Interrelationships between surface wind speed, surface wind stress magnitude, and SST variations with spatial scales of 100-1000 km are investigated using satellite measurements of surface winds by the QuikSCAT scatterometer and sea surface temperature (SST) by the Advanced Microwave Scanning Radiometer on the EOS-Aqua satellite (AMSR--E). On these spatial scales, statistical analysis of satellite observations have shown that variations in the surface wind speed and surface wind stress magnitude are both related linearly to SST variations despite the inherently nonlinear dependence of the surface stress on the surface wind speed. This paradox is solved by showing analytically that the spatially-filtered surface wind stress magnitude can be linearized about the spatially-filtered surface wind speed with a factor of proportionality containing a nonlinear function of the unfiltered and large-scale surface wind speed. Through this proportionality factor, it is shown that the large-scale surface wind speed modulates the strength of the coupling between the surface wind stress magnitude and SST relative to the coupling between surface wind speed and SST. Based on these analytical derivations, the linear wind stress-SST and wind speed-SST dependencies can be explained by this direct proportionality between the surface wind stress magnitude and surface wind speed variations. This analytical result is confirmed observationally using monthly-averaged QuikSCAT wind and AMSR--E SST fields for the period June 2002--August 2007 over five regions of the World Ocean known to contain strong ocean-atmosphere interactions: the Kuroshio Extension, Gulf Stream, eastern tropical Pacific, South Atlantic, and Agulhas Return Current.

A similar decomposition is performed for the SST-induced responses of the surface wind stress curl and divergence. Small-scale wind stress curl and divergence perturbations are mainly composed of: 1) the curl and divergence of the surface wind with a proportionality factor that is a nonlinear function of the surface wind speed; and 2) terms proportional to the crosswind and downwind gradients in the small-scale wind speed, respectively. It is shown that spatial gradients in small-scale wind speed acting independently of the curl and divergence of the surface winds contribute strongly to the SST-induced wind stress curl and divergence responses.

As a consequence of the surface wind speed modulation of the SST-induced wind stress response, geographical and seasonal variability of the SST-induced wind stress response is directly proportional to geographical and seasonal wind speed variability. Over mid-latitudes, the wind stress coupling is strongest in the winter hemisphere when the surface wind speed is strongest. In the northern hemisphere, the small-scale stress variations nearly vanish during the low wind speed regime characteristic of the mid-latitude summertime. The seasonal variability of the wind stress response to SST is, at present, an unappreciated source of seasonal forcing of the ocean.