An inverse technique for reconstructing ocean's density stratification from surface data

TL;DR

This paper introduces an inverse method that reconstructs ocean density stratification profiles from surface elevation data by analyzing internal tide spectra, demonstrating high accuracy in realistic scenarios.

Contribution

It presents a novel inverse technique linking surface data to internal ocean structure using a simplified layered model and dispersion relations.

Findings

Reconstruction accuracy of 90.2% without shear.

Reconstruction accuracy of 94.2% with shear.

Method effectively captures density profiles from surface signatures.

Abstract

In this article, we propose an inverse technique that accurately reconstructs the ocean's density stratification profile simply from free surface elevation data. Satellite observations suggest that ocean surface contains the signature of internal tides, which are internal gravity waves generated by the barotropic tides. Since internal tides contain the information of ocean's density stratification, the latter can in principle be reconstructed from the free surface signature. We consider a simple theoretical model that approximates a continuously stratified ocean as discrete layers of constant buoyancy frequency; this facilitates the derivation of a closed-form dispersion relation. First, we numerically simulate internal tide generation for toy ocean scenarios and subsequently perform Space-Time Fourier Transform (STFT) of the free surface, which yields internal tide spectra with wavenumbers corresponding to the tidal frequency. The density profile is reconstructed by substituting these wavenumbers into the dispersion relation. Finally, we consider a more realistic situation with rotation, bottom topography, shear and density profiles representative of the Strait of Gibraltar. Density reconstruction in the presence and absence of shear are respectively found to be $90.2\%$ and $94.2\%$ accurate.