Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).
The Normalized Interpolated Convolution from an Adaptive Subgrid (NICAS) method
Benjamin Ménétrier
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.
Received: 21 Nov 2025 – Discussion started: 02 Jan 2026
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The application of very large correlation operators to vectors is an persistent challenge for variational data assimilation. It must be accurate, fast and scalable. This article proposes a new generic method that works for any model grid, relying on adaptive subgrids to achieve this goal, even with advanced correlation functions. It describes the motivations and advantages of this method and its limitations depending on a few key parameters of the problem.
The application of very large correlation operators to vectors is an persistent challenge for...
