Image-well solution for island aquifers with pumping, recharge, and complex coastlines
Bibliographic record
Abstract
This study presents an innovative mathematical framework that integrates a new analytical solution with the image-well method to model island aquifers under the combined influences of pumping, recharge, and complex coastline geometries. Past analytical solutions often rely on simplified boundary conditions and assume axially or radially symmetric coastline geometries, limiting their ability to address multiple stressors and complex island geometries. In contrast, the proposed framework leverages the computational speed and simplicity of analytical modeling while incorporating an image-well approach to accommodate boundaries with arbitrary shapes. To validate the method accuracy and robustness, convergence analyses and comparisons with an established analytical solution are conducted. Additionally, new indices are introduced to evaluate the sensitivity of the freshwater–saltwater interface depth to various forcings and to assess uncertainties in vulnerability indices. An illustrative case study, based loosely on Kinmen Island, Taiwan, is used to demonstrate the applicability of the approach to optimize the pumping rates for multiple wells while ensuring that the interface depth remains within safe limits. Overall, the presented methodology provides a flexible and efficient tool for groundwater resource management in coastal regions, enabling assessment of saltwater intrusion risk and informing sustainable water-use strategies for coastal regions under dynamic environmental conditions. • A new analytical solution is integrated with the image-well method to model freshwater lenses with enhanced complexity. • The solution yields the head and freshwater–saltwater interface depth and accommodates pumping and recharge. • The solution is applied for an illustrative example and pumping optimization of an island aquifer.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".