A Simple Method for Diagnosing the Bottom Current Field of the World’s Oceans

Abstract

A simple diagnostic method presented here uses the already well-known dynamics for large-scale, time-averaged circulation (i.e., depth-integrated vorticity balance or topographic Sverdrup balance) and takes into account the material conservation of bottom density. It yields a unique solution from prescribed climatological datasets of water density, wind stress, and bottom topography, which guarantees the conservation of total transport. Unlike previous diagnostic models, this method is based on local calculations and does not require any spatial integration, thus avoiding the cumbersome encounter with planetary islands (where there are closed contours of f/h, with f being the Coriolis parameter and h the bottom depth). Comparison with previous work in the North Atlantic, including other diagnostic and inverse solutions, shows that this method compares reasonably well with generally accepted large-scale abyssal circulation patterns, and yields results that are comparable to previously suggested solutions. The solution is robust for the prescribed data noise, but very sensitive to the arbitrary, excessive smoothing of density and bottom topography; it is generally insensitive to that of wind stress. This is due to the overwhelming contribution of the baroclinic effect (or minor effect of wind stress curl) to the vorticity balance, for a given topography. The solution thus appears highly dependent upon the nature of the original hydrographic data, in particular their spatial resolution and degree of smoothing. Although the method has some inherent limitations due to the assumed nonmixing density conservation (i.e., purely isopycnal flow), a simple test in which the constraint of isopycnal flow is relaxed suggests that the bottom current field is not very sensitive to the cross-isopycnal mixing.