Evaluation of simulated responses to climate forcings: a flexible statistical framework using confirmatory factor analysis and structural equation modelling – Part 2: Numerical experiment

Abstract. The performance of a new statistical framework, developed for
the evaluation of simulated temperature responses to climate forcings against
temperature reconstructions derived from climate proxy data for the last millennium, is evaluated
in a so-called pseudo-proxy experiment, where the true unobservable temperature is replaced
with output data from a selected simulation with a climate model. Being an extension of the statistical
model used in many detection and attribution (D&A) studies,
the framework under study involves two main 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.
Within the present pseudo-proxy experiment, each statistical model was fitted
to seven continental-scale regional data sets. In addition, their performance for each defined
region was compared to the performance of the corresponding statistical model used in D&A studies. The results of
this experiment indicated that the SEM specification is the most appropriate one for describing
the underlying latent structure of the simulated temperature data in question.
The conclusions of the experiment have been confirmed in a cross-validation study, presuming
the availability of several simulation data sets within each studied region. Since the experiment is
performed only for zero noise level in the pseudo-proxy data, all statistical models, chosen as final
regional models, await further investigation to thoroughly test their performance for realistic levels of
added noise, similar to what is found in real proxy data for past temperature variations.
