On closure parameter estimation in chaotic systems

Nonlinear Processes in Geophysics

Volumn 19, Issue 1, 2012, Pages 127-143

  Hakkarainen, J ^a,b   Ilin, A ^c   Solonen, A ^a,b   Laine, M ^a   Haario, H ^b   Tamminen, J ^a   Oja, E ^c   Jarvinen H ^a  

^a FINNISH METEOROLOGICAL INSTITUTE   (Finland)

^b LAPPEENRANTA UNIVERSITY OF TECHNOLOGY   (Finland)

^c AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; CLIMATE MODELING; NUMERICAL MODEL; PARAMETERIZATION; WEATHER FORECASTING;

EID: 84882582986     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-19-127-2012     Document Type: Article

References (44)

1. Annan, J. and Hargreaves, J.: Efficient estimation and ensemble generation in climate modelling, Phil. Trans. R. Soc. A, 365, 2077-2088, doi:10.1098/rsta.2007.2067, 2007.
2. Annan, J. D., Lunt, D. J., Hargreaves, J. C., and Valdes, P. J.: Parameter estimation in an atmospheric GCM using the Ensemble Kalman Filter, Nonlin. Processes Geophys., 12, 363-371, doi:10.5194/npg-12-363-2005, 2005. (Pubitemid 40518138)
3. Auvinen, H., Bardsley, J. M., Haario, H., and Kauranne, T.: Large-Scale Kalman Filtering Using the Limited Memory BFGS Method, Electron. T. Numer. Ana., 35, 217-233, 2009.
4. Auvinen, H., Bardsley, J., Haario, H., and Kauranne, T.: The variational Kalman filter and an efficient implementation using limited memory BFGS, Int. J. Numer. Meth. Fl., 64, 314-335, 2010.
5. Bishop, C. M.: Pattern Recognition and Machine Learning, Information Science and Statistics, Springer, New York, 2nd Edn., 2006.
6. Bonavita, M., Torrisi, L., and Marcucci, F.: The ensemble Kalman filter in an operational regional NWP system: preliminary results with real observations, Q. J. Roy. Meteor. Soc., 134, 1733-1744, doi:10.1002/qj.313, 2008.
7. Cappe, O., Godsill, S., and Moulines, E.: An overview of existing methods and recent advances in sequential Monte Carlo, Proceedings of IEEE, 95, 899-924, doi:10.1109/JPROC.2007.893250, 2007.
8. Cornuet, J.-M., Santos, F., Beaumont, M. A., Robert, C. P., Marin, J.-M., Balding, D. J., Guillemaud, T., and Estoup, A.: Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation, Bioinformatics, 24, 2713-2719, 2008. (Pubitemid 352722613)
9. DelSole, T. and Yang, X.: State and Parameter Estimation in Stochastic Dynamical Models, Physica D, 239, 1781-1788, 2010.
10. Dowd, M.: Estimating parameters for a stochastic dynamic marine ecological system, Environmetrics, 22, 501-515, doi:10.1002/env.1083, 2011.
11. Evensen, G.: Data assimilation: The ensemble Kalman filter, Springer, 2007.
12. Gauthier, P., Tanguay, M., Laroche, S., Pellerin, S., and Morneau, J.: Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada, Mon. Weather Rev., 135, 2339-2354, 2007. (Pubitemid 47050426)
13. Gelman, A., Carlin, J., Stern, H., and Rubin, D.: Bayesian Data Analysis, Chapman & Hall, 2nd Edn., 2003.
14. Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223-242, 2001. (Pubitemid 33793059)
15. Haario, H., Laine, M., Mira, A., and Saksman, E.: DRAM: Efficient adaptive MCMC, Stat. Comput., 16, 339-354, doi:10.1007/s11222-006-9438-0, 2006. (Pubitemid 44581755)
16. Houtekamer, P., Herschel, L., Mitchell, G., Buehner, M., Charron, M., Spacek, L., and Hansen, B.: Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations, Mon. Weather Rev., 133, 604-620, 2005.
17. Hunt, B. R., Kostelich, E. J., and Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230, 112-126, 2007. (Pubitemid 46776911)
18. Ionides, E., Breto, C., and King, A.: Inference for nonlinear dynamical systems, Proc. Nat. Aca. Sci., 103, 18438-18443, 2006. (Pubitemid 44913429)
19. 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, doi:10.1175/2008JCLI2112.1, 2008.
20. J̈arvinen, H., R̈ais̈anen, P., Laine, M., Tamminen, J., Ilin, A., Oja, E., Solonen, A., and Haario, H.: Estimation of ECHAM5 climate model closure parameters with adaptive MCMC, Atmos. Chem. Phys., 10, 9993-10002, doi:10.5194/acp-10-9993-2010, 2010.
21. J̈arvinen, H., Laine, M., Solonen, A., and Haario, H.: Ensemble prediction and parameter estimation system: the concept, Q. J. Roy. Meteor. Soc., doi:10.1002/qj.923, published online, 2011.
22. Kalman, R.: A New Approach to Linear Filtering and Prediction Problems, Transactions of the ASME-Journal of Basic Engineering, Series D, 82, 35-42, 1960.
23. Kitagawa, G.: A self-organizing state space model, J. Am. Stat. Assoc., 93, 1203-1215, 1998.
24. Kivman, G. A.: Sequential parameter estimation for stochastic systems, Nonlin. Processes Geophys., 10, 253-259, doi:10.5194/npg-10-253-2003, 2003. (Pubitemid 36755755)
25. Laine, M., Solonen, A., Haario, H., and J̈arvinen, H.: Ensemble prediction and parameter estimation system: the method, Q. J. Roy. Meteor. Soc., published online, doi:10.1002/qj.922, 2011.
26. Leutbecher, M.: Predictability and Ensemble Forecasting with Lorenz-95 systems, Lecture notes, ECMWF meteorological training course on Predictability, diagnostics and seasonal forecasting, available at: http://www.ecmwf.int/ newsevents/training/meteorological presentations/pdf/PR/Practice L95.pdf, 2010.
27. Lorenz, E.: Predictability: A problem partly solved, Proceedings of the Seminar on Predicability, European Center on Medium Range Weather Forecasting, 1, 1-18, 1995.
28. Marjoram, P. and Tavaŕe, S.: Modern computational approaches for analysing molecular genetic variation data, Nat. Rev. Genet., 7, 759-770, 2006. (Pubitemid 44413220)
29. 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.
30. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E.: Equations of State Calculations by Fast Computing Machines, J. Chem. Phys., 21, 1087-1092, 1953.
31. Molteni, F., Buizza, R., Palmer, T., and Petroliagis, T.: The ECMWF Ensemble Prediction System: Methodology and validation, Q. J. Roy. Meteor. Soc., 122, 73-119, 1996.
32. Nocedal, G. and Wright, S.: Numerical Optimization, Springer, Berlin, 1999.
33. Ott, E., Hunt, B., Szunyogh, I., Zimin, A., Kostelich, E., Corazza, M., Kalnay, E., Pati, D., and Yorke, J.: A local ensemble Kalman filter for atmospheric data assimilation, Tellus A, 56, 415-428, 2004. (Pubitemid 39533058)
34. Palmer, T., Shutts, G., Hagedorn, R., Doblas-Reyes, F., Jung, T., and Leutbecher, M.: Representing Model Uncertainty inWeather and Climate Prediction, Ann. Rev. Earth Planet. Sci., 33, 163-193, 2005. (Pubitemid 40849782)
35. Rabier, F., J̈arvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.: The ECMWF implementation of four dimensional variational assimilation, Part I: Experimental results with simplified physics, Q. J. Roy. Meteor. Soc., 126, 1143-1170, 2000. (Pubitemid 30309377)
36. Rougier, J. C.: Efficient Emulators for Multivariate Deterministic Functions, J. Comput. Graphic. Stat., 17, 827-843, 2008.
37. Sexton, D., Murphy, J., Collins, M., and Webb, M.: Multivariate Prediction Using Imperfect Climate Models Part I: Outline of Methodology, Clim. Dynam., 1-30, doi:10.1007/s00382-011-1208-9, 2011.
38. Shapiro, A., Dentcheva, D., and Ruszczynski, A.: Lectures on Stochastic Programming: Modeling and Theory, MOS-SIAM Series on Optimization 9, Soc. Ind. Appl. Math., 2009.
39. Singer, H.: Parameter estimation of nonlinear stochastic differential equations: Simulated maximum likelihood versus extended Kalman filter and Ito-Taylor expansion, J. Comput. Graph. Stat., 11, 972-995, 2002. (Pubitemid 36047116)
40. Tippett, M., Anderson, J., Bishop, G., Hamill, T., and Whitaker, J.: Ensemble Square Root Filters, Mon. Weather Rev., 131, 1485-1490, doi:10.1175/1520-0493(2003)1312.0.CO;2, 2003. (Pubitemid 36953823)
41. Villagran, A., Huerta, G., Jackson, C. S., and Sen, M. K.: Computational Methods for Parameter Estimation in Climate Models, Bayesian Analysis, 3, 823-850, doi:10.1214/08-BA331, 2008.
42. Whitaker, J. and Hamill, T.: Ensemble data assimilation without perturbed observations, Mon. Weather Rev., 130, 1913-1924, 2002. (Pubitemid 34825252)
43. Wilks, D.: Effects of stochastic parametrizations in the Lorenz '96 system, Q. J. Roy. Meteor. Soc., 131, 389-407, doi:10.1256/qj.04.03, 2005. (Pubitemid 41600142)
44. Zupanski, M.: Maximum Likelihood Ensemble Filter: Theoretical Aspects, Mon. Weather Rev., 133, 1710-1726, 2005. (Pubitemid 41300134)