Multiple linear regression analysis of stratospheric temperature and ozone changes: Assessment of uncertainties in model based attribution

Multiple Linear Regression (MLR) can be applied to coupled chemistry-climate model results in order to estimate the individual effects of different forcings on simulated variables. For example, in an earlier study we applied MLR to the results from a transient simulation over 1960-2100 with the Canadian Middle atmosphere Model (CMAM) in order to attribute past and future changes in stratospheric ozone and temperature to changes in greenhouse gases (GHGs) and ozone depleting substances (ODSs). We noted, however, that MLR assumes that sensitivities are linear, and furthermore, that regressors must be sufficiently orthogonal to clearly separate between the effects of the considered forcings. Thus MLR attribution results can be associated with significant uncertainty.

In this study we examine a new set of CMAM simulations for which the GHG and ODS forcings were added individually in separate simulations, providing the true response of stratospheric ozone and temperature to the applied forcings. Comparison of these new results with attribution estimates achieved from MLR analysis of a simulation including all considered forcings simultaneously enables us to explore how well MLR analysis performs in different regions of the stratosphere and for different sets of explanatory variables. Furthermore, this allows us to evaluate the intrinsic limitations of MLR analysis for stratospheric attribution, estimate uncertainties and examine non-linear effects.