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© Author(s) 2015. Artículo firmado por 24 autores. This work is distributed under the Creative Commons Attribution 3.0 License. This study is based on discussions held during the joint workshop of the PAGES 2k network and PAST2k-PMIP Integrated analyses of reconstructions and multimodel simulations for the past two millennia, Madrid, Spain, 4-6 November 2013. PAGES and FECYT (FCT-13-6276) are greatly thanked for supporting this workshop. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP. The US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support for CMIP and led the development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. H. Goosse is Research Director with the Fonds National de la Recherche Scientifique (F.R.S.-FNRS, Belgium). This work is supported by the F.R.S.-FNRS and by the Belgian Federal Science Policy Office (Research Programme on Science for a Sustainable Development). C. C. Raible and F. Lehner are supported by the Swiss National Science foundation. P. Yiou is supported by the MILEX project of the Swedish Research Council. J. Gergis is funded by Australian Research Council project DE130100668. O. Bothe was supported by LOCHMES (Leibniz Society), PRIME-II (within DFG INTERDYNAMIK), and CliSAP. L. Fernández Donado was funded by a FPU grant: AP2009-4061. A. Moberg and A. Hind are supported by the Swedish Research Council grants B0334901 and C0592401. G. Hegerl and A. Schurer are supported by the ERC advanced grant TITAN (320691). L. Fernández Donado, E. García Bustamente, and J. F. González Rouco were supported by grants CGL2011-29677-CO2-02 and CGL2014-59644-R. Gabi Hegerl was also supported by a Royal Society Wolfson Research Merit Award and by NCAS. This is LDEO contribution number 7956. N. McKay was funded through the US National Science Foundation (ARC-1107869)., Estimated external radiative forcings, model results, and proxy-based climate reconstructions have been used over the past several decades to improve our understanding of the mechanisms underlying observed climate variability and change over the past millennium. Here, the recent set of temperature reconstructions at the continental-scale generated by the PAGES 2k project and a collection of state-of-the-art model simulations driven by realistic external forcings are jointly analysed. The first aim is to estimate the consistency between model results and reconstructions for each continental-scale region over the time and frequency domains. Secondly, the links between regions are investigated to determine whether reconstructed global-scale covariability patterns are similar to those identified in model simulations. The third aim is to assess the role of external forcings in the observed temperature variations. From a large set of analyses, we conclude that models are in relatively good agreement with temperature reconstructions for Northern Hemisphere regions, particularly in the Arctic. This is likely due to the relatively large amplitude of the externally forced response across northern and high-latitude regions, which results in a clearly detectable signature in both reconstructions and simulations. Conversely, models disagree strongly with the reconstructions in the Southern Hemisphere. Furthermore, the simulations are more regionally coherent than the reconstructions, perhaps due to an underestimation of the magnitude of internal variability in models or to an overestimation of the response to the external forcing in the Southern Hemisphere. Part of the disagreement might also reflect large uncertainties in the reconstructions, specifically in some Southern Hemisphere regions, which are based on fewer palaeoclimate records than in the Northern Hemisphere., Unión Europea. FP7, Fonds de la Recherche Scientifique (F.R.S.-FNRS), Francia, Belgian Federal Science Policy Office (Research Programme on Science for a Sustainable Development), Swiss National Science foundation, MILEX project of the Swedish Research Council, Australian Research Council, LOCHMES (Leibniz Society), Precipitation in the past millennium in Europe (PRIME-II), Cluster of Excellence Integrated Climate System Analysis and Prediction (CliSAP), Formación del Profesorado Universitario (FPU) MECD, España, Swedish Research Council, Royal Society of London for Improving Natural Knowledge, National Centre for Atmospheric Science (NCAS), Reino Unido, US National Science Foundation, Integrated Analysis of Interglacial Climate Dynamics (INTERDYNAMIC), Deutsche Forschungsgemeinschaft (DFG), Alemania, Ministerio de Educación, Cultura y Deporte (MECD), España, Depto. de Física de la Tierra y Astrofísica, Fac. de Ciencias Físicas, TRUE, pub

Modeling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes. However, most commonly used approaches require strong assumptions and are either too simplistic or over-parameterized. From a machine learning perspective, generative adversarial networks (GANs) are a powerful tool to model dependencies in high-dimensional spaces. Yet in the standard setting, GANs do not well represent dependencies in the extremes. Here we combine GANs with extreme value theory (evtGAN) to model spatial dependencies in summer maxima of temperature and winter maxima in precipitation over a large part of western Europe. We use data from a stationary 2000-year climate model simulation to validate the approach and explore its sensitivity to small sample sizes. Our results show that evtGAN outperforms classical GANs and standard statistical approaches to model spatial extremes. Already with about 50 years of data, which corresponds to commonly available climate records, we obtain reasonably good performance. In general, dependencies between temperature extremes are better captured than dependencies between precipitation extremes due to the high spatial coherence in temperature fields. Our approach can be applied to other climate variables and can be used to emulate climate models when running very long simulations to determine dependencies in the extremes is deemed infeasible.

High-resolution climate model simulations for the last millennium were used to elucidate the main winter Northern Hemisphere atmospheric pattern during enhanced Eastern Mediterranean Transient (EMT-type) events, a situation in which an additional overturning cell is detected in the Mediterranean at the Aegean Sea. The differential upward heat flux between the Aegean Basin and the Gulf of Lion was taken as a proxy of EMT-type events and correlated with winter mean geopotential height at 500 mbar in the Northern Hemisphere (20–90∘ N and 100∘ W–80∘ E). Correlations revealed a pattern similar to the East Atlantic/Western Russian (EA/WR) mode as the main driver of EMT-type events, with the past 1000 years of EA/WR-like mode simulations being enhanced during insolation minima. Our model results are consistent with alkenone sea surface temperature (SST) reconstructions that documented an increase in the west–east basin gradients during EMT-type events.

The long-term relationship between temperature and hydroclimate has remained uncertain due to the short length of instrumental measurements and inconsistent results from climate model simulations. This lack of understanding is particularly critical with regard to projected drought and flood risks. Here we assess warm-season co-variability patterns between temperature and hydroclimate over Europe back to 850 CE using instrumental measurements, tree-ring based reconstructions, and climate model simulations. We find that the temperature-hydroclimate relationship in both the instrumental and reconstructed data turns more positive at lower frequencies, but less so in model simulations, with a dipole emerging between positive (warm and wet) and negative (warm and dry) associations in northern and southern Europe, respectively. Compared to instrumental data, models reveal a more negative co-variability across all timescales, while reconstructions exhibit a more positive co-variability. Despite the observed differences in the temperature-hydroclimate co-variability patterns in instrumental, reconstructed and model simulated data, we find that all data types share relatively similar phase-relationships between temperature and hydroclimate, indicating the common influence of external forcing. The co-variability between temperature and soil moisture in the model simulations is overestimated, implying a possible overestimation of temperature-driven future drought risks.

In this thesis, using the principles of confirmatory factor analysis (CFA) and the cause-effect concept associated with structural equation modelling (SEM), a new flexible statistical framework for evaluation of climate model simulations against observational data is suggested. The design of the framework also makes it possible to investigate the magnitude of the influence of different forcings on the temperature as well as to investigate a general causal latent structure of temperature data. In terms of the questions of interest, the framework suggested here can be viewed as a natural extension of the statistical approach of 'optimal fingerprinting', employed in many Detection and Attribution (D&A) studies. Its flexibility means that it can be applied under different circumstances concerning such aspects as the availability of simulated data, the number of forcings in question, the climate-relevant properties of these forcings, and the properties of the climate model under study, in particular, those concerning the reconstructions of forcings and their implementation. It should also be added that although the framework involves the near-surface temperature as a climate variable of interest and focuses on the time period covering approximately the last millennium prior to the industrialisation period, the statistical models, included in the framework, can in principle be generalised to any period in the geological past as soon as simulations and proxy data on any continuous climate variable are available. Within the confines of this thesis, performance of some CFA- and SEM-models is evaluated in pseudo-proxy experiments, in which the true unobservable temperature series is replaced by temperature data from a selected climate model simulation. The results indicated that depending on the climate model and the region under consideration, the underlying latent structure of temperature data can be of varying complexity, thereby rendering our statistical framework, s, At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 3: Manuscript.

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

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) 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. 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

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) 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

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

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) 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) 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

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