GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus GmbHGöttingen, Germany10.5194/gmd-8-2587-2015Photolysis rates in correlated overlapping cloud fields: Cloud-J 7.3cPratherM. J.mprather@uci.eduhttps://orcid.org/0000-0002-9442-8109Earth System Science Department, University of California, Irvine, California, USAM. J. Prather (mprather@uci.edu)14August2015882587259529April201527May201531July20155August2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/8/2587/2015/gmd-8-2587-2015.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/8/2587/2015/gmd-8-2587-2015.pdf
A new approach for modeling photolysis rates (J values) in atmospheres with
fractional cloud cover has been developed and is implemented as Cloud-J – a
multi-scattering eight-stream radiative transfer model for solar radiation
based on Fast-J. Using observations of the vertical correlation of cloud
layers, Cloud-J 7.3c provides a practical and accurate method for modeling
atmospheric chemistry. The combination of the new maximum-correlated cloud
groups with the integration over all cloud combinations by four quadrature
atmospheres produces mean J values in an atmospheric column with
root mean square (rms) errors of 4 % or less compared with 10–20 % errors
using simpler approximations. Cloud-J is practical for chemistry–climate
models, requiring only an average of 2.8 Fast-J calls per atmosphere vs.
hundreds of calls with the correlated cloud groups, or 1 call with the
simplest cloud approximations. Another improvement in modeling J values,
the treatment of volatile organic compounds with pressure-dependent cross
sections, is also incorporated into Cloud-J.
Introduction
Photolysis, the dissociation of molecules upon absorbing sunlight, drives
atmospheric chemistry and controls the composition of the air we breathe.
Photolysis rates are governed by the intensity and spectral distribution of
sunlight, which is altered by scattering and absorption processes within the
atmosphere. Clouds, aerosols, and gases control these processes, but
ambiguity in the representation of clouds in atmospheric models is currently
the largest source of uncertainty in photolysis rates. This paper presents a
new, pragmatic approach for representing the overlap of clouds derived from
observations and cloud models, and then provides several practical
approximations with marginal computational costs that can be readily
incorporated in atmospheric chemistry models. This computer code is a major
expansion of Fast-J (Wild et al., 2000; Bian and Prather, 2002; Neu et al.,
2007) and is presented here as Cloud-J version 7.3c. Cloud-J contains Fast-J
and thus continues that numbering sequence, for which Fast-J 7.2 was the last
released version. Fast-J has gone through several variants: Fast-J began with
7 bands, full scattering, for the troposphere; Fast-J2 added 11 bands,
absorption only, for the stratosphere; Fast-JX applied full scattering to all
18 bands. Fast-J is used here throughout, although some recent code versions
use the JX notation.
Clouds can increase photolysis rates through scattered sunlight, but they can
greatly reduce them by shadowing. Modeling the scattering by cloud layers in
a column atmosphere and resulting photolysis rates is practical, as in
Fast-J, if the layers are horizontally uniform across the modeled air parcel
(defined typically as a rectilinear box bounded by latitude, longitude, and
pressure surfaces). Clouds layers, however, have horizontal scales of a few
kilometers (Slobodda et al., 2015), and thus are represented in global and
regional models as fractional coverage in each parcel. In calculating the
average photolysis or heating rates through the column atmosphere, one must
know how the cloud fractions overlap. Early modeling assumed that model
layers consisted of maximally overlapped groups (MAX) that were randomly
overlapped relative to one another (MAX-RAN) (Briegleb, 1992; Feng et al.,
2004). A more accurate description of cloud overlap is that clouds are highly
correlated (i.e., maximally overlapped) when they are vertically near each
other, but they become randomly overlapped when separated by greater
distances. The cloud decorrelation length is the vertical distance over which
the overlap e-folds to random. From a range of observations and cloud models,
we estimate a cloud decorrelation length increasing from 1.5 km for the
boundary layer to 3 km in the upper troposphere (Pincus et al., 2005;
Naud and DelGenio, 2006; Kato et al., 2010; Oreopoulis et al., 2012).
A practical application of this cloud-overlap information, merging maximally
overlapped groups that are correlated with each other (MAX-COR), is defined
in Sect. 2, where the impact of cloud-overlap models on photolysis rates
(J values) is also shown. Cloud-overlap models generate statistics that
lead to a large number of weighted independent column atmospheres (ICAs),
where the number is too large to be used directly to calculate photolysis or
heating rates in global models. Section 3 looks at the simplified cloud
models and the approaches to approximate the sum over ICAs, examining their
errors. Another recent development in modeling photolysis rates is the
treatment of volatile organic compounds with pressure-dependent cross
sections, presented in Sect. 4. Recommendations for the cloud-overlap model
and the ICA-approximation method are discussed in Sect. 5.
Overlap models for fractionally cloudy atmospheres
Typically, meteorological forecasts or climate model data used in atmospheric
chemistry models report fractionally cloudy atmospheres (FCAs) in each
grid square. Computation of the photolysis or heating rates in an FCA
requires knowledge of how the clouds in each layer overlap. The calculation
of J values in most atmospheric chemistry models today involves solving the
radiative transfer equations in a plane-parallel atmosphere where the
vertical layers can be highly inhomogeneous but the horizontal planes are
uniform (Stamnes et al., 1988; Wild et al., 2000; Tie et al., 2003). Thus,
the only workable method (other than 3-D radiative transfer) is to represent
the FCA by a number of ICAs where each ICA
is either 100 % cloudy or clear in each layer. The fractional cloud-overlap model determines the layer structure, weighting, and number of ICAs.
Other simple cloud models approximate overlap by (i) ignoring clouds
entirely (clear sky); (ii) averaging the cloud fraction, f, over each
layer, conserving total cloud water (average clouds); and (iii) decreasing
the cloud fraction and cloud water in a layer by using a reduced cloud
fraction, f3/2 followed by averaging across the layer (Briegleb, 1992).
These methods are compared with cloud-overlap models in Sect. 3. Here, we
focus on how the ICAs differ across cloud-overlap models.
Random overlap
The ways in which fractionally cloudy layers can overlap is shown
schematically in Fig. 1. One assumption is random overlap (RAN). In this case
the likelihood (fractional weight, w) of having the cloud in layer L1 fall
below the cloud in layer L2 is random and hence equals fL1. This
particular pairing – cloud below cloud – becomes ICA #1. Superscripts in
the equations below refer to atmospheric layers. The likelihood for the clear
layer under the cloudy layer is by default the complement.
wL1(#1)=fL1wL1(#2)=1-fL1
The likelihood of the cloudy layer in L2 above is
wL2(#1)=wL2(#2)=fL2.
The total weight W for each ICA #1 and #2 is then the product of
wL1 and wL2.
Schematic of overlapping fractional cloud layers. See text.
WL1-L2(#1)=wL1(#1)wL2(#1)=fL1fL2=0.15×0.20=3%(see Fig.1)WL1-L2(#2)=wL1(#2)wL2(#2)=(1-fL1)fL2=0.85×0.20=17%
Similar rules apply to ICAs #3 and #4,
wL1(#3)=fL1andwL2(#3)=1-fL2,wL1(#4)=1-fL1andwL2(#4)=1-fL2,
and thus
WL1-L2(#3)=wL1(#3)wL2(#3)=fL1(1-fL2)=0.15×0.80=12%(see Fig.1),WL1-L2(#4)=wL1(#4)wL2(#4)=(1-fL1)(1-fL2)=0.85×0.80=68%.
ICAs #1 and #3 are tagged as cloudy in L1, and ICAs #2 and #4 are
tagged as clear in L1. The sum of cloudy fractions in L1 must be conserved:
3 % + 12 % = 15 % =fL1. One of the
problems in implementing a full-RAN model is that the number of ICAs scales
as 2NL, where NL is the number of cloudy layers in the RAN group.
Correlated overlap
When correlated, the likelihood of a cloudy layer lying under a cloud above
is greater than random, wL1(#1) >fL1, by a factor
of
gL1> 1. The cloud correlation factor cc ranges from 0 (random)
to 1 (maximal overlap), and gL1 is the interpolating function
linear in cc between random and maximal overlap.
gL1=1+cc(1/fL2-1),subject togL1≤1/fL1andgL1≤1/fL2
Hence for cc > 0 we have an increased likelihood of the cloud in L1 falling
underneath the cloud in L2. For the example in Fig. 1, cc = 0.5 and
gL1=3.
wL1(#1)=gL1fL1=3×0.15=45%wL1(#2)=1-gL1fL1=1-0.45=55%
The likelihood of clouds in L1 falling below the clear section in L2 is
reduced and is calculated from the requirement that the sum of cloudy
fractions in L1 is still fL1.
wL1(#3)=fL1(1-gL1fL2)/(1-fL2)=0.15×(1-3×0.20)/0.80=7.5%
By complement, the weighting of clear sky in layer L1 under clear sky in
layer L2 is
wL1(#4)=1-wL1(#3)=1-0.075=92.5%.
Note that if cc = 0, or fL2=1, or fL1=1, then
gL1=1 and correlated overlap (COR) defaults to RAN. The two additional limits on
gL1 in Eq. (10) are required to keep wL1(#2) and
wL1(#3) positive. The wL2 weights do not include a g
factor.
wL2(#1)=wL2(#2)=fL2wL2(#3)=wL2(#4)=(1-fL2)
The combined ICA weights are
WL1-L2(#1)=wL1(#1)wL2(#1)=gL1fL1fL2=3×0.15×0.20=9%,WL1-L2(#2)=wL1(#2)wL2(#2)=(1-gL1fL1)fL2=0.55×0.20=11%,WL1-L2(#3)=wL1(#3)wL2(#3)=fL1(1-gL1fL2)=0.15×0.40=6%,WL1-L2(#4)=wL1(#4)wL2(#4)=1-fL2-fL1+gL1fL1fL2=1-0.20-0.06=74%.
As in RAN, ICAs #1 and #3 are tagged as cloudy in layer L1, ICAs
#2 and #4 are tagged as clear in layer L1, and the sum of cloudy
fractions is conserved
(9 % + 6 % = 15 % =fL1 ) but with
different weightings. The COR model also has ICAs scaling as 2NL.
Maximal overlap
For maximal overlap of clouds (MAX) as in Fig. 1, the two layers L1 and L2
form a MAX group G1 consisting of one clear-sky column (80 % fractional
coverage) and 2 cloudy columns – one with clouds in both layers
(f1G1=15 %) and one with a cloud only in the upper layer
L2 (f2G1=5 %). For a MAX group, there can be several ICAs
with cloud fractions, each with a unique combination of cloudy layers. The
clear-sky column does not occur if any of the MAX layers has a cloud fraction
of 100 %. For continuous cloud fractions, the number of ICAs equals the
number of unique cloud fractions present (plus 1 if clear sky is present).
A MAX group is characterized by the number of cloudy columns (N1) consisting
of combinations of cloudy or clear sky in different layers of the group and
having a fractional area equal to f1G1, f2G1,
f3G1, …fN1G1. The total cloudy
fraction is FG1=f1G1+f2G1+f3G1+…+fN1G1≤1, with the
(possible) clear-sky column fraction of 1-FG1, giving N1 + 1
ICAs for that group. As in the earlier Fast-J work (Neu et al., 2007), the
cloud fractions in Cloud-J are quantized to limit the number of ICAs in a MAX
group. The examples here use 10 bins, and hence cloud fractions are limited
to 0, 10, 20, 30, … 100 %. With this binning, the in-cloud water
content is scaled to conserve the cloud-water content in each layer. This
approximation is now resolution independent in terms of the number of model
layers and limits each MAX group to 10 ICAs.
Maximal groups with correlated overlap
The MAX-COR model generates ICAs from upper and lower layers that are MAX
groups. For a general approach, we assume that the upper group G2 consists of
N2 cloudy column members with fractions f1G2+f2G2+f3G2+…+fN2G2=FG2 and one
clear-sky column member of fraction 1-FG2. Similarly, the lower
group G1 has N1 + 1 ICAs (see Sect. 2.3). Each of the N1 + 1 ICAs in
group G1 are paired with the N2 + 1 ICAs above in group G2. The total
number of ICAs combining both groups is the product (N1 + 1)(N2 + 1),
assuming that there are clear-sky members in both groups. The ICA sequence
defining each unique pairing (J1, J2) is then
(1,1),(2,1),(3,1),…(N1+1,1),(1,2),(2,2),(3,2),…(N1+1,N2+1),
such that ICA #M is composed of members
J1=(M-1)modulo(N1+1)+1,J2=integer((M-1)/(N1+1))modulo(N2+1)+1.
The cloud correlation factor of group G1 with group G2 is the same for all
cloudy ICAs and is derived from the total cloudy fractions FG1 and
FG2.
gG1=1+cc(1/FL2-1),subject togG1≤1/FG1andgG1≤1/FG2
For convenience denote J1 ≤ N1 as cloudyG1,
J1 = N1 + 1 as clearG1, J2 ≤ N2 as
cloudyG2, and J2 = N2 + 1 as clearG2. Then the
weightings for the G1 members are
wG1(cloudyG1,cloudyG2)=gG1fJ1G1,wG1(clearG1,cloudyG2)=1-gG1f1G1+f2G1+f3G1+…+fN1G1=1-gG1FG1.
By conserving each cloudy group member's fractional area in G1, the weights
under G2 clear sky are
wG1(cloudyG1,clearG2)=fJ1G1(1-gG1FG2)/(1-FG2),wG1(clearG1,clearG2)=1-FG1(1-gG1FG2)/(1-FG2).
All of these formulae also work if FG1>FG2 and if
FG1=0 or 1 (same for FG2). A special case of MAX-COR is
MAX-RAN when cc = 0. With the cloud fractions binned into 10 intervals,
then the number of ICAs for MAX-COR or MAX-RAN models scales as
10NG, where NG is the number of MAX groups.
J value errors
Our recommended cloud-overlap model uses the information on vertical
correlations (Pincus et al., 2005; Naud and DelGenio, 2006; Kato et al.,
2010; Oreopoulis et al., 2012), which shows cloud decorrelation lengths on the order of 1.5 km in the lower atmosphere increasing to 3 km or more in the
upper troposphere. Since a true COR model scales as 2NL and becomes
rapidly impractical for high-resolution models, we define vertical groups of
cloud layers globally according to the decorrelation lengths: 0–1.5 km
altitude, 1.5–3.5, 3.5–6, 6–9, 9–13, and > 13 km. We assume that the
cloud layers within a decorrelation length are highly correlated with one
another and thus form a MAX group. When such MAX groups are adjacent they
have a mean separation of one decorrelation length, and we choose a cloud
correlation factor of cc = 0.33, similar to 1 e-fold. When there is a
clear-sky gap between a pair of G6 layers, the MAX groups are separated by
more than one decorrelation length; thus, we reduce the factor cc with
successive multiples (i.e., with two missing G6 MAX groups between two cloudy
layers, the effective cc = 0.333= 0.036). This model is denoted
G6/.33. Two other G6 models were tested: cc = 0.00 corresponds to
randomly overlapped adjacent groups (MAX-RAN, G6/.00); and cc = 0.99 is
almost maximally overlapped (MAX, G6/.99).
In looking at how this model aligned the clouds for realistic FCAs, we found
that extensive cirrus fractions in the uppermost layers prevented the
expected overlap of small-fraction cumulus below. Thus, a seventh MAX group is
added if there was a cirrus shield (defined from top down as adjacent
ice-only clouds with f> 0.5). Because of the cloud-fraction binning
into 10 % intervals, the number of ICAs is bounded by
5 × 106 (including the cirrus shield). This limit is resolution
independent and was never reached in any FCAs examined here (highest number
of ICAs for one FCA was 3500). The major computational cost comes with the
Fast-J computation, and the methods for approximating the average of
J values over all ICAs (Sect. 3) use at most four Fast-J calculations no
matter how many ICAs.
Two other cloud-overlap models tested here are the MAX-RAN groupings G0 and
G3 (Feng et al., 2004; Neu et al., 2007). Model G0 assumes that all
vertically adjacent cloudy layers are a MAX group (maximally overlapped), and
all such groups separated by a clear layer are RAN overlapped. This model
seems logical but has difficulty finding a clear layer when the FCA has been
averaged over several hours or taken from a parameterized cloud-resolving
model. It our tests, using meteorological data with NL = 36, the maximum
number of G0 ICAs was 375. Model G3 has at most three MAX-RAN groups demarcated
by atmospheric regimes: a fixed altitude (1.5 km, stratus top) and
temperature (the liquid-to-ice cloud transition). The maximum possible number
of ICAs per FCA for G3 is 103, and in our tests we found 288.
Our recommended cloud-overlap model is G6/.33 since it is based on the
observed–modeled cloud decorrelation lengths. For a given FCA, we treat the
J values calculated by summing Fast-J over all the ICAs generated by G6/.33
as the correct value. We calculate errors for the other cloud-overlap models
(here) or various ICA-approximation models using the G6/.33 model (Sect. 3).
The errors in photolysis rates are calculated for different cloud-overlap
models by generating all the ICAs, using Fast-J to calculate J values, and
computing the weighted sum of J's. This study focuses on two J values
that are critical in tropospheric chemistry and emphasize different
wavelength ranges from near 300 nm, where O3 absorption and molecular
scattering are important, to 600 nm, where clouds are the predominant
factor. J-O1D refers to the photolysis rate of O3+hν→ O2+ O(1D); and J-NO3 includes both channels
of the rate of NO3+hν→ NO + O2 and
NO2+ O. We tested other key J values like those of HNO3 and
NO2, but found that their errors fell between the first two.
Models for cloud overlap and approximation of ICAs including errors
in J values.
Cloud-overlap models to generate ICAs ICAsaavg err 0–1 km rms error 0–1 km rms error 0–16 km J-O1DJ-NO3J-O1DJ-NO3J-O1DJ-NO3G0MAX-RAN with MAX groups bounded by layers with CF = 019+2 %+2 %21 %17 %6 %11 %G33 MAX-RAN groups split at 1 km and at the ice-only cloud level21+2 %+2 %15 %15 %5 %7 %G6/.006 MAX-COR groups, cc = 0.00169-1 %-1 %5 %4 %2 %3 %G6/.336 MAX-COR groups, cc = 0.33b169G6/.996 MAX-COR groups, cc = 0.99169+2 %+1 %11 %8 %4 %7 %Simple cloud models ICAsClSkyclear sky, ignore clouds1+14 %+10 %24 %20 %14 %23 %AvCldaverage fractional cloud acrosslayer1-5 %+1 %11 %11 %8 %15 %CF3/2increase CF to CF3/2 and average over layer1+7 %+11 %10 %15 %5 %8 %ICA approximations J callsAvDiraverage direct beam from all ICAs1+5 %+11 %6 %13 %3 %7 %MdQCAquadrature column atmospheres uses mid-point in each QCA2.8+1 %0 %4 %4 %4 %5 %AvQCAQCAs, uses average in each QCAb2.8-1 %0 %3 %2 %2 %4 %Ran-3Select 3 ICAs at random3+2 %+1 %12 %12 %9 %12 %
a Average number of ICAs for a tropical atmosphere; see
Fig. 2. b Recommended cloud-overlap model and reference model for
calculation of errors.
The J value tests are summarized in Table 1. We use a high-resolution
snapshot from the European Center for Medium-range Weather Forecasts, similar
to what is used (at lower resolution) in the UC Irvine and University of Oslo
chemistry-transport models (Søvde et al., 2012; Hsu and Prather, 2014).
The 640 FCAs are a 3 h average of a single longitudinal belt just above the
Equator (T319L60 Cycle 36) and have clouds only in the lowermost 36 layers.
Profiles of temperature and ozone are taken from tropical mean observations;
the Rayleigh-scattering optical depth at 600 nm is about 0.12, and a mix of
aerosol layers has a total optical depth of 0.23. J value errors are
calculated separately for each FCA and then averaged. The number of ICAs per
FCA averages 169 for model G6, 21 for model G3, and 19 for model G0; see
Fig. 2 for the probability distribution of ICA numbers. Errors are
pressure weighted and include the average error over 0–1 km altitude, the
root mean square (rms) error over 0–1 km, and the full tropospheric rms
error (0–16 km). The average 0–1 km differences across the models are
small (< 2 %), but the rms 0–1 and 0–16 km differences are large,
indicating that 640 different FCAs produce canceling errors in the mean. The
rms errors for G0 and G3 are worrisome: more than 15 % in the boundary
layer and 5 to 11 % in the full troposphere. The G6 errors are almost
linear with the cc value. The G6/.99 with highly correlated overlap is
similar to G3 which has MAX overlap throughout most of the atmosphere. The
G6/.00 with random overlap is the closest to the correlated model G6/0.33.
Number of independent column atmospheres (ICAs) generated by three
different cloud-overlap models (G0, G3, G6) from 640 different tropical
fractionally cloudy atmospheres (FCAs) and sorted in order of increasing ICA
number. The different cloud correlation factors used in the G6 model do not
change the number of ICAs, only their weights. The average number of ICAs per
FCA is given in the legend. See text for definition of models.
Approximating the exact sum over ICAs
Quadrature column atmospheres (QCAs) have been defined previously (Neu et
al., 2007) as four representative ICA-like atmospheres that represent four domains
of ICAs with total cloud optical depths at 600 nm of 0–0.5 (clear sky),
0.5–4 (cirrus-like), 4–30 (stratus-like), and > 30 (cumulus-like).
The original model sorted the ICA optical depths to get the weightings of
each QCA and then picked the ICA that occurred at the mid-point in terms of
fractional area (MdQCA). Thus, there can be up to four separate calls to Fast-J
for each of the QCAs, but on average there are 2.8 QCAs per FCA because not
all four of the QCA ranges of cloud optical depths (0–0.5, 0.5–5, 5–30,
> 30) are present in each FCA. Here we extend that approach with three new
methods for approximating the integral over ICAs: define each QCA from the
average ICAs in its domain (AvQCA); use the averaged direct solar beam from
all ICAs to derive an effective scattering optical depth from clouds in each
layer (AvDir); and selecting three random ICAs based on their weights (Ran-3;
with comparable computational costs to either QCA).
The AvQCA model comes easily from the MdQCA formalism, but all ICAs in each
of the four total optical depth domains are used to calculate the average
cloud-water content in each QCA. The AvDir model calculates the weighted
direct solar beam from each ICA, where only 600 nm cloud extinction is
included. In this case it was found that an equivalent isotropic extinction
is needed as in two-stream methods (Joseph et al., 1976), and we scaled the
optical depth of each cloud layer by a factor of 1-1.1P1/3, with a
minimum value of 0.04. P1 (3 times the asymmetry factor) is the second
term in the Legendre expansion of the scattering phase function for the cloud
in that layer. The derived optical depth in each layer is calculated from the
reduction in direct beam across the layer (Beer–Lambert law) and put into
the single Fast-J calculation with the original cloud properties of that
layer, not the equivalent isotropic properties.
In addition to these ICA approximations, we also compare the G6/.33 exact sum
over ICAs with three simple cloud models often used in chemistry models that
do not generate ICAs: clear sky (ClSky); averaged cloud over each layer
(AvCld); and cloud fraction to the 3/2(f3/2, CF3/2).
Profile of the average bias in J value approximations relative to
the J value calculated from the weighted average of all ICAs using model
G6/.33. Values here are calculated using a solar zenith angle of
13.6∘ and a surface albedo of 0.10 and averaged over 640 FCAs (108,
125 ICAs) derived from the equatorial statistics (all longitudes) of cloud
fraction, liquid water content, and ice water content from a snapshot of a
T319L60 meteorology from the European Centre for Medium-range Weather
Forecasts. Three simple cloud methods (dashed lines) do not use any
cloud-overlap model, and three approximations for the ICAs (solid lines) use
the G6/.33 model described here. The MdQCA ICA approximation was developed in
Neu et al. (2007); the AvQCA and AvDir approximations are developed in this
paper. The J-O1D refers to the photolysis rate of O3+hν→ O2+ O(1D), with average values of 4 (z=0 km)
to 9 (z=16 km) × 10-5 s-1; and J-NO3, to all
channels of the rate NO3+hν→, with average values of 2
to 4 × 10-1 s-1. These two J values emphasize sunlight
from 310 to 600 nm, and thus span the typical range of errors
in tropospheric photolysis rates.
A sample of mean and rms errors for the seven approximate methods is given in
Table 1. In addition, a tropospheric profile of the mean bias in J values
is shown in Fig. 3. As expected the ClSky and AvCld methods show opposite
biases and large rms errors. The CF3/2 method produces reasonable averages,
but still has rms errors of 10 % or more. The AvDir method does not
perform as well as expected and looks only slightly better than CF3/2;
however, the profile of mean error (Fig. 3) is preferable to that of CF3/2.
Both QCA methods performed excellently and deliver rms errors of less than
5 % with mean biases in the boundary layer on the order of ±1 %. The new
AvQCA method has smaller rms errors, but the original MdQCA method has a
slightly better profile for the mean error. Ran-3 is computationally
comparable to the QCAs; it has a reasonable mean bias as expected given the
number of samples (3 × 640), but a much worse rms error, typically
> 10 %.
Cloud-J and volatile organic compounds
Volatile organic compounds (VOCs) cover a wide class of gaseous species
containing C, H, O and sometimes N or S. They play a major role in the
chemical reactivity of the troposphere, including production and loss of
O3 and loss of CH4 (e.g., Jacob et al., 1993; Horowitz et al.,
1998; Ito et al., 2009; Emmons et al., 2010), plus the formation of secondary
organic aerosols (SOAs; e.g., Ito et al., 2007; Fu et al., 2008; Galloway et
al., 2011). For most VOCs (and H2O2) photolysis is the dominant
loss; see Fig. 4. Daily photolysis rates (loss frequencies) range from 0.03
to 20 per day and some vary greatly with altitude. For 9 of the 14 species
shown in Fig. 4, the photolysis rates are larger or comparable to the loss
rates for reaction with OH (given in the legend). Thus, accurate calculation
of their J values is important in atmospheric chemistry models.
Volatile organic compounds (VOCs) and related species photolysis
rates (per day) as a function of altitude (km). The
complex structure with altitude is due to a combination of increasing UV
radiation with altitude and Stern–Volmer pressure dependences on quantum
yields. Changes in slope occur at the interpolation points, temperature, or
pressure of the cross sections. We assume that the
12:00 LT J's (clear-sky, tropical
atmosphere, albedo = 0.10, SZA = 15∘) apply for 8 of 24 h.
Equivalent rates for OH loss are shown with the species name in the legend
and assume a 12:00 LT OH density of
6 × 106 cm-3. Asterisks denote species for which
photolysis loss is greater than or comparable to OH loss. VOC abbreviations
are MGlyxl: methyl glyoxal, Glyxl: glyoxal, PropAld: propionaldehyde, GlyAld:
glycol aldehyde, ActAld: acetaldehyde, MEKeto: methylethyl ketone, MeVK:
methylvinyl ketone, MeOOH: CH3OOH, MeAcr: methacrolein, MeNO3: methyl
nitrate, and PAN: peroxyacetyl nitrate.
VOCs present a particular problem for any photolysis code that averages over
wavelength intervals. For most chemical species, cross sections including
quantum yields are parameterized as a function of wavelength (ν) and
temperature (T) (e.g., Atkinson et al., 2008; Sander et al., 2011). In this
case, Fast-J calculates solar-flux-weighted, average cross sections for each
wavelength bin (Wild et al., 2000; Bian and Prather, 2002). These tables are
created for a set of fixed T's, and then the cross section used for each bin
in each atmospheric layer is interpolated in T. Many VOCs have complex,
pressure-dependent quantum yields (e.g., Blitz et al., 2006) that follow the
Stern–Volmer formulation, where photolysis cross sections (for dissociation)
are a function of wavelength, temperature, and pressure (P), typically of
the form A(T,v)/(1+B(T,v)P), where A and B can be rational polynomial
functions of T and ν (see Sander et al., 2011). For most VOCs the
pressure dependence changes across the wavelengths within a model bin, and
thus the T dependence averaged cross sections has different values at
different P, but cannot be simply post-interpolated as a function of P
because of the wavelength dependence of B. A 2-D set of cross
sections for each wavelength bin, interpolated as a function of T and P,
could be developed but would add to the complexity and cost of Fast-J.
Recognizing that VOCs are predominantly tropospheric and that T and P are
highly correlated in the troposphere, Cloud-J, and the new Fast-J that sits
within it, has devised an alternative method of interpolating the cross
sections for each atmospheric layer: T is the traditional method used for
most species; but P is used for VOCs with highly pressure-dependent quantum
yields. For P interpolation, the cross sections are averaged over
wavelength at three points along a typical tropospheric lapse rate: 0 km,
295 K, 999 hPa; 5 km, 272 K, 566 hPa; and 13 km, 220 K, 177 hPa.
Currently species with P interpolation include:
acetaldehyde, methylvinyl ketone, methylethyl
ketone, glyoxal, methyl glyoxal, and one branch of acetone photolysis. Fast-J
does not extrapolate beyond its supplied tables, and thus currently it
applies 177 hPa cross sections for these VOCs throughout the stratosphere,
but this has minimal impact on stratospheric chemistry. Depending on the
available laboratory data, the number of cross section tables per species in
the new Fast-J (either T or P interpolation) can be 1, 2, or 3. Cloud-J,
new with version 7.3, includes an updated version of Fast-J version 7.1,
whose only change is in the formatting of the input files to allow for more
flexible numbering and labeling of species with their cross sections and of
the cloud–aerosol scattering tables.
Discussion and recommendations
We recommend use of the G6/.33 MAX-COR model for cloud overlap with AvQCA to
approximate the average photolysis rates over the ICAs. This combination of
algorithms best matches the exact solution for average J values at a single
time within each FCA. Averaging J values for an air parcel that includes a
mix of cloudy and clear air is not the same as averaging the chemical
reactivity across cloudy and clear. Nevertheless, for species with photolysis
rates that are less than the frequency at which clouds form and air is
processed through them (on the order of 24 day-1), the average J is the
relevant quantity for chemistry modeling.
A next step would be to model at high-enough resolution so that air parcels
are either cloudy or clear. This could resolve the 3-D correlation of clouds
at scales of 1–4 km, which will in turn require a 3-D radiative transfer
model (Norris et al., 2008; Davis and Marshak, 2010). A more interesting
approach that is practical with typical global model resolution is the
treatment of inhomogeneous cloud fields as being composed of independently
scattering cloudlets (Petty, 2002). This cloudlet approximation could be
readily integrated into the plane-parallel framework of Fast-J.
The added computational cost with G6/.33+AvQCA occurs with the additional
calls to Fast-J, as the MAX-COR model and sorting of ICAs is fast. Computing
photolysis rates 2.8 times per atmospheric column instead of once may add to
the overall computational burden, but Fast-J is efficient and the costs will
be much less than the overall chemistry-solver and tracer-transport codes.
Code availability
The most recent version of Cloud-J and earlier versions of Fast-J can be
found at ftp://128.200.14.8/public/prather/Fast-J/. Cloud-J 7.3c as
described here is included as a zip file and includes new coding to correct
failures in compilation or execution (v7.3b) as well as reducing the cloud
correlation factor when there are decorrelation-length gaps between any of
the MAX-COR groups (v7.3c). Although with v7.3c some J values changed in
the third decimal place, changes in the GMDD figures and tables were
undiscernible. Subscribe to the listserv UCI-Fast-J@uci.edu or check the ftp
site for updates. Send questions or suggestions for Cloud-J features to the
listserv or the author (mprather@uci.edu).
The Supplement related to this article is available online at doi:10.5194/gmd-8-2587-2015-supplement.
Acknowledgements
Research at UCI was supported by NASA grant NNX13AL12G and DOE BER award
DE-SC0012536. The author is indebted to T. Reddmann, R. Sander and an
anonymous reviewer for finding the coding inconsistencies/errors, and Cloud-J
should now be more reliable across platforms.
Edited by: R. Sander
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