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J. E. Hansen


Solutions are obtained for the problem of multiple scattering by a plane parallel atmosphere with anisotropic phase functions typical of cloud and haze particles. The resulting albedos, angular distributions of intensities, and planetary magnitudes are compared to solutions obtained with approximate analytic phase functions and, in the case of the cloud phase function, to the solution obtained with the forward diffraction peak omitted from the phase function.

It is shown that the cloud phase function with the truncated peak yields results practically identical to those obtained with the complete cloud phase function, not only for albedos and magnitudes, but also for the angular distribution; the approximation introduces errors of several per cent in the angular distribution for direct backscattering (the region of the glory), for emergent angles near grazing regardless of the incident angle, and, of course, a larger error occurs for total scattering angles near 0°. However, the errors are unimportant for many applications, and hence a large reduction in computer time is possible. This is particularly useful, for example, in making practical the computations needed for interpreting the phase curve, limb darkening and spectral reflectivity of Venus.

It is shown that the Henyey-Greenstein phase function, based on the asymmetry factor 〈cosθ〉, yields spherical and plane albedos and planetary magnitudes (for optically thick atmospheres) close to those obtained with the cloud and haze phase functions. The Kagiwada-Kalaba phase function, based on the ratio of forward to backward scattering, gives significantly less satisfactory results for the same quantities. Neither of the two analytic phase functions can accurately duplicate the true angular distribution of scattering by thin clouds; however, the results are better with thick layers, especially for hazes. The results indicate that the Henyey-Greenstein phase function may be useful for problems such as line formation in planetary atmospheres.

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James E. Hansen and J. W. Hovenier


The linear polarization of sunlight reflected by Venus is analyzed by comparing observations with extensive multiple scattering computations. The analysis establishes that Venus is veiled by a cloud or haze layer of spherical particles. The refractive index of the particles is 1.44±0.015 at λ=0.55 μm with a normal dispersion, the refractive index decreasing from 1.46±0.015 at λ=0.365 μm to 1.43±0.015 at λ=0.99 μm. The cloud particles have a narrow size distribution with a mean radius of ∼1 μm; specifically, the effective radius of the size distribution is 1.05±0.10 μm and the effective variance is 0.07±0.02. The particles exist at a high level in the atmosphere, with the optical thickness unity occurring where the pressure is about 50 mb.

The particle properties deduced from the polarization eliminate all but one of the cloud compositions which have been proposed for Venue. A concentrated solution of sulfuric acid (H2SO4-H2O) provides good agreement with the polarization data.

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R.C.J. Somerville, P.H. Stone, M. Halem, J.E. Hansen, J.S. Hogan, L.M. Druyan, G. Russell, A.A. Lacis, W.J. Quirk, and J. Tenenbaum


A model description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection.

Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover. In the five forecasting experiments, after 48 hr, the average rms error in temperature is 3.9K, and the average rms error in 500-mb height is 62 m. The model is successful in simulating the 2-day evolution of the major features of the observed sea level pressure and 500-mb height fields in a region surrounding North America.

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