SPARTACUS 3D radiation algorithm
Overview
Threedimensional 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 largescale
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 twostream 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 twostream 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 Nstream representation of the radiation field. The resulting
"SPARTACUSUrban" 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 walltowall 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 SPARTACUSSurface
radiation scheme (GitHub) is an opensource Fortran 2003
implementation of the SPARTACUS vegetation and urban radiative
transfer algorithms..
Publications
 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 twostream radiation
schemes. J. Atmos. Sci., 70,
708724: PDF
 Extension to longwave
Schäfer, S. A. K.,
R. J. Hogan, C. Klinger, J.C. Chiu and B. Mayer, 2016:
Representing 3D cloudradiation effects in twostream schemes:
1. Longwave considerations and effective cloud edge
length. J. Geophys. Res.,
121, 85678582: 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
cloudradiation effects in twostream schemes: 2. Matrix
formulation and broadband evaluation. J. Geophys. Res.,
121, 85838599: PDF
 Sophia Schäfer's thesis
Schäfer, S. A. K., 2016: What is
the global impact of 3D cloudradiation 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,
19902008: 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,
21232141: PDF
 Application to vegetation canopies: SPARTACUSVegetation
Hogan, R. J.,
T. Quaife and R. Braghiere, 2018: Fast matrix treatment of 3D
radiative transfer in vegetation canopies: SPARTACUSVegetation
1.1. Geosci. Model Dev., 11,
339350: PDF
 Exponential model of street geometry underpinning
SPARTACUSUrban
Hogan, R. J., 2019a: An exponential model
of urban geometry for use in radiative transfer
applications. BoundaryLayer Meteorol., 170,
357472: PDF
 Application to urban areas: SPARTACUSUrban
Hogan,
R. J., 2019b: Flexible treatment of radiative transfer in complex
urban canopies for use in weather and climate
models. BoundaryLayer Meteorol., 173,
5378: PDF
 Shortwave evaluation in urban areas
Stretton, M. A.,
W. Morrison, R. J. Hogan and C. S. R. Grimmond, 2022: Evaluation of
the SPARTACUSUrban radiation model for vertically resolved
shortwave radiation in urban areas. Bound. Layer
Meteorol., 184,
301331, doi:10.1007/s10546022007069.
 Longwave evaluation in urban areas
Stretton, M. A.,
W. Morrison, R. J. Hogan and S. Grimmond, 2023: Evaluation of
vertically resolved longwave radiation in SPARTACUSSurface 0.7.3
and the sensitivity to urban surface temperatures. EGUsphere
[preprint], doi:10.5194/egusphere20221002.
Talks
 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,
MeteoFrance, Toulouse, 21 November
2018: hogan_2018_meteo_france.pptx
Software
