A method for imposing surface-stress and heat–flux conditions in finite–difference models with steep terrain

A numerical implementation of the surface-stress condition is presented for atmospheric models in which the terrain slope cannot necessarily be considered small. The method involves reducing the discretized stress condition in terrain-following coordinates to a pair of coupled linear systems for the two horizontal velocity components at the boundary. The linear systems are then solved iteratively at each model time step to provide the unique boundary values of velocity consistent with the specified values of the stress. Similar methods are used to prescribe the normal flux of heat across the boundary. The stability and performance of the boundary conditions is demonstrated through application to a series of simplified test problems involving flows past high-aspect-ratio topography and thermally driven flows on steep slopes.