The relationship between diameter and depth of potholes eroded by running water
Bibliographic record
Abstract
Geometrical analyses of 3930 potholes (3565 fluvial potholes, 237 marine potholes and 128 hillside potholes) from 33 localities in the world reveal a consistent, linear relationship: D = Nh + M, where h and D are, respectively, the depth and mean diameter of pothole, M is a critical size of the initial concavities (seminal potholes) that subsequently underwent growth, and N is the ratio of diameter expanding (wall erosion) speed to deepening (floor abrasion) speed. For the stream potholes, N is generally less than 1 with an average value of 0.67, M varies from 5.3 cm to 40.5 cm with an average of 20 cm, and N decreases gently with increasing M. However, the marine and hillside potholes are generally characterized by N > 1 and M < 10–14 cm, and a power-law relationship N = 4.24M−0.78 (coefficient of determination R2 = 0.75, M is in cm) exists. The results indicate that depth increases faster than diameter for stream potholes due to the larger size of grinding stones (>5–10 cm), while depth increases slower than diameter for marine potholes and hillside potholes due to the smaller size of grinding stones (<5–10 cm). The pothole h-D relationship is nearly independent of rock type. Knowledge of the pothole depth–diameter relationship is useful in a number of contexts, including simulation of hydraulic dynamics, theoretical considerations of erosion, comprehension of channel incision and development of canyons and gorges, and accurate estimation of excavation volume and mechanical strength of potholed bedrock in the design and stability analysis of hydraulic and environmental engineering projects (e.g. dam construction and river dredging).
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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 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".