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Sensitivity of a shallow-water model to parameters. (English) Zbl 1239.76016
Summary: An adjoint based technique is applied to a shallow water model in order to estimate the influence of the model’s parameters on the solution. Among parameters, the bottom topography, initial conditions, boundary conditions on rigid boundaries, viscosity coefficients, Coriolis parameter and the amplitude of the wind stress tension are considered. Their influence is analyzed from three points of view: $\bullet$flexibility of the model with respect to a parameter that is related to the lowest value of the cost function that can be obtained in the data assimilation experiment that controls this parameter;$\bullet$possibility to improve the model by the parameter’s control, i.e., whether the solution with the optimal parameter remains close to observations after the end of control;$\bullet$sensitivity of the model solution to the parameter in a classical sense. That implies the analysis of the sensitivity estimates and their comparison with each other and with the local Lyapunov exponents that characterize the sensitivity of the model to initial conditions. Two configurations have been analyzed: an academic case of the model in a square box and a more realistic case simulating Black sea currents. It is shown in both experiments that the boundary conditions near a rigid boundary highly influence the solution. This fact points out the necessity to identify optimal boundary approximation during a model development.

##### MSC:
 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35Q35 PDEs in connection with fluid mechanics