Calculations of the wind-driven ocean circulation are frequently based on atmospheric pressure observations. Geostrophic winds are computed from the pressure field at sea level and then rotated and reduced in magnitude to approximate the 'surface* winds at some nominal height (10-15 meters) above the sea surface. The rotation is usually assumed to be 15°-20° and the reduction in magnitude about 30-40% [Montgomery, 1936; Fofonoff, 1960; Blackford and Tsang, 1964]. Significant departures from some assumed value of the ratio between surface and geostrophic wind speeds have considerable effect on computed wind-driven transports in the ocean, since the field of wind stress at the sea surface depends approximately on the square of the surface wind speed.
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Knut Aagaard (1969) studied this question.