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Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings: Part III
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Physical Geography.
Stockholm University, Faculty of Science, Department of Mathematics.
(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 [en]
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: urn:nbn:se:su:diva-148204OAI: oai:DiVA.org:su-148204DiVA: diva2:1150165
Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2017-10-31Bibliographically approved
In thesis
1. Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings
Open this publication in new window or tab >>Towards a flexible statistical modelling by latent factors for evaluation of simulated responses to climate forcings
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
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:nbn:se:su:diva-148208 (URN)978-91-7797-055-2 (ISBN)978-91-7797-056-9 (ISBN)
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

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