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 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 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. We are currently working on obtaining more accurate estimates of the global 3D effect, which require better estimates of the sizes of different clouds around the globe.

Application to vegetation and urban areas

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..


  • 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.
  • Incorporation into the ECMWF radiation scheme
    Hogan, R. J., and A. Bozzo, 2018: A flexible and efficient radiation scheme for the ECMWF model. J. Adv. Modeling Earth Sys., 10, 1990-2008: PDF
  • Extension to model the "entrapment" mechanism
    Hogan, R. J., M. D. Fielding, H. W. Barker, N. Villefranque and S. A. K. Schäfer, 2019: Entrapment: An important mechanism to explain the shortwave 3D radiative effect of clouds. J. Atmos. Sci., 76, 2123-2141: PDF
  • Application to vegetation canopies: SPARTACUS-Vegetation
    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
  • Exponential model of street geometry underpinning SPARTACUS-Urban
    Hogan, R. J., 2019a: An exponential model of urban geometry for use in radiative transfer applications. Boundary-Layer Meteorol., 170, 357-472: PDF
  • Application to urban areas: SPARTACUS-Urban
    Hogan, R. J., 2019b: Flexible treatment of radiative transfer in complex urban canopies for use in weather and climate models. Boundary-Layer Meteorol., 173, 53-78: PDF
  • Shortwave evaluation in urban areas
    Stretton, M. A., W. Morrison, R. J. Hogan and C. S. R. Grimmond, 2022: Evaluation of the SPARTACUS-Urban radiation model for vertically resolved shortwave radiation in urban areas. Bound. Layer Meteorol., 184, 301-331, doi:10.1007/s10546-022-00706-9.
  • Longwave evaluation in urban areas
    Stretton, M. A., W. Morrison, R. J. Hogan and S. Grimmond, 2023: Evaluation of vertically resolved longwave radiation in SPARTACUS-Surface 0.7.3 and the sensitivity to urban surface temperatures. EGUsphere [preprint], doi:10.5194/egusphere-2022-1002.


  • 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
  • How can we represent the 3D interaction of radiation with clouds, cities and forests in global models?
    CNRM seminar, Meteo-France, Toulouse, 21 November 2018: hogan_2018_meteo_france.pptx


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