Holopainen, E. O., and A. H. Oort, 1981: Mean surface stress curl over the oceans as determined from the vorticity budget of the atmosphere. Journal of the Atmospheric Sciences, 38 (2), 262-269.

Abstract: The vertically integrated atmospheric vorticity budget over the oceans offers, in principle, a possibility of determining the surface stress curl from upper wind data without the need to specify a relationship between the surface stress and surface wind. Results for the wind stress curl obtained by this vorticity method, using upper wind data for the period 1968-73, are compared with the recent stress-curl calculations by Hellerman from surface data.
The two completely independent methods give basically similar mean latitudinal distribution of the stress curl. In the midlatitudes of the Southern Hemisphere, where the transient eddies are the main mechanism of vorticity transfer, the two estimates of the basin-wide longitudinal averages of the stress curl do not deviate from each other by more than approximately 20%. However, in the Northern Hemisphere the agreement is less. This seemingly strange result appears to be due to the sensitivity of the vorticity method to errors in the estimates of vorticity advection by the standing waves.
It is concluded that for the time being the geographical pattern of the mean surface stress curl can, at least in the Northern Hemisphere, be estimated from surface data (using a drag formulation) more accurately than from upper wind data (using the vorticity method). Together the two methods offer a useful quality check for the upper air data.