A model function for ocean microwave brightness temperatures

We derive a relatively simple, yet accurate, relationship between the microwave brightness temperature of the ocean and conventional oceanographic and meteorological parameters. To begin with, the brightness temperature of the ocean and the intervening atmosphere is expressed in terms of integrals for the radiative scattering and emission from the sea surface and the radiative absorption and emission by the atmosphere. We then find closed‐form approximations for these integrals and obtain a simplified model for the radiative transfer and scattering. The model is reduced to a function giving brightness temperature in terms of five variables: sea‐surface temperature, sea‐surface friction velocity, atmospheric columnar water vapor content, atmospheric columnar liquid water content, and surface air temperature« In the derivation of the model, the absorption coefficient for rain clouds and the wind‐induced sea‐surface emissivity are found from SEASAT SMMR observations. The remainder of the derivation is based on wellaccepted microwave theory. The model function is referenced to the five frequencies and 49° incidence angle at which the SEASAT and Nimbus 7 SMMR operate. When compared with the more precise integral formulation, the model function accuracy is 0.2 K at 6.6 GHz and gradually degrades to 2.1 K at 37 GHz, horizontal polarization. These accuracies are an average over an ensemble of winds and atmospheres ranging from a specular surface and clear skies to a 21 m/s wind and a very heavy cloud layer containing 60 mg/cm2 of liquid water, but excluding rain. An uncertainty of about 10% in the wind‐induced emissivity introduces some additional error into the model function. Several of the derived model parameters are compared with values obtained in other experiments and theoretical investigations. The frequency ratios of the SMMR‐inferred absorption coefficients for rain clouds are in very close agreement with that given by Mie scattering theory. The large‐scale sea‐surface slope variance found from the SMMR data is consistent with the slope variance computed from a sea wave spectrum, with that inferred from microwave scatterometer measurements at nadir, and with the Cox and Munk value deduced from sun glitter. The SMMR‐inferred foam coverage correlates better with whitecap coverage than streak coverage, indicating that the increase in brightness temperature due to sea foam is more a result of whitecapping than streaking. A layered dielectric model for sea foam predicts the same frequency and polarization variation in the foam reflectivity as observed by the SMMR. The consistency of these results support the premise that the sea‐surface emissivity is accurately represented by a composite model in which the emission from the rough, foam‐free water is given by twoscale scattering theory and the foam emission is given by a layered dielectric theory.