Dependence of the Monin–Obukhov Stability Parameter on the Bulk Richardson Number over the Ocean

Abstract

Recent measurements made onboard the R/P FLIP in the San Clemente Ocean Probing Experiment in September 1993 and onboard the R/V Moana Wave during Tropical Ocean Global Atmosphere Coupled Ocean?Atmosphere Response Experiment are used to evaluate the direct dependence between the Monin?Obukhov stability parameter (ratio of height to Obukhov length) ? and the bulk Richardson number Rib derived from standard meteorological mean observations of water surface temperature, wind speed, air temperature, and humidity. It is found that in the unstable marine surface layer, ? = C Rib(1 + Rib/Ribc)?1, where the numerical coefficient C and the saturation Richardson number Ribc are analytical functions of the standard bulk exchange coefficients. For measurements at a height of 10?15 m, C is about 10 and Ribc is about ?4.5. Their values are insensitive to variations of Rib and ? over three decades. Thus, a simple dependence between ? and Rib has a much wider range of applicability than previously believed. The authors show that this behavior is the result of the effects of ?gustiness? driven by boundary layer?scale convective eddies. The derived relationship can be used as a first guess for ? in bulk flux routines and reduces or eliminates the need for lengthy iterative solutions. Using this approximation yields errors in the latent heat flux of a few watts per square meter, compared to the full iterative solution.