Full‐Bayesian Inversion of the Edwards Aquifer
Bibliographic record
Abstract
The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor's series for the exponential terms introduced by sinks and sources or the Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity-denoted as ln(T)-perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can be performed. This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with an R2 coefficient = 0.96 for an ln(T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln(T) estimates, in comparison to simply interpolating the sparse ln(T) data alone. The new Bayesian code is also employed to calibrate a high-resolution finite difference MODFLOW model of the Edwards Aquifer in southwest Texas. The posterior ln(T) field from this application yields better head fit when compared to the prior ln(T) field determined from upscaling and cokriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers.
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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) | 0.001 | 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 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".