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A nonlinear stochastic low-order energy balance climate model

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Abstract

The effects of stochastic forcing on a one-dimensional, energy balance climate model are considered. A linear, stochastic model is reviewed in analogy with the Brownian motion problem from classical statistical mechanics. An analogous nonlinear model is studied and shows different behavior from the linear model. The source of the nonlinearity is the dynamical heat transport. The role of nonlinearity in coupling different temporal and spatial scales of the atmosphere is examined. The Fokker-Planck equation from statistical mechanics is used to obtain a time evolution equation for the probability density function for the climate, and the climatic potential function is calculated. Analytical solutions to the steady-state Fokker-Planck equation are obtained, while the time-dependent solution is obtained numerically. The spread of the energy produced by a stochastic forcing element is found to be characterized by movement mainly from smaller to larger scales. Forced and free variations of climate are also explicitly considered.

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Author notes

  1. Charles A Lin

    Present address: Department of Meteorology, McGill University, H3A 2K6, Montreal, Quebec, Canada

Authors and Affiliations

  1. Department of Physics, University of Toronto, M5S 1A7, Toronto, Ontario, Canada

    Charles A Lin & John N Koshyk

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  1. Charles A Lin
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  2. John N Koshyk
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Lin, C.A., Koshyk, J.N. A nonlinear stochastic low-order energy balance climate model. Climate Dynamics 2, 101–115 (1987). https://doi.org/10.1007/BF01054493

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