Three-dimensional radiative effects are potentially important in a number of environmental modelling contexts, but traditional approaches (e.g. Monte Carlo) are far too slow to incorporate into large-scale models. SPARTACUS (the SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides) is an algorithm that can fill the gap. It takes as a starting point the two-stream equations, which take as input a 1D description of the atmosphere and produce a profile of upwelling and downwelling fluxes. SPARTACUS divides each layer of the atmosphere into one, two or three regions (which may represent clouds, vegetation elements or buildings) and explicitly computes the horizontal transport of radiation between regions. However, the shape of the regions and their vertical overlap is described statistically, so SPARTACUS avoids the computational cost of an explicit 3D description of the scene.
The original SPARTACUS application was clouds. Hogan and Shonk (2013) introduced the modified two-stream equations in the shortwave, and showed that the only quantity required to describe the shape of the regions was the length of the interface between them. Schäfer et al. (2016) extended the scheme to the longwave and demonstrated the need to account for cloud clustering and the fractal nature of clouds. This work was highlighted by EOS. Hogan et al. (2016) introduced a more elegant solution method using matrix exponentials, and performed a broadband evaluation of the shortwave and longwave schemes for a cumulus scene. Hogan et al. (2019) performed a detailed shortwave evaluation using Monte Carlo calculations on a large number of scenes, which revealed the importance of the "entrapment" mechanism.
Our ultimate aim is to incorporate a validated scheme for representing 3D effects into a weather/climate model and to compute the impact of 3D effects on a global scale. SPARTACUS is already available as an option in ecRad (Hogan and Bozzo 2018), the radiation scheme used in the ECMWF weather forecast model, and preliminary results are shown in the talks below.
Please note: Comparison to explicit Monte Carlo calculations reveals that the longwave component of SPARTACUS can significantly overestimate the 3D effect of high clouds. This is believed to be due to one of SPARTACUS's assumptions (that radiation is evenly distributed horizontally within each region of each layer) being inaccurate in optically thin clouds when the source of the radiation is the clouds themselves. We are considering alternative formulations to address this conceptual issue, but for the moment SPARTACUS is not recommended for quantitiative calculations in the longwave. This does not apply the urban/vegetation case described below.
In temperate forests, 3D radiation transport between trees and the clear regions between them can have a significant effect on the albedo of the scene and the amount of absorbed photosynthetically active radiation. Hogan et al. (2018) have demonstrated the accuracy of SPARTACUS via comparison with reference Monte Carlo calculations for the scenes of the RAMI4PILPS intercomparison study. The Matlab code used in this study is available below.
Hogan (2019b) adapted SPARTACUS to cities, including the option to move from a 2- to an N-stream representation of the radiation field. The resulting "SPARTACUS-Urban" model can represent realistic urban geometry, buildings of different height, street trees and atmospheric absorption, emission and scattering. It exploits the finding of Hogan (2019a) that wall-to-wall separation distances in urban environments tend to follow an exponential distribution. Stretton et al. (2022) evaluated the shortwave fluxes computed by the model against explicit calculations by the DART model in which every building is represented, while Stretton et al. (2023) evaluated its longwave capabilities.
The SPARTACUS-Surface radiation scheme (GitHub) is an open-source Fortran 2003 implementation of the SPARTACUS vegetation and urban radiative transfer algorithms..