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

AbstractUnivariate quantile mapping (QM), a technique often used to statistically post-process 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 inter-variable relationship. 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 post-processed, with the CFSR reanalysis used as the reference product. For type I, results indicate that direct post-processing 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 hig...