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Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings
Stockholm University, Faculty of Science, Department of Mathematics.
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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, serving as a basis for a wide range of CFA- and SEM-models, a powerful and flexible tool. Thanks to these properties, its application ultimately may contribute to an increased confidence in the conclusions about the ability of the climate model in question to simulate observed climate changes.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2017.
Keyword [en]
Confirmatory Factor Analysis, Measurement Error models, Structural Equation models, Wald confidence interval, Fieller confidence set, Climate model simulations, Climate forcings, Climate proxy data, Detection and Attribution
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-148208ISBN: 978-91-7797-055-2 (print)ISBN: 978-91-7797-056-9 (electronic)OAI: oai:DiVA.org:su-148208DiVA, id: diva2:1150197
Public defence
2017-12-12, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

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.

Available from: 2017-11-17 Created: 2017-10-18 Last updated: 2017-11-15Bibliographically approved
List of papers
1. Evaluation of climate model simulations by means of statistical methods
Open this publication in new window or tab >>Evaluation of climate model simulations by means of statistical methods
2015 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2015
Keyword
Climate models, Climate proxy, Pseudo-proxy experiment, Factor analysis, the Wald confidence interval, the Fieller confidence set.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-122032 (URN)
Presentation
2015-11-17, room 306, hus 6, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2015-10-29 Created: 2015-10-20 Last updated: 2017-10-18Bibliographically approved
2. Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part I
Open this publication in new window or tab >>Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part I
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword
Confirmatory Factor Analysis, Structural Equation models, Measurement Error models, Climate model simulations, Climate forcings, Climate proxy data, Detection and Attribution
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-148202 (URN)
Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2017-10-31Bibliographically approved
3. Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part II
Open this publication in new window or tab >>Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part II
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword
Confirmatory Factor Analysis, Structural Equation models, Measurement Error models, Climate model simulations, Climate forcings, Climate proxy data, Detection and Attribution
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-148203 (URN)
Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2017-10-31Bibliographically approved
4. Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part III
Open this publication in new window or tab >>Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part III
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword
Confirmatory Factor Analysis, Structural Equation models, Measurement Error models, Climate model simulations, Climate forcings, Climate proxy data, Detection and Attribution
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-148204 (URN)
Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2017-10-31Bibliographically approved

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