A statistical description method of global sub-grid topography for numerical models

Slope and aspect are important topographic elements for thermodynamics and dynamics of atmospheric circulation, especially for local radiation and topographic precipitation. We propose a simple realistic statistical method based on trigonometric function transformation to calculate sub-grid slope and aspect for describing the orographic characteristics of complex areas over the globe. It is found that the transformed conditional probability density function (PDF) conforms to the Gaussian distribution in most of the global areas (~98%), and this feature is not eliminated with the increasing of horizontal resolution. The reasonability of this method is tested over the Tibetan Plateau. The results show that the improvement ratio of surface solar radiation downward (SSRD) over the Tibetan Plateau improved significantly compared with the results from the grid average scheme, especially in autumn. The improvement of root mean square error (RMSE) is approximately 18.2 W/m², and the improvement ratio reached 38.4%. The improvements of maximum and regional-averaged SSRD over the whole Tibetan Plateau were ~130 W/ m² and ~44.3W/m² respectively. Although we only consider the effect of sub-grid slope and aspect on solar shortwave radiation, which has a certain bias with the observation data, it is sufficient to prove the rationality of the statistical method compared with the unobstructed horizontal surfaces scheme (CTL). After that, we applied this sub-grid parameterization scheme for topographic vertical motion in CAM5 to revise the original vertical velocity by adding the topographic vertical motion and then resulting a significant improvement of simulation in precipitation over steep mountains.