Simulated Space-borne Retrievals of Tropospheric Methane Profiles
Zhan Su1*, Vijay Natraj2, King-Fai Li1, Run-Lie Shia1, Charles E. Miller2, and Yuk L. Yung1
1. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA,
USA
2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA.
*
To whom correspondence should be addressed: zhan@gps.caltech.edu
Submitted to JGR, November 29, 2012
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Abstract
A better understanding of atmospheric methane (CH4) is critical to our ability to predict future
climate change because of its high global-warming potential. For accurate estimation of seasonal
CH4 sources/sinks and characterization of underlying vertical transport processes, highspatiotemporally resolved CH4 vertical profiles are required. Here a new strategy for estimating
CH4 mixing ratio profiles from space-borne measurements is presented. This technique employs
high-resolution spectra of reflected sunlight taken simultaneously in the near-infrared 2.3 and 1.6
μm CH4 band and the 0.76 μm O2-A band. Information content analysis shows that ~1% of the
potential CH4 spectral channels (~600 out of 56,000) contain more than 95% of the total CH4
information. Using such channel selection can significantly increase the speed of CH4 profile
retrievals form satellite remote sensing data while sacrificing minimal information content or
accuracy. Analysis of the retrieval Jacobians demonstrates that CH4 spectral sensitivity varies
significantly across the CH4 absorption spectrum and that pressure broadening of individual CH4
absorption line shapes provides the vertical information necessary to retrieve CH4 profiles. Linear
error analysis and simulation experiments demonstrate that, for clear sky soundings, our retrieval
strategy is capable of retrieving 3 to 4 bulk layers of CH4 with less than ~ 1% (19 ppb) bias per bulk
layer; these bulk layers have vertical resolutions of 3–6 km, as indicated by the associated
averaging kernels. Our algorithm is capable of distinguishing CH4 concentration differences
between the planetary boundary layer and the free troposphere, which is crucial for improving
estimates of local CH4 fluxes and places rigorous constraints on estimates of vertical transport. The
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retrieval strategy presented in the present study is completely general and can be applied to CH4
profile retrievals from current and future satellite sensors as well as be adapted to retrieve vertical
profiles of other geophysical variables (e.g., CO2 and temperature).
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1. Introduction
Methane (CH4) is the second most important anthropogenic greenhouse gas (GHG) after carbon
dioxide (CO2) [IPCC, 2001], and plays a very important role in atmospheric chemistry [Seinfeld
and Pandis, 2006]. Using the 2005, the global mean mixing ratio of 1774 ± 1.8 parts per billion
(ppb), atmospheric CH4 contributes a direct radiative forcing of 0.48 ± 0.05 W m–2 [Forster et al.,
2007] and an indirect radiative forcing of 0.86 ± ??? W m–2 [Shindell et al., 2005] to the climate
system. The global warming potential (GWP) of CH4 is high: 72 times that of CO2 over 20 years,
and 25 times over 100 years [IPCC, 2007]. Therefore, changes in atmospheric CH4 have a
particularly pronounced impact on near-term (decadal scale) climate forcing. Human activities have
rapidly increased atmospheric CH4 concentrations from 715 ppb in the preindustrial era to the
present value [Etheridge et al., 1998; Forster et al., 2007; IPCC, 2007; Petit et al., 1999]. Evidence
from ice core data indicates that the present levels of CH4 are unprecedented during the last 800,000
years [Spahni et al., 2005]. Atmospheric CH4 concentrations leveled off from 2000 to 2006
[Bousquet et al., 2006]; however, CH4 began increasing again in 2007 [Dlugokencky et al., 2009;
Sussmann et al., 2012]. It is unclear whether this recent trend is a temporary anomaly or the
beginning of a new period of increasing CH4 levels [Frankenberg et al., 2011; Heimann, 2011].
Both anthropogenic activities and potential feedbacks from climate change are expected to induce
further increase in CH4 concentrations throughout the 21st century [Dentener et al., 2005].
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It is important to obtain a comprehensive understanding of the global CH4 budget to model future
changes in its atmospheric concentration; however, the global methane budget is uncertain with
significant discrepancies across estimates for the location, magnitude and variability of the major
source and sink terms [Bergamaschi et al., 2007]. The average annual growth rate from 2000 to
2005, 0.2 ppb yr-1, is well constrained by the global atmospheric measurement network. In contrast,
estimates of the total global source range from 500 to 600 Tg(CH4) yr-1 and uncertainties in the
atmospheric lifetime (8.7 ± 1.3 years) and the overall sink strength (±15%) limit top-down
estimates of the CH4 budget [IPCC 2007]. Ground-based measurements of CH4, such as those from
the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) network [Dlugokencky et al.,
2005], the Network for Detection of Atmospheric Composition Change (NDACC) Fourier
Transform Spectrometer (FTS) network [Dils et al., 2006], and the Total Carbon Column
Observing Network (TCCON) [Wunch et al., 2011] place excellent constraints on global and
hemispheric CH4 budgets, but are too sparse to resolve regional CH4 budgets conclusively. These
measurements have a precision and accuracy of 0.1–0.2% [Dlugokencky et al., 2005; Toon et al.,
2009]; hence, they can serve as good validation datasets for other measurements [Dils et al., 2006;
Parker et al., 2011; Schneising et al., 2012]. Vertical profiles of CH4 from radiosondes [Sun et al.,
2010], aircraft sampling such as the NOAA CCGG aircraft program [Ejiri et al., 2006; Miller et al.,
2012], and balloon-borne remote sensing instruments such as MkIV and FIRS-2 [Ejiri et al., 2006;
Kovalenko et al., 2007] although sparse, have high vertical resolution and have been used as
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“ground truth” for calibration and validation of retrievals from other measurements [Wunch et al.,
2010]. This information is fundamental to setting up the satellite retrieval question and gives a basis
for estimating how well vertical profiles of CH4 might be measured.
Satellite remote sensing measurements of CH4 complement measurements from the ground-based
networks by providing dramatically increased spatial coverage and sampling density, although
space-based measurement precisions are typically 1–2% [Butz et al., 2010]. Over the past several
decades, three basic observing strategies have been used for space-based CH4 detection. Profiles of
CH4 in the upper atmosphere (generally altitude z > 10 km) with vertical resolutions of 2–5 km
have been reported from infrared solar occultation sensors such as ATMOS [Gunson et al., 1990]
and ACE [Bernath et al., 2005], and limb sounders such as MIPAS on ENVISAT [Payan et al.,
2009]. Nadir-viewing thermal infrared (TIR) sounders such as IMG/ADEOS [Kobayashi et al.,
1999a; Kobayashi et al., 1999b], AIRS [Xiong et al., 2010], IASI [Crevoisier et al., 2009] and TES
[Worden et al., 2012] provide maximum sensitivity to CH4 in the middle to upper troposphere (5–
12 km). Near-infrared (NIR) observations of sunlight reflected from the Earth’s surface from
sensors such as SCIAMACHY [Bovensmann et al., 1999], GOSAT [Kuze et al., 2009] and the
planned Sentinel-5 precursor [Butz et al., 2012] and CarbonSat missions [Bovensmann et al., 2010]
provide observations of the column-averaged CH4 dry air mole fraction (  CH 4 ) with maximum
sensitivity near the surface. Retrieval algorithms based on ratios against simultaneously retrieved
column CO2 [Frankenberg et al., 2008; Frankenberg et al., 2005a; Frankenberg et al., 2005b;
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Parker et al., 2011; Schneising et al., 2009], as well as more sophisticated methods which
simultaneously retrieve light scattering properties and CH4 concentration [Butz et al., 2011; Butz et
al., 2010; Schepers et al., 2012; Yoshida et al., 2011], have demonstrated the potential to retrieve
 CH 4 with a precision of ~19 ppbv (1%). Chevallier et al. [2005] studied the impacts of satellite
measurements in inverse estimates of CH4 surface fluxes, and found that NIR reflectance
measurements resulted in the largest reductions in flux estimate uncertainties. In fact,
SCIAMACHY  CH 4 data have been used to assess global and regional CH4 budgets [Bergamaschi
et al., 2007; Bergamaschi et al., 2009; Buchwitz et al., 2012].
Unlike CO2, which has sinks only at the surface, CH4 has significant, altitude-dependent chemical
loss mechanisms in the atmosphere. Thus, column integrated  CH 4 should not be interpreted in the
same way as measurements of suface CH4 concentrations. Frankenberg et al. [2011] used yearly
averaged results from the TM5 model to show that differences between  CH 4 and the surface CH4
concentration can be as large as 200 ppb over vast continental regions such as Europe, China and
North America (see their Figure 5). Furthermore, the seasonal variation of  CH 4 can differ from that
of the surface CH4 concentration. Figure 1 shows the seasonal CH4 variations at different height
layers (50, 189, 365, 507, 653, 840 and 973 hPa ) over the Sahara (15°N–30°N, 0°E–13°E) from the
TM5 transport model (see details in [Frankenberg et al., 2011]). This seasonal variation difference
at different height layers can be as large as ~ 100 ppb and even exhibit opposite sign, which are due
to seasonal variations of tropopause height, OH radicals, and CH4 emissions. Thus, accurate
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quantifications of these seasonal CH4 sources/sinks require spatial and temporal observations of
CH4 profiles rather than just  CH 4 [Bergamaschi et al., 2007].
Furthermore, vertically resolved CH4 profile measurements could provide powerful constraints on
atmospheric transport, especially convection, in inverse modeling of CH4 fluxes [Bergamaschi et
al., 2009]. Solar occultation and limb sounders have excellent sensitivity to CH4 profiles in the
stratosphere and upper troposphere, but profiles with at least one piece of vertical information in the
boundary layer [Crutzen, 1991] and 2–3 pieces of vertical information in the troposphere would
provide significantly improved CH4 flux estimates. Additionally, vertically resolved CH4 profiles
should lead to more accurate total column values and the correct vertical transport. Current
retrievals using NIR satellite measurements do not provide CH4 profile information
[Frankenberg et al., 2011] but do have the advantage of maximizing information near the
surface and thus reducing flux estimate uncertainties [Chevallier et al., 2005].
This paper examines the potential of present and future NIR satellite measurements to
profile tropospheric CH4 using information content analysis and numerical simulation
[Rodgers, 2000]. It is organized as follows. In Section 2, a brief description of the radiative
transfer model is given. In Section 3, a retrieval technique based on optimal estimation and
information content analysis is discussed. Absorption band selection for the CH4 retrieval based on
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degree of freedom of signal is presented in Section 4. In Section 5, we demonstrate that
tropospheric CH4 profile retrieval with high accuracy and precision (~ 1%) can be achieved using
the 2.3 μm CH4 absorption band. Conclusions and implications of this study follow in Section 6.
2. Radiative Transfer Model
We use the linearized vector RT model Vector LInearized Discrete Ordinate Radiative Transfer
model (VLIDORT) [Spurr, 2006] for computing the radiance spectrum in a multiply-scattering,
inhomogeneous (multilayer) medium. Here, the same model was used to generate the ‘‘observed’’
spectrum and the ‘‘retrieved’’ spectrum. VLIDORT uses the discrete ordinates approach to
approximate multiple scatter integral source terms in the RT equation. Most of previous studies
[Butz et al., 2012; Schepers et al., 2012; Spurr, 2006] assume the plane-parallel approximation in
the RT models, which may induce errors of ~ 5–10% in radiance for viewing zenith angles (VZAs)
of 55–70° [Spurr, 2004]. VLIDORT avoids this error by including a pseudo-spherical correction for
the treatment of incoming solar beam attenuation in a spherical-shell atmosphere. Furthermore,
VLIDORT can perform a precise single-scattering calculation for both incoming solar and outgoing
line-of-sight beams in a curved atmosphere. Using the source function integration technique,
VLIDORT can produce the Stokes vector at any level in the atmosphere and for any angular
distribution. Moreover, VLIDORT can handle bidirectionally reflecting surfaces in addition to the
traditional Lambertian surface. It can also handle the case of coupled thermal emission and multiple
9
scattering [Natraj et al., 2011]. VLIDORT has been validated against Rayleigh [Coulson et al.,
1960] and aerosol benchmark results [Siewert, 2000].
The forward model includes physical processes pertaining to attenuation and scattering of sunlight
propagating through the atmosphere (including reflection by the surface). It consists of VLIDORT,
a solar spectral model and an instrument model. The Reference Forward Model (RFM) [Dudhia et
al., 2002] is employed to produce the trace gas optical depths required by VLIDORT. RFM is a
GENLN2-based [Edwards, 1992] line-by-line radiative transfer code (the latest version of RFM can
be accessed from http://www.atm.ox.ac.uk/RFM/). The solar spectral model is based on the solar
irradiance data from the MODTRAN 4.0 database [Berk et al., 1999], which has high spectral
resolution and is a good basis for generating synthetic solar irradiance data based on the spectral
solar irradiance curves from various sources with an arbitrary selected error of only a few percent
[Nieke and Fukushima, 2001]. The instrument model simulates the instrument’s spectral resolution
and spectral sampling by convolving the highly resolved monochromatic radiance spectrum with
the instrument line shape function (ILS), and subsequently with a boxcar function to take into
account the spectral range covered by a detector pixel.
In our model, the atmosphere is divided uniformly in the pressure coordinate into 15 layers
(pressure layers) from one bar to zero bars. 15 layers are usually good enough for realistic CH4
retrieval [Butz et al., 2011; Schepers et al., 2012]. The pressure layer scheme is better than one with
10
layers of equal geometrical thickness because CH4 is not uniformly distributed in altitude. An
updated list of CH4 absorption lines from the HITRAN 2008 database [Rothman et al., 2009] is
adopted. In this updated list, erroneous CH4 and H2O spectroscopic parameters that are known to
have caused bias in the SCIAMACHY  CH 4 retrieval [Frankenberg et al., 2008] have been
corrected. In the model, we employ a state vector that is composed of the CH4 concentration profile
(15 layers), the ground surface albedo for different bands, the H2O concentration profile bias, the
temperature profile bias and radiance adjustment factors [Yoshida et al., 2011]. We also include the
aerosol optical depth profile and surface pressure in the state vector to represent the equivalent
optical path modification [Kuang et al., 2002] and to reduce associated retrieval error.
The tropospheric aerosol has been chosen according to the climatological categories developed by
Kahn et al. [2001]. The stratospheric aerosol is assumed to be a 75% solution of sulfuric acid
(H2SO4) with a modified gamma function size distribution [WCP, 1986]. The complex refractive
index of the H2SO4 solution is taken from the tables prepared by Palmer and Williams [1975]. For
spherical aerosol particles, the optical properties are computed using a polydisperse Mie scattering
code [de Rooij and van der Stap, 1984]. In addition to extinction/scattering coefficients and
distribution parameters, this code generates coefficients for the expansion of the scattering matrix in
generalized spherical functions that are used by VLIDORT. For nonspherical aerosols such as
mineral dust, optical properties are computed using a T-matrix code [Mishchenko and Travis, 1998].
The atmosphere is bounded below by a Lambertian reflecting surface, for which the reflectance has
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been taken from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)
[Abrams, 2000] spectral library.
Calculation of the Jacobian matrix (derivatives of radiance with respect to atmospheric or surface
parameters) is the most time-consuming process in a typical retrieval [Yoshida et al., 2011]. Since
VLIDORT is fully linearized, it can compute the Jacobians with respect to any atmospheric and
surface properties simultaneously along with the radiances themselves, which greatly reduces the
computational expense compared to the finite difference method. This linearization is very useful
for generating the Jacobians with respect to CH4 concentrations.
3. Optimal Estimation and CH4 Vertical Profile Information Content Analysis
A measurement y can be represented as the sum of a physically based forward model F(x, b) with
measurement error ε:
(1)
where x is the state vector to be retrieved, and b is the set of forward model parameters that are not
retrieved. The optimal estimation theory [Rodgers, 2000] combines prior information about x and
the measurement y to obtain a stable retrieval solution, by minimizing the cost function:
(2)
where x a and Sa are the a priori state vector and the associated covariance matrix, representing the
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statistical mean and variance of our prior knowledge for x respectively, and
is the error
covariance matrix. The a priori constraints for temperature, CH4, water vapor and surface pressure
here are estimated from climatological data and transport model results. For CH4 mixing ratios of
different layers, its a priori uncertainty is assumed to be ~ 90 ppbv (~5%) [Worden et al., 2012]. As
significant uncertainty remains for the aerosol optical depth, its a priori uncertainty is assumed to
be ~ 100%. The band-averaged albedos are considered to vary by ~ 20% and are independent
among different bands. We assume no correlation between different quantities.
The minimization of Eq. (2) is done using the Levenberg-Marquardt method [Levenberg, 1944;
Marquardt, 1963] by the iterative formula below:
(3)
where the subscript i denotes the i th iteration step and K is the Jacobian matrix.
is chosen at
each step to optimize the speed of convergence [Fletcher, 1971; Rodgers, 2000]. The a posteriori
covariance for the state vector is:
(4)
which can be used to estimate the precision of the retrieved variables [Kuang et al., 2002; Rodgers,
2000].
We apply information content analysis [Kuai et al., 2010; Shia et al., 2012] to the CH4 retrieval
system to estimate its degrees of freedom for signal (DOF) or the number of independent vertical
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CH4 bulk layers. Note that we want to maximize the DOF for CH4 and the DOF for other variables
in the state vector do not matter as long as the CH4 retrieval is good enough. DOF of CH4 is
determined by the CH4 a priori covariance matrix Sa , the error covariance
and the CH4 Jacobian
K:
(5)
where
are the singular values of the normalized Jacobian
[Shia et al., 2012].
Within the optimal estimation framework, information from the measurement dominates for cases
when the signal to noise ratio (SNR) is large while information from the prior dominates for cases
when the SNR is low. Since our goal is to maximize the information contributed by the problem
from the measurements, we desire CH4 absorption features within the observed radiance spectrum
that can be detected with high SNR and are sensitive to CH4 concentration changes in different
atmospheric layers. The Jacobian associated with such a CH4 radiance spectrum will lead to
increased DOF and benefit the CH4 profile retrieval. Selection of the CH4 absorption band(s) for the
retrieval is therefore crucial.
4. CH4 Absorption Channel Selection
Here we first investigate the CH4 bands used in previous studies of  CH 4 retrievals from
backscattered NIR satellite observations, as summarized in Table 1. In the present study, we focus
on the CH4 absorption bands at 2.3 μm (4190–4510 cm–1) and 1.6 μm (5880–6120 cm–1). Both
spectral regions have absorptions that are the correct strength for accurate retrievals of  CH 4 from
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nadir-viewing observations of reflected sunlight. Other spectral regions in the solar absorption
region contain methane absorptions that are too weak to be useful. The 2.3 μm band contains a
dense number of methane lines belonging to the v2+2v4, v2+v3 and v1+v4 bands. And the 2v3 band is
the major component at 1.6 μm. The 2.3 μm band provides stronger absorption (Figure 2) while the
absorptions at 1.6 μm are less dense and distributed among fewer absorption features (Figure 3).
However, there are some isolated lines in the 1.6 μm band that have peak absorptions comparable to
the absorptions in the 2.3 μm band.
Different channels can provide very different retrieval information and the inclusion or exclusion of
some channels may make a significant difference for retrieval. For instance, Frankenberg et al.
[2011] reported that some crucial CH4 spectrum detector pixels (1664–1667 nm or 5999-6010 cm-1)
of SCIAMACHY experienced a serious degradation at the end of 2005. The non-inclusion of these
degrading channels seriously influenced the  CH 4 retrieval quality over vast continents (up to 18
ppb) compared to previous retrieval versions, [Frankenberg et al., 2011]. However, a strategy with
complete spectral coverage of the 2.3 μm (4190–4510 cm–1) and 1.6 μm (5880–6120 cm–1) bands
at high spectral resolution creates a challenging retrieval problem. Assuming a spectral resolution of
0.01 cm-1 leads to ~32,000 and ~24,000 independent spectral radiances in the 2.3 and 1.6 μm bands,
respectively. Retrievals with these dimensions will introduce large amounts of redundant CH4
information, excess noise, and increases the chances of unwanted bias from interfering absorptions.
This will lead to a sparse, ill-conditioned Jacobian, and the potential for poor quality retrievals. On
the other hand, it is possible to use smaller number of selected channels as in Chahine et al. [2005],
15
who employed only a small number of CO2-sensitive channels to retrieve CO2 mixing ratios with
high accuracy.
All these indicate the possibility to reduce the dimensionality of the CH4 retrieval while maximizing
the vertical profile information content using information theoretic methods similar to those used by
Kuai et al. [2010; 2012] and Shia et al. [2012]. Here we apply these techniques to select a small
subset of the CH4 spectral radiances that nonetheless yields multiple DOF in the CH4 vertical
profile. We analyze the 2.3 μm (4190–4510 cm–1) and 1.6 μm (5880–6120 cm–1) bands in detail
with high spectrum resolution of 0.01 cm–1. We assume that the continuum SNR is ~ 300 that is
consistent with existing satellite instruments such as GOSAT [Yoshida et al., 2011]. Cases for other
combinations of SNR and spectral resolution will be shown later in this section.
Simulated top of atmosphere (TOA) radiance spectra of the aforementioned two CH4 bands and the
associated DOF values are shown in Figures 2-4 using Eq. (5). Note the DOF here is only for CH4
profile and not for other variables in the state vector. The CH4 transmittance is defined as the ratio
of the reflected TOA radiance with CH4 to the reflected TOA radiance without CH4. The DOF value
associated with each spectral radiance has a value from 0 to 1, representing the DOF of CH4 in that
particular radiance measurement. Figure 2 shows that many strong and dense CH4 lines exist in the
2.3 μm band, of which a large number of channels have large values of DOF for CH4. The value of
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DOF correlates with the CH4 absorption strength as illustrated by the pattern in the 4215–4220 cm-1
and 4310–4320 cm-1 windows. This correlation can also been seen in Figure 4. However, this
correlation is not linear due to the influence of line broadening, as demonstrated by Shia et al.
[2012]. A spectral radiance with ~50% absorption can contribute a DOF approaching 1.0 if it
provides high-SNR information on a poorly constrained portion of the state vector. For example,
the 4203.2 cm–1 line in Figure 4 has a DOF of 0.99. Similarly, the radiance changes associated with
the subtle variations in the CH4 line shapes as a function of atmospheric state can contribute
significantly to the overall solution. A spectrum like 4215–4220 cm-1 with continuous strong
absorptions can lead to continuously large values of DOF (≥ 0.8). Compared with the 2.3 μm band,
the 1.6 μm band is much less dense and has fewer channels with large DOF, as shown in Figure 3.
The number of channels with DOF ≥ 0.9 is 6291 (~ 19.7%) for the 2.3 μm band and 606 (~ 2.5%)
for the 1.6 μm band. Therefore the 2.3 μm band seems to be much more useful than the 1.6 μm
band for CH4 profile retrieval. And it is statistically significant that ~ 20% channels in the 2.3 μm
band contain huge amount of CH4 retrieval information. However, we should not apply all these (~
7000) channels with DOF ≥ 0.9 for CH4 profile retrieval as these channels may contain similar
retrieval information that is not independent of each other. Furthermore, including too many
channels will seriously increase the computationally expense and complicate the retrieval procedure.
We choose 1000 to be the upper limit of number of channels used for retrieval; We divide the 1.6
and 2.3 μm bands into windows with intervals of 10 cm–1 and each window has 1000 channels by
17
the definition: 10 cm–1 / 0.01 cm-1 =1000. All the 1000 channels of each window are combined to
calculate its CH4 DOF. Note that the upper limit for DOF is the smaller value of the number of
channels and the number of variables in the state vector. In our study, the upper limit for DOF is 15,
which is the number of CH4 layers in the model. Figure 5 shows the results: there are 22 windows
in the 2.3 μm band with a DOF ≥3.0. The 1.6 μm band does not even have one window with DOF
≥3.0 due to its smaller number of strong lines, as shown in Figures 2–3. Note that we cannot simply
sum the DOF values from channels in Figs 2-3 to get the DOF shown in Fig 5 as the DOF has
nonlinear correlation with spectra as shown in Eq. (5). The two largest DOF in Figure 5 are found
in the 4210–4220 cm–1 window (DOF=4.15) and the 4310–4320 cm–1 window (DOF=3.5), which
correspond to the two strongest absorptions in the CH4 spectra in Figure 2. The values of CH4 DOF
of 3-4 for the 2.3 μm windows should be compared with the upper limit of the DOF=15, which
indicates that these 2.3 μm windows have the potential for retrieving 20% ~ 27% of all CH4 layers.
An important question to investigate is how to maximize the vertical profile CH4 DOF without
including redundant information and insensitive channels. As an example, Figure 6 (left) shows
how DOF accumulates with number of channels from 4210 to 4220 cm-1 with a resolution of 0.01
cm–1. This calculation begins at 4210.0 cm-1 and then start summing DOF value from 4210.01 to,
4220.00 cm-1 in steps of 0.01 cm-1. The channels with DOF contribution >0.005 are marked as red
circles while the rest are marked as blue circles. 125 out of 1000 channels have DOF contribution
>0.005 and their total DOF contribution is 3.69/4.15≈89%, which means 12.5% of the channels
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contain ~ 89% retrieval information of this window. We collect these few but sensitive channels
among strong CH4 windows in Figure 5 (totally 619 sensitive channels) and expect them to contain
nearly all the available CH4 retrieval information, as summarized in Table 2. We then calculate the
accumulated DOF of the 619 selected channels as shown in Figure 6 (right), with the same method
as for Figure 6 (left). Although each selected channel contributes more than 0.005 to the DOF for
its own window, our result shows that only 110 (~ 18%) channels can contribute this amount of
DOF (red circles) when they are combined together. This means that all these 615 channels contain
strong but usually non-independent CH4 retrieval information from each other, which is consistent
with the conclusion of [Shia et al., 2012]. The total DOF from all these 615 channels is ~ 4.22 while
the DOF from the 110 channels marked by red circles is ~ 3.8 (90%). Thus, DOF ~ 4.22 can be
regarded as the maximum DOF for CH4 profile retrieval with the assumptions made for SNR,
spectral resolution and the CH4 a priori covariance. In fact from our numerical study, we found that
the DOF by all the 56,000 channels (32,000 from 2.3 μm band and 24,000 from 1.6 μm bands)
should not exceed 4.4. Thus we select 615 CH4 channels out of 56,000 CH4 channels (~ 1.1%) to
provide more than 95% (~ 4.22/4.4) of the total CH4 information. This shows the power of CH4
band selection. Again, the conclusion of these values should depend on the instrument SNR,
spectral resolution, CH4 a priori covariance and the RT model.
CH4 a priori covariance was tested to not have strong influence on the DOF value if it is within the
reasonable range based on the climatological data. Some parameters in the RT model such as solar
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zenith angle (SZA), surface albedo and surface pressure can have large influence on the DOF of
CH4. The details of these influences are not shown here but will be included in a future paper. Here
we specifically examine the influence of the instrument spectral resolution and SNR for the
retrieval information of CH4. Note the spectral resolution we use in the above simulations is 0.01
cm–1, which is similar to the resolution of TCCON [Wunch et al., 2011]. However, the resolution of
existing satellite instruments like GOSAT is about twenty times lower (~ 0.2 cm–1). Figure 7 shows
how the DOF of CH4 changes with instrument spectral resolution and SNR in the 4210–4220 cm-1
window. Note that this window is the one containing the largest DOF compared with other
windows as shown in Figure 5. It is obvious from Figure 7 that higher resolution or SNR result in
larger value of DOF, which is consistent with the information theory. However, the correlation
between resolution/SNR and DOF is nonlinear. As shown in Figure 7, maximum sensitivity of DOF
to spectral resolution is located at resolution of 0.01 to 0.07 cm-1 while maximum sensitivity of
DOF to SNR is located at SNR of 100 to 350. On the other hand, DOF has very low sensitivity to
resolution and SNR in the region where SNR of 500 to 1000 and resolution of 0.31 to 0.51 cm-1.
Actually, DOF at SNR of 1000 and resolution of 0.31 cm-1 is only ~ 0.6 larger than the DOF at SNR
of 500 and resolution of 0.51 cm-1. In comparison, DOF at SNR of 600 and resolution of 0.01 cm-1
is ~ 2.4 larger than the DOF at SNR of 100 and resolution of 0.21 cm-1. So the DOF in the latter
case is ~ 4 times more sensitive to instrument resolution and SNR than in the previous region. This
analysis has implications for the design of future satellite instruments for CH4 retrieval. GOSAT
has a spectral resolution ~ 0.2 cm-1 and SNR ~ 300 (but note GOSAT does not measure spectra of
4210–4220 cm-1 window shown in Figure 7). This brings into sensitive DOF range for improving
20
the spectral resolution and SNR. So it is very effective to improve the retrieved information of CH4
profile by increasing the spectral resolution or SNR of an instrument like GOSAT. This analysis is
not limited to the 4210–4220 cm-1 window but can well apply to other CH4 bands. Furthermore, this
information analysis above can also apply to the retrieval of other geophysical variables such as
CO2 and temperature.
5. CH4 Profile Retrieval
In this section we carry out numerical simulations to demonstrate that we can retrieve the number of
pieces of CH4 vertical layers as indicated by the analysis of CH4 DOF in the last section. Note that
the spectra of CH4 bands alone cannot yield CH4 profile retrieval with sufficient precision, as spacebased measurements of absorption in these bands are influenced by some other factors besides the
CH4 profile. Both topographic variation over land and local weather can induce uncertainties in
surface pressure that contributes to errors in CH4 retrieval. In addition, scattering by clouds/aerosols
can further introduce uncertainties to the atmospheric path length. Previous studies [O'Brien et al.,
1998; Trauger and Lunine, 1983] demonstrate that the 0.76 μm O2 A-band could constrain both
surface pressure and optical path length variation induced by clouds/aerosols. Stephens and
Heidinger [2000]suggest that both strong and weak lines of the O2 A-band contain additional
information on the vertical distribution of cloud/aerosols. Here we use the O2 A-band (13125.0–
13155.0 cm–1) with resolution of 0.3 cm–1 and limit our discussion to relatively clear sky conditions
21
[Yoshida et al., 2011]. With both the CH4 band and the O2 A-band, our model simultaneously
retrieves several atmospheric and surface properties such as CH4 profile, temperature, water vapor,
surface pressure, surface albedo, cloud/aerosol and other variables as discussed in Section 3.
With SNR of 300 [Yoshida et al., 2011] and a priori uncertainty of CH4 ~ 90 ppbv [Worden et al.,
2012], the information analysis in Section 4 indicates that DOF of CH4 with resolution of 0.01 cm–1
(the spectral resolution of TCCON) can reach a theoretical upper limit ~ 4.2, which means possible
retrieval of 4 CH4 vertical bulk layers. Here we use two CH4 windows: 4214.5–4219.5 cm–1 and
4313.8–4316.8 cm–1, with a total of 800 channels and DOF of 4.21, to retrieve four CH4 bulk layers
(Case 1). On the other hand, with existing satellite instrument resolution of ~ 0.2 cm–1 (e.g.,
GOSAT), we also attempt to use the CH4 window: 4190.0–4350.0 cm–1, with 800 channels and
DOF of 3.34, to retrieve three CH4 bulk layers (Case 2). Here we retain 15 pressure layers in the
model. The method to divide the 15 layers into three or four bulk layers is according to the principle
that each bulk layer should contain approximately equal DOF [Kuai et al., 2012]. Rodgers [2000]
shows that the diagonal elements of the Averaging Kernel matrix can indicate DOF of each layer.
The Averaging Kernel of Case 1 and Case 2 are plotted in Figure 8, which exhibits high
sensitivities of spectra to CH4 at upper troposphere and planetary boundary layer for both cases.
This result is based on the scheme of dividing the atmosphere into 15 layers equally in pressure so
that each layer contains equal number of air molecule and same order of magnitude of CH4
molecules, which is the basis to compare the sensitivity of spectra to CH4 at different layers. This
22
scheme is better than the one of dividing layers by equal thickness because CH4 number density is
not uniformly distributed in altitudes. Table 3 lists the diagonal elements of the Averaging Kernel,
from which we can divide atmosphere into bulk layers for Case 1 and Case 2 as shown in Table 4.
Our dividing principle ensures DOF of each bulk layer ~ 1.0 and thus, contain enough retrieval
information for CH4 profile retrieval.
The result of Figure 8 can be further explained by investigating the Jacobian (d[Radiance]/d[CH4])
profiles in the CH4 window 4210-4219 cm-1. Figure 9 shows that the Jacobian profile can vary
significantly with wavenumber, which indicates strong variability of spectra sensitivity to CH4
profile. Some parts of the spectra have high sensitivities to CH4 at upper troposphere and some
others have high sensitivities to CH4 at planetary boundary layer, which is consistent with the result
of Figure 8. Shia et al. [2012]used an analytical model to demonstrate that the pressure broadening
can lead to such variability of spectral sensitivity to GHG profile. This analysis explains the source
of vertical information for CH4 profile retrieval according to the basic retrieval theory.
Before performing a realistic retrieval, we conduct a linear covariance analysis according to Eq. (4)
[Kuang et al., 2002; Rodgers, 2000]to estimate the retrieval precision of CH4 profiles. Table 5
shows that both Case 1 and Case 2 have the potential to retrieve CH4 mixing ratio profile with each
bulk layer precision better than 1%, which can be very helpful to provide a strong constraint for
23
CH4 horizontal and vertical flux estimates [Bergamaschi et al., 2009]. For Case 1 in Tables 3-5, we
propose three tests (A, B, and C) as shown in Figure 10. The three tests have the same true CH4
profile but different a priori CH4 profiles to study the sensitivity of profile retrieval with respect to
a priori profiles. Circles in top figures denote the position of 15 layers in the model. Solid lines
denote different bulk layers and dashed lines connect the bulk layers to compose the total vertical
profile. Squares in bottom figures indicate the averaged CH4 biases of each bulk layer from the
profile retrieval. Figure 10 shows that although a priori profiles deviates from true profile up to ~
100 ppbv, the retrieved CH4 profiles in all three tests agree well with the true profiles. We need to
note that as we only retrieve averaged CH4 of each bulk layer, the retrieved bulk layer profiles are
determined by the a priori bulk layer profiles. The bias of CH4 bulk layer retrieval in all the three
tests are within 10 ppbv (< 1%) as shown in Figure 10 and Table 6. The three tests demonstrate that
the retrieval information in Case 1 is mainly from the spectral measurement and has a weak
dependence on the choice of a priori profile if it is within the reasonable range (with deviation
<6%). We also carry out three tests (D, E and F) for the Case 2 in Table 3-5. The results are shown
in Figure 11 and Table 6. Like Case 1, the retrieved CH4 bulk layer profiles in Case 2 also agree
well with the true profiles with bias less than 10 ppbv (<1%).
The true profiles in previous tests (A-F) for Case 1 or Case 2 is continuous. However, as large
uncertainties of bottom-up CH4 estimates exist due to high variability of emissions of many CH4
source categories. Accurate quantifications of CH4 fluxes require our retrieval algorithm capable of
24
detecting local CH4 sources especially near the surface. Therefore we perform four more tests (G, H,
I and J) for Case 1 and three more tests (K, L and M) for Case 2 with local source at different bulk
layers. The results are shown in Figure 12, Figure 13 and Table 6. As previous tests have
demonstrated the weak dependence on reasonable a priori profiles for CH4 profile retrieval, the new
tests (G-M) here employ the same a priori profile. The local sources in all these tests are significant
enough with deviation up to ~ 100 ppbv. Simulation results in all the tests exhibit good agreements
between retrieved CH4 profile and true CH4 profile, including the layers of local source. And the
corresponding biases of each bulk layer in all the tests are less than 18 ppbv (~ 1%) as shown in
Table 6. These simulations validate the conclusions of our information analysis that our retrieval
algorithm is capable of retrieving four CH4 bulk layers with CH4 windows 4214.5–4219.5 cm–1 and
4313.8–4316.8 cm–1 by a resolution of 0.01 cm–1, and is capable of retrieving three CH4 bulk layers
with the 4190.0–4350.0 cm–1 CH4 window by a resolution of 0.2 cm–1.
6. Discussion and Conclusions
Atmospheric CH4 is the second most important anthropogenic greenhouse gas. In the past decade,
satellites such as SCIMACHY and GOSAT have enabled substantial progress towards retrieving
global  CH 4 distributions from NIR backscattered sunlight observations. However, the variations of
column-averaged CH4 are usually not in phase with the surface CH4 concentrations, especially in
the seasonal timescale [Frankenberg et al., 2011]. Therefore precise observation of global  CH 4 is
25
still not enough for an accurate estimate and prediction of CH4 seasonal fluxes due to the large
variability of emissions of many CH4 source categories [Bergamaschi et al., 2009]. Accurate
estimation of seasonal CH4 sources, sinks and horizontal/vertical transport requires high spatial and
temporal observations of CH4 profiles [Bergamaschi et al., 2007]. Since the largest CH4 sources
and sinks are located in the planetary boundary layer, tropospheric CH4 profile retrieval is
especially important. In this paper, we have introduced a strategy for global tropospheric CH4
profile retrieval from NIR satellite measurements with a vertical resolution of 3–6 km.
The linearized vector radiative transfer model VLIDORT [Spurr, 2006]and the optimal estimation
algorithm [Rodgers, 2000] were used in our retrieval model. Information content analysis was
carried out for two NIR CH4 bands, 4190–4550 cm–1 (2.3 μm band) and 5880–6120 cm–1 (1.6 μm
band), with resolution of 0.01 cm–1. Our results show that the DOF of CH4 channel has a nonlinear
positive correlation with the absorption strength. The 2.3 μm band contains much more retrievaluseful channels than the 1.6 μm band; 6291 (~ 19.7%) channels in 2.3 μm band have DOF≥0.9
while only 606 (~ 2.5%) channels in 1.6 μm band satisfies the same criterion. However, because of
repeated retrieval information among different channels, DOF increase very slowly with the number
of channels when the retrieval information has already saturated (Figure 6). Using a SNR level of ~
300 typical of existing instruments and CH4 a priori uncertainty ~ 90 ppbv, we found that the upper
limit of CH4 DOF is ~ 4.22 if spectra resolution is 0.01 cm–1 (resolution level of TCCON). In fact
from our numerical study, we found that the DOF by all 56,000 channels (32,000 from 2.3 μm band
26
and 24,000 from 1.6 μm band) should not exceed 4.4. Thus we select 615 CH4 channels out of
56,000 CH4 channels (~ 1.1%) to provide more than 95% (~ 4.22/4.4) of the total CH4 information.
This shows the power of channel selection. If the spectral resolution is 0.2 cm–1 that is the resolution
of present satellite instruments, the upper limit of CH4 DOF is ~ 3.3.
Note that CH4 DOF depends on the CH4 a priori covariance, the RT model, instrument SNR and the
spectral resolution. The CH4 a priori covariance does not have large influence on CH4 DOF if it is
within the reasonable range constrained by climatological data. On the other hand, RT model
parameters such as surface albedo, surface pressure and SZA can have non-negligible influence on
CH4 DOF and these effects need to be further investigated in the following papers. The instrument
SNR and spectral resolution were examined to have nonlinear positive correlation with CH4 DOF.
However, the sensitivity of CH4 DOF to instrument SNR and spectral resolution vary considerably
in different region of SNR and resolution (Figure 7). In the window of 4210–4220 cm-1, it is found
that DOF has low sensitivity in the region of SNR of 500 to 1000 and resolution of 0.31 to 0.51 cm1
while DOF has large sensitivity in the region of SNR of 100 to 600 and resolution of 0.01 cm-1 to
0.21 cm-1. This sensitivity analysis indicates the present satellite instrument has high potential to
increase the retrieval information by increasing its SNR or spectral resolution. The analysis of
Jacobians demonstrates that spectra sensitivity to CH4 profile can vary significantly at different
wavenumbers, which mathematically explains the information source of CH4 profile retrieval.
Physically, the strength of pressure broadening can determine the vertical information for CH4
27
profile retrieval.
We carried out CH4 profile retrieval of four bulk layers (Case 1) using the CH4 windows 4214.5–
4219.5 cm–1 and 4313.8–4316.8 cm–1 with resolution of 0.01 cm–1, which provide a CH4 DOF of
4.2. We also performed CH4 profile retrieval of three CH4 bulk layers (Case 2) using the CH4
window 4190.0–4350.0 cm–1 with resolution of 0.2 cm–1, which lead to a CH4 DOF of 3.3. In
addition to the CH4 bands, we also include the O2-A band to constrain the surface pressure and
optical path modification by aerosols. The approach to divide the atmosphere into three or four bulk
layers is according to the principle that each bulk layer should contain approximately equal DOF,
which can be achieved by analyzing the Averaging Kernel. Using the CH4 and O2-A bands, our
retrieval algorithm simultaneously retrieves CH4 profiles and several influential atmospheric and
surface properties such as temperature, aerosol, water vapor, surface pressure, surface albedo, and
etc. The linear covariance analysis and the retrieval experiments for both Case 1 and Case 2
demonstrate that our retrieval strategy is capable of retrieving CH4 in 3–4 bulk layers with less than
~ 1% bias for each bulk layer. Furthermore, Our retrieval algorithm has a weak dependence on a
reasonable a priori profile. The algorithm is capable of detecting local sources at different bulk
layers, which is crucial for improving the estimation of local CH4 fluxes and the effects of transport.
All these simulation experiments validate the usefulness of Rodgers information content analysis in
GHG profile retrieval, which can help select channels and decide the number of bulk layers to
retrieve and the way to divide atmosphere into bulk layers. In subsequent papers, we will
28
investigate how much the vertically resolved CH4 profiles with the above characteristics can reduce
uncertainties in CH4 flux estimates for the inverse modeling of flow and transport. Also, applying
this algorithm to radiance data from existing satellite instruments will be considered in the
subsequent papers.
Realistic global CH4 profile retrieval by satellite measurement can encounter various atmospheric
and surface situations. Numerical experiments indicate that the accuracy of profile retrieval by our
algorithm is not very sensitive to the distribution of temperature profile, water vapor profile, surface
albedos and surface height (results not shown). This demonstrates that the selected CH4 and O2-A
bands (with good SNR) include enough retrieval information to constrain the influences of the
variables listed above. Note that the accurate CH4 retrieval in this paper is for relatively clear sky
scenario. To approach such accuracy in a cloudy atmosphere, some additional techniques to account
for cloudy effect need to be included in the retrieval. Recently, it has been demonstrated that
retrieving information on the aerosol and cirrus particle amount, type, size and height distribution
simultaneously can lead to similar retrieval quality in cloudy condition as in clear sky condition
[Bril et al., 2009; Bril et al., 2007; Butz et al., 2011; Butz et al., 2010; Rodgers, 2000]. This
methodology of parameterizing aerosol and cirrus cloud effects will be included in our CH4 profile
retrieval algorithm for cloudy scenario in subsequent papers.
29
Channel selection for retrieval is not just an approach to greatly reduce the computational expense
by abandoning the repeated information; it is also an effective way to improve the retrieval
accuracy by excluding useless channels with low SNR. Our information analysis shows that it
usually only needs < 10% of channels to include more than 90% of retrieval information (see Table
2). From the basic retrieval theory, introducing large amounts of repeated or useless information in
the retrieval can turn the Jacobian into a sparse matrix and make the retrieval problem more
underdetermined. This partly explains why Chahine et al. [2005], using only dozens of selected
channels, was able to achieve a successful CO2 retrieval. Furthermore, our retrieval algorithm can
separate near surface CH4 variations from the free troposphere and from the stratosphere. This is
very useful as these regions have different CH4 source, sink and transport mechanisms. In realistic
retrieval by satellite measurement, one way to validate the global retrieval is to compare it with the
global 3-D chemical transport model (CTM) such as GEOS-Chem. However, as the inversion of
GEOS-Chem usually has large uncertainties of CH4 at stratosphere but much smaller uncertainties
at troposphere, distinguishing troposphere CH4 from stratosphere CH4 by our retrieval algorithm is
very helpful for the validation. Furthermore, one principle of the channel selection presented in this
paper is to provide nearly homogeneous information at different layers in order to get similar
retrieval quality at different bulk layers. However, sometimes our interests may focus on some
specific layers such as planetary boundary layer (PBL) where the largest CH4 sources and sinks
locate. In this case, the principle of channel selection can be changed, similar to Chahine et al.
[2005], to mainly select channels with maximum sensitivities to CH4 at PBL, which will lead to
more accurate retrieval of CH4 at PBL than other layers. This strategy can also be applied for
30
specific retrieval of CH4 at stratosphere and free troposphere. Note also that our band selection
scheme can be repeated for other possible CH4 absorption bands or combination of bands.
Our analysis and results have meaningful implications for present spaceborne CH4 profile retrievals
and future GHG satellite design. GOSAT measures the 1.6 μm band with SNR of 300 and
resolution of 0.2 cm–1. Information analysis based on our model indicates it can retrieve ~ 1.7 CH4
bulk layers with selected channels. Again, this result is for relatively clear sky scenario and also
depends on the value of SZA, surface albedo, surface pressure and other factors in the RT process.
In realistic cases of local surface geology and weather, there are large possibility for the CH4 DOF
of GOSAT to be less than 1.0 (i.e., cannot measure  CH 4 accurately) or larger than 1.7. For
CarbonSat to be launched in 2016 or later [Bovensmann et al., 2010], it will measure the 1.6 μm
CH4 band with a high SNR ~ 600 and a resolution of < 0.15 nm (~ 0.59 cm-1). Our information
analysis show it can retrieve > 1.4 CH4 bulk layers and its spectral resolution will matter a lot for
the retrieval result. Sentinel-5 precursor (due for launch in 2014) will measure the 2.3 μm CH4 band
with a SNR > 100 and a resolution of ~ 0.25 nm (~ 0.47 cm-1) [Butz et al., 2012]. With selected
bands, Sentinel-5 precursor can also retrieve > 2 CH4 bulk layers according to the same information
analysis. For other future GHG-measurement satellites such as GOSAT-2, we propose that the
inclusion of the selected 2.3 μm bands with the present SNR (~ 300) and resolution (~ 0.2 cm-1)
would be capable of measuring three tropospheric CH4 bulk layers. And with a better SNR ~ 500
and resolution ~ 0.1 cm-1, the satellite would be capable of retrieving four tropospheric CH4 bulk
31
layers, which can greatly improve the accuracy of CH4 flux estimates. If CH4 concentration is to be
measured at five or even more bulk layers, an instrument of higher SNR and higher resolution, such
as the versatile PEPSIOS [Trauger and Lunine, 1983], which was originally designed and built for
the study of trace constituents (HD, O2, CO) in planetary spectra at visible and NIR wavelengths
from ground-based telescopes, will be needed.
Our retrieval strategy can be similarly applied to CH4 profile retrieval from ground-based
observation network such as TCCON, whose high resolution (~ 0.01 cm-1) and SNR (~ 1000) can
potentially yield CH4 profile retrievals up to 5 bulk layers according to the information analysis.
Improvement of CH4 profile retrieval is possible by including the thermal infrared radiance (TIR) in
the retrieval. Worden et al. [2012] performed the CH4 retrieval through TIR of Tropospheric
Emission Spectrometer (TES). Their spectra shows sensitivity to methane from approximately 800
hPa to 200 hPa and the TIR of TES can contribute up to 2 DOF for CH4 profile retrieval. Another
possible approach to increase the information of CH4 profile is to employ polarizations in the
retrieval. Our first results show that polarization has its greatest sensitivity to CH4 near the surface.
The Jacobian profile of polarization is very different from the Jacobian profile of radiance due to
the effect of scattering. Such difference can provide us additional information for CH4 profile
retrieval according to the basic retrieval theory. Validation of these approaches will be presented in
subsequent papers.
32
Acknowledgments
We thank Dr. J. Margolis, Dr. J. Worden and Dr. C. Frankenberg for their valuable comments. This
research is supported in part by the Orbiting Carbon Observatory 2 (OCO-2) project, a NASA Earth
System Science Pathfinder (ESSP) mission and Project JPL.1382974 to the California Institute of
Technology.
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Table 1. Spectral ranges used for different  CH 4 retrievals
SatelliteInstrument
SCIAMACHY
SCIAMACHY
GOSAT
Sentinel-5
precursor
CarbonSat
Mission
45
CH4 window
(cm-1)
4277-4423
References
Frankenberg et al.,
[2005a];
Buchwitz et al.,
[2005];
Gloudemans et al.,
[2008]
5988-6135
5900-6135
4190-4340
Bergamachi et al.,
Yoshida et al., [2011];
[2007; 2009];
Butz et al., [2010; 2011];
Frankenberg et al.,
Parker et al., [2011];
[2005b; 2011]
Schepers et al., [2012]
Butz et al., [2012];
Galli et al., [2012]
5970-6414
Bovensmann et al.,
[2010]
Table 2. Selected channels and their contribution to DOFa
CH4 window (cm-1)
4190-4200
4210-4220
4230-4240
4240-4250
4250-4260
4270-4280
4310-4320
48/1000
125/1000
67/1000
59/1000
117/1000
111/1000
92/1000
3.18/3.49
3.69/4.15
3.14/3.40
3.12/3.47
3.16/3.49
3.13/3.40
3.04/3.50
Selected channels
fraction
DOF contribution by
selected channels
a
The CH4 windows here are the strong ones with total DOF≥3.40 in Figure 5. Selected channel in each window here has DOF
contribution >0.005
46
Table 3. Diagonal elements of Averaging Kernel of CH4 profile retrieval for Case 1 and Case 2
Layer index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Starting pressure
(hpa)
Ending pressure
(hpa)
0
101
169
237
304
372
439
506
574
642
710
778
846
914
982
101
169
237
304
372
439
506
574
642
710
778
846
914
982
1050
Case 1
0.61
0.54
0.36
0.33
0.28
0.23
0.21
0.24
0.21
0.16
0.14
0.17
0.23
0.31
0.19
Case 2
0.43
0.49
0.27
0.25
0.21
0.19
0.18
0.16
0.14
0.13
0.13
0.16
0.21
0.26
0.15
Diagonal elements
Of Averaging Kernel
47
Table 4. Configurations of Case 1 and Case 2a
1st bulk layer
2nd bulk layer
3rd bulk layer
4th bulk layer
Total
1-2
3-5
6-10
11-15
1-15
2
3
5
5
15
Altitude range (km)
>13.0
7.7-13.0
2.9-7.7
0-2.9
>0
DOF
1.15
0.97
1.05
1.04
4.21
1-3
4-8
9-15
1-15
3
5
7
15
Altitude range (km)
>10.7
4.6-10.7
0-4.6
>0
DOF
1.19
0.98
1.17
3.34
Case 1 (4 bulk layers)
Layers included (by index)
Number of layers
Case 2 (3 bulk layers)
Layers included (by index)
Number of layers
a
The order of bulk layers (i.e., 1st to 4th or 1st to 3rd) is from top to bottom, see text for more details
48
Table 5. The CH4 window and estimated precisions of CH4 profile retrieval for Case 1 and Case 2a
Resolution (cm-1),
1st bulk layer
2nd bulk layer
3rd bulk layer
4th bulk layer
Number of CH4 channels
precision (ppb)
precision (ppb)
precision (ppb)
precision (ppb)
0.01, 800
1.80
5.09
11.74
9.10
0.2, 800
5.12
6.94
1.65
-1
CH4 window (cm )
4214.5-4219.5 and
Case 1
4313.8-4316.8
Case 2
a
4190.0-4350.0
The order of bulk layers (i.e., 1st to 4th or 1st to 3rd) is from top to bottom, see text for more details
49
Table 6. Bulk layer averaged CH4 bias from profile retrievals, in Test A – Test Ma
Case 1
Case 2
Case 1
Case 2
Test A
Test B
Test C
Test D
Test E
Test F
Test G
Test H
Test I
Test J
Test K
Test L
Test M
1st bulk layer (ppb)
-0.05
-1.96
0.30
-7.95
7.04
-9.91
-8.26
-1.85
-6.55
-2.43
0.73
-0.70
-9.75
2nd bulk layer (ppb)
-7.29
3.96
-5.42
3.07
-4.35
-1.51
1.36
-6.98
-0.98
-7.24
-2.68
-12.18
5.43
3rd bulk layer (ppb)
5.29
-1.14
-0.79
-5.54
-1.28
-1.26
-1.37
4.18
-3.67
8.70
-5.23
1.76
-10.37
4sth bulk layer (ppb)
-9.45
-8.46
-6.19
-10.00
-13.49
-7.66
-16.12
Averaged CH4 bias of
a
The order of bulk layers (i.e., 1st to 4th or 1st to 3rd) is from top to bottom, see text for more details
50
Figure 1. Time series of the TM5 model at different model layers over the Sahara (15°N–30°N,
0°E–13°E), from Frankenberg et al. [2011]. Seasonal variations at different height layers can show
opposite behavior, all affecting  CH 4 that therefore exhibits a different seasonal cycle than surface
CH4 concentration.
51
Figure 2. The transmittance and DOF of the 2.3 μm CH4 band (4190–4510 cm–1) with resolution of
0.01 cm–1 for standard midlatitude summer atmosphere, assuming a solar zenith angle (SZA) of 45°
and a nadir viewing geometry, see text for more details.
52
Figure 3. Same as Figure 2 but for the 1.6 μm CH4 band (5880–6120 cm–1).
53
Figure 4. Same as Figure 2 but for a small 2.3 μm CH4 window (4190–4230 cm–1) in detailed
features, to illustrate the correlation between transmittance and DOF more clearly.
54
Figure 5. Same as Figure 2 but include 1000 channels (i.e., every 10 cm-1 with the resolution of
0.01 cm-1) for each DOF calculation (denoted as circle). (top) for the 2.3 μm band. (bottom) for the
1.6 μm band.
55
Accumulated DOF
4.1
4.1
3.7
3.7
3.3
3.3
2.9
2.9
2.5
2.5
2.1
2.1
1.7
1.7
1.3
1.3
0.9
1
200
400
600
800
Number of channels
1000
0.9
1
100
200
300
400
500
600
Number of channels
Figure 6. (left) Accumulated DOF of CH4 in the window 4210–4220 cm–1 with resolution of 0.01
cm–1. (right) Accumulated DOF of CH4 by the selected 615 channels in Table 2. The red circles
denote channels with DOF contribution ≥0.005 while blue circles denote the other channels.
56
Figure 7. DOF of CH4 by the window 4210–4220 cm–1 with spectral resolution and SNR.
Generally speaking, higher resolution and SNR lead to larger DOF. The resulting DOF due to
different resolution and SNR can be very different (from ~ 1 to 5).
57
Figure 8. Averaging kernel matrix of CH4 retrieval for Case 1 (left) and Case 2 (right). High
sensitivities of spectra to CH4 in both cases locate at upper troposphere and planetary boundary
layer. This result is based on the scheme of dividing layers equally in pressure coordinate, which
ensures the same order of CH4 molecule number in each layer and thus the fairness to compare
sensitivity of spectra to CH4 at different layers. See text and Table 3 for more details.
58
Figure 9. Normalized Jacobian (J=d[Radiance]/d[CH4]) profiles in the CH4 window of 4210-4219
cm-1. The channel wavenumber for each Jacobian profile can be inferred from the colorbar. This
figure shows that the spectra sensitivity to CH4 profile can vary significantly with wavenumber,
which explains the information source for CH4 profile retrieval. Some spectra have high
sensitivities to CH4 at upper troposphere and some others have high sensitivities to CH4 at planetary
boundary layer.
59
Figure 10. Test A, B and C of CH4 profile retrieval in Case 1 (see Table 3-5). Circles in top figures
denote the position of 15 layers in the model. Solid lines denote different bulk layers which are
connected by dashed lines. Blue, red and black colors in top figures represent the true, a priori and
retrieved CH4 profiles respectively in the three tests. Squares in bottom figures indicate that the
averaged CH4 biases of each bulk layer are within 18 ppb (~ 1%) (see Table 6 for more details).
The three tests include the same continuous true profile but different a priori profiles.
60
Figure 11. Same as Figure 10 but for Test D, E and F of CH4 profile retrievals in Case 2 (see Table
3-5). The three tests here include the same continuous true profile but different a priori profiles.
Bottom figures indicate that the averaged CH4 biases of each bulk layer are within 18 ppb (~ 1%)
(see text and Table 6 for more details).
61
Figure 12. Same as Figure 10 but for Test G, H, I and J of CH4 profile retrievals in Case 1 (see
Table 3-5). The four tests here include the same a priori profile but different local CH4 sources in
true profiles. Bottom figures indicate that the averaged CH4 biases of each bulk layer are within 18
ppb (~ 1%) (see text and Table 6 for more details).
62
Figure 13. Same as Figure 10 but for Test K, L and M of CH4 profile retrievals in Case 2 (see
Table 3-5). The three tests here include the same a priori profile but different local CH4 sources in
true profiles. Bottom figures indicate that the averaged CH4 biases of each bulk layer are within 18
ppb (~ 1%) (see text and Table 6 for more details).
63