Heterogeneity measures in hydrological frequency analysis: review and new developments
Bibliographic record
Abstract
Abstract. Some regional procedures to estimate hydrological quantiles at ungauged sites, such as the index-flood method, require the delineation of homogeneous regions as a basic step for their application. The homogeneity of these delineated regions is usually tested providing a yes/no decision. However, complementary measures that are able to quantify the degree of heterogeneity of a region are needed to compare regions, evaluate the impact of particular sites, and rank the performance of different delineating methods. Well-known existing heterogeneity measures are not well-defined for ranking regions, as they entail drawbacks such as assuming a given probability distribution, providing negative values and being affected by the region size. Therefore, a framework for defining and assessing desirable properties of a heterogeneity measure in the regional hydrological context is needed. In the present study, such a framework is proposed through a four-step procedure based on Monte Carlo simulations. Several heterogeneity measures, some of which commonly known and others which are derived from recent approaches or adapted from other fields, are presented and developed to be assessed. The assumption-free Gini index applied on the at-site L-variation coefficient (L-CV) over a region led to the best results. The measure of the percentage of sites for which the regional L-CV is outside the confidence interval of the at-site L-CV is also found to be relevant, as it leads to more stable results regardless of the regional L-CV value. An illustrative application is also presented for didactical purposes, through which the subjectivity of commonly used criteria to assess the performance of different delineation methods is underlined.
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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 | 0.005 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.006 | 0.010 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".