A divergence-free spatial interpolator for large sparse velocity data sets

Abstract

A 2-D divergence-free interpolator is presented which is demonstrated to give more realistic values between sparse velocity data than interpolating velocity components independently. The interpolator enforces physical dependence between the velocity components by ensuring mass is conserved. Tests using data for a synthetic eddy show that independent interpolation of components can give unrealistic velocities between widely spaced data. However, divergence-free interpolation can reproduce the eddy almost as well with sparse data as with dense data. In the synthetic tests the divergence-free radial basis function (RBF) interpolator performed as well as, or better than, optimal interpolation. A significant advantage of the "greedy fit" RBF interpolator implemented here is the small number of coefficients required to describe the interpolating surface. For large data sets this gives the interpolator a significant computational advantage over techniques, like Optimal Interpolation, which require one coefficient per data point. The RBF's economy of parameters and imposing physics with the divergence-free constraint makes RBF interpolation of sparse data much more resistant to following the noise. The 2-D divergence-free interpolator can be used to interpolate geostrophic velocities or the horizontal transport of high-frequency flows such as tidal currents. Tests with data from the local dynamics experiment moorings and from moving vessel acoustic Doppler current profiler measurements of tidal flow show the divergence-free interpolator is better able to reproduce data left out of the interpolation than interpolating velocity components independently. Copyright 2009 by the American Geophysical Union.