Radiation transport model for ablation hollows on snowfields
Bibliographic record
Abstract
The ablation hollows or “suncups” that form on the surface of snowfields in summer are a wonderful example of pattern formation in nature. Suncups reduce the albedo of the snow and set a characteristic length for interaction of wind with the snowpack. They also contain information about the properties of the snow and its ablation rate, which could be extracted if we had a more quantitative understanding of how suncups form. A mathematical model is proposed that explains the shape, size, and dynamical behavior of suncups in terms of the interaction of solar radiation with the snowpack. Using a perturbation method, we derive a nonlinear partial differential equation for the time‐dependent shape of the snow surface from an approximate physical model for the interaction of solar radiation with snow. The resulting equation, which is similar to the Kuramoto‐Sivashinsky equation in fluid mechanics, has solutions with characteristic length and amplitude. We find expressions for the characteristic size of suncups in terms of the spectrally averaged diffusion length of solar radiation in snow. The model correctly describes the shape of suncups, with their spatially ordered patterns of parabolic valleys and V‐shaped ridges. It is also in remarkably good agreement with the observed length scales and growth rates. Depending on the relative values of the coefficients of the nonlinear terms in the differential equation, the suncup patterns can be either stationary in time or chaotic.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".