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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D01S90, doi:10.1029/2006JD007088, 2007
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A comparison of radiative transfer models for simulating
Atmospheric Infrared Sounder (AIRS) radiances
R. Saunders,1 P. Rayer,1 P. Brunel,2 A. von Engeln,3 N. Bormann,4 L. Strow,5 S. Hannon,5
S. Heilliette,6 Xu Liu,7 F. Miskolczi,7 Y. Han,8 G. Masiello,9 J.-L. Moncet,10
Gennady Uymin,10 V. Sherlock,11 and D. S. Turner12
Received 17 January 2006; revised 6 June 2006; accepted 17 July 2006; published 4 January 2007.
[1] A comparison of radiative transfer models for simulating radiances from the
Atmospheric Infrared Sounder (AIRS), has been undertaken. Results from 14 line-by-line
and fast parameterized infrared models were submitted. Several aspects of the models
were compared. First, the forward model calculations for all 2378 AIRS channels for
52 diverse atmospheric profiles and one tropical Pacific profile coincident with AIRS data
were performed for three local zenith viewing angles: nadir, 45, and 60 degrees. Second,
for a subset of the models and only 20 AIRS channels the transmittances from each layer
to space were provided. Finally, for some models the Jacobians with respect to
temperature, water vapor, and ozone were also computed. For the forward model
calculations, most models agree to within 0.02 K when compared to a reference lineby-line model averaged over a subset of profiles, with the exception of a few spectral
regions. When compared with AIRS observations, however, the mean differences increase
to 0.2 K, and for a few models even greater differences are seen. The transmittance
differences highlighted regions of the spectrum where the spectroscopy of the models
differs, particularly in the carbon dioxide absorption bands at 667 cm1 and 2386 cm1.
For the Jacobians all models have some profiles/channels that do not fit the reference
well, and the main problems are documented here. The model differences only increase
slightly for off-nadir viewing angles for both forward and Jacobian calculations.
Citation: Saunders, R., et al. (2007), A comparison of radiative transfer models for simulating Atmospheric Infrared Sounder (AIRS)
radiances, J. Geophys. Res., 112, D01S90, doi:10.1029/2006JD007088.
1. Introduction
[2] Fast radiative transfer (RT) models are now an integral component of any numerical weather prediction (NWP)
model assimilating satellite radiances or using radiances for
model validation purposes. Given the significant impacts of
radiances in NWP model forecasts [Andersson et al., 1994;
English et al., 2000] it is important that we strive to develop
fast RT models which achieve the required level of accuracy
1
Met Office, Exeter, UK.
MétéoFrance, CMS, Lannion, France.
3
Institute of Environmental Physics, Bremen University, Bremen,
Germany.
4
European Centre for Medium Range Weather Forecasts, Reading, UK.
5
Department of Physics, University of Maryland Baltimore County,
Baltimore, Maryland, USA.
6
CNRS, Laboratoire Meteorologie Dynamique, Palaiseau, France.
7
NASA Langley Research Center, Hampton, Virginia, USA.
8
NOAA/NESDIS, Camp Springs, Maryland, USA.
9
IMAA-CNR, Tito Scalo, Potenza, Italy.
10
Atmospheric and Environmental Research, Incorporated, Lexington,
Massachusetts, USA.
11
National Institute of Water and Atmospheric Research, Wellington,
New Zealand.
12
Met Service Canada, Downsview, Ontario, Canada.
2
Published in 2007 by the American Geophysical Union.
while at the same time having error characteristics which are
well understood. In this way the impact of the satellite
radiances on the NWP analyses can be optimized. Ideally
the errors in the RT forward model used for assimilation
should be small relative to the instrument noise and uncorrelated. Fast RT models are also important for providing
retrievals of the atmospheric state for climate data sets and
providing simulated satellite data sets from NWP model
fields. For both assimilation and retrieval applications it is
important to emphasize that it is not only the forward model
calculations (i.e., top of atmosphere radiances computed
from a given atmospheric state) which are significant but
also the gradients of the RT model radiances with respect to
the profile variables strictly referred to as the Jacobian (but
see later) and defined as
H¼
@y
@X
ð1Þ
where y is the vector of channel radiances (2378 for
Atmospheric Infrared Sounder (AIRS)), X is the vector of
atmospheric state variables (typically dimensions of number
of levels number of active gases plus a few surface
variables which for this study came to 310) and H is the
Jacobian matrix with dimensions of y by X. It is the
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Table 1. Fast Models Which Participated in the Comparison
Model Name and
Reference
RTTOV-7
[Saunders et al., 1999]
RTTOV-8
[Saunders et al., 1999]
Optran v7
[Xiong and McMillin,
2005; McMillin et al., 2005]
OSS
[Moncet et al., 2004]
s-IASI
[Amato et al., 2002]
Gastropod 0.3.0
[Sherlock et al., 2003]
SARTAv 1.05
[Strow et al., 2003]
PCRTM Liu et al., 2006]
Base Model Spectroscopy
Water Vapor Continuum
Line Mixing
Participant
Results Submitted
Transmittances/Jacobian
Method
GENLN2v2 Hitran-96
CKD2.1 [Strow et al., 1994]
kCARTA (1.11)a Hitran-2004
Modified MTCKD 1.0
[DeSouza-Machado et al., 1999]
LBLRTM v7.04 HITRAN-2000
MTCKD 1.0 [Hoke et al., 1989]
R. Saunders,
Met Office
R. Saunders, P. Brunel,
Met Office
Yes/Analytic
Regression
Yes/Analytic
Regression
Y. Han, NESDIS
Yes/Analytic
Regression
LBLRTMV8.3 HITRAN-2000
MTCKD 1.0 [Hoke et al., 1989]
LBLRTMV8.1 HITRAN-2000
MTCKD 1.0 [Hoke et al., 1989]
kCARTA 2000a Hitran-1998b
CKD2.4 [Strow et al., 2003]
kCARTA (1.07)a Hitran-2000
Modified MTCKD 1.0
[DeSouza-Machado et al., 1999]
LBLRTM v8.3 Hitran-2000
MTCKD 1.0 [Hoke et al., 1989]
J.-L. Moncet,
G. Uymin, AER
G. Masiello, C. Serio,
DIFA, UniBas
V. Sherlock, NIWA
None/Analytic
Precomputed LUT
Yes/Analytic
Precomputed LUT
Yes/Analytic
Regression
S. Hannon, L. Strow,
UMBC
None/None
Regression
Xu Liu, NASA,
LaRC
Yes/Analytical
LUT/Regression
a
kCARTA is described in Strow et al. [1998].
Includes the Toth H2O lines.
b
Jacobian which allows increments in ‘‘radiance space’’ to be
mapped back into increments in model state variables,
assuming linearity about the model state X, thereby bringing
the NWP model state closer to the radiance observations.
[3] Several years ago comparisons of radiative transfer
(RT) models for ATOVS (Advanced TIROS Operational
Vertical Sounder) infrared and microwave channels were
made [Soden et al., 2000; Garand et al., 2001] that helped
to better define the radiative transfer modeling errors for
ATOVS. More recently, with the advent of high spectral
resolution infrared sounders, e.g., Atmospheric Infrared
Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI), enhanced versions of the fast ATOVS
radiative transfer models have evolved to include simulations of these sounders. The success of the AIRS spectrometer in providing very stable high spectral resolution top of
atmosphere infrared radiances has provided an impetus to
improve and assess the RT modeling for atmospheric
sounding applications in the thermal infrared. A recent
study by Tjemkes et al. [2003] comparing line-by-line RT
models for IASI simulations has also helped quantify the
errors in the line-by-line models.
[4] This AIRS radiative transfer model comparison was
proposed at the first workshop for Soundings from High
Spectral Resolution Observations at Madison, Wisconsin
in May 2003, and was undertaken under the auspices of
the International TOVS Working Group. The aims of the
intercomparison were defined to be (1) to compare the
forward model calculations for all AIRS channels for a set
of diverse atmospheric profiles and one tropical Pacific
profile coincident with AIRS data; (2) to compare the
profile transmittances for a representative subset of 20
channels; and (3) to compare temperature, water vapor
and ozone Jacobians from each model for these 20 channels.
The results from this study would then allow the error
characteristics of AIRS fast RT models to be better estimated
for retrieval and data assimilation applications and to
compare them with the AIRS instrument noise. In the
process of this comparison exercise, several models had
problems identified in their implementation as a result of the
comparison and they were able to be corrected before the
final analysis was undertaken.
[5] The paper is structured as follows: section 2 describes
the models submitted, section 3 the details of the comparison process, section 4 the results for the forward model
comparisons, section 5 the results for the transmittances and
Jacobians, and section 6 summarises the conclusions of the
intercomparison and identifies areas requiring further study.
2. Models Submitted
[6] The 14 radiative transfer models that participated in
this study are listed in Tables 1 and 2 together with
references for each model. All models provided brightness
temperatures for all 2378 AIRS channels for 3 viewing
angles and for the 52 diverse atmospheres. The comparison
was performed in terms of equivalent black body brightness
temperatures for ease of interpretation although this does
introduce a small additional uncertainty through the
assumptions made in the conversion from radiance to
brightness temperature. In addition, one profile from the
Western Tropical Pacific Atmospheric Radiation Measurement (ARM) site coincident with an AIRS observation was
also modeled by all the participants. Results were submitted
for three viewing angles, 0, 45, and 60 degrees surface
incidence, for the European Centre for Medium-Range
Weather Forecasts (ECMWF) model profile simulations,
and at the AIRS viewing angle (11.56 degrees) for the
tropical ARM site profile.
[7] Table 1 lists the participating fast models. These
models sacrifice accuracy for speed of computation to
enable calculations to be made in real time as the AIRS
radiances are received. For simplicity they can be regarded
as being in two classes: those using regression techniques
on the profile variables and those employing precomputed
look up tables (LUT). The references in Table 1 give
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Table 2. Line-by-Line Models Which Participated in the Comparison
Model Name and
Reference
RFM
(http://www.atm.ox.ac.uk/RFM)
LBLRTM v8.3
[Clough et al., 1992]
ARTS 1.0.136
[Buehler et al., 2005]
4A [Scott and Chedin, 1981],
(http://www.noveltis.net/4AOP/)
FLBL-3 [Turner, 1995]
HARTCODE [Miskolczi et al., 1989]
Base Model Spectroscopy
Water Vapor Continuum
Line Mixing
GENLN2 HITRAN-2000
CKD2.4 [Strow et al., 1994]
HITRAN-2000 MTCKD
1.0 [Hoke et al., 1989]
HITRAN-2003 MTCKD
1.0 None
STRANSAC GEISA 2001
[Rodriguez et al., 1999]
HITRAN-2001 CKD2.4
[Strow et al., 1998]
HITRAN-2000 CKD2.4
[Rodriguez et al., 1999]
Method
N. Bormann, ECMWF
Yes/Finite diff
Full LbL computation
J.-L. Moncet, AER
None/Finite diff
Full LbL computation
A. von Engeln, Bremen
None/None
Full LbL computation
S. Heilliette, LMD
Yes/Analytic
Precomputed LUT
D.S. Turner, MSC
Yes/Analytic
Precomputed LUT
F. Miskolczi, NASA, LaRC
None/None
Full LbL computation
descriptions of the individual models and the methods used
to enable fast simulations.
[8] Table 2 lists the line by line models with their
references. For most of these models the full transmittance
calculation at a particular frequency is computed using the
line parameters from a spectroscopic database and an
assumed line shape plus continuum absorption parameterisation. Two of the models in Table 2 use large precomputed
look up tables but cannot be regarded as fast models. A
subset of the models indicated in Tables 1 and 2 also
computed layer to space transmittances and temperature,
water vapor and ozone Jacobians for 20 representative
AIRS channels listed in Table 3.
3. Definition of Comparison
[9] The process by which the comparison was undertaken
is described in this section.
3.1. Profile Data Sets
[10] The profiles were extracted from the diverse set of
13495 profiles generated from the ECMWF 40 year reanalysis, ERA-40. The methodology for extracting a small
number of profiles (49 in this case) to represent the full
variability of the atmosphere in temperature, water vapor
and ozone is described by Chevallier et al. [2000] and the
full characteristics of the ERA-40 data set are described by
Chevallier [2001]. The profile data set used and
corresponding surface parameters are available from the
following web site: http://www.metoffice.gov.uk/research/
interproj/nwpsaf/rtm/. The profiles were provided to participants on 101 levels defined by the AIRS science team.
These levels were originally derived by evaluating
7=
Pð xÞ ¼ ax2 þ bx þ c 2
Results Submitted
Transmittances/Jacobian
Participant
various gases, were used. This was imposed above 5 hPa for
water vapor and above 0.1 hPa for temperature, while a
linear extrapolation in pressure of the top model value was
used to extend the ozone profile. Some of the profiles lie
above elevated land or icecaps and the surface pressure
indicates this. The convention adopted for the subsurface
levels was to maintain constant values of temperature,
relative humidity, and ozone abundance below the surface.
The model calculations assumed the surface was defined by
the surface pressure which was provided.
[11] The characteristics of the 49 profiles used here are
summarised in Figure 1 and Table 4. The use of modelbased profiles ensured that the temperature profile was
everywhere consistent with the abundance of both water
vapor and ozone. Profiles 50– 52 are synthetic and contain
the adjusted minimum, adjusted maximum and mean profiles of the variables in the 13495-profile data set respectively. Model simulation results were submitted for the
artificially extreme profiles (50, 51), but they are not
included in this analysis as they are not a fair test of the
models in realistic atmospheric conditions. Profile interpolation software was provided for those models not using the
Table 3. AIRS Channels Used for Transmittance and Jacobian
Comparisonsa
Channel
Number
AIRS
Channel
Frequency, cm1
Jacobian
Computed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
71
77
305
453
672
787
1021
1090
1142
1437
1449
1627
1766
1794
1812
1917
1958
1995
2107
2197
666.7
668.2
737.1
793.1
871.2
917.2
1009.2
1040.1
1074.3
1323.8
1330.8
1427.1
1544.3
1563.5
1576.1
2229.3
2268.7
2305.5
2385.9
2500.3
T
T
T
T, Q
T, Q
T
T, O3
O3
Q
Q
Q
Q
Q
Q
Q
T
T
T
T
T
ð2Þ
given that P = 0.005 hPa, P = 300.0 hPa, P = 1100.0 hPa,
when x = 1, x = 38, x = 101 respectively, and values of the
three coefficients are a = 1.55 104, b = 5.59 102,
c = 7.45. These levels define a set of 100 layers with the
depth decreasing from several km at the top to less than
200m at the surface. The ERA-40 model-based profiles only
reach to 0.1 hPa. To extend them to the top of the 101 level
set at 0.005 hPa, data from the Halogen Occultation
Experiment (HALOE), which used solar occultation to
measure simultaneous vertical profiles of temperature and
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a
AIRS: Atmospheric Infrared Sounder.
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SAUNDERS ET AL.: RT MODEL COMPARISON FOR AIRS RADIANCES
Figure 1. The ERA-40 diverse profiles used for the comparisons. The extreme profiles (not included in
the results) are indicated by dashed lines and the profile mean by the thicker line. Plots for temperature,
water vapor and ozone are shown.
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Table 4. Characteristics of 49 Profiles Used for Comparison
Profile
Ps, hPa
Ts, K
Total Column
Water, Kg/sq m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Mininum
Maximum
Mean
972.2
970.5
1049.4
1030.9
628.1
1005.0
1009.8
983.0
871.7
1018.9
1016.8
976.9
1011.4
870.8
991.5
1015.6
987.6
1029.1
833.9
841.0
1007.4
870.8
806.6
804.7
1001.5
968.3
846.4
993.6
1022.2
993.0
1006.8
824.9
1008.0
949.4
1014.5
1008.8
989.2
1004.7
1011.8
989.4
975.9
1022.2
996.3
977.3
1017.1
885.1
1017.7
803.1
1013.4
1013.3
1013.3
1013.3
334.3
273.3
240.2
289.5
214.2
302.1
293.7
281.9
240.5
255.7
273.0
267.3
236.1
231.7
262.3
298.9
279.7
284.8
249.7
228.1
302.6
252.4
259.1
241.4
315.0
298.6
235.2
243.9
275.5
274.4
287.1
230.3
300.4
233.6
293.6
302.7
272.3
215.2
291.5
296.0
272.0
275.1
273.1
273.8
297.7
230.4
276.0
232.2
228.5
234.0
305.8
286.5
36.1
11.5
0.6
22.2
0.4
76.7
44.0
22.9
0.9
2.8
15.4
9.4
0.8
0.3
7.0
58.3
8.2
8.2
2.0
0.5
91.2
2.7
5.6
1.2
57.2
90.5
0.5
2.0
4.9
7.9
44.2
0.2
74.2
1.1
20.8
93.3
8.0
0.3
17.8
81.6
3.7
4.4
11.6
7.4
34.6
1.0
20.3
0.4
1.0
0.1
123.4
36.1
Total Ozone,
DU
273.6
390.1
364.2
281.3
273.2
264.7
305.1
280.5
217.0
419.1
298.7
360.7
427.1
288.4
223.2
249.3
335.4
276.2
234.1
261.9
220.4
347.6
312.6
286.0
274.4
283.8
300.3
243.8
376.0
375.3
284.3
302.1
252.8
314.3
298.6
238.2
296.8
377.5
329.8
254.4
426.4
292.4
304.1
334.8
265.1
192.7
258.0
301.0
436.8
59.2
825.1
303.2
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and ozone profile. The radiative skin temperature was from
a retrieval using the AIRS window channels. The total
column CO amount was adjusted empirically to best fit
the measured radiance data. The AIRS zenith angle at the
surface was 11deg at the ARM site.
3.2. AIRS Channels
[13] The definition of the spectral response of the 2378
AIRS channels was provided using the 18 August 2002
instrument spectral response function (ISRF) version 1 from
http://asl.umbc.edu/pub/airs/srf/. There have been small
changes in the AIRS ISRF since then but they are small
in terms of simulated radiances. This ISRF was also a good
choice to compare with the observed radiances over the
tropical ARM site.
[14] Some of the AIRS channels have been identified as
bad for instrumental reasons and are often referred to as
‘‘popping’’ channels. The AIRS science team have identified a set of 276 channels which are bad and these were
excluded from the comparison between the models and
the AIRS observations. There were, in addition, a further
9 channels listed in Table 5 that were excluded from the
analysis as they had obvious spikes when compared with all
the models. These are probably also instrumental in origin
but not yet included on the list of popping channels. The list
of the ‘‘official’’ popping channels is available as part of the
AIRS ISRF information.
[15] The 20 channels for transmittance and Jacobian
comparisons were chosen because they are part of the
324 channel set distributed to NWP centres in real time, have
different responses to temperature, water vapor and ozone and
cover the complete spectrum. They are also high in information content as defined by degrees of freedom of signal
[Rodgers, 1998] for NWP assimilation purposes.
AIRS 101 levels. For the surface the supplied skin temperature and a constant emissivity of 0.99 was assumed and the
radiance of space set to zero ensuring the surface reflection
effects as calculated by each model were included in the
calculations. Solar effects were not included in the comparison. For other gases all modelers were asked to assume
their own default profiles. RTTOV-8 uses the 52 profiles as
its dependent set for training the model coefficients and so
for this model the results are not independent.
[12] For the profile coincident with the AIRS measurements on 8 December 2002 over the tropical Pacific ARM
site at 0.5°S; 167°E the temperature (below 60 hPa) and
water vapor (below 200 hPa) profiles were taken from a
radiosonde. ECMWF analyses provided the surface pressure, temperature above 60 hPa, water vapor above 200 hPa
3.3. Results Submitted
[16] The participants were requested to submit top of
atmosphere equivalent black body brightness temperatures
for all 2378 AIRS channels for 3 viewing angles, nadir, 45
and 60 degrees local zenith angles at the surface for the 52
diverse profiles described above. In addition, brightness
temperatures for the one profile over the tropical ARM site
(0.5S; 167E) at an incidence angle of 11degrees on
8 December 2002 were also requested to compare with
the AIRS observed brightness temperatures.
[17] Optionally participants were also requested to provide, for the 20 AIRS channels defined in Table 3, layer to
space transmittances and Jacobians scaled by a factor DX
for changes in brightness temperature with respect to
temperature, water vapor and ozone for all the 52 profiles.
Table 5. AIRS Channels Not on ‘‘Popping’’ List but Excluded
From Comparison of Models With Observations
Channel Number
Frequency, cm1
326
342
415
432
571
919
923
1397
1791
743.80
748.88
772.94
778.77
837.53
967.43
969.04
1300.30
1561.63
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Figure 2. Comparison of AIRS RT models for the mean profile of the 52 set. The differences around
channel 590 are due to the different treatment of CFCs in the different models.
For the models computing finite difference Jacobians the
perturbations were defined as follows: (1) ±0.5K for the
temperature Jacobians; (2) ±0.5% of the absorber layer
mean mass mixing ratio.
[18] The comparisons were then made of the ‘‘scaled
Jacobians’’, J defined as
J ¼ H DX
ð3Þ
where DX was +1 K for temperature and 1% of the
absorber layer mean mass mixing ratio for water vapor and
ozone. The remaining text will refer to J as a Jacobian for
convenience even though this is not the true definition of a
Jacobian defined in equation (2). Most of the models
submitted results on the 100 layers between the levels
defined in equation (1) but RTTOV-7 and s-IASI were
submitted on 43 and 60 layers respectively. To allow
comparisons with other models, the transmittance profiles
were linearly interpolated/extrapolated in pressure to the
101 levels. The Jacobians were remapped on to the 100
layers using the adjoint of the interpolation routine. This
worked well for RTTOV-7 but the s-IASI Jacobians
remapped to 100 layers could not be reconciled with the
other models for some profiles and channels and so the
results for the s-IASI Jacobians although included need to
be treated with caution.
[19] For both the forward model comparisons and the
Jacobians the results from each model were differenced with
RFM, one of the line-by-line models, in order to be able to
conveniently examine the intermodel differences. For the
Jacobians the ‘‘measure of fit’’ adopted by Garand et al.
[2001] was used defined as
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
uP
u
Pi Piref
u
M ¼ 100 u
t P ref 2
Pi
ð4Þ
where Pi is the profile variable at level i and Pref
is the
i
reference profile variable which was taken to be the RFM
Jacobian or transmittance profile for this study. For the
results presented here P is either the level to space
transmittance profile or the ‘‘scaled Jacobian’’ J as defined
in equation (3). The summation over levels was restricted to
the range 0.35 – 959 hPa (or the level above the surface if
the surface pressure was less than 959 hPa) to avoid
problems due to extrapolation above the top layer of
RTTOV-7 and s-IASI and interactions with the surface.
4. Forward Model Comparisons
4.1. Results for ECMWF Model Profiles
[20] As an illustration of the forward model comparisons, Figure 2 shows a portion of the spectrum from 810 to
880 cm1 (channels 500 – 700) for the profile mean
(number 52). Some differences between the different RT
models are clear in this part of the spectrum. The obvious
differences in the region of channel 590 (845 cm1) are
due to the different way each model treats the absorption
due to chlorofluorocarbons, CFCs, which in this case is
CFC-11. There are also significant differences in the
‘‘window’’ regions between the lines due to differences
in the water vapor continuum formulation. Those fast
models which are based on a line-by-line model included
in the study generally follow the model on which they
were trained. For example, OSS follows LBLRTM closely.
RTTOV-7, based on GENLN-2, which is similar to RFM,
does follow RFM below 850 cm1 (channel 600) but there are
significant differences in the window regions at higher
frequencies due to water vapor continuum differences between the GENLN2 run and the current version of RFM.
[21] To summarise the mean nadir view brightness
temperature differences between each model and RFM
Figures 3a and 3b show for all channels that the differences,
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Figure 3. The mean difference from RFM for the 49 diverse profiles for all AIRS channels. (a) Fast
models; (b) Line-by-line models.
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Table 6. Comparison of all Models Simulated Brightness
Temperatures With RFMa
Nadir
45 degrees
60 degrees
Model
Bias
Sdev
Bias
Sdev
Bias
Sdev
LBLRTM
4A
HARTCODE
SIGMA_IASI
ARTS
FLBL
Gastropod
OPTRAN
PCRTM
OSS
SARTA
RTTOV-7
RTTOV-8
0.01
0.01
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.04
0.05
0.12
0.11
0.07
0.05
0.05
0.08
0.05
0.05
0.08
0.06
0.07
0.01
0.01
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.05
0.06
0.11
0.12
0.08
0.06
0.05
0.09
0.06
0.05
0.09
0.07
0.08
0.01
0.01
0.02
0.03
0.02
0.02
0.01
0.02
0.01
0.01
0.02
0.02
0.02
0.05
0.06
0.12
0.26
0.08
0.07
0.06
0.11
0.07
0.05
0.09
0.08
0.08
a
The differences are model-RFM in deg K and averaged over the
49 diverse profiles to form the mean and standard deviation (sdev) of the
differences for each channel. The individual channel mean and standard
deviation values are then all averaged to produce the numbers in the table.
Bold numbers show values >0.02 K in bias and >0.1 K in standard
deviation.
when averaged over the 49 profiles, are below the 0.1 K level
except in a few narrow spectral bands. s-IASI is slightly
warmer (0.05 K) than the other models in the atmospheric
window and cooler in the shortwave CO2 band. Hartcode
has a warm bias in most parts of the spectrum except the
‘‘window’’ regions. SARTA generally has a cool bias in the
water vapor band. It is important to bear in mind that these
biases are with respect to the RFM model and not with
respect to an absolute truth. RFM may not provide the best
reference in all spectral regions. With a few exceptions, the
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differences of the models from RFM are similar. It is worth
noting that the differences between line-by-line models
(Figure 3b) are of the same order of magnitude as for the
fast models (Figure 3a) suggesting that the different
assumptions made in the spectroscopy and use of different
line data sets dominate the RT model error statistics.
[22] To summarise the overall differences between models Table 6 gives the mean bias and standard deviation of
the brightness temperature differences from RFM averaged
over all the AIRS channels and the 49 diverse profiles. For
all models except Hartcode the mean and standard deviation
of the differences increase slightly with incident viewing
angle but there is no great variation. Note all models assume
a plane parallel atmosphere for these simulations and for
60 degrees at least this assumption introduces small biases
(0.2 K) with real data.
[23] The model differences are also compared over discrete spectral regions as plotted in Figure 4 and listed in
Table 7 which represent areas of the spectrum used for
temperature, water vapor, ozone or surface sounding. In
terms of mean bias (not plotted) most differences are below
±0.02 K, but most models depart from RFM in the 2350–
2420 cm1 band being warmer except ARTS. Many models
have a cool bias (0.01 K) for the longwave CO2 bands
relative to RFM. Both Hartcode and s-IASI exhibit larger
biases for most bands relative to RFM than other models
with the 2350– 2420 cm1 band in particular for Hartcode
showing a large positive mean bias of greater than 0.1 K and
standard deviation of 0.5 K. In addition, Figure 4 shows the
AIRS instrument noise for each of the bands which is
greater than the model differences with the exception of
the 2350 – 2420 cm1 band. This is encouraging as it
suggests the RT models are on average accurate enough
for forward calculations of AIRS radiances. However over
Figure 4. A histogram of the RT model nadir view differences from RFM for different spectral regions.
The columns on the far right give the AIRS instrument noise for a 250 K brightness temperature scene.
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Table 7. Comparison of Model-RFM Brightness Temperature Differences for Several Spectral Regionsa
Frequency
Range cm1 RTTOV 7
ARTS
650 – 770
Temp
770 – 980
Sfc + Cloud
1000 – 1070
Ozone
1250 – 1350
Water Vap
2150 – 2250
Temp
2350 – 2420
Temp
2420 – 2600
Surface
0.031 0.010
0.189
0.102
0.006
0.008
0.037
0.044
0.003
0.000
0.038
0.035
0.002
0.008
0.032
0.044
0.001 0.001
0.012
0.025
0.040 0.023
0.215
0.175
0.001 0.001
0.009
0.006
0.009
0.058
0.007
0.048
0.005
0.045
0.026
0.131
0.010
0.055
0.025
0.123
0.004
0.025
FLBL
Gastropod LBLRTM OPTRAN PCRTM
0.006
0.086
0.002
0.018
0.001
0.049
0.023
0.109
0.003
0.044
0.011
0.112
0.001
0.006
0.016
0.087
0.000
0.020
0.000
0.015
0.004
0.036
0.008
0.038
0.025
0.143
0.001
0.011
0.017
0.112
0.006
0.081
0.002
0.068
0.006
0.097
0.002
0.100
0.026
0.157
0.001
0.042
OSS
SARTA
4A
0.007 0.017 0.002 0.002
0.106
0.088
0.086
0.046
0.004
0.000
0.007
0.003
0.036
0.020
0.055
0.038
0.005
0.000
0.010
0.000
0.039
0.018
0.053
0.046
0.008
0.004 0.018 0.005
0.053
0.037
0.105
0.059
0.007
0.008 0.010 0.005
0.042
0.039
0.076
0.025
0.020
0.025
0.004
0.020
0.138
0.143
0.140
0.095
0.000
0.001 0.007 0.001
0.011
0.013
0.050
0.011
HARTCODE Sigma- IASI RTTOV 8
0.005
0.078
0.021
0.136
0.010
0.073
0.027
0.141
0.015
0.065
0.108
0.490
0.003
0.022
0.006
0.075
0.025
0.109
0.031
0.128
0.025
0.123
0.031
0.150
0.000
0.257
0.013
0.059
0.008
0.093
0.004
0.042
0.009
0.052
0.004
0.061
0.000
0.037
0.014
0.143
0.007
0.053
a
Upper number: bias; lower number: standard deviation. Larger differences are highlighted in bold.
narrow spectral regions as shown in Figure 3 it may still be
the case that the RTM errors may exceed the instrument
noise.
4.2. Comparison With AIRS Measurements
[24] The comparison with observed AIRS radiances was
made for one profile over the tropical western Pacific ARM
site as described in section 3.1. The results are shown in
Figures 5a and 5b and the first thing to note is the much
greater difference between models and observations than
between models and models shown in Figure 3, with
differences from the observations typically up to ±1 K
and in some spectral regions up to ±3 K. All models
show a negative difference of 2 – 3 K with respect to the
AIRS observations around the 9.8 micron ozone band
(channels 1023– 1153), suggesting that the ozone profile
from the ECMWF model is in error. High-peaking CO2 bands
(channels 1 – 406, 1912 –2121) also have consistent differences across all models again probably due to errors in the
ECMWF upper stratospheric temperature profile. Table 8
summarizes the differences showing that SARTA has the
best agreement with the AIRS observations in terms of
root mean square difference and this is clear around
AIRS channel 2150 which is due to the improved CO2
R-branch line mixing formulation in kCARTA and also a
new water vapor continuum. Table 8 shows the cool
biases of most of the models can be attributed to the
deficiencies in the profile as shown by the statistics
which exclude the ozone and high-peaking CO2 bands.
The RMSD values of all models are also reduced,
especially for SARTA, when these bands are excluded
from the statistics. The good fit of SARTA is not
surprising as the spectroscopic parameters it uses (e.g.,
gaseous absorption coefficients, water vapor continuum)
were tuned on an AIRS radiosonde match-up data set that
included this profile (see Strow et al. [2006], for more
details). RFM the reference model for this study agrees
reasonably well except at the CO2 4.3 mm band edge and
at the peak of the CO2 15 mm band and so this needs to be
noted for the comparisons with RFM in section 4.1. Notable
departures from the observations for the other models seen in
Figures 5a and 5b include several cool biases at discrete
frequencies for OPTRAN and ARTS which have two significant negative biases of 8K at 4.18 mm close to the band
edge and at 13.9 mm. Hartcode differences from the observations show a large warm peak on the CO2 4.3 mm band edge.
5. Comparison of Layer to Space Transmittances
and Jacobians
5.1. Layer to Space Transmittances
[25] Profiles of layer to space transmittance were computed by some of the RT models for the 52 profiles and the
20 AIRS channels as indicated in Table 3. The results are
summarized in Table 9 as the mean transmittance difference
from RFM computed using equation (4) for each profile and
then averaged over the 49 diverse profiles. There are a few
channels from the set which are modeled less consistently
compared to RFM, i.e., 71, 77 and 2107 and these channels
are all close to strong CO2 absorption bands. As both lineby-line and fast models exhibit differences this is likely to
be due to spectroscopic differences rather than fast model
problems. Also worth noting are the larger differences for
the 4A model for most of the water vapor and shortwave
infrared channels. For some of the AIRS water vapor
channels (1766, 1812) RTTOV-8 transmittances also depart
from RFM more than the other models.
5.2. Jacobians
[26] An example of the temperature Jacobians computed
is shown in Figure 6a. For this profile, in general the models
are in good agreement. Figure 7 summarizes the fit for
temperature Jacobians for temperature sensitive channels.
These box and whisker plots show both the range and mean/
median of the fit to RFM for all 49 profiles. Some channels
have better fits (e.g., 77) than others (e.g., 787) and some
channels have worse fits between models (e.g., 71).
[27] The first point to note is that for some of the channels
the s-IASI deviations from the RFM Jacobians are large and
this is due to the resampling of the 60 level values supplied
to 100 levels to enable comparisons to be made. For channel
787, a window channel, both OPTRAN and FLBL seem to
have problems computing a Jacobian for this weak absorption domain as the fit to RFM is poor for most profiles.
[28] The goodness of fit values are a useful metric to
assess the overall performance of the models. However they
do not show more subtle problems in computed Jacobians
which could be detrimental to retrieval and data assimilation
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Figure 5a. The difference between each model and AIRS observations over the tropical ARM site on
8 December 2002 for a surface incidence angle of 11 degrees.
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Figure 5b. As in Figure 5a.
applications. One example for channel 787 is shown in
Figure 6b which the majority of the models show as a weak
smooth peak in the temperature Jacobian close to the
ground (800 hPa). Some models however have a more
variable structure in the vertical (e.g., 4A, PCRTM) which
are obviously unphysical. The issue this comparison is
unable to resolve is whether these features matter for
assimilation/retrievals as it is a relatively weak Jacobian in
terms of absolute temperature changes.
[29] Figure 8 shows the box and whisker plots for the
water vapor Jacobians and again the sigma-IASI results
should be treated with caution. In general the accuracy of
AIRS water vapor Jacobians were poorest for cold, dry
profiles. In particular, Gastropod and RTTOV-7 showed
poor performance for these profiles in channels 672 and
1142 (associated with extrapolation of the fast model
regression bounds in the case of the Gastropod model),
and the poorer fits for FLBL in channels 1437 and 1449
also appear to be associated with profiles with high surface
elevation over Antarctica. However, some poor fits to RFM
Jacobians appear likely to be associated with differences in
spectroscopy, e.g., the systematic difference in model Jacobians in channel 453, and poor fits (and associated significant
differences in simulated transmittances) for RTTOV-8 Jacobians in channel 1766 and RTTOV-7 in channel 1812.
Table 8. Model Minus AIRS Observed Brightness Temperature
Differences Averaged Over All Nonpopping Channels for the
Tropical ARM Profile and for Those Excluding Ozone and HighPeaking CO2 Channelsa
All Valid Channels
Model
RFM
RTTOV7
RTTOV8
FLBL
Gastropod
LBLRTM
OPTRAN
PCRTM
OSS
SARTA
4A
HARTCODE
SIGMA_IASI
ARTS
No Ozone and Strong CO2
Mean deg K RMSD deg K Mean deg K RMSD deg K
0.02
0.07
0.06
0.01
0.09
0.05
0.11
0.13
0.05
0.19
0.03
0.09
0.22
0.16
0.75
0.75
0.64
0.75
0.71
0.72
0.82
0.74
0.72
0.57
0.68
0.96
0.76
0.98
0.18
0.03
0.13
0.20
0.10
0.18
0.27
0.04
0.18
0.02
0.10
0.36
0.38
0.12
0.57
0.59
0.44
0.58
0.52
0.54
0.59
0.48
0.54
0.23
0.53
0.75
0.64
0.51
a
The bold figures are for mean differences >0.2 K and standard deviation
>0.6 K. ARM: Atmospheric Radiation Measurement.
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Table 9. Mean Transmittance Differences From RFM Using Goodness of Fit Formula (Equation (2))a
AIRS Channel
Gastropod
PCRTM
Optran
4A
FLBL
RTTOV-8
RTTOV-7
Sigma-IASI
71
77
305
453
672
787
1021
1090
1142
1437
1449
1627
1766
1794
1812
1917
1958
1995
2107
2197
6.42E-03
1.18E-01
8.23E-03
4.29E-05
2.19E-03
1.22E-05
1.09E-03
6.28E-03
1.24E-03
2.95E-03
1.80E-03
1.33E-03
8.80E-04
4.27E-04
3.34E-03
2.21E-03
1.74E-03
8.95E-03
1.41E-01
0.00E+00
3.79E-02
2.94E-01
8.07E-03
4.96E-04
7.73E-04
6.06E-04
5.35E-04
4.12E-03
5.92E-05
2.56E-03
2.72E-03
3.12E-04
4.67E-04
7.29E-04
1.71E-03
2.58E-03
7.86E-03
5.82E-03
1.88E-01
8.98E-05
2.12E-02
5.44E-03
1.11E-02
1.02E-03
1.42E-03
5.87E-03
7.84E-04
3.97E-03
4.69E-04
1.99E-03
2.37E-03
2.18E-04
8.98E-05
5.96E-04
1.37E-03
2.63E-03
3.28E-03
1.28E-03
2.17E-01
9.80E-05
2.50E-01
9.32E-01
3.12E-02
1.01E-02
6.97E-03
3.00E-03
2.53E-03
1.06E-01
7.62E-03
4.14E-02
5.76E-02
1.25E-01
1.12E-01
1.42E-01
6.58E-02
3.71E-02
1.02E-01
1.18E-01
2.39E-02
3.61E-04
2.12E-03
2.19E-01
1.06E-02
1.00E-03
1.79E-03
4.79E-03
2.45E-04
5.55E-03
1.10E-03
1.96E-03
9.27E-04
6.67E-04
4.08E-06
3.35E-04
1.34E-03
4.71E-04
3.86E-03
4.20E-03
2.91E-01
0.00E+00
5.29E-03
1.49E-01
1.23E-02
3.88E-04
9.67E-04
1.28E-03
1.77E-03
4.88E-03
8.43E-04
4.76E-04
4.27E-04
2.24E-03
8.67E-02
2.30E-03
1.69E-02
2.53E-04
5.03E-03
2.88E-03
1.15E-01
1.82E-03
6.64E-03
2.65E-02
1.82E-04
1.93E-03
1.92E-02
1.45E-04
1.25E-03
2.96E-03
1.64E-03
1.17E-02
1.28E-02
1.98E-03
8.43E-03
1.64E-02
1.62E-02
5.23E-03
3.20E-04
1.91E-03
1.82E-03
1.38E-03
5.02E-02
5.00E-02
2.04E-03
6.06E-04
7.53E-04
1.39E-03
4.81E-03
1.86E-02
1.33E-03
4.77E-03
3.72E-03
1.56E-03
6.71E-03
4.93E-03
7.77E-03
2.95E-02
1.92E-02
2.02E-02
2.36E-01
7.14E-05
a
The transmittance is in units from 0 – 1, and differences greater than 0.05 are highlighted in bold.
[30] Finally for ozone Jacobians Figure 9 summarizes the
fit to RFM for the 2 selected channels. PCRTM has the best
fit to RFM for ozone but most models have good fits
compared with the water vapor Jacobians. RTTOV-7
departs from the reference more at the peak of the Jacobian
but this may be due to the 43 levels on which the
computation is done compared with 100 levels for the other
models rather than inaccuracies in the model itself.
[31] The results above all refer to Jacobians computed for
nadir views. Computations were also made for viewing
angles of 45 and 60 degrees. The results were all similar to
the nadir view Jacobians presented here and so viewing
angle does not appear to be a factor which affects the
Jacobian errors significantly.
6. Summary
[32] Results of comparisons of AIRS radiative transfer
models are presented here in order to better understand the
error characteristics of AIRS RT models important for data
assimilation and retrieval applications using AIRS data. For
the forward model comparisons when averaged over 49
profiles all the models agree within 0.06 K and most models
to within 0.02 K of the RFM model used as a reference.
Exceptions to this are in regions affected by CFCs, water
vapor continuum or CO2 line mixing where larger differences can be found. The differences between the line-byline models are as large as between the fast models
suggesting the dominant error sources are related to the
spectroscopic assumptions and line parameters used rather
than the fast model formulations. Other possible sources of
error include the treatment of the surface reflection, Plank
constants assumed, and treatment of layers in the integration
of the radiative transfer equation.
[33] The mean biases shown by each model can be
removed by a bias correction procedure as is standard
practice in data assimilation applications (although there
will be associated, uncorrected Jacobian errors). It is
encouraging that the standard deviation of the differences
between the models and RFM is for all models less than
the AIRS instrument noise. This suggests that the forward
model error is not the dominant error source but instrument noise and errors of representativity are likely to be
more important when comparing simulated with measured
radiances.
[34] The comparison against AIRS observations for a
single profile shows bigger differences with mean brightness temperature differences at the 1 K level. The SARTA
model fits the AIRS observations best especially in the
2100– 2200 cm1 region but has been tuned using data
including this profile. Some of the differences with the
AIRS observations are due to our inadequate representation of the atmospheric state for ozone and stratospheric
variables.
[35] In terms of transmittances the 4A model, and to a
lesser extent RTTOV-8, are consistently different from RFM
but this may just reflect the fact that these models have
recently been updated and include more up to date spectroscopy than RFM. The performance of the models in
terms of Jacobian accuracy varies with most models having
problems for some profiles. For temperature the AIRS
917 cm1 channel appears to be the most problematic
channel for modeling Jacobians with 4 out of the 8 models
diverging significantly from RFM. For water vapor
RTTOV-8 is consistently different from the RFM response
for most water vapor channels but this may be due to the
new spectroscopy in the kCARTA data set on which this
version of RTTOV-8 was trained. The ozone Jacobians were
in general more consistent between models. Further study is
needed to assess the impact of model-specific Jacobian
errors (e.g., erratic weak Jacobians, poorly modeled Jacobians in cold, dry atmospheres) and Jacobian errors associated with bias correction, on retrieval accuracy. Sherlock
[2005] has started to address this with a study of the effect
of fast model errors, including Jacobians, on AIRS retrieval
accuracies.
[36] To allow other modelers who did not participate in
this comparison to compare their models with the data sets
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Figure 6. (a) An example of the temperature Jacobian comparison for profile 1 and AIRS channel 77
and (b) a temperature Jacobian for profile 22 and channel 787.
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Figure 7. Box and whisker plots which show the range of the fits to the RFM temperature Jacobians as defined in equation
(2) for each model. The box gives the bounds of the upper and lower quartiles, the solid line through the box is the median,
the dashed line is the average, and the whiskers indicate the maxima and minima of the differences.
SAUNDERS ET AL.: RT MODEL COMPARISON FOR AIRS RADIANCES
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Figure 8. As in Figure 7 for the water vapor Jacobians.
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Figure 9. As in Figure 7 for the ozone Jacobians.
presented in this paper the International TOVS Working
Group have set up a web site which includes the raw model
output data that produced the results presented here. The
link is at: http://cimss.ssec.wisc.edu/itwg/groups/rtwg/
rtairs.html.
[37] Acknowledgments. The support of Anu Dudhia (University of
Oxford) in making the RFM available for this study is gratefully acknowledged. Also the International TOVS Working Group is acknowledged for
providing the Web site to coordinate the comparison.
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P. Brunel, MétéoFrance, CMS, BP147, Lannion 22302, France.
Y. Han, NOAA, 5200 Auth Road, Camp Springs, MD 20746-4304, USA.
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D01S90
SAUNDERS ET AL.: RT MODEL COMPARISON FOR AIRS RADIANCES
X. Liu and F. Miskolczi, MS 401A Atmospheric Sciences Competency,
NASA Langley Research Center, Hampton, VA 23681, USA.
G. Masiello, IMAA-CNR, Tito Scalo, Potenza, 85050, Italy.
J.-L. Moncet and G. Uymin, Atmospheric and Environmental Research,
131 Hartwell Avenue, Lexington, MA 02421-3126, USA.
P. Rayer and R. Saunders, Met Office, Exeter, EX1 3PB UK.
D01S90
V. Sherlock, National Institute of Water and Atmospheric Research,
Private Bag 14-901, Wellington, New Zealand.
D. S. Turner, Environment Canada, 4905 Dufferin Street, Toronto, ON,
Canada, M3H 5T4.
A. von Engeln, Institute of Environmental Physics, Bremen University,
28334 Bremen, Germany.
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