Sensitivity of a Shallow-Water Model to Parameters

TL;DR

This study uses an adjoint-based technique to analyze how various parameters affect a shallow water model's accuracy, stability, and sensitivity, highlighting the importance of boundary conditions in model performance.

Contribution

It introduces a comprehensive sensitivity analysis of a shallow water model using adjoint methods, considering multiple parameters and configurations, including realistic and academic cases.

Findings

Boundary conditions near rigid boundaries have the greatest influence on the solution.

Optimal boundary approximation is crucial for model development.

Sensitivity estimates align with local Lyapunov exponents in both cases.

Abstract

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: 1. 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; 2. 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; 3. 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 influence the most the solution. This fact points out the necessity to identify optimal boundary approximation during a model development.