Supporting Material
1) Aura TES and TERRA MOPITT data
Data from the Version 5 Aura TES data and Terra MOPITT satellite instruments as well
as the GEOS-Chem global chemical transport model. Version 5 TES CH4 profile data
from the TES “Lite Products” (http://tes.jpl.nasa.gov/data/) are used for this analysis.
Worden et al. (2013) discusses the data quality flags used for data selection, data bias
corrections, and comparison approach used to make robust comparisons to the GEOSChem model estimates of CH4 and CO. In summary, we use TES CH4 and CO profiles in
which the degrees-of-freedom-for signal (or DOFS) in the troposphere are larger than
1, which indicates that the data can fully capture variations of CH4 and CO in the free
troposphere. The TES CH4 data is bias corrected by 1.5%, as evaluated by
aircraft data
(Wecht et al., 2012). In all comparisons between TES data and the GEOS- Chem model
we average data and model from the surface to the tropopause because the retrieval
constraint allows for profile variability that is larger than expected from models but
reduces to physically realistic values when averaged over the troposphere (as indicated by
the DOFS). After averaging the TES CH4 and CO data have an uncertainty of
approximately 1% or less [Worden et al., 2013]
We use profiles of CO estimated from MOPITT thermal-infrared (TIR) and near- infrared
(NIR) channels, with sensitivity to the boundary layer (H. Worden et al., 2010) to provide
an independent estimate of CH4 fire emissions using the a priori CH4/CO emissions
factor and also to quantify the potential impact of vertical transport error on the CH4
emissions. These multispectral CO profiles provide increased sensitivity to surface
emissions and are also more sensitive to the role of convection on the vertical distribution
of CO (Jiang et al., 2013). These data are biased vertically in the tropics by
approximately 5% in the upper free troposphere for pressures less than 400 hPa but
biased low by 1-5% for pressures greater than 600 hPa (Deeter et al., 2013)
2. GEOS-Chem model inputs and comparison approach
The inputs for the GEOS-Chem model run are described in detail in Picket-Heaps et al.,
(2011) and Worden et al. (2012). The methane and fire emissions are constrained by the
Global Fire Emissions Database (GFED) and the model transport is from re- analysis
meteorological fields from the NASA Global Modeling and Assimilation Office.
Methane emissions are based on measured emissions factors discussed in Andreae and
Merlet (2001) and Van der Werf et al (2010).
When comparing the satellite data to GEOS-Chem we want to remove the impact of the
TES a priori and account for the vertical sensitivity of the TES estimate. Therefore, the
averaging kernels and a priori constraints are first applied to the model fields (e.g, Jones
et al., 2003, Kopacz et al., 2010; Worden et al., 2013):
𝐱̂ 𝐆𝐂 = 𝐱 𝐚 + 𝐀(𝐱𝐆𝐂 − 𝐱 𝐚 )
(1)
where xGC is a GEOS-Chem profile, xa is the a priori constraint used for the
corresponding (in space and time) TES methane retrieval. If the TES retrieval has
converged, which we can determine by looking at the RMS difference between the TES
measured radiance and the forward model of the atmospheric radiative transfer that
depends on this estimate (Bowman et al., 2006), then the TES estimate is related to the
“true” methane distribution and uncertainties affecting the estimate by (Rodgers and
Connor 2003):
𝐱̂ = 𝐱 a + 𝐀(𝐱 − 𝐱 a ) + 𝐆𝐧 + 𝐆𝐊 b (𝐛 − 𝐛a )
(2)
̂ is the TES CH4 (or CO) estimate, the x is the “true” methane profiles, 𝒏 is a
where 𝒙
vector equivalent to the measurement noise of the TES spectral radiances. 𝒃 and 𝒃a
represent the true state and a priori of the state for those parameters which also affect the
model radiance. The sensitivities of the radiance to those parameters (Jacobians) are
𝜕𝑳
𝐊 b = 𝜕𝒃. 𝐆 is the gain matrix, which is defined by
𝝏𝒙
−1 𝐓 −1
𝐆 = 𝝏𝑳 = (𝐊 𝐓 𝐒𝑛−1 𝐊 + 𝐒−1
a ) 𝐊 𝐒𝑛
(3)
where G maps from measurement (spectral radiance) space into retrieval space. 𝐀 is the
averaging kernel matrix, which describes the sensitivity of the retrieval to the true state.
̂
𝝏𝒙
𝐀 = 𝝏𝒙 = 𝐆𝐊
(4)
The other terms are the covariance of the noise: Sn, and Sa which is the a priori
covariance representative of the statistics of tropospheric methane (or CO).
Comparisons between the TES estimate and the GEOS-Chem profile become more
quantitatively robust because the a priori constraint and vertical sensitivity can now be
explicitly removed or accounted for in the comparison:
𝐱̂ − 𝐱̂ 𝐆𝐂 = 𝐀(𝐱 − 𝐱 𝐆𝐂 ) + 𝐆𝐧 + 𝐆𝐊 𝐛 (𝐛 − 𝐛𝐚 )
(5)
Differences between the TES estimate and GEOS-Chem now represent differences
between the true methane distribution (x), the modeled methane distribution (xGC) and
the observations errors of the TES data (𝐆𝐧 + 𝐆𝐊 𝐛 (𝐛 − 𝐛𝐚 )). Of course we don't
actually know the true noise vector n or the exact systematic errors but we can quantify
the statistics of these terms using calibration or validation data or by propagating the
statistics of the (b-ba) term through the gain matrix and Jacobians:
𝐒𝐨𝐛𝐬 = 𝐆𝐒𝐧 𝐆𝐓 + 𝐆𝐊 𝐛 𝐒𝐛 (𝐆𝐊 𝐛 )𝐓
(6)
where Sobs is the covariance matrix describing the observation error and is included with
every TES profile estimate. Note that the mapping of the methane profile by averaging
the volume mixing ratios of the profile is performed by simply matrix multiplying the
estimates and the covariance by a function which averages the profile (e.g., Worden et al.
2004). In addition, the TES free-tropospheric measurements are not sensitive to surface
methane variability but instead representative of air-parcels at larger scales because of the
long mixing time-scales of the free-troposphere. Consequently we ignore uncertainties in
the comparison (Equation 5) due to representation error related to differences between
the model 2x2.5 grid and the TES 5x8 km footprint [Jones et al., 2003].
3) Methane Estimation Approach.
We use the optimal estimation (OE) framework for quantifying methane emissions using
the TES methane data and the GEOS-Chem model (e.g., Bowman et al., 2006). Typically
OE involves finding the minimum of a cost function which depends, for this problem, on
the TES methane concentrations and their uncertainties as well as the total methane
emissions for September, October, and November of 2006 for Indonesia and then “the
rest of the world”. The emissions component of the cost function depends on the
assumed a priori uncertainties of these emissions (e.g., Bowman et al., 2006). However,
because of the relatively good agreement between the a priori distribution of
atmospheric methane and that observed by the Aura TES instrument (Worden et al.,
2013), we instead perform a linear update to the a priori emissions (Rodgers and Connor
2003):
−𝟏
−𝟏
𝐱 − 𝐱 𝐚 = (𝐊 𝐓 𝐒𝐦
𝐊 + 𝐒𝐚−𝟏 )−𝟏 𝐊 𝐓 𝐒𝐦
(𝐲𝐓𝐄𝐒 − 𝐲𝐆𝐂 )
(7)
where x is the emissions estimate, the subscript “a” refers to the a priori values. For this
problem, the vector x has six elements; three of these vector elements are the total
Indonesian methane emissions for September, October, and November and the other
three are the “rest-of-the-world” emissions for the same time period. The K is the
Jacobian or partial derivative of the modeled methane concentrations (ygc) with respect to
the emissions x. The Sm term is the covariance describing the uncertainties in the
observations of yTES; the diagonal values of Sm are the square of the observation error
(Worden et al., 2012) of each observation. The Sa term describes the a priori
uncertainties in the monthly emissions x.
As discussed in Worden et al. (2012), typical observation errors for tropical TES
observation range between 8 to 14 ppb for an average of all tropospheric concentration
(volume mixing ratio). Note that this average has little sensitivity to methane variations
for pressures greater than 800 hPa so consequently the estimate is representative of fretropospheric methane, which, for the Indonesia case, primarily originates from the
Indonesian fires for the fall of 2006. Figure 1 shows the finite difference Jacobians
(partial derivative of a fraction change in emissions relative to methane concentrations).
These Jacobians are first adjusted by the TES a priori constraint and averaging kernel
matrix to account for the regularization used by the TES retrieval (e.g., Jones et al.,
2003), followed by the same mapping used on the TES CH4 profiles to obtain an average
over the free troposphere. The Jacobians are normalized by the observation error;
effectively a 10% change in emissions in October can result in up to a factor of 80%
change in some of the observations relative to the observation error.
As can be seen in Figure S1, a perturbation of the September emissions over Indonesia
affects concentrations in October and November. The largest sensitivity occurs in
October when peak CO and CH4 concentrations over Indonesia occur.
Figure S1: Sensitivity (or Jacobian) of atmospheric methane from GEOS-Chem to the
total Indonesian emissions. The Jacobians are first adjusted by the TES instrument
operator, averaged over the free-troposphere and then normalized by the corresponding
TES observation uncertainty.
4. The 4-Dimensional Variational (4D-Var) Data Assimilation Approach
In the 4D-Var approach, we seek an optimal estimate of the CO sources that is consistent
with both the observed atmospheric concentrations and the a priori constraints on the
sources by minimizing the cost function J(x),
1 N
1
J(x) = å (F(x) - y j )T S-1
(x - xa )T Sa-1 (x - xa )
S (F(x) - y j ) +
2 j=1
2
(8)
where x is the state vector of emissions, yi is a vector of the N observations of CO, which
are distributed in time over the assimilation period, and F(x) is the forward model, which
represents the transport of the CO emissions in the GEOS-Chem model and accounts for
the vertical smoothing of the MOPITT retrieval. A discussion of the influence of the
vertical smoothing of the MOPITT retrieval, in the context of the inversion, is given in
Jiang et al. (2013). Here x a is the a priori estimate and S  and S a are the observational
and a priori error covariance matrices, respectively. The observational error covariance is
the sum of the retrieval errors (errors in y) and the forward model errors (errors in F(x),
the model simulation of the observations). The first term on the right in equation S2
represents the mismatch between the simulated and observed concentrations weighted by
the observational error covariance. The inversion tries to minimize the mismatch between
the model and observations by adjusting the CO emissions in each model grid box so that
the model better reproduces the observations over the assimilation period (which is one
month for the work presented here). The second term represents the departure of the
estimate from the a priori, weighted by the a priori uncertainty. In minimizing J, we seek
N
-1
ÑJ(x) = å K TS-1
S (F(x) - y j ) + Sa (x - x a ) = 0
(9)
j=1
where
K = ¶F(x) ¶x is the Jacobian that gives the sensitivity of the model simulation
of the CO observations to the emissions. The analytical solution to this is given by an
expression that is analogous to Equation (7). However, because we are trying to optimize
the CO emissions in each grid box in the model, the size of the matrices is too large to
use Equation (7) directly and so the cost function in minimized numerically. The GEOSChem 4D-Var system has been used for inversion modeling of atmospheric CO by
Kopacz et al. (2009, 2010) and Jiang et al. (2011, 2013).
Because the life time of CO is about two months, model errors can accumulate and bias
the initial CO distribution at the beginning of the assimilation period. We produce an
improved initial condition (the initial CO distribution) by assimilating MOPITT v5 data,
using the sequential sub-optimal Kalman filter, between 1 June 2006 to 1 November 2006,
following the approach of Parrington et al. (2008) and Jiang et al. (2013). This provides
optimized CO distributions at the beginning of September, October and November,
which are used as initial conditions in the inversion analysis. Following Jiang et al.
[2013], the MOPITT retrievals at pressures less than the 200 hPa retrieval level are
dropped in this work to avoid the influence of potential bias in the data at these altitudes
(Jiang et al., 2013). Figure S2 shows the a priori and a posteriori CO emissions for
October 2006. Emissions over South America are decreased while African emissions are
increased. Overall Indonesian emissions are approximately the same as reported in Table
2 in the main text.
Figure S2: (Top) A priori CO emissions for October 2006. (Bottom) A posteriori CO
emissions for October 2006. Units are 1012 molec /cm2/s
Supporting Material References
Bowman, K. W. et al. (2006), Tropospheric Emission Spectrometer: RetrievalMethod
and Error Analysis, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE
SENSING, 44(5), 1297–1307, doi:10.1109/TGRS.2006.871234.
Dlugokencky, E. J., E. G. Nisbet, R. Fisher, and D. Lowry (2011), Global atmospheric
methane: budget, changes and dangers, Philosophical Transactions of the Royal Society
A: Mathematical, Physical and Engineering Sciences, 369(1943), 2058–2072,
doi:10.1098/rsta.2010.0341.
Jiang, Z., D. B. A. Jones, H. M. Worden, M. N. Deeter, D. K. Henze, J. Worden, K. W.
Bowman, C. A. M. Brenninkmeijer, and T. J. Schuck (2013), Impact of model errors in
convective transport on CO source estimates inferred from MOPITT CO retrievals,
Journal of Geophysical Research-Atmospheres, 118(4), 2073–2083,
doi:10.1002/jgrd.50216
Jones, D. B. A., K. W. Bowman, P. I. Palmer, J. R. Worden, D. J. Jacob, R. N. Hoffman,
I. Bey, and R. M. Yantosca (2003), Potential of observations from the Tropospheric
Emission Spectrometer to constrain continental sources of carbon monoxide, J. Geophys.
Res, 108(D24), 4789, doi:10.1029/2003JD003702.
Kopacz, M., D. J. Jacob, D. K. Henze, C. L. Heald, D. G. Streets, and Q. Zhang (2009),
Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian
sources of carbon monoxide using satellite (MOPITT) measurements of CO columns, J.
Geophys. Res., 114, D04305, doi:10.1029/2007JD009264.
Kopacz, M., D. J. Jacob, J. A. Fisher, J. A. Logan, L. Zhang, I. A. Megretskaia, R. M.
Yantosca, K. Singh, D. K. Henze, and J. P. Burrows (2010), Global estimates of CO
sources with high resolution by adjoint inversion of multiple satellite datasets (MOPITT,
AIRS, SCIAMACHY, TES), Atmos. Chem. Phys, 10(3), 855–876.
Parrington, M., D. B. A. Jones, K. W. Bowman, A. M. Thompson, D. W. Tarasick, J.
Merrill, S. J. Oltmans, T. Leblanc, J. C. Witte, and D. B. Millet (2009), Impact of the
assimilation of ozone from the Tropospheric Emission Spectrometer on surface ozone
across North America, Geophys. Res. Lett, 36(4), L04802, doi:10.1029/2008GL036935.
Rodgers, C. D., and B. J. Connor (2003), Intercomparison of remote sounding
instruments, Journal of Geophysical Research-Atmospheres, 108, 4116,
doi:10.1029/2002JD002299.
Wecht, K. J., D. J. Jacob, S. C. Wofsy, E. A. Kort, J. R. Worden, S. S. Kulawik, D. K.
Henze, M. Kopacz, and V. H. Payne (2012), Validation of TES methane with HIPPO
aircraft observations: implications for inverse modeling of methane sources, Atmospheric
Chemistry and Physics, 12(4), 1823–1832, doi:10.5194/acp-12-1823-2012.
Worden, J., S. Kulawik, M. Shepard, S. Clough, H. Worden, K. Bowman, and A.
Goldman (2004), Predicted errors of tropospheric emission spectrometer nadir retrievals
from spectral window selection, J. Geophys. Res, 109(D9), D09308,
doi:10.1029/2004JD004522.
Worden, J., S. Kulawik, C. Frankenberg, V. Payne, K. Bowman, K. Cady-Peirara, K.
Wecht, J.-E. Lee, and D. Noone (2012), Profiles of CH4, HDO, H2O, and N2O with
improved lower tropospheric vertical resolution from Aura TES radiances, Atmos. Meas.
Tech., 5(2), 397–411, doi:10.5194/amt-5-397-2012.