the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Feb 2026
Accurate and Robust Geometric Algorithms for Regridding on the Sphere
Abstract. Regridding is one of the most common operations in geoscientific modeling and data analysis. There are many types of regridding, each drawing from a common set of fundamental computational geometry algorithms. However, these algorithms are rarely documented together or systematically compared in a manner that elucidates their relative strengths and appropriate use. In particular, several recent studies have highlighted the importance of careful treatment of floating point operations in the implementation of these algorithms to ensure numerical robustness and stability. In this work, we organize non-conservative and conservative regridding operations end-to-end, from spatial indexing, great-circle and constant latitude geometry, and spherical predicates to spherical clipping, triangulation, and area calculation with constant latitude corrections, into a coherent set of geometric kernels on the sphere. When known, we present numerically stable floating-point formulas and characterize their error behavior. We also indicate where higher-precision techniques, such as Error Free Transformations, can be incorporated when additional accuracy is needed. The resulting framework establishes a practical and performance-portable baseline for accurate and robust regridding on the sphere.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Geoscientific Model Development.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 15 Apr 2026)
- RC1: 'Comment on egusphere-2026-636', Anonymous Referee #1, 25 Mar 2026 reply
Data sets
Benchmark data and test cases code for spherical regridding algorithmns Hongyu Chen et al. https://github.com/hongyuchen1030/regridding-geom-benchmark/tree/main
Model code and software
Benchmark data and test cases code for spherical regridding algorithmns Hongyu Chen et al. https://github.com/hongyuchen1030/regridding-geom-benchmark/tree/main
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This manuscript provides a systematic treatment of the geometric algorithms underpinning spherical regridding operations. The paper addresses a genuine and longstanding gap in the geoscience modeling literature: these algorithms are widely used but poorly documented, implemented with varying degrees of rigor, and rarely compared systematically. The text will be a valuable reference for model developers.
Although I have developed an appreciation for this work, I cannot recommend publication until the following major revisions are made.
Major Comments:
1. The paper’s central prescriptive recommendations, such as the use of Kahan’s formula for edge length calculations, the preference for Eriksson’s formula over L’Huilier and quadrature-based methods for face area computation, and the conclusion that k-d trees and ball trees exhibit broadly similar performance, are supported by benchmark results presented only in the supplementary material. Readers should not need to consult the supplement to assess whether the paper’s core numerical claims are well supported.
I encourage the authors to incorporate the key quantitative findings from Supplement into the main text, including, at a minimum, representative error magnitudes and relative performance comparisons for the recommended approaches. Supplement can still serve an important role by presenting complete tables and additional comparisons.
2. The AccuCross and AccuXGCA algorithms represent key novel contributions of the paper. However, the manuscript does not currently include error bounds or empirical demonstrations of their accuracy, noting instead that such analysis is deferred to future work. To strengthen the paper, it would be helpful for the authors to include, at a minimum, either asymptotic error bounds or a concise empirical assessment of accuracy for AccuCross and AccuXGCA in the main text or appendix.
3. Several contributions are described as being implemented in existing tools such as TempestRemap but documented here for the first time, including the extremal latitude formula and the sweep-line bounding rectangle algorithm. While documenting previously undescribed algorithms is valuable, the paper would benefit from a clearer and more explicit delineation, ideally in the introduction or in a dedicated summary, of which elements are algorithmically novel and which are being formally described for the first time.
Minor Comment:
The manuscript is well written, and the English is of a high standard throughout. Nevertheless, a careful final proofreading pass is recommended to catch isolated typographical errors before resubmission. As one example, Section 5.4 contains a duplicated word: "we we find from (3) that".Â