Assessment of uncertainties in stage–discharge rating curves: a large-scale application to Quebec hydrometric network
Bibliographic record
Abstract
Rating curves (RCs), which establish a relationship between stage and discharge at a given cross-section of a river, are largely used by national agencies to measure flow. RCs are constructed from gauging measurements and are usually represented by power functions (also called “power laws”), mathematical functions frequently used to represent stage–discharge relationships of standard hydraulic structures. Uncertainties in estimated flows based on rating curves can be significant, especially for high- and low-flow regimes. It is therefore important to report these uncertainties as accurately as possible. Many approaches estimating the sources of uncertainties in flows have been proposed but are generally too complex for large-scale application to hydrometric networks. This paper proposes an approach to develop rating curves and to assess the corresponding uncertainties in estimated flow that can be readily applied to large-scale hydrometric networks. This approach takes into consideration possible changes in RCs over time due to hydraulic or geomorphologic modifications and assesses whether one or two power functions are needed to adequately represent the stage–discharge relationship over the available range of gauged stages. RCs at Quebec hydrometric stations have been constructed. Relative differences between flows estimated from the RCs and gauged flows are used to assess uncertainties in estimated flow. They were adjusted to normal or logistic distributions with constant (stage-independent uncertainties) or stage-dependent scale parameters (stage-dependent uncertainties). The mean standard deviation of estimated flows for RCs with stage-independent uncertainties (75.0 % of the RCs) is 6.5 %, while, for RCs with stage-dependent uncertainties, they increase significantly at low stages, reaching values larger than 20 % for some RCs at the lowest-gauged stage.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".