Q. J. R. Meteorol. Soc. (2003), 129, pp. 2719–2740
doi: 10.1256/qj.02.180
AIRS channel selection for CO2 and other trace-gas retrievals
By CYRIL CREVOISIER¤ , ALAIN CHEDIN and NOELLE A. SCOTT
IPSL, Laboratoire de Météorologie Dynamique, Ecole Polytechnique, France
(Received 3 September 2002; revised 1 April 2003)
S UMMARY
New high-resolution infrared sounders, such as the National Aeronautics and Space Administration’s Aqua
satellite Atmospheric Infrared Sounder (AIRS) or the European Meteorological Satellite systems, MetOp Infrared
Atmospheric Sounding Instrument (IASI), are expected to improve our capability to monitor atmospheric carbon
dioxide (CO2 ) and other trace-gas concentrations from space. As they present thousands of channels, the Ž rst
problem arising is the selection of a set of channels presenting the best properties to retrieve these concentrations.
A new method, the Optimal Sensitivity ProŽ le (OSP) method, based on the study of the sensitivities of AIRS
channels to variations in the vertical of the different atmospheric components, is proposed. It is then compared
with two ‘classical’ methods based on the information content and the degrees of freedom for signal of the AIRS
channels regarding CO2 . Applying the OSP method to a set of 82 representative atmospheric situations obtained
from the 2311 situations of the Thermodynamic Initial Guess Retrieval (TIGR) dataset, divided into three air
masses (tropical, temperate and polar), and using simulated AIRS observations, a global set of 43 channels,
well covering the whole atmospheric column, is selected for CO2 retrieval. The OSP method is Ž nally used to
select channels for retrieval of atmospheric nitrous oxide (N2 O), carbon monoxide (CO) and methane (CH4 )
concentrations.
K EYWORDS: Greenhouse-gas sensitivity
1.
High-resolution infrared sounders
Information content
I NTRODUCTION
Progress in both basic earth-system science and in managing the carbon cycle to
mitigate climate change requires robust and veriŽ able understanding of the current behaviour of the system (Schimel et al. 1995; IGBP 1998). Without knowledge of today’s
carbon sources and sinks, including their spatial distribution and their variability in
time, theoretical predictions of future levels cannot be veriŽ ed. The atmosphere is a
superb integrator of spatially and temporally varying surface  uxes (Tans et al. 1990).
The distribution of carbon dioxide (CO2 ) in the atmosphere and its time evolution can
thus be used to quantify surface  uxes (Rayner and O’Brien 2001). The feasibility of using satellite measurements to obtain the temporal and spatial variability of atmospheric
CO2 concentration has been proven with existing, low-spectral-resolution instruments
(Chédin et al. 2002a,b, and submitted to J. Geophys. Res.), with the National Oceanic
and Atmospheric Administration’s Television Infrared Observation Satellite (TIROS-N)
Operational Vertical Sounder (TOVS). New satellites such as the National Aeronautics and Space Administration’s (NASA) Terra, launched in December 1999, NASA’s
SAGE-3 launched in December 2001, the European Space Agency’s Envisat, launched
in March 2002, NASA’s Aqua, launched in May 2002, NASA’s Aura, scheduled for
early 2004, or the European Meteorological Satellite systems’ MetOp scheduled for
2005, will  y numerous instruments that should improve our capability to monitor CO2
and other trace gases from space.
In particular, the advanced infrared sounders, Aqua’s Atmospheric Infrared
Sounder (AIRS) and MetOp’s Infrared Atmospheric Sounding Instrument (IASI), will
present thousands of channels (respectively 2378 and 8461), covering most of the infrared spectrum. Using all the channels to retrieve CO2 or any other trace gas is of
course prohibitive in terms of operational cost and unnecessary as only a small part
of these channels is sensitive to the gases. Therefore, the Ž rst problem arising is the
¤
Corresponding author: Laboratoire de Météorologie Dynamique, Ecole Polytechnique, 91128 Palaiseau Cedex,
France. e-mail: [email protected] ue.fr
c Royal Meteorological Society, 2003.
°
2719
2720
C. CREVOISIER et al.
choice of a set of channels presenting the best properties regarding the retrieval of each
trace gas. To reach this goal, different methods can be used. First, following Chédin
et al. (1999, 2003), we can study the sensitivity of the channels to trace gases and other
atmospheric and surface thermodynamic components. This leads to the Optimal Sensitivity ProŽ le (OSP) method presented here. Another way to select channels is to make
a study of the information, deŽ ned by a given Ž gure of merit, brought by each channel.
Two Ž gures of merit will be used in the following: the Shannon information content (IC)
and the degrees of freedom for signal (DFS), the latter being a measure of the number
of statistically independent quantities of any one measurement. Most articles published
on the selection of individual channels are based on objective criteria (Rodgers 1996;
Lerner et al. 2002; Rabier et al. 2002). However, they all deal with temperature and
humidity. We propose here to extend these methods to the study of CO2 and other trace
gases.
We will use simulated AIRS data computed from a set of representative atmospheric
conditions obtained from the Thermodynamic Initial Guess Retrieval (TIGR) climatological dataset (Chédin et al. 1985; Chevallier et al. 1998). Data and models are described in section 2. The three methods used to select channels for CO2 retrieval are presented in section 3 (OSP method) and in section 4 (methods based on information study).
Section 5 intercompares the sets of channels obtained. Section 6 presents the channels
selected for the retrieval of other trace gases. Section 7 presents the conclusions.
2.
DATA AND MODELS
Only two spectral bands are of interest for CO2 study: the band from 650 cm¡1
to 810 cm¡1 (hereafter referred to as the 15 ¹m band) and the band from 2150 cm¡1
to 2450 cm¡1 (hereafter referred to as the 4.3 ¹m band). The 10 ¹m band will not
be considered as the CO 2 signal obtained in these regions is too weak and well below
the ozone signal. For AIRS, this leads to the study of 775 channels with a spectral
resolution of º=±º D 1200 (497 channels in the 15 ¹m band with a spectral resolution
of about 0.5 cm¡1 and 278 channels in the 4.3 ¹m band with a resolution of 2 cm¡1 ).
In the 15 ¹m band, two other gases are active (water (H2 O) and ozone (O 3 )) while, in
the 4.3 ¹m band, three other gases are active (H2 O, nitrous oxide (N2 O) and carbon
monoxide (CO)).
Our study is based on the 2311 atmospheric situations of the TIGR dataset.
These 2311 situations were clustered into 82 classes, the respective means of which
are enough to represent the dynamics of the atmospheric variables considered here with
a lower computing cost. The 82 resulting situations can Ž nally be classiŽ ed into three
types of air mass: tropical (28 situations), temperate (27) and polar (27). Each situation
is described by its temperature, water-vapour and ozone atmospheric proŽ les, the
atmosphere being divided into 40 pressure levels, regularly spaced (Chevallier et al.
1998).
For each atmospheric situation and for each AIRS channel, we have computed
the brightness temperatures which would be seen by AIRS, assuming a cloud-free
scene, and the Jacobians (partial derivative of the channel brightness temperature
with respect to a layer physical variable such as a gas mixing ratio, a temperature
or the emissivity). This was done using the Automatized Atmospheric Absorption
Atlas (4A) line-by-line radiative-transfer model (Scott and Chédin 1981) in its latest
version 2000 with up-to-date spectroscopy from the ‘Gestion et Etudes des Informations
Spectroscopiques Atmospheriques (GEISA): Management and Study of Atmospheric
Spectroscopic Information’ (Jacquinet-Husson et al. 1999), with the option of allowing
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
2721
the Jacobians to be computed analytically (Chéruy et al. 1995). Concentrations of
trace gases were assumed to be constant. For CO 2 , N2 O, CO, and CH4 , we assumed
concentrations equal to 372 ppmv, 324 ppbv, 100 ppbv and 1800 ppbv, respectively.
These are the predicted concentration values for the year 2003 (IPCC 2001). For each
situation and each AIRS channel, we have also computed the noise due to the instrument,
using the following equation
@B
.Tref /
NE1T fT .º/g D NE1T fTref .º/g @T
@B
fT .º/g
@T
(1)
where NE1T fT .º/g is the equivalent noise temperature taken at the brightness temperature T .º/ of the channel located at frequency º, and B is the radiance. The reference
noise corresponding to a reference temperature Tref of 250 K was provided to us by the
AIRS science team.
3.
T HE O PTIMAL S ENSITIVITY P ROFILE METHOD
To be selected, a channel has to present the best potential to detect CO2 changes
from the top-of-the-atmosphere radiance measurements (the ‘signal’) and has to present
the lowest possible sensitivity to other gases or thermodynamic variables of the atmosphere (the ‘noise’). Therefore, one way to select channels is to study their sensitivities
to different components and then to select the channels presenting the highest ‘signal’to-‘noise’ ratio.
(a) Sensitivity studies for AIRS channels
The response of a given channel to the perturbation of a relevant atmospheric
component (gas, surface characteristics, . . . ) may be obtained by the product, pressure
layer by pressure layer, of the component Jacobian and the perturbation proŽ le. For CO2
we chose to perturb the proŽ le by half the value of the mean peak-to-peak amplitude of
the seasonal CO2 cycle. This is 4 ppmv for tropical situations and 9 ppmv for temperate
and polar situations (Conway et al. 1994). The corresponding signal obtained in the
CO2 bands is shown in Fig. 1(a) for the 15 ¹m band and in Fig. 2(a) for the 4.3 ¹m
band, for a representative tropical proŽ le. The signal is of the same level in the two
bands. It should be noted that IASI measurements will present a higher resolution,
under 0.5 cm¡1 unapodized throughout the whole spectrum, in the 4.3 ¹m band (see for
example Chédin et al. 2002b). In both bands, some regions present negative signals
(around 650 cm¡1 or 2350 cm¡1 ). They are regions where the channels essentially look
in the stratosphere. By contrast, channels located in regions presenting a positive signal
essentially look in the troposphere. This can be conŽ rmed by the study of the CO2
Jacobians (not shown).
Indeed, each channel favours that part of the atmosphere where the corresponding
Jacobian is the most important. A channel whose Jacobian is more important in the troposphere (stratosphere) will be referred to as a ‘tropospheric’ (‘stratospheric’) channel.
Another difference with IASI is AIRS instrument noise, plotted as dotted line on
Figs. 1(a) and 2(a). It has the same level in both bands whereas, for IASI, the noise
is greater in the 4.3 ¹m band (results from laboratory experiments). A plot showing
the noise at a given temperature can be found on the website of the AIRS team
(http://www.airs.jpl.nasa.gov/, April 2003).
2722
C. CREVOISIER et al.
(b)
0.8
0.8
0.6
0.6
0.4
TB (K)
TB (K)
(a)
Noise
0.2
H O
0.4
0.2
0
0
CO
0.2
f
650
700
2
750
0.2
f
650
800
1
f
800
1
f
(c)
(d)
0.8
O
3
0.4
0.2
0.2
0
0
700
Surface T
0.6
TB (K)
TB (K)
750
wave number (cm )
0.4
0.2
f
650
700
wave number (cm )
0.8
0.6
2
750
800
1
f
wave number (cm )
0.2
f
650
Emissivity
700
750
800
1
f
wave number (cm )
Figure 1. Atmospheric Infrared Sounder (AIRS) channel sensitivities to (a) CO2 for a 4 ppmv perturbation,
(b) H2 O, (c) O3 , and (d) surface characteristics for the 15 ¹m band and a representative tropical situation.
For water vapour, we assume the proŽ le to be known to within an uncertainty given
by the mean error in the background model Ž elds (from a 6-hour forecast) of the European Centre for Medium-Range Weather Forecasts (ECMWF) for each latitude band.
This represents the background error assumed in the retrieval/assimilation schemes.
These errors were taken from the 1999 version of the ECMWF model analysis system
(Derber and Bouttier 1999). It is likely that future developments in data assimilation
systems, numerical weather-prediction model formulation, and increased use of satellite data will reduce these errors, so those assumed here are an upper limit. The signal
obtained is shown in Figs. 1(b) and 2(b).
Surface temperature and emissivity are supposed to be known to within 1 K and
0.01, respectively. These values are the expected retrieval errors (see Chédin et al.
2002b). The signals are shown in Figs. 1(d) and 2(d). For the three remaining gases,
in the same way as for CO2 , the perturbations are assumed to be constant and equal
to 20% for O3 , 2% for N2 O and 40% for CO (IPCC 2001). The signals are plotted in
Figs. 1(c) and 2(c).
In the following, we will not consider the sensitivity of the channels to temperature.
Indeed, although the channels sensitive to CO2 are, as any other channel, Ž rst sensitive
to temperature, the effect of CO2 variations is likely to be a bias, whereas the signal from
the perturbed temperature proŽ le is in general expected to be randomly distributed over
a reasonable time period (about two weeks) and should, therefore, average out when
2723
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
(a)
(b)
0.8
0.8
0.6
Noise
B
0.4
T (K)
B
T (K)
0.6
0.2
H O
2
0.4
0.2
0
0
CO
2
f.2
0
2150 2200 2250 2300 2350 2400 2450
f.2
0
2150 2200 2250 2300 2350 2400 2450
1
f
1
f
wave number (cm )
wave number (cm )
(c)
(d)
CO
0.8
2
B
0.4
0.6
N O
T (K)
B
T (K)
0.6
0.8
0.2
0.2
0
0
f.2
0
2150 2200 2250 2300 2350 2400 2450
1
f
wave number (cm )
Surface T
0.4
Emissivity
f.2
0
2150 2200 2250 2300 2350 2400 2450
1
f
wave number (cm )
Figure 2. Atmospheric Infrared Sounder (AIRS) channel sensitivities to (a) CO2 , (b) H2 O, (c) N2 O and CO, and
(d) surface characteristics for the 4.3 ¹m band and for the same representative tropical situation as Fig. 1.
a large sample of radiances is considered (Chédin et al. 2002b). However, there are
conditions where the temperature errors in the model and CO2 errors may be correlated
and this will need to be studied in more detail with in situ data.
(b) General scheme of the Optimal Sensitivity ProŽ le method
Figures 1 and 2 show several ‘window’ regions around 700 cm¡1 or 2300 cm¡1
where the CO2 signal is greater than the signals due to other components, these will be
called ‘interference’ signals in the following. So the Ž rst criterion for selecting channels
is to study the ratio of the CO2 signal to the sum of the interference signals, hereafter
referred to as the STI ratio (for signal-to-interference ratio).
High STI values, up to 2000, may come from very low interference values, which is
the case for the ‘stratospheric’ regions (around 2350 cm¡1 , for example) whereas, in the
‘tropospheric’ regions (around 770 cm¡1 , for example), it can be as low as 0.01. This is
due to the fact that either water vapour, surface characteristics, or other gases like N2 O
or CO, essentially affect the tropospheric channels. However, low interference values
may also result in large STI values even if the CO2 signal is low. As a consequence, a
second criterion has to be introduced: the value of the numerator, the CO2 signal, must
be greater than a Ž xed threshold, here taken equal to 0.05 K. This value was chosen to
avoid selecting too many channels, considering the perturbation values used.
2724
C. CREVOISIER et al.
As the STI ratio is a quantity integrating the whole atmospheric column, using it
as the only consideration could lead to selecting channels regardless of the region of
the atmosphere they are observing. For that reason, a third criterion, using weighting
functions (Smith et al. 1979), is introduced. Based on the consideration of the layer
observed by each channel (determined by the peak of the CO2 Jacobian associated with
the atmosphere considered), it leads to the separate examination of all the channels
peaking at a given layer.
Summarizing, three criteria are used to select channels: the STI ratio, the signal due
to CO2 , and the altitude of the maximum of the Jacobians. For each layer of a given
atmosphere, the channels for which the CO 2 Jacobian is maximum are Ž rst selected;
then the STI ratio is computed, and the channels for which both the signal due to
CO2 and the STI ratio are too low are eliminated; and then the remaining channels
are ordered, the Ž rst one being the one which presents the highest STI. Finally, for each
layer, channels with an STI ten times as small as the STI of the Ž rst channel selected in
the layer are rejected.
We applied the method to each of the 82 atmospheres presented in section 2.
For each of them, the order of selection of the channels is of course different. To arrive
at a single set of channels, to be used whatever the atmospheric situation is, a weight
is given to all the channels for each atmosphere, the maximum weight, equal to n if n
is the total number of channels, being given to the Ž rst channel selected in each layer.
For the second channel selected, the weight is n ¡ 1, and so on. Then, for each layer
the channels are ordered by the average of their weights. This can be done for all the
situations taken together or divided into three air masses, the latter allowing the study of
the differences that may appear between them.
(c) Results
We Ž rst present the results obtained with the 28 tropical atmospheric situations.
The corresponding ‘tropical set’ is made up of 74 channels. Figure 3 shows the spectral
location of these channels. Figure 4 illustrates the three criteria of the OSP method for
each channel, ordered according to their wave number. The channels are located equally
in the two CO2 bands (37 each). In addition, the channels cover both the stratospheric
and the tropospheric regions. However, the number of tropospheric channels is more
important: 56 channels are tropospheric whereas 18 are stratospheric. To explain this
phenomenon, the CO 2 Jacobians of these channels are shown in Fig. 5.
Almost all the stratospheric channels observe a large part of the stratosphere, with
large overlaps. Their CO2 Jacobians are quite thick: they peak at different pressure
levels and extend from about 0.5 hPa to the tropopause (see for example the channels
located around 670 cm¡1 , labelled 1 to 6 in Fig. 4). By contrast, the Jacobians of
the tropospheric channels are thinner (see for example the channels selected around
2400 cm¡1 , labelled 68 to 74 in Fig. 4). Therefore, more channels are needed to cover
the whole troposphere than the whole stratosphere. Moreover, the lower troposphere
(roughly below 700 hPa) and the tropopause are out of reach. This is the case for
all the channels located in the two CO2 bands. Indeed, for the lower troposphere, an
increase of CO2 decreases the emission by the surface and increases the emission by
the atmosphere: the two terms compensate one another. On the other hand, a channel
peaking around the tropopause generally mixes two parts of the temperature proŽ le, one
with a positive slope and one with a negative slope. Once again, an increase of CO2
gives two signals compensating one another.
2725
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
0.4
0.3
B
T (K)
0.2
0.1
0
0 .1
f
0 .2
f
650
700
750
800
2200
2250
wave number (cm 1f)
2300
2350
2400
2450
Figure 3. Spectral location of the 74 channels of the tropical set obtained with the Optimal Sensitivity ProŽ le
(OSP) method and response to a 4 ppmv perturbation of the CO2 proŽ le for a representative tropical situation.
(a)
©TB(CO 2) (K)
0.4
0.2
0
0.2
0
10
20
30
0
10
20
30
0
10
20
30
(b)
40
50
60
70
40
50
60
70
50
60
70
2
STI
10
0
10
10
2
0
(c)
Pressure (hPa)
10
1
10
2
10
3
10
40
channel number
Figure 4. Illustration of the three criteria for the 74 channels of the tropical set (28 situations) obtained with the
Optimal Sensitivity ProŽ le (OSP) method: (a) the CO2 signal, (b) the signal-to-noise ratio, (c) the pressure of the
maximum of the CO2 Jacobians.
2726
C. CREVOISIER et al.
(a)
1f
Pressure (hPa)
10
10
0
10
1
10
2
10
3
1
0
800
1
f
750
x 10
2
f
700
3
f
650
4
Normalized CO Jacobians
wave number (cm 1 )
f
2
(b)
10
1
f
0
Pressure (hPa)
10
1
10
2
10
3
10
2400
1
0
2350
1
f
2300
2200
wave number (cm f1)
Figure 5.
4
2
f
2250
3
f
x 10
Normalized CO Jacobians
2
The 74 CO2 Jacobians of the tropical set obtained with the Optimal Sensitivity ProŽ le (OSP) method
for (a) the 15 ¹m band and (b) the 4.3 ¹m band.
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
TABLE 1.
AIR MASS
2727
N UMBER OF SELECTED CH ANNELS FO R THE THREE TYPES OF
(Tr D TRO PI CAL, Te D TEMPERATE, Po D POLA R ) AND NUMBER OF
CH ANNELS IN CO MMON BETWEEN THE THREE SUBSET S
Two bands
15 ¹m band
4.3 ¹m band
No. of channels
Channels in common between the subsets
Tr
Te
Po
Tr/Te
Tr/Po
Te/Po
Tr/Te/Po
74
37
37
69
34
35
73
43
30
53
22
31
50
24
26
56
30
26
42
19
23
Figure 4(b) shows the STI ratio, for all the channels selected. As expected, the STI
ratio takes higher values for the stratospheric channels, indicating that they are essentially sensitive to CO 2 and not to other atmospheric components. In the troposphere,
lower STI values may be compensated for by the selection of more channels in each
layer.
We now compare the results obtained for the 82 situations clustered into three
air masses: tropical, temperate and polar. Table 1 shows that the number of selected
channels is about 70 for each ‘air-mass subset’. More 15 ¹m channels are selected
for the polar subset whereas channels are selected equally in both CO2 bands for the
tropical and temperate subsets. This may be due to the lower tropopause for the polar
situations resulting in more stratospheric levels. Now, the channels peaking in the new
lower-stratospheric levels are located in the 15 ¹m band, whereas the channels located
in the 4.3 ¹m band peak at higher levels. Therefore, more 15 ¹m channels are selected
for the polar situations. Table 1 also gives the number of channels in common for two
subsets (tropical/temperate, tropical/polar and temperate/polar) and for the three subsets
taken together.
For each pressure level, the rank of the channels ordered according to the STI
is almost the same for the three air masses. The main difference between the three
selections comes from the pressure levels seen by the channels. Indeed, as the altitude
of the tropopause varies with the air mass, the channels selected for each level may also
vary.
In conclusion, according to the number of common channels shown in Table 1,
a global set of 40–50 channels seems to be enough to characterize well the three types
of air mass.
4.
S TUDY OF AIRS CHANNELS CO 2 INFORMATION
Another way to select channels with the aim of retrieving CO2 from space is based
on the study of the information contained in the observations and measured by special
Ž gures of merit. Two such quantities are of interest: the CO2 information content (IC)
of the channels (in the Shannon sense) and the number of degrees of freedom for
CO2 signal (DFS). The information content of a measurement, a concept developed
in the context of information theory by Shannon (Shannon and Weaver 1949), can be
deŽ ned as the factor by which knowledge of a given state is improved by making the
measurement. It is a generalization of the concept of signal-to-noise ratio. The degrees
of freedom for a signal in a measurement is the number of useful independent quantities
there are in the measurement. Both methods are brie y described in the following.
A more detailed description can be found in Rodgers (1996).
2728
C. CREVOISIER et al.
(a) Method
Let x be the state vector, y the observation vector. These vectors are linked by the
radiative-transfer equation
yD
.x/ C ²M C ²F
(2)
where ²M and ²F are, respectively, the measurement error and the forward model error.
Those errors are assumed to be Gaussian and unbiased with covariance matrices SM and
SF . The global error covariance matrix is denoted S² D SM C SF .
The prior estimate of x is represented by the background vector xa and its covariance
error by Sa . Assuming the radiative-transfer equation to be weakly nonlinear, it can be
simpliŽ ed by
.x/ D .xa / C H.x ¡ xa /
(3)
where H is the so-called Jacobian matrix.
The retrieval b
x in the sense of the posterior estimate of x has a Gaussian probability
density function and, assuming that observation and background errors are Gaussian and
unbiased, its covariance matrix is given by
b
S¡1 D S¡1 C HT S¡1 H:
(4)
a
²
Following Rodgers (1996), a sequential approach is used to select the channels.
First, the channel which best maximizes the Ž gure of merit from the background state
is selected. A new state, represented by a new covariance matrix obtained from that of
the background and modiŽ ed by the channel chosen, is then obtained. The next step is
to select the channel which maximizes the Ž gure of merit for this new state, and then to
iterate the method until the desired number of channels is reached.
Let us Ž rst normalize the Jacobian matrix by the error covariance matrix. This gives
the new matrix
¡1
K D S² 2 H:
(5)
Let us suppose i ¡ 1 channels have already been selected. The covariance matrix
for this step is denoted b
Si¡1 . Following Eq. (4), the new covariance matrix obtained for
step i by selecting channel j is
b
S¡1 D b
S¡1 C kj kT
(6)
i
i¡1
j
where kj is the vector linked to the j th channel, i.e. the j th row of K. To initiate the
selection, the covariance matrix b
S0 is the background one.
The gain in information content is then given by
Ij D 12 ln.jb
Si¡1 j/ ¡ 12 ln.jb
Si j/
(7)
where jj stands for determinant, and the degrees of freedom for signal by
dj D tr.b
Si¡1 / ¡ tr.b
Si /;
(8)
where tr./ stands for trace.
These equations can be simpliŽ ed as
ln.1 C kTj b
Si¡1 kj /
.b
Si¡1 ki /T .b
Si¡1 ki /
dj D
:
T
b
.1 C kj Si¡1 kj /
Ij D
1
2
(9)
(10)
The channel selected at this step is the one that maximizes Ij (IC) or dj (DFS), j varying
over all the channels not yet selected.
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
2729
(b) Study context
x is now the atmospheric CO2 proŽ le. Water vapour, trace gases and surface
characteristics are supposed to be known within some residual indetermination as we
have seen in section 3. These are taken into account in the measurement error. We still
restrict our study to the channels of the two CO 2 bands. The method is applied to the 82
atmospheric situations used in section 3.
We assume the covariance matrix S² to be diagonal. The matrix SM takes into
account the instrument noise and the interference. For each channel, the instrument
noise is computed for the atmospheric situation studied. The ‘noise’ due to the residual
indetermination of water vapour, trace gases and surface characteristics, is deŽ ned as the
root mean square of the perturbations in brightness temperature described in section 3.
The forward-model error variance in SF is taken constant and equal to .0:2/2 K2 for all
the channels. This representation of forward model noise is not realistic and attention
needs to be paid to improving our knowledge of this error. Nevertheless, this value has
been used in most publications (Rodgers 1996; Prunet et al. 1998).
Unfortunately, the prior knowledge of CO2 is quite poor due to the scarcity of measurements that, however, indicate relatively constant values for CO 2 concentration in
the troposphere and in the stratosphere. Therefore, we assume that the prior covariance
matrix Sa has a constant variance taken equal to 102 ppmv2 for the stratosphere and the
boundary layer, and equal to 82 ppmv2 for the troposphere. Larger values were taken
for the stratosphere and the boundary layer, as CO2 concentration in these two parts of
the atmosphere is expected to be harder to retrieve than in the troposphere. A correlation between the stratosphere and the troposphere, and between the troposphere and the
boundary layer, is assumed, using a Gaussian correlation function with a scale length of
about 10 km. This choice is discussed in section 5. These assumptions will be improved
in the future with the Ž rst results obtained from ongoing studies (aircraft campaigns,
analysis of NOAA TOVS and AIRS data, etc.). We have checked that the values of the
variances themselves did not affect the order of the selection.
(c)
Results
(i) CO2 Shannon information content. Figure 6 shows the spectral location of the 775
channels and their rank in the IC selection, for a representative tropical situation chosen
from among the 28. Among them, the channel labelled 1 in the ordinate and located at
2258.03 cm¡1 is the Ž rst to be selected: it is the one which presents the largest gain
in information from the background. After the selection of this channel, the covariance
matrix is updated and then the IC of the remaining channels relative to this new state are
computed. Selecting, for example, ten channels consists of retaining the Ž rst ten highest
vertical bars. This is very different from the OSP method. Now, channels are ordered
by their IC, stratospheric and tropospheric channels mixed together. But the idea of
ordering the channels level by level is lost.
Creating a set of channels presenting the best properties regarding CO 2 retrieval is
via the study of the gain in information from the background due to the selection of a
few channels. Following the selection of, for example, ten channels, a new information
spectrum can be computed. To see the gain in information, Fig. 7 plots the difference
between the initial information spectrum and the spectrum obtained after the selection,
normalized by the initial spectrum (starred line). A gain equal to 1 for a channel means
that all the information content of the channel has been assimilated by the selection.
The other curves show the gain in information obtained for the selection of 50 and
90 channels. The gain in information obtained with the Ž rst 50 channels selected is
2730
C. CREVOISIER et al.
1
100
150
200
250
300
350
400
450
500
550
600
650
700
750
775
650
700
750
800
2200
2250
2300
2350
2400
2450
1
wave number (cm )
Figure 6.
Rank of Atmospheric Infrared Sounder (AIRS) channels in the information-content selection for the
tropical set.
1
0.9
0.8
Gain in information
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
650
700
750
800
2200
2250
wave number (cm 1)
2300
2350
2400
2450
Figure 7. Gain in information for a representative tropical atmospheric situation after the selection of 10 channels
(starred line), 50 channels (dashed line) and 90 channels (solid line) using the information-content method.
2731
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
Pressure (hPa)
10
1
f
10
0
10
1
10
2
10
3
3
f
2
f.5
2
f
1.5
1
0.5
f
f
f
Normalized CO Jacobians
2
Figure 8.
0
0.5
1
4
x 10
CO2 Jacobians of the Ž rst 40 channels selected with the information-content method for a representative tropical situation.
important. But the increase in information when going from 50 (dashed line) to 90
(solid line) channels is smaller. Thus, selecting a reduced set of channels is enough
to get most of the information content of the whole set of channels.
The Ž rst channels selected are located in the two CO 2 bands and, more precisely, in
three restrictive domains: one centred at 2380 cm¡1 , the second at 2250 cm¡1 and the
third at 700 cm¡1 (see Fig. 6). These three regions correspond to tropospheric channels.
So, if we stop the selection at ten channels, information from the stratosphere will not
be taken into account. This is conŽ rmed by Fig. 7 (starred line): when only ten channels
are selected, the gain in information in the stratospheric parts of the spectrum is nil.
The selection of the Ž rst stratospheric channel occurs after 11 iterations. Then, the
channels next selected are of both kinds. Therefore, according to the IC method, few
stratospheric channels are needed to get most of the information from the stratosphere,
whereas more tropospheric channels are needed for the troposphere.
To see which part of the atmosphere is seen by the Ž rst 40 selected channels,
their CO2 Jacobians are plotted in Fig. 8 for the representative tropical atmosphere.
As already pointed out with the OSP method, almost all the atmosphere is seen with
two exceptions, the lower part of the troposphere (from 700 hPa to the surface) and the
tropopause. The Jacobians of the Ž rst selected channels are the lowest, thinnest ones.
The stratospheric ones cover almost the same large part of the stratosphere, with large
overlaps, and peak at the same level.
The results given above hold for the three air masses (tropical, temperate and polar).
However, as for the OSP method (see section 3(c)), more 15 ¹m channels are selected
Ž rst for the polar situations.
2732
C. CREVOISIER et al.
Pressure (hPa)
10
1
f
10
0
10
1
10
2
10
3
3
f
2
f.5
2
f
1.5
1
0.5
f
f
f
Normalized CO Jacobians
0
0.5
2
Figure 9.
1
4
x 10
CO2 Jacobians of the Ž rst 40 channels selected with the degrees of freedom for signal (DFS) method
for the representative tropical situation.
(ii) Degrees of freedom for CO2 signal. Once again, the Ž rst channels selected are
located in the two CO2 bands, in restricted domains close to the ones obtained with the
IC method. The main difference comes from the channels selected in the stratospheric
regions: the channels located around 2300 cm¡1 and, to a lesser extent, around 675 cm¡1
are part of the Ž rst channels selected. Now, if we stop the selection at ten channels,
information from the stratosphere is taken into account via three channels.
This is conŽ rmed by the study of the CO2 Jacobians of the Ž rst 40 selected channels
which are shown in Fig. 9 for the representative tropical situation. As expected, they
cover the whole atmosphere better than the IC method, especially the stratosphere with
channels peaking at different levels.
This better coverage of the levels is due to the Ž gure of merit considered here.
The method is constructed to measure the number of degrees of freedom existing per
level and then to Ž nd the number of useful independent quantities there are per level
in the measurement made with each channel. Hence, this method is closer to the OSP
method, whose aim is to select the optimal channel for each level, compared with the IC
method whose aim is to maximize the total information content regardless of the levels.
5.
C OMPARISON BETWEEN THE OSP AND DFS METHODS
To compare the OSP and the DFS methods for AIRS channel selection, they are
now applied to each atmospheric situation divided into three air masses, providing
six subsets of channels (two tropical, two temperate and two polar) which are now
compared. The comparison is essentially made between the OSP method and the DFS
method as we have seen that they are the closest ones in principle.
2733
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
0
10
1
Pressure (hPa)
10
2
10
3
10
10
3
10
2
1
10
STI/STI(OSP)
0
10
1
10
Figure 10. Pressure layers covered by the Atmospheric Infrared Sounder (AIRS) channels (dashed lines).
Also shown is the highest signal-to-interference (STI) ratio reached in each level divided by the highest STI
ratio that can be reached, for an 18-channel Optimal Sensitivity ProŽ le (OSP) selection (open circles) and an
18-channel degrees of freedom for signal (DFS) selection (stars).
First, the sets obtained by the two methods present similar characteristics. They are
made of channels selected in the two CO2 bands. For the tropical and temperate subsets,
the number of channels selected in each band is almost the same. For the polar subset,
more stratospheric channels are selected in the 15 ¹m band than in the 4.3 ¹m band.
However, a major difference concerns the way each method covers the atmospheric
column. Figure 10 shows the 18 pressure levels seen by the channels (dashed lines).
The Ž rst 18 OSP selected channels cover these 18 pressure levels, one channel per
level, and present the best STI that can be reached (dashed lines with open circles).
By contrast, the 18 Ž rst channels selected by the DFS method only cover nine levels,
shown by the starred dashed lines. The stratosphere is not well covered by these
channels (three levels covered out of six) and some levels are lacking in the troposphere.
The position of the star gives, for each level covered by the Ž rst 18 DFS channels, the
value of the highest STI ratio reached by these channels divided by the highest STI
ratio that can be reached (given, by deŽ nition, by the OSP method). For Ž ve levels
(two stratospheric and three tropospheric), the STI are equal, showing that the same
channels have been selected by the two methods. But elsewhere, the STI ratios are not
optimal for the channels selected by the DFS method, a low STI ratio indicating that the
channel is more sensitive to other signals (H2 O, N2 O, etc.). This is the case for the IC
method too, with even fewer levels covered in the stratosphere, as seen in Fig. 8.
The lack of stratospheric channels resulting from the IC method could be due to
the background covariance matrix Sa used. Indeed, the actual correlation between the
stratosphere and the troposphere is unknown. Even if the order of the selection of
2734
C. CREVOISIER et al.
the tropospheric channels taken alone and of the stratospheric channels taken alone
is not affected by this correlation, the rank of the Ž rst stratospheric channel selected
may change. For example, when assuming a diagonal covariance matrix, the Ž rst
stratospheric channel is selected after 25 iterations whereas, with the covariance used
in section 4, the same Ž rst stratospheric channel is selected after only 11 iterations.
Another point is the error covariance matrix S² used. A change in the correlation would
change the selection for the tropospheric channels which are the only ones sensitive to
other trace gases as can be seen when plotting their Jacobians (see section 6(b)).
For the DFS method, the impact of the covariance is less important, as the selection
tries to cover all the levels. For two 40-channel DFS selections, one with the correlation
length used in section 4 and the other with a doubled length, 35 channels are in common
and the rank of the channels selected is almost the same. The Ž ve remaining channels
are both tropospheric (three) and stratospheric (two).
Finally, both IC and DFS methods more or less depend on the a priori information given by the background covariance matrix and the error covariance matrix.
This information, which in uences the selection made, is not available for CO2 and the
other trace gases. The OSP method only uses the known values of the typical variations
of CO2 (to derive the sensitivities), and we have checked that these values are not at all
critical for the selection. The OSP method considers each level individually and rejects
channels looking in the troposphere and in the stratosphere at the same time (as such a
case would result in a low CO2 signal).
6.
A GLOBAL SET OF CHANNELS FOR CO2 AND OTHER TRACE - GAS RETRIEVALS
OBTAINED USING THE OSP METHOD
(a) A global set of channels for CO2 retrieval
To create a single global set of AIRS channels that may be used for CO 2 atmospheric concentration retrieval, whatever the atmospheric situation is, we now use the
three air-mass subsets obtained with the OSP method. From them, the channels presenting a high STI ratio simultaneously for the three types of air mass are kept. However,
if, for a given level, a channel presenting a high STI ratio for only one type of air mass
misses, it is added to the set, allowing some particularities of each air mass to be taken
into account. The global set thus obtained is made up of 43 channels that are detailed
in Table 2. Twenty-one are located in the 15 ¹m band and 22 in the 4.3 ¹m band.
Thirty-three are tropospheric channels and ten stratospheric channels.
Table 3 presents the number of channels, among the 43, taken into each air-mass
subset. Twenty-seven channels are common to the three air-mass subsets. Other channels
are associated with only one or two air masses (for example, channel 308 was only
selected in the tropical set whereas channel 190 comes from the temperate and polar
sets). Table 3 also gives the number of channels in common between the OSP subsets
and the subsets provided by a 40-channel DFS selection. Because the OSP method
selects channels that cover the stratosphere and the troposphere better, only 20 DFS
channels are in the global set.
The CO2 Jacobians of the 43 channels of the global set are shown in Fig. 11 for a
representative tropical situation. They cover most of the atmosphere, with the exception
of the boundary layer and the tropopause (see section 3).
More CO2 channels could of course be selected by the OSP method to increase
the signal (which only reaches a few tenths of a kelvin), but this could also lead to an
increase in the noise, in particular spectroscopic, due to the increasing ‘pollution’ of the
additional channels by other gases (H 2 O, O3 , etc.). The 43 channels of the global set are
2735
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
TABLE 2.
T HE 43 ATMOSPH ERI C I NFRARED S OUNDER (AIRS) CHA NNELS OF THE
GLOBA L SET PROV IDED BY THE O PTI MAL S ENSITIVITY P ROFILE ME THOD FOR CO 2
ATMOSPHERI C CON CENTRATION RETRI EVAL
AIRS channel no.
62
77
79
151
156
172
173
175
180
185
190
193
213
218
239
248
250
251
308
309
318
Wave number (cm¡1 )
664.43894
668.21233
668.71887
692.95488
694.32529
698.74834
699.02671
699.58412
700.98165
702.38492
703.79396
704.64216
710.35068
711.79259
717.91418
720.57056
721.16357
721.46045
738.08281
738.39350
741.20138
AIRS channel no.
(s)
(s)
(s)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(s)
(t)
(t)
(t)
(t)
(t)
Wave number (cm¡1 )
1938
1939
1946
1947
1948
1958
1971
1973
1988
1995
2084
2085
2097
2098
2106
2107
2108
2109
2110
2111
2112
2113
2249.3488
2250.3105
2257.0651
2258.0332
2259.0022
2268.7365
2281.5134
2283.4915
2298.4335
2305.4713
2363.7251
2364.6821
2376.2284
2377.1958
2384.9638
2385.9384
2386.9139
2387.8901
2388.8672
2389.8451
2390.8238
2391.8033
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(s)
(s)
(s)
(s)
(s)
(s)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t)
(t) indicates a tropospheric channel and (s) a stratospheric channel.
TABLE 3. O RIG IN OF THE 43 ATMO S PHERI C I NFRARED S OUNDER (AIRS) CH AN NELS OF THE GLOBA L SET
Total
15 ¹m/4.3 ¹m
Tropo/Strato
In common
Tr
Te
Po
37
16/21
27/10
34
14/20
26/8
33
14/19
24/9
26
22
28
The channels come from the tropical (Tr), temperate (Te) or Polar (Po) subsets, from the
15 ¹m or 4.3 ¹m bands, and peak in the troposphere (Tropo) or stratosphere (Strato). The last
line gives the number of channels in common in
the two subsets provided by the Optimal Sensitivity ProŽ le (OSP) and degrees of freedom for
signal (DFS) methods.
the most important channels that should be used in a retrieval procedure, according to the
OSP method. These channels have recently been added to the National Environmental
Satellite, Data, and Information System (NESDIS) restricted list of distributed AIRS
channels.
(b) OSP channel selection for other trace-gas retrievals
The OSP method may also be used to select channels for the retrieval of other trace
gases. We now focus particularly on N2 O, CO and CH4 .
The best signals for N2 O can be found in the 4.3 ¹m band. In this region, CO
is also active. The sensitivities of the corresponding AIRS channels are shown in
Fig. 2(c), for a 2% perturbation of the N2 O proŽ le and for a 40% perturbation of the
2736
C. CREVOISIER et al.
10
1
f
0
Pressure (hPa)
10
1
10
2
10
3
10
3
f
2
f.5
2
f
1
1
0
f.5
f
f.5
Normalized CO Jacobians
0
0.5
Figure 11.
1
4
x 10
2
CO2 Jacobians of the 43 Atmospheric Infrared Sounder (AIRS) channels of the global set.
TABLE 4. ATMOSPH ERI C I NFRA RED S OUNDER (AIRS) CHA NNELS PROV IDED BY THE O PTI MAL
S ENSI TIVITY P RO FI LE METHOD FOR N2 O, CO AND CH4 ATMOSPHERI C CON CENTRATION RETRIEVALS
AIRS channel no.
Wave number (cm ¡1 )
Gas
AIRS channel no.
Wave number (cm¡1 )
Gas
1883
1884
1897
1901
1917
1921
1923
1924
2197.91
2198.83
2210.85
2214.57
2229.59
2233.38
2235.27
2236.22
N2 O
N2 O
N2 O
N2 O
N2 O
N2 O
N2 O
N2 O
1867
1869
1875
1877
1400
1401
1402
1403
2183.30
2185.12
2190.58
2192.41
1302.03
1302.61
1303.19
1303.77
CO
CO
CO
CO
CH4
CH4
CH4
CH4
CO proŽ le. Unfortunately, very few channels are sensitive to CO variations. Indeed, CO
is essentially active around 2150 cm¡1 , which is at the limit of the 4.3 ¹m band covered
by AIRS channels. However, despite their small number, the channels present a high
sensitivity to N2 O and CO variations: the CO signal can be Ž ve times as large as the
CO2 one, due to the three sharp absorption lines that can be seen in Fig. 2, and may
allow good retrievals.
Applying the OSP method to the same set of atmospheric situations used for
CO2 gives the eight channels for N2 O and four channels for CO that are detailed in
Table 4. They are only tropospheric as shown by their corresponding Jacobians plotted
in Figs. 12(a) and 12(b). IASI, which will cover the whole infrared spectrum, should in
principle allow the most interesting channels for CO retrieval to be selected, but with a
higher noise.
2737
10
1
10
2
(a)
Pressure (hPa)
Pressure (hPa)
AIRS CHANNEL SELECTION FOR CO2 RETRIEVAL
3
10
2.5
f
f
2
1.5
f
1
f
0.5
f
0
Normalized N2O Jacobians
0.5
x 10
10
1
10
2
10
3
(c)
3
2.5
1
10
2
10
3
5
x 10
6
(d)
2
1.5
1
CH
4
0.5
0
N2 O
1250
1300
1350
1400
Pressure (hPa)
TB (K)
10
f5
1
10
f
5
f
0
Normalized CO Jacobians
H O
2
f.5
0
1200
2
f0
7
(b)
1
f0
1
f
wave number (cm )
8
f
6
f
4
f
2
f
Normalized CH Jacobians
4
0
x 10
6
Figure 12. For the representative tropical situation: (a) N2 O Jacobians for the eight channels selected in the
4.3 ¹m band by the Optimal Sensitivity ProŽ le (OSP) method, (b) same as (a) for CO, (c) Atmospheric Infrared
Sounder (AIRS) channel sensitivities to CH4 , H2 O and N2 O in the 7 ¹m band, (d) CH4 Jacobians for the four
channels selected in the 7 ¹m by the OSP method.
The best signal for methane can be found in two parts of the infrared spectrum,
the 7 ¹m and 3.3 ¹m bands. Only the Ž rst region is covered by AIRS channels.
The response of AIRS channels to a 10% perturbation of CH 4 is shown in Fig. 12(c),
as are the responses to the perturbations of the H 2 O and N2 O proŽ les used in section 2.
For most of the channels, the CH4 signal is below the H2 O signal. Thus, only four
channels, detailed in Table 4, are selected by the OSP method. They are tropospheric as
shown by their corresponding Jacobians plotted in Fig. 12(d).
7.
C ONCLUSIONS
In this paper, three methods for selecting AIRS channels with the purpose of
retrieving CO2 concentration were presented. The new Optimal Sensitivity ProŽ le
(OSP) method relies on the study, pressure level by pressure level, of the sensitivity
of each channel to the variations of CO 2 atmospheric concentration compared with the
sensitivities to other atmospheric components (gases, surface characteristics). The other
two methods select channels by their information content or their degrees of freedom
for signal, the latter being closer to the OSP method. These two methods assume a
Gaussian behaviour of the variables and rely on the knowledge, unfortunately presently
2738
C. CREVOISIER et al.
very limited, of the background and observation error covariance matrices. The OSP
method only uses the known values of the typical range of variation of the gases.
Concerning CO2 retrieval, all methods select channels in the two CO2 bands, centred at 15 ¹m and 4.3 ¹m. These channels cover the troposphere and stratosphere, with
the exception of the tropopause and the lower troposphere. The OSP method provides
channels that cover the stratosphere and the troposphere better, by selecting channels
peaking at different levels. Applying the method to a set of representative atmospheric
situations leads to the selection of a global set of 43 AIRS channels, well distributed
along the atmospheric column, with a reduced sensitivity to other atmospheric components, that should be used to retrieve CO2 atmospheric concentration. A recent CO2
data assimilation study performed at ECMWF and based on the ECMWF background
covariance with simulated AIRS data has indicated that the use of the 43 channels given
by the OSP method indeed improved the CO2 retrieval compared with other channel selections carried out with respect to the information content of temperature, water vapour,
and CO2 together. Such channel selections tend to favour the Ž rst two variables, which
have a much larger sensitivity signal in the observed radiances (R. J. Engelen, personal
communication).
The OSP method was extended to other trace gases (N2 O, CO and CH 4 ). As the
43 channels selected for CO2 retrieval, the resulting 16 channels have been added to the
NESDIS restricted set of distributed AIRS channels. The OSP method can be applied to
other high-resolution infrared sounders, such as the MetOp IASI instrument which will
present more than 1500 channels in the two CO 2 bands. However, the results should be
different because of the spectral resolution which is larger for IASI and the noise which
is higher in the 4.3 ¹m band than the AIRS one.
An important point, not taken into account in our study, is the role of clouds. All the
atmospheric situations studied here were assumed to be cloud free. Nevertheless, well
known techniques exist to detect clouds, making it possible to work under clear-sky
conditions at the precise time of the satellite pass. However, in particular for low clouds,
due to the relative sharpness of the CO2 Jacobians of the tropospheric channels and
their good distribution within the troposphere, it should be possible to get information
above the clouds. Another issue is the non-Local Thermodynamic Equilibrium (LTE)
effects clearly identiŽ ed on AIRS measurements in a number of 4.3 ¹m channels, which
precludes the use of them during daytime.
ACKNOWLEDGEMENTS
This work was partly supported by the European project on measuring CO2 from
space exploiting planned missions 2002–2004 (known as COCO). Calculations were
performed using the resources of the Institut du Développement et des Ressources en
Informatique ScientiŽ que computing centre. The authors thank L. L. Strow for providing
them with AIRS characteristics (spectral response function and noise), and ECMWF for
data from their background model Ž elds. We would also like to thank Mathieu Vrac for
helpful discussions, Raymond Armante for his help throughout this work, Gaby Rädel
for her proof reading, and the associate editor J. Joiner and the two anonymous reviewers
for their constructive comments.
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