A dynamic approach to three-dimensional radiative transfer in numerical weather prediction models: the dynamic TenStream solver v1.0
Authors: Maier Richard , Jakub Fabian , Emde Claudia , Manev Mihail , Voigt Aiko , Mayer Bernhard 
Published: October 2023

Abstract. The increasing resolution of numerical weather prediction models makes three-dimensional (3D) radiative effects 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 ten instead of two 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 solver. Compared to traditional solvers, this speed-up 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 radiative field based on the result from the previous radiation time step. Secondly, the model is based on incomplete solves, performing just the first few steps of an iterative scheme towards convergence every time it is called. At its core, the model thereby just uses the ingoing fluxes of a grid box to update its outgoing fluxes. Combined, these two approaches put radiative transfer much closer to the way advection in the dynamical core of an NWP model is handled, as both use previously calculated results to update their variables and thereby just require access to the neighboring values of an individual model 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 both in terms of speed and accuracy. In terms of speed, our new solver is shown to be about three times slower than a traditional 1D δ-Eddington solver, but noticeably faster than currently available 3D solvers. To evaluate the accuracy of our new solver, we compare its results, as well as calculations carried out by a 1D δ-Eddington solver and the original TenStream solver, to benchmark calculations performed with the 3D Monte Carlo solver MYSTIC. We demonstrate that our new solver is able to calculate heating rates and net surface irradiances very close to those obtained by the original TenStream solver, thus offering a noticeable improvement compared to the 1D δ-Eddington results even when operated at lower calling frequencies. At these lower calling frequencies, the incomplete solves in the dynamic TenStream solver lead to the build-up of a bias with time, which becomes larger the lower the calling frequency is. However, this increase in bias flattens out after a while and remains smaller than the heating rate bias introduced by the 1D δ-Eddington solver at any point in time. Most importantly, our new solver is shown to produce significantly better results when compared to 1D δ-Eddington solves carried out with a similar computational demand.