Primitive Equation Alternatives to the Wave Equation Formulation
Bibliographic record
Abstract
In the late 1970's, the wave equation formulation of the shallow water equations appeared to be one of the few options for finite-element model development. Spurious pressure modes occurred in most primitive equation formulations because of the coupling between the gravity wave terms in the continuity and momentum equations. However, several new and rediscovered elements make a primitive equation approach viable and offer advantages over the wave equation methods. Some of the strengths of the wave equation formulation are the amplitude and phase accuracy for the explicit version, good efficiency, and absence of spurious pressure modes. Some major shortcomings are poor accuracy for the implicit version and poor stability when advection becomes important. A finite element that provides a close replacement for the wave equation formulation is the P1NC-P1 element which has linear non-conforming bases for velocity and linear conforming bases for sea level. The latter are the same as the linear bases used with the wave equation approach; hence, there is a close correspondence in data structure between the two approaches. Used in conjunction with the primitive equations, the approach with this element provides all the same strengths as the wave equation formulation but not the weaknesses. This approach has better amplitude and phase accuracy for both explicit and implicit methods, has good efficiency, has no spurious modes, and can be used with a wide variety of advection operators including ELM and semi-Lagrangian methods. In addition, investments in software infrastructure can be retained because of the similar data structure in the two approaches.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.021 | 0.006 |
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".