Baroclinic Modes over Rough Bathymetry and the Surface Deformation Radius

The deformation radius is widely used as an indication of the eddy length scale at different latitudes. The radius is usually calculated assuming a flat ocean bottom. However, bathymetry alters the baroclinic modes and hence their deformation radii. In a linear quasigeostrophic two-layer model with realistic parameters, the deep flow for a 100-km wave approaches zero with a bottom ridge roughly 10m high, leaving a baroclinic mode that is mostly surface trapped. This is in line with published current meter studies showing a primary EOF that is surface intensified and has nearly zero flow at the bottom. The deformation radius associated with this "surface mode'' is significantly larger than that of the flat bottom baroclinic mode. Using World Ocean Atlas data, the surface radius is found to be 20%-50% larger over much of the globe, and 100% larger in some regions. This in turn alters the long Rossby wave speed, which is shown to be 1.5-2 times faster than over a flat bottom. In addition, the larger deformation radius is easier to resolve in ocean models.