The Adaptive Spectral Element Method and Comparisons with More Traditional Formulations for Ocean Modeling
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Bibliographic record
Abstract
Triangular spectral elements offer high accuracy in complex geometries, but solving the related matrix problem can be cumbersome and time consuming. In restricted applications, recent developments have led to a family of discontinuous Galerkin formulations in which each element of the mesh leads to a local matrix problem. The main restriction is that all the fluid equations must be prognostic and solved explicitly in time. Such is the case for a hydrostatic ocean with a free surface and a Boussinesq approximation. Furthermore, there is a strong need for variable resolution in ocean modeling since the width of synoptic eddies and strong western currents such as the Gulf Stream are nearly two orders of magnitude smaller than the typical width of an ocean. Triangular elements also offer high flexibility for the adaptive problem. Some applications for shallow water test case problems are shown with comparisons to a traditional finite-difference model and to a finite-element coastal ocean model. These comparisons are made in rectangular domains where the finite-difference method has an inherent advantage. For a nonlinear wind-driven application, the spectral element model proved to be more expensive to run at reasonable accuracy than a second-order-accurate finite-difference model. Nonetheless the spectral element model appears to be a large improvement compared to finite-element models of low order, an encouraging result. A simple adaptive strategy is also investigated, with favorable results.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it