Articles | Volume 8, issue 2
https://doi.org/10.5194/ascmo-8-225-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-8-225-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Evaluation of simulated responses to climate forcings: a flexible statistical framework using confirmatory factor analysis and structural equation modelling – Part 1: Theory
Katarina Lashgari
CORRESPONDING AUTHOR
Department of Mathematics, Division of Mathematical Statistics, Stockholm University, 106 91 Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden
previously published under the name Ekaterina Fetisova
Gudrun Brattström
Department of Mathematics, Division of Mathematical Statistics, Stockholm University, 106 91 Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden
Anders Moberg
Department of Physical Geography, Stockholm University, 106 91 Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden
Rolf Sundberg
Department of Mathematics, Division of Mathematical Statistics, Stockholm University, 106 91 Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden
Related authors
Katarina Lashgari, Anders Moberg, and Gudrun Brattström
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 249–271, https://doi.org/10.5194/ascmo-8-249-2022, https://doi.org/10.5194/ascmo-8-249-2022, 2022
Short summary
Short summary
The performance of a new statistical framework containing various structural equation modelling (SEM) models is evaluated in a pseudo-proxy experiment in comparison with the performance of statistical models used in many detection and attribution studies. Each statistical model was fitted to seven continental-scale regional temperature data sets. The results indicated the SEM specification is the most appropriate for describing the underlying latent structure of the simulated data analysed.
Katarina Lashgari, Anders Moberg, and Gudrun Brattström
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 249–271, https://doi.org/10.5194/ascmo-8-249-2022, https://doi.org/10.5194/ascmo-8-249-2022, 2022
Short summary
Short summary
The performance of a new statistical framework containing various structural equation modelling (SEM) models is evaluated in a pseudo-proxy experiment in comparison with the performance of statistical models used in many detection and attribution studies. Each statistical model was fitted to seven continental-scale regional temperature data sets. The results indicated the SEM specification is the most appropriate for describing the underlying latent structure of the simulated data analysed.
Cited articles
Boomsma, A.: Reporting Analyses of Covariance Structures, Struct. Equ. Modeling,
7, 461–483, https://doi.org/10.1207/S15328007SEM0703_6, 2000. a
Brohan, P., Kennedy, J. J., Harris, I., Tett, S. F. B., and Jones, P. D.: Uncertainty estimates in regional and
global observed temperature changes: A new data set from 1850, J. Geophys. Res., 111, D12106,
https://doi.org/10.1029/2005JD006548, 2006. a
Cheng, C.-L. and van Ness, J. W.: Statistical regression with measurement error,
Kendall's Library of Statistics, Oxford University Press Inc., New York, ISBN 0340614617, 1999. a
Cubasch, U., Wuebbles, D., Chen, D., Facchini, M. C., Frame, D., Mahowald, N., and Winther, J.-G.: Introduction, in: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2013. a
DelSole, T., Trenary, L., Yan, X., and Tippett, M. K.: Confidence intervals in optimal fingerprinting.
Clim. Dynam., 52, 4111–4126, https://doi.org/10.1007/s00382-018-4356-3, 2019. a, b
Deser, C., Phillips, A., Bourdette, V., and Teng, H.: Uncertainty in climate change projections: the role of internal
variability, Clim. Dyna,, 38, 527–546, https://doi.org/10.1007/s00382-010-0977-x, 2012. a
Eyring, V., Bony, S., Meehl, G. A., Senior, C. A., Stevens, B., Stouffer, R. J., and Taylor, K. E.: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization, Geosci. Model Dev., 9, 1937–1958, https://doi.org/10.5194/gmd-9-1937-2016, 2016. a
Faes, C., Molenberghs, G., Aerts, M., Verbeke, G., and Kenward, M. K.:
The effective sample size and analternative small-sample degrees-of-freedom method,
Am. Stat., 63, 389–399, https://doi.org/10.1198/tast.2009.08196, 2009. a
Fetisova, E.: Towards a flexible statistical modelling by
latent factors for evaluation of simulated climate forcing effects, doctoral thesis, Department of Mathematics,
Stockholm University, http://su.diva-portal.org/smash/record.jsf?pid=diva2%3A1150197&dswid=9303 (last access: 11 November 2022), 2017. a, b
Feulner, G.: Are the most recent estimates for Maunder Minimum solar irradiance in agreement
with temperature reconstructions?, Geophys. Res. Lett., 38, L16706, https://doi.org/10.1029/2011GL048529, 2011. a
Finney, S. J., and DiStefano, C.: Non-normal and categorical data in structural equation modeling
in: Structural equation modeling: A second course, edited by: Hancock, G. R. and Mueller, R. O.,
Greenwich, Connecticut: Information Age Publishing, 269–314, 2006. a
Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S. C., Collins, W., Cox, P.,
Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P., Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and
Rummukainen, M.: Evaluation of Climate Models, in: Climate Change 2013:
The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment
Report of the Intergovermental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K.,
Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M.,
Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, https://doi.org/10.1017/CBO9781107415324.020, 2013. a
Fox, J.: TEACHER'S CORNER: Structural Equation Modeling With the sem Package in R, Struct. Equ. Modeling,
13, 465–486, https://doi.org/10.1207/s15328007sem1303_7, 2006. a
Gettelman, A., and Sherwood, S.C.: Processes Responsible for Cloud Feedback.
Current Climate Change Reports 2, 179–189, https://doi.org/10.1007/s40641-016-0052-8, 2016. a
Gillett, N. P., Weaver, A. J., Zwiers, F. W., and Flannigan, M. D.: Detecting the effect of climate change on Canadian forest fires,
Geophys. Res. Lett., 31, L18211, https://doi.org/10.1029/2004GL020876, 2004a. a
Gillett, N. P., Wehner, M. F., Tett, S. F., and Weaver, A. J.:
Testing the linearity of the response to combined greenhouse gas and sulfate aerosol forcing, Geophys.
Res. Lett., 31, L14201, https://doi.org/10.1029/2004GL020111, 2004b. a
Goosse, H.: Climate system dynamics and modelling, Cambridge university press, USA, ISBN 9781107445833, 2015. a
Hasselmann, K.: On the signal-to-noise problem in atmospheric response studies, edited by: Shaw, D. B.,
Royal Meteorological Society, 251–259, 1979. a
Hasselmann, K.: Optimal Fingerprints for the detection of time-dependent climate
change, J. Climate, 6, 1957–1971, https://doi.org/10.1175/1520-0442(1993)006<1957:OFFTDO>2.0.CO;2, 1993. a
Hasselmann, K.: Multi-pattern fingerprint method for detection and attribution of climate change,
Clim. Dynam., 13, 601–611, https://doi.org/10.1007/s003820050185, 1997. a
Hegerl, G. C. and Zwiers, F.: Use of models in detection and attribution of climate
change, Adv. Rev., 2, 570–591, https://doi.org/10.1002/wcc.121, 2011. a, b
Hegerl, G. C., Zwiers, F. W., Braconnot, P., Gillett, N. P., Luo, Y., Marengo Orsini, J. A., Nicholls, N.,
Penner, J. E., and Stott, P. A.: Understanding and Attributing Climate Change, in: Climate Change 2007:
The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovermental Panel on Climate Change, edited by:
Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L.,
Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2007. a, b, c, d
Hegerl, G. C., Hoegh-Guldberg, O., Casassa, G., Hoerling, M. P., Kovats, R. S., Parmesan, C., Pierce, D. W.,
and Stott, P. A.: Good Practice Guidance Paper on Detection and Attribution Related to Anthropogenic Climate Change,
in: Meeting Report of the Intergovernmental Panel on Climate Change Expert Meeting on Detection and Attribution
of Anthropogenic Climate Change, edited by: Stocker, T. F., Field, C. B., Qin, D., Barros, V., Plattner, G.-K.,
Tignor, M., Midgley, P. M., and Ebi, K. L., IPCC Working Group I Technical Support Unit,
University of Bern, Bern, Switzerland, 2010. a
Hegerl, G. C., Luterbacher J., Gonźalez-Rouco, F., Tett, S. F. B., Crowley, T., and Xoplaki, E.:
Influence of human and natural forcing on European seasonal temperatures, Nat. Geosci., 4, 99–103,
https://doi.org/10.1038/NGEO1057, 2011. a
Hind, A. and Moberg, A.: Past millennial solar forcing magnitude.
A statistical hemispheric-scale climate model versus proxy data comparison,
Clim. Dynam., 41, 2527–2537, https://doi.org/10.1007/s00382-012-1526-6, 2013. a
Hind, A., Moberg, A., and Sundberg, R.: Statistical framework for evaluation of climate model simulations by use of climate proxy data from the last millennium – Part 2: A pseudo-proxy study addressing the amplitude of solar forcing, Clim. Past, 8, 1355–1365, https://doi.org/10.5194/cp-8-1355-2012, 2012. a
Hu, L. and Bentler, P. M.: Fit indices in covariance structure modeling: sensitivity to
underparameterized model misspecification, Psychol. Meth., 3, 424–453, https://doi.org/10.1037/1082-989X.3.4.424,
1998. a
Hu, L. and Bentler, P. M.: Cutoff criteria for fit indexes in covariance structure analysis: Conventional
criteria versus new alternatives, Struct. Eq. Modeling, 6, 1–55,
https://doi.org/10.1080/10705519909540118, 1999. a, b
Huntingford, C., Stott, P. A., Allen, M. R., and Lambert, F. H.: Incorporating model uncertainty into attribution of observed temperature change,
Geophys. Res. Lett., 33, L05710, https://doi.org/10.1029/2005GL024831, 2006. a
Jones, P. D., Briffa, K. R., Osborn, T. J., Lough, J. M., van Ommen, T. D., Vinther, B. M., Luterbacher, J.,
Wahl, E. R., Zwiers, F. W., Mann, M. E., Schmidt, G. A., Ammann, C. M., Buckley, B. M., Cobb, K. M., Esper, J.,
Goosse, H., Graham, N., Jansen, E., Kiefer, T., Kull, C., Küttel, M., Mosley-Thompson, E., Overpeck, J. T.,
Riedwyl, N., Schulz, M., Tudhope, A. W., Villalba, R., Wanner, H., Wolff, E., and Xoplaki, E.: High-resolution palaeoclimatology of the last millennium: a review of current
status and future prospects, Holocene, 19, 3–49, https://doi.org/10.1177/0959683608098952, 2009. a
Jungclaus, J. H., Bard, E., Baroni, M., Braconnot, P., Cao, J., Chini, L. P., Egorova, T., Evans, M., González-Rouco, J. F., Goosse, H., Hurtt, G. C., Joos, F., Kaplan, J. O., Khodri, M., Klein Goldewijk, K., Krivova, N., LeGrande, A. N., Lorenz, S. J., Luterbacher, J., Man, W., Maycock, A. C., Meinshausen, M., Moberg, A., Muscheler, R., Nehrbass-Ahles, C., Otto-Bliesner, B. I., Phipps, S. J., Pongratz, J., Rozanov, E., Schmidt, G. A., Schmidt, H., Schmutz, W., Schurer, A., Shapiro, A. I., Sigl, M., Smerdon, J. E., Solanki, S. K., Timmreck, C., Toohey, M., Usoskin, I. G., Wagner, S., Wu, C.-J., Yeo, K. L., Zanchettin, D., Zhang, Q., and Zorita, E.: The PMIP4 contribution to CMIP6 – Part 3: The last millennium, scientific objective, and experimental design for the PMIP4 past1000 simulations, Geosci. Model Dev., 10, 4005–4033, https://doi.org/10.5194/gmd-10-4005-2017, 2017. a, b, c, d
Jöreskog, K. G.: A general approach to confirmatory maximum likelihood factor analysis, Psychometrika,
34, 183–202, https://doi.org/10.1007/BF02289343, 1969. a, b, c, d
Jöreskog, K. G.: Structural equation models in the social sciences: specification, estimation and testing,
Research rapport 16, University of Uppsala, Departments of Statistics, 33 pp., 1976. a
Kodra, A., Chatterjee, S., and Ganguly, A. R.: Exploring Granger causality between global average observed
time series of carbon dioxide and temperature, Theor. Appl. Climatol., 104, 325–335, https://doi.org/10.1007/s00704-010-0342-3, 2011. a
Kutzbach, J. E.: The nature of climate and climatic variations, QuaternaryRes., 6, 471–480,
https://doi.org/10.1016/0033-5894(76)90020-X, 1976. a
Lashgari, K., Moberg, A., and Brattström, G.: Evaluation of simulated responses to climate forcings:
a flexible statistical framework using confirmatory
factor analysis and structural equation modelling
– Part 2: Numerical experiment, Adv. Stat. Clim. Meteorol. Oceanogr., 8, 249–271,
https://doi.org/10.5194/ascmo-8-249-2022, 2022. a
Levine, R. A. and Berliner, L. M.: Statistical principles for climate change studies, J. Climate, 12,
564–574, https://doi.org/10.1175/1520-0442(1999)012<0564:SPFCCS>2.0.CO;2, 1999. a
Li, Y., Chen, K., Yan, J., and Zhang, X.: Uncertainty in optimal fingerprinting is underestimated,
Environ. Res. Lett., 8, 084043. https://doi.org/10.1088/1748-9326/ac14ee, 2021. a
Liang, X. S.: Unraveling the cause-effect relation between time series,
Phys. Rev. E, 90, 052150, https://doi.org/10.1103/PhysRevE.90.052150, 2014. a
Liepert, B. G.: The physical concept of climate forcing, WIREs Clim. Change 1, 786-802,
https://doi.org/10.1002/wcc.75, 2010. a, b
Marvel, K., Schmidt, G. A., Shindell, D., Bonfils, C., LeGrande, A. N. Nazarenko, L., and Tsigaridis, K.:
Do responses to different anthropogenic forcings add linearly in climate models?, Environ. Res. Lett.,
10, 104010, https://doi.org/10.1088/1748-9326/10/10/104010, 2015. a, b
McGuffie, K. and Henderson-Sellers, A.: The climate modelling primer, 4th Edn., Chichester, Wiley Blackwell, 2014. a
Mitchell, J. F. B., Karoly, D. J., Hegerl, G. C., Zwiers, F. W., Allen, M. R., and Marengo, J.:
Detection of climate change and attribution of causes, in: Climate Change 2001: The Scientific Basis,
Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate
Change, edited by: Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., van der Linden, P. J., Dai, X., Maskell, K., and Johnson, C. A.,
Cambridge University press, Cambridge, United Kingdom and New York, NY, USA, 881 pp., 2001. a
Moberg, A. and Hind, A.: Simulated seasonal temperatures 850–2005 for the seven PAGES 2k regions derived from the CESM last millennium ensemble, Dataset version 1, Bolin Centre Database, https://doi.org/10.17043/moberg-2019-cesm-1, 2019. a, b
Moberg, A., Sundberg, R., Grudd, H., and Hind, A.: Statistical framework for evaluation of climate model simulations by use of climate proxy data from the last millennium – Part 3: Practical considerations, relaxed assumptions, and using tree-ring data to address the amplitude of solar forcing, Clim. Past, 11, 425–448, https://doi.org/10.5194/cp-11-425-2015, 2015. a
Morice, C. P., Kennedy, J. J., Rayner, N. A., and Jones, P. D.: Quantifying uncertainties in global and regional temperature
change using an ensemble of observational estimates: The HadCRUT4 data set, J. Geophys. Res., 117,
D08101, https://doi.org/10.1029/2011JD017187, 2012. a
Myhre, G., Shindell, D., Bréon, F.-M., Collins, W., Fuglestvedt, J., Huang, J., Koch, D., Lamarque, J.-F.,
Lee, D., Mendoza, B., Nakajima, T., Robock, A., Stephens, G., Takemura, T., and Zhang, H.: Anthropogenic and
Natural Radiative Forcing, in: Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by:
Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and
Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, https://doi.org/10.1017/CBO9781107415324.018, 2013. a
Otto-Bliesner, B. L., Brady, E. C., Fasullo, J., Jahn, A., Landrum, L., Stevenson, S., Rosenbloom, N., Mai,
A., and Strand, G.: Climate variability and changes since 850 CE: An Ensemble Approach with the Community
Earth System Model, B. Am. Meteorol. Soc., 97, 735–754,
https://doi.org/10.1175/BAMS-D-14-00233.1, 2016. a, b
PAGES 2k Consortium: Continental-scale temperature variability during the past two millennia, Nat. Geosci., 6, 339–346,
https://doi.org/10.1038/NGEO1797, 2013. a, b, c
PAGES 2k-PMIP3 group: Continental-scale temperature variability in PMIP3 simulations and PAGES 2k regional temperature reconstructions over the past millennium, Clim. Past, 11, 1673–1699, https://doi.org/10.5194/cp-11-1673-2015, 2015. a, b, c, d
R Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria,
http://www.R-project.org/ (last access: 11 November 2022), 2013. a
Ribes, A., Planton S., and Terray L.: Application of regularised optimal fingerprinting to attribution. Part I:
method, properties and idealised analysis, Clim. Dynam., 41, 2817–2836, https://doi.org/10.1007/s00382-013-1735-7, 2013. a
Rindskopf, D.: Structural Equation Models: empirical identification, Heywood cases, and related problems,
2nd Edn., Sociol. Method. Res., 13, 109–119, https://doi.org/10.1177/0049124184013001004, 1984. a
Runge, J., Bathiany, S., Bollt, E., Camps-Valls, G., Coumou, D.,
Deyle, E., Glymour, C.., Kretschmer, M., Mahecha, M. D., Muñoz-Marí, J., van Nes, E. H., Peters, J., Quax, R.,
Reichstein, M., Scheffer, M., Schölkopf, B., Spirtes, P., Sugihara, G., Sun, J., Zhang, K., and Zscheischler, J.:
Inferring causation from time series in Earth system sciences, Nat. Commun., 10, 2553, https://doi.org/10.1038/s41467-019-10105-3,
2019. a
Santer, B. D., Po-Chedley, S., Zelinka, M. D., Cvijanovic, I., Bonfils, C., Durack, P. J.,
Fu, Q., Kiehl, J., Mears, C., Painter, J., Pallotta, G., Solomon, S., Wentz, F. J., and Zou, C.-Z.:
Human influence on the seasonal cycle of tropospheric temperature, Science, p. 361, https://doi.org/10.1126/science.aas8806,
2018. a
Schurer, A. P., Mann, M. M., Tett, S. F. B., and Phipps, S. J.: Separating Forced from Chaotic Climate
variability over the Past Millenium, J. Climate, 26, 6954–6973, https://doi.org/10.1175/JCLI-D-12-00826.1, 2013. a
Schurer, A. P., Tett S. F., and Hegerl G. C.: Small influence of solar variability on climate over the past
millennium, Nat. Geosci., 7, 104–108, https://doi.org/10.1038/NGEO2040, 2014. a, b, c, d
Shapiro, S. S. and Wilk, M. B.: An analysis of variance test for normality (complete samples),
Biometrika, 52, 591–611, https://doi.org/10.1093/biomet/52.3-4.591, 1965. a
Shiogama, H., Stone, D., Emori, S., Takahashi, K., Mori, S., Maeda, A., Ishizaki, Y., and Allen, M. R.:
Predicting future uncertainty constraints on global warming projections, Sci. Rep., 6, 18903,
https://doi.org/10.1038/srep18903, 2016. a
Sörbom, D.: Model Modification, Psychometrika, 54, 371–384, https://doi.org/10.1007/BF02294623, 1989. a
Steiger, J. H., Shapiro, A., and Browne, M. W.:
On the multivariate asymptotic distribution of sequential Chi-square statistics, Psychometrika 50, 253–263,
https://doi.org/10.1007/BF02294104, 1985. a
Stips, A., Macias, D., Coughlan, C., Garcia-Gorriz, E., and Liang, X. S.: On the causal structure
between CO2 and global temperature, Sci. Rep., 6, 21691, https://doi.org/10.1038/srep21691, 2016.
a
Sundberg, R., Moberg, A., and Hind, A.: Statistical framework for evaluation of climate model simulations by use of climate proxy data from the last millennium – Part 1: Theory, Clim. Past, 8, 1339–1353, https://doi.org/10.5194/cp-8-1339-2012, 2012. a, b
Tett, S. F. B., Stott, P. A., Allen, M. R., Ingram, W. J., and Mitchell, J. F. B.: Causes of twentieth-century
temperature change near the Earth's surface, Nature, 399, 569–572, https://doi.org/10.1038/21164, 1999. a
Wall, M. M.: Spatial Structural Equation Modeling, in:
Handbook of Structural Equation Modeling, edited by: Hoyle, R. H., The Guilford press, New York, London, 674–689, ISBN 978-1-60623-077-0,
2012. a
Wigley, T. M. L. Karoly, D. J., Hegerl, G. C., Zwiers, F. W., Allen, M. R., and Marengo, J.:
Detection of the Greenhouse Effect in the Observations, chap. 8 in: Climate Change 1990:
The IPCC Scientific Assessment, Report prepared for Intergovernmental Panel on Climate Change by Working
Group I, edited by: Houghton, J. T., Jenkins, G. J., and Ephraums, J. J.,
Cambridge University Press, Cambridge, Great Britain, New York, NY, USA and Melbourne, Australia, 410 pp., 1990. a
Short summary
This work theoretically motivates an extension of the statistical model used in so-called detection and attribution studies to structural equation modelling. The application of one of the models suggested is exemplified in a small numerical study, whose aim was to check the assumptions typically placed on ensembles of climate model simulations when constructing mean sequences. he result of this study indicated that some ensembles for some regions may not satisfy the assumptions in question.
This work theoretically motivates an extension of the statistical model used in so-called...