Open AccessSensitivity of functionals of variational data assimilation problems
Author(s) -
V. P. Shutyaev,
F.X. Le Dimet
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524864421-425
Subject(s) - hessian matrix , data assimilation , mathematics , sensitivity (control systems) , optimal control , nonlinear system , function (biology) , basis (linear algebra) , mathematical optimization , physics , geometry , quantum mechanics , electronic engineering , evolutionary biology , meteorology , engineering , biology
The problem of variational data assimilation for a nonlinear evolutionary model is formulated as an optimal control problem to find simultaneously unknown parameters and the initial state of the model. The response function is considered as a functional of the optimal solution found as a result of assimilation. The sensitivity of the functional to observational data is studied. The gradient of the functional with respect to observations is associated with the solution of a nonstandard problem involving a system of direct and adjoint equations. On the basis of the Hessian of the original cost function, the solvability of the nonstandard problem is studied. An algorithm for calculating the gradient of the response function with respect to observational data is formulated and justified.