Two Types of Physical Inconsistency to Avoid with Univariate Quantile Mapping: A Case Study over North America Concerning Relative Humidity and Its Parent Variables
Bibliographic record
Abstract
Abstract Univariate quantile mapping (QM), a technique often used to statistically postprocess climate simulations, may generate physical inconsistency. This issue is investigated here by classifying physical inconsistency into two types. Type I refers to the attribution of an impossible value to a single variable, and type II refers to the breaking of a fixed intervariable relationship. Here QM is applied to relative humidity (RH) and its parent variables, namely, temperature, pressure, and specific humidity. Twelve sites representing various climate types across North America are investigated. Time series from an ensemble of ten 3-hourly simulations are postprocessed, with the CFSR reanalysis used as the reference product. For type I, results indicate that direct postprocessing of RH generates supersaturation values (>100%) at relatively small frequencies of occurrence. Generated supersaturation amplitudes exceed observed values in fog and clouds. Supersaturation values are generally more frequent and higher when RH is deduced from postprocessed parent variables. For type II, results show that univariate QM practically always breaks the intervariable thermodynamic relationship. Heuristic proxies are designed for comparing the initial bias with physical inconsistency of type II, and results suggest that QM generates a problem that is arguably lesser than the one it is intended to solve. When physical inconsistency is avoided by capping one humidity variable at its saturation level and deducing the other, statistical equivalence with the reference product remains much improved relative to the initial situation. A recommendation for climate services is to postprocess RH and deduce specific humidity rather than the opposite.
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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 | 0.006 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".