Stability of the optimal solution to the problem of variational assimilation with error covariance matrices of observational data for the sea thermodynamics model
V.P. Shutyaev1,2, E.I. Parmuzin1
1Institute of Numerical Mathematics, RAS, Gubkina st., 8, Moscow, 119333, Russia
2Marine Hydrophysical Institute of RAS, Каpitanskaya Str., 2, Sevastopol, 299011, Russia
Keywords: вариационное усвоение данных наблюдений, оптимальное управление, сопряженные уравнения, ковариационные матрицы, устойчивость к погрешностям, температура поверхности моря, variational data assimilation, optimal control, adjoint equations, covariance matrices, stability with respect to errors, sea surface temperature
Abstract
A mathematical model of the sea thermodynamics, developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences is considered. The problem of variational assimilation of daily-averaged sea surface temperature (SST) data is formulated and investigated taking into account the observation error covariance matrices. On the basis of variational assimilation of satellite observation data, the inverse problem of restoring a heat flux on the sea surface is solved. The stability of the optimal solution of the problem of variational data assimilation is studied, and the results of numerical experiments for the model of the Baltic Sea dynamics are presented.
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