Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.