Earth System Dynamics Discussions www.earth-syst-dynam-discuss.net 2190-4995 1 1 2010 10.5194/esdd-1-247-2010 http://www.earth-syst-dynam-discuss.net/1/247/2010/ http://www.earth-syst-dynam-discuss.net/1/247/2010/esdd-1-247-2010.html http://www.earth-syst-dynam-discuss.net/1/247/2010/esdd-1-247-2010.pdf 247 296 2010-10-01 A multi-model ensemble method that combines imperfect models through learning L. A. van den Berge F. M. Selten selten@knmi.nl W. Wiegerinck G. S. Duane Royal Netherlands Meteorological Institute, Wilhelminalaan 10, 3732 GK, De Bilt, The Netherlands Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Geert Grooteplein 21, 6525 EZ, Nijmegen, The Netherlands Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309, USA In the current multi-model ensemble approach climate model simulations are combined a posteriori. In the method of this study the models in the ensemble exchange information during simulations and learn from historical observations to combine their strengths into a best representation of the observed climate. The method is developed and tested in the context of small chaotic dynamical systems, like the Lorenz 63 system. Imperfect models are created by perturbing the standard parameter values. Three imperfect models are combined into one super-model, through the introduction of connections between the model equations. The connection coefficients are learned from data from the unperturbed model, that is regarded as the truth. <br><br> The main result of this study is that after learning the super-model is a very good approximation to the truth, much better than each imperfect model separately. These illustrative examples suggest that the super-modeling approach is a promising strategy to improve climate simulations. Compo,~G., Whitaker,~J., and Sardeshmukh,~P.: Feasibility of a~100-year reanalysis using only surface pressure data, B Am. Meteor. Soc., 87, 175–189, 2006. Duane,~G. and Tribbia,~J.: Synchronized chaos in geophysical fluid dynamics, Phys. Rev. Lett., 86, 4298–4301, 2001. Duane,~G. and Tribbia,~J.: Weak Atlantic-Pacific teleconnections as synchronized chaos, J Atmos. Sci., 61, 2149–2168, 2004. Duane, G. S., Tribbia, J. J., and Weiss, J. B.: Synchronicity in predictive modelling: a new view of data assimilation, Nonlin. Processes Geophys., 13, 601–612, doi:10.5194/npg-13-601-2006, 2006. Duane,~G., Yu,~D., and Kocarev,~L.: Identical synchronization, with translation invariance, implies parameter estimation, Phys. Lett A, 371, 416–420, 2007. Duane,~G., Tribbia,~J., and Kirtman,~B.: Consensus on Long-Range Prediction by Adaptive Synchronization of Models, EGU General Assembly, Vienna, Austria, 2009. Fletcher,~R. and Reeves,~C.: Function minimization by conjugate gradients, Comp J., 6, 149–154, 1963. IPCC: Climate Change 2007: The Physical Science Basis, Contribution of Working Group~I to the Fourth Assessment Report of the Intergovernmental 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, UK and New York, USA, 2007. Kirtman,~B., Min,~D., Schopf,~P., and Schneider,~E.: A~new approach for CGCM sensitivity studies, COLA Technical Report, 154, 50~pp., 2003. Lorenz,~E.: Deterministic nonperiodic flow, J Atmos. Sci., 20, 130–140, 1963. Lorenz,~E.: Irregularity, a~fundamental property of the atmosphere, Tellus~A, 36, 98–110, 1984. Nelder,~J. and Mead,~R.: A~simplex method for function minimization, Comp J., 7, 308–313, 1965. Pecora,~L. and Carroll,~T.: Synchronization in chaotic systems, Phys. Rev. Lett., 64, 824–824, 1990. Rodwell,~M. and Jung,~T.: Understanding the local and global impacts of model physics changes: an aerosol example, Q J. Roy. Meteor. Soc., 134, 1479–1497, 2008. Rössler,~O.: An equation for continuous chaos, Phys. Lett., 75A, 397–398, 1976. Tebaldi,~C. and Knutti,~R.: The use of the multi-model ensemble in probabilistic climate projections, Philos T. Roy. Soc A, 365, 2053–2075, 2007. van Veen,~L.: Active and passive ocean regimes in a~low-order climate model, Tellus~A, 53, 616–628, 2001. Yang, S.-C., Baker, D., Li, H., Huff, M., Nagpal, G., Okereke, E., Villafane, J., Kalnay, E., and Duane, G.: Data assimilation as synchronization of truth and model: experiments with the 3-variable Lorenz system, J. Atmos. Sci., 63, 2340–2354, 2006