A Stochastic Data‐Driven Ensemble Forecasting Framework for Water Resources: A Case Study Using Ensemble Members Derived From a Database of Deterministic Wavelet‐Based Models
Bibliographic record
Abstract
Abstract In water resources applications (e.g., streamflow, rainfall‐runoff, urban water demand [UWD], etc.), ensemble member selection and ensemble member weighting are two difficult yet important tasks in the development of ensemble forecasting systems. We propose and test a stochastic data‐driven ensemble forecasting framework that uses archived deterministic forecasts as input and results in probabilistic water resources forecasts. In addition to input data and (ensemble) model output uncertainty, the proposed approach integrates both ensemble member selection and weighting uncertainties, using input variable selection and data‐driven methods, respectively. Therefore, it does not require one to perform ensemble member selection and weighting separately. We applied the proposed forecasting framework to a previous real‐world case study in Montreal, Canada, to forecast daily UWD at multiple lead times. Using wavelet‐based forecasts as input data, we develop the Ensemble Wavelet‐Stochastic Data‐Driven Forecasting Framework, the first multiwavelet ensemble stochastic forecasting framework that produces probabilistic forecasts. For the considered case study, several variants of Ensemble Wavelet‐Stochastic Data‐Driven Forecasting Framework, produced using different input variable selection methods (partial correlation input selection and Edgeworth Approximations‐based conditional mutual information) and data‐driven models (multiple linear regression, extreme learning machines, and second‐order Volterra series models), are shown to outperform wavelet‐ and nonwavelet‐based benchmarks, especially during a heat wave (first time studied in the UWD forecasting literature).
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".