SPARTACUS 3D radiation algorithm


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 even 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.

Application to clouds

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.

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 the latest version of the ECMWF weather forecast model; preliminary results are shown in the talk below. However, the SPARTACUS algorithm is currently undergoing a more detailed evaluation using Monte Carlo calculations on a large number of scenes, which has led to further refinements to the SPARTACUS algorithm. Further papers will be written describing our results.

Application to vegetation

SPARTACUS is also applicable to vegetation canopies, in particular temperate forests where 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 the method via comparison with reference Monte Carlo calculations for the scenes of the RAMI4PILPS intercomparison study. Work to apply SPARTACUS to urban areas is also underway.


  • Original shortwave scheme for clouds
    Hogan, R. J., and J. K. P. Shonk, 2013: Incorporating the effects of 3D radiative transfer in the presence of clouds into two-stream radiation schemes. J. Atmos. Sci., 70, 708-724: PDF
  • Extension to longwave
    Schäfer, S. A. K., R. J. Hogan, C. Klinger, J.-C. Chiu and B. Mayer, 2016: Representing 3D cloud-radiation effects in two-stream schemes: 1. Longwave considerations and effective cloud edge length. J. Geophys. Res., 121, 8567-8582: PDF
  • Reformulation in terms of matrices and broadband evaluation
    Hogan, R. J., S. A. K. Schäfer, C. Klinger, J.-C. Chiu and B. Mayer, 2016: Representing 3D cloud-radiation effects in two-stream schemes: 2. Matrix formulation and broadband evaluation. J. Geophys. Res., 121, 8583-8599: PDF
  • Sophia Schäfer's thesis
    Schäfer, S. A. K., 2016: What is the global impact of 3D cloud-radiation interactions? PhD thesis, University of Reading.
  • Application to vegetation canopies
    Hogan, R. J., T. Quaife and R. Braghiere, 2018: Fast matrix treatment of 3-D radiative transfer in vegetation canopies: SPARTACUS-Vegetation 1.1. Geosci. Model Dev., 11, 339-350: PDF


  • What is the impact of 3D radiative transfer on the global radiation budget?
    Earth Radiation Budget Workshop, ECMWF, Reading, 21 October 2016: 2016_hogan_erbe_3d.pptx


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