Analytical Models of Exoplanetary Atmospheres. IV. Improved Two-stream Radiative Transfer for the Treatment of Aerosols

Abstract

We present a novel generalization of the two-stream method of radiative transfer, which allows for the accurate treatment of radiative transfer in the presence of strong infrared scattering by aerosols. We prove that this generalization involves only a simple modification of the coupling coefficients and transmission functions in the hemispheric two-stream method. This modification originates from allowing the ratio of the first Eddington coefficients to depart from unity. At the heart of the method is the fact that this ratio may be computed once and for all over the entire range of values of the single-scattering albedo and scattering asymmetry factor. We benchmark our improved two-stream method by calculating the fraction of flux reflected by a single atmospheric layer (the reflectivity) and comparing these calculations to those performed using a 32-stream discrete-ordinates method. We further compare our improved two-stream method to the two-stream source function (16 streams) and delta-Eddington methods, demonstrating that it is often more accurate at the order-of-magnitude level. Finally, we illustrate its accuracy using a toy model of the early Martian atmosphere hosting a cloud layer composed of carbon-dioxide ice particles. The simplicity of implementation and accuracy of our improved two-stream method renders it suitable for implementation in three-dimensional general circulation models. In other words, our improved two-stream method has the ease of implementation of a standard two-stream method, but the accuracy of a 32-stream method.

Accepted by ApJS. 7 pages, 5 figures

References in corpus (13)

• A Unified Theory for the Atmospheres of the Hot and Very Hot Jupiters: Two Classes of Irradiated Atmospheres
• Scattering by Interstellar Dust Grains: Optical and Ultraviolet
• Atmospheric circulation of hot Jupiters: Coupled radiative-dynamical general circulation model simulations of HD 189733b and HD 209458b
• The Climate of Early Mars
• Quantitatively Assessing the Role of Clouds in the Transmission Spectrum of GJ 1214b
• HELIOS: An Open-source, GPU-accelerated Radiative Transfer Code For Self-consistent Exoplanetary Atmospheres
• Exoplanet albedo spectra and colors as a function of planet phase, separation, and metallicity
• Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-stream Approximation
• On the effects of clouds and hazes in the atmospheres of hot Jupiters: semi-analytical temperature-pressure profiles
• Analytical Models of Exoplanetary Atmospheres. III. Gaseous C-H-O-N Chemistry with 9 Molecules
• Revisiting the scattering greenhouse effect of CO2 ice clouds
• Analytical Models of Exoplanetary Atmospheres. I. Atmospheric Dynamics via the Shallow Water System
• Clouds in the atmospheres of extrasolar planets. IV. On the scattering greenhouse effect of CO2 ice particles: Numerical radiative transfer studies

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