Influences of 3D Sub‐Grid Terrain Radiative Effect on the Performance of CoLM Over Heihe River Basin, Tibetan Plateau

Abstract

As a component of the surface heat budget, surface solar radiation (SSR) is the primary source of energy for the earth surface. It controls both water and energy exchanges between land surface and overlying atmosphere and is thus a major forcing for the land surface models, hydrological models, and ecological models (L.

Development of a Clear‐Sky 3D Sub‐Grid Terrain Solar Radiative Effect Parameterization Scheme Based on the Mountain Radiation Theory

“…As mentioned in Zhang et al. (2022), we generate the grid‐scale $${\text{SFC}}_{p}$$ by a statistical method as follows: First, we divide $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}$$ which ranges from 0 to 1 into $$M=100$$ levels ($$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 0.01$$, $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 0.02$$, ……, and $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 1$$) on sub‐grids at 360 azimuth directions. Second, we count the total number of sub‐grids with $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 0.01$$, $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 0.02$$, ..., $$\,\mathrm{sin}{\varepsilon }_{{\phi }_{\mathrm{k}}}\le 1$$ at a given azimuth direction within a model grid with a given horizontal resolution, that is, there are $${n}_{1}$$, $${n}_{2}$$, ..., $${n}_{100}$$ sub‐grids with $$\mathrm{sin}{\varepsilon }_{{\phi }_{k}}\le 0.01$$, …”

“…The negative biases are mainly attributed to the parameterized calculation of downward direct solar radiation (Equation ), specifically the simplified replacement of $$< \mathrm{sec}{\alpha }_{i}\cdot \mathrm{cos}{I}_{i}\cdot S{F}_{i}{ > }_{i\to p}$$ with $$< \mathrm{sec}{\alpha }_{i}\cdot \mathrm{cos}{I}_{i}{ > }_{i\to p}< S{F}_{i}{ > }_{i\to p}$$ without considering the regional mean product of their perturbation terms, resulting in the overestimation of terrain shadow effect. These negative biases are the main error source of the preliminary version of clear‐sky 3DSTSRE scheme (Zhang et al., 2022). To reduce the error in the preliminary clear‐sky 3DSTSRE scheme, the $${\text{SFC}}_{p}\,$$ related to the shadow effect of surrounding terrains in Equation is further adjusted by: $$${\text{SFC}}_{p}=1-{C}_{\text{ad}}\left(1-< {\text{SF}}_{i}{ > }_{i\to p}\right)$$$ $$${C}_{\text{ad}}=0.1849d{x}^{-1.443}+0.04561$$$ $${C}_{\text{ad}}$$ is an adjustment factor depending on the model horizontal resolution $$dx$$ (Figure 8), it ranges from 0 to 1.…”

“…We ignore the differences in the surface albedo 𝐴𝐴 𝐴𝐴 , solar zenith angle 𝐴𝐴 𝐴𝐴 , solar azimuth angle 𝐴𝐴 𝐴𝐴 , atmospheric transmittance 𝐴𝐴 𝐴𝐴𝑏𝑏 of direct solar radiation, and transmittance 𝐴𝐴 𝐴𝐴𝑑𝑑 of diffuse solar radiation among the sub-grids It is difficult to obtain the grid-scale 𝐴𝐴 SFC𝑝𝑝 by a formula because it is a time-variant variable jointly determined by the solar azimuth angle and zenith angle at every model time step. As mentioned in Zhang et al (2022), we generate the grid-scale 𝐴𝐴 SFC𝑝𝑝 by a statistical method as follows: First, we divide 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 which ranges from 0 to 1 into 𝐴𝐴 𝐴𝐴 = 100 levels ( 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 ≤ 0.01 , 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 ≤ 0.02 , ……, and 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 ≤ 1 ) on sub-grids at 360 azimuth directions. Second, we count the total number of sub-grids with 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 ≤ 0.01 , 𝐴𝐴 sin𝜀𝜀𝜙𝜙 𝑘𝑘 ≤ 0.02 , ..., 𝐴𝐴 sin𝜀𝜀𝜙𝜙 k ≤ 1 at a given azimuth direction within a model grid with a given horizontal resolution, that is, there are The grid-scale downward SSR components with the consideration of 3DSTSRE are calculated every time step in terms of the methods indicated above.…”

“…The negative biases are mainly attributed to the parameterized calculation of downward direct solar radiation (Equation 15), specifically the simplified replacement of 𝐴𝐴 𝐴sec𝛼𝛼𝑖𝑖 ⋅ cos𝐼𝐼𝑖𝑖 ⋅ 𝑆𝑆𝑆𝑆𝑖𝑖 >𝑖𝑖→𝑝𝑝 with 𝐴𝐴 𝐴sec𝛼𝛼𝑖𝑖 ⋅ cos𝐼𝐼𝑖𝑖 >𝑖𝑖→𝑝𝑝𝐴 𝑆𝑆𝑆𝑆𝑖𝑖 >𝑖𝑖→𝑝𝑝 without considering the regional mean product of their perturbation terms, resulting in the overestimation of terrain shadow effect. These negative biases are the main error source of the preliminary version of clear-sky 3DSTSRE scheme (Zhang et al, 2022). To reduce the error in the preliminary clear-sky 3DSTSRE scheme, the 𝐴𝐴 SFC𝑝𝑝 related to the shadow effect of surrounding terrains in Equation 24 is further adjusted by:…”

“…For the reasons mentioned above, an efficient upscaling method or parameterization scheme should be developed to convert the explicit calculations of downward SSR flux at sub‐grid scale (DEM data resolution) into the grid scale (model resolution) to fully consider the impact of 3D terrain configuration on the downward SSR flux in numerical models. We presented a preliminary version of clear‐sky 3DSTSRE scheme (Zhang et al., 2022), however, it still has problems of overestimating the terrain shadow effect and neglecting the effect of rugged surface area change on the fluxes. Also, the sensitivity of the scheme's performance to the model resolution remains unclear.…”