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

Abstract 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° to 0.8°, 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 · m −2 with a relative underestimation of 4∼10%. The 3DSTLRE scheme can clearly reduce the biases of plane‐parallel scheme and exhibits wide application prospects in various numerical models.