Surface drag and heat flux conditions for atmospheric models with steep terrain

A numerical implementation of the surface drag and heat flux conditions is presented for atmospheric models in which the terrain slope cannot necessarily be considered small. The tangential stress across the lower boundary is derived in terms of the velocity components and then discretized to give a coupled set of 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 boundary values of velocity consistent with the specified surface stress. Similar methods are used to prescribe the normal heat flux across the surface of the terrain. The stability and performance of the boundary conditions is then demonstrated for a series of test problems and the overall impact of the conditions is evaluated in the context of flows past isolated topography and thermally driven flows on steep slopes.