, China, 2022 Winter Olympic Games) with grid spacing of Δx, varying from 1 to 37 m. The simulation results are verified against observations collected during the Mountain Terrain Atmospheric Observations and Modeling (MOUNTAOM) field study. With realistic forcing, we try to evaluate the model applicability over complex terrain. Five sensitivity experiments are conducted with different PBL treatments, including the Yonsei University (YSU) and the Shin and Hong (SH) PBL schemes, and three LES SGS stress models. Uncertainties in the modeling results with different PBL treatments at gray-zone scales and microscale are quantitatively analyzed.
2. Case, observations, and model configuration
a. MOUNTAOM field campaign
This study focuses on the Xiaohaituo Mountain area (Fig. 1b), which is located to the northwest of Beijing with a peak elevation of 2199 m above sea level (MSL). The Xiaohaituo Mountain area has been selected as a game zone of the Beijing 2022 Winter Olympic Games. A series of outdoor games are planned to be held there, including Alpine skiing, bobsled/skeleton, and luge. All of these games require high-resolution and accurate meteorological information, especially surface wind (Rotach et al. 2017; Chen et al. 2018; Liu et al. 2018). Driven by the meteorological service and research needs, the MOUNTAOM field campaign was conducted as a pilot study of the enhanced meteorological observation program of the Beijing 2022 Winter Olympic Games (Chen et al. 2018). The MOUNTAOM was conducted in the winter seasons from 2016 to 2018. Several intensive operating periods (IOPs) were conducted during 10–17 January 2017 and 22–30 January 2018 with a focus on the structures of wind (mountain–valley), temperature, and boundary layer. The purpose of this pilot study is to evaluate and improve the performance of high-resolution (10–100-m grids) numerical models.
Observations used to evaluate WRF-LES performance are collected during the MOUNTAOM; 10-m winds at intervals of 10 min are obtained from 14 automatic weather stations (AWSs; Fig. 1b), among which AWSs 1–9 are deployed along the ski slopes. Enhanced radiosondes (Sparv Embeded AB Windsond) are launched every 3 h at site 15 with a 1-Hz sampling rate during the IOPs. AWSs 13 and 14 are the supersites with more instrumentations, such as surface flux stations that monitor the near-surface atmospheric stability variations, and sonic anemometers (Campbell Scientific, Inc., CSAT3) with an open-path infrared gas analyzer (LiCor, Inc., Li-7500A) mounted at 3-m height above ground level (AGL) on a boom facing south. By applying a sonic tilt correction algorithm (Wilczak et al. 2001), the data are used to calculate turbulence statistics.
b. Case selection
The case in this study (27–28 January 2018) is selected for three reasons: 1) it occurred during an IOP with abundant observations, 2) no precipitation occurred, which makes us able to avoid complicated physical mechanisms associated with wet processes, and 3) the case demonstrates a typical winter weather scenario with strong winds. The wind speed (WSP) averaged at six stations (AWSs 1–3, 5, 10–11, and 14) exceeds the mean WSP threshold (14 m s−1) specified for the sports event, and the gusts at nine stations (AWSs 1–3, 5–7, 10–11, and 14) exceed the gust threshold (17 m s−1). Under such circumstances, holding a sports event is not recommended because high wind speeds would pose threats to the safety of athletes.
The synoptic condition during the case study period is illustrated in Fig. 2 based on the Rapid-Refresh Multiscale Analysis and Prediction System (RMAPS-ST) analysis data (Fan 2015; Liang et al. 2018), which are provided by the Institute of Urban Meteorology. The RMAPS-ST domain covers northern China, with a spatial resolution of 3 km, and data are available at 1-h intervals. The RMAPS-ST assimilates several observational data including surface observation data, sounding data, AWS data, aircraft data over Beijing, water data over the Beijing–Tianjin–Hebei region, and radar wind and reflectivity data collected by 29 Doppler weather radars distributed in the Beijing–Tianjin–Hebei region.
The case in this study is characterized by a strong gale, which was caused by an eastward-moving upper-level trough and accompanied with strong cold air. At 0000 UTC (0800 LST; hereinafter, all times are in UTC) 27 January (Fig. 2a), straight zonal flows prevailed at 700 hPa. At 1200 UTC (Fig. 2b), the circulation at 700 hPa shows that the cold trough in the upper level entered Beijing. Following the approach of the cold air and the diurnal variation, temperature at 850 hPa dropped by about 4°C. The sea level pressure field (figure omitted) shows that the Beijing area was located in front of a high pressure center and that a cold surface front was passing through the city. In the meantime, the surface pressure gradient began to rise quickly in the Xiaohaituo Mountain area (yellow frame), and surface winds increased correspondingly. During 0000–1200 UTC 28 January (Figs. 2c,d), the Xiaohaituo Mountain area was under the control of northwesterly flows while the upper-level trough was passing through Beijing (surface front began to pass through), and strong cold advection occurred. By 0000 UTC 29 January, the upper-level trough moved out of the study area and surface winds began to decrease.
c. WRF-LES setup
To simultaneously represent scales from the synoptic to turbulent eddies, the WRF-LES (version 126.96.36.199) model system is configured with a four-domain one-way online nested setup (Table 1). The online approach allows continuous realistic environmental weather forcing at lateral boundaries of the inner domains. Essentially, it is faster than offline because all domains run simultaneously (Talbot et al. 2012). Furthermore, this approach saves storage space by directly transmitting information to inner domains at every time step. The model domains cover different regions (Fig. 1a). D01 covers the whole Beijing city, and d04 focuses on the Xiaohaituo Mountain area. All domains share the same center point (AWS 4: 40.52°N, 115.78°W) and have the same grid numbers and vertical levels. The horizontal grid spacings Δx are 1 km (d01), 333 m (d02), 111 m (d03), and 37 m (d04). When using a large grid refinement ratio of 11 (Muñoz-Esparza et al. 2014a,b), there might exist discrepancies of terrain height along the lateral boundaries of the nested domains, which can result in rapid model crash. For this reason, we did not specify a large grid refinement ratio to avoid the gray zone.
It is optimal to use an aspect ratio Δz/Δx that is smaller than 1 below the PBL height in the innermost domain (Rai et al. 2017). Fine vertical grid spacing has been found to be a necessity for PBL schemes to avoid overestimating the height of observed low-level jet and overdiffusing the jet structure (Muñoz-Esparza et al. 2017). In the model, 33 vertical levels are set below 1 km AGL. Take d04 for example: the height of the first model vertical level z at AWS 13 is about 13 m AGL (Δz/Δx = 0.35); below 400 m, Δz is set to a uniform value of 26 m (Δz/Δx = 0.70); from 400 m upward to 1 km, Δz ranges from 26 m to approximately 36 m (Δz/Δx = 0.70–1.0); above 1 km, Δz increases from approximately 36 m to 1.2 km at the model top. The time steps dt are set to decrease by a factor of 5, and a very short time step of 1/25 s is required for d04 to ensure numerical stability. This is partly because the abrupt topography changes in the mountain region can potentially introduce vigorous vertical motions in lower levels close to the ground, leading to a violation of the Courant–Friedrichs–Lewy criterion in the vertical direction.
The model configuration and physical parameterizations used in this study are presented in Table 1. The YSU PBL scheme (Hong et al. 2006) has been applied in d01 to simulate the PBL mixing. In the inner domains, the PBL scheme is turned off and the boundary layer turbulence is simulated by LES. In this study, the 1.5-order turbulence kinetic energy closure model (1.5TKE) has been used to parameterize SGS motions. In addition to the use of a length scale and a model coefficient, it also computes the SGS TKE as a prognostic variable to obtain the eddy viscosity (Lilly 1966).
Two topographic datasets with differing resolution are applied to test the influence of terrain on surface wind. One is the traditional U.S. Geological Survey 30 arc s (≈900 m) dataset (USGS_30s; details can be found at http://www.usgs.gov/), and the other is the high-resolution Shuttle Radar Topography Mission 1 arc s (≈30 m) dataset (SRTM1; details can be found at http://www2.jpl.nasa.gov/srtm/). Figures 3a and 3b show the model terrain height over d04 derived from USGS_30s and SRTM1 topographic datasets, respectively. Figure 3c shows their difference. When compared with USGS_30s, the SRTM1 topographic dataset shows more details in complex terrain, has higher terrain height at mountaintops and ridges, and has lower terrain height in valleys. The mean error of the elevations of the 14 AWSs for USGS_30s is 107.4 m when compared with their actual heights, and for SRTM1 the mean error is reduced by 64.7 m.
The initial and boundary conditions (IBCs) for the mesoscale d01 are derived from the RMAPS-ST dataset, which is at 1-h intervals with horizontal grid spacing of 3 km. It is worth noting that the IBCs of the microscale LES domain (from a smooth mesoscale inflow) do not contain all scales of atmospheric motions resolvable by the microscale mesh. Therefore, a fetch of some distance is needed for the turbulence associated with the missing scales to develop within the nested microscale domain (Haupt et al. 2019). Several turbulence initialization methods have been studied for initializing turbulence along the inflow, such as the generalized cell perturbation method (Muñoz-Esparza et al. 2014a) that is based upon finite-amplitude perturbations of the potential temperature field along the microscale domain inflow boundaries. However, turbulence initialization method is not applied in this study. First, the real complex topography and the heterogeneous land surface type provide a broad range of scales of atmospheric motions, which accelerates turbulence development within the microscale LES domain (Xue et al. 2016; Mirocha et al. 2014); second, for the sensitivity experiments described in section 4, simulation results over the inner microscale domains using different IBCs from parent domain d02 are compared and analyzed. Applying turbulence initialization method would interfere with the results of the sensitivity experiments. All the simulations are initialized at 2000 UTC 26 January 2018 and run for 52 h. The model outputs of the four domains have an interval of 1-min for all variables. In addition, velocity components (u, υ, and w), TKE budget, and SGS stress at AWSs 1–15 have been saved every time step.
3. Analysis and verification of WRF-LES results
To evaluate the capability of the high-resolution WRF-LES model for wind simulation over the Xiaohaituo Mountain area, instantaneous results of the simulations are discussed. In addition, time series of horizontal wind speed and vertical profiles of wind speed over all domains are compared with observations. Because temperature is not an important variable for Alpine skiing events, and the differences in simulated temperature at various scales are not as significant as the differences in simulated wind speed, the verification is only focused on winds in this study.
Figure 4 shows simulation results using SRTM1 topographic dataset. Figures 4a–d show vertical cross sections of instantaneous wind speeds at 0400 UTC 28 January for all domains along the purple line shown in Fig. 1b. The cross section runs across AWS 1 (located at the mountaintop) and AWS 13 (located in the valley) and is approximately perpendicular to the prevailing northwesterly predominant winds. It is obvious that more detailed topography features (such as the shapes of the slopes and valleys) and more accurate model terrain height are clearly presented in d04, where the horizontal resolution of the model is the finest. In contrast, the topography in d01 is more terrace shaped and the locations of the mountaintops/valleys can only be roughly recognized. In the mesoscale run, negative values of wind speeds (arrows pointing to the left of the plot) occupy almost the whole cross section except over two windward slopes, where the flows are blocked by the ridges and either stagnate or reverse. These features can be seen with great details in d04. In addition, a wake region (wind speed deficit) can be found in the downstream from the ridge to the valley in d04. In this region, the spatial structure of the wind flow demonstrates more detailed features than its surrounding areas due to changes in the predominant flow direction and terrain height. Note that these features are vanished in the results of the mesoscale runs.
Figures 4e–l show spatial patterns of u and w at the first vertical model level in d04. In d01, the downslope flows originate from the northwestern mountaintop and reach the valley along the ravines and are blocked by a ridge in the southeast. Therefore, positive values of u occur over almost the whole area, except for the southeast corner. In d03 and d04, areas of negative values of u enlarge, and more turbulent structures can be found. This indicates that more local circulations have developed due to improved representation of topography in d03 and d04, which explains why more negative values of u are found in the two domains. Strong updrafts and downdrafts associated with the terrain forcing can be seen in Figs. 4i–l. The case selected for the present study is a typical winter case with strong winds over complex terrain, and thus convective cells close to the surface do not show any typical hexagonal structures that can be found in some convection real case studies over flat terrain (Schmidt and Schumann 1989). The distribution pattern of w is much similar to that of topography. As the air flows over the mountain, the air rises on the windward slope and descends on the leeward slope. The value of w at the mountain ridge is much higher than that in the valley, while the most intense turbulence is found in the valley area (red and blue interlaced distribution). As a result of changes in the predominant mean flow direction (almost perpendicularly to the ridge) and terrain elevation (elevation in the downstream region of the mountain ridge is much lower than that in the upstream region), a wake region with significant velocity deficit forms in the valley region. In d04, the value of w at the mountain ridge is much higher than that in the valley. Furthermore, more detailed structures can be found in the spatial distributions of those wind components in the valley than in its surrounding areas, which is attributed to the gust disturbances produced by the shear effect of strong winds in the upper layer. The gust disturbances transport energy downward as they propagate downward (Whiteman 2000). The coherent gust structure is broken into turbulent structure by the shear and drag effects of topography, which are important for flux transfer in the surface layer (Hunt and Carlotti 2001).
Figure 5 shows simulation results in d04 using USGS_30s topographic dataset. Wind speeds along the vertical cross sections and in the horizontal planes both show significant differences compared to Figs. 4d, 4h, and 4l, especially in the valleys. The distribution of u using USGS_30s in d04 (Fig. 5b) is similar to that using SRTM1 in d01 (Fig. 4e), the values of u are positive in most of the northwestern area, and negative values only appear in the southeast corner. When using SRTM1, with the increase in model resolution (Figs. 4f–h), negative values of u of emerge over a large area in central of d04 (valleys). These negative values caused by reversed flows in the valleys, which are produced by local topographic impacts on the mesoscale flow field. This phenomenon cannot be well described when using a coarse topographic dataset. Besides, the distribution of w in d04 (Fig. 5c) displays square-shaped artificial error, as the horizontal grid spacing is increased to 37 m.
Figure 6 shows the simulated and observed diurnal variations of 10-m wind speed at the mountaintop (AWSs 10, 11) and valley (AWSs 12, 13). Jia et al. (2019) analyzed observed data collected at AWSs within the game zone in the winters from 2016 to 2018. AWSs 10 and 11 are typical “mountaintop type” stations, where wind speeds are strongly influenced by background wind fields, and wind directions are similar to that of background winds. AWSs 12 and 14 are two “deep valley type” stations, where wind speeds are mainly affected by the local thermal circulations generated by the topography around. In this case, the Xiaohaituo Mountain area is mainly controlled by typical large-scale synoptic northwesterly flow. Wind speeds at the mountaintop are significantly higher than that in the valley.
In the first 12 h of the simulation, wind speeds are relatively small when high-level trough had not started to affect the Xiaohaituo Mountain area. From 1200 to 1400 UTC 27 January, high-level trough moved eastward and entered Beijing, and a surface front started to pass through. The wind speed at all stations began to increase significantly, and high wind speed maintained until 0000 UTC 29 January. Comparing the time series of simulated and observed wind speeds, we can see that WRF-LES can reasonably capture the overall large-scale wind evolution in each domain using either SRTM1 or USGS_30s. Obviously, the time series of simulated wind speed with SRTM1 (Figs. 6a,c) in d01 is much smoother than that of observations. With the increase of resolution in d03 and d04, we can see more reasonable wind speed fluctuations, which are associated with microscale eddy motions that can be resolved in high-resolution simulations. However, in the experiment using USGS_30s, neither d03 nor d04 simulations show the same improvement.
The above phenomena can be seen more clearly in the scatterplots of wind speed (Fig. 7). The underestimation of wind speed at the mountaintop (Fig. 7, top) and overestimation in the valley (Fig. 7, bottom) (Jiménez and Dudhia 2012) are partially alleviated by using high model resolution and SRTM1. However, with the same resolution but using USGS_30s (Figs. 7e,j), the accuracy of the simulated wind speed has not been effectively improved compared to the case using SRTM1. Figures 6 and 7 suggest that correct topography representation is more important than the choice of PBL treatment for realistic simulation of wind speed. This result is consistent with the findings of Wagner et al. (2014).
Quantitative comparisons of mean biases are shown in Table 2. When using SRTM1, compared with d01, the biases of d02, d03, and d04 respectively decrease by 36%, 68%, and 80% at the mountaintop and by 70%, 88%, and 96% at the valley. Compared to USGS_30s, the biases of SRTM1 decrease by 66% at the mountaintop and 91% in the valley. More statistical evaluations of model results are shown in Fig. 8, which gives the Taylor diagrams (Taylor 2001) of 10-min 10 m wind speed comparison in the four domains. We can see that when using SRTM1, the normalized RMS difference (NRMSD) between the simulated and observed wind speeds has been reduced with increasing model resolution, and the correlation coefficient has been increased. In contrast, when using USGS_30s, both the NRMSD and the correlation coefficient remain nearly constant in d02, d03, and d04, regardless of the high-resolution of inner domains. The above analysis indicates that using a coarse topographic dataset would not be able to make full use of high-resolution model grids. In addition, it indicates that LES has the capability to capture and regenerate microscale atmospheric motions caused by complex terrain on the scale less than 100 m. Therefore, SRTM1 dataset is implemented in the subsequent experiments.
Temporal evolutions of vertical profiles of the simulated and observed wind speeds at 3-h interval are shown in Fig. 9, together with the Taylor diagram of wind speed comparisons at different heights in the four domains. The observed profiles came from radiosondes at site 15 as described in section 2a. The most distinct feature in the observed profile is that the wind speed had a sudden increase at around 0200 UTC 28 January. This feature is well captured in the simulations over all domains. After 0200 UTC, the maximum observed wind speed reached 28 m s−1 at 2.0 km, and several scattered wind speed centers (16 m s−1) appeared from 1.2 to 1.6 km. However, d01 (Fig. 9b) has exhibited underestimation of wind speed at approximately 1.6~2.0 km (Table 3), and no finescale structure is produced in the middle of PBL. Simulation results over d02 to d04 (Figs. 9c–e) agree better with observations. The correlation coefficients at all levels (Fig. 9f) increase as the model resolution increases. Evidently, more near-surface wind information can be captured by d04 (Figs. 9e,f), and mean biases of wind speed decrease by 81%, 56%, and 88% from surface to the upper layer relative to d01. On one hand, YSU is originally designed to capture basic characteristics of the diurnal variation of PBL properties, not to accurately simulate the momentum/wind profiles caused by strong turbulent motions (Hong et al. 2006). In contrast, LES is designed to analyze microscale motions. On the other hand, it may still relate to the terrain resolution. The elevation of the mountain (d01: 1800 m, d04: 2195 m) and characteristics of the slope (d01: 15°; d04: 40°) described in domains of different resolutions play an important role. In addition, the momentum transported downward from the maximum wind speed zone to the ground level may produce a velocity deficit region downstream from the ridge (Rai et al. 2017). In the deficit region, the spatial structures of the wind components become finer (Chow et al. 2013) at 1.2–1.6 km height as shown in Fig. 9a. The nested d04, which includes more detailed terrain features in high resolution, has again obtained the closest characteristics to observation.
4. Sensitivity to PBL treatments
a. Description of sensitivity experiments
The previous sections have shown that WRF-LES is a potential reliable tool for complex terrain airflow simulation. The uncertainty of different PBL treatments (two PBL schemes and three SGS stress models of LES) has been analyzed in this section. PBL schemes used in the present study are YSU and its scale-aware version SH (Shin and Hong 2015). The difference between YSU and SH is the strength of the parameterized vertical transport of momentum and heat fluxes. YSU is a nonlocal PBL scheme that includes a nonlocal term in addition to the local transport, and profiles of mixing within the PBL is parameterized based on bulk PBL characteristics. SH is the scale-aware version of YSU, in which the total SGS vertical transport is parameterized based on Δx and the nonlocal transport strength. Three SGS stress models used here are the SMAG linear eddy-viscosity model (Smagorinsky 1963), 1.5TKE model (Lilly 1966), and NBA model based on SMAG (Kosović 1997; Mirocha et al. 2010). The difference between them is that the eddy-viscosity equations are linear (SMAG; 1.5TKE) or nonlinear (NBA), and the turbulence kinetic energy closure is done based on either predictive energy closure equations (1.5TKE) or diagnostic equations (SMAG; NBA based on SMAG). Linear SGS models with a positive eddy viscosity are absolutely dissipative. Unlike NBA, they cannot account for important effects, such as the backscatter of energy from small and unresolved scales of motion toward resolved eddies. Results of the diagnostic approach are similar to that of the prognostic approach. However, differences are large near the surface (Muñoz-Esparza et al. 2014a).
Table 4 lists the details of five sensitivity experiments:
YSU is used in d01 for all five experiments to generate mesoscale IBCs.
YSU and SH PBL scheme are used respectively in two different experiments over d02, whose inner domains (d03 and d04) use LES with 1.5TKE SGS stress model. Hereinafter, these experiments are named YSU-TKE and SH-TKE.
In the other three experiments, LES with 1.5TKE, SMAG, and NBA SGS stress models are respectively used in d02 and inner domains (d03 and d04), named TKE-TKE, SMAG-SMAG, and NBA-NBA, respectively.
By comparing results between YSU-TKE, SH-TKE, and TKE-TKE, we intend to find the differences between simulations of PBL and LES in the gray zone and the importance of scale-aware PBL treatment. By comparing results between TKE-TKE, SMAG-SMAG, and NBA-NBA, we attempt to determine the effect of SGS stress model of LES in d03 and d04.
Because of the diurnal variation, the gray zone is not unique and not so clearly defined in the real world. In qualitative description, the range of gray-zone scale is near the size of the dominant eddy motion lm (Zhou et al. 2014). In complex terrain, it also depends on the scales of flow structures (Cuxart 2015). In several previous gray-zone studies, Zhou et al. (2014) selected 400 m as the minimum gray-zone scale, and Shin and Hong (2015) used 250 m. In addition, 100-m resolution is considered as an LES-resolved scale in many real case studies of LES (Liu et al. 2011; Xue et al. 2016; Doubrawa et al. 2017). In the present study, we use 333 m as a reasonable resolution for gray-zone analysis. Hereinafter, d02 is referred to as the “gray zone domain” and d03 and d04 are referred to as “microscale domains.”
b. Horizontal and vertical mean quantities
1) 10-m wind speed
Mean errors of 10-m wind speed are calculated every 10 min at AWSs 1–14 for the entire simulation period. Figure 10 shows the median, 25th, and 75th percentiles of mean errors as a function of time discretized in 3-h bins in d02 and d04. Wind speeds in d02 of all experiments are overestimated in the daytime and underestimated in the nighttime (Fig. 10a), whereas the biases of d04 (Fig. 10b) remain relatively stable, which indicates that running in microscale can reduce time-dependent errors of wind speed. Wind speeds in d04 agree very well (median bias < 1 m s−1) with observations.
The time averaged errors only represent the simulation of average wind speed, and the effect of strong and weak winds (0–3 and 12–18 m s−1) has been ignored. In fact, model errors have a close relation with wind speed values. Figures 11c and 11e display the errors as a function of observed wind speed discretized in 2 m s−1 bins. Most of the observations are between 3 and 9 m s−1 (Fig. 11a), in which the biases are relatively small. Outside this range, the values of absolute errors (Figs. 11c,e) show a decreasing tendency with wind speed increasing. The modeling accuracy of d04 is obviously better than that of d02, especially at the extreme wind speeds (<5 or >15 m s−1). An important result is that the difference between YSU and SH in the d02 is not significant (<1 m s−1) and is remarkably lower than the model error (from −6 to 6 m s−1) itself. SH PBL scheme is intended for simulations of the convective boundary layer based on YSU scheme (Shin and Hong 2015). Simulations presented in this paper refer to a typical winter weather scenario (neutral or stably stratified regimes). Therefore, SH is not able to yield significantly improved results and should default to YSU. In the Xiaohaituo Mountain area, for most cases during the Winter Olympic Games period (February and March), buoyancy-driven turbulence is weak and wind forcing is strong. Therefore, for the region and period of the present study, it is difficult for SH to have nonlocal [Δ*; see Fig. 2a in Shin and Hong (2015)] and local [; see Eqs. (1)–(3) in Shin and Hong (2015)] heat transport less than 0.5 (with PBL height higher than 700 m) to achieve more effective results.
In the gray zone (Figs. 11c,d), three SGS models on average outperform PBL parameterized schemes. In the microscale domain (Figs. 11e,f), differences in the model results between YSU-TKE/SH-TKE and TKE-TKE runs, which use the same 1.5TKE SGS model in d03/d04 but have different lateral boundary conditions (LBCs) from d02, are relatively small. Nevertheless, the differences between the three runs of SMAG-SMAG, TKE-TKE and NBA-NBA, which use different SGS models in d03/d04 but have the same LBCs forcing from d02, are much larger. Thus, results in the inner domains are more influenced by SGS models than by the initial and boundary conditions.
Wind speed errors versus observed wind directions are shown in Figs. 11d and 11f. The gray zone with 333 m grid spacing is too coarse to describe topographic features of Xiaohaituo Mountain. With the resolution increasing to 37 m, the median error and error distribution are significantly reduced, which demonstrates the advantages of the high-horizontal-resolution model on simulating surface wind over complex terrain. In d02 (333 m) and d04 (37 m), wind speeds in the northwestern (270° < wind direction < 330°) and southeastern (90° < wind direction < 150°) sectors, where the wind directions are similar to local prevailing winds in the winter season, are closer to observations. For the winds in the southwestern (180° < wind direction < 270°) and northeastern (360° < wind direction < 60°) sectors, where the wind directions are nearly perpendicular to the prevailing wind direction in the winter and the flows are mainly influenced by topographic features, the wind speeds are evidently overestimated. Simulations in the LES domains are still significantly different to the observed winds, but they are generally better than the simulations with PBL schemes.
2) Wind profile
Figure 12 presents the differences in wind profiles between simulations of each experiment and sounding data during the daytime (0300–0900 UTC) and nighttime (1500–2100 UTC). Relative to that in the nighttime, the simulations of the five experiments have shown smaller median errors and wider error distributions in the daytime for both d02 and d04. The main differences between these experiments occur in the bottom levels below 400 m, where strong up–down atmospheric exchanges occurred. Below 400 m, YSU-TKE and SH-TKE obviously overestimate wind speed. Three SGS models generally outperform the two PBL schemes, especially in the night, which further confirms that LES model enhances the momentum mixing near the surface. For the three SGS models, differences between them are greater during the daytime than that during the nighttime, and NBA yields smaller errors both in the daytime and the nighttime. Median errors of wind direction are veered in the clockwise direction by 20° relative to observation, which is also true in the simulations with higher resolutions. This is probably related to the deviation of the initial field in the upper free atmosphere. It implies that the simulated wind field is greatly affected by the background wind field above 400 m and is not sensitive to the treatment of PBL. It is worth noting that this conclusion may only apply for cases with strong dynamic forcing such as the case in the present study. The PBL schemes have more prominent impacts on the vertical profiles of the wind when a thermally induced circulation is present. More detailed discussion of this issue can be found in the studies of Wagner et al. (2014) (idealized case) and Goger et al. (2018) (real case).
c. Turbulence characterization
1) Total TKE budget
Total TKE budget is decomposed into two components and calculated for turbulence characteristics assessment:
where TKEΔ represents TKE, which is explicitly resolved by model at current resolution scale. The resolved TKE is calculated as follows:
where u, υ, and w are the wind components. A 10-min interval is considered to obtain turbulent fluctuations after detrending of the signal to remove any mesoscale variability. To get the same number of samples, the 10-Hz sonic data are subsampled to 1 Hz to match the frequency of signals in d02 (1 Hz). Similarly, simulation over d04 (25 Hz) is subsampled to 10 Hz to match observations. TKESGS is the component that is produced by the SGS stress models and the PBL parameterization schemes.
Figure 13 shows the total TKE as a function of time (discretized in 3-h bins) and wind speed (discretized in 2 m s−1 bins). In Figs. 13a and 13b, we can see that the TKE begins to increase after sunrise (0000 UTC) and reaches its peak value in the afternoon (0600–0900 UTC). It then begins to decrease until 1200–1500 UTC and rises again during the night. The first rise is due to the enhancement of thermodynamic forcing, and the second rise is caused by the enhancement of dynamic forcing as the observed wind speed increases during the nighttime (Fig. 6). In Figs. 13c and 13d, the median value of the observed TKE reaches its minimum (<1 m2 s−2) when wind speed lies between 3 and 9 m s−1, and the discrete range is also minimized (<2 m2 s−2). When wind speed becomes higher, the median value increases and the discrete range has widened sharply.
At the gray zone (Fig. 13c), all experiments underestimate TKE, especially for PBL schemes. Although the observations are subsampled, the variability in all bins is still much larger than that in the simulations. This result indicates that at the gray-zone scales, both the PBL schemes and LES models are not able to simulate high values of TKE under high wind speed conditions (9–18 m s−1). Experiments using LES models have larger values of TKE than those using PBL parameterization schemes, especially when the wind speed is higher than 11 m s−1. This is because in the LES simulations, the SGS stress models can increase TKESGS, whereas PBL schemes cannot. PBL schemes are designed under the assumption of horizontal homogeneity, which is obviously violated in complex terrain (Serafin et al. 2018). Furthermore, they only consider the vertical exchange. However, horizontal exchange is also important in complex terrain (Goger et al. 2018, 2019).
At the microscale (Fig. 13d), the simulated total TKE of all experiments are much larger than those in d02, though still underestimated. Among them, NBA has the most similar distribution to the observations. Compared with the PBL schemes, three LES models yield results much closer to the observed values. Although YSU-TKE and SH-TKE also use the 1.5TKE SGS stress model in d04 as TKE-TKE does, the simulated TKE in these two experiments are much smaller. According to the idealized case, Mirocha et al. (2014) surmised that the SGS TKE still can be developed in the nested LES with no turbulence information from the mesoscale domain. In the present study, we found a similar phenomenon in the YSU-TKE and SH-TKE experiments by comparing the simulated TKE in d02 (Fig. 13a) and d04 (Fig. 13b). In d02, the simulated TKE is close to zero, while in d04 the simulated TKE increases significantly. This indicates that the SGS TKE can still be developed in the nested LES with no turbulence information from the mesoscale domain. Compared to TKE-TKE, the LBCs (from d02) of YSU-TKE and SH-TKE are more difficult to spin up turbulent motions adequately in inner domains, since the LBCs of YSU-TKE and SH-TKE contain no turbulence information. Errors in the LBCs are propagated into the nested inner domain and affect the turbulence generation. This is why a large development fetch is always required when an inflow turbulence generation method is not used (Muñoz-Esparza et al. 2014a; Muñoz-Esparza and Kosović 2018).
It is worth noting that the sonic data are collected at 3 m GL whereas the simulated data are at about 13-m height. Therefore, the simulated TKE are smaller than observed ones as expected. (Stull 1988). In addition, the simulated TKE are at the lowest model level. Therefore, the TKE underestimation suggests that there may have turbulence stress not fully resolved close to the surface.
2) Power spectral density of velocity components
To get information about the scale distribution of TKE in the flow, spectral analysis is conducted. For the kth block of the data, the power spectral density (PSD) function of the quantity x is written as
where X* is the complex conjugate of X, T is the time period for the kth block of the data, and f is the frequency in hertz.
Figure 14 shows PSDs as a function of frequency for u and w wind components at AWS 13. Time series of simulated u and w are sampled at 1 Hz, which are created from every time step output at the first model level (z ≈ 13 m). Observations are also sampled at 1 Hz, which are created from 10 Hz original sonic data (z = 3 m). PSDs are computed following the steps below: four individual 30-min time series are considered over the period 0400–0515 UTC 28 January, and the 30-min series are constructed for 0400–0430 UTC, 0415–0445 UTC, and so on. The 15-min overlap between the 30-min time series provides four spectra to be averaged and can help to remove noises and obtain a better identification of trend in the PSD signals.
As shown in Fig. 14, w obviously exhibits less power than u, which is true for both the observations and model results. This is attributed to the anisotropy and energy redistribution as the surface is approaching (i.e., vertical velocity variance is reduced at the expense of increased horizontal velocity fluctuations). Again, the effects of YSU-TKE and SH-TKE can hardly be distinguished. In d04, both model results and observations deviate from the −5/3 slope (Figs. 14c,d) with an agreement for low frequencies. For f > 0.02 Hz, the implicit filter in the numerical model results in a dissipation of energy, which leads to a significant departure from the observed energy spectrum.
In d02 (Figs. 14a,b), the PSDs reveal a clear and consistent underestimation of kinetic energy content by all experiments, especially in the higher-frequency region where the grid is not fine enough to resolve this range of scales. The results clearly show the gray-zone properties described in section 1. Running the gray-zone scale model with the LES models appears to yield better results in terms of variance of the stream wise velocity than that using the PBL schemes. For the frequency larger than 10−2 Hz (time scales less than 1.7 min), five PSDs show straight lines with a slope of −5/3, indicating that all models have failed to capture the high-frequency turbulent motion at gray-zone scale due to the insufficient resolution. The spectral densities of the three LES (TKE-TKE, SMAG-SMAG, and NBA-NBA) experiments are larger than that of the other two experiments, which implies the importance of the inflow provided by the gray-zone domain. In particular, NBA exhibits the highest frequency with energy content similar to the observations. The energy decay follows an f−1 slope for frequencies between 10−3 and 10−2 Hz, which is indicative of turbulence production. The energy decay follows an f−5/3 slope for frequencies below 6 × 10−2 Hz, which is also the drop-point frequency.
3) PDFS of wind speed fluctuations
PDFs of wind speed fluctuations are used to characterize turbulence variability. These analyses include the higher-order moments skewness S and kurtosis K, which depict different SGS model capabilities for resolving spatial and temporal variations of wind speed within the PBL over complex terrain. The PDFs of wind speed fluctuations at AWS 13 during the daytime (0400–0600 UTC 28 January) are shown in Fig. 15a. Results from the experiments using the two PBL schemes show fatter tails with smaller probabilities of extreme turbulent fluctuations (K = 2.69–2.79) and with a slightly larger probability for u′ > 3 m s−1. This strong non-Gaussian distribution may be attributed to the presence of anisotropic horizontal convective rolls shown in the model. Meanwhile, results from the LES experiments are closer to Gaussian distribution. NBA-NBA appears to outperform other runs and is capable of capturing extreme velocity fluctuations that occur less frequently. TKE-TKE and SMAG-SMAG rank the second and third, respectively. The PDFs show that the wind speed perturbations have large variability (from −6 to 6 m s−1).
However, the single site PDF cannot represent spatial variability of turbulence, particularly over complex terrain. To reveal the spatial turbulence variability, the averaged PDFs across the whole d04 region at 0400, 0500, and 0600 UTC are given in Fig. 15b. Since there is only one supersonic anemometer that is located at AWS 13, we can only compare the results between the experiments. PDFs from the three LES experiments show more peaked values than that from the two PBL schemes. PDFs of each experiment are skewed to negative values, which implies that fluctuations are asymmetrical, probably due to the heterogeneity of the complex terrain and surface. Three experiments that use LES in the gray zone still have larger kurtosis than the two experiments that use PBL schemes.
5. Conclusions and future work
In this study, a full-physics WRF-LES is employed to simulate a 2-day real-weather case over the Xiaohaituo Mountain area. Verifications against observations from MOUNTAOM show good agreement with regard to the averaged meteorological elements and statistical characteristics of turbulence. The quality of the underlying topography used in the model was found to be the most important driving factor for obtaining a successful finescale wind simulation. High-resolution topographic data improve the performance of high-resolution modeling. By comparing the influence of horizontal resolution and terrain data resolution in this case, it is found that the model horizontal resolution plays a slightly more significant role. WRF-LES appears to be capable of capturing the heterogeneous surface fluxes and microscale circulations over the region of interest, such as the mountain site for the Winter Olympic Games.
Another objective of the present study is to analyze the uncertainty of different PBL treatments at the gray-zone scales, and three sensitivity experiments with LES, YSU, and SH have been conducted and results are compared. Major conclusions are as follows:
The difference between YSU-TKE and SH-TKE is negligible. Since the selected case is a typical winter windy weather case, which is in the neutral or stably stratified regimes, SH should default to YSU. In the Xiaohaituo Mountain area, scale-aware parameterization SH should have larger nonlocal and local heat transport to achieving more effective results.
In general, LES models outperform PBL parameterization schemes at the gray-zone scale for real flow simulation over complex terrain. PBL schemes yield larger horizontal and vertical wind speed errors, underestimate the total TKE and energy content of PSD, and present a skewed PDF distribution. In recent years, more research has been conducted to compare the performance of LES and PBL. The similar and complementary conclusion was submitted by Ching et al. (2014), who demonstrated that convectively induced secondary circulations (CISCs) are more correctly handled by LES than by PBL in the gray zone. We have noted that similar treatments on this subject was submitted at about the same time (Rai et al. 2019; Johnson and Wang 2019).
Wind field features in the boundary layer over complex terrain are more sensitive to the choice of PBL treatments. Above the boundary layer, they are greatly affected by the initial condition.
To analyze the uncertainty of SGS stress model at the microscale, three commonly used SGS stress models in the LES, 1.5TKE, SMAG, and NBA are compared. At the gray-zone scale, each SGS model has smaller effect on both simulated mean quantities and turbulence statistics. Meanwhile, at the microscale, the effect becomes more significant. SGS stress models have more impact than that of IBCs constructed by different PBL treatments in the parent gray-zone domain. Among these models, NBA has the best performance, which is consistent with the idealized simulation over a symmetrical 2D hill conducted by Kirkil et al. (2012) and Mirocha et al. (2010, 2014).
In recent years, research on the PBL has significantly advanced with measurement campaigns and modeling efforts, and lots of work have been conducted to improve PBL parameterizations in complex terrain (De Wekker and Kossmann 2015; Lehner and Rotach 2018; Goger et al. 2018). However, the PBL is not yet a robust approach over complex terrain. On the other hand, although idealized studies have suggested that LES has great capability of modeling the boundary layer winds (Kosović and Curry 2000; Mirocha et al. 2010), it does not provide a perfect solution over complex terrain either. Further study should focus on improving LES model capability for modeling vertical momentum structures in the realistic complex environmental settings.
This work demonstrates the potential of WRF-LES as a useful tool to gain new insights into PBL processes over complex terrain. WRF-LES has a wide application prospect for fine simulation of complex terrain flow field. It is worth noting that the conclusions of this paper are from a single case only for dry flows and should be evaluated with more case scenarios and verified against more observations. Meanwhile, this study focuses on large-scale synoptic flow impinging on the topography. A contrast test where large-scale flow is negligible and thermally driven conditions are unchanged is in progress. Further modeling refinements, such as scale-aware parameterization development for the gray zone and adaptive SGS stress models in finer resolution, are expected to further enhance multiscale modeling capabilities.
This research was supported by the National Natural Science Foundation of China (41705006 and 11472272), the National Key Research and Development Program of China (2018YFF0300100), Beijing Natural Science Foundation (8184074 and 8194060), and the Young Beijing Scholars Program. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Please contact the corresponding author for use of the data.