Analysis of system drought for Manitoba Hydro using stochastic methods
Bibliographic record
Abstract
Stochastic time series models are commonly used in the analysis of large-scale water resources systems. In the stochastic approach, synthetic flow scenarios are generated and used for the analysis of complex events such as multi-year droughts. Conclusions drawn from such analyses are only plausible to the extent that the underlying time series model realistically represents the natural variability of flows. Traditionally hydrologists have favoured autoregressive moving average (ARMA) models to describe annual flows. In this research project, a class of model called Markov-Switching (MS) model (also referred to as a Hidden Markov model) is presented as an alternative to conventional ARMA models. The basic assumption underlying this model is that a limited number of flow regimes exists and that each flow year can be classified as belonging to one of these regimes. The persistence of and switching between regimes is described by a Markov chain. Within each regime, it is assumed that annual flows follow a normal distribution with mean and variance that depend on the regime. The simplicity of this model makes it possible to derive a number of model characteristics analytically such as moments, autocorrelation, and crosscorrelation. Model estimation is possible with the maximum likelihood method implemented using the Expectation Maximization (EM) algorithm. The uncertainty in the model parameters can be assessed through Bayesian inference using Markov Chain Monte Carlo (MCMC) methods. A Markov-Switching disaggregation (MSD) model is also proposed in this research project to disaggregate higher-level flows generated using the MS model into lower-level flows. The MSD model preserves the additivity property because for a given year both the higher-level and lower-level variables are generated from normal distributions. The 2-state MS and MSD models are applied to Manitoba Hydro's system along with more conventional first order autoregressive and disaggregation models and parameter and missing data uncertainty are identified in the analysis of system drought.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".