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Effects of a Modified Sub-grid-scale Terrain Parameterization Scheme on the Simulation of Low-layer Wind over Complex Terrain
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摘要: 复杂地形区域风场模拟的准确率一直是风能研究领域的难点和重点。WRF模式是目前风能评估领域应用最广泛的天气数值模式之一，但该模式在复杂地形区域存在对平原、山谷风速高估且对山顶风速低估的系统性误差，并有研究建立次网格地形方案以订正误差。而次网格地形方案在不同水平分辨率下常出现错误的修正结果，该文基于高精度地形高程数据分析了方案失效的主要原因，发现其方程组中判断山体形态特征的阈值-20在过低和过高水平分辨率下均失去参考性。针对这一原因，将方案中影响关键参数Ct的地形高度算子与模式水平分辨率进行拟合，形成地形高度算子与水平分辨率相依赖的线性关系，获得不同分辨率下更适合的山体形态阈值。通过与自动气象站10 m风速对比分析了修正前后WRF对低层风速的模拟效果，结果显示：修正后的次网格地形方案能够分别在较低和较高分辨率下，部分矫正原方案错误的订正结果，使低层风速模拟更接近实况。修正后的次网格地形方案可为复杂地形区域开展高分辨率风场模拟提供参考。Abstract: Due to the limited representation of observation over complex terrain, high resolution model becomes a favorable tool. Fine numerical simulation of wind field is quite important for micro-siting wind farms and wind energy resources assessment, especially in the complex terrain area. The accuracy of low-layer wind simulation over mountain area is one of the difficulties and key points in the field of wind energy research. The state-of-the-art WRF (Weather Research and Forecasting) model is one of the most widely used mesoscale numerical weather models for wind energy assessment in recent years. However, effects of sub-grid-scale topographic shape on surface wind field are not considered. With the new WRF version 3.4.1, a sub-grid-scale terrain parameterization scheme named Jiménez scheme is added into the YSU (Yonsei University) planet boundary layer parameterization scheme. The Jiménez scheme is designed aiming to reduce the systematic error of wind speed overestimation over valleys or plains and underestimation over hills conversely. However, correction effects of original WRF simulated 10 m wind speed by Jiménez scheme show great differences under different horizontal resolutions, particularly when over high hills. A series of sensitive numerical experiments are carried out under windy days for the Taihang Mountains in the west of Beijing-Tianjin-Hebei area. The main purpose of these experiments is to address some of issues regarding Jiménez scheme and try to solve the existing problems by establishing a relationship between the key topographic parameter Ct and the model grid spacing(dx/dy) to fit different numerical simulation for high resolution based on secondly SRTM topographic dataset. The simulated 10 m wind speed results of WRF without Jiménez scheme, with original Jiménez scheme and modified Jiménez scheme version are compared with observations of 3 automatic weather stations during the MOUNTAOM (MOUNtain Terrain Atmospheric Observations and Modeling) campaign which is prepared for 2022 winter Olympic Games. Results show that the modified Jiménez scheme can partially correct the error of the original Jiménez scheme at lower and higher resolutions. The simulated 10 m wind speed near the ground by modified version is closer to the actual condition. The correction method for Jiménez sub-grid-scale terrain scheme can provide reference for high resolution wind simulations over complex terrain and help users to obtain more detailed information on the surface wind field for wind energy related researches and applications.
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图 1 模拟区域和分析区域(填色为地形高度)
(黑框为模拟范围，蓝框为小海坨山所在区域)
Fig. 1 Computational and analytical domains with the terrain elevation (the shadeded denotes terrain)
(black frame denotes simulation domain, blue frame denotes Xiaohaituo mountain)
图 2 小海坨山地形(填色)
(黑色圆点为自动气象站)
Fig. 2 Analytical domain for Xiaohaituo Mountain (the shaded)
(black dots denote automatic weather stations)
图 3 3个个例10 m风速差值集合平均场(填色)(等值线表示地形高度，单位：m)
(a)T1_1与T0_1的差值，(b)T1_2与T0_2的差值，(c)T1_3与T0_3的差值
Fig. 3 Ensenble averaged bias of 10 m wind speed of 3 cases (the shaded)(the contour denotes the terrain height, unit:m)
(a)difference between T1_1 and T0_1, (b)difference between T1_2 and T0_2, (c)difference between T1_3 and T0_3
图 4 3个个例西大庄科站、二海陀站、小海陀站T0和T1试验10 m风速模拟与实测偏差的平均日变化
Fig. 4 Ensemble averaged daily bias of simulated and observed 10 m wind speed at Xidazhuangke, Erhaituo and Xiaohaituo of T0 and T1 from 3 cases
图 5 模拟区域和小海坨山区域不同水平分辨率Δ2h水平分布(填色)
(等值线表示地形高度，单位：m)
Fig. 5 Δ2h distribution of computational domain and Xiaohaituo Mountain with different resolutions (the shaded)(the contour denotes the terrain height, unit:m)
图 6 小海坨山区域30个点的分布
(填色表示地形)
Fig. 6 The distribution of 30 points in Xiaohaituo Mountain (the shaded denotes terrain)
图 7 30个点不同水平分辨率下对应的Δ2h及拟合曲线
Fig. 7 The corresponding Δ2h values of 30 points at different resolutions
图 8 3个个例小海坨山区域10 m风速差值集合平均场(填色)(等值线表示地形高度，单位：m)
(a)T1C_1与T1_1差值，(b)T1C_2与T1_2差值，(c)T1C_3与T1_3差值
Fig. 8 Ensenble averaged bias of 10 m wind speed of 3 cases in Xiaohaituo Mountain (the shaded) (the contour denotes the terrain height, unit:m)
(a)difference between T1C_1 and T1_1, (b)difference between T1C_2 and T1_2, (c)difference between T1C_3 and T1_3
图 9 3个个例西大庄科站、二海陀站、小海陀站T1C和T1试验10 m风速模拟与实测偏差的平均日变化
Fig. 9 Ensemble averaged daily bias of simulated and observed 10 m wind speed at Xidazhuangke, Erhaituo and Xiaohaituo of T1C and T1 from 3 cases
表 1 模拟试验设计
Table 1 Schemes of different experiments
试验组名称 试验名称 水平分辨率 时间积分步长/s 次网格地形方案 T0_1 3 km×3 km 18 T0 T0_2 1 km×1 km 6 T0_3 333 m×333 m 2 T1_1 3 km×3 km 18 Jiménez方案 T1 T1_2 1 km×1 km 6 Jiménez方案 T1_3 333 m×333 m 2 Jiménez方案 T1C_1 3 km×3 km 18 修正Jiménez方案 T1C T1C_2 1 km×1 km 6 修正Jiménez方案 T1C_3 333 m×333 m 2 修正Jiménez方案 
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表 2 10 m风速统计检验结果(单位：m·s-1)
Table 2 Statistic results of simulated 10 m wind speed (unit:m·s-1)
试验 平均偏差 均方根误差 西大庄科站 二海陀站 小海陀站 西大庄科站 二海陀站 小海陀站 T0_1 4.057 -0.411 -1.791 1.860 2.626 3.098 T0_2 1.270 -2.103 -3.955 2.499 2.136 2.473 T0_3 0.744 -1.838 -0.248 1.873 2.850 3.433 T1_1 5.813 1.191 0.420 2.497 2.021 2.458 T1_2 -0.461 1.062 -2.118 1.764 2.042 1.746 T1_3 -0.742 -3.506 -2.598 1.811 3.820 4.108 T1C_1 3.135 -0.588 -0.392 1.776 2.391 2.689 T1C_2 0.055 0.129 -1.200 1.644 1.565 1.591 T1C_3 0.279 -0.639 -0.016 1.300 1.583 1.791
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