Charles N. Adams

Radiative transfer in spherical shell atmospheres: I. Rayleigh scattering

Abstract A comparison is made between the plane-parallel approximation and the more realistic spherical shell approximation for the radiance reflected from a planetary atmosphere. In this paper we have considered a planet of radius 6371 km (the Earth) with a homogeneous, conservative, Rayleigh scattering atmosphere extending to a height of 100 km. We have found significant departures from the plane-parallel approximation. Radiance versus height distributions for both single and multiple scattering are presented. Results are presented for the fractional radiance from altitudes in the atmosphere which contribute to the total unidirectional reflected radiance at the top of the atmosphere. We have referred to this as the radiance versus height distribution in the sequel. These data will be very useful for both remote sensing applications and planetary spectroscopy. We have also found that gross violations of the principle of reciprocity do occur in the spherical shell approximation.

The Influence of Ozone and Aerosols on the Brightness and Color of the Twilight Sky

Abstract The radiance and color of the twilight sky are calculated for single scattered radiation with the use of spherical symmetric models of the earths atmosphere. Spherical geometry is used throughout the calculations with no plane parallel approximations. Refraction effects are taken into account through fine subdivision of the atmosphere into spherical shells of fixed index of refraction. Snells law of refraction is used to calculate a new direction of travel each time that a photon traverses the interface between layers. Five different models of the atmosphere were used: a pure molecular scattering atmosphere; molecular atmosphere plus ozone absorption; and three models with aerosol concentrations of one, three and ten times normal together with molecular scattering and ozone absorption. The results of the calculations are shown for various observation positions and local viewing angles in the solar plane for wavelengths in the range of 0.40 to 0.75 µm.

Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system.

We have developed a Monte Carlo program that is capable of calculating both the scalar and the Stokes vector radiances in an atmosphere-ocean system in a single computer run. The correlated sampling technique is used to compute radiance distributions for both the scalar and the Stokes vector formulations simultaneously, thus permitting a direct comparison of the errors induced. We show the effect of the volume-scattering phase function on the errors in radiance calculations when one neglects polarization effects. The model used in this study assumes a conservative Rayleigh-scattering atmosphere above a flat ocean. Within the ocean, the volume-scattering function (the first element in the Mueller matrix) is varied according to both a Henyey-Greenstein phase function, with asymmetry factors G = 0.0, 0.5, and 0.9, and also to a Rayleigh-scattering phase function. The remainder of the reduced Mueller matrix for the ocean is taken to be that for Rayleigh scattering, which is consistent with ocean water measurement.

Errors in radiance calculations induced by using scalar rather than Stokes vector theory in a realistic atmosphere-ocean system

Virtually all calculations to date dealing with radiance calculations in an atmosphere-ocean system have been performed using a scalar theory approach where polarization effects have been neglected. This approach is always in error; however, neither the nature nor the magnitude of the errors induced has been studied. We have written a large scale Monte Carlo program to calculate the complete four component Stokes vector at any region in a fully inhomogenous atmosphere ocean system with inclusion of a stochastic interface. The program uses as input the Mueller matrices for both the aerosols in the atmosphere as well as the hydrosols in the ocean. The Mueller matrix for the stochastic interface is also accurately accounted for. The correlated sampling technique is used to compute radiance distributions for both the scalar and the Stokes vector formulations in a single computer run, thus allowing a direct comparison of the errors induced. Results will be presented for a realistic atmosphere-ocean system where Rayleigh scattering is assumed for both the atmosphere and ocean

Radiative transfer in spherical shell atmospheres. II - Asymmetric phase functions

Abstract In this paper we investigate the effects of sphericity on the radiation reflected from a planet with a homogeneous, conservative scattering atmosphere of optical thicknesses of 0.25 and 1.0. We considered a Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7. Significant differences were found when these results were compared with the plane-parallel calculations. Also, large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle. These results will be useful to researchers in the field of remote sensing and planetary spectroscopy.

Errors induced when polarization is neglected in radiance calculations for an atmosphere-ocean system

Virtually all calculations to date dealing with radiance calculations in an atmosphere-ocean system have been performed using a scalar theory approach where polarization effects have been neglected. This approach is always in error; however, neither the nature nor the magnitude of the errors induced has been studied. We have written a large scale Monte Carlo program to calculate the complete four component Stokes vector at any region in a fully inhomogenous atmosphere-ocean system with inclusion of a wind ruffled stochastic interface. The program uses as input the Mueller matrices for both the aerosols in the atmosphere as well as the hydrosols in the ocean. The Mueller matrix for the stochastic interface is also accurately accounted for. The correlated sampling technique is used to compute radiance distributions for both the scalar and the Stokes vector formulations in a single computer run, thus allowing a direct comparison of the errors induced. Results are presented for a realistic atmosphere-ocean system to show the effects of the volume scattering function, the dielectric interface, and waves on the induced errors.

Radiative Transfer In An Atmosphere-Ocean System: Comparison Of Vector And Scalar Approaches

Radiative transfer in an atmosphere-ocean system has, until recently, concentrated on radiance calculations involving the scalar theory. The only correct approach is to include the full Stokes vector treatment. The authors have developed a very powerful Monte Carlo program which utilizes the method of correlated samples to calculate simultaneously both the scalar and vector radiances using the same photon histories. This technique has an advantage. Though the absolute radiances may be in error by a significant amount, the relative differences can be quite accurate. Complete inhomogeneity in both the atmosphere and ocean can be handled as long as the Mueller matrix for the scattering processes is known. The program is also able to accurately incorporate a stochastic dielectric interface. The error analysis will be presented as a function of both the inherent optical properties of the ocean and a calm wind.

Monte Carlo Calculations Of The Complete Stokes Vector For An Inhomogeneous Atmosphere-Ocean System With A Wind Ruffled Sea

We have developed a Monte Carlo program which will compute the complete Stokes vector in the I,Q,U and V representation for multiply scattered radiation in an inhomo-geneous atmosphere-ocean system including a wind ruffled surface. The program is quite general and will allow detectors to be placed at any depth both in the atmosphere and in the ocean. In the atmosphere both Rayleigh and aerosol scattering are accounted for using correct Mueller matrix input. In the ocean both Rayleigh and hydrosol scattering and absorption are accounted for. The Mueller matrix for a dielectric interface is also used to accurately emulate reflection, refraction, and also complete internal reflection. The program has been tested by creating a virtual interface which will allow comparison with more accurate techniques involving Rayleigh scattering.