Application of Fast Automatic Differentiation in the Soil Surface Evaporation Problem

Evaporation from the soil surface is an important and often hard-determined part of modeling the vertical water transfer in soil. The study considers the problem of determining evaporation and formulates it as an optimal control problem. The objective function is mean-square deviation of modeled values of soil moisture at various depths from some prescribed values. We found the numerical solution by the steepest descent method, and we calculated the gradient of the objective function by formulas of fast automatic differentiation (FAD). Moreover, we applied FAD method to estimate the sensitivity of soil moisture at various depths to changes of evaporation. The findings of the research made it possible to determine the effective subsurface soil layer in which it is advisable to compute the objective function. Numerical results showed that this subsurface soil layer determination has accelerated the convergence of finding solutions process and has reduced its run time.

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