Well posedness of a regularized-Hibler model of sea-ice dynamics
Bibliographic record
Abstract
The viscous-plastic equations (VPE) of sea-ice dynamics and some of their variants are arguably the most widely used model to track the evolution of Arctic and Antarctic sea ice in current climate models. However, because of the inherent highly non-linear rheology and particularly singular viscosity coefficients, both their numerical and analytical treatments remain a challenge. Regularization and relaxation techniques are often used to make the equations tractable both numerically and theoretically. Here, a particular regularization which smooths the bulk and shear viscosities via a hyperbolic tangent, originally proposed for numerical simulations, is studied from the partial differential equation (PDE) analysis point of view. Using a combination of analytical results and numerical exploration, it is suggested here that the linearized equations in 2d dimensions, of these regularized equations, are well-posed, as a mixed hyperbolic-parabolic system of PDEs, for all background ice-flow solutions with finite gradient but it loses parbolicity in some isolated flow configurations when the flow gradient is infinite. This result extends a previous finding by the authors where it is shown that the smoothed 1d VPE model is uniformly linearly well-posed and it is in contrast to existing results that demonstrated that for the original-unsmoothed case, the VPEs in 1d are ill posed under divergent ice flows while in the 2d case the analysis is inconclusive in most cases.
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How this classification was reachedexpand
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) | 0.001 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".