Stochastic dynamics of storm surge with stable noise

TL;DR

This paper introduces a stochastic model for storm surge prediction incorporating stable noise to account for external forces, analyzing its effects on surge height simulation accuracy and sensitivity during different tide conditions.

Contribution

The study extends existing storm surge models by integrating uncorrelated alpha-stable noise, exploring its impact on surge height simulation and model sensitivity to external forces.

Findings

Stochastic model sensitive to external forces during low tide.

No significant overall improvement over deterministic models.

Large jumps occur with smaller alpha, requiring very small noise scale for stability.

Abstract

The Advanced Circulation (ADCIRC) and Simulating Nearshore Waves (SWAN) coupled model is modified to include a stochastic term in the shallow water equations that represents random external forces from debris carried by surge and short-term local scale atmospheric fluctuations. We added $\alpha$-stable noise, uncorrelated in space and time, in the forcing terms of the coupled model. Inputs to the model are unstructured computational mesh derived from topography and bathymetry, land cover classification, tidal potential constituents and atmospheric forcing. The model simulated surge height of around five meters rushing at four meters per second near Tacloban City downtown. Underestimation of simulated surge height is expected with use of bare earth model and absence of fluid sources on the governing equations, while overestimation of simulated peak height also occurs due to presence of concrete barriers that reduced surge height and inundation extent. The stochastic model is sensitive to random external forces during low tide and relatively higher fluid speed. Low tide happens when the fluid speed is maximum and water elevation is lowest, while higher fluid speed is brought by external forces like storm surge. However, the difference of stochastic solutions from the deterministic solution averages to zero and there is no significant improvement of the storm surge model in general when it comes to additive noise. This is an expected result since the noise used has zero mean. As $\alpha$ goes to zero larger jumps occur more frequently so $\sigma$ needs to be as small as $10^{-8}$ for simulation stability.