A Normal Mode for Predicting Storm Surges on a Lake
Bibliographic record
Abstract
A mathematical procedure for determining the two-dimensional time-dependent response of a rotating lake with arbitrary topography is presented.The procedure depends on prior knowledge of the normal modes of oscillation of the lake.These may be found numerically for an arbitrary lake by the method of Rao and Schwab (1974).The space-dependent part of the forced solution is represented by an expansion in terms of the spectrum of normal modes.This results in a system of uncoupled first-order inhomogeneous differential equations which depend only on time and can be solved simply and efficiently by implicit numerical integration.The normal mode method avoids the problem of grid-dispersion inherent in the traditional approach of direct finite difference integration of the governing equations on a numerical space-time grid.It is also more economical in terms of computation time than the finite difference method.Furthermore, the normal mode method provides physical insight by determining exactly how the total energy of the lake is distributed among the individual modes.Results of the application of this technique to an ideal rectangular basin compare well with the solution by a finite difference technique.Favor able comparisons are also obtained for a natural basin, Lake Ontario, sub jected to a uniform wind stress and a natural wind stress.The computational efficiency of the normal mode technique is evident in all cases.An Appendix compares the results of these two -dimensional methods to the solution of the channel equations for Lake Ontario with uniform wind stress.vi
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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) | 0.028 | 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".