Subgrid-scale parameterization with conditional markov chains

Journal of the Atmospheric Sciences

Volumn 65, Issue 8, 2008, Pages 2661-2675

  Crommelin, Daan ^a   Vanmden Eijden, Eric ^b  

^a CWI   (Netherlands)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; MATHEMATICAL MODELS; RISK ASSESSMENT; STOCHASTIC MODELS;

MARKOV CHAINS; NEW APPROACHES;

MARKOV PROCESSES;

ALGORITHM; ATMOSPHERIC CIRCULATION; ATMOSPHERIC MODELING; CORRELATION; ENSEMBLE FORECASTING; MARKOV CHAIN; OCEANIC CIRCULATION; PARAMETERIZATION; PROBABILITY;

EID: 51749115945     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/2008JAS2566.1     Document Type: Article

References (27)

1. Berner, J., 2005: Linking nonlinearity and non-Gaussianity of planetary wave behavior,by the Fokker-Planck equation. J. Atmos. Sci., 62, 2098-2117.
2. Bladt, M., and M. Sørensen, 2005: Statistical inference for discretely observed Markov jump processes. J. Roy. Stat. Soc., 67B, 395-410.
3. Boffetta, G., P. Giuliani, G. Paladin, and A. Vulpiani, 1998: An extension of the Lyapunov analysis for the predictability problem. J. Atmos. Sci., 55, 3409-3416.
4. 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, 2887-2908.
5. Crommelin, D. T., 2004: Observed nondiffusive dynamics in large-scale atmospheric flow. J. Atmos. Sci., 61, 2384-2396.
6. Crommelin, D. T., and E. Vanden-Eijnden, 2006: Fitting timeseries by continuous-time Markov chains: A quadratic programming approach. J. Comput. Phys., 217, 782-805.
7. Egger, J., 2001: Master equations for climatic parameter sets. Climate Dyn., 18, 169-177.
8. Fatkullin, I., and E. Vanden-Eijnden, 2004: A computational strategy for multiscale systems with applications to Lorenz 96 model. J. Comput. Phys., 200, 605-638.
9. Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble forecasts. Mon. Wea. Rev., 129, 550-560.
10. 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, 782-787.
11. 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, 453-478.
12. Katsoulakis, M. A., A. J. Majda, and A. Sopasakis, 2006: Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems. Nonlinearity, 19, 1021-1047.
13. 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, 11 941-11 946.
14. Lin, J. W.-B., and J. D. Neelin, 2000: Influence of a stochastic moist convective parameterization on tropical climate variability. Geophys. Res. Lett., 27, 3691-3694.
15. Lin, J. W.-B., and J. D. Neelin, 2002: Considerations for stochastic convective parameterization. J. Atmos. Sci., 59, 959-975.
16. Lorenz, E. N., 1995: Predictability - A problem partly solved. Proc. 1995 ECMWF Seminar on Predictability, Reading, United Kingdom, ECMWF, 1-18.
17. Majda, A. J., and B. Khouider, 2002: Stochastic and mesoscopic models for tropical convection. Proc. Natl. Acad. Sci. USA, 99, 1123-1128.
18. Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 1999: Models for stochastic climate prediction. Proc. Natl. Acad. Sci. USA, 96, 14 687-14 691.
19. Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 2003: Systematic strategies for stochastic mode reduction in climate. J. Atmos. Sci., 60, 1705-1722.
20. Orrell, D., 2003: Model error and predictability over different timescales in the Lorenz '96 systems. J. Atmos. Sci., 60, 2219-2228.
21. 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, 279-304.
22. Penland, C., and L. Matrosova, 1994: A balance condition for stochastic numerical models with application to the El Niño-Southern Oscillation. J. Climate, 7, 1352-1372.
23. Plant, R. S., and G. C. Craig, 2008: A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci., 65, 87-105.
24. Shutts, G., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 131, 3079-3102.
25. Sura, P., 2003: Stochastic analysis of Southern and Pacific Ocean sea surface winds. J. Atmos. Sci., 60, 654-666.
26. Vanden-Eijnden, E., 2003: Numerical techniques for multi-scale dynamical systems with stochastic effects. Commun. Math. Sci., 1, 385-391.
27. Wilks, D. S., 2005: Effects of stochastic parameterizations in the Lorenz '96 system. Quart. J. Roy. Meteor. Soc., 131, 389-407.