Evaluation of simulated responses to climate forcings: a flexible statistical framework using confirmatory factor analysis and structural equation modelling – Part 1: Theory

Abstract. Evaluation of climate model simulations is a crucial task in climate research. Here, a new statistical framework is proposed for evaluation of simulated temperature responses to climate forcings against temperature reconstructions derived from climate proxy data for the last millennium. The framework includes two types of statistical models, each of which is based on the concept of latent (unobservable) variables: confirmatory factor analysis (CFA) models and structural equation modelling (SEM) models. Each statistical model presented is developed for use with data from a single region, which can be of any size. The ideas behind the framework arose partly from a statistical model used in many detection and attribution (D&A) studies. Focusing on climatological characteristics of five specific forcings of natural and anthropogenic origin, the present work theoretically motivates an extension of the statistical model used in D&A studies to CFA and SEM models, which allow, for example, for non-climatic noise in observational data without assuming the additivity of the forcing effects. The application of the ideas of CFA is exemplified in a small numerical study, whose aim was to check the assumptions typically placed on ensembles of climate model simulations when constructing mean sequences. The result of this study indicated that some ensembles for some regions may not satisfy the assumptions in question.