Derivation of unit hydrograph using a transfer function approach
Bibliographic record
Abstract
The unit hydrograph (UH) concept and model have been widely used in the hydrological field over the past decades. However, the estimation of such a model in practice has always been a challenge for researchers and practitioners because such a model is usually ill formed in mathematical terms. The large number of parameters (or the number of ordinates) in a unit hydrograph model are correlated to a certain degree, and this could cause unstable results. So far, the research has been mainly focused on restricting the negative values and smoothing the oscillation by brute force methods, such as linear programming, and has achieved a certain degree of success. However, the number of parameters involved and the lack of stable model response are still a problem. In this study, a new model structure has been proposed that would inherently remove the negative UH ordinates and guarantee a smooth curve. This model is derived by the unit pulse response of a given discrete transfer function in the time domain by restricting its poles along the positive real axis in its Z domain (that is, there are no imaginary components and no negative real values). The model is termed the physically realizable transfer function. The strengths of its structure are that it is numerically stable, physically realizable, parsimonious in parameters, and easy to implement in real time for its state and parameter updating. Its shortcomings are that it has nonlinear pole positions and a more complicated parameter estimation process. A case study with two events in England has been used to demonstrate the application of such a model.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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) | 0.004 | 0.001 |
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".