Variational interpolation of high-frequency radar surface currents using DIVAnd

Alexander Barth,Charles Troupin,Emma Reyes,Jean-Marie Beckers,Aida Alvera-Azcárate,Joaquín Tintoré

doi:10.1007/s10236-020-01432-x

Abstract

DIVAnd (Data-Interpolating Variational Analysis, in n-dimensions) is a tool to interpolate observations on a regular grid using the variational inverse method. We have extended DIVAnd to include additional dynamic constraints relevant to surface currents, including imposing a zero normal velocity at the coastline, imposing a low horizontal divergence of the surface currents, temporal coherence and simplified dynamics based on the Coriolis force, and the possibility of including a surface pressure gradient. The impact of these constraints is evaluated by cross-validation using the HF (high-frequency) radar surface current observations in the Ibiza Channel from the Balearic Islands Coastal Ocean Observing and Forecasting System (SOCIB). A small fraction of the radial current observations are set aside to validate the velocity reconstruction. The remaining radial currents from the two radar sites are combined to derive total surface currents using DIVAnd and then compared to the cross-validation dataset and to drifter observations. The benefit of the dynamic constraints is shown relative to a variational interpolation without these dynamical constraints. The best results were obtained using the Coriolis force and the surface pressure gradient as a constraint which are able to improve the reconstruction from the Open-boundary Modal Analysis, a quite commonly used method to interpolate HF radar observations, once multiple time instances are considered together.

Highlights

High-frequency (HF) radars allow one to derive twodimensional maps of ocean surface currents over a wide coastal area by measuring the Doppler shift of electromagnetic waves undergoing Bragg-scattering (Crombie 1955; Wait 1966; Stewart and Joy 1974; Barrick 1978) of surface gravity waves whose wavelength is exactly one-half the radar wavelength
The traditional approach consists in interpolating the radial currents on a common grid and inverting a linear system to compute the zonal and meridional velocity components from the radial currents
The cost function depends on the gridded velocity field, and on a series of parameters involved in the considered dynamical constraints

Summary

Introduction

High-frequency (HF) radars allow one to derive twodimensional maps of ocean surface currents over a wide coastal area by measuring the Doppler shift of electromagnetic waves undergoing Bragg-scattering (Crombie 1955; Wait 1966; Stewart and Joy 1974; Barrick 1978) of surface gravity waves whose wavelength is exactly one-half the radar wavelength. The combined total current fields have gaps which can prevent several applications which typically require full fields such as search and rescue (O’Donnell et al 2005; Ullman et al ; Ullman et al 2006), oil spill tracking (Abascal et al 2009), and ecological applications (Emery et al 2006; Helbig and Pepin 2002; Zelenke et al 2009)

Methods

Results

Conclusion