Large Eddy Simulation of the Impacts of Surface Heating Heterogeneity on the Applicability of Similarity Theory in the Surface Layer
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摘要: 利用非均匀地表加热的大涡模拟试验，研究了不稳定条件下地表热力非均匀性对近地层相似理论适用性的影响。结果发现，边界层的平均廓线基本不受地表热力非均匀性的影响。进一步分析发现，较大尺度的地表非均匀加热可以激发出有组织的大尺度次级环流，冷暖斑块的通量直到边界层上部才混合均匀；而当地表非均匀尺度较小时，次级环流难以形成有组织的结构，冷暖斑块的通量很快就可以混合均匀。然而，不管是哪种尺度的非均匀地表，非均匀斑块间的平流都对各斑块近地层结构产生重要影响，进而斑块近地层通量—梯度关系与相似理论产生偏差，其中风速梯度关系的偏差更为明显。最后，对目前大气模式中常用的基于相似理论的次网格非均匀地表通量参数化方法——Mosaic方法提出了改进思路。Abstract: The impacts of surface heating heterogeneity on the applicability of similarity theory in the unstable surface layer are investigated using idealized Large-Eddy Simulation (LES) experiments with prescribed heterogeneous surface heat flux forcing. It is found that the mean profiles in the boundary layer are hardly affected by surface heterogeneity. However, heterogeneous surface heating on a relatively large scale can induce organized large-scale secondary circulations. In this case, the fluxes between COLD and WARM patches are distinct up to the upper boundary layer. On the other hand, there is no such organized secondary circulation developed in smaller heterogeneous scales, and the fluxes are mixed quickly in the low boundary layer. For all heterogeneous cases (from small to large heterogeneous scales), the inter-patch advection greatly impacts the surface layer structure of patches. Therefore, the flux-gradient relationship in those surface layers deviates from the similarity theory, with the deviation more for momentum than for heat. Finally, an improvement to the Mosaic approach based on the similarity theory and widely used for estimating subgrid heterogeneous surface fluxes in current atmosphere models is proposed.
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图 1 非均匀试验（a）Het_L、（b）Het_M、（c）Het_S的地表感热通量分布。黑色区域和白色区域的感热通量分别为0.11 K m/s和0.01 K m/s
Figure 1. Distributions of surface sensible heat flux of the three heterogeneous LES experiments (a) Het_L, (b) Het_M, and (c) Het_S. The sensible heat fluxes in the black and white areas are 0.11 K m/s and 0.01 K m/s, respectively
图 2 试验Het_L冷斑块（左列）、暖斑块（右列）上的高度—时间剖面：（a1、a2）垂直风；（b1、b2）水平u风异常；（c1、c2）水平v风
Figure 2. Height−time profiles on the cold (left) and warm (right) patches of experiment Het_L: (a1, a2) Vertical wind; (b1, b2) horizontal u wind anomaly; (c1, c2) horizontal v wind
图 3 非均匀试验（a1、a2）Het_L、（b1、b2）Het_M和（c1、c2）Het_S动量通量（上）和感热通量（下）随高度分布情况。黑色、蓝色和红色实线分别代表区域平均值、冷斑块平均值和暖斑块平均值
Figure 3. Distributions of momentum flux (above) and sensible heat flux (below) with height of the heterogeneous experiments (a1, a2) Het_L, (b1, b2) Het_M, and (c1, c2) Het_S. Solid black, blue, and red lines represent grid averages, cold patch averages, and warm patch averages, respectively
图 4 非均匀试验（a1、a2）Het_L、（b1、b2）Het_M和（c1、c2）Het_S的摩擦速度（左列）和温度尺度（右列）随时间的变化情况。黑色、蓝色和红色实线分别代表网格平均值、冷斑块平均值和暖斑块平均值
Figure 4. Time series of friction velocity (left) and temperature scale (right) of the heterogeneous LES experiments: (a1, a2) Het_L; (b1, b2) Het_M; (c1, c2) Het_S. Solid lines in black, blue, and red are grid averages, cold patch averages, and warm patch averages, respectively
图 5 非均匀试验（a1−a4）Het_L、（b1−b4）Het_M、（c1−c4）Het_S在不同方案中的Obukhov长度随时间分布情况。黑色、蓝色和红色实线分别代表网格平均值、冷斑块平均值和暖斑块平均值
Figure 5. Time series of Obukhov Length of the heterogeneous LES experiments according to (a1−a4) Het_L, (b1−b4) Het_M, and (c1−c4) Het_S with different schemes. The solid lines in black, blue and red are grid averages, cold patch averages, and warm patch averages, respectively
图 6 各个试验根据方案S1计算得到的（a）无量纲风速梯度和（b）无量纲温度梯度与稳定度参数（z/L）之间的关系。黑色虚线是Högström（1996）提出的经验曲线
Figure 6. Dimensionless (a) wind gradient and (b) temperature gradient against stability parameter (z/L) according to scheme S1 of the four LES experiments. The dashed lines are the empirical curves suggested by Högström (1996)
图 7 试验Het_L根据不同方案计算得到的无量纲风速梯度与稳定度参数（z/L）之间的关系：（a）方案S2；（b）方案S3；（c）方案S4；（d）方案S5。黑色虚线是Högström（1996） 提出的经验曲线。黑色的点代表网格平均值（方案S1），蓝色和红色的点分别代表冷暖斑块在不同高度上的值
Figure 7. Dimensionless wind gradient against stability parameter (z/L) of experiment Het_L according to (a) S2, (b) S3, (c) S4, and (d) S5 schemes. The dashed lines are the empirical curves suggested by Högström（1996）. The black dots are the grid averages (Scheme S1), and the blue and red dots are the warm and cold patch averages with different heights
图 10 试验Het_L根据（a）方案S2、（b）方案S3、（c）方案S4、（d）方案S5计算得到的无量纲温度梯度与稳定度参数（z/L）之间的关系。黑色虚线是Högström（1996） 提出的经验曲线。黑色的点代表网格平均值（方案S1），蓝色和红色的点分别代表冷暖斑块在不同高度上的值
Figure 10. Dimensionless temperature gradient against stability parameter (z/L) of experiment Het_L according to (a) S2, (b) S3, (c) S4, and (d) S5 scheme. The dashed lines are the empirical curves suggested by Högström（1996）. The black dots are the grid averages (Scheme S1), and the blue and red dots are the warm and cold patch averages with different heights
表 1 大涡模拟试验设计方案
Table 1. Settings of LES experiments
试验
名称区域的
边长/m背景风
速/m s−1地表热通量/K m s−1 非均匀斑
块尺度/m区域 冷斑块 暖斑块 Hom 2000 4 0.06 — — — Het_L 2000 4 0.06 0.01 0.11 1000 Het_M 2000 4 0.06 0.01 0.11 200 Het_S 2000 4 0.06 0.01 0.11 40 
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表 2 5种通量—梯度关系计算方案
Table 2. Five flux-gradient relationship calculation schemes.
参数 方案 S1 S2 S3 S4 S5 摩擦速度（u*） G P P P P 温度尺度（θ*） G P P P P 平均风速梯度（$ \partial\overline u / \partial z$） G P P P P 平均温度梯度（$\partial\overline \theta / \partial z $） G P P P P Obukhov长度L中的摩擦速度（u*L） G P P G G Obukhov长度L中的温度尺度（θ*L） G P G P G 注： P代表斑块平均值，G代表网格平均值。
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