Retrieval of balanced fields: an optimal control method

Abstract

The nonlinear balance equation links the stream function and the geopotential in a steady-state approximation of the atmosphere. It has been widely used to retrieve coherent wind and mass fields in limited areas under the assumptions that one of these fields was known without error within the domain and the other partially known on the boundary. The method which is proposed in this paper is based on optimal control techniques; it permits one to alleviate the above assumptions. In a first part of the paper, we describe an iterative algorithm, the geopotential and mass term of the balance equation are adjusted, and the boundary conditions are controlled in such a way that the discrepancy between the observations and a solution of the balance equation is minimized. The convergence of the method is discussed and a numerical example is carried out. The nonlinear balance equation uses the wind fields through the stream function. Of course, only the wind fields are observed, and the second part is devoted to an algorithm which permits one to compute the stream function and the potential velocity from wind observations in a limited area. The method is also based on the control of the boundary conditions.