# Evaluating explanatory models of the spatial pattern of surface climate trends using model selection and bayesian averaging methods

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## Abstract

We evaluate three categories of variables for explaining the spatial pattern of warming and cooling trends over land: predictions of general circulation models (GCMs) in response to observed forcings; geographical factors like latitude and pressure; and socioeconomic influences on the land surface and data quality. Spatial autocorrelation (SAC) in the observed trend pattern is removed from the residuals by a well-specified explanatory model. Encompassing tests show that none of the three classes of variables account for the contributions of the other two, though 20 of 22 GCMs individually contribute either no significant explanatory power or yield a trend pattern negatively correlated with observations. Non-nested testing rejects the null hypothesis that socioeconomic variables have no explanatory power. We apply a Bayesian Model Averaging (BMA) method to search over all possible linear combinations of explanatory variables and generate posterior coefficient distributions robust to model selection. These results, confirmed by classical encompassing tests, indicate that the geographical variables plus three of the 22 GCMs and three socioeconomic variables provide all the explanatory power in the data set. We conclude that the most valid model of the spatial pattern of trends in land surface temperature records over 1979–2002 requires a combination of the processes represented in some GCMs and certain socioeconomic measures that capture data quality variations and changes to the land surface.

## Keywords

GCM testing Spatial trend patterns Climate data contamination, spatial autocorrelation Non-nested tests Encompassing tests Bayesian model averaging## References

- Anselin L, Bera AK, Florax R, Yoon MJ (1996) Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics 26:77–104CrossRefGoogle Scholar
- Berk RA, Fovell RG, Schoenberg F, Weiss RE (2001) The use of statistical tools for evaluating computer simulations. Climatic Change 51(2):119–130Google Scholar
- Brohan P, Kennedy JJ, Harris I, Tett SFB, Jones PD (2006) Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850. J Geophys Res 111:D12106. doi: 10.1029/2005JD006548 CrossRefGoogle Scholar
- CCSP (2008) Climate models: an assessment of strengths and limitations. A report by the U.S. Climate Change Science Program and the Subcommittee on Global Change Research In: Bader DC, Covey C, Gutowski Jr WJ, Held IM, Kunkel KE, Miller RL, Tokmakian RT, Zhang MH (eds), Department of Energy, Office of Biological and Environmental Research, Washington, DCGoogle Scholar
- Covey C, AchutaRao KM, Cubasch U, Jones P, Lambert SJ, Mann ME, Phillips TJ, Taylor KE (2003) An overview of results from the Coupled Model Intercomparison Project. Global Planet Change 37:103–133CrossRefGoogle Scholar
- Davidson R, MacKinnon JG (1981) Several tests for model specification in the presence of alternative hypotheses. Econometrica 49(3):781–793CrossRefGoogle Scholar
- Davidson R, MacKinnon JG (2004) Econometric theory and methods. Toronto, OxfordGoogle Scholar
- De Laat ATJ, Maurellis AN (2004) Industrial CO
_{2}emissions as a proxy for anthropogenic influence on lower tropospheric temperature trends. Geophys Res Lett 31:L05204. doi: 10.1029/2003GL019024 CrossRefGoogle Scholar - De Laat ATJ, Maurellis AN (2006) Evidence for influence of anthropogenic surface processes on lower tropospheric and surface temperature trends. Int J Climatol 26:897–913CrossRefGoogle Scholar
- Easterly W, Sewadeh M (2003) World Bank global development network growth data base. http://www.worldbank.org/research/growth/GDNdata.htm. Accessed fall 2003
- Fernandez C, Ley E, Steel M (2001) Benchmark priors for Bayesian model averaging. Journal of Econometrics 100:381–427CrossRefGoogle Scholar
- Gleckler PJ, Taylor KE, Doutriaux C (2008) Performance metrics for climate models. J Geophys Res 113:D06104. doi: 10.1029/2007JD008972 CrossRefGoogle Scholar
- Hegerl G, Hasselmann K, Cubash U, Mitchell J, Roeckner E, Voss R, Waszkewitz J (1997) Multi-fingerprint detection and attribution analysis of greenhouse gas, greenhouse gas-plus-aerosol and solar forced climate change. Clim Dyn 13(9):613–634CrossRefGoogle Scholar
- Hegerl GC, Zwiers FW, Braconnot P, Gillett NP, Luo Y, Marengo Orsini JA, Nicholls N, Penner JE, Stott PA (2007) Under-standing and attributing climate change. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds), Climate Change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New YorkGoogle Scholar
- Hoeting J, Madigan D, Raftery A, Volinsky C (1999) Bayesian model averaging: a tutorial. Statistical Science 14:382–417CrossRefGoogle Scholar
- Jenne RL (1974) Jenne’s northern hemisphere climatology, monthly, 1950–64. National Center for Atmospheric Research Dataset DS205.0. National Center for Atmospheric Research, Boulder, COGoogle Scholar
- Jun M, Knutti R, Nychka DW (2008) Spatial analysis to quantify numerical model bias and dependence: how many climate models are there? Journal of the American Statistical Association 108(483):934–947. doi: 10.1198/016214507000001265 CrossRefGoogle Scholar
- Kaufmann RK, Stern DI (2004) A statistical evaluation of atmosphere–ocean general circulation models: complexity vs. simplicity. Rensselaer Polytechnic Institute Department of Economics Working Paper 0411, May 2004Google Scholar
- Kiehl JT (2007) Twentieth century climate model response and climate sensitivity. Geophys Res Lett 34:L22710. doi: 10.1029/2007GL031383 CrossRefGoogle Scholar
- Knutson TR, Delworth TL, Dixon KW, Held IM, Lu J, Ramaswamy V, Schwartzkopf MD, Stenchikov G, Stouffer RJ (2006) Assessment of twentieth-century regional surface temperature trends using the GFDL CM2 coupled models. J Clim. 19:1624–1651Google Scholar
- Knutti R (2008) Why are climate models reproducing the observed global surface warming so well? Geophys Res Lett 35:L18704. doi: 10.1029/2008GL034932 CrossRefGoogle Scholar
- Knutti R, Hegerl G (2008) The equilibrium sensitivity of the Earth’s temperature to radiation changes. Nat Geosci 1:735–743. doi: 10.1038/ngeo337 CrossRefGoogle Scholar
- Madigan D, York J (1995) Bayesian graphical models for discrete data. International Statistical Review 63:215–232CrossRefGoogle Scholar
- McKitrick RR (2010) Atmospheric oscillations do not explain the temperature-industrialization correlation. Stat Polit Policy 1(1)Google Scholar
- McKitrick R, Michaels PJ (2004) A Test of Corrections for Extraneous Signals in Gridded Surface Temperature Data. Climate Research 26:159–173CrossRefGoogle Scholar
- McKitrick RR, Michaels PJ (2007) Quantifying the influence of anthropogenic surface processes and inhomogeneities on gridded global climate data. J Geophys Res 112:D24S09. doi: 10.1029/2007JD008465 CrossRefGoogle Scholar
- McKitrick RR, Nierenberg N (2010) Socioeconomic patterns in climate data. J Econ Social Meas 35(3,4):149–175. doi: 10.3233/JEM-2010-0336 Google Scholar
- McKitrick RR, McIntyre S, Herman C (2010) Panel and Multivariate Methods for Tests of Trend Equivalence in Climate Data Sets. Atmospheric Science Letters. doi: 10.1002/asl.290 Google Scholar
- Mears CA, Schabel MC, Wentz FJ (2003) A reanalysis of the MSU channel 2 tropospheric temperature record. J Clim 16(22):3650–3664CrossRefGoogle Scholar
- Michaels PJ, Knappenberger PC, Balling RC Jr, Davis RE (2000) Observed warming in cold anticyclones. Climate Research 14:1–6CrossRefGoogle Scholar
- Mizon GE (1984) The encompassing approach in econometrics. In: Hendry DF, Wallis KF (eds) Econometrics and quantitative economics. Basil Blackwell, Oxford, pp 135–172Google Scholar
- Parry ML, Canziani OF, Palutikof JP, van der Linden PJ, Hanson CE (eds) (2007) Contribution of working group II to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge and New YorkGoogle Scholar
- Pisati M (2001) Tools for spatial data analysis. Stata Tech Bull STB-60, March 2001, pp 21–37Google Scholar
- Randall DA, Wood RA, Bony S, Colman R, Fichefet T, Fyfe J, Kattsov V, Pitman A, Shukla J, Srinivasan J, Stouffer RJ, Sumi A, Taylor KE (2007) Climate Models and Their Evaluation. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M Miller HL (eds) Climate change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New YorkGoogle Scholar
- Santer BD, Thorne PW, Haimberger L, Taylor KE, Wigley TML, Lanzante JR, Solomon S, Free M, Gleckler PJ, Jones PD (2008) Consistency of modelled and observed temperature trends in the tropical troposphere. Int J Climatol. doi: 10.1002/joc.1756 Google Scholar
- Schmidt G (2009) Spurious correlation between recent warming and indices of local economic activity. Int J Climatol. doi: 10.1002/joc.1831 Google Scholar
- Schwartz SE, Charlson RJ, Rodhe H (2007) Quantifying climate change—too rosy a picture? Nat Rep Clim Change 2:23–24CrossRefGoogle Scholar
- Shukla J, DelSole T, Fennessy M, Kinter J, Paolino D (2006) Climate model fidelity and projections of climate change. Geophy Res Lett 33:L07702, doi: 10.1029/2005GL025579
- Spencer RW, Christy JC (1990) Precise monitoring of global temperature trends from satellites. Science 247:1558–1562CrossRefGoogle Scholar