The Normalized Interpolated Convolution from an Adaptive Subgrid (NICAS) method

Abstract

This article presents an innovative method to apply a correlation operator to a vector in a high-dimensional system, as often needed in variational data assimilation algorithms. The Normalized Interpolated Convolution from an Adaptive Subgrid (NICAS) method is very appealing as it can work for any grid, on domains with complex boundaries, producing inhomogeneous and anisotropic correlation functions, and it is very efficient for large correlation support radii. In this study, we detail the method motivations and theoretical background, we describe the practical implementation of several important features, and we assess its computational cost in various configurations to exhibit its strengths and limitations. Finally, we compare these characteristics to the similar existing methods.