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We consider the Euler equation of quasi-geostrophic fluids which is widelyused in weather forecast. Our goal is to study explicit volume-preservingnumerical methods for very long simulations on an energy and enstrophypreserving discretization. To this purpose, we compute the average fields andestimate statistical parameters. It is observed that the statistical parametersdepend on the integrals of the discretization and that the computed parametersare affected by the error in those, even if the volume of the phase space iscorrectly preserved. We conclude that monitoring the error in the integrals bythe explicit volume preserving method can be used as an indication of how goodthe estimated parameters are.

The Euler equation of quasi-geostrophic fluids and volume preserving numerical methods