Reconstructing wave profiles from inundation data

TL;DR

This paper presents a variational data assimilation method to reconstruct wave profiles from inundation data, effectively handling noise and applied successfully to tsunami data with high accuracy.

Contribution

It introduces an adjoint wetting and drying scheme for efficient sensitivity analysis in wave profile reconstruction from inundation observations.

Findings

Robust reconstruction of wave profiles from noisy inundation data.

Successful application to real tsunami data with less than 1% error.

Demonstrated effectiveness on idealised and real-world scenarios.

Abstract

This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean boundary from inundation observations. This problem is solved with derivative-based optimisation and an adjoint wetting and drying scheme to efficiently compute sensitivity information. The capabilities of this approach are demonstrated on an idealised sloping beach setup in which the profile of an incoming wave is reconstructed from wet/dry interface observations. The method is robust against noisy observations if a regularisation term is added to the optimisation objective. Finally, the method is applied to a laboratory experiment of the Hokkaido-Nansei-Oki tsunami, where the wave profile is reconstructed with an error of less than 1% of the reference wave signal.