Validity of the one and one-half layer quasi-geostrophic model and effective topography

Andrew Majda, Xiaoming Wang

We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio< of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time dependent) topography for the top layer. Such an one and one-half layer model is utilized in recent successful quantitaive prediction of the Great Red Spot on Jupiter (see Turkington et al (2001)).