Variational Data Assimilation in the Mathematical Model of the Black Sea Dynamics

Abstract

Purpose. In order to simulate the sea hydrothermodynamics, the problem of variational assimilation of the sea surface temperature data is solved. The data assimilation permits to adjust the numerical model calculations to the measurement data obtained in the environment under study. Methods and Results. The mathematical model of hydrothermodynamics of the Black and Azov seas, developed at the Institute of Numerical Mathematics of RAS and written in the sigma coordinate system, is considered. The distinctive feature of the model consists in applying the splitting method to physical processes and spatial coordinates that can significantly simplify the variational data assimilation algorithm. The problem of variational assimilation of the sea surface temperature data is formulated. A cost functional has been introduced; it includes the control function – heat flux at the sea upper boundary and satellite observations of the sea surface temperature. The necessary condition for the functional minimum is reformulated through the optimality system including the direct and adjoint problems, and the control condition. Using the variational assimilation of the satellite-derived observations, the algorithm for solving the stated problem was developed. It takes into account the observational errors’ covariance matrix calculated based on the statistical characteristics of the sea surface temperature observational data. The algorithm implies a sequential solution of the optimality system in the iterative process with the specially selected iterative parameter. The results of numerical solution of this problem are represented by the example of the Black and Azov seas. Conslusion. The results of numerical modeling with the observational data assimilation and without it are compared; efficiency of the observational data assimilation procedures is shown. Influence of the sea surface temperature assimilation upon the other system parameters is investigated. It is shown that when assimilating the sea surface temperature, only temperature in the upper layers is affected, whereas, provided that the depth is sufficient, the profile in the lower layers remains practically unchanged. The impact on the other system parameters is either minimal or not manifested at all.