• Berner, J., 2005: Linking nonlinearity and non-Gaussianity of planetary wave behavior by the Fokker–Planck equation. J. Atmos. Sci., 62 , 20982117.

    • Search Google Scholar
    • Export Citation
  • Bladt, M., and M. Sørensen, 2005: Statistical inference for discretely observed Markov jump processes. J. Roy. Stat. Soc., 67B , 395410.

    • Search Google Scholar
    • Export Citation
  • Boffetta, G., P. Giuliani, G. Paladin, and A. Vulpiani, 1998: An extension of the Lyapunov analysis for the predictability problem. J. Atmos. Sci., 55 , 34093416.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., M. Miller, and T. N. Palmer, 1999: Stochastic representation of model uncertainty in the ECMWF ensemble prediction system. Quart. J. Roy. Meteor. Soc., 125 , 28872908.

    • Search Google Scholar
    • Export Citation
  • Crommelin, D. T., 2004: Observed nondiffusive dynamics in large-scale atmospheric flow. J. Atmos. Sci., 61 , 23842396.

  • Crommelin, D. T., and E. Vanden-Eijnden, 2006: Fitting timeseries by continuous-time Markov chains: A quadratic programming approach. J. Comput. Phys., 217 , 782805.

    • Search Google Scholar
    • Export Citation
  • Egger, J., 2001: Master equations for climatic parameter sets. Climate Dyn., 18 , 169177.

  • Fatkullin, I., and E. Vanden-Eijnden, 2004: A computational strategy for multiscale systems with applications to Lorenz 96 model. J. Comput. Phys., 200 , 605638.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble forecasts. Mon. Wea. Rev., 129 , 550560.

  • Katsoulakis, M. A., A. J. Majda, and D. G. Vlachos, 2003: Coarse-grained stochastic processes for microscopic lattice systems. Proc. Natl. Acad. Sci. USA, 100 , 782787.

    • Search Google Scholar
    • Export Citation
  • Katsoulakis, M. A., A. J. Majda, and A. Sopasakis, 2005: Multiscale couplings in prototype hybrid deterministic/stochastic systems. Part II: Stochastic closures. Commun. Math. Sci., 3 , 453478.

    • Search Google Scholar
    • Export Citation
  • Katsoulakis, M. A., A. J. Majda, and A. Sopasakis, 2006: Intermittency, metastability and coarse graining for coupled deterministic–stochastic lattice systems. Nonlinearity, 19 , 10211047.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., A. J. Majda, and M. Katsoulakis, 2003: Coarse grained stochastic models for tropical convection and climate. Proc. Natl. Acad. Sc.i USA, 100 , 1194111946.

    • Search Google Scholar
    • Export Citation
  • Lin, J. W-B., and J. D. Neelin, 2000: Influence of a stochastic moist convective parameterization on tropical climate variability. Geophys. Res. Lett., 27 , 36913694.

    • Search Google Scholar
    • Export Citation
  • Lin, J. W-B., and J. D. Neelin, 2002: Considerations for stochastic convective parameterization. J. Atmos. Sci., 59 , 959975.

  • Lorenz, E. N., 1995: Predictability—A problem partly solved. Proc. 1995 ECMWF Seminar on Predictability, Reading, United Kingdom, ECMWF, 1–18.

  • Majda, A. J., and B. Khouider, 2002: Stochastic and mesoscopic models for tropical convection. Proc. Natl. Acad. Sci. USA, 99 , 11231128.

    • Search Google Scholar
    • Export Citation
  • Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 1999: Models for stochastic climate prediction. Proc. Natl. Acad. Sci. USA, 96 , 1468714691.

    • Search Google Scholar
    • Export Citation
  • Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 2003: Systematic strategies for stochastic mode reduction in climate. J. Atmos. Sci., 60 , 17051722.

    • Search Google Scholar
    • Export Citation
  • Orrell, D., 2003: Model error and predictability over different timescales in the Lorenz ’96 systems. J. Atmos. Sci., 60 , 22192228.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 2001: A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parameterization in weather and climate prediction models. Quart. J. Roy. Meteor. Soc., 127 , 279304.

    • Search Google Scholar
    • Export Citation
  • Penland, C., and L. Matrosova, 1994: A balance condition for stochastic numerical models with application to the El Niño–Southern Oscillation. J. Climate, 7 , 13521372.

    • Search Google Scholar
    • Export Citation
  • Plant, R. S., and G. C. Craig, 2008: A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci., 65 , 87105.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 131 , 30793102.

    • Search Google Scholar
    • Export Citation
  • Sura, P., 2003: Stochastic analysis of Southern and Pacific Ocean sea surface winds. J. Atmos. Sci., 60 , 654666.

  • Vanden-Eijnden, E., 2003: Numerical techniques for multi-scale dynamical systems with stochastic effects. Commun. Math. Sci., 1 , 385391.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2005: Effects of stochastic parameterizations in the Lorenz ’96 system. Quart. J. Roy. Meteor. Soc., 131 , 389407.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 13 13 13
PDF Downloads 13 13 13

Subgrid-Scale Parameterization with Conditional Markov Chains

View More View Less
  • 1 CWI, Amsterdam, Netherlands
  • | 2 Courant Institute, New York University, New York, New York
Restricted access

Abstract

A new approach is proposed for stochastic parameterization of subgrid-scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients: first, the unresolved processes are represented by a Markov chain whose properties depend on the state of the resolved model variables; second, the properties of this conditional Markov chain are inferred from data. The parameterization approach is tested by implementing it in the framework of the Lorenz ’96 model. Performance of the parameterization scheme is assessed by inspecting probability distributions, correlation functions, and wave properties, and by carrying out ensemble forecasts. For the Lorenz ’96 model, the parameterization algorithm is shown to give good results with a Markov chain with a few states only and to outperform several other parameterization schemes.

Corresponding author address: Daan Crommelin, CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands. Email: daan.crommelin@cwi.nl

Abstract

A new approach is proposed for stochastic parameterization of subgrid-scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients: first, the unresolved processes are represented by a Markov chain whose properties depend on the state of the resolved model variables; second, the properties of this conditional Markov chain are inferred from data. The parameterization approach is tested by implementing it in the framework of the Lorenz ’96 model. Performance of the parameterization scheme is assessed by inspecting probability distributions, correlation functions, and wave properties, and by carrying out ensemble forecasts. For the Lorenz ’96 model, the parameterization algorithm is shown to give good results with a Markov chain with a few states only and to outperform several other parameterization schemes.

Corresponding author address: Daan Crommelin, CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands. Email: daan.crommelin@cwi.nl

Save