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In numerical models of geophysical fluid systems, parametrization schemes are needed to account for the effect of unresolved processes on processes that are resolved explicitly. Usually, these parametrization schemes require tuning of their parameters to achieve optimal performance. We propose a new type of parametrization that requires no tuning, as it is based on an assumption that is not specific to any particular model. The assumption is that the unresolved processes can be represented by a probability density function that has maximum information entropy under the constraints of zero average time derivatives of key integral quantities of the unresolved processes. In the context of a model of a simple fluid dynamical system, it is shown that this approach leads to definite expressions for the mean effect of unresolved processes on processes that are resolved. The merits of the parametrization, regarding both short-range forecasting and long-term statistics, are demonstrated by numerical experiments in which a low-resolution version of the model is used to simulate the results of a high-resolution version of the model. For the fluid dynamical system that is studied, the proposed parametrization turns out to be related to the anticipated potential vorticity method with definite values of its parameters.

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The principle of maximum entropy is used to obtain energy and enstrophy spectra as well as average relative vorticity fields in the context of geostrophic turbulence on a rotating sphere. In the unforcedundamped (inviscid) case, the maximization of entropy is constrained by the constant energy and enstrophy of the system, leading to the familiar results of absolute statistical equilibrium. In the damped (freely decaying) and forced-damped case, the maximization of entropy is constrained by either the decay rates of energy and enstrophy or by the energy and enstrophy in combination with their decay rates. Integrations with a numerical spectral model are used to check the theoretical results for the different cases. Maximizing the entropy, constrained by the energy and enstrophy, gives a good description of the energy and enstrophy spectra in the inviscid case, in accordance with known results. In the freely decaying case, not too long after the damping has set in, good descriptions of the energy and enstrophy spectra are obtained if the entropy is maximized, constrained by the energy and enstrophy in combination with their decay rates. Maximizing the entropy, constrained by the energy and enstrophy in combination with their (zero) decay rates, gives a reasonable description of the spectra in the forced-damped case, although discrepancies remain here.

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