Construction of a Clear-Sky Three Dimensional Sub-Grid Terrain Long-Wave Radiative Effect Parameterization Scheme Under Isotropic Assumption

Rugged topography considerably regulates the surface downwelling long-wave radiation (SDLR) flux and further affects the surface radiation and energy balances. The three dimensional sub-grid terrain long-wave radiative effect (3DSTLRE) is absent in most current numerical models, which usually adopt plane-parallel schemes to simulate the SDLR flux. This study has developed a clear-sky 3DSTLRE parameterization scheme based on the isotropic assumption of SDLR at rugged terrains and systematically evaluated its ability over the Tibetan Plateau (TP). Results show that the 3DSTLRE scheme achieves good and stable performance regardless of the horizontal resolution, time of the year, and sub-grid terrain complexity. At different model horizontal resolutions ranging from 0.025 degrees to 0.8 degrees, the normalized mean absolute errors (NMAE) of the daily SDLR flux simulated by the clear-sky 3DSTLRE scheme over most of TP are less than 0.9%, and the NMAE of the daily SDLR flux produced by the clear-sky 3DSTLRE scheme regionally averaged over the grids with different sub-grid terrain complexity are less than 0.25% in different months. Neglecting the 3DSTLRE in the plane-parallel schemes may lead to clearly underestimated SDLR flux over the rugged areas, and the underestimation increases with the horizontal resolution and sub-grid terrain complexity. At different model horizontal resolutions, the mean underestimation of the clear-sky daily SDLR flux simulated by the plane-parallel scheme over most of TP ranges from 5 to 20 W center dot m-2 with a relative underestimation of 4 similar to 10%. The 3DSTLRE scheme can clearly reduce the biases of plane-parallel scheme and exhibits wide application prospects in various numerical models. Terrain greatly affects the surface downwelling long-wave radiation (SDLR) flux and further modulates the surface radiation and energy balance and thereafter weather and climate at local to regional scales. But most current numerical models do not consider the 3-dimensional sub-grid terrain long-wave radiative effect (3DSTLRE). This study has developed a clear-sky 3DSTLRE parameterization scheme to describe the 3DSTLRE in the numerical models. Several experiments have been conducted to test the accuracy of the 3DSTLRE parameterization scheme in Tibetan Plateau and to indicate the necessity of considering the 3DSTLRE over the areas with rugged sub-grid terrains in numerical models. Results show that the clear-sky 3DSTLRE scheme can accurately calculate the SDLR flux at the model grids with different horizontal resolutions. The plane-parallel schemes without considering the 3DSTLRE tend to clearly underestimate the SDLR flux over the rugged areas. The 3DSTLRE parameterization scheme can obviously reduce the biases of the SDLR flux simulated by the plane-parallel scheme over the regions with complex terrain. Due to the advantages of a solid physical foundation, high accuracy, and strong flexibility, the 3DSTLRE scheme developed in this study exhibits wide application prospects in various numerical models. A clear-sky three-dimensional sub-grid terrain long-wave radiative effect (3DSTLRE) parameterization scheme has been developed The 3DSTLRE scheme shows high accuracy and is portable to the models with different horizontal resolutions Without considering the 3DSTLRE, the surface downwelling long-wave radiation over the rugged terrain areas is underestimated