A conservative adaptive wavelet method for the shallow‐water equations on the sphere
Bibliographic record
Abstract
We introduce an innovative wavelet‐based approach to adjust local grid resolution dynamically to maintain a uniform specified error tolerance. Extending the work of Dubos and Kevlahan, a wavelet multiscale approximation is used to make the Thuburn‐Ringler‐Skamarock‐Klemp (TRiSK) model dynamically adaptive for the rotating shallow‐water equations on the sphere. This article focuses on the challenges encountered when extending the adaptive wavelet method to the sphere and ensuring an efficient parallel implementation using message passing interface (MPI). The wavelet method is implemented in Fortran 95 with an emphasis on computational efficiency and scales well up to processors for load‐unbalanced scenarios and up to at least processors for load‐balanced scenarios. The method is verified using standard smooth test cases and a nonlinear test case proposed by Galewsky et al. The dynamical grid adaption provides compression ratios of up to 50 times in a challenging homogenous turbulence test case. The adaptive code is about three times slower per active grid point than the equivalent non‐adaptive TRiSK code and about four times slower per active grid point than an equivalent spectral code. This computationally efficient adaptive dynamical core could serve as the foundation on which to build a complete climate or weather model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".