the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Jan 2026
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.
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Status: open (until 27 Feb 2026)
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CC1: 'Comment on egusphere-2025-5780', Michael Tsyrulnikov, 08 Jan 2026
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AC1: 'Reply on CC1', Benjamin Ménétrier, 12 Jan 2026
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I agree with you: the analysis increment lies indeed in the range of B, so its effective resolution is that of the coarse grid. Theoretically, we could perform the minimization at this coarse resolution, and then interpolate the analysis increment to the resolution of the first guess in order to add it to the first guess and produce the analysis. If the NICAS method is used as a localization operator in an EnVar framework, we could even store the ensemble perturbations on the coarse grid to save more on memory and CPU usage.
In practice, this option is difficult to implement because we must apply the linearized observation operator to the increment. Doing so on the coarse NICAS grid introduces a dependency between the background error covariance B and the linearized observation operator H that we would prefer to avoid. Moreover, the coarse NICAS grid is not column-based, but may be different for each selected vertical level. This means that horizontal interpolation would be necessary anyway to reconstruct vertical columns for vertically integrated observations (e.g. from satellites). It is much easier to keep this interpolation within B (in NICAS) and apply the linearized observation operator on the predefined, column-based grid of the first guess.
I recognize that this is not an entirely satisfactory answer, and I will take a look at the JEDI code to evaluate how much work would be needed to use the NICAS grid in the observation operator.
Citation: https://doi.org/10.5194/egusphere-2025-5780-AC1
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AC1: 'Reply on CC1', Benjamin Ménétrier, 12 Jan 2026
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RC1: 'Comment on egusphere-2025-5780', Nathan Crossette, 30 Jan 2026
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The description of the NICAS method outlined in this manuscript is clear, well-written, and thorough. It provides an excellent outline of the method including the motivation behind developing the process, the flexibility and extra features (such as the non-isotropic extension, in-homogeneous sub-grid generation, and modifying interpolation methods), descriptions of the best-use cases for the method, and a study of the computational performance and scalability of the method. The examples and demonstrations showcasing the method, and associated figures, tie together very well.
I have a few very minor suggestions that may improve this manuscript. First, adding a figure in section 2.1 "Motivations" that shows a full-resolution grid side-by-side with an associated sub-grid generated from the full grid would help the reader follow the argument on computational affordability and prepare them for the illustration of the application of the method in Figures 8 & 9. Second, Section 3.5 "Steps illustration" should add a few-sentence written description of the NICAS 'setup' step with some more details what happens during the setup to help give more context for the results in Figures 10, 11, and 12. Finally, adding a figure around section 3.1 "Splitting horizontal and vertical directions" to illustrate the two-step vertical and horizontal sub-sampling would be a nice, though not-necessary, addition.Citation: https://doi.org/10.5194/egusphere-2025-5780-RC1
Model code and software
SABER bundle: code and illustrations scripts Benjamin Ménétrier https://doi.org/10.5281/zenodo.17660617
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The effective resolution of the analysis increment is determined by the effective resolution of the background-error covariance matrix B (because the analysis increment vector lies in the range of B). So, if B is defined via interpolation from a coarse grid, then the effective resolution of the analysis will be equal to the resolution of the coarse grid.
But we can achieve a lower analysis resolution (and save computer time) just by defining the analysis increment on this coarse grid, can't we?