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.
