The distinct problems of physical inconsistency and of multivariate bias potentially involved in the statistical adjustment of climate simulations

Abstract

Bias adjustment of numerical climate model simulations involves several technical and epistemological arguments wherein the notion of physical inconsistency is often referred to, either for rejecting the legitimacy of bias adjustment in general or for justifying the necessity of sophisticated multivariate techniques. However, this notion is often mishandled, in part because the literature generally proceeds without defining it. In this context, the central objective of this study is to clarify and illustrate the distinction between physical inconsistency and multivariate bias, by investigating the effect of bias adjustment on two different kinds of inter-variable relationships, namely a physical constraint expected to hold at every step of a time series and statistical properties that emerge with potential bias over a climatic time scale. The study involves the application of 18 alternative bias adjustment techniques on 10 climate simulations and over 12 sites across North America. Adjusted variables are temperature, pressure, relative humidity and specific humidity, linked by a thermodynamic constraint. The analysis suggests on the one hand that a clear instance of potential physical inconsistency can be avoided with either a univariate or a multivariate technique, if and only if the bias adjustment strategy explicitly considers the physical constraint to be preserved. On the other hand, it also suggests that sophisticated multivariate techniques alone aren’t complete adjustment strategies in presence of a physical constraint, as they cannot replace its explicit consideration. As a supplementary objective, this study relates common optional adjustment procedures with likely effects on diverse basic statistical properties, as an effort to guide climate information users in the determination of adequate bias adjustment strategies for their research purposes.