Atmospheric Chemistry and Physics www.atmos-chem-phys.net 1680-7316 1680-7324 9 3 2009 10.5194/acp-9-813-2009 http://www.atmos-chem-phys.net/9/813/2009/ http://www.atmos-chem-phys.net/9/813/2009/acp-9-813-2009.html http://www.atmos-chem-phys.net/9/813/2009/acp-9-813-2009.pdf 813 822 2009-02-02 On the diagnosis of climate sensitivity using observations of fluctuations D. B. Kirk-Davidoff dankd@atmos.umd.edu Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD 20742, USA It has been shown that lag-covariance based statistical measures, suggested by the Fluctuation Dissipation Theorem (FDT), may allow estimation of climate sensitivity in a climate model. Recently Schwartz (2007) has used measures of the decay of autocorrelation in a global surface temperature time series to estimate the real world climate sensitivity. Here we use a simple climate model, and analysis of archived coupled climate model output from the IPCC AR4 runs, for which the climate sensitivity is known, to test the utility of this approach. Our analysis of these archived model output data show that estimates of climate sensitivity derived from century-long time scales typically grossly underestimate the models' true climate sensitivity. We analyze the behavior of the simple model with adjustable heat capacity in two surface layers, subject to various stochastic forcings and for various climate sensitivities, modulated by albedo and water vapor feedbacks. We use our simple climate model to demonstrate: 1. that a much longer time series would be required to accurately diagnose the earth's climate sensitivity than is presently available 2. that for shorter time series there is a systematic bias towards underpredicting climate sensitivity, 3. that the addition of a second heat reservoir weakly coupled to the first greatly reduces the decorrelation timescale of short temperature time series produced by the model, aggravating the tendency to underestimate climate sensitivity, and 4. that because of this it is possible to have a selection of models in which the climate sensitivity is inversely related to the decorrelation time scale, as is true for the IPCC models. Abramov, R. and A. Majda: Blended response algorithms for linear ﬂuctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 20, 2793–2821, 2007. Bell, T. L.: Climate sensitivity from fluctuation dissipation: some simple model tests, J. Atmos. Sci., 37, 1700–1707, 1980. Callen, H. B. and Greene, R. F.: On a theorem of irreversible thermodynamics, Phys. Rev., 86, 702–710, 1952. Cionni, I., Visconti, G., and Sassi, F.: Fluctuation dissipation theorem in a general circulation model, Geophys. Res. Lett., 31, L09206, doi:10.1029/2004GL019739, 2004. Dymnikov, V. and Gritsun, A.: Current problems in the mathematical theory of climate, Izv. Acad. Sci. USSR, Atmos. Oceanic Phys., 41, 294–314, 2005. Forest, C. E., Stone, P. H., and Sokolov, A. P.: Estimated PDFs of climate system properties including natural and anthropogenic forcings, Geophys. Res. Lett., 33, L01705, doi:10.1029/2005GL023977, 2006. Foster G., Annan J. D., Schmidt G. A. and Mann, M. E.: Comment on "Heat Capacity, Time Constant, and Sensitivity of Earth Climate System" by S Schwartz, J. Geophys. Res., 113, D15102, doi:10.1029/2007/JD009373, 2008. Goody, R. M., Anderson, J. G., North, G. R.: Testing climate models: an approach, Bull. Am. Met. Soc., 79, 2541–2549, 1998. Gritsun, A.: Interactive comment on "On the diagnosis of climate sensitivity using observations of fluctuations" by D. Kirk-Davidoff, Atmos. Chem. Phys. Discuss., 8, S5939-S5944, 2008. Gritsun, A. and Branstator, G.: Climate response using a three-dimensional operator based on the ﬂuctuation-dissipation theorem, J. Atmos. Sci., 64, 2558–2575, 2007. Gritsun, A., Branstator, G., and Dymnikov, V.: Construction of the linear response operator of an atmospheric general circulation model to small external forcing, Num. Anal. Math. Modeling, 17, 399–416, 2002. Gritsun, A. and Dymnikov, V.: Barotropic atmosphere response to small external actions, theory and numerical experiments, Atmos. Ocean Phys., 35(5), 511–525, 1999. Hansen, J., Ruedy, R., Sato, M., and Reynolds, R.: Global surface air temperature in 1995: Return to pre-Pinatubo level, Geophys. Res. Lett., 23, 1665–1668, 1996, updated at: http://data.giss.nasa.gov/gistemp/. Knutti, R., Krähenmann, S., Frame, D. J., and Allen, M. R.: Comment on "Heat capacity, time constant and sensitivity of Earth�'s climate system" by S. E. Schwartz, J. Geophys. Res., 113, D15103, doi:10.1029/2007JD009473, 2008. Langen, P. L. and Alexeev, V. A.: Estimating 2×CO2 warming in an aquaplanet GCM using the fluctuation-dissipation theorem, Geophys. Res. Lett., 32, L23708, doi:10.1029/2005GL024136, 2005. Leith, C. E.: Climate response and fluctuation dissipation, J. Atmos. Sci., 32, 2022–2026, 1975. Levitus, S., Antonov, J., and Boyer, T.: Warming of the world ocean, 1955–2003, Geophys. Res. Lett., 32, L02604, doi:02610.01029/02004GL021592, 2005. Majda, A., Abramov, R., and Grote, M.: Information Theory and Stochastics for Multiscale Nonlinear Systems, CRM Monograph Series of Centre de Recherches Mathematiques, Universite de Montreal, Vol 25, American Mathematical Society, ISBN: 0-8218-3843-1, 2005. North, G. R., Bell, R. E., and Hardin, J. W.: Fluctuation dissipation in a general circulation model, Clim. Dynam., 8, 259–264, 1993. Penland, C. and Sardeshmukh, P. D.: The optimal growth of tropical sea surface temperature anomalies, J. Climate, 8, 1999–2024, 1995. Scafetta, N.: Comment on "Heat capacity, time constant, and sensitivity of Earth's climate system" by S Schwartz, J. Geophys. Res.,113, D15104, doi:10.1029/2007JD009586, 2008. Schwartz, S. E.: Heat capacity, time constant, and sensitivity of Earth's climate system, J. Geophys. Res., 112, D24S05, doi:10.1029/2007JD008746, 2007. Schwartz, S. E.: Response to Comments on "Heat capacity, time constant, and sensitivity of Earth's climate system", J. Geophys. Res., 113, D15105, doi:10.1029/2007JD009872, 2008. von Storch, J. S.: On statistical dissipation in GCM-climate, Clim. Dynam., 23, 1–15, 2004.