A Non-Reflective Upper Boundary Condition for Limited-Height Hydrostatic Models

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Abstract
A simple upper boundary condition for hydrostatic, Boussinesq models is derived from a linear internal wave theory, assuming a uniform stratification and no Coriolis effects. This condition is applied in a two-dimentional nonlinear model of the planetary boundary layer. The numerical implementation and some stability problems are discussed. A comparison of the results of numerical experiments using different vertical extensions with analytical solutions is used to show that the condition provides a satisfactory solution to the problems of radiation of upward propagating energy.