A simple model of the thermohaline circulation of the World Ocean is considered, in which fluctuations in internal oceanic mixing and in freshwater forcing are represented by stochastic processes. The effects on the stationary probability density function of correlations between fluctuations in mixing and freshwater forcing, and of finite autocorrelation time in oceanic mixing, are determined using a mixture of analytical and numerical techniques. The quantitative behaviour of the system is found to depend on the strength and correlation character of the noise processes, quite sensitively so in some regions of parameter space. The results of this analysis suggest the importance of accurately modelling high-frequency variability in nonlinear models of the climate system.
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