Two Types of Physical Inconsistency to Avoid with Univariate Quantile Mapping: A Case Study over North America Concerning Relative Humidity and Its Parent Variables

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.