Development of a clear‐sky 3D Sub‐grid Terrain Solar Radiative Effect Parameterization Scheme Based on the Mountain Radiation Theory

Terrains strongly affect the surface solar radiation (SSR) and energy balance, and further greatly modulate the weather and climate in rugged areas. In this study, we have developed a clear-sky 3-dimensional sub-grid terrain solar radiative effect (3DSTSRE) parameterization scheme based on the mountain radiation theory with full consideration of the influences of 3-dimensional configuration of terrains. Results show that the 3DSTSRE scheme achieves the equivalent effect of the downward SSR flux at the model grids derived from those explicitly calculated at the sub-grids without reducing the calculating efficiency of numerical models. It performs well at model grids with different horizontal resolutions. The instant downward SSR flux calculated by the 3DSTSRE scheme at 76.8%, 84.8%, 88.7%, 91.6%, 93.0%, and 87.1% model grids with the horizontal resolution of 0.025 degrees, 0.05 degrees, 0.1 degrees, 0.2 degrees, 0.4 degrees, and 0.8 degrees in the areas featured by complex terrains shows relative errors within +/- 1.0% against those derived from the explicit calculations at sub-grids, respectively. The normalized mean absolute errors of the instant downward SSR flux calculated by the 3DSTSRE scheme are below 1% (2%) throughout the day and the year for the model grids with resolutions ranging from 0.05 degrees to 0.8 degrees (of 0.025 degrees). Although the performance of 3DSTSRE scheme decreases slightly under the conditions with much lower solar zenith angle and finer model horizontal resolution, the 3DSTSRE scheme developed in current study shows broad application prospects in various numerical models with the advantages of a solid physical foundation, high accuracy, strong portability and flexibility.