Toward three-dimensional radiative transfer computations via adaptive mesh refinement in both space and angle

Radiative transfer plays a key role in the atmosphere’s thermodynamics as photons from the Sun interact with the atmosphere and with other photons being emitted by the earth itself. In climate modeling and numerical weather prediction, it is very common to simplify radiative transfer into a one-dimensional, purely vertical, phenomenon for the sake of saving computational resources. This is because solving the radiative transfer equation requires building and solving what is essentially a five-dimensional problem (three spatial dimensions and two angular dimensions). Improvements in computational resources have resulted in higher-resolution simulations for both climate and weather modeling, and this increase in resolution makes the assumption of purely vertical radiative transfer more and more difficult to justify. However, these improvements to computing power make it possible to attempt to solve a three-dimensional radiative transfer equation as part of a larger atmospheric model and in doing so take into account the three-dimensional effects that are commonly neglected. Doing this efficiently requires the use of adaptive mesh refinement, which while commonly used in the CFD community, is not a technique that is widely used in simulations of the atmosphere. In this work, Jexpresso.jl, an open source flexible general conservation law solver, is extended to solve the full equations of Radiative transfer. Adaptive mesh refinement in both space and angle is then used
to make it possible to speed up solving the three-dimensional radiative transfer equation and couple the solution to an atmospheric model which uses adaptive mesh refinement around clouds. The objective is to allow for improvements in the prediction of atmospheric flow behaviors around clouds and the resulting radiative heat fluxes, which are highly sensitive to cloud cover.