Multivariate-Spline and Scale-Specific Solution for Variational Analyses

Abstract

A recipe for a cubic B-spline-based solution for multivariate variational formulation of a data analysis and assimilation problem is provided. To represent a signal whose smallest wavelength is L, the spline scale must be at most L/2, or approximately the Nyquist wavelength. This spline scale defines the computational grid, which tends to be coarser than the typical grid required for finite-difference discretization and hence offers a significant advantage in computational efficiency. The geostrophy?thin-plate model is introduced and applied to a set of analysis problems to demonstrate the effectiveness of the solution technique.