A mathematical theory of de‐integrating long‐time integrated rainfall statistics. Part II: from 1 day to 1 minute
Bibliographic record
Abstract
SUMMARY We have developed, tested and discussed a theory for de‐integrating the probability distribution (PD) of the daily rain rate to the PD of the rain rate integrated in 1 min, through many simple steps, with a good or very good precision, for a large range of probabilities and in many sites. The theory can also estimate the number of rain events (in the sense of rainstorms), N R , their average duration and the (conditional) PD of daily rainy time. The theory needs only three inputs, measured on site: the daily rain rate PD, the number of rainy days, N D (only for finding N R ) and the PD of the rain rate integrated in two consecutive and disjoint couples of days. The theory contains two complementary parts, both successfully tested: the first deals mainly with duration of daily rainy time and rain events, and the second deals with the main issue, namely de‐integrating daily rain rate PDs in 1‐min PDs. We have tested the theory on duration of rainy time in Spino d'Adda, Gera Lario, Fucino and Prague and subsequently with real (blind) field tests in Milan, Lugano, many sites in the USA, and Canada. The sites tested belong to very different climatic regions. Nevertheless, the predictions are generally very close to the experimental data. The theory, and its powerful predictions, can be useful for several research communities: radio propagation, agriculture, climatology, hydrology and applied meteorology. For all disciplines and applications, seasonal studies or even monthly studies could be pursued because the data banks available can be very large, even for restricted sub‐data banks. The theory will estimate its parameters on on‐site seasonal, or monthly, measurements. Future developments could deal with de‐integrating large‐area and long‐time integrated rain rate, observed by means of meteorological satellites, for obtaining ‘point’ 1‐min rain rate PDs concerning a small homogeneous area. We have tested the theory to sites with very different climates and for latitudes between 65°N and 28°N. Therefore, we think that the theory can be applied globally in this latitude range because its parameters are derived from local measurements and, perhaps, down to the tropics. Because of the simplicity of the theory, and its use of few local measurements, it may be applied also to equatorial sites. This, however, is only a conjecture because we have not tested the theory directly there. Copyright © 2013 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".