Introduction
A major challenge in simulating the Earth's climate is the tracking of solar
energy, its absorption, and scattering within and reflection from the Earth
system in the presence of heterogeneously distributed clouds and aerosols.
The fifth assessment of Intergovernmental Panel on Climate Change (IPCC,
chap. 7, Boucher et al., 2013) summarizes that the net radiative feedback
due to all cloud types is likely to be positive but with large uncertainty,
mostly attributed to the uncertain impact of warming on low clouds. The
confidence in the aerosol–climate feedback, through both aerosol and cloud
albedo, is even lower, and the uncertainty is ±0.2 W m-2 ∘C-1.
Major modeling challenges naturally point to the
sub-grid parameterizations of clouds and cloud–aerosol interactions in
coarsely gridded global models, and the IPCC reports have documented
substantial developments in the modeling of the chemical–physical properties
of aerosols and clouds (Boucher et al., 2013). In comparison, relatively
little attention has been paid to improving the treatment of aerosol and
cloud scattering in climate models. This is both surprising and not.
Solutions of the radiative transfer (RT) equations in scattering media are
well documented with numerous methods and readily available packages such as
TUV (Tie et al., 2003; Palancar et al., 2011) and SCIATRAN (Rozanov et al.,
2014). However, these more accurate reference codes have always been viewed
as too computationally expensive. In terms of climate model development,
this is a solved problem with little intellectual interest but is too onerous
to improve, and thus low-order approximations remain in place.
Solar-J extends Cloud-J's solar wavelength bands by combining and
modifying RRTMG-SW's bands 24 and 25 (442–778 nm) and adopts all RRTMG's
bands longwards of 778 nm (see text for details).
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We present here Solar-J version 7.5, a radiative transfer model based on the
computationally optimized photolysis code, Cloud-J (Prather, 2015). Cloud-J
combined an improved cloud overlap algorithm based on observed decorrelation
lengths with the cloud quadrature scheme (Neu et al., 2007) for averaging
over independent column atmospheres. It includes an eight-stream scattering
photolysis code with semi-spherical geometry and wavelength integration over
18 spectral bins from 177 to 850 nm. In the most recent version (v7.4), the
spectrum was shortened to 778 nm (see Fig. 1). Prior released versions,
known in the community as Fast-JX or simply Fast-J (see Søvde et al., 2012;
Telford et al., 2013; Sukhodolov et al., 2016), were based on the work of
Fast-J2 (Bian and Prather, 2002) and the original Fast-J (Wild et al.,
2000), separately optimizing the absorptions of photon fluxes into 12
stratospheric bins (177–292 nm) and seven tropospheric bins (292–850 nm).
Although this is the first version of Solar-J, we retain the numbering of
the released versions of the core photolysis code. For simplicity, we will
refer to Cloud-J, not Fast-J, as the starting point of Solar-J throughout the
text. The accurate treatment of cloud and aerosol scattering has been an
essential requirement for atmospheric chemistry modeling, and Cloud-J or
alternative models (fast-TUV, Tie et al., 2003) are used standardly in
global chemistry models. Solar-J is an extension of the Cloud-J wavelength range
(0.18–0.8 µm) out to 12 µm and includes an eight-stream scattering
solution for the absorption and reflection of sunlight over the full
spectrum. Scattering and absorption by large aerosols (dust) and clouds are
important for heating rates at these longer wavelengths. The long-term goal
is to develop Solar-J as a single module for climate models, albeit with
increased computational cost, delivering photolysis rates and more accurate
shortwave heating rates, particularly for aerosol and cloud radiative
forcing.
As finer grid resolutions and massively parallel computing are being pursued
to enable more realistic atmospheric interactions with the land, ocean, and
biosphere in climate modeling, the radiative transfer codes implemented in
most of the global models remain in their simplest possible analytical form
of two-stream scattering. With this approximation, all upward and downward
scattering occurs at a single angle, and the scattering must be treated as
isotropic, i.e., independent of sun angle. The ubiquitous adoption of
two-stream RT codes by the global climate and weather-forecasting models
(e.g., the US Department of Energy (DOE) Accelerated Climate Modeling for Energy (ACME),
the National Center for Atmospheric Research (NCAR)
Community Earth System Model (CESM), the European Centre for Medium-Range
Weather Forecasts (ECMWF) model) has been enabled by standardized packages
like the Rapid Radiative Transfer Model for general circulation model (GCM) applications (RRTMG),
developed based on the correlated-k approach (Mlawer et al., 1997; Clough et
al., 2005). A two-stream model was certainly necessary at a time when the need
for computational efficiency exceeded that for accuracy. With the rapid
advancement of massively parallel computing, it is time to ask if an upgrade
to a higher-order scheme is needed for improved accuracy in climate
modeling, particularly with regard to cloud and aerosol forcing. The
two-stream scattering approximation has been in use for decades in climate
models and evaluating its systematic errors remains an active research topic
(Li et al., 2015; Barker et al., 2015). The errors are mostly from the
inadequacy of using a single angle to represent the scattering of cloud
particles and aerosols. For example, the anisotropic, forward-peaked
scattering of all relevant atmospheric aerosols and cloud particles cannot
be represented with the two-stream approach, and all scattering must be
reduced to isotropic. To address this problem, a commonly used delta-scaling
technique is applied by removing the large forward-scattering peak, thus
reducing the optical depth (Joseph et al., 1976; Wiscombe, 1977). In
addition, the Henyey–Greenstein (HG) phase function (Henyey and Greenstein,
1941) is often used to tune the two-stream scattering to better represent the
scattering of large particles for specific sun angles. Unfortunately, the HG
phase function lacks the realistic back-scattering peak found for cloud
particles, particularly ice crystals (Zhou and Yang, 2015). Li et al. (2015)
find biases caused by the HG phase function and conclude that higher-order
moments of the phase function coupled with a multi-stream radiative transfer
algorithms are needed to improve accuracy. They demonstrate this point with
a four-stream delta-Eddington code developed by Li and Ramaswamy (1996).
Wild et al. (2000) tested the accuracy of different-order codes for
computing the mean radiation field in the presence of thick water clouds
and found that eight streams were necessary to have errors of only a few percent
relative to a 160-stream code that resolved the scattering phase function.
For Solar-J, we adopt the Wild et al. (2000) optimization for water clouds
and use Mie (liquid) or Mishchenko (ice) (Mishchenko et al., 1996, 2004)
full phase functions for scattering, truncate the expansion in Legendre
polynomials to order 8, and solve the scattering with eight streams with no
delta scaling of the optical depth.
The Solar-J model and tests are described in Sect. 2. The resulting
comparisons with RRTMG-SW are presented in Sect. 3. In this paper, we use
RRTMG as shorthand for RRTMG-SW. Section 4 examines computational costs for
Solar-J and options for optimization. Conclusions and a path forward are
discussed in Sect. 5.
Methods: model configuration and test cases
Solar-J spectral configuration
The 18 bins of Cloud-J make up the first 18 bins of Solar-J and were
optimized for calculating photolysis rates below 64 km (Wild et al., 2000;
Bian and Prather, 2002). The first 11 bins (177–291 nm) are optimized around
the Schumann–Runge bands of O2 and the Hartley bands of O3, and
the next 7 bins are optimized for tropospheric photolysis (291–778 nm). The bins
were chosen to have relatively uniform opacities for the principal absorbing
species O2 and O3 across the wavelengths in each bin. In some
cases, this includes combining different wavelength regions on either side
of the O3 maximum cross section near 255 nm. Effectively, the 18 bins
extend the use of opacity distribution functions used to calculate O2
photolysis rates in the Schumann–Runge bands (Fang et al., 1974), an
equivalent to the correlated-k method in the infrared (Lacis and Oinas,
1991). An inherent assumption is that any other scatterers and absorbers are
uniform across each wavelength bin, justified by the narrowness of the bins
and the lack of sharp spectral features in clouds and aerosols. Because
Cloud-J has been optimized against high-resolution spectral data for
stratospheric ozone photolysis and continually updated with new cross
sections (Sander et al., 2011), and tested against other codes (Palancar et
al., 2011; PhotoComp, Eyring et al., 2010), we have confidence in our
stratospheric photolysis and heating rates.
The large bin 18 (412–778 nm) that includes the O3 Chappuis band is
unusual for Cloud-J: it assumes a uniform absorption cross section for
O3, and it has a large, factor of 2 change in wavelength. The O3 cross sections vary smoothly over bin 18 and are > 0.5×10-21 cm2
over the range 475–725 nm with a broad maximum of
5×10-21 cm2 about 600 nm. Overhead opacity ranges from 0.4 to
4 % over this band. With optically thin absorption, one can use the
flux-weighted average cross section, 1.94×10-21 cm2, for the
entire bin. Both the attenuation of sunlight and the absorption of photons
to calculate the O3 photolysis rate use this average. At very large air
masses (solar zenith angles of 89–95∘) the atmospheric path (vertical
optical path ×1/cos(SZA)) in the Chappuis band approaches 1 and modest
errors appear. If highly accurate calculation of the photolysis and heating
rates due in the Chappuis band is required, then further analysis of bin 18
is warranted, but otherwise this treatment is sufficiently accurate to
follow these rates as the sun sets. Another possible source of error is that
these cross sections are photon weighted, and for heating rates the cross
sections should be energy weighted (W m-2). Fortunately, the
energy-weighted O3 cross section, 1.91×10-21 cm2, differs
little from the photon-weighted one (with the result of
< 0.04 K day-1
difference in clear-sky stratospheric heating).
RRTMG-SW has nine large bins extending to wavelengths longer than the end point
of Cloud-J, and we adopt the flux-weighted average optical properties of
clouds and aerosols for these bins as an extension to Cloud-J v7.4 to become
Solar-J v7.5. Figure 1 shows the overlap of the spectral bins of Fast-J
v7.3, Solar-J v7.5, and RRTMG-SW. Also shown is the revised Cloud-J v7.4 for
which the long-wavelength edge of bin 18 has been shortened from 850 to
778 nm to match the transition to RRTMG bins. The flux-weighted cross
sections for several Cloud-J species have been recalculated to account for
this. Be aware that these rescaled cross sections apply to Cloud-J versions
7.4 and later. Cloud-J remains a key component of Solar-J, as it produces
representative samples of independent column atmospheres after considering
the topology of cloud fractions (Prather, 2015). Solar-J has 27 major bins,
referred to here as S-bins, e.g., S1–S27 in Table 4. Bins S1–S17 are taken
directly from Cloud-J and have no sub-bins. The transition bin S18 combines
Cloud-J's uniform treatment of Chappuis-band O3 absorption with four small
non-overlapping sub-bins (17.5 out of a total of 608.7 W m-2) to include
RRTMG's H2O and O2 absorptions from their bins B24–B25. These four
sub-bins have strong cross sections with their own distinct optical depth
structures, and they do not overlap with the major O3 absorption in bin
S18. The rest of the non-ozone sub-bins (weak cross sections) are lumped
into one more sub-bin and added to Solar-J's Chappuis band. In all, we took
RRTMG's 14 sub-bins from B24 and B25 and optimized these into 5 sub-bins for
S18. The last 9 bins, S19–S27, are directly implemented from RRTMG and
contain 78 sub-bins. The logic of having wavelength bins and then sub-bins
within them is to allow the gaseous absorbers with similar opacities to be
gathered into one sub-bin but to treat the scattering and absorption by
aerosols and clouds as uniform across the major bin (see Sect. 2.2). The
fidelity of the spectral extension of Solar-J to match RRTMG-SW is verified
with the clear-sky case presented in Sect. 3.1.
Clouds and aerosols
Like the photolysis rates calculated in Cloud-J, the heating rates in
RRTMG-SW and Solar-J are highly sensitive to the scattering and absorption
from tropospheric and stratospheric aerosols, and from liquid-water and
ice-water clouds. Cloud-J v7.4 has pre-computed tables of optical properties
for typical aerosols and for both liquid- and ice-water clouds. For bins
S1–S18, many of these are effectively non-absorbing. With the extension to
longer wavelengths, it becomes important to treat the absorption by clouds
and the stratospheric sulfate layer. We take the refractive indices for
liquid water, ice water, and sulfuric acid and calculate solar-flux-weighted
mean values for each bin (S12–S27). Sunlight over wavelengths for bins
S1–S11 does not reach the troposphere in significant amounts, and hence the
optical properties of bin S12 are used for S1–S11 for simplicity. For the
first 18 bins, optical properties are weighted by the solar photon flux
(photons cm-2 s-1), and for the last 9 bins they are weighted by
the solar energy flux (W m-2). These refractive indices are combined
with a Mie scattering code and a model for the size distribution of
particles to calculate the effective radius (re), single scattering
albedo (SSA), ratio of optical to geometric cross section (Q), and the first
eight terms in the expansion of the scattering phase function (A0:7) that
include the asymmetry parameter (g=A1/3).
For liquid water, we take the refractive index from FORTRAN codes developed
at the University of Wisconsin–Madison by M. A. Walters for liquid water (NDXWATER: Hale
and Querry, 1973; Palmer and Williams, 1974; Downing and Williams, 1975)
and ice water (NDXICE, based on Warren, 1984). Liquid-water clouds use
Deirmendjian's C.1 gamma distribution of drop sizes (α=6; see
Deirmendjian, 1969) and the Mie code from Hansen and Travis (1974) for a
range of effective radii: re=1.5, 3, 6, 12, 24, 48 µm; see
also Hess et al. (1998). Optical properties (SSA, Q, A0:7, g) are
calculated for bins S12–S27 for these effective radii and then individual
cloud properties at each bin are interpolated piecewise linearly in re.
For ice-water clouds, we have two T-matrix computations supplied by M.
Mishchenko for Cloud-J (Mishchenko et al., 2004) for warm (irregular) and
cold (hexagonal) ice clouds. These included Q and the scattering phase
function (including A0:7) for the visible region (∼ 600 nm) and were used at all Solar-J wavelengths. When there is significant
absorption, the values of SSA, and to some extent Q, are complex functions
of re and do not simply scale as total mass. For this first version of
Solar-J, we made a simplifying assumption and used the Mie code with the
ice-water refractive index to calculate SSA and Q as a function of re = 3, 6, 12, 24, 48, 96 µm using the liquid-water clouds' C.1
distribution. Effectively, we assumed that the ice particles were spheres.
For the phase function A0:7, we kept the two T-matrix results
(irregular and hexagonal ice particles) and used them for all re of
that type of ice cloud. The obvious next upgrade to Solar-J is a redo of the
ice-water clouds with a broader, better mix of cloud types (Mishchenko et
al., 2016; Yang et al., 2015).
The refractive index for mixtures of sulfuric acid and water is also well
characterized (Beyer et al., 1996; Biermann et al., 2000; Krieger et al.,
2000; Lund-Myhre et al., 2003), and we use the tables from Lund-Myhre et al. (2003).
For the stratospheric sulfate layer, we chose background and
volcanic bimodal log-normal size distributions based on Deshler et al. (2003):
the background distribution has a dominant mode (98 %) with re=0.125 µm and a secondary mode with re= 0.432 µm for an
average of re=0.131 µm; the volcanic distribution has a dominant mode
(81 %) with re=0.487 µm and a secondary mode with re
= 0.149 µm for an average of re= 0.422 µm. The
stratospheric aerosol properties are tabulated for bins S5–S27 for a
combination of temperatures (220–250–280 K) and weight-percent sulfuric acid
(50–70–90 %) with 220 K and 70 % being typical for the stratosphere
(McGouldrick et al., 2011). The refractive indices and size distributions of
tropospheric aerosols are not as well characterized. Cloud-J has a
collection of aerosol optical properties for wavelengths 300–800 nm based on
community contributions (e.g., Liousse et al., 1996; Martin et al., 2003),
and this has been propagated for testing in Solar-J. However, if heating by
tropospheric aerosols such as brown and black carbon and dust is to be
accurately modeled with Solar-J, then one must go to the specific models to
acquire the physical and optical properties, e.g., NCAR's CESM 1.2 (Tilmes
et al., 2015).
Some key configuration parameters for Solar-J v7.5 wavelength bins:
solar-flux-weighted wavelength (λeff) within the range between
λbeg and λend, solar fluxes in
photons cm-2 s-1 (Sphot) and in W m-2 (Swatt), Rayleigh cross section
(XRayl), and yields for photosynthetically active radiation
(Ypar).
bin
λeff (µm)
λbeg (µm)
λend (µm)
Sphot (cm-2 s-1)
SWatt (W m-2)
XRayl (cm2)
YPAR (/phot)
S01
0.187
1.391E+12
0.0147
5.073E-25
S02
0.191
1.627E+12
0.0168
4.479E-25
S03
0.193
1.664E+12
0.0170
4.196E-25
S04
0.196
9.278E+11
0.0094
3.906E-25
S05
0.202
7.842E+12
0.0766
3.355E-25
S06
0.208
4.680E+12
0.0445
2.929E-25
S07
0.211
9.918E+12
0.0930
2.736E-25
S08
0.214
1.219E+13
0.1128
2.581E-25
S09
0.261
6.364E+14
4.818
1.049E-25
S10
0.267
4.049E+14
2.962
9.492E-26
S11
0.277
3.150E+14
2.218
8.103E-26
S12
0.295
0.2910
0.2982
5.893E+14
3.703
6.135E-26
S13
0.303
0.2982
0.3074
7.670E+14
4.670
5.424E-26
S14
0.310
0.3074
0.3124
5.041E+14
3.063
4.925E-26
S15
0.316
0.3124
0.3203
8.895E+14
5.414
4.516E-26
S16
0.333
0.3203
0.3450
3.852E+15
22.28
3.644E-26
0.0514
S17
0.383
0.3450
0.4124
1.547E+16
77.17
2.082E-26
0.4855
S18
0.599
0.4124
0.7780
1.805E+17
608.68
4.427E-27
0.6760
S19
0.973
0.778
1.242
349.96
5.380E-28
S20
1.267
1.242
1.299
25.59
1.559E-28
S21
1.448
1.299
1.626
102.96
9.578E-29
S22
1.767
1.626
1.942
56.01
4.241E-29
S23
2.039
1.942
2.151
22.40
2.347E-29
S24
2.309
2.151
2.500
23.50
1.441E-29
S25
2.748
2.500
3.077
20.20
7.290E-30
S26
3.404
3.077
3.846
12.25
3.117E-30
S27
5.362
3.846
12
12.58
8.053E-31
The Solar-J bins, solar fluxes (Sphot in photons cm-2 s-1 and
SWatt in W m-2), and Rayleigh cross sections (XRayl cm2)
are summarized in Table 1. The spectral properties for examples of
liquid-water clouds (re= 12 µm), ice-water clouds (re=48 µm, cold, hexagonal), background stratospheric 70 wt %
sulfuric acid aerosols, and volcanically enhanced stratospheric aerosols for
each Solar-J bin are given in Table 2. This table gives wavelength data for
the real and imaginary refractive indices based on the flux-weighted means,
as well as the Mie-derived values for Q, SSA, and g. The relative importance
of cloud heating in each bin can be estimated by multiplying the solar
energy by the absorbing fraction, SWatt×(1- SSA). One finds that
absorption for bins S1–S20 is negligible, that both types of clouds and
stratospheric sulfate aerosols have large absorption in bins S25–S27, and
that ice-water clouds have large absorption per optical depth in bins
S21–S24 while liquid-water clouds do not. Ice-water and liquid-water clouds have
real refractive indices that differ by at most 5 %, and imaginary
refractive indices that differ typically by a factor of 2 (except for S27).
The cause of this difference in specific absorption is the ratio of mass
(which controls absorption) to surface area (which controls optical depth),
i.e., it is proportional to re, and ice-water clouds typically have
4 times greater re.
Spectral properties of liquid-water and ice-water clouds and
stratospheric sulfate aerosols: the real and imaginary refractive indices
(nr and ni), ratio of optical to geometric cross section (Q),
single scattering albedo (SSA), and the asymmetry factor (g).
Bin
Liquid-water cloud: re= 12 µm, ρ= 1.00 g cm-3
Ice-water cloud: re= 48 µm, ρ= 0.917 g cm-3
nr
ni
Q
SSA
g
nr
ni
Q
SSA
g
S12
1.350
1.8E-08
2.054
1.0000
0.867
1.336
5.8E-09
2.021
1.0000
0.812
S13
1.349
1.5E-08
2.053
1.0000
0.869
1.333
5.4E-09
2.021
1.0000
0.812
S14
1.348
1.4E-08
2.052
1.0000
0.869
1.332
5.1E-09
2.022
1.0000
0.812
S15
1.347
1.3E-08
2.055
1.0000
0.869
1.331
4.8E-09
2.022
1.0000
0.812
S16
1.345
9.5E-09
2.057
1.0000
0.869
1.328
4.3E-09
2.023
1.0000
0.812
S17
1.340
3.4E-09
2.062
1.0000
0.869
1.321
3.0E-09
2.025
1.0000
0.812
S18
1.333
3.1E-08
2.089
1.0000
0.863
1.310
1.7E-08
2.034
1.0000
0.812
S19
1.328
2.8E-06
2.118
0.9996
0.858
1.302
1.7E-06
2.047
0.9991
0.812
S20
1.324
1.2E-05
2.144
0.9986
0.852
1.297
1.3E-05
2.055
0.9946
0.812
S21
1.321
1.6E-04
2.155
0.9851
0.854
1.293
2.4E-04
2.060
0.9246
0.812
S22
1.313
3.2E-04
2.179
0.9752
0.852
1.284
2.2E-04
2.069
0.9413
0.812
S23
1.302
9.2E-04
2.197
0.9427
0.858
1.272
1.2E-03
2.076
0.7876
0.812
S24
1.283
6.7E-04
2.220
0.9610
0.855
1.251
4.7E-04
2.083
0.9088
0.812
S25
1.239
1.0E-01
2.211
0.4979
0.970
1.125
1.0E-01
2.071
0.5107
0.812
S26
1.428
5.1E-02
2.268
0.5240
0.939
1.496
1.6E-01
2.102
0.5408
0.812
S27
1.317
2.2E-02
2.409
0.6809
0.861
1.326
2.9E-02
2.144
0.5245
0.812
Bin
Strat. sulf., volc.: re= 0.422 µm, ρ= 1.69 g cm-3
Strat. sulf., bkgrd: re= 0.130 µm, ρ= 1.69 g cm-3
nr
ni
Q
SSA
g
nr
ni
Q
SSA
g
S05
1.505
0.0E+00
2.612
1.0000
0.732
1.505
0.0E+00
2.966
1.0000
0.698
S06
1.505
0.0E+00
2.638
1.0000
0.728
1.505
0.0E+00
2.936
1.0000
0.698
S07
1.505
0.0E+00
2.620
1.0000
0.735
1.505
0.0E+00
2.919
1.0000
0.699
S08
1.505
0.0E+00
2.628
1.0000
0.734
1.505
0.0E+00
2.904
1.0000
0.699
S09
1.472
0.0E+00
2.604
1.0000
0.718
1.472
0.0E+00
2.435
1.0000
0.711
S10
1.469
0.0E+00
2.606
1.0000
0.710
1.469
0.0E+00
2.379
1.0000
0.711
S11
1.464
0.0E+00
2.556
1.0000
0.707
1.464
0.0E+00
2.271
1.0000
0.711
S12
1.456
0.0E+00
2.500
1.0000
0.695
1.456
0.0E+00
2.087
1.0000
0.709
S13
1.452
0.0E+00
2.474
1.0000
0.690
1.452
0.0E+00
1.998
1.0000
0.708
S14
1.451
0.0E+00
2.461
1.0000
0.686
1.451
0.0E+00
1.940
1.0000
0.706
S15
1.451
0.0E+00
2.449
1.0000
0.683
1.451
0.0E+00
1.892
1.0000
0.704
S16
1.450
0.0E+00
2.432
1.0000
0.676
1.450
0.0E+00
1.766
1.0000
0.698
S17
1.445
0.0E+00
2.475
1.0000
0.675
1.445
0.0E+00
1.432
1.0000
0.683
S18
1.431
1.7E-08
3.017
1.0000
0.723
1.431
1.7E-08
0.620
1.0000
0.593
S19
1.424
1.5E-06
2.212
1.0000
0.663
1.424
1.5E-06
0.193
1.0000
0.434
S20
1.417
8.6E-06
1.431
0.9999
0.605
1.417
8.6E-06
0.090
0.9998
0.336
S21
1.430
9.4E-05
1.173
0.9988
0.570
1.430
9.4E-05
0.065
0.9972
0.291
S22
1.422
4.7E-04
0.724
0.9910
0.511
1.422
4.7E-04
0.033
0.9782
0.225
S23
1.410
1.3E-03
0.475
0.9672
0.456
1.410
1.3E-03
0.021
0.9184
0.182
S24
1.388
2.1E-03
0.305
0.9288
0.397
1.388
2.1E-03
0.013
0.8166
0.148
S25
1.319
5.1E-02
0.253
0.3855
0.302
1.319
5.1E-02
0.040
0.0768
0.106
S26
1.366
1.7E-01
0.424
0.1714
0.214
1.366
1.7E-01
0.098
0.0219
0.074
S27
1.406
2.1E-01
0.274
0.0744
0.091
1.406
2.1E-01
0.073
0.0066
0.033
Test cases: clear-sky, clouds, and the optical properties
To compare Solar-J and RRTMG-SW, we adopt a standard atmospheric column
model, typical of the tropical oceans (surface albedo is 0.06) and define
three cases: clear sky, a stratus liquid-water cloud, and a cirrus ice-water
cloud. Both cloudy cases assume 100 % cloud cover; the cloud overlap
algorithms of Cloud-J are not invoked. Aerosols are not included either.
Atmosphere and cloud properties are given in Table 3. Each test case is
evaluated at four different solar zenith angles (SZAs) at 0,
21, 62, and 84∘, whose respective cosine
values are 1.0, 0.93, 0.47, and 0.10.
The two cloud profiles are extracted from the 3-hourly, July 2005
ECMWF Integrated Forecast System (IFS) data. This data set has a horizontal
resolution of 1∘ × 1∘ in longitude and latitude, and 37 vertical
layers with about 0.5 km vertical resolution in the
troposphere. Our example of marine stratus clouds has liquid-water content
(LWC, g m-3) only below 2 km, while the cirrus example has non-zero
ice-water content (IWC, g m-3) above 6 km and no liquid water anywhere. The
total cloud water content (CWC, g m-3) and effective radius (re)
are also listed in Table 3. Solar-J has default values for re: for
cirrus, they are parameterized as re=164 × IWC0.23 µm, based on a fit to the data described in Heymsfield et al. (2003). For
liquid-water clouds, they are based loosely on observations of clean
maritime stratus (Boers et al., 1998; Gerber, 1996; Miles et al., 2000),
with re= 9.6 µm at pressures greater than 810 hPa and increasing
linearly to 12.7 µm at 610 hPa and above. When implemented in an
atmospheric model, re will ideally be supplied by the atmospheric model
driving Solar-J.
The standard tropical atmosphere and the two cloud profiles
implemented in both Solar-J and RRTMG-SW. Height (Z) and pressure (P) are
edge values; others are layer averages.
Layer
Zedge
Pedge
T
O3
H2O
Stratus cloud LWC
Cirrus cloud IWC
(km)
(hPa)
(K)
(cm-3)
(kg kg-1)
LWC (g m-3) re (µm)
IWC (g m-3) re (µm)
58
75.25
0.020
57
59.58
0.200
232.4
1.27E+09
3.85e-06
0
0
0
0
56
54.95
0.384
242.4
1.17E+10
3.85e-06
0
0
0
0
55
51.11
0.636
259.9
2.81E+10
3.85e-06
0
0
0
0
54
47.91
0.956
268.1
5.79E+10
3.82e-06
0
0
0
0
53
45.25
1.345
266.9
1.07E+11
3.78e-06
0
0
0
0
52
42.97
1.806
263.9
1.84E+11
3.63e-06
0
0
0
0
51
40.97
2.348
259.9
3.01E+11
3.42e-06
0
0
0
0
50
39.18
2.985
255.2
4.66E+11
3.20e-06
0
0
0
0
49
37.52
3.740
250.7
6.78E+11
3.00e-06
0
0
0
0
48
35.96
4.646
245.1
9.63E+11
2.74e-06
0
0
0
0
47
34.46
5.757
240.3
1.30E+12
2.55e-06
0
0
0
0
46
32.97
7.132
237.2
1.70E+12
2.47e-06
0
0
0
0
45
31.50
8.837
234.3
2.20E+12
2.42e-06
0
0
0
0
44
30.04
10.95
231.6
2.87E+12
2.27e-06
0
0
0
0
43
28.61
13.57
228.7
3.56E+12
2.18e-06
0
0
0
0
42
27.20
16.81
225.2
4.24E+12
2.11e-06
0
0
0
0
41
25.81
20.82
221.4
4.88E+12
2.04e-06
0
0
0
0
40
24.45
25.80
216.0
4.67E+12
1.90e-06
0
0
0
0
39
23.12
31.96
211.9
4.36E+12
1.87e-06
0
0
0
0
38
21.80
39.60
211.4
3.93E+12
1.85e-06
0
0
0
0
37
20.48
49.07
209.8
3.31E+12
1.84e-06
0
0
0
0
36
19.25
60.18
205.9
2.01E+12
1.90e-06
0
0
0
0
35
18.10
73.07
202.2
1.47E+12
2.04e-06
0
0
0
0
34
17.05
87.73
196.6
1.02E+12
3.27e-06
0
0
1.10E-06
6.99
33
16.08
104.2
191.1
4.10E+11
3.49e-06
0
0
5.88E-05
17.45
32
15.17
122.6
192.1
4.06E+11
4.76e-06
0
0
1.32E-04
21.03
31
14.28
142.8
197.6
3.25E+11
9.07e-06
0
0
3.49E-04
26.29
30
13.43
165.0
203.6
3.28E+11
1.83e-05
0
0
8.40E-04
32.17
29
12.59
188.9
209.8
3.23E+11
3.54e-05
0
0
1.02E-03
33.66
28
11.78
214.6
216.6
3.45E+11
6.38e-05
0
0
1.46E-03
36.54
27
11.00
242.1
223.4
3.55E+11
1.12e-04
0
0
2.01E-03
39.31
26
10.23
271.2
230.0
3.88E+11
1.95e-04
0
0
2.19E-03
40.12
25
9.48
302.1
236.2
4.29E+11
3.21e-04
0
0
3.41E-03
44.39
24
8.76
334.6
242.4
4.66E+11
4.94e-04
0
0
1.92E-04
22.90
23
8.06
368.6
248.2
5.02E+11
7.14e-04
0
0
3.35E-04
26.03
22
7.38
403.9
253.4
5.40E+11
9.80e-04
0
0
1.85E-05
13.38
21
6.73
440.3
258.1
5.80E+11
1.31e-03
0
0
2.59E-07
5.01
20
6.10
477.5
262.2
6.21E+11
1.78e-03
0
0
8.58E-08
3.89
19
5.51
515.4
266.0
6.22E+11
2.37e-03
0
0
2.13E-07
4.79
18
4.94
553.7
269.6
6.46E+11
3.13e-03
0
0
5.98E-08
3.58
17
4.41
591.9
272.7
6.84E+11
4.02e-03
0
0
0
0
16
3.91
629.9
275.3
7.23E+11
5.14e-03
0
0
0
0
15
3.44
667.2
278.0
6.80E+11
6.31e-03
0
0
0
0
14
3.00
703.7
280.8
6.19E+11
7.49e-03
0
0
0
0
13
2.60
738.9
282.9
6.46E+11
8.67e-03
0
0
0
0
12
2.22
772.7
284.9
6.72E+11
1.00e-02
0
0
0
0
11
1.88
804.6
286.9
6.97E+11
1.17e-02
2.66E-02
9.60
0
0
10
1.57
834.6
288.6
7.20E+11
1.35e-02
2.05E-02
9.60
0
0
9
1.30
862.3
290.3
7.41E+11
1.45e-02
8.66E-02
9.60
0
0
8
1.05
887.6
291.8
6.30E+11
1.54e-02
1.21E-01
9.60
0
0
7
0.83
910.3
293.0
6.22E+11
1.62e-02
9.67E-02
9.60
0
0
6
0.64
930.3
294.2
6.34E+11
1.71e-02
4.22E-02
9.60
0
0
5
0.49
947.7
295.3
6.45E+11
1.79e-02
1.53E-02
9.60
0
0
4
0.35
962.3
296.1
6.54E+11
1.84e-02
6.62E-03
9.60
0
0
3
0.25
974.3
296.7
6.62E+11
1.89e-02
3.01E-03
9.60
0
0
2
0.10
990.9
297.7
6.69E+11
1.98e-02
5.69E-04
9.60
0
0
1
0.00
1002.0
298.9
6.76E+11
2.09e-02
1.56E-04
9.60
0
0
Heating rates and the changes in the radiative energy budget due to clouds
are evaluated with the clear-sky component subtracted. In both Solar-J and
RRTMG-SW, when re and CWC are given, the corresponding
wavelength-dependent properties are derived from tables or formulae. In
Solar-J, the scattering phase function is truncated at eight terms, but in
RRTMG-SW's two-stream model only the first term (A1/3=g) is retained.
For liquid water, RRTMG-SW adopts the parameterization scheme by Hu and
Stamnes (1993). For ice clouds, three different parameterizations are
available, and all are tested here (Ebert and Curry, 1992, henceforth EC92;
Key, 2002, henceforth Key02; Fu, 1996, henceforth Fu96).
These parameterization schemes in RRTMG-SW aim to fit the ice-cloud optical
properties – extinction coefficient, SSA, and g – as a polynomial function of
re and CWC. Note that Fu's parameterization is based on the generalized
effective diameter (Dge) but can be related to the input re
through Eq. (3.12) of Fu (1996). Ebert and Curry's parameterization has
been applied in the Community Atmosphere Model (CAM version 4.0 and prior
versions). According to the documentation in RRTMG-SW, Key's
parameterization was taken from the Mie-calculated spherical shapes of ice
particles from the Streamer radiative transfer codes (Key, 2002) and thus
should be similar to the Solar-J approximation. The two-stream solution to
the radiative transfer problem, as implemented in RRTMG-SW, requires that
the scattering optical depth (τscat) be reduced with what is
described as the delta-Eddington approximation (Huang, 1968; Joseph et
al., 1976). The purpose is to remove the forward-scattering peak typical of
large particles and have only isotropic-equivalent scattering. The
absorption optical depth is not changed to ensure correct absorption in the
limit of optically thin clouds. The basic problem with these approximations
is that the cloud optical depth is reduced by as much as a factor of 5,
and thus substantially more sunlight is transmitted through the cloud as a
direct solar beam rather than as scattered light. In RRTMG-SW (except for
the Fu96 ice-cloud approximation), the HG phase function
(Henyey and Greenstein, 1941) is further used to approximate the scattering
of aerosols and clouds because of its simple power series formulation. The
HG phase function does not represent realistic scattering because it does
not have the backward-scattering peak of real aerosols and clouds. As might be
expected, errors in two-stream approximations are ubiquitous and vary widely
with solar zenith angle (Boucher et al., 1998).
Results: Solar-J versus RRTMG-SW
Clear sky
Aerosol-free cloudless atmospheric heating profiles of Solar-J
(solid lines) and RRTMG-SW (dashed lines) and the difference, Solar-J minus
RRTMG-SW, for a typical July tropical atmosphere at four solar zenith angles
with Lambertian surface albedo of 0.06 (left and right sides). The plot is
further split into the stratosphere and the troposphere (top and bottom
rows). Note that the scale of the x-axis, K day-1, is 10 times larger for the
stratosphere on the top panels.
![]()
The clear-sky comparison between Solar-J and RRTMG-SW for overhead sun (SZA
= 0∘) is summarized in Table 4 and Fig. 2. Table 4 lists the
band-by-band radiation budget in W m-2, with Solar-J's spectral bins
labeled as S-bins and RRTMG's as B bands (B16–B29 follow the same band
numbers as in RRTMG's codes). For easy comparison, several Solar-J's
spectral bins of higher resolution from the UV range are lumped together to
best match the RRTMG's bin of similar range, and vice versa with RRTMG's B24
and B25 bins combined to compare to Solar-J's S18 bin. The incoming spectral
solar irradiance is slightly different for the two codes and so for easier
comparison we scale each of them to a total of 1360.8 W m-2 (Kopp and
Lean, 2011). RRTMG-SW adopts the solar source function from Kurucz (1992),
while Solar-J integrates high-resolution (0.05 nm) photon fluxes (Meier et
al., 1992) by wavelength to obtain the solar irradiance. Clear-sky summary
comparisons for the other three SZAs (21, 62,
84∘) are shown in Table 5 under clear-sky columns.
Spectral shortwave radiation energy budget in W m-2 under clear
aerosol-free July tropical conditions: Solar-J versus RRTMG. The solar constant is
set at 1360.8 W m-2. For easy comparison, some Solar-J bins are
combined to best match RRTMG's band of similar range and vice
versa. Note that the atmospheric absorption is further split into the stratospheric and tropospheric components (see numbers in italics).
(a) Clear-sky solar radiation budget comparison (W m-2)
Solar-J S-bins
S1–S4
S5–S9
S10–S16
S17
S18
λ (nm)
177–200
200–275
275–345
345–412
412–778
TOA (down)
0.06
5.14
44.31
77.17
608.68
TOA (up)
0.00
0.01
7.52
16.89
54.36
Atmosphere
0.06
5.14
18.01
0.05
31.96
-Stratosphere
0.06
5.14
16.97
0.04
9.41
-Troposphere
0.00
0.00
1.04
0.01
22.55
Surface
0.00
0.00
18.78
60.23
522.43
RRTMG bands
/
B28
B27
B26
B25+B24
λ (nm)
/
200–263
263–345
345–442
442–778
TOA (down)
/
3.06
49.88
128.79
562.34
TOA (up)
/
0.02
7.37
25.75
50.44
Atmosphere
/
3.05
23.24
0.00
28.77
-Stratosphere
/
3.04
22.11
0.00
8.60
-Troposphere
/
0.01
1.13
0.00
20.17
Surface
/
0.00
19.29
103.04
483.13
(b) Clear-sky solar radiation budget comparison (W m-2)
Solar-J S-bins
S19
S20
S21
S22
S23
λ(µm)
0.78–1.24
1.24–1.30
1.30–1.63
1.63–1.94
1.94–2.15
TOA (down)
349.96
25.59
102.96
56.01
22.40
TOA (up)
15.33
1.28
2.17
1.43
0.6
Atmosphere
87.94
2.36
60.53
29.41
9.48
-Stratosphere
0.00
0.12
0.29
0.20
0.41
-Troposphere
87.95
2.23
60.24
29.21
9.07
Surface
246.69
21.96
40.25
25.17
12.32
RRTMG bands
B23
B22
B21
B20
B19
λ(µm)
0.78–1.24
1.24–1.30
1.30–1.63
1.63–1.94
1.94–2.15
TOA (down)
343.86
24.16
102.37
55.32
22.31
TOA (up)
14.91
1.20
2.03
1.40
0.57
Atmosphere
86.60
2.22
61.73
29.09
9.52
-Stratosphere
0.00
0.12
0.30
0.20
0.42
-Troposphere
86.60
2.10
61.43
28.89
9.11
Surface
242.35
20.74
38.61
24.85
12.22
(c) Clear-sky solar radiation budget comparison (W m-2)
Solar-J S-bins
S24
S25
S26
S27
All bands
λ (nm)
2.15–2.50
2.50–3.08
3.08–3.85
3.85–12
0.18–12
TOA (down)
23.50
20.20
12.25
12.58
1360.80
TOA (up)
0.75
0.00
0.19
0.05
100.53
Atmosphere
8.32
20.17
7.28
10.36
291.06
-Stratosphere
0.07
1.65
0.17
1.28
35.80
-Troposphere
8.25
18.52
7.11
9.08
255.26
Surface
14.43
0.03
4.78
2.17
969.23
RRTMG bands
B18
B17
B16
B29
All bands
λ (nm)
2.15–2.50
2.50–3.08
3.08–3.85
3.85–12
0.20–12
TOA (down)
23.60
20.25
12.04
12.82
1360.80
TOA (up)
0.76
0.00
0.18
0.05
104.45
Atmosphere
7.96
20.22
7.17
10.57
290.27
-Stratosphere
0.06
1.66
0.16
1.30
37.91
-Troposphere
7.84
18.56
7.01
9.26
252.36
Surface
14.88
0.03
4.69
2.22
966.08
In Table 4, the incoming spectral solar irradiance at top of the atmosphere
(TOA down) is balanced by components of (1) the reflected flux going back to
space (TOA up positive), (2) the absorption in the atmosphere, separated
into the stratosphere and troposphere, and (3) surface heating. Several
differences in the configuration of spectral bands between Solar-J and
RRTMG-SW affect these results. For one, RRTMG-SW does not include the small
amount of solar irradiance at wavelengths (λ)<200 nm
(0.06 W m-2) and thus ignores photodissociation of O2 molecules
in the Schumann–Runge bands and part of the Herzberg continuum that heats
the upper stratosphere and mesosphere. Second, for λ=200–345 nm,
Solar-J has 3 W m-2 (6 %) less solar energy than RRTMG-SW and the
difference appears in RRTMG's larger heating of the stratosphere. Third, the
bin division between 345 and 778 nm is at 412 nm for Solar-J (i.e., between
S17 and S18), but at 442 nm for RRTMG-SW (between B26 and B25+B24). This
interval, 412–442 nm, has very low O3 absorption, significant Rayleigh
scattering, and a large amount of solar energy (∼ 51 W m-2). Both the shorter-wavelength bins (S17 or B26) reflect about
20 % of the incoming radiation, but in the adjacent bin with the Chappuis
O3 band it is only about 9 %. Thus, placing the 412–442 nm interval
with the Chappuis band results in greater atmospheric absorption and less
reflection. The benefit of moving the Solar-J (and Cloud-J) band edge to 442 nm should be investigated.
Radiation budget comparison (W m-2) between Solar-J and
RRTMG-SW for top of atmosphere (TOA), atmosphere, and surface across four
SZAs. Also shown is the cloud radiative effect (CRE) of a typical marine
stratus cloud, for which the atmospheric absorption is split into
above cloud, in cloud, and below cloud, and the values are shown in italics.
SZA
0∘
21.2∘
62.2∘
84.0∘
Flux (W m-2)
1360.8
1268.4
634.2
149.1
Clear-sky radiation budget (W m-2)
Solar-J
RRTMG
Solar-J
RRTMG
Solar-J
RRTMG
Solar-J
RRTMG
TOA (up)
100.5
104.5
96.2
100.3
63.9
67.3
28.2
28.5
Atmosphere (absorbed)
291.1
290.2
276.6
275.3
166.5
164.0
56.6
54.9
Surface (absorbed)
969.2
966.1
895.7
892.8
403.8
402.9
64.3
65.6
Cloud radiative effect (CRE) of a marine stratus cloud (W m-2)
Solar-J
RRTMG
Solar-J
RRTMG
Solar-J
RRTMG
Solar-J
RRTMG
TOA
+473.4
+459.4
452.7
+441.2
+262.7
+255.8
+52.2
+50.3
Atmosphere
+87.8
+88.2
+77.7
+78.2
+20.3
+18.5
-3.2
-3.3
Above cloud
+21.1
+23.8
+17.7
+22.8
+11.3
+12.0
+3.0
+1.6
In cloud
+77.5
+73.7
+70.5
+64.7
+16.1
+12.9
–3.9
–3.0
Below cloud
–10.8
–9.3
–10.6
–9.2
–7.1
–6.4
–2.2
–1.8
Surface
-561.2
-547.6
-530.4
-519.4
-282.9
-274.4
-49.1
-47.0
Cirrus ice cloud optical properties: total optical depth τ
for Solar-J and delta-scaled τ′ for RRTMG-SW, asymmetry
factor g, and absorption optical depth, τabs, for bins S18 to S27.
See Table 1 for wavelength ranges and RRTMG-SW-equivalent bins.
S-bins
S18
S19
S20
S21
S22
S23
S24
S25
S26
S27
λeff
599 nm
973 nm
1.27 µm
1.45 µm
1.77 µm
2.04 µm
2.31 µm
2.75 µm
3.40 µm
5.36 µm
Total optical depth (τ for Solar-J and reduced τ′ for RRTMG schemes)
Solar-J
0.4287
0.4322
0.4345
0.4360
0.4383
0.4404
0.4425
0.4380
0.4470
0.4591
EC92
0.2488
0.2462
0.2462
0.2385
0.2385
0.2276
0.2276
0.3313
0.3313
0.3313
Fu96
0.1535
0.1581
0.1563
0.1627
0.1640
0.1575
0.1932
0.3709
0.3382
0.3177
Key02
0.0923
0.0943
0.0950
0.1041
0.1032
0.1277
0.1065
0.1783
0.2159
0.2266
Asymmetry factor, g =A1/3
Solar-J
0.7643
0.7642
0.7641
0.7640
0.7639
0.7639
0.7638
0.7639
0.7635
0.7631
EC92
0.4406
0.4425
0.4425
0.4484
0.4484
0.4579
0.4579
0.4907
0.4907
0.4907
Fu96
0.4591
0.4680
0.4803
0.4987
0.5168
0.5670
0.5870
0.6744
0.3411
0.0000
Key02
0.4694
0.4692
0.4691
0.4707
0.4707
0.4757
0.4731
0.4866
0.4807
0.4858
Total absorbing optical depth (τabs)
Solar-J
0.0000
0.0003
0.0018
0.0257
0.0201
0.0758
0.0317
0.2163
0.2075
0.2126
EC92
0.0000
0.0004
0.0004
0.0247
0.0247
0.0558
0.0558
0.3063
0.3063
0.3063
Fu96
0.0000
0.0003
0.0022
0.0232
0.0231
0.0743
0.0289
0.1294
0.1743
0.1972
Key02
0.0000
0.0001
0.0011
0.0178
0.0162
0.0619
0.0290
0.1491
0.1788
0.1983
These differences, particularly the 412–442 nm interval, explain most of the
total budget difference where, overall, Solar-J reflects 4 W m-2 (4 %)
less back to space, absorbs 2 W m-2 (6 %) less in the stratosphere, 3 W m-2 (1 %) more in the troposphere, and 3 W m-2 (1/2 %) more
at the surface. For SZAs of 21 and 62∘ (Table 5),
Solar-J continues to reflect 3–4 W m-2 less energy back to space, but at
a large SZA of 84∘ the two models match closely. While spherical
effects may play some role in this shift, we suspect that Rayleigh
scattering may contribute. The forward–backward enhancement in Rayleigh
scattering is not represented in two-stream isotropic scattering. Thus, RRTMG
– Solar-J differences will shift as the primary beam shifts from vertical
to horizontal as a much greater fraction of the visible light is scattered.
At low sun, the Rayleigh optical slant path along the solar beam is much
greater than 1 for bin S17 and even ∼ 1 for S18.
Ozone photolysis rates (JO3) from Solar-J (a) and
the corresponding atmospheric heating rates under clear sky (b)
from Solar-J (solid lines) and RRTMG-SW (dashed lines) for large solar
zenith angles at four different altitudes. RRTMG-SW's heating rates reduce to
zeros at an SZA of 90∘ due to the lack of sphericity correction in the
plane-parallel approximation, whereas the impact of sphericity on the direct
solar beam path is included in Solar-J.
![]()
Figure 2 compares the vertical profiles of clear-sky heating rates (K day-1)
for overhead sun (SZA = 0∘) with the abscissa axis scaled
separately for the stratosphere and the troposphere. Both models produce
similar structures with the heating maximum of ∼ 30 K day-1 in
the stratosphere at about 45 km altitude and ∼ 3 K day-1 in the
lower troposphere. The ability of Solar-J to match these structures
demonstrates that Solar-J has correctly implemented the RRTMG-SW spectral
model. Solar-J minus RRTMG-SW differences are shown in the right two panels
of Fig. 2. As shown in Fig. 2d, the consistent difference of < 0.1 K day-1
near the surface come from Solar-J's simplification of combing
RRTMG's 14 sub-bins with O2 and H2O absorption in bins B24–B25
into the five sub-bins of S18. In the troposphere these are small, but in the
stratosphere there is a clear bias with Solar-J producing more heating above
40–50 km and less heating below. Differences at the top, above 50 km, are
due in part to the lack of λ<200 nm radiation in
RRTMG-SW, and in part due to a better resolution of the O3 and
O2 cross sections in Solar-J. Overall, RRTMG-SW deposits more energy in
the lower stratosphere, below 35 km, except at larger SZA where it deposits
less. Thus, for the tropics and midlatitudes, RRTMG will overheat the lower
stratosphere, possibly changing the stability and wave propagation to the
high latitudes (Hsu et al., 2013). At high latitudes, RRTMG error is in the
opposite direction, resulting in a colder polar stratosphere with possibly
stronger winter vortices.
Solar-J traces the solar beam through a spherical atmosphere back to the
sun. RRTMG assumes a flat Earth. Both then calculate the subsequent
scattering and absorption in a plane-parallel, flat atmosphere, but with
different solar source terms at each level. Solar-J is able to simulate both
photolysis and heating rates throughout twilight, even when the sun is no
longer directly visible at the layer. Figure 3a shows the smooth decline in
O3 photolysis rates as the SZA passes from 84 to
95∘. Figure 3b shows the corresponding heating rates from both
RRTMG-SW and Solar-J. The lack of sphericity in RRTMG leads to large
systematic negative biases in the heating rates at low sun. Sphericity
errors extend up to an SZA of 80∘ but are largest of course at
twilight. The high-latitude atmosphere will have SZAs greater than 80∘ for much of the day, and thus RRTMG may lead to a cold bias
for the high latitudes.
Low-level marine stratus cloud
(a) Marine stratus cloud profile in terms of liquid-water path
(LWP, g m-2) and effective radius (re, µm). The optical
depth and delta-scaled optical depth (τ, τ′) are
shown in parentheses for the top five cloud layers. (b) Cloud heating
profiles from Solar-J (solid lines) and RRTMG-SW (dashed lines) at four
SZAs.
![]()
For the stratus cloud, the liquid-water path (LWP, g m-2) in each layer
is derived from the LWC and height of each layer (Table 3) and is plotted
versus altitude in Fig. 4a as described in Sect. 2.3. The resulting cloud
optical depth in each layer, τ, (evaluated at 600 nm) is also written
in pairs with Solar-J's as the first number and RRTMG's reduced delta-scaled
optical depth (τ′) as the second. Both RRTMG and Solar-J start with
same value of τ because the Mie-based scattering phase functions for
liquid water are unambiguous and both adopt the same values for re, Q,
and density of liquid water. The re is set to 9.6 µm through
most of this cloud profile. The LWC increases from the surface to a maximum
of 0.12 g m-3 at 1.25 km and falls to zero by 2.3 km altitude.
Because of the increasing thickness of the model layers with altitude, the
LWP and layer τ are not as smoothly peaked. We deem this profile
realistic from comparing to the observed range for coastal marine low clouds
(see Fig. 4 of Hu et al., 2007 for July liquid cloud radii distribution
and Fig. 1a of Painemal et al., 2016 for LWP).
Table 5 summarizes the clear-sky radiative budget and the stratus cloud
radiative effect (CRE, W m-2, calculated as change relative to clear
sky) for Solar-J and RRTMG-SW for the four SZAs used here. At overhead sun
(SZA = 0∘) with the solar input at 1360.8 W m-2, the effect
of this low-level marine stratus cloud (per Solar-J) is to reflect an
additional 473 W m-2 back to space, absorb an additional 88 W m-2
in the atmosphere primarily within the cloud, and thus reduce the surface
heating from 969 to 408 W m-2. As in the clear-sky comparison, both
models look broadly similar but with some large systematic biases. For SZAs
of 0–62∘, Solar-J reflects ∼ 10 W m-2
(2–3 %) more sunlight back to space, both models calculate about the same
increase in atmospheric absorption, and RRTMG-SW consistently absorbs less
energy within the cloud but more above it; thus, Solar-J calculates
greater reduction in surface heating (also about 2–3 %) than RRTMG-SW.
These differences in solar heating are large compared with anthropogenic
climate forcing from greenhouse gases (∼ 4 W m-2) (Myhre
et al., 2013), but of course stratus clouds occupy only a fraction of the
surface. Within the atmosphere, there is a large difference in the
distribution of CRE, with Solar-J calculating 5 % (SZA = 0∘) to
25 % (SZA = 62∘) more in-cloud heating than RRTMG. The profile
of heating rates (Fig. 4b) shows a double peak at 1.9 km (visible τ ∼ 1) and 1.2 km (τ ∼ 6) even though the
LWC has a smooth maximum at 1.1 km. The longer wavelength bins (S25–S27) are
fully absorbed in the uppermost part of the cloud (τ<1),
while the shorter wavelengths (S19–S24) penetrate the cloud to scattering
optical depths of order τ∼ 8. RRTMG consistently
calculates lower in-cloud rates; see below. It is possible that Solar-J's
greater heating in stratus clouds may change the dynamics of stratus clouds
relative to a model using RRTMG-SW (Harrington et al., 2000). At low sun
(SZA = 84∘), Solar-J calculates 4 % greater reflectance change,
both models calculate less atmospheric heating within the cloud but more
heating above it, and the surface heating in Solar-J is about 2 W m-2
less than in RRTMG-SW. Both models show enhanced heating only in the
uppermost cloud layers above 1.7 km (Fig. 4b).
We believe that the RRTMG-SW biases identified here are errors caused by the
two-stream approximation. This is supported by the study of Li et al. (2015;
see their Fig. 2), who show small negative errors in absorption from the
calculation of delta-Eddington (two-stream) approximation in the case of
the single-layer liquid cloud (re=10 µm, τ∼4)
with cos(SZA) > 0.2 (i.e., our SZAs of 0–62∘). For our
SZA of 84∘, this absorption bias reverses as is also found by Li et
al. (2015) for cos(SZA) < 0.2. In their study, the two-stream
calculations are compared to the 128-stream DISORT (discrete–ordinate)
benchmark calculations using accurate phase functions and no delta scaling (similar to the study of Wild et al., 2000). One other source of
error in RRTMG's model is the choice of delta-scaling factor, which they
base on the HG phase function using only g. Alternatively, one can use the
second moment of the true Mie phase function (Wiscombe, 1977). We revised the
RRTMG-SW code to do this using Solar-J's scattering phase functions and
found a modest reduction in this error from -14 to -9 W m-2
for reflected sunlight (SZA = 0∘).
Tropical cirrus clouds
(a) Profiles of ice-water content (IWC, g m-3) and (b)
effective radius (re, µm) as prescribed for both Solar-J and
RRTMG-SW. The in-cloud region, about 4–18 km, is enclosed by two horizontal
dashed lines. (c) Profiles of cumulative optical depth τ at 600 nm
from Solar-J and from the three RRTMG-SW parameterizations for which τ is
delta scaled. (d) Cirrus cloud heating rate profiles (K day-1) at
an SZA of 0∘.
![]()
For the cirrus cloud comparison, we use all three ice-water parameterization
options in RRTMG-SW and Solar-J's single parameterization. Figure 5a, b show
the prescribed profiles of model input of IWC and re (Table 3). The
cumulative overhead τ at 600 nm is shown in Fig. 5c. The delta scaling
varies considerably across the RRTMG parameterizations: Solar-J's
unscaled τ ∼ 0.43 compares with EC92's τ∼ 0.25, Fu96's τ∼ 0.15, and Key02's τ∼ 0.09 (see also Table 6). Thus, the fraction of sunlight
scattered by the cloud varies widely across all four. The asymmetry
parameter g from Mishchenko's phase functions for hexagonal and irregular
ice used in Solar-J ranges from 0.75 to 0.81 (as compared to 0.88 for
equivalent-size liquid-water clouds), but g values for all RRTMG ice clouds
range from 0.4 to 0.6 for wavelengths where scattering is important
(S12–S24). The absorbing optical depth, τabs, is a very important
diagnostic because in an optically thin cloud the overall heating should be
proportional to it. Table 6 shows that all four ice cloud models have
similar τabs up to S22, and if we average S23 and S24 (which
appears to have been done in EC92), then all four models remain similar in
terms of solar absorption. As noted for the stratus cloud, all models
predict a large, factor of 5, jump in τabs for S25–S27 (λ>2.5 µm), which are the most important bins for cirrus
cloud heating. At these wavelengths, EC92 has the largest absorption τabs, about 0.3, followed by Solar-J's 0.21.
Percent changes (%) in shortwave radiation energy budget
relative to the aerosol-free clear sky (surface albedo of 0.06) caused by a
cirrus cloud using four different models: Solar-J and the three RRTMG-SW
parameterizations for ice clouds. Results are shown for four different solar
zenith angles. Changes in the vertical column are divided into five regions:
top of atmosphere, atmospheres above, within, and below the cirrus cloud, and
at the surface. Single numbers in bold shown in the corner of each panel are
the clear-sky energy budget in W m-2 averaged over Solar-J and RRTMG-SW
for each region. Note that different y-axis scales have been used for large
SZAs.
![]()
Cloud heating rate profiles at an SZA of 0∘ are shown in Fig. 5d,
and the large range clearly reflects the τabs for S25–S27. The
cirrus CRE for four SZAs and for five components (reflected at top of
atmosphere, absorbed in above-cloud atmosphere, in-cloud atmosphere,
below-cloud atmosphere, and absorbed at the surface) are shown as a set of 20
bar charts in Fig. 6. The CRE percent changes relative to clear sky are
shown as four color bars representing Solar-J (red), EC92 (blue), Fu96
(green), and Key02 (yellow). The clear-sky energy flux (W m-2) averaged
over the four models is shown in a larger font in each bar chart. For
example, at an SZA of 21∘ the energy absorbed by clear-sky
atmosphere over the altitude range of the cirrus cloud is 98.4 W m-2.
The CRE in W m-2 within the cirrus cloud for Solar-J is then 98.4 × 10.7 % (red bar) =+ 10.5. The y axes in Fig. 6 have different
scales at different SZAs.
A key cirrus CRE is the increase in albedo, the top-of-atmosphere reflected
sunlight, as shown for all models and a range of SZAs in Fig. 6 (top row).
The percent increase across RRTMG-SW models (13–131 %) scales in
proportion to τ, with EC92 being the largest and Key02, the smallest.
This relative order stays the same across all SZAs, but the range across
RRTMG-SW models decreases and the relative percent increases for larger SZAs.
The Solar-J model also increases in percent with SZA, but the pattern is
different from that of RRTMG-SW models. At overhead sun, Solar-J has about
the same CRE percent as EC92 even though it has a 1.7 times greater τ. This
can be understood in that Solar-J cirrus is highly forward scattering and
less of the scattered light is reflected backward and upward. As the SZA
increases to 21–62∘, however, the peak in backscatter at
180∘ becomes less important and Solar-J shifts lower
relative to EC92 to look like Fu96. At very large SZA of
84∘, with most of the sunlight being scattered at least
once within the cloud, the Solar-J model again looks like the largest τ, model EC92. To first order, the Solar-J model is calculating the correct
SZA dependence of the CRE by using both a more realistic scattering phase
function and eight-stream scattering. The use of Mishchenko's sample T-matrix
phase function may not be a perfect choice for cirrus, but it is clearly
more realistic than the isotropic scattering used in RRTMG-SW. Solar-J
captures the cirrus albedo curve similar to Fig. 2 of Mishchenko et al. (1996) for τ=0.1
in which the slope increases rapidly as the cosine
(SZA) approaches 0. While the RRTMG-SW two-stream models can be tuned to be
correct at some SZAs, they will have errors of 15 W m-2 at
others. The change in surface heating (fifth row) looks like the reverse
of the top-of-atmosphere bars with similar relative weighting of the
RRTMG-SW models. Again, it shows that two-stream scattering cannot mimic the
correct SZA dependence of reduced surface heating under cirrus.
With greater reflection of sunlight, the atmospheric heating above the cloud
increases in all cases. With RRTMG-SW, the scattered light has only one
angle, and thus the above-cloud heating (second row of Fig. 6) is
strictly proportional to the top-of-atmosphere increases. With Solar-J, the
reflected light is calculated at four zenith angles with the flux at larger
zenith angles producing more heating (i.e., longer slant path through the
atmosphere). This is most apparent in the case of the SZA of 84∘
where the low-angle scattering driven by the low solar elevation produces
relatively much more atmospheric heating.
In-cloud heating (third row) is expected to be proportional to τabs at high sun (SZA = 0–62∘), and for
flux-weighted bins S25–S27 these τabs are 0.31 (EC92), 0.21
(Solar-J), 0.17 (Key02), and 0.16 (Fu96). While the actual heating of the
cirrus ice particles may be in similar proportionality, all we calculate is
the total change of heating over the in-cloud layers. As seen in Fig. 6,
there is substantial clear-sky absorption by atmospheric water vapor in the
cloudy layers (∼ 100 W m-2) at high sun. Thus, the small
perturbation caused by the cloud (< 10 %, third row) results
from in-cloud heating of ice particles (proportional to τabs)
countered by reduced heating of the water vapor in the region because of the
increased upward scattered light (top row). The extreme case of the SZA of 84∘ has all models calculating 20–35 % reductions in
heating because of the reduced sunlight.
Computational costs
The major computational costs of Solar-J and similar codes within a
chemistry–climate model centers on three key components: matrix operations
required for multi-stream scattering, wavelength bins representing the
spectrum of optical properties, and approximation of the multitude of
independent column atmospheres (ICAs) resulting from a complex overlapping
cloud field within a grid cell. What is a reasonable requirement for
multi-stream scattering in a climate model? From this work as well as a
history of publications noted above, the analytic two-stream approximation has
errors that cannot simply be corrected or averaged over, that create
large-scale biases in cloud radiative forcing with latitude, and that
significantly misrepresent the direct–diffuse ratio of solar radiation at
the surface. The original Fast-J work (Wild et al., 2000) examined a range
of multi-stream scattering models and found that for typical clouds, an
eight-stream solution was able to match within a few percent that of a
100-stream code for the mean intensity above, within and below the
cloud. A major advantage of the eight-stream system was that no delta scaling was needed
and a simply truncated scattering phase function could be used directly. The
parent RRTM-SW code has the option of using a more accurate 16-stream
scattering code but would in general be computationally much more expensive
than the eight-stream Solar-J. The basic costs of the matrix inversions (Fast-J
via Feautrier, 1964) or eigenvalue solutions (RRTM via DISORT; Stamnes et
al., 1988) scale as
n3. For the same eight-stream solution, DISORT performs
eigenvalue decomposition of 8×8 matrices at each level at a cost of order
83, while the Feautrier approach solves the finite-difference equations
with 4×4 matrices at split levels for a cost of order 2×43. As a
first guess, the Feautrier code should run 4 times faster than the equivalent DISORT
code. We examine the costs and options of wavelength binning and cloud-field
approximations below.
Solar-J versus RRMTG-SW
Cloud-J (and hence Fast-J) has been extensively tested in the UC Irvine
chemistry-transport model (CTM). Cloud-J timings are estimated by comparing
full cloud quadrature (2.75 calls per column atmosphere per time step; see
below) versus an average-cloud approximation (1 call). We find that 12 %
of the CTM wall-clock time is spent in Cloud-J using average clouds and
28 % when using cloud quadrature. Because the UCI CTM runs a minimalist
tropospheric chemistry and a linearized stratospheric chemistry (see Hsu and
Prather, 2010), it keeps track of only 32 species. More complete models like
Oslo CTM3 (Søvde et al., 2012) and WACCM (Marsh et al., 2013) calculate
transport and chemistry of about 100 species. In CTMs like these, the
fractional cost of Cloud-J should be only 4–7 %. Comparing Solar-J to
Cloud-J in single-atmosphere tests shows what is expected; Solar-J costs are
3.5 times greater because of the much larger number of spectral bands needed for
heating (100 versus 18). A minor feature is that cloudy atmospheres cost about
10 % more than clear atmospheres because Cloud-J inserts extra layers at
the top of clouds to enhance the accuracy of the finite-difference
equations.
In a series of comparisons on a single-socket multi-threaded CPU, we find
that Solar-J takes 5 times more wall clock time than RRTMG-SW. This is not
surprising given the cost of solving an eight-stream versus two-stream RT problem. An
additional cost of Solar-J (not included above) is spherical geometry. With
RRTMG-SW, 50 % of the grid cells are in sunlight and require RT solutions.
With Solar-J, however, important photochemistry and solar heating occur in
the atmosphere when the surface is past sunset (see Fig. 3) involving
about 56 % of the grid cells, a 12 % increase in radiatively active
grid cells. One could expect that RRTMG-SW will correct this error and end
up with similar increases in coverage and cost.
Most climate models, even at the highest resolutions, have individual grid
cells with fractional, overlapping cloud layers. Although 3-D RT models can
be used to solve for the average heating and photolysis rates, most climate
models decompose the cloud structures into ICAs, for example, through
cloud-resolving models (Khairoutdinov et al., 2005) or from cloud fractional
coverage and a decorrelation distance for overlapping cloud layers (Prather,
2015). The ICAs are horizontally homogeneous and can be solved using the 1-D
RT codes of RRTMG-SW or Solar-J. Comparisons between Solar-J and RRTMG-SW for
clouds in Sect. 3 are done with a single 1-D plane-parallel, ICA-like
atmosphere (i.e., 100 % cloud fraction in each cloud layer), an idealized
case.
Although the different approaches for fractional cloud cover were not
directly tested here, it is worth looking at how Solar-J and RRTMG might
treat cloud fields in climate models. The Monte Carlo ICA (McICA; Pincus et
al., 2003) method selects both ICAs and spectral intervals randomly in each
grid square. Every spectral interval is sampled only once, and each may have
a different ICA selected according to its fractional area (frequency of
occurrence). With 100+ bin–ICA combinations, the ICAs are well sampled,
but there may be instances in which a few key large-energy bins are not
sampled accurately. The McICA approach, when suitably averaged over time,
has no mean bias in average heating rates but very large root mean square
(rms) errors: e.g., ±105 W m-2 in surface heating with an SZA of 45∘; ±3 K day-1 in layers with partly cloudy
atmospheres (Pincus et al., 2003). It is cost efficient in that each
wavelength bin requires only one ICA calculation. Solar-J uses cloud
quadrature, introduced by Neu et al. (2007), selecting up to four cloud
profiles (QCAs) based on total optical depth to represent four types of
atmospheres: mostly clear, typical cirrus clouds, typical stratus clouds,
and very thick frontal or cumulus clouds. While each grid cell may have up
to four QCAs, on average there are only 2.75. Solar-J then calculates all
wavelength bins using all QCAs to compute the average. Cloud-J (Prather
2015) compared several approximations for calculating average photolysis
rates (Js) within a sample of 640 tropical atmospheres where the generated
number of ICAs per grid cell ranged from 1 to 3500 and averaged 170.
Compared to the exact answer defined by separate calculations with all the
weighted ICAs, cloud quadrature achieves rms errors in instantaneous
cell-averaged Js of 0 to 3 % throughout the troposphere, with most levels
being 0–1 %. When Cloud-J is run selecting random ICAs (using all
wavelengths for each ICA, not the McICA approach), 50 random ICAs (18 times
greater cost) are needed to achieve the accuracy of cloud quadrature.
From the point of view of chemistry–climate models, large rms errors in Js
cannot be tolerated because the chemistry is non-linear and such errors are
not likely to average. In climate models, there are threshold processes
like aerosol and ozone heating preventing cloud formation (e.g., Koch and
DelGenio, 2010), for which heating noise may not simply average out. Errors
in heating rates do not always have symmetric responses in terms of climate
(e.g., Hsu et al., 2013). Although Pincus et al. (2003) tested climate
forecasting with an early version of McICA, it is not clear how forecast
skill with modern, high-resolution models is impacted by the biases in
RRTMG-SW. Alternatively, RRTMG-SW could adopt cloud quadrature with 2.8 times
greater cost and eliminate most of their rms errors in heating.
All of these standard features of Solar-J (eight streams, spherical geometry,
cloud quadrature) increase the computational cost, but one can argue that
the improved fidelity in the solar heating of the atmosphere and radiative
forcing of the climate is worth the cost. The question is what fraction of
the total computational cost of a climate simulation would be used by
Solar-J. If we estimate the fractional cost of RRTMG in a full
atmosphere–ocean climate simulation to be 1–3 %, then replacing it with
Solar-J (5 times greater) and including cloud quadrature (2.8 times greater), would increase this to
13–39 %. At the lower end of this range, the substantially improved and less
noisy physics is probably worth it, but at the upper end it is prohibitive.
In either case, it is worthwhile to pursue a range of computer science and
algorithmic approaches to reduce these costs as discussed in Sect. 4.2
and 4.3 below.
Computer science options
A profiling of the Solar-J code shows that the Fast-J core, consisting of a
scattering matrix generator and block-tridiagonal solver, is the dominant
cost. These two subroutines are already well optimized in terms of single
CPU multi-threading; however, porting Fast-J to computers with graphical
processing units (GPUs) has shown promise for greater speed. One effort
targeted a single GPU and demonstrated speedups via CUDA (Compute Unified
Device Architecture) tuning of ∼ 50 times more relative to the CPU time
if a large number of column atmospheres (200+) were concurrently evaluated
(Artico et al., 2015). Another effort used a field-programmable gate array
(FPGA) with the advantage that it applies to a single column calculation.
The FPGA resulted in a ∼ 4 times greater speedup and a rather dramatic
35 times more energy savings compared to the multicore processor computation (Rezaei et
al., 2016). Fast-J was also optimized for the Xeon Phi on the Babbage test
platform at DOE National Energy Research Scientific Computing Center (NERSC) and achieved ∼ 3 times faster speedups with only a
subset of the cores.
Great computational acceleration could be realized with GPU systems when a
number of column atmospheres are being simultaneously evaluated. For each
grid cell, Solar-J calculates about 100 wavelength bins and an average of
2.75 ICAs per grid square. Giving each CPU/GPU node a 3×3 grid cell square
(∼ 2500 column atmospheres) could achieve 10 times greater or faster
speedups for Solar-J and be appropriate for a massively parallel climate
simulation (e.g., 32 000 nodes for a 50 km global grid). With such speedups,
Solar-J costs would be comparable or possibly less than those of the current
RRTMG-SW and thus become a marginal cost in the climate simulation.
Other parameterizations for wavelength bins
Solar-J uses its own optimization of wavelength bins at ultra-violet and
visible wavelengths (0.18 to 0.8 µm), which is based on previously
established experience with O2 and O3 cross sections and the need
to calculate accurate J values. We accept that RRTMG-SW and its parent code
RRTM represent current best practice and accuracy in characterizing the
absorption of infrared sunlight (0.8 to 12 µm) in the Earth's
atmosphere and have adopted the RRTMG-SW code exactly for bins and all
gaseous absorbers. Solar-J's computational cost is clearly driven by the
additional 82 infrared bins adopted from RRTMG-SW. Alternative methods of
parameterizing these infrared bins need to be examined: e.g., 14 bins (Chou,
1992; Grant and Grossman, 1998), 34 bins (Fu and Liou, 1992), and 36 bins (Cole,
2005). Any of these would result in 1.5–2.5 times more savings for Solar-J. We
recognize that the infrared bins adopted in RRTMG-SW are based on accurate
representation of the line-by-line calculations, and thus adopting these
reduced-bin parameterizations will introduce new errors, but further
research will be needed to determine whether these errors maybe an
acceptable trade-off for speed gain.
Many of these other parameterizations (e.g., Chou, 1992) are based only on
water vapor and do not include the other trace gases that are represented in
RRTMG-SW: O2 in the visible and infrared, CH4, and CO2. These
gases add to the complexity of the RRTM-SW model, and thus we investigate
their importance in tropospheric heating rates. For our clear-sky case here
(Table 4, Fig. 2), we find an average
tropospheric heating rate of 2.4 K day-1. The contribution of CH4 to this
total is 0.1 %; that of CO2 is complex because of the stratospheric
self-shielding but is less than ±1 % in the troposphere, and that
of O2 is about 3 % uniformly throughout the troposphere. If we can
find a way of treating the O2 heating separately, then the effort to
find an abbreviated number of spectral intervals can focus on water vapor.
Conclusions
We present a new solar radiation module. Solar-J version 7.5 aims for
consistent calculation of atmospheric photolysis and solar heating rates by
combining the strengths of both Cloud-J and RRTMG-SW. In a chemistry–climate
model, Solar-J supplies the needs of solar heating of the atmosphere and
surface, photolysis rates, and photosynthetic activity. Climate models are
increasingly including short-lived gases and aerosols as radiative forcing
components, and the accurate simulation of these under different climates
requires some level of interactive chemistry and photolysis rates.
The components of Solar-J are chosen and balanced to achieve the best
possible overall accuracy for a module intended as a standard component of
chemistry–climate simulations. From Cloud-J, we take the eight-stream scattering
model, semi-spherical geometry, ultraviolet transmission, and cloud
quadrature. From RRTMG-SW, we take the detailed spectral intervals for the
visible and infrared developed from the RRTM reference code. Solar-J matches
RRTMG-SW except where the improved physics leads to more accurate results.
Selecting the best physics for all these components comes with a cost: a
simple comparison shows the cost of Solar-J is 5 times that of RRTMG-SW for a
single atmosphere, and if the cloud quadrature scheme for overlapping cloud
fields (Neu et al., 2007; Prather, 2015) is applied to either code, the cost
increases additionally by 2.8 times. We show that Solar-J can be optimized on
GPUs and achieve speeds similar to RRTMG-SW. While this opens up great
opportunities for the new generation of high-performance computers, it also
complicates the simple implementation of Solar-J in a climate model.
Solar-J is a starting point. In assessing the fidelity of Solar-J in terms
of interaction with the many components of the climate system, we can focus
on the three major sources of costs/error (spectral intervals, multi-stream
radiative transfer, and complex cloud systems) and, in parallel, on the
opportunities for accelerated performance with new computational
architectures. Ideally, the community would optimize computational costs
across modules to have comparable (small) errors in all. In addition, these
parameterization errors need to be evaluated for the impact they might have
on climate simulations (e.g., Pincus et al., 2003). For Solar-J, the next
steps consist of (i) moving the S17–S18 boundary to the beginning of the
O3 Chappuis absorption near 0.5 µm, and (ii) developing a more
realistic and diverse range of cirrus clouds and their optical properties
(e.g., Yang et al., 2015). Another inquiry is to test some of the
published, simpler models for water vapor absorption against RRTMG-SW. A
larger project will be to put Solar-J into a climate model and evaluate how
errors in modeling solar radiation may affect the climate simulations.