Stochastic parameterization schemes for use in realistic climate models

Journal of the Atmospheric Sciences

Volumn 68, Issue 2, 2011, Pages 284-299

  Culina, Joel ^a   Kravtsov, Sergey ^b   Monahan, Adam H ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Climate models; Parameterization; Quasigeostrophic models

Indexed keywords

CONCEPTUAL MODEL; EFFICIENT ALGORITHM; FAST MODE; GENERAL CIRCULATION MODEL; LIMIT THEOREM; LOW FREQUENCY VARIABILITY; MULTIPLICATIVE NOISE; NON-LINEARITY; PARAMETERIZATION SCHEMES; PARAMETERIZATIONS; QUASI-GEOSTROPHIC MODEL; QUASIGEOSTROPHIC MODELS; REDUCED MODEL; S-METHOD; SLOW DYNAMICS; STATISTICAL SIGNATURES; SUBGRID SCALE; SYSTEMATIC METHOD; TIME-SCALES;

ALGORITHMS; ASTROPHYSICS; CLIMATE MODELS; EARTH ATMOSPHERE; PARAMETERIZATION; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

ALGORITHM; CLIMATE MODELING; CONCEPTUAL FRAMEWORK; GENERAL CIRCULATION MODEL; PARAMETERIZATION; QUASI-GEOSTROPHIC FLOW; STOCHASTICITY;

EID: 79953170959     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/2010JAS3509.1     Document Type: Article

References (39)

1. Arnold, L., P. Imkeller, and Y.Wu, 2003: Reduction of deterministic coupled atmosphere-oceanmodels to stochastic ocean models: Anumerical case study of the Lorenz-Maas system. Dyn. Syst., 18, 295-350.
2. Berner, J., 2005: Linking nonlinearity and non-Gaussianity of planetary wave behavior by the Fokker-Planck equation. J. Atmos. Sci., 62, 2098-2117.
3. Berner, J., F. J.Doblas-Reyes,T.N.Palmer,G. Shutts, andA.Weisheimer, 2008: Impact of quasi-stochastic cellular automaton backscatter scheme on the systematic error and seasonal prediction skill of a global climate model. Philos. Trans. Roy. Soc., 366A, 2561-2579.
4. Bogolyubov, N., and Y. Mitroplskii, 1961: Asymptotic Methods in the Theory ofNonlinear Oscillations.Gordon&Breach, 537 pp.
5. Crommelin, D., and A. Majda, 2004: Strategies formodel reduction: Comparing different optimal bases. J. Atmos. Sci., 61, 2206-2217.
6. Culina, J., 2009: Stochastic parameterization schemes based on rigorous limit theorems. Ph. D. thesis, University of Victoria, 173 pp.
7. D'Andrea, F., and R. Vautard, 2001: Extratropical low-frequency variabilityas a low-dimensional problem. Part I: A simplified model. Quart. J. Roy. Meteor. Soc., 127, 1357-1374.
8. Ehrendorfer, M., 2000: The total energy norm in a quasigeostrophic model. J. Atmos. Sci., 57, 3443-3451.
9. Ewald, B., and C. Penland, 2009: Numerical generation of stochastic differential equations in climate models. Computational Methods for the Atmosphere and the Oceans, Elsevier, 279-306.
10. Farrell, B. F., and P. J. Ioannou, 1995: Stochastic dynamics of the midlatitude atmospheric jet. J. Atmos. Sci., 52, 1642-1656.
11. 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.
12. Franzke, C., and A. Majda, 2006: Low-order stochastic mode reduction for a prototype atmospheric GCM. J. Atmos. Sci., 63, 457-479.
13. Franzke, C., A. Majda, and E. Vanden-Eijnden, 2005: Low-order stochastic mode reduction for a realistic barotropic model climate. J. Atmos. Sci., 62, 1722-1745.
14. Grabowski, W., 2001: Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (CRCP). J. Atmos. Sci., 58, 978-997.
15. Hasselmann, K., 1976: Stochastic climate models. Part I: Theory. Tellus, 28, 473-484.
16. Just, W., H. Kantz, C. Rödenbeck, and M. Helm, 2001: Stochastic modelling: Replacing fast degrees of freedomby noise. J. Phys., 34A, 3199-3213.
17. Khasminskii, R. Z., 1966: On stochastic processes defined by differential equations with a small parameter. Theory Probab. Appl., 11, 211-228.
18. 2 diffusion approximation for slow motion in averaging. Stoch. Dyn., 3, 213-246.
19. Kondrashov, D., S. Kravtsov, and M. Ghil, 2006: Empirical mode reduction in a model of extratropical low-frequency variability. J. Atmos. Sci., 63, 1859-1877.
20. Kravtsov, S., A. W. Robertson, and M. Ghil, 2005: Bimodal behavior in the zonal mean flow of a baroclinic β-channel model. J. Atmos. Sci., 62, 1746-1769.
21. Kurtz, T., 1973: A limit theorem for perturbed operator semigroups with applications to random evolutions. J. Funct. Anal., 12, 55-67.
22. Kwasniok, F., 1996: The reduction of complex dynamical systems using principal interaction patterns. Physica D, 92, 28-60.
23. Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 2001: A mathematical framework for stochastic climate models. Commun. Pure Appl. Math., 54, 891-974.
24. Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 2003: Systematic strategies for stochastic mode reduction in climate. J. Atmos. Sci., 60, 1705-1722.
25. Majda, A. J., I. Timofeyev, and E. Vanden-Eijnden, 2006: Stochastic models for selected slow variables in large deterministic systems. Nonlinearity, 19, 769-794.
26. Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci., 50, 1792-1818.
27. Mitchell, J., 1966: Stochastic models of air-sea interaction and climatic fluctuations. Rand Corp. Memo. RM-5233-NSF, 45-74.
28. Monahan,A. H., J. C. Fyfe, M. H. P. Ambaum, D. Stephenson, and G. R. North, 2009: Empirical orthogonal functions: The medium is the message. J. Climate, 22, 6501-6514.
29. Pandolfo, L., 1993: Observational aspects of the low-frequency intraseasonal variability of the atmosphere in middle latitudes. Advances in Geophysics, Vol. 34, Academic Press, 93-174.
30. Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 621 pp.
31. Penland, C., 2003: A stochastic approach to nonlinear dynamics: A review. Bull. Amer. Meteor. Soc., 84, 925-926.
32. Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8, 1999-2024.
33. Preisendorfer, R. W., 1988: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 425 pp.
34. Selten, F., 1995: An efficient description of the dynamics of barotropic flow. J. Atmos. Sci., 52, 915-936.
35. Strounine, K., S. Kravtsov, D. Kondrashov, and M. Ghil, 2010: Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance. Physica D, 239, 145-166.
36. Sura, P., M. Newman, C. Penland, and P. Sardeshmukh, 2005: Multiplicative noise and non-Gaussianity: A paradigm for atmospheric regimes? J. Atmos. Sci., 62, 1391-1409.
37. Vanden-Eijnden, E., 2003: Numerical techniques for multi-scale dynamical systems with stochastic effects. Comm. Math Sci., 1, 385-391.
38. Weinan, E., D. Liu, and E. Vanden-Eijnden, 2005: Analysis of multiscale methods for stochastic differential equations. Commun. Pure Appl. Math., 58, 1544-1585.
39. Whitaker, J. S., and P. D. Sardeshmukh, 1998: A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci., 55, 237-258.