Retrieval of Initial Value and Estimation of Parameter for Nonlinear Convection-Diffusion Problem Based on Variational Adjoint Method: Theoretical Aspects

As a kind of promising and potential data assimilation technique to which various countries´ meteorologists had attached great importance, the variational data assimilation had so far become the main development direction in meteorological data assimilation. So this paper is limited to illustrate the main idea of the variational adjoint method by constructing the variational adjoint system which here has a nonlinear variable-coefficient convection-diffusion equation at its core, and show how this method can be achieved from the mathematical point of view. As a result, the desired gradient formulas required for the descent of objective function are derived.