Optimization of upstream profiles in modelled flow over complex terrain

This paper describes an adjoint method for data assimilation into upstream boundary conditions of numerical models using optimal control theory. Mathematical formalisms are given along with the numerical implementation of the scheme in a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solution in a model of turbulent flow in complex terrain. To contrast this with other methods, two solutions for flow over an isolated hill are calculated, one with an optimized upstream solution and one with a simple surface-layer formulation for the upstream solution. These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to produce solutions of flow in complex terrain that are substantively different at the two solutions, with the optimized solution giving more accurate results.