ACS  Vol.2 No.4 , October 2012
Bayesian Learning of Climate Sensitivity I: Synthetic Observations
ABSTRACT
The instrumental temperature records are affected by both external climate forcings—in particular, the increase of long-lived greenhouse gas emissions—and natural, internal variability. Estimates of the value of equilibrium climate sensitivity—the change in global-mean equilibrium near-surface temperature due to a doubling of the pre-industrial CO2 concentration—and other climate parameters using these observational records are affected by the presence of the internal variability. A different realization of the natural variability will result in different estimates of the values of these climate parameters. In this study we apply Bayesian estimation to simulated temperature and ocean heat-uptake records generated by our Climate Research Group’s Simple Climate Model for known values of equilibrium climate sensitivity, T2x direct sulfate aerosol forcing in reference year 2000, FASA, and oceanic heat diffusivity, ΔT2x. We choose the simulated records for one choice of values of the climate parameters to serve as the synthetic observations. To each of the simulated temperature records we add a number of draws of the quasi-periodic oscillations and stochastic noise, determined from the observed temperature record. For cases considering only values of ΔT2x and/or κ, the Bayesian estimation converges to the value(s) of ΔT2x and/or κ used to generate the synthetic observations. However, for cases studying FASA, the Bayesian analysis does not converge to the “true” value used to generate the synthetic observations. We show that this is a problem of low signal-to-noise ratio: by substituting an artificial, continuously increasing sulfate record, we greatly improve the value obtained through Bayesian estimation. Our results indicate Bayesian learning techniques will be useful tools in constraining the values of ΔT2x and κ but not FASA In our Group’s future work we will extend the methods used here to the observed, instrumental records of global-mean temperature increase and ocean heat uptake.

Cite this paper
M. J. Ring and M. E. Schlesinger, "Bayesian Learning of Climate Sensitivity I: Synthetic Observations," Atmospheric and Climate Sciences, Vol. 2 No. 4, 2012, pp. 464-473. doi: 10.4236/acs.2012.24040.
References
[1]   M. J. Ring, D. Lindner, E. F. Cross and M. E. Schlesinger, “Causes of the Global Warming Observed Since the 19th Century,” Atmospheric and Climate Sciences, 2012, in Press.

[2]   M. E. Schlesinger, N. G. Andronova, B. Entwistle, A. Ghanem, N. Ramankutty, W. Wang and F. Yang, “Modeling and Simulation of Climate and Climate Change,” In: G. Cini Castagnoli and A. Provenzale, Eds., Past and Present Variability of the Solar-Terrestrial System: Measurement, Data Analysis and Theoretical Models. Proceedings of the International School of Physics “Enrico Fermi” CXXXIII, IOS Press, Amsterdam, 1997, pp. 389-429.

[3]   C. P. Morice, J. J. Kennedy, N. A. Rayner and P. D. Jones, “Quantifying Uncertainties in Global and Regional Temperature Change Using an Ensemble of Observational Estimates: The HadCRUT4 Dataset,” Journal of Geophysical Research, Vol. 117, 2012, Article ID: D08101. doi:10.1029/2011JD017187

[4]   J. Hansen, R. Ruedy, M. Sato and K. Lo, “Global Surface Temperature Change,” Reviews of Geophysics, Vol. 48, 2010, Article ID: RG4004. doi:10.1029/2010RG000345.

[5]   T. M. Smith, R. W. Reynolds, T. C. Peterson and J. H. Lawrimore, “Improvements to NOAA’s Historical Merged Land-Ocean Surface Temperature Analysis,” Journal of Climate, Vol. 21, No. 10, 2008, pp. 2283-2296. doi:10.1175/2007JCLI2100.1.

[6]   K. Ishihara, “Calculation of Global Surface Temperature Anomalies with COBE-SST (Japanese),” Weather Service Bulletin, Vol. 73, 2006, pp. S19-S25.

[7]   K. Ishihara, “Estimation of Standard Errors in Global Average Surface Temperature (Japanese),” Weather Service Bulletin, Vol. 74, 2007, pp. 19-26.

[8]   S. Levitus, J. I. Antonov, T. P. Boyer, R. A. Locarnini, H. E. Garcia and A. V. Mishonov, “Global Ocean Heat Content 1955-2008 in Light of Recently Revealed Instrumentation Problems,” Geophysical Resarch Letters, Vol. 36, 2009, Article ID: L07608. doi:10.1029/2008GL037155.

[9]   D. Lindner, “Characterization of the Modes of Interannual-to-Centennial Variability in Observed Near-Surface Temperatures,” Master Thesis, University of Illinois at Urbana-Champaign, Urbana, 2010.

[10]   N. G. Andronova and M. E. Schlesinger, “Objective Estimation of the Probability Density Function for Climate Sensitivity,” Journal of Geophysical Research, Vol. 106, No. D19, 2001, pp. 22605-22611. doi:10.1029/2000JD000259.

[11]   A. R. Solow, “Bootstrapping Correlated Data,” Mathematical Geology, Vol. 17, No. 7, 1985, pp. 769-775. doi:10.1007/BF01031616.

[12]   A. Neumeier and T. Schneider, “Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models,” ACM Transactions on Mathematical Software, Vol. 27, 2001, pp. 27-57.

[13]   T. Schneider and A. Neumeier, “Algorithm 808: ARFit— A MATLAB Package for the Estimation of Parameters and Eigenmodes of Multivariate Autogressive Models,” ACM Transactions on Mathematical Software, Vol. 27, 2001, pp. 58-65.

[14]   E. S. Epstein, “Statistical Inference and Prediction in Climatology: A Bayesian Approach,” American Meteorological Society, 1985.

[15]   P.-S. Chu and X. Zhao, “Bayesian Analysis for Extreme Climatic Events: A Review,” Atmospheric Research, Vol. 102, No. 3, 2011, pp. 243-262. doi:10.1016/j.atmosres.2011.07.001.

[16]   C. E. Forest, P. H. Stone, A. P. Sokolov, M. R. Allen and M. D. Webster, “Quantifying Uncertainties in Climate System Properties with the Use of Recent Climate Observations,” Science, Vol. 295, No. 5552, 2002, pp. 113-117. doi:10.1126/science.1064419.

[17]   C. E. Forest, P. H. Stone and A. P. Sokolov, “Estimated PDFs of Climate System Properties Including Natural and Anthropogenic Forcings,” Geophysical Research Letters, Vol. 33, 2006, Article ID: L01705. doi:10.1029/2005GL023977.

[18]   L. Tomassini, P. Reichert, R. Knutti, T. F. Stocker and M. E. Borsuk, “Robust Bayesian Uncertainty Analysis of Climate System Properties Using Markov Chain Monte Carlo Methods,” Journal of Climate, Vol. 20, No. 7, 2007, pp. 1239-1254. doi:10.1175/JCLI4064.1.

[19]   C. E. Forest, P. H. Stone and A. P. Sokolov, “Constraining Climate Model Parameters from Observed 20th Century Changes,” Tellus A, Vol. 60, No. 5, 2008, pp. 911-920. doi:10.1111/j.1600-0870.2008.00346.x.

[20]   J. D. Annan and J. C. Hargraves, “On the Generation and Interpretation of Probabilistic Estimates of Climate Sensitivity,” Climatic Change, Vol. 104, No. 3-4, 2011, pp. 423-436. doi:10.1007/s10584-009-9715-y.

[21]   S. S. Leroy, “Detecting Climate Signals: Some Bayesian Aspects,” Journal of Climate, Vol. 11, No. 4, 1998, pp. 640-651. doi:10.1175/1520-0442(1998)011<0640:DCSSBA>2.0.CO;2.

[22]   T. C. K. Lee, F. W. Zwiers, G. C. Hegerl, X. Zhang and M. Tsao, “A Bayesian Climate Change Detection and Attribution Assessment,” Journal of Climate, Vol. 18, No. 13, 2006, pp. 2429-2440. doi:10.1175/JCLI3402.1.

[23]   S. S. Leroy and J. G. Anderson, “Optimal Detection of Regional Trends Using Global Data,” Journal of Climate, Vol. 23, No. 16, 2010, pp. 4438-4446. doi:10.1175/2010JCLI3550.1.

[24]   L. Tomassini, R. Knutti, G.-K. Plattner, D. P. van Vuuren, T. F. Stocker, R. B. Howarth and M. E. Borsuk, “Uncertainty and Risk in Climate Projections for the 21st Century: Comparing Mitigation to Non-Intervention Scenarios,” Climatic Change, Vol. 103, No. 3-4, 2010, pp. 399-422. doi:10.1007/s10584-009-9763-3.

[25]   S.-K. Min and A. Hense, “A Bayesian Assessment of Climate Change Using Multi-Model Ensembles. Part I: Global Mean Surface Temperature,” Journal of Climate, Vol. 19, No. 13, 2006, pp. 3237-3256. doi:10.1175/JCLI3784.1.

[26]   S.-K. Min, D. Simonis and A. Hense, “Probabilistic Climate Change Predictions Applying Bayesian Model Averaging,” Philosophical Transactions of the Royal Society A, Vol. 365, No. 1857, 2007, pp. 2103-2116. doi:10.1098/rsta.2007.2070.

[27]   R. L. Smith, C. Tebaldi, D. Nychka and L. O. Mearns, “Bayesian Modeling of Uncertainty in Ensembles of Climate Models,” Journal of the American Statistical Association, Vol. 104, No. 485, 2009, pp. 97-116. doi:10.1198/jasa.2009.0007.

[28]   R. Furrer, R. Knutti, S. R. Sain, D. W. Nychka and G. A. Meehl, “Spatial Patterns of Probabilistic Temperature Change Projections from a Multivariate Bayesian Analysis,” Geophysical Research Letters, Vol. 34, 2006, Article ID: L06711. doi:10.1029/2006GL027754.

[29]   R. Furrer, S. R. Sain, D. Nychka and G. A. Meehl, “Multivariate Bayesian Analysis of Atmosphere-Ocean General Circulation Models,” Environmental and Ecological Statistics, Vol. 14, No. 3, 2007, pp. 249-266. doi:10.1007/s10651-007-0018-z.

[30]   C. Tebaldi and B. Sanso, “Joint Projections of Temperature and Precipitation Change from Multiple Climate Models: A Hierarchical Bayesian Approach,” Journal of the Royal Statistical Society A, Vol. 172, No. 1, 2009, pp. 83-106. doi:10.1111/j.1467-985X.2008.00545.x.

[31]   F. Beltran, B. Sanso, R. Lemos and R. Mendelssohn, “Joint Projections of North Pacific Sea Surface Temperature from Different Global Climate Models,” University of California, Santa Cruz, 2011.

[32]   C. Tebaldi, L. O. Mearns, D. Nychka and R. W. Smith, “Regional Probabilities of Precipitation Change: A Bayesian Analysis of Multimodel Simulations,” Geophysical Research Letters, Vol. 31, 2004, Article ID: L24213.

[33]   C. Tebaldi, R. W. Smith, D. Nychka and L. O. Mearns, “Quantifying Uncertainty in Projections of Regional Climate Change: A Bayesian Approach to the Analysis of Multimodel Ensembles,” Journal of Climate, Vol. 18, No. 10, 2005, pp. 1524-1540. doi:10.1175/JCLI3363.1.

[34]   S.-K. Min and A. Hense, “A Bayesian Assessment of Climate Change Using Multi-Model Ensembles. Part II: Regional and Seasonal Mean Surface Temepratures,” Journal of Climate, Vol. 20, No. 12, 2007, pp. 2769-2790. doi:10.1175/JCLI4178.1.

[35]   J. B. Elsner and B. H. Bossak, “Bayesian Analysis of US Hurricane Climate,” Journal of Climate, Vol. 14, No. 23, 2001, pp. 4341-4350. doi:10.1175/1520-0442(2001)014<4341:BAOUSH>2.0.CO;2.

[36]   P.-S. Chu and X. Zhao, “Bayesian Change-Point Analysis of Tropical Cyclone Activity: The Central North Pacific case,” Journal of Climate, Vol. 17, No. 24, 2004, pp. 4893-4901. doi: 10.1175/JCLI-3248.1.

[37]   J. B. Elsner and T. H. Jagger, “Prediction Models for Annual US Hurricane Counts,” Journal of Climate, Vol. 19, No. 12, 2006, pp. 2935-2952. doi:10.1175/JCLI3729.1.

[38]   X. Zhao and P.-S. Chu, “Bayesian Multiple Changepoint Analysis of Hurricane Activity in the Eastern North Pacific: A Markov Chain Monte Carlo Approach,” Journal of Climate, Vol. 19, No. 4, 2006, pp. 564-578. doi:10.1175/JCLI3628.1.

[39]   S. J. Camargo, A. W. Robertson, S. J. Gaffney, P. Smyth and M. Ghil, “Cluster Analysis of Typhoon Tracks. Part I: General Properties,” Journal of Climate, Vol. 20, No. 14, 2007, pp. 3635-3653. doi:10.1175/JCLI4188.1.

[40]   P.-S. Chu and X. Zhao, “A Bayesian Regression Approach for Predicting Seasonal Tropical Cyclone Activity over the Central North Pacific,” Journal of Climate, Vol. 20, No. 15, 2007, pp. 4002-4013. doi:10.1175/JCLI4214.1.

[41]   C.-H. Ho, H. S. Kim, P.-S. Chu and J.-H. Kim, “Seasonal Prediction of Tropical Cyclone Frequency over the East China Sea through a Bayesian Poisson-Regression Method,” Asia-Pacific Journal of Atmospheric Sciences, Vol. 45, No. 1, 2009, pp. 45-54.

[42]   J.-Y. Tu, C. Chou and P.-S. Chu, “The Abrupt Shift of Typhoon Activity in the Vicinity of Taiwan and Its Association with Western North Pacific-East Asian Climate Change,” Journal of Climate, Vol. 22, No. 13, 2009, pp. 3617-3628. doi:10.1175/2009JCLI2411.1.

[43]   S. S. Chand, K. J. E. Walsh and J. C. L. Chan, “A Bayesian Regression Approach to Seasonal Prediction of Tropical Cyclones Affecting the Fiji Region,” Journal of Climate, Vol. 23, No. 13, 2010, pp. 3425-3445. doi:10.1175/2010JCLI3521.1.

[44]   P.-S. Chu, X. Zhao, C.-H. Ho, H.-S. Kim, M.-M. Lu and J.-H. Kim, “Bayesian Forecasting of Seasonal Typhoon Activity: A Track Pattern-Oriented Categorization Approach,” Journal of Climate, Vol. 23, No. 24, 2010, pp. 6654-6668. doi:10.1175/2010JCLI3710.1.

[45]   T. H. Jagger and J. B. Elsner, “A Consensus Model for Seasonal Hurricane Prediction,” Journal of Climate, Vol. 23, No. 22, 2009, pp. 6090-6099. doi:10.1175/2010JCLI3686.1.

[46]   M.-M. Lu, P.-S. Chu and Y.-C. Lin, “Seasonal Prediction of Tropical Cyclone Activity in the Vicinty of Taiwan Using the Bayesian Multivariate Regression Method,” Weather and Forecasting, Vol. 25, No. 6, 2010, pp. 1780-1795. doi:10.1175/2010WAF2222408.1.

[47]   M. Kallache, E. Maksimovich, P.-A. Michelangeli and P. Naveau, “Multi-Model Combination by a Bayesian Hierarchical Model: Assessment of Ice Accumulation over the Oceanic Arctic Region,” Journal of Climate, Vol. 23, No. 20, 2010, pp. 5421-5436. doi:10.1175/2010JCLI3107.1.

[48]   B. F. Hobbs, “Bayesian Methods for Analysing Climate Change and Water Resource Uncertainties,” Journal of Environmental Management, Vol. 49, No. 1, 1997, pp. 53-72. doi:10.1006/jema.1996.0116,

[49]   L. Perreault, J. Bernier, B. Bobee and E. Parent, “Bayesian Change-Point Analysis in Hydrometeorological Time Series. Part 1: The Normal Model Revisited,” Journal of Hydrology, Vol. 235, No. 3-4, 2000, pp. 221-241. doi:10.1016/S0022-1694(00)00270-5.

[50]   L. Perreault, J. Bernier, B. Bobee and E. Parent, “Bayesian Change-Point Analysis in Hydrometeorological Time Series. Part 2: Comparison of Change-Point Models and Forecasting,” Journal of Hydrology, Vol. 235, No. 3-4, 2000, pp. 242-263. doi:10.1016/S0022-1694(00)00271-7.

[51]   B. Renard, M. Land and P. Bois, “Statistical Analysis of Extreme Events in A Non-Stationary Context via a Bayesian Framework: Case Study with Peak-over-Threshold Data,” Stochastic Environmental Research and Risk Assessment, Vol. 21, No. 2, 2006, pp. 97-112. doi:10.1007/s00477-006-0047-4.

[52]   C. H. R. Lima and U. Lall, “Spatial Scaling in a Changing Climate: A Hierarchical Bayesian Model for Non-Stationary Multi-Site Annual Maximum and Monthly Streamflow,” Journal of Hydrology, Vol. 383, No. 3-4, 2010, pp. 307-318. doi:10.1016/j.jhydrol.2009.12.045.

[53]   D. Peavoy and C. Franzke, “Bayesian Analysis of Rapid Climate Change during the Last Glacial Using Greenland Delta O-18 Data,” Climate of the Past, Vol. 6, No. 6, pp. 787-794. doi:10.5194/cp-6-787-2010.

[54]   K. Riahi, et al., “RCP8.5—A Scenario of Comparatively High Greenhouse Emissions,” Climatic Change, Vol. 109, No. 1-2, 2011, pp. 33-57. doi:10.1007/s10584-011-0149-y.

[55]   M. Ghil, M. R. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. W. Robertson, A. Saunders, Y. Tian, F. Varadi and P. Yiou, “Advanced Spectral Methods for Climatic Time Series,” Reviews of Geophysics, Vol. 40, No. 1, 2002, Article ID: 1003. doi:10.1029/2000RG000092.

[56]   S. J. Smith, J. van Aardenne, Z. Klimont, R. Andres, A. C. Volke and S. Delgado Arias, “Anthropogenic Sulfur Dioxide Emissions 1850-2005,” Atmospheric Chemistry and Physics, Vol. 11, 2011, pp. 1101-1116. doi:10.5194/acp-11-1101-2011.

[57]   D. P. van Vurren, et al., “RCP2.6: Exploring the Possibility to Keep Global Mean Temperature Increase below 2℃,” Climatic Change, Vol. 109, No. 1-2, 2011, pp. 95-116. doi:10.1007/s10584-011-0152-3.

[58]   A. M. Thomson, et al., “RCP4.5: A Pathway for Stabilization of Radiative Forcing by 2100,” Climatic Change, Vol. 109, No. 1-2, 2011, pp. 77-94. doi:10.1007/s10584-011-0151-4.

[59]   T. Masui, et al., “An Emission Pathway for Stabilization at 6 Wm-2 Radiative Forcing,” Climatic Change, Vol. 109, No. 1-2, 2011, pp. 59-76. doi:10.1007/s10584-011-0150-5.

 
 
Top