Determining evaporation as a solution of the optimal control problem

The problem of determining evaporation is stated as an optimal control problem. The controlled process of vertical water transfer in soil is described by one-dimensional nonlinear parabolic equation. The daily evaporation is a control and, the objective function is the mean-square deviation of calculated values of the soil moisture from some prescribed values. As a result of finite difference approximation, the optimal control problem is reduced to a nonlinear programming problem. The problem obtained is proposed to be solved by the steepest descent method. The objective function gradient is computed using exact formulas of fast automatic differentiation. It is assumed that the prescribed values coincide with some solution of the direct problem on the set of comparisons of the calculated values and prescribed values of soil moisture. How does the type of this set affect the accuracy of the solution? Several variants of such a set are considered. The analysis of numerical solutions of the corresponding problems allows to choose the optimal variant in the sense of the accuracy of the solution and the number of measurements of the required soil moisture data.