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 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 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.
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.
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.
 Application to vegetation canopies
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
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
Software
