Improved Nonlinear Muskingum Model with Variable Exponent Parameter
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Bibliographic record
Abstract
The nonlinear Muskingum model has three parameters (storage parameter, weighting parameter, and exponent parameter) that are assumed in model estimation to be constant. The exponent parameter, which has no physical meaning, represents the average nonlinear behavior of the flood during the entire routing period. To address the variations of nonlinearity during the routing period, this paper considers a variable exponent parameter that varies with the inflow level. The boundaries of the inflow levels are considered to be dimensionless parameters. The problem is formulated as a mathematical optimization model that minimizes the sum of the squared (SSQ) or absolute deviations between the observed and estimated outflows. An efficient spreadsheet-based software is implemented. The proposed model was applied by using three examples involving single peak, multipeak, and nonsmooth hydrographs. The results show that the range of the optimal exponent parameters is small, yet the improvement in the fit of the nonlinear Muskingum model is substantial; the SSQ reduction reaches 35%, compared with the case of a constant exponent parameter. The proposed model should be of interest to researchers and engineers working in the area of flood management.
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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 it