Improved Stefan Equation Correction Factors to Accommodate Sensible Heat Storage during Soil Freezing or Thawing
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract In permafrost regions, the thaw depth strongly controls shallow subsurface hydrologic processes that in turn dominate catchment runoff. In seasonally freezing soils, the maximum expected frost depth is an important geotechnical engineering design parameter. Thus, accurately calculating the depth of soil freezing or thawing is an important challenge in cold regions engineering and hydrology. The Stefan equation is a common approach for predicting the frost or thaw depth, but this equation assumes negligible soil heat capacity and thus exaggerates the rate of freezing or thawing. The Neumann equation, which accommodates sensible heat, is an alternative implicit equation for calculating freeze‐thaw penetration. This study details the development of correction factors to improve the Stefan equation by accounting for the influence of the soil heat capacity and non‐zero initial temperatures. The correction factors are first derived analytically via comparison to the Neumann solution, but the resultant equations are complex and implicit. Explicit equations are obtained by fitting polynomial functions to the analytical results. These simple correction factors are shown to significantly improve the performance of the Stefan equation for several hypothetical soil freezing and thawing scenarios. Copyright © 2015 John Wiley & Sons, Ltd.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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