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
1
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
2
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
5
“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
7
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
8
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 radiance errors of ~ 5–10% for viewing zenith angles (VZAs) of
55–70° [Spurr, 2004]. VLIDORT avoids these errors 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 atmospheric model 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 an
atmospheric absorption model, the VLIDORT radiative transfer model, a solar spectral model and
an instrument model. The trace gas optical depths required as input by VLIDORT are generated
from the atmospheric state using the Reference Forward Model (RFM) [Dudhia et al., 2002]. RFM
is a line-by-line radiative transfer code based on GENLN2 [Edwards, 1992] (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.
The state vector divides the atmosphere into 15 uniform pressure layers from one bar to the top of
the atmosphere. Previous studies have demonstrated that 15 layers are sufficient for accurate CH4
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retrievals [Butz et al., 2011; Schepers et al., 2012]. The pressure layer scheme is better than a
scheme employing pressure levels of equal geometrical thickness because CH4 varies significantly
with altitude, especially in the upper troposphere/lower stratosphere. We generate the CH4
absorption spectrum using an updated list of CH4 spectral parameters from the HITRAN 2008
database [Rothman et al., 2009]. This list corrects erroneous CH4 and H2O spectroscopic parameters
that are known to have caused bias in the retrieval of  CH 4 from SCIAMACHY observations
[Frankenberg et al., 2008]. The final state vector is composed of the CH4 concentration profile (15
layers), the ground surface albedo for each spectral band, 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 observation of near infrared CH4 absorption bands alone cannot yield profile retrievals with
high precision since the spectral radiances in these bands are strongly influenced by 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
11
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
[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.
We model tropospheric aerosol according to the climatological categories developed by Kahn et al.
[2001]. 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, the Mie scattering code generates coefficients for the expansion of the scattering matrix
in generalized spherical functions required 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
been taken from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)
[Abrams, 2000] spectral library.
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Calculation of the Jacobian matrix (derivatives of radiance with respect to atmospheric or surface
parameters) is the most computationally expensive process in a typical retrieval algorithm [Yoshida
et al., 2011]. We exploit the fact that VLIDORT is fully linearized and computes the Jacobians with
respect to any atmospheric and surface properties simultaneously along with the radiances
themselves to significantly reduce the computational expense compared to eg finite difference
methods. We will make extensive use of this linearization for generating 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
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
13
here are estimated from climatological data and transport model results. Following Worden et al.
[Worden et al., 2012], we assume an a priori uncertainty of 90 ppbv (~5%) for CH4 mixing ratios
in different layers. We assume an a priori uncertainty of 100% for the aerosol optical depth given
the significant uncertainty in its profile. The band-averaged albedos are assigned a priori
uncertainties of 20% and are assumed to be independent of each other. We assume no correlation
between different uncertainties ie the error covariance matrix is diagonal for the simulations
presented here.
The minimization of Eq. (2) is performed using the Levenberg-Marquardt method [Levenberg,
1944; Marquardt, 1963] by the iterative formula:
(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
14
CH4 bulk layers which may be retrieved. We will adjust the retrieval strategy to maximize the DOF
for CH4 while preserving the retrieval precision. We are not concerned with the DOF for other
variables in the state vector as long as the quality of the CH4 retrieval remains high. We calculate
the CH4 DOF from 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, our retrieval strategy is to preferentially select CH4 absorption features or
microwindows 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 reduced CH4 radiance spectrum will increase CH4 DOF and thus an improved CH4
profile retrieval. Selection of the CH4 absorption features and microwindows for the retrieval is
therefore crucial and is the central focus of the present study.
4. CH4 Absorption Channel Selection
The CH4 absorption bands used in previous studies to retrieve  CH 4 retrieval from backscattered
NIR satellite observations are summarized in Table 1. In the present study, we focus on the CH4
15
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 nadir-viewing
observations of reflected sunlight. Other CH4 bands in the near infrared and visible spectral regions
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. We omit thermal infrared absorption bands from the present
study since we are trying to simulate observations from a single instrument.
We frame our analysis in terms of the spectrally resolved radiances or channels produced by
satellite remote sensing instruments such as SCIAMACHY or GOSAT. Different channels 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 exclusion 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
16
to ~32,000 and ~24,000 independent spectral radiances in the 2.3 and 1.6 μm bands, respectively.
Retrievals with so many spectral radiances 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, Chahine et al. [2005] showed that for CO2 a small number of optimally selected
channels can lead to robust, high accuracy retrievals.
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
using a specrtral resolution of 0.01 cm–1 and a continuum SNR of ~300. We also present results for
other combinations of SNR and spectral resolution later in this section.
Simulated top of atmosphere (TOA) radiance spectra for the two CH4 bands and the associated DOF
values calculated using Eq. (5) are shown in Figures 2-4. Note the DOF here is only for CH4 profile
and does not include any 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
17
value associated with each spectral radiance has a normalized value from 0 to 1, representing the
DOF of CH4 in that particular radiance measurement. Figure 2 shows that the 2.3 μm CH4 band
consists of a strong, dense spectrum, with many lines having CH4 DOF values near 1.0. The value
of 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 [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 large numbers of strong absorptions leads to
extended regions of large CH4 DOF values (≥ 0.8).
In contrast, the CH4 spectrum in the 1.6 μm band is much less dense and has fewer channels with
large DOF, as shown in Figure 3. Assuming 0.01 cm-1 spectral resolution, the number of channels
with DOF ≥ 0.9 for the 2.3 μm band is 6291 (~ 19.7%) while it is only 606 (~ 2.5%) for the 1.6 μm
band – a 10-fold reduction in the number of high-DOF channels. From an information theory
perspective, the 2.3 μm band thus appears to contain much more useful CH4 vertical profile
information than the 1.6 μm band. However, we need a strategy for reducing the number of
channels used in our retrieval since not all of the ~6000 channels in the 2.3 μm band with DOF ≥
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0.9 contain independent information. Furthermore, including too many channels will seriously
increase the computational expense and complicate the retrieval procedure.
Based on past experience [Kuai, Shia], we hypothesize that the majority of the CH4 profile
information can be obtained from a subset of the high information channels that numbers much less
than 6000. We therefore set 1000 as the upper limit on the potential number of channels used for
the retrieval. We divide the 1.6 and 2.3 μm bands into 10 cm–1 windows, with each window having
10 cm–1 / 0.01 cm-1 =1000 spectral radiance channels. All 1000 channels of each window are
combined to calculate the CH4 DOF for that window. 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 absorption regions in the
CH4 spectra of Figure 2. Values of 3-4 for CH4 DOF in each of these 2.3 μm windows should be
compared with the theoretical limit of DOF=15, which indicates that these 2.3 μm windows have
the potential for retrieving 20% ~ 27% of all CH4 layers.
19
An important question is how to maximize the vertical profile CH4 DOF without including
excessive redundant information or low information content 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. We find a total CH4 DOF of
4.15 in this window. Examining this result more closely, we find that 125 of the 1000 channels have
DOF contribution >0.005 and their total DOF is 3.69, which means 12.5% of the channels contain
3.69/4.15 ≈ 89% of the retrieval information in this window.
REWRITE THIS PARAGRAPH TO GIVE THE TOTAL 2.3 + 1.6 um DOF (4.4), THEN THE
ESTIMATES FOR INDIVIDUAL BANDS, THEN 10 CM-1 WINDOWS. THIS CONVEYS THE
IDEA THAT A 10 CM-1 WINDOW CAN, IN PRINCIPLE, DELIVER SOMETHING
APPROACHING 90% OF THE TOTAL POSSIBLE CH4 DOF SINCE SO MUCH OF THE
REMAINING INFORMATION IS REDUNDANT
We analyze each of the strong CH4 windows in Figure 5 and identify a total of 619 high
information content channels in the entire spectrum. We expect this subset contains nearly all the
available CH4 retrieval information, as summarized in Table 2. We then calculate the accumulated
DOF of the 619 selected channels with the same method as for Figure 6 (left). The results are
20
shown in the right panel of Fig 6. Although each of the 619 channels contributes more than 0.005
DOF to its own window, when they are combined together only 110 (~ 18%) channels contribute
DOF > 0.005 (red circles). This means that the other 80% of the channels contain strong but
redundant CH4 retrieval information, which is consistent with the conclusions of [Shia et al., 2012].
The total CH4 DOF from the 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.
The choice of CH4 a priori covariance was found to not have a strong influence on the resulting
CH4 DOF value if the covariances were within the 90 ppb range expected from climatological data
[Worden]. Some parameters in the RT model such as solar zenith angle (SZA), surface albedo and
surface pressure can exert a significant influence on the CH4 DOF. The details of these results will
be presented in a future paper. Here we focus on the influence of the instrument spectral resolution
and SNR for the CH4 information content. Note the spectral resolution we use in the above
21
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 for the 4210–4220 cm-1 window. Note that this window contains the largest DOF of any
window in the present study (Fig 5). It is obvious from Figure 7 that higher resolution or SNR result
in larger value of DOF, as expected. However, the correlation between resolution/SNR and DOF is
nonlinear. The maximum sensitivity of DOF to spectral resolution is located at resolutions of 0.01
to 0.07 cm-1 while maximum sensitivity of DOF to SNR is located at SNRs of 100 to 350. DOF is
relatively insensitivity to changes in resolution/SNR for SNRs of 500 to 1000 and resolutions of 0.3
to 0.5 cm-1. Actually, DOF at SNR of 1000 and resolution of 0.31 cm-1 is only a factor of 0.6 larger
than the DOF at SNR of 500 and resolution of 0.5 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 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.
22
12/11/12 – New comments start here for file *-cem4.docx
5. CH4 Profile Retrieval
In this section we perform numerical simulations to demonstrate that up to four independent CH4
vertical layers can be retrieved from satellite measurements of spectrally resolved near infrared
radiances reflected from the Earth’s surface as suggested by the CH4 DOF analysis presented in
Section 4. To evaluate the potential for CH4 profile retrievals, we create a simulation with the
hypothetical instrument performance of SNR = 300 and spectral resolution = 0.01 cm–1 (similar to
TCCON) and set the a priori CH4 covariance in each layer = 90 ppbv [Worden et al., 2012],
resulting in a CH4 DOF with a theoretical upper limit ~ 4.2. We retrieve CH4 from two windows:
4214.5–4219.5 cm–1 and 4313.8–4316.8 cm–1, giving a total of 800 channels and a theoretical DOF
of 4.21 (Case 1). For comparison, we construct another simulation instrument performance
characteristics similar to those of GOSAT [Yoshida et al., 2011]: SNR = 300 and spectral resolution
= 0.2 cm–1. Methane profiles are retrieved using the 4190.0–4350.0 cm–1 window, resulting in 800
channels and a theoretical DOF of 3.34 (Case 2). Both cases retain 15 pressure layers in the
retrieval model. We divide the 15 pressure layers into three or four bulk layers according to the
principle that each bulk layer should contain approximately equal CH4 DOF [Kuai et al., 2012].
Rodgers [2000] shows that the diagonal elements of the averaging kernel matrix provide the DOF
23
of each layer. The averaging kernels for Case 1 and Case 2 are plotted in Figure 8, which illustrates
that both cases have high CH4 sensitivities extending through the troposphere and into the planetary
boundary layer. Table 3 lists the diagonal elements of the averaging kernel for each case, from
which we can divide atmosphere into bulk layers for Case 1 and Case 2 as shown in Table 4. Our
dividing principle allocates a CH4 DOF of ~1.0 to each bulk layer and thus providing enough
information for CH4 profile retrievals.
The result of Figure 8 can be further explained by investigating the Jacobian (d[Radiance]/d[CH4])
profiles. Figure 9 shows the Jacobian profile in the CH4 window 4210-4219 cm-1. The Jacobians
vary significantly with wavenumber, following the strengths of individual CH4 absorption features.
Figure 9 also shows how different absorptions map to sensitivity to different pressure levels in the
CH4 profile. Shia et al. [2012] showed that the pressure broadening of individual absorption
features contributes significantly to such variability of spectral sensitivity to the trace gas profile.
Taken together, Figs 8 and 9 and Tables 3 and 4 quantify the CH4 vertical profile information that
can be retrieved from our example cases.
To estimate the precision of the retrieved CH4 profiles, we performed a linear covariance analysis
according to Eq. (4) [Kuang et al., 2002; Rodgers, 2000]. Table 5 shows that retrievals for both
24
Case 1 and Case 2 have the potential to yield CH4 mixing ratio profiles with a precision better than
1% in each bulk layer. , Such vertically resolved measurements provide a strong constraint on
atmospheric transport and thus CH4 horizontal and vertical flux estimates [Bergamaschi et al.,
2009].
We further test Case 1 by retrieving the same true CH4 profile from three different a priori CH4
profiles (A, B, and C) as shown in Figure 10. These tests study the sensitivity of our profile
retrieval strategy with respect to a priori profiles. Circles in three top figures of Fig 10 indicate the
position of the 15 pressure layers and their associated CH4 mixing ratios in the model. Solid lines
define the four different bulk layers, connecting the pressure levels involved in each bulk layer, and
dashed lines connect the bulk layers to compose the total vertical profile. Squares in the bottom
three figures show the differences between the retrieved and true CH4 mixing ratios in each bulk
layer. Figure 10 shows that the retrieved CH4 profiles in all three tests agree well with the true
profiles despite the fact that the a priori profiles deviate up to ±100 ppbv from the true profile or
have a markedly different profile shape. The impact of retrieving the averaged CH4 mixing ratio for
each bulk layer can be clearly seen in the upper panels of Fig 10 where the retrieved profiles
generally succeed in capturing the mean CH4 value in each layer, but are restricted by the a priori
profile shape from simulating the true profile more accurately The CH4 bulk layer retrieval bias in
all three tests is within ±10 ppbv (< 0.6%) as shown in Figure 10 and Table 6. The three tests
suggest that the retrieval information in Case 1 comes predominantly from the observed spectral
25
radiances and, within our model framework, has a weak dependence on the choice of a priori
profile given normal climatological covariances (~6%). These results suggest that retrievals on
spectral radiances from a Case 1 class instrument should deliver reasonable CH4 vertical profiles
with four DOF of vertical information, including a well-characterized planetary boundary layer.
We performed similar tests (D, E and F) for Case 2. The results are shown in Figure 11 and Table 6.
The retrieved CH4 bulk layer profiles for Case 2 also agree well with the true profiles, yielding
retrieved-true biases less than ±18 ppbv (<1%) for each pressure level. The upper panels in Fig 11
clearly show the increased bias results from greater mismatch between the a priori and true profile
shapes given the smaller number of CH4 vertical DOFs with which Case 2 has to optimize the fit. It
is quite encouraging to see that within our modeling framework an instrument with GOSAT-like
performance can return three CH4 vertical profile DOFs.
NEED SOME WORDS ABOUT THE TOTAL COLUMN FITS, WHICH SHOULD BE VERY
GOOD GIVEN THE AVERAGING IN EACH PRESSURE LAYER.
The tests A-F were constructed with continuous, well-behaved true CH4 profiles. We provide a
more stringent test for Cases 1 and 2 by constructing discontinuous vertical CH4 profiles as might
be encountered for a significant mid-troposphere plume. We performed four more tests (G, H, I and
J) for Case 1 and three more tests (K, L and M) for Case 2 in which the CH4 mixing ratios were
26
enhanced by up to 100 ppbv separately in each bulk layer. The results are given in Table 6 and in
Figures 12 and Figure 13 for Cases 1 and 2, respectively. We initiate the retrievals for each set of
tests with an a priori CH4 profile that underestimates the mixing ratio in each pressure level by
~100 ppbv. The results demonstrate that our retrieval strategy does an excellent job of capturing the
enhanced concentration plume for all of the Case 1 and Case 2 tests, with retrieved-true mean CH4
mixing ratio biases less than ±18 ppbv in each pressure layer including the discontinuously
enhanced layers (Table 6). These simulations support the conclusions of our information analysis
and show that our algorithm is capable of retrieving three to four CH4 bulk layers from space-based
spectral radiances measured using windows in the 2.3 um absorption band.
6. Discussion and Conclusions
Points I would expect to be highlighted here:
This work demonstrates the feasibility of CH4 vertical profile retrievals for NIR spectral radiances
Vertical profile retrievals of CH4 with a GOSAT-class instrument using the 2.3 um channel to yield
3 pieces of vertical information, including one that is predominantly PBL. Moving to a much higher
spectral resolution (0.01 cm-1) only gains 1 more piece of vertical information
Information analysis suggests that CH4 profile retrievals can be accomplished with significant
computational cost savings by using carefully selected spectral windows. We find that even in an
27
optimally selected spectral window that ~90% of the CH4 profile information is contained in only
~10% of the spectral radiance channels. Retrieval strategies that employ channel selection therefore
merit renewed investigation.
Future studies: combining 2.3 and 1.6 um or TIR channels to obtain greater vertical profile
information (DOF > 3)
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
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.
28
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
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
29
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. 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 cm-1 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 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
30
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
atmospheric 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 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
31
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.
Channel selection for retrieval is not just an approach to greatly reduce the computational expense
by omitting redundant information; it is also an effective way to improve the retrieval accuracy by
excluding low information content 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
32
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
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
33
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
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.
34
For ground-based paragraph – need to read and discuss Sussmann et al Strategy for highaccuracy-and-precision retrieval of atmospheric methane from the mid-infrared FTIR
network
http://www.atmos-meas-tech.net/4/1943/2011/amt-4-1943-2011.html
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.
35
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
48
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
49
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
50
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
51
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
52
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
53
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.
54
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.
55
Figure 3. Same as Figure 2 but for the 1.6 μm CH4 band (5880–6120 cm–1).
56
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.
57
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.
58
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.
59
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).
60
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.
61
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.
62
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.
63
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).
64
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).
65
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).
66