A dynamic approach to three-dimensional radiative transfer in subkilometer-scale numerical weather prediction models: the dynamic TenStream solver v1.0

Abstract

The increasing resolution of numerical weather prediction models makes inter-column three-dimensional (3D) radiative transport more and more important. However, 3D radiative-transfer solvers are still computationally expensive, largely preventing their use in operational weather forecasting. To address this issue, Jakub and Mayer (2015) developed the TenStream solver. It extends the well-established two-stream method to three dimensions by using 10 instead of 2 streams to describe the transport of radiative energy through Earth's atmosphere. Building upon this method, this paper presents the dynamic TenStream solver, which provides a further acceleration of the original TenStream model. Compared to traditional solvers, this speedup is achieved by utilizing two main concepts. First, radiation is not calculated from scratch every time the model is called. Instead, a time-stepping scheme is introduced to update the radiation field, based on the result from the previous radiation time step. Secondly, the model is based on incomplete solves, with just the first few steps of an iterative scheme towards convergence performed every time it is called. Essentially, the model thereby just uses the ingoing fluxes of a grid box to update its outgoing fluxes. Combined, these two approaches move radiative transfer much closer to the way advection is handled in the dynamical core of a numerical weather prediction (NWP) model, as both use previously calculated results to update their variables and thereby just require access to the neighboring values of an individual grid box, facilitating model parallelization. To demonstrate the feasibility of this new solver, we apply it to a precomputed shallow-cumulus-cloud time series and test its performance in terms of both speed and accuracy. In terms of speed, the dynamic TenStream solver is shown to be about 3 times slower than a traditional 1D δ-Eddington approximation but noticeably faster than currently available 3D solvers. To evaluate the accuracy of the dynamic TenStream solver, we compare its results as well as calculations carried out using a 1D δ-Eddington approximation and the original TenStream solver, to benchmark calculations performed with the 3D Monte Carlo solver MYSTIC. We demonstrate that at the grid box level, dynamic TenStream is able to calculate heating rates and net irradiances at domain boundaries that are very close to those obtained by the original TenStream solver, thus offering a much better representation of the MYSTIC benchmark than the 1D δ-Eddington results. By calling the dynamic TenStream solver less frequently than the δ-Eddington approximation, we furthermore show that our new solver produces significantly better results than a 1D δ-Eddington approximation carried out with a similar computational demand. At these lower calling frequencies, however, the incomplete solves in the dynamic TenStream solver also lead to a buildup of bias with time, which becomes larger the lower the calling frequency is.