A mathematical theory of de‐integrating long‐time integrated rainfall and its application for predicting 1‐min rain rate statistics
Bibliographic record
Abstract
SUMMARY To date, the methods devised for converting long‐term experimental probability distribution (pd), , of the rain rate ρT integrated in T min (T > > 1 min) to 1‐min pd, PR(R), of the instantaneous rain rate R, are based on flawed T‐min data and, as such, are not based on fully reliable first principles. is not only an upward translated version of PR(R) but also rotated clockwise and distorted. The current methods do not correct these errors. We propose and discuss a mathematical theory, which corrects these errors and thus de‐integrates T‐min experimental pds into the corresponding 1‐min pd, the input required by all rain attenuation prediction methods. The theory is based on simple first principles whose parameters are calibrated by means of a large and reliable rain‐rate data bank recorded in Spino d'Adda, a site held as an experimental laboratory and used for exploratory data analysis. We show that PR(R) is modelled by four distinct functions in four disjoint ranges, and that this modelling is physically meaningful. We have tested the theory up to integration times of 12 h, with a large experimental data bank of 1‐min rain‐rate time series recorded in Gera Lario, Fucino, Rome, Prague, and Montreal, besides Spino d'Adda. Defined the fraction of rainy time in an average year, Po (%), we have found that: (a) the modelling is very good up to 6 h; (b) in the range from about Po to 0.001%, the error values are constant, with average error set at about − 3% and RMS error less than 8% for T ≤ 120 min, less than about 9% for 120 < T ≤ 360 min. We have also applied the theory to rain‐rate time series provided by meteorological agencies with integration time T = 60 min (blind test) with excellent result. Copyright © 2011 John Wiley & Sons, Ltd.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".