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Simple climate models

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Stochastic Climate Models

Part of the book series: Progress in Probability ((PRPR,volume 49))

Abstract

Climate modelling strategies are demonstrated by toy models of the greenhouse planet, the atmosphere, and the ocean. A minimum energy balance model of the greenhouse provides the setting for a review on the construction and analysis of climate systems, which are simple and noisy. Two prominent climate compartments follow; these are the mid-latitude atmosphere and the wind-driven ocean, which are also subjected to stochastic forcing. The atmosphere’s dynamics is derived analytically for a periodic channel; the (linearised) quasi-geostrophic, baroclinic flow shows a response on stochastic forcing which may serve as a parameterisation of the eddies. A wind driven ocean circulation is analysed numerically in a high resolution square basin employing the (nonlinear) shallow water system. Imposing spatially inhomogeneous random wind stress forcing generates a response with regime transitions which do not exist otherwise. From a more general perspective, a modular stochastic climate system emerges in the outlook.

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References

  1. M.I. Budyko, The effect of solar radiation variations on the climate of the earth. Tellus, 21 (1969), 611–619.

    Article  Google Scholar 

  2. P. Cessi and G.R. Ierley, Symmetry-Breaking multiple equilibria in quasigeostrophic, wind-driven Flow. J. Phys. Oceanogr., 25 (1995), 1196–1205.

    Article  Google Scholar 

  3. T. DelSole and B.F. Farrell, A stochastically excited linear system as a model for quasigeostrophic turbulence: analytic results for one-and two-layer fluids. J. Atmos. Sci., 52 (1995), 2531–2547.

    Article  Google Scholar 

  4. E. Eliasen and L. Laursen, A seasonal global climate model with an equivalent meridional atmospheric circulation. Tellus, 34 (1982), 514–525.

    Article  Google Scholar 

  5. E.T. Eady, Long waves and cyclone waves. Tellus, 1 (1949), 33–52.

    Article  MathSciNet  Google Scholar 

  6. K. Fraedrich, Structural and stochastic analysis of a zero-dimensional climate system. Q. J. R. Meteorol. Soc., 104 (1978), 461–474.

    Article  Google Scholar 

  7. K. Fraedrich, Atmospheric variability: modelling, diagnostics, and forecasting. International School of Physics ‘Enrico Fermi’ Course CXXXIII ‘Past and Present Variability of the Solar-Terrestrial System: Measurements, Data Analysis and Theoretical Models’, (G. Cini Castagnoli and A. Provenzale, eds.) (1997), 431-483.

    Google Scholar 

  8. K. Fraedrich, Catastrophes and resilience of a zero-dimensional climate system with ice-albedo and greenhouse feedback. Q. J. R. Meteorol. Soc, 89 (1979), 147–167.

    Article  Google Scholar 

  9. K. Fraedrich and E. Kietzig, Statistical Analysis and wavenumber-frequency spectra of the 500mb geopotential at 50°S. J. Atmos. Sci., 40 (1983), 1037–1045.

    Article  Google Scholar 

  10. C.W. Gardiner, Handbook of Stochastic Methods, Springer-Verlag, (1985), 442pp.

    Google Scholar 

  11. D.L. Hartmann, Global Physical Climatology Academic Press, (1994), 411pp.

    Google Scholar 

  12. K. Hasselmann, Stochastic climate models. Part I. Theory. Tellus, 28 (1976), 473–484.

    Article  Google Scholar 

  13. J.R. Holton, An Introduction to Dynamic Meteorology, Academic Press, (1992), 511pp.

    Google Scholar 

  14. W. Horsthemke and R. Lefever, Noise-Induced transitions: theory and applications in physics, chemistry, and biology, Springer-Verlag, (1984), 318pp.

    Google Scholar 

  15. I.N. James, Introduction to Circulating Atmospheres, Cambridge University Press, (1994), 422pp.

    Google Scholar 

  16. E. Källen, C. Craford and M. Ghil, Free oscillations in a climate model with ice-sheet dynamics. J. Atmos. Sci., 36 (1979), 2292–2303.

    Article  Google Scholar 

  17. J.E. Kutzbach and R. Bryson, Variance spectrum of holocene climate fluctuations in the North Atlantic sector. J. Atmos. Sci., 31 (1974), 1958–1963.

    Article  Google Scholar 

  18. P. Lemke, Stochastic climate models, Part 3. Application to zonally averaged energy models. Tellus, 29 (1977), 385–392.

    Article  Google Scholar 

  19. B. Legras and M. Ghil, Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci., 42 (1985), 433–471.

    Article  Google Scholar 

  20. M. Margules, Über die Energie der Stürme, Jahrbücher KK Zentralanstalt für Meteorologie und Erdmagnetismus, NF 40 (1905), 1–26.

    Google Scholar 

  21. J. McCalpin and D.B. Haidvogel, Phenomenology of the low-frequency variability in a reduced-gravity quasigeostrophic double-gyre model. J. Phys. Oceanogr., 26 (1996), 739–752.

    Article  Google Scholar 

  22. G.R. North, R.F. Cahalan and J.A. Coakley, Energy balance climate models. Rev. Geophys. Space Phys., 19 (1981), 91–121.

    Article  Google Scholar 

  23. J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag, (1987), 710 pp.

    Google Scholar 

  24. J. Pedlosky, Ocean Circulation Theory, Springer-Verlag, (1996), 453 pp.

    Google Scholar 

  25. F.W. Primeau, Multiple Equilibria of a double-gyre ocean model with super-slip boundary conditions. J. Phys. Oceanogr., 28 (1998), 2130–2147.

    Article  Google Scholar 

  26. B. Saltzman, A survey of statistical-dynamical models of the terrestrial climate. Advances in Geophysics, 20 (1978), 184–304.

    Google Scholar 

  27. B. Saltzman, A. Sutera and A. Evenson, Structural stochastic stability of a simple auto-oscillatory climatic feedback system. J. Atmos. Sci., 38 (1981), 494–503.

    Article  Google Scholar 

  28. B. Saltzman, Climatic systems analysis. In: Theory of Climate (ed.: B. Saltzman), Advances in Geophysics, 25 (1983), 173–233.

    Google Scholar 

  29. J.-S. von Storch, Complex Climate Models. Progress in Probability, Birkhäuser Verlag.

    Google Scholar 

  30. P. Sura, K. Fraedrich and F. Lunkeit, Regime transitions in a stochastically forced double-gyre model. J. Phys. Oceanogr., 30 (2000), in press.

    Google Scholar 

  31. W.C. Swinbank, Long-wave radiation from clear skies. Q. J. R. Meteorol. Soc, 89 (1963), 339–348.

    Article  Google Scholar 

  32. R. Thorn, Structural stability and morphogenesis, Benjamin Inc., Reading, Mass. (1975), 347pp.

    Google Scholar 

  33. R.T. Wetherald and S. Manabe, The effects of changing the solar constant on the climate of a general circulation model. J. Atmos. Sci., 32 (1975), 2044–2059.

    Article  Google Scholar 

  34. P.B. Wright, An atlas based on the COADS data set: Fields of mean wind, cloudiness and humidity at the surface of the global ocean, Max-Planck-Institut für Meteorologie, 14 (1988), 68pp.

    Google Scholar 

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© 2001 Springer Basel AG

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Fraedrich, K. (2001). Simple climate models. In: Imkeller, P., von Storch, JS. (eds) Stochastic Climate Models. Progress in Probability, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8287-3_2

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  • DOI: https://doi.org/10.1007/978-3-0348-8287-3_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9504-0

  • Online ISBN: 978-3-0348-8287-3

  • eBook Packages: Springer Book Archive

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