Evaluation of climate model simulations is a key issue within climate research. The statistical framework proposed by Sundberg et al., 2012, provides a theoretical underpinning of methods for evaluation of climate models by use of climateproxy data from the last millennium. In the present work, the statistical framework above is used to suggest several latent factor models of different complexity that can be used for estimating the amplitude of a forcing effect in aclimate model by comparison with the observed/reconstructed climate. The performance of the models is evaluated and compared in a pseudo-proxy experiment, in which the true unobservable temperature series is replaced by selected realizations of a climate simulation model. For different levels of added noise, different conclusions can be drawn. However, for realistic noise levels, we find that the simplest model, the just-identified two-indicator one-factor model, denoted j.i.FA(2,1), is a competitive alternative to models with more complicated structure. Moreover, we discover that the Fieller method of constructing confidence regions, associated with the j.i.FA(2,1)-model, outperforms the Wald confidence interval, which in most cases fails to provide sensible and interpretable conclusions about the climate model under consideration. Last but not least, the results indicate a good performance of the j.i.FA(2,1)-model even in the presence of heteroscedasticity.

Evaluation of climate model simulations is a crucial task in climate research. In a work consisting of three parts, we propose a new statistical framework for evaluation of simulated responses to climate forcings, based on the concept of latent (unobservable) factors. Here, in Part I, we suggest several latent factor models of different complexity that can be used for evaluation of temperature data from climate model simulations against climate proxy data from the last millennium. Each factor model is developed for use with data from a single region, which can be of any size. To be able to test the hypotheses of interest, we have applied the technique of confirmatory factor analysis. We also elucidate the link between our factor models and the statistical methods used in Detection and Attribution (D\&A) studies. In particular, we demonstrate that our factor models can be used as an alternative approach to the methods used in D\&A studies. An additional advantage of their use is that they, in contrast to the commonly used D\&A methods, make it, in principle, possible to investigate whether the forcings of interest act additively or if any interaction effects exist.In Part II we investigate and illustrate the expansion of factor models to structural equation models, which permits the statistical modelling of more complicated climatological relationships. The performance of some of our statistical models suggested in Part I and Part is evaluated and compared in a numerical experiment, whose results are presented in Part III.

Evaluation of climate model simulations is a crucial task in climate research. In a work consisting of three parts, we propose a new statistical framework for evaluation of simulated responses to climate forcings, based on the concept of latent (unobservable) variables. In Part I, several latent factor models were suggested for evaluation of temperature data from climate model simulations, forced by a varying number of forcings, against climate proxy data from the last millennium. Here, in Part II, focusing on climatological characteristics of forcings, we deepen the discussion by suggesting two alternative latent variable models that can be used for evaluation of temperature simulations forced by five specific forcings of natural and anthropogenic origin. The first statistical model is formulated in line with confirmatory factor analysis (CFA), accompanied by a more detailed discussion about the interpretation of latent temperature responses and their mutual relationships. Introducing further\emph{causal links} between some latent variables, the CFA model is extended to a structural equation model (SEM), which allows us to reflect more complicated climatological relationships with respect to all SEM's variables. Each statistical model is developed for use with data from a single region, which can be of any size. Associated with different hypotheses, the CFA and SEM models can, as a beginning, be fitted to observable simulated data only, which allows us to investigate the underlying latent structure associated with the simulated climate system. Then, the best-fitting model can be fitted to the data with real climate proxy data included, to test the consistency between the latent simulated temperature responses and their real-world counterparts embedded in observations. The performance of both these statistical models and some models suggested in Part I is evaluated and compared in a numerical experiment, whose results are presented in Part III.

Evaluation of climate model simulations is a crucial task in climate research. In a work consisting of three parts, we propose a new statistical framework for evaluation of simulated responses to climate forcings, based on the concept of latent (unobservable) variables. In Part I, several latent factor models were suggested for evaluation of temperature data from climate model simulations, forced by a varying number of forcings, against climate proxy data from the last millennium. In Part II, focusing on climatological characteristics of forcings, we deepen the discussion by suggesting two alternative latent variable models that can be used for evaluation of temperature simulations forced by five specific forcings of natural and anthropogenic origin. The first statistical model is formulated in line with confirmatory factor analysis (CFA), accompanied by a more detailed discussion about the interpretation of latent temperature responses and their mutual relationships. Introducing further causal links between some latent variables, the CFA model is extended to a structural equation model (SEM), which allows us to reflect more complicated climatological relationships with respect to all SEM's variables. Each statistical model is developed for use with data from a single region, which can be of any size. Here, in Part III, the performance of both these statistical models and some models suggested in Part I is evaluated and compared in a pseudo-proxy experiment, in which the true unobservable temperature is replaced by temperature data from a selected climate model simulation. The present analysis involves seven regional data sets. Focusing first on the ability of the models to provide an adequate and climatologically defensible description of the unknown underlying structure, we may conclude that given the climate model under consideration, the SEM model in general performed best. As for the factor model, its assumptions turned out to be too restrictive to describe the observed relationships in all but one region. The performance of another factor model, reflecting the assumptions typically made in many D\&A studies, can be characterised as unacceptable due to its high sensitivity to insignificant coefficient estimates. Regarding the fourth statistical model analysed - a factor model with two indicators and one latent factor - it can be recommended to apply it with caution due to its sensitivity to departures from the independence assumptions among the model variables, which can make the interpretation of the latent factor unclear. The conclusions above have been confirmed in some form of a cross-validation study, presuming the availability of several data sets within each region of interest. Importantly, the present pseudo-proxy experiment is performed only for zero noise level, implying that the five SEM models and one factor model await further investigation to fully test their performance for realistic levels of added noise.