Modelling Hydrological Droughts in Canadian Rivers Based on Markov Chains Using the Standardized Hydrological Index as a Platform
Bibliographic record
Abstract
The standardized hydrological index (SHI) is the standardized but not normalized (normal probability variate) value of the streamflow used to characterize a hydrological drought, akin to the standardized precipitation index (SPI, which is both standardized and normalized) in the realm of the meteorological drought. The time series of the SHI can be used as a platform for deriving the longest duration, LT, and the largest magnitude, MT (in standardized form), of a hydrological drought over a desired return period of T time units (year, month, or week). These parameters are predicted based on the SHI series derived from the annual, monthly, and weekly flow sequences of Canadian rivers. An important point to be reckoned with is that the monthly and weekly sequences are non-stationary compared to the annual sequences, which fulfil the conditions of stochastic stationarity. The parameters, such as the mean, standard deviation (or coefficient of variation), lag 1 autocorrelation, and conditional probabilities from SHI sequences, when used in Markov chain-based relationships, are able to predict the longest duration, LT, and the largest magnitude, MT. The product moment and L-moment ratio analyses indicate that the monthly and weekly flows in the Canadian rivers fit the gamma probability distribution function (pdf) reasonably well, whereas annual flows can be regarded to follow the normal pdf. The threshold level chosen in the analysis is the long-term median of SHI sequences for the annual flows. For the monthly and weekly flows, the threshold level represents the median of the respective month or week and hence is time varying. The runs of deficit in the SHI sequences are treated as drought episodes and thus the theory of runs formed an essential tool for analysis. This paper indicates that the Markov chain-based methodology works well for predicting LT on annual, monthly, and weekly SHI sequences. Markov chains of zero order (MC0), first order (MC1), and second order (MC2) turned out to be satisfactory on annual, monthly, and weekly scales, respectively. The drought magnitude, MT, was predicted satisfactorily via the model MT = Id × Lc, where Id stands for drought intensity and Lc is a characteristic drought length related to LT through a scaling parameter, ɸ (= 0.5). The Id can be deemed to follow a truncated normal pdf, whose mean and variance when combined implicitly with Lc proved prudent for predicting MT at all time scales in the aforesaid relationship.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 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".