The barotropic response of the ocean over smoothly varying topography is directly related to the potential vorticity gradient ∇f/H. A global estimate of f/H and ∇f/H have been constructed from a high-resolution digital topographic data base. Four different regimes of the barotropic response of the ocean are suggested by these maps: (1) In the tropical latitudes from 20 ¿S to 20 ¿N, ∇f/H~β/H. The response will be similar to a flat-bottom Sverdrup regime. (2) In mid-latitudes (20¿ to 70¿) north of 30 ¿S, ∇f/H≫β/H. The response will be quasi-stationary, weak, and dominated by nonlocal forcing (flow along isolines of f/H). (3) In a number of small regions throughout the mid-latitudes in both hemispheres, ∇f/H≪β/H. In these regions the local response (flow across isolines of f/H) should be amplified, and wavelike motions may occur over a broader bandwidth of frequencies. (4) South of 30 ¿S, the mid-ocean ridge system becomes zonal and isolates several large regions within closed lines of f/H. In these regions, principally the abyssal plains of the southern ocean, the low-frequency barotropic response of the ocean may be wavelike in character and much stronger than the Sverdrup response. Consequently, this analysis suggests that the southern ocean may have a stronger barotropic response to wind forcing than the other five major ocean basins.