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Continuous dynamic assimilation of the inner region data in hydrodynamics modelling: optimization approach

Feodor Pisnitchenko,I. A. Pisnichenko,J. Martínez,S. Santos

Published 2008 in Nonlinear Processes in Geophysics

ABSTRACT

In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving a Cauchy- Dirichlet problem. The boundary conditions are obtained by linear interpolation of coarse-grid data provided by a global model. Errors in boundary conditions due to interpolation may cause large deviations from the correct regional solu- tion. The methods developed to reduce these errors deal with continuous dynamic assimilation of known global data avail- able inside the regional domain. One of the approaches of this assimilation procedure performs a nudging of large-scale components of regional model solution to large-scale global data components by introducing relaxation forcing terms into the regional model equations. As a result, the obtained solu- tion is not a valid numerical solution to the original regional model. Another approach is the use a four-dimensional vari- ational data assimilation procedure which is free from the above-mentioned shortcoming. In this work we formulate the joint problem of finding the regional model solution and data assimilation as a PDE-constrained optimization prob- lem. Three simple model examples (ODE Burgers equa- tion, Rossby-Oboukhov equation, Korteweg-de Vries equa- tion) are considered in this paper. Numerical experiments indicate that the optimization approach can significantly im- prove the precision of the regional solution.

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