Abstract
We provide a statistical review of the “optimal fingerprinting" approach presented in Allen and Tett (Clim Dyn 15:419-434, 1999) in light of the severe criticism of McKitrick (Checking for model consistency in optimal fingerprinting: a comment. Clim Dyn 58:405–411, 2022). Our review finds that the “optimal fingerprinting" approach would survive much of McKitrick (2022)’s criticism by enforcing two conditions related to the conduct of the null simulation of the climate model, and the accuracy of the null setting climate model. The conditions we proposed are simpler and easier to verify than those in McKitrick (2022). We provide additional remarks on the residual consistency test in Allen and Tett (1999), showing that it is operational for checking the agreement between the residual covariance matrices of the null simulation and the physical internal variation under certain conditions. We further provide the reason why the Feasible Generalized Least Square method, much advocated by McKitrick (2022), is not regarded as operational by geophysicists.
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References
Allen MR, Stott PA (2003) Estimating signal amplitudes in optimal fingerprinting, part i: theory. Clim Dyn 21(5–6):477–491
Allen M, Tett S (1999) Checking for model consistency in optimal fingerprinting. Clim Dyn 15:419–434
Anderson TW (2003) An introduction to multivariate statistical analysis, 3rd edn. Wiley-Interscience, Hoboken
Bai Z, Silverstein J (2010) Spectral analysis of large dimensional random matrices, 2nd edn. Springer, New York
Bell TL (1982) Optimal weighting of data to detect climatic change: application to the carbon dioxide problem. J Geophys Res 87:11,161-11,170
Carroll RJ (1982) Adapting for heteroscedasticity in linear models. Ann Stat 10(4):1224–1233
Cressie N (1993) Statistics for spatial data. Wiley
Guttorp P, Gneiting T (2006) Studies in the history of probability and statistics XLIX On the Matérn correlation family. Biometrika 93(4):989–995
Hasselmann K (1979) On the signal-to-noise problem in atmospheric response studies. In: Shawn T (ed) Meteorology of tropical oceans. Royal Meteorological Society, London, UK, pp 251–259
Hegerl GC, North GR (1997) Comparison of statistically optimal approaches to detecting anthropogenic climate change. J Clim 10:1125–1133
Ledoit O, Wolf M (2004) A well-conditioned estimator for large-dimensional covariance matrices. J Multivar Anal 88(2):365–411
McKitrick R (2022) Checking for model consistency in optimal fingerprinting: a comment. Clim Dyn 58:405–411
North GR, Kim KY, Shen SSP et al (1995) Detection of forced climate signals. part 1: filter theory. J Clim 8(3):401–408
Ribes A, Planton S, Terray L (2013) Application of regularised optimal fingerprinting to attribution. part i: method, properties and idealised analysis. Clim Dyn 41(11):2817–2836. https://doi.org/10.1007/s00382-013-1735-7
Stott P, Allen M, Jones G (2003) Estimating signal amplitudes in optimal fingerprinting. part ii: application to general circulation models. Clim Dyn 21:493–500
Tett S, Jones G, Stott P et al (2002) Estimation of natural and anthropogenic contributions to twentieth century temperature change. J Geophys Res. https://doi.org/10.1029/2000JD000028
van der Vaart AW (1998) Asymptotic statistics. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press
White H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817–838
Wooldridge JM (2010) Econometric analysis of cross section and panel data. The MIT Press
Acknowledgements
We thank the reviewers of Climate Dynamics for comments and suggestions which have led to improvement in the presentation, and Hongbin Lin and Shanshan Luo for assistance.
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This research was supported by the National Natural Science Foundation of China Grant 12292983.
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Chen, H., Chen, S.X. & Mu, M. A statistical review on the optimal fingerprinting approach in climate change studies. Clim Dyn 62, 1439–1446 (2024). https://doi.org/10.1007/s00382-023-06975-5
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DOI: https://doi.org/10.1007/s00382-023-06975-5