Stochastic aspects of climatic transitions–Additive fluctuations

C. Nicolis; G. Nicolis

doi:10.3402/tellusa.v33i3.10710

Stochastic aspects of climatic transitions–Additive fluctuations

Tellus

Volume 33 (1981): Issue 3

By: C. Nicolis and G. Nicolis

Open Access

|Jan 1981

Abstract

The Fokker-Planck equation corresponding to a zero-dimensional climatic model showing bistable behavior is analyzed. A climatic potential function is introduced, whose variational properties determine the most probable states of the stationary probability distribution. A study of the time-dependent properties leads to the identification of the characteristic time scales of evolution.

References

Arnold , L . 1973 . Stochastic differential equations . New York : Wiley .
Search in Google Scholar Back to article
Caroli B. , Caroli , C. and Roulet , T . 1979 . Diffusion in a bistable potential: a systematic W.K.B . treatment. J. Stat. Phys . 21 , 415 – 437 .
Search in Google Scholar Back to article
Cess , R. D . 1976 . Climate change: An appraisal of atmospheric feedback mechanisms employing zonal climatology . J. Atmos. Sci . 33 , 1831 – 1842 .
Search in Google Scholar Back to article
Chang , J. S. and Cooper , G . 1970 . A practical difference scheme for Fokker-Planck equations . J. Computa-tional Phys . 6 , 1 – 16 .
Search in Google Scholar Back to article
Crafoord , C. and Källen , E . 1978 . A note on the condition for existence of more than one steady-state solution in Budyko-Sellers type models. J. Atmos. Sc i . 35 , 1123 – 1125 .
Search in Google Scholar Back to article
Fraedrich , K . 1978 . Structural and stochastic analysis of a zero-dimensional climate system . Quart. J. R. Met. Soc . 104 , 461 – 474 .
Search in Google Scholar Back to article
Ghil , M . 1976 . Climate stability for a Sellers-type model . J. Atmos. Sci . 33 , 3 – 20 .
Search in Google Scholar Back to article
Haken , H . 1977 . Synergetics . Berlin : Springer-Verlag .
Search in Google Scholar Back to article
Hasselmann , K . 1976 . Stochastic climate models, Part 1 . Theory. Tellus 28 , 473 – 485 .
Search in Google Scholar Back to article
Landau , L. D. and Lifshitz , I. M . 1959 . Statistical physics . Oxford : Pergamon Press .
Search in Google Scholar Back to article
Lemke , P . 1977 . Stochastic climate models, Part 3, Application to zonally averaged energy models . Tellus 30 , 97 – 103 .
Search in Google Scholar Back to article
Matthews , J. and Walker , R. L . 1965 . Mathematical methods of physics . New York : W. A. Benjamin .
Search in Google Scholar Back to article
Nicolis , C . 1980 . Derivation of zero-dimensional from one-dimensional climate models . J. Geophys. and Astrophys. Fluid Dyn . 14 , 91 – 103 .
Search in Google Scholar Back to article
Nicolis , C. and Nicolis , G . 1979 . Environmental fluctuation effects on the global energy balance . Nature 281 , 132 – 134 .
Search in Google Scholar Back to article
Nicolis , G. and Prigogine , I . 1977 . Self organization in non-equilibrium systems . New York : Wiley .
Search in Google Scholar Back to article
Nicolis , G. and Turner , J . 1979 . Effect of fluctuations on bifurcation phenomena . Ann. N.Y. Acad. Sci . 316 , 251 – 262 .
Search in Google Scholar Back to article
North , G. R . 1975 . Theory of energy-balance models . J. Atmos. Sci . 32 , 2033 – 2043 .
Search in Google Scholar Back to article
North , G. R. , Howard , L. , Pollard , D. and Wielicki , B . 1979 . Variational formulation of Budyko-Sellers climate models . J. Atmos. Sci . 36 , 255 – 259 .
Search in Google Scholar Back to article
Paltridge , G. W ., 1979 . Climate and thermodynamic systems of maximum dissipation . Nature 279 , 630 – 631 .
Search in Google Scholar Back to article
Robock , A . 1978 . Internally and externally caused climatic change . J. Atmos. Sci . 35 , 1111 – 1122 .
Search in Google Scholar Back to article
Suzuki , M . 1977 . Scaling theory of transient phenomena near the instability point . J. Stat. Phys . 16 , 11 – 32 .
Search in Google Scholar Back to article
van Kampen , N. G . 1977 . A soluble model for diffusion in a bistable potential . J. Stat. Phys . 17 , 71 – 88 .
Search in Google Scholar Back to article
Wax , N . 1954 . Selected topics in noise and stochastic processes . New York : Dover .
Search in Google Scholar Back to article