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In this paper seven vector radiative transfer codes are inter-compared for the case of underlying black surface. They include three techniques based on the discrete ordinate method (DOM), two Monte-Carlo methods, the successive orders scattering method, and a modified doubling-adding technique. It was found that all codes give very similar results. Therefore, we were able to produce benchmark results for the Stokes parameters both for reflected and transmitted light in the cases of molecular, aerosol and cloudy multiply scattering media. It was assumed that the single scattering albedo is equal to one. Benchmark results have been provided by several studies before, including Coulson et al. [22], Garcia and Siewert [7,8], Wauben and Hovenier [10], and Natraj et al. [11] among others. However, the case of the elongated phase functions such as for a cloud and with a high angular resolution is presented here for the first time. Also in difference with other studies, we make inter-comparisons using several codes for the same input dataset, which enables us to quantify the corresponding errors more accurately.

While several papers deal with effects of truncation techniques on the total radiance there is a lack of such studies concerning polarized radiance. We present our first results obtained in studying the impact of phase matrix truncation on the accuracy of polarized radiance. Like for the total radiance, the single scattering (TMS) correction is crucial and efficient in case of the polarized radiance. We show that there is a systematic error on polarized radiance that increases with truncation factor and optical depth. This error is not induced by the restitution of the phase matrix angular dependency as a function of the number of terms in the Legendre polynomials expansion. Given a truncation factor, this error reaches a maximum asymptotic value for optical depth corresponding to the saturation of polarization. For the cloud droplet that we use in our study, the maximum error is 4.5% at λ=412nm. It raises the question of whether the condition for scale invariance of the scalar radiative transfer equation...

A polarized atmospheric radiative transfer model for the computation of radiative transfer inside three-dimensional inhomogeneous mediums is described. This code is based on Monte Carlo methods and takes into account the polarization state of the light. Specificities introduced by such consideration are presented. After validation of the model by comparisons with adding-doubling computations, examples of reflectances simulated from a synthetic inhomogeneous cirrus cloud are analyzed and compared with reflectances obtained with the classical assumption of a plane parallel homogeneous cloud (1D approximation). As polarized reflectance is known to saturate for optical thickness of about 3, one could think that they should be less sensitive to 3D effects than total reflectances. However, at high spatial resolution (80 m), values of polarized reflectances much higher than the ones predicted by the 1D theory can be reached. The study of the reflectances of a step cloud shows that these large values are the results of illumination and shadowing effects similar to those often observed on total reflectances. In addition, we show that for larger spatial resolution (10 km), the so-called plane-parallel bias leads to a non-negligible overestimation of the polarized reflectances of about 7–8%.

In the near future, more and more spaceborne or airborne instruments will be able to measure polarized reflectance issued from the atmosphere. To give some examples, currently, the POLarization and Directionality of the Earth’s Reflectance instrument POLDER3/ PARASOL, which is the successor of POLDER2/ADEOS2 and POLDER/ADEOS (Deschamps et al., 1994) measures, since 2005, the polarized signal in the visible spectral range with up to 14 viewing directions. The airborne version of this instrument, called OSIRIS (observing system including polarization in the solar infrared spectrum (Auriol et al., 2008)), is nowadays extended to the near-infrared range and will maybe, in the future, generate a spaceborne version. The Aerosol Polarimetry Sensor (APS), the spaceborne version of the Research Scanning Radiometer (RSP) will be able to measure reflected total and polarized light in visible, near infrared, and short-wave infrared and should be launched in the framework of the Glory mission in 2010 (Mishchenko et al., 2007).