A Simple Thaw‐Freeze Algorithm for a Multi‐Layered Soil using the Stefan Equation
Bibliographic record
Abstract
ABSTRACT The Stefan equation is one of the simplest approximate analytical solutions for the thaw‐freeze problem. It provides a useful method for predicting the depth of thawing/freezing in soils when little site‐specific information is available. The limited number of parameters in the Stefan equation makes possible its application in a multi‐layered system. We demonstrate that a widely used algorithm (JL‐algorithm), which has been frequently used in permafrost regions, was derived by an incorrect mathematical method. It will inevitably result in systematic errors in the simulation if this algorithm is used in a multi‐layered soil. We present another simple thaw‐freeze algorithm (XG‐algorithm) for multi‐layered soils. The new algorithm can be used to determine the freeze/thaw front in multi‐layered soils no matter how thick each layer is and how many layers the soil profile contains. Simulation results of the JL‐algorithm and the XG‐algorithm are compared using hypothetical soil profiles, and the XG‐algorithm is also used to simulate the thaw depth at three permafrost monitoring sites on the Qinghai‐Tibet Plateau and one on the Loess Plateau, China. These applications show that the XG‐algorithm could be readily used to analyse the factors that affect active‐layer thickness. It can also be coupled with hydrological or land surface models to simulate the freeze‐thaw cycles in permafrost regions and for related engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".