Sensitivity of Entropy Method to Time Series Length in Hydrometric Network Design
Bibliographic record
Abstract
The design of optimal hydrometric networks is an important starting point in water resources planning and management. Redundant or inappropriate networks may require unnecessary monitoring costs, while a sparse network may cause a lack of understanding of the process being monitored. Many studies employ information theory, which uses the Shannon entropy, as a measure of the information to design optimal hydrometric networks measuring various hydrologic parameters, such as streamflow and precipitation. The majority of entropy application methods in hydrometric network design have had two common objectives, i.e., maximizing joint entropy and minimizing total correlation. However, it is still unclear what data lengths should be adequate to properly use the entropy approach to network design and how the data lengths affect the entropy values. In this study, four different data lengths (e.g., 5, 10, 15, and 20 years) of daily time series are used to determine the optimal streamflow and precipitation networks using entropy theory coupled with multiobjective optimization. The spatial distributions of the optimal monitoring locations appeared similarly for each data length. Specifically, the hot-spots where the selection likelihood from optimization results is high were not significantly changed; this is more obvious when the data length of daily time series was 10 years or greater. Additionally, the joint entropy and total correlation of the optimal networks were calculated from 10 days to 20 years with a 10-day increment. The joint entropy increased significantly during the first 5 years and then gradually increased without significant change after 10 years. Similarly, the total correlation stabilized after 5 years of daily time series lengths with no major change after 10 years. Therefore, it is recommended to use at least 10 years of data for information theory–based hydrometric network design when using daily time series.
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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 | 0.010 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".