Probabilistic Capture Zone Delineation Based on an Analytic Solution
Bibliographic record
Abstract
A major tool used in the design of wellhead protection areas is the delineation of a capture zone for a pumping well by use of a simple, steady-state analytic solution. This simple approach has been useful for many small municipalities because of the high costs associated with obtaining the hydrogeologic information needed for detailed numerical modeling. This analytic solution, however, is deterministic, and uncertainty in the mean value estimates of the hydraulic parameters used in this model can be a major source of error in predicting capture zones. To address this problem, a statistical theory was developed for including the uncertainty in the transmissivity and the magnitude and direction of the hydraulic head gradient in the analytic solution for both the ultimate and time-dependent capture zone for an arbitrary reliability level. To demonstrate the method and investigate the effect of varying magnitudes of uncertainty on time-dependent capture zones, the method is applied to three synthetic data sets based on data from the Borden Aquifer in Ontario, Canada. In general, the results show that uncertainty in the length of the time-dependent capture zone at a given reliability level is dependent on the uncertainty in the magnitude of the mean regional flow, which is equal to the transmissivity multiplied by the hydraulic head gradient; uncertainty in the maximum width of the capture zone is dependent primarily on the uncertainty in the mean direction of the regional flow.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| 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".