The thermal radiation field emitted by anistropically scattering cloudy planetary atmospheres

Abstract

The Mie theory is used to compute particle albedos ω 0 , phase functions p(cos θ), and extinction cross sections χ E for a variety of particle-size distribution functions and complex indexes of refraction n ̃ = n ⇔k . It is found that ω 0 and χ E are quite dependent on n ̃ , but that the shape of p(cos θ) is not. It is concluded that because of the way in which these parameters enter the equation of radiative transfer, it is impossible to deduce uniquely the complex index of refraction of cloud materials by observing cloudy atmospheres over a single wavelength interval in the thermal infrared. Next, two methods-the method of discrete ordinates and an exact method— are used to investigate the outgoing thermal radiation field at the top of cloudy atmospheres as a function of the scattering and thermal properties of the atmosphere. Both isothermal and uniformly mixed convective atmospheres are considered in some detail. For limb-darkening observations over a single wavelength interval it is concluded that (1) the optical thickness τ1 can be fairly well determined except for the special set of cases {1.5≲ τ1⪡∞; ω 0>0.4} ; (2) the particle albedo ω 0 can be determined only for the cases 1.5≲ τ1≲4, and only if ω 0≲0.4 ; and (3) no information is available regarding either the particle sizes or the shape of p(cos θ) under any circumstances. On the other hand it is found that the outgoing flux at the top of the atmosphere is sensitive to almost all the relevant single-scattering parameters, implying that observations of the limb function at several independent wavelengths would be extremely useful. In particular it may be possible to obtain some information about the wavelength variation of n ̃ , especially if 1.5≲ τ1≲4and ω 0≲0.4 over most of the spectral range of interest. This is turn would be of extreme importance in connection with the chemical identification of the relevant particulate medium.