Application of the Forward Sensitivity Method to a GWCE-Based Shallow Water Model

Abstract

The Forward Sensitivity Method (FSM) is applied to a GWCE-based shallow water model to analyze the sensitivity to the numerical parameter, G, that determines the balance between the wave and primitive forms of the continuity equation. Results show that the sensitivity to G calculated in the sensitivity evolution portion of the FSM is consistent with the actual sensitivity to G computed from multiple simulations using finite differences. The data assimilation step in the FSM is shown to be effective in selecting G that minimizes an objective function, in this case model errors based on sensitivities. Additionally, the FSM sensitivity results show 2 Δ x oscillations in the elevation and velocity fields develop when G is increased too high, suggesting the FSM may be an effective tool for determining the upper limit of G for real-world applications.

Keywords

• shallow water equations
• GWCE
• forward sensitivity method
• data assimilation