Do Nonorthogonally and Irregularly Sampled Scalar Velocities Contain Sufficient Information to Reconstruct an Orthogonal Vector Current Field?

Abstract

This paper addresses how well a two-dimensional orthogonal vector current field can be reconstructed from a set of nonorthogonally and irregularly sampled scalar velocity data. High-frequency radar (HFR)derived surface radial scalar velocities are sampled on a polar or elliptical coordinate grid as a directional projection of two-dimensional vector currents for a viewing angle of the individual HFRs. Synthetic radial velocity maps are generated by sampling two-dimensional surface vector currents obtained from a simple spectral model and a realistic regional circulation model on the polar or elliptical grid points configured similarly as the operational HFRs. Then, the sampled radial velocity maps are combined into a vector current field using inverse methods: least squares fitting and optimal interpolation. In this paper, uncertainty and misfit are defined as the degrees of insufficiency to resolve the vector current and the difference between the true and estimated vector currents, respectively. The uncertainty and misfit are evaluated in terms of several simulation parameters built into the simple spectral model and the degrees of the quality and the observational error of the radial velocity maps associated with the simulated missing data and noise level, respectively. A greater number of missing data and higher observational errors correspond to an increase in the standard deviation of the misfit and a significant reduction in the effective spatial coverage of the vector current fields. This paper provides technical details for resolving a vector current field and guidelines for the practical design of the spatial sampling of the current field using the HFRs.