Bivariate flood frequency analysis. Part 2: a copula‐based approach with mixed marginal distributions
Bibliographic record
Abstract
Abstract Karmakar and Simonovic (2008) describe the methodology of assigning appropriate marginal distributions for three flood characteristics. It is found that the gamma distribution is best fitted for peak flow ( P ), and a nonparametric distribution from the orthonormal series method best fits to volume ( V ) and duration ( D ), based on the root mean square error, Akaike information criterion and Bayesian information criteria. In addition, the chi‐square test is performed to check the significance of fitness. In this paper, a methodology is developed to derive bivariate joint distributions of the flood characteristics using the concept of copulas, considering a set of parametric and nonparametric marginal distributions for P, V and D to mathematically model the correlated structure among them. In the conventional method of flood frequency analysis, the marginal distribution functions of peak flow, volume and duration are assumed to follow some specific parametric distribution function. The concept of copulas relaxes the restriction of traditional flood frequency analysis by selecting marginals from different families of probability distribution functions for flood characteristics. The present study performs a better selection of marginal distribution functions for flood characteristics by parametric and nonparametric estimation procedures, and demonstrates how the concept of copulas may be used for establishing a joint distribution function with mixed marginal distributions. The results obtained are useful for hydrologic design and planning purposes. The methodology is demonstrated with 70 years of stream flow data of Red River at Grand Forks of North Dakota, USA.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".