General sensitivity analysis in data assimilation
François-Xavier Le Dimet, V. P. Shutyaev, Thu Ha Tran · Russian Journal of Numerical Analysis and Mathematical Modelling · 2014
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The operator of the model, and hence the optimal solution, depend on the parameters which may contain uncertainties. A response function is considered as a functional of the solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the parameters of the model is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The solvability of the non-standard problem is studied. Numerical algorithms for solving the problem are developed. The results are applied for 2D hydraulic and pollution models. Numerical examples on computation of the gradient of the response function are presented.