Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model

Abstract

A method is described for incorporating surface-emitted surface-reflected (SESR) radiation into the calculation of infrared sea surface emissivity. Firstly, the direct emissivity is obtained by ignoring SESR emission. Next, the first order SESR emissivity is obtained by using the direct emission as a radiation source. Finally, the ith order SESR emissivity is iteratively obtained by using the i − 1st order SESR emission. Computational results are in good agreement with a Monte Carlo calculation, where the SESR emissivity increases from an emission angle of 50° showing a maximum value of about 0.03 at an emission angle of 80°. The direct emissivity is smaller than the measured emissivity by 0.02∼0.03 around a wavelength of 10 μm at an emission angle of 73.5°. By incorporating the SESR emission into the emissivity model, the discrepancy between the computed and the measured emissivity is significantly reduced. The advantage of the present method over the previous works is that we need not to specify a cutoff angle to differentiate the radiation from the sea and that from the sky for calculating SESR emission. Instead of using a cutoff angle, the probability that radiation originates from the sea is derived from the probability distribution function of sea surface slope. As a result, the uncertainty in the computation of sea surface emissivity attributed to the uncertainty in cutoff angle could be effectively suppressed.