Radiative Transfer For Variable 3D Atmospheres

TL;DR

This paper introduces a fast numerical method for solving 3D radiative transfer equations in variable atmospheres, enabling detailed temperature analysis with high efficiency and accuracy.

Contribution

The paper presents a novel H-matrix based numerical implementation for radiative transfer in 3D atmospheres, capable of handling variable absorption and scattering efficiently.

Findings

Achieved rapid computation for 50,000 points and multiple frequencies in under 5 minutes.

Demonstrated the method's ability to detect temperature differences due to greenhouse gases.

Validated the approach with real-world data from the Chamonix valley.

Abstract

To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is a very fast: 50K physical points, all directions of radiation and 680 frequencies require less than 5 minutes on an Apple M1 Laptop. The method is capable of handling variable absorptioN and scattering functionS of spatial positions and frequencies. The implementation is done using htool, a matrix compression library interfaced with the PDE solver freefem++. Applications to the temperature in the French Chamonix valley is presented at different hours of the day with and without snow / clouds and with a variable absorption taken from the Gemini measurements. The result is precise enough to assert temperature differences due to increased absorption in the vibrational frequency subrange of greenhouse gasses.