ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-10-9993-2010 Estimation of ECHAM5 climate model closure parameters with adaptive MCMC Järvinen H. 1 Räisänen P. 1 Laine M. 1 Tamminen J. 1 Ilin A. 2 Oja E. 2 Solonen A. 3 Haario H. 3 Finnish Meteorological Institute, Helsinki, Finland Aalto University School of Science and Technology, Espoo, Finland Lappeenranta University of Technology, Lappeenranta, Finland 25 10 2010 10 20 9993 10002 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/10/9993/2010/acp-10-9993-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/10/9993/2010/acp-10-9993-2010.pdf

Climate models contain closure parameters to which the model climate is sensitive. These parameters appear in physical parameterization schemes where some unresolved variables are expressed by predefined parameters rather than being explicitly modeled. Currently, best expert knowledge is used to define the optimal closure parameter values, based on observations, process studies, large eddy simulations, etc. Here, parameter estimation, based on the adaptive Markov chain Monte Carlo (MCMC) method, is applied for estimation of joint posterior probability density of a small number (<i>n</i>=4) of closure parameters appearing in the ECHAM5 climate model. The parameters considered are related to clouds and precipitation and they are sampled by an adaptive random walk process of the MCMC. The parameter probability densities are estimated simultaneously for all parameters, subject to an objective function. Five alternative formulations of the objective function are tested, all related to the net radiative flux at the top of the atmosphere. Conclusions of the closure parameter estimation tests with a low-resolution ECHAM5 climate model indicate that (i) adaptive MCMC is a viable option for parameter estimation in large-scale computational models, and (ii) choice of the objective function is crucial for the identifiability of the parameter distributions.

 References AMIP Project Office: AMIP II guidelines, AMIP Newsletter, 8, http://www-pcmdi.llnl.gov/projects/amip/NEWS/amipnl8.php, 1996. Andrieu, C. and Moulines, E.: On the ergodicity properties of some adaptive MCMC algorithms, Ann. Appl. Prob., 16, 1462–1505, doi:10.1214/105051606000000286, 2006 Annan, J D. and Hargreaves, J C.: Efficient estimation and ensemble generation in climate modeling, Phil. Trans. R. Soc. A, 365, 2077–2088, \doi10.1098/rsta.2007.2067, 2007. Dee, D P.: Bias and data assimilation, Q. J. R. Meteorol. Soc., 131, 3323–3343, \doi10.1256/qj.05.137, 2005. Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223–242, 2001. Haario, H., Laine, M., Lehtinen, M., Saksman, E., and Tamminen, J.: MCMC methods for high dimensional inversion in remote sensing (with discussion), J. Roy. Stat. Soc. B, 66, 591–607, 2004. Haario, H., Saksman, E., and Tamminen, J.: Componentwise adaptation for high dimensional MCMC, Comput. Stat., 20, 265–273, \doi10.1007/BF02789703, 2005. Haario, H., Laine, M., Mira, A., and Saksman, E.: DRAM: Efficient adaptive MCMC, Stat. Comput., 16, 339–354, \doi10.1007/s11222-006-9438-0, 2006. Ilin, A., Valpola, H., and Oja, E.: Exploratory Analysis of Climate Data Using Source Separation Methods, Neural Networks, 19, 155–167, 2006. Jackson, C S., Sen, M K., Huerta, G., Deng, Y., and Bowman, K P.: Error Reduction and Convergence in Climate Prediction, J. Climate, 21, 6698–6709, \doi10.1175/2008JCLI2112.1, 2008. Loeb, N G., Wielicki, B A., Doelling, D R., Smith, G L., Keyes, D F., Kato, S., Manalo-Smith, N., and Wong, T.: Toward optimal closure of the Earth's top-of-atmosphere radiation budget, J. Climate, 22, 748–766, 2009. Martin, G M., Johnson, D W., and Spice, A.: The measurement and parameterization of effective radius of droplets in warm stratocumulus, J. Atmos. Sci., 51, 1823–1842, 1994. Mellor, G L. and Yamada, A.: A hierarchy of turbulence closure models for planetary boundary layers, J. Atmos. Sci., 31, 1791–1806, 1974. Metropolis, N., Rosenbluth, A W., Rosenbluth, M N., Teller, A H., and Teller, E.: Equation of State Calculations by Fast Computing Machines, J. Chem. Phys., 21, 1087–1092, 1953. Navon, I M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dynam. Atmos. Ocean., 27, 55–79, 1993. Rinne, J. and Järvinen, H.: Estimation of the Cressman term for a barotropic model through optimization with use of the adjoint model, Mon. Weather Rev., 121, 825–833, 1993. Robert, C P. and Casella, G.: Monte Carlo Statistical Methods, Springer, New York, USA, second edn., 2005. Roeckner, E., Bäuml, G., Bonaventura, L., Brokopf, R., Esch, M., Giorgetta, M., Hagemann, S., Kirchner, I., Kornblueh, L., Manzini, E., Rhodin, A., Schlese, U., Schulzweida, U., and Tompkins, A.: The atmospheric general circulation model ECHAM5, Part I Model Description, Tech. Rep. No. 349, Max-Planck-Institut für Meteorologie, 2003. Roeckner, E., Brokopf, R., Esch, M., Giorgetta, M., Hagemann, S., Kornblueh, L., Manzini, E., Schlese, U., and Schulzweida, U.: Sensitivity of simulated climate to horizontal and vertical resolution in the ECHAM5 atmosphere model, J. Climate, 19, 3771–3791, 2006. Rossow, W. and Dueñas, E N.: The International Satellite Cloud Climatology Project (ISCCP) web site: An online resource for research., Bull. Am. Meteorol. Soc., 85, 167–172, 2004. Rossow, W B., Walker, A., and Roiter, M.: International Satellite Cloud Climatology Project (ISCCP) documentation of new cloud datasets, Tech.\ Rep. WMO/TD-737 349, World Meteorological Organization, 1996. Tuomi, M., Thum, T., Järvinen, H., Fronzek, S., Berg, B., Harmon, M., Trofymow, J A., Sevanto, S., and Liski, J.: Leaf litter decomposition – Estimates of global variability based on Yasso07 model, Ecological Modelling, 220, 3362–3371, \doi10.1016/j.ecolmodel.2009.05.016, 2009. Uppala, S M., KÃ¥llberg, P W., Simmons, A J., Andrae, U., Bechtold, V D C., Fiorino, M., Gibson, J K., Haseler, J., Hernandez, A., Kelly, G A., Li, X., Onogi, K., Saarinen, S., Sokka, N., Allan, R P., Andersson, E., Arpe, K., Balmaseda, M A., Beljaars, A C M., Berg, L V D., Bidlot, J., Bormann, N., Caires, S., Chevallier, F., Dethof, A., Dragosavac, M., Fisher, M., Fuentes, M., Hagemann, S., Hólm, E., Hoskins, B J., Isaksen, L., Janssen, P A E M., Jenne, R., McNally, A P., Mahfouf, J., Morcrette, J., Rayner, N A., Saunders, R W., Simon, P., Sterl, A., Trenberth, K E., Untch, A., Vasiljevic, D., Viterbo, P., and Woollen, J.: The ERA-40 re-analysis, Q. J. Roy. Meteorol. Soc., 131, 2961–3012, \doi10.1256/qj.04.176, 2005. Villagran, A., Huerta, G., Jackson, C S., and Sen, M K.: Computational Methods for Parameter Estimation in Climate Models, Bay. Anal., 3, 1–27, 2008. Xie, P. and Arkin, P.: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs, Bull. Am. Meteorol. Soc., 78, 2539–2558, 1997.