Phase space invariances yield exactly soluble evolution equations

lohmann [ at ]


The dynamics and predictability of Stommel's (1961) box model of the thermohaline circulation is studied. This nonlinear model with idealized geometry of the North Atlantic is solved exactly. A phase space analysis of the model reveals that the optimal perturbation affecting long-term climate variability is provided by high latitude haline forcing in the Atlantic ocean, although this perturbation has little resemblance with the most unstable mode of the system and the leading EOF.Furthermore, the predictability problem is investigated by means of singular vector analysis and the evolution of the probability distribution function. Uncertainties in the oceanic initial conditions do increase in the phase space of the model. In the stochastically forced box model with identical oceanic initial conditions, the climate predictability is examined for the damped persistence forecast. We find that the loss of the predictability is related to the different stages of the variance evolution which is also measured by the relative entropy. Our analysis shows that the non-normal system matrix of Stommel's model does affect the dynamics and predictability of the system which is useful for the interpretation of long-term climate variability and predictability.ConfigurationPhase Space DynamicsPhase space invariances yield exactly soluble evolution equations.A class of exactly solvable nonlinear evolution equations is presented that arise in the context of the oceanic circulation and population dynamics. Using Lyapunov techniques the solution of this type of equations is obtained by isolating their invariant subsets in phase space. It is shown that some solutions have finite escape time. In extension, the method is applicable to the analysis of partial differential equations of similar structure.

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Lohmann, G. (2003): Phase space invariances yield exactly soluble evolution equations , Balkan Physics Letters, 11 (2), pp. 77-81 .

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