ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-235-2017Global inverse modeling of CH4 sources and sinks: an overview of methodsHouwelingSanders.houweling@uu.nlhttps://orcid.org/0000-0002-6189-1009BergamaschiPeterhttps://orcid.org/0000-0003-4555-1829ChevallierFrederichttps://orcid.org/0000-0002-4327-3813HeimannMartinhttps://orcid.org/0000-0001-6296-5113KaminskiThomasKrolMaartenMichalakAnna M.PatraPrabirhttps://orcid.org/0000-0001-5700-9389SRON Netherlands Institute for Space Research, Utrecht, the NetherlandsInstitute for Marine and Atmospheric Research (IMAU), Utrecht University, Utrecht, the NetherlandsEuropean Commission Joint Research Centre, Institute for Environment and Sustainability, Ispra (Va), ItalyLe Laboratoire des Sciences du Climat et l'Environnement (LSCE), Gif-Sur-Yvette, FranceMax-Planck-Institute for Biogeochemistry, Jena, GermanyThe Inversion Lab, Hamburg, GermanyDepartment of Meteorology and Air Quality (MAQ), Wageningen University and Research Centre, Wageningen, the NetherlandsDepartment of Global Ecology, Carnegie Institution for Science, Stanford, USAJapanese Agency for Marine-Earth Science and Technology, Yokohama, JapanSander Houweling (s.houweling@uu.nl)4January20171712352561July20167July201611October201631October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/17/235/2017/acp-17-235-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/235/2017/acp-17-235-2017.pdf
The aim of this paper is to present an overview of inverse modeling methods
that have been developed over the years for estimating the global sources and
sinks of CH4. It provides insight into how techniques and estimates have
evolved over time and what the remaining shortcomings are. As such, it
serves a didactical purpose of introducing apprentices to the field, but it
also takes stock of developments so far and reflects on promising new
directions. The main focus is on methodological aspects that are particularly
relevant for CH4, such as its atmospheric oxidation, the use of methane
isotopologues, and specific challenges in atmospheric transport modeling of
CH4. The use of satellite retrievals receives special attention as it is
an active field of methodological development, with special requirements on
the sampling of the model and the treatment of data uncertainty. Regional
scale flux estimation and attribution is still a grand challenge, which calls
for new methods capable of combining information from multiple data streams
of different measured parameters. A process model representation of sources
and sinks in atmospheric transport inversion schemes allows the integrated
use of such data. These new developments are needed not only to improve our
understanding of the main processes driving the observed global trend but
also to support international efforts to reduce greenhouse gas emissions.
Introduction
Thanks to the efforts of surface monitoring networks, the global trends of
long-lived greenhouse gases over the past decades are known to high accuracy
. However, deciphering the causes of observed
growth rate variations remains a challenge, and it is an active field of
scientific research and development. The large variations in the methane
growth rate that have been observed in the past years are a particularly good
example. A wide variety of possible scenarios have been discussed in
recent literature, but only limited consensus has been reached so far
.
The reason why the origin of these growth rate variations is difficult
to identify was already discussed extensively during the late 1980s and early
1990s, when the first inverse modeling techniques were developed for
inferring greenhouse gas sources and sinks from atmospheric measurements
. The inverse problem was qualified as “ill posed”
because of the wide range of surface flux configurations that could explain
the measurements about equally as well. Such problems require regularization
using a priori assumptions on the surface fluxes needed to fill in
critical flux information that the measurement networks are unable to
provide.
Since then several approaches have been investigated to strengthen the
constraints brought in by the measurements, for example, by increasing the
number of data using regional tall tower networks and
satellites or by using different types
of measurements, including methane isotopologues
. Accommodating new kinds of data in the
inversion framework posed new methodological challenges: not only the
computational challenge of solving an inverse problem of significantly
increased size was posed but also the treatment of new measurements with poorly
quantified error statistics . Then, with improved measurement
capabilities increasing the flux resolving power of the inversions, transport
model uncertainties were recognized to play an increasingly important role
.
Despite methodological limitations, the inverse modeling approach allowed us
to derive important constraints on the global sources and sinks of CH4.
Examples are the dominant role of the tropical and temperate northern
latitudes as drivers of the observed methane increase since 2007
. These constraints exist despite the limited availability of
surface measurements in the tropics. The extension of global inversions with
satellite retrievals from SCIAMACHY and GOSAT confirmed and even reinforced
the importance of tropical fluxes . Initially,
using SCIAMACHY, it took a correction to account for an overestimated role of
the tropics due to spectroscopic errors affecting the XCH4 retrieval
. For the boreal and Arctic latitudes, inversions confirm the
sensitivity of methane fluxes to climatic variability, but
without significant trends in response to global warming yet
. Regarding the atmospheric sink strength, inversions
have put bounds on the plausible range of OH interannual variability,
although it remains difficult to quantify surface sources and atmospheric
sinks independently of each other using the available measurements
.
The purpose of this paper is to review methods in global inverse modeling of
CH4 and directions in which the field is developing. The discussion is
limited mostly to global and contemporary methane, although the range of
applications has expanded over the years, covering scales ranging from
paleoclimate studies to the estimation of single point sources
. Inverse modeling of CH4 has taken advantage of
methodological advances gained in the application of inverse modeling to
CO2, except for some aspects that are specific to CH4, such as its
limited atmospheric lifetime, which will receive special attention.
The next section starts with an overview of how CH4 inversions evolved
over the years. The treatment of atmospheric sinks is discussed separately in
Sect. . Sections – look closely at the use of isotopic measurements, satellites, and the role of chemistry
transport models. Finally, new developments and directions are discussed in
Sect. .
The evolution of methods and estimates
The first inverse modeling analyses of global CH4 made use of concepts and
techniques that were developed earlier for studying CO2, as published for
example by and . The first synthesis of global
methane was performed by , who assessed the contribution of
various processes to the observed concentrations using a 3-D atmospheric
transport model. Sources were not yet optimized using an objective
mathematical procedure. Instead, seven scenarios were presented that agreed
with the available information on emissions and photochemical oxidation of
methane as well as observed quantities, such as global mean CH4,
13CH4, and 14CH4; the amplitudes of their seasonal cycles;
and latitudinal gradients.
was the first to apply a matrix inversion approach to
the available background measurements to derive optimized monthly methane
fluxes in 18 latitudinal bands. In the number of unknowns was
kept equal to the number of knowns in order to derive a unique solution. In
the follow up study this condition was relaxed through the
use of a truncated singular value decomposition approach. Both studies
accounted for the atmospheric sink of methane by prescribing model-calculated
OH fields, which had been optimized to bring the global lifetime of methyl
chloroform (MCF) in agreement with measurements (see for example
).
followed the “synthesis inversion” concept of ,
which made use of a Bayesian formulation of the cost function penalizing
deviations from a first guess (a priori) set of CH4 fluxes. In this
study, the state vector consisted of global and seasonal patterns of each
source and sink process, as well as process-specific δ13C isotopic
fractionation factors. relaxed the hard constraint on global
flux patterns by using the adjoint of the TM2 transport model, coded by
, to optimize the net CH4 surface flux per month and at the
resolution of the transport model. In addition, an attempt was made to take
the spatial and temporal correlation of the uncertainty of the monthly fluxes
between surrounding grid boxes into account. An iterative procedure was used
to minimize the cost function in order to account for the weak nonlinearity
introduced by optimizing the global OH sink (see Sect. ). In
later studies flux regions have been defined in various ways, ranging between
the global patterns of and the grid-scale fluxes of
, such as the use of 11 continental TransCom
regions in .
Up to this stage, inverse modeling studies had addressed multiyear mean
sources and sinks and their average seasonal variability. For example, the
results of represented a quasi stationary state, reflecting the
mean CH4 increase during the analyzed time window of a few years, caused
by the mean imbalance between the global sources and sinks during that
period. Consistent with this approach, the atmospheric transport model
recycled a single representative meteorological year. Important CH4 growth
rate fluctuations that were observed in the 1990s, such as in the years after
the eruption of Mount Pinatubo and during the strong 1997–1998 El-Niño,
raised interest in methods that could address interannual variability.
To do this, the use of actual meteorology in atmospheric transport modeling
was recognized as being critical, since an important fraction of the observed
interannual variability in CH4 could be explained by variability in
transport .
The first so-called “time-dependent” inversion of methane was published by
using the Kalman filter for the optimization of CH4 fluxes
. In this inversion, surface emissions were optimized given a
scenario for the sinks, i.e., without co-optimizing atmospheric sinks. This
approach avoided spurious covariance between the inversion-optimized sources
and sinks resulting from the surface network providing insufficient
information to constrain these terms independently. Later studies, such as
, introduced independent information about the sink through the
combined use of CH4 and MCF measurements. Although this approach limits
the trade-off between sources and sinks, some degree of influence remains,
depending on the weight of the CH4 data relative to those of MCF. The
weight of CH4 data increased in particular with the use of satellite data.
Several studies using SCIAMACHY satellite retrievals returned to the use of
prescribed OH fields .
The availability of satellite data, starting with the SCIAMACHY instrument
onboard ENVISAT , triggered new methodological developments to
deal with the large number of data becoming available, and it triggered the
use of the improved measurement coverage. Several groups adopted the 4D-VAR
technique, developed by the weather prediction community, which makes use of
the adjoint of the atmospheric transport model for efficient calculation of
source receptor relationships and the cost function gradient
. With the increasing power of massively
parallel super computers, the ensemble Kalman filter (EnKF) gained popularity
.
To use satellite data, the inversions were extended with bias correction
algorithms to account for systematic errors in the satellite retrievals.
Various approaches were tested (see Sect. ) with
spatiotemporally varying bias functions either optimized within the inversion
or separately using measurements from the Total Column Carbon Observing
Network TCCON,. Because of known short-comings of atmospheric
transport models, for example in simulating the stratosphere–troposphere
exchange, inversion-optimized bias corrections were found to account in part
for model deficiencies . Compared with CO2,
stratosphere–troposphere exchange is relatively important for the column
average mixing ratio of CH4 because of the steeper vertical gradient of
CH4 in the stratosphere caused by its chemical transformation. Low CH4
mixing ratios in the stratosphere matter because concentration gradients
provide the flux information that is used in inversions and should therefore
be represented well in models.
The proxy retrieval method, developed for the retrieval of CH4 from
SCIAMACHY , has an additional source of systematic error from
the use of transport model output . In this method,
XCH4 is derived from the satellite-retrieved ratio of XCH4 and
XCO2 to mitigate errors due to light scattering on cirrus and aerosol
particles. To translate the retrieved ratios into XCH4, model-derived
estimates of XCO2 are used. When proxy retrievals are used in inversions,
inaccuracies in the modeled XCO2 variations are projected on the CH4
fluxes . To deal with this problem, dual CO2 and CH4
inversions were developed, which directly assimilate satellite-retrieved
ratios of XCH4 and XCO2, together with
surface measurements.
Figure presents large-scale estimates from published global
CH4 inversion and how they evolved over time. The global flux is the best-constrained property and shows reasonable consistency across the published
studies. The range of estimates reflects mostly the improving capability to
constrain the atmospheric oxidation of methane, which was still limited
during the 1990s. explicitly mentions that the difference with
is largely due to the choice of methane lifetime. Notice that
the large error margin reported in is consistent with this
difference. Apart from this study, the inversion-derived estimates until 2006
cluster in two groups that differ by 80–100 Tg CH4 yr-1. The global flux
estimates in more recent studies suggest that a consensus has been reached in
favor of the lower cluster of estimates at 490–520 TgCH4 yr-1 for the
1990s. The increasing number of studies covering the period of renewed
methane growth show an upward tendency consistent with the CH4 increase.
Note that these numbers are intended to include the soil sink, estimated to
be in the range of 26–42 Tg CH4, but it is not always clear
if reported global emissions include or exclude this sink. Furthermore, the
use of MCF to constrain tropospheric methane oxidation does not account for
the contribution of other potentially important oxidants, such as chlorine
radicals in the marine boundary layer .
Evolution of inversion-derived estimates for the global total CH4
flux (a), its hemispheric distribution (b), and the
anthropogenic contribution (c). Horizontal solid lines indicate the
time range of the estimate. The right end of dotted lines point to the date
of publication. Note that the CH4 trends that are seen are influenced by
the evolution of the inversion methods that were used. Numbered circles refer
to publication references, as follows: 1: ; 2: ; 3:
, inv.S0; 4: ; 5: ; 6: ;
7: , inv.S2; 8: ; 9: ; 10:
, inv.S3; 11: , inv.S1; 12: ; 13:
, inv.3; 14: , inv.S1SCIA; 15: ,
inv.FPNO; 16: , inv.SQflex; 17: ; 18:
; 19: , inv.SU10.6; 20: ,
inv.TA0.0750.6; 21: ; 22: ; 23:
.
The contribution of the Northern Hemisphere to global emissions varies
between 67 and 88 % without a clear trend. The differences between the
inversions may be explained largely by differences in the interhemispheric
exchange rate of the transport models that are used . In
the exchange of the TM2 model was found to be too slow, which
is consistent with the TM models showing relatively low contributions of
northern hemispheric emissions. The anthropogenic contribution varies between
57 and 73 %, with inversions accounting for process-specific information
through the use of isotopes showing a smaller range of 60–63 %.
Treatment of atmospheric sinks
In this section, we discuss the treatment of atmospheric methane oxidation in
inversions. The change in CH4 mixing ratio in an air parcel i due to
local sources and sinks is described by
∂zi∂t=Ei-∑jki,j[Oxj]izi+∑lTlzl,
with zi and [Oxj]i the mixing ratios of CH4 and its main
photochemical oxidants OH, Cl, and O(1D), reacting at rate ki,j.
Ei is the emission into air parcel i and transport operator Tl
accounts for the advection and mixing of zi with its surroundings l (l
includes i). The purpose of inverse modeling is to estimate scaling factors
x of the surface emissions and chemical transformation rates by fitting mixing ratios simulated by an atmospheric transport model to a set of measurements
y. The relation between model-simulated measurements zf and
the sources and sinks of CH4 can be expressed as
zf=HMexe-HMsZxs+HM0Z0x0,
where M is a linear chemistry and transport operator translating the
state vector x into model-simulated CH4 mixing ratios z, which
are sampled using observation operator H to obtain zf. The notation
follows as much as possible (see Appendix B), except that we
separate the state vector x in its source, sink, and initial
concentration components indicated by subscripts “e”, “s”, and
“0”. We use M because the transport model propagates the
concentration state, needed to compute the methane sink, from one time step
to the next (as in Eq. ). Matrix Z is introduced
because the state vector components xs and x0
are usually not defined at the dimension of the modeled mixing ratios z.
Z is defined such that the product Zx yields z
scaled according to the definition of x. Note that the model-simulated
observations zf are not linearly dependent on xs because
unlike xe the sink magnitudes depend on the methane mixing ratios
z, which are influenced by changes in xs. This
introduces a nonlinearity in CH4 inversions that optimizes the
transformation rate. In the Bayesian formulation of the cost function, the a
priori estimate of xs is usually derived from a chemistry
transport model (CTM). In that model the oxidant abundances also depend on
the mixing ratio of CH4, adding further nonlinearity. Following our
notation, the CTM changes [Oxj] in Eq. (), which is
incorporated in Ms of Eq. (). This means that when
photochemical feedbacks are taken into account, Ms becomes a
nonlinear operator.
Since CH4 is a long-lived gas, i.e., long compared with the typical time
window of inversions, the uncertainties in its sources and sinks influence
only a small fraction of its average mixing ratio. Therefore, as long as the
inversion uses realistic initial concentrations, e.g., derived from the global
surface network, and the a priori source and sink estimates are in
reasonable balance with the observed global growth rate, the relative changes
in z remain minor. In this case, the inverse problem is only weakly
nonlinear. As we have seen, the CTM-calculated oxidant fields are usually
applied to the inversion after correcting global mean OH to match the
measurement-inferred lifetime of MCF of 5.5 ± 0.2 yr . This
step eliminates any modification of global mean OH in the CTM in response to
updated CH4 concentrations coming from the inversion. Because of this, the
influence of optimized CH4 mixing ratios on CTM-calculated OH is usually
ignored. Aside from global mean OH, it seems reasonable to assume that as long
as the relative modifications in CH4 remain small, changes in CTM-calculated OH distributions are not significant.
What remains to be accounted for is the nonlinearity introduced by
optimizing the transformation rate xs within the
uncertainty of the methyl chloroform analysis. For this purpose,
Eq. () can be linearized around an approximation of the CH4
mixing ratios (zn) as follows:
zn+1f=HMexe,n-HMsZnxs,n+HZ0x0,n,
which can then be used to solve the inverse problem using the iterative
procedure
xn+1=xn-MnTHTR-1HMn+B-1-1MnTHTR-1HMnxn-y+B-1(xn-xb).
Here xn is a trial state vector after iteration n (combining “e”,
“s”, and “0”). The other elements in this equation follow the standard
notation of . Usually, the a priori CH4 source and sink
estimates lead to an atmospheric state that is realistic enough for
Eq. () to converge within only a few iterations.
Equation () can be simplified further by ignoring
uncertainties in xs and solving only for surface emissions.
In this case the inverse problem becomes linear, and the analytical solution
is obtained in a single iteration. If xng is replaced by
xb and xn+1g by xa then Eq. ()
indeed reduces to the least squares solution of the linear inverse problem
. The reason why this is commonly done is not primarily out of
computational convenience, but rather because surface measurements and
satellite-retrieved total columns provide insufficient information to
distinguish between source and sink influences. If sources and sinks are
optimized simultaneously, solutions are obtained where source adjustments
compensate for sink adjustments and vice versa. Depending on the freedom of
the inversion to adjust the sink, solutions will be obtained that show
unrealistic compensating adjustments between sources and sinks.
To deal with this problem, MCF measurements are used to independently
constrain the sink, either within the inversion
see for example or in a separate inversion preceding the CH4 inversion see
for example. Usually, this step only optimizes a
climatological global OH sink, i.e., ignoring year-to-year variations and
uncertainties in its geographical distribution. Given the importance of the
methane sinks, their estimated temporal variations , and the
associated uncertainties (; ; ), these methods are not
satisfactory. This will be even more true in the future when MCF mixing
ratios approach a new steady state to unreported residual sources at
concentration levels that will be difficult to measure accurately
. We will return to this discussion in Sect. .
The use of isotopes
Using measurements of CH4 mixing ratios, only limited information is
obtained about source and sink processes. Attempts have been made to use a priori information on spatiotemporal emission patterns to optimize the
contribution of specific emission classes. If the state vector is defined at
a lower resolution than the model, then the a priori emission
distribution within the source regions provides some process-specific
information as in. For inversions that solve at the
resolution of the model grid, process-specific flux patterns can be specified
only as temporal and spatial correlations in the a priori flux error
covariance matrix as in, turning this information into a weak
constraint. Alternatively, one may just rely on the a priori
contribution of each process per grid box and partition the inversion-optimized flux accordingly. However, for CH4 the a priori patterns
themselves are rather uncertain, and therefore it is questionable whether
these methods allow any useful process-specific information to be gained from
the inversion. The hope may be that this situation will improve in the future
with improved measurement coverage, for example, from high-resolution
satellite imagers capable of separating source processes geographically.
Box-model-calculated relaxation times to hemispheric disturbances in
CH4 and 13CH4 with respect to a steady-state equilibrium (“Eq”).
Theoretical disturbances of the steady state are either global mass conserved
(“MC”) or not (“D.Eq”).
Alternatively, isotopic measurements provide truly independent
process-specific information. For this purpose, several inversion studies
used measurements of δ13C-CH4. So far, however, the
impact has been limited because of limitations in network coverage, the low
single measurement precision, and differences in calibration standards
between laboratories . Furthermore, this approach requires
accurate knowledge of the process-specific isotopic fractionation factors,
which are not well separated, for example, for different microbial sources
such as ruminants, wetlands, and waste treatment. These factors may also vary strongly
for a single-source class depending on specific conditions
. Nevertheless, a rough distinction is possible between
the contribution of emissions from microbial sources (wetlands, agriculture,
waste processing), energy use (fossil fuel production and consumption), and
biomass burning. In addition, measurement techniques are under development
with the potential to significantly improve the availability of high-quality
data in the future (; ).
The additional constraints gained by isotopic measurements can be derived
starting from the 13C analogue of Eq. ():
Rzzf=HMeRexe-HMsα12,s13RzZxs+HM0R0Z0x0,
with the diagonal matrix R containing the 13C /12C
ratios of CH4. Likewise, α12,s13 contains the
isotopic fractionation of the oxidation reactions in s. Note that this
equation and those that follow also apply to CH3D.
Equation () can be reformulated in δ notation as
follows:
αzzf=HMeαexe-HMs(α12,s13+α12,s13αz-I)Zxs+HM0α0Z0x0,
where αz and αe contain the
isotopic δ values of atmospheric CH4 and its emissions,
respectively. For the derivation of Eq. () see Appendix A.
Different approaches are taken for solving inversions using isotopic
measurements depending on whether sink strengths and/or δ values are
optimized. If both are optimized, the use of isotopic measurements introduces
additional nonlinearity since the observed δ values are influenced by
the product of source strength and fractionation. In , the
inverse problem is solved by linearizing Eq. () around the
first guess state as in Eq. () and iteratively solving the
problem as in Eq. (). As in CH4 inversions where sinks are
optimized, the problem is only weakly nonlinear. If the initial state is
realistic, subsequent iterations do not modify the solution significantly. As
shown in , Eq. () can be further simplified
with a few approximations taking out the nonlinearity. If sinks and isotopic
fractionation constants are not optimized, including the delta value of the
initial condition, then the inversion becomes linear again see,
e.g.,.
The role of the initial condition in inversions using isotopic measurements
has received special attention. and demonstrated
that δ13C-CH4 takes longer to reach steady state after a
perturbation than CH4 itself. The question was raised how long the spin-up
time of inversions should be to avoid errors in the assumed initial
concentration field influencing the results. If this time is too short, the
inversion may fit the data by compensating errors in the initial condition
with artificial emission adjustments. It should be noted, however, that the
perturbation recovery time for CH4 is also much longer than the spin-up
time that is used in inversions using only CH4 data (i.e., without using
isotopes). This does not cause problems, as long as the inverse problem is
defined such that the initial condition is given sufficient freedom to be
optimized itself. The same holds for 13CH4 in inversions using
isotopic measurements.
Second in importance is the representation of initial spatial gradients that
take longest to equilibrate, such as the interhemispheric difference and
vertical gradients in the stratosphere. However, as long as these gradient
components do not contribute to the global burden (i.e., their global integral
adds up to zero), the corresponding relaxation times of both CH4 and
δ13C-CH4 remain in the order of the corresponding dynamic
mixing times. To demonstrate this point, we performed three simulations using
a two-box model with the boxes representing the Northern and Southern
hemispheres (see Fig. ). In the reference simulation the
initial condition is in balance with the steady state, and, as expected in
this case, nothing changes during the simulation. In a second simulation, the
initial concentrations are modified changing the interhemispheric gradient
but without changing the global burdens of CH4 and 13CH4. As can
be seen, this simulation recovers at the timescale of the interhemispheric
exchange (here set to 1 year). Only in the third simulation, where the
initial concentrations are perturbed without conserving global mass, the
recovery times become of the order of the CH4 lifetime. Interestingly, in
this case the north–south gradient of CH4 still recovers at the timescale
of interhemispheric mixing, whereas the gradient of δ13C takes
much longer to equilibrate.
From this experiment it follows that long relaxation times, and therefore
long spin-up times, can be avoided if the inversion is capable of recovering
the right initial burdens of CH4 and 13CH4. Therefore, the
inversion should be given sufficient freedom to achieve this, i.e to correct
errors in the initial global burdens assumed a priori. Additional
errors in the global distribution of the initial concentrations call for a
spin-up time of the order of the longest dynamical mixing timescale, which
is the same for CH4 and δ13C-CH4. The required spin-up time
can be reduced further for CH4 and δ13C-CH4 by introducing
additional degrees of freedom to the initial condition, such as the
difference between the Northern and Southern hemispheres and between the
stratosphere and troposphere, such that these gradients can also be optimized from
the data.
Application to satellite data
The use of satellites in inverse modeling is attractive because of their
superior spatial coverage compared with the surface networks. Although a
significant step forward has indeed been made using SCIAMACHY and GOSAT,
especially in regions that are poorly covered by the surface network, the
coverage is still limited by the need for clear sky conditions to retrieve
XCH4. In addition, the temporal coverage is limited by the revisit time
of the satellite. The most useful remote sensing instruments for the
quantification of CH4 emissions from space make use of spectral
measurements in the shortwave infrared (SWIR) of Earth-reflected sunlight.
Since these photons have traveled the whole atmosphere twice, the
measurements are sensitive to CH4 absorption across the full column down
into the planetary boundary layer where the signals of surface emissions are
largest . To obtain sufficient signal puts requirements on the
sun angle, which limits the coverage at high latitudes. Techniques exist to
further reduce these coverage limitations, e.g., using active instrumentation
, an elliptical orbit , or a large measurement
swath , but these have not been tested out in space yet.
Therefore, further improvements in measurement coverage are expected for
future missions.
To make efficient use of the growing stream of spaceborne greenhouse
measurements, inversion methods need adaptation. Important steps in this
direction have been taken by the application of the 4D-VAR technique to the
inversion of CH4 emissions , which we refer to as the
variational approach to avoid confusion about the applicability of “4-D” to
the optimization of surface emissions. In this technique, the use of an
adjoint model allows evaluation of the cost function gradient at computing
time and memory costs that do not scale with the number of measurements, as
is the case for the classical matrix inversion technique. However, with the
growing information content of the data, a growing number of fluxes can
independently be resolved, increasing the required number of iterations. A
major limitation of the variational approach is the use of sequential search
algorithms to minimize the cost function. Each step in the sequence involves
an evaluation of the cost function gradient, requiring a forward and adjoint
model simulation for the full time span of the inversion. Because this
procedure is strictly sequential, it is difficult to take advantage of the
computational power of massive modern parallel computers. Although parallel
search algorithms exist see e.g.,, they have not been applied
to CH4 emission optimization yet. An alternative approach is the use of
ensemble methods such as the ensemble Kalman filter ,
which allows efficient use of large numbers of processors, although the
number of regions for which emissions are estimated is still far less
compared with the variational approach.
Finding the solution of a large dimensional inverse problem is not the only
challenge in using satellite data. Estimating the corresponding posterior
uncertainties is an even harder computational problem to solve because
methods to approximate the Hessian of the cost function (i.e., the inverse of
the posterior covariance matrix; see for details) tend to
converge more slowly than the solution itself. This is true in particular at the
smallest spatiotemporal scales that are solved for; hence, the problem is
expected to become worse when moving to higher resolutions using instruments that
provide more spatiotemporal detail . High-resolution posterior
uncertainty estimates are particularly useful in observing system simulation
experiments (OSSEs) for testing the performance of inversions using new
concepts for measuring greenhouse gases from space
. A popular method to derive such uncertainties
is a Monte Carlo application of the variational approach introduced by
. This method is computationally demanding, however, because of
the large number of inversions needed to determine the posterior uncertainty
at a precision of a few %. More precise methods exists
, but they can only be applied to the uncertainty of a
limited number of fluxes.
Sampling the model for comparison to satellite retrievals involves
application of the retrieval-averaging kernel to the modeled vertical profile
of CH4 as follows:
zf=tlTAl,lzl+tlT(Il,l-Al,l)zlb.
Here the total column operator tl contains normalized partial columns
Δpi/psurf for each layer i of the retrieved profile of l
layers. The product of tlT and the profile-averaging kernel Al,l
is the column-averaging kernel al. If the retrieval uses profile scaling
then only al is available see, e.g.,. zl is the
modeled vertical profile of methane at the vertical grid of the retrieval.
Since the averaging kernel values depend on the vertical discretization of
the retrieved state, the model profile should be discretized the same way
(i.e., according to the retrieval grid). Furthermore, the averaging kernel
depends on the unit in which the state vector (of the retrieval) is
expressed, either absorber amount or mixing ratio, and so the model profile
has to be expressed accordingly . It is advised to correct
errors in the CH4 column amount due to regridding from the vertical grid
of the model to that of the retrieval to ensure that the regridding conserves
mass. zlb is the a priori profile that was used in the retrieval, and
Il,l is the identity matrix. For retrievals that use profile scaling the
second right hand side (RHS) term in Eq. () should be close to
zero see. Deviations point to the use of a different a
priori profile than was used in the retrieval.
For proxy XCH4 retrievals the use of Eq () introduces an
additional complication because of the way information about CH4 and
CO2 is combined. The correct way to deal with this can be readily
understood looking at its equation,
XCH4proxy=XCH4retXCO2ret×XCO2mod,
showing how the proxy retrieval is derived from the ratio of non-scattering
retrievals XCH4ret and XCO2ret and a model-derived estimate
XCO2mod as already discussed in Sect. . Suppose that
XCO2mod and XCO2ret were perfect, then the contribution of CO2
to the RHS of Eq. () would cancel out. However, this also
requires that the averaging kernel of XCO2ret is applied to
XCO2mod, which is therefore the correct way to specify XCO2mod.
What remains is weighted according to the averaging kernel of XCH4ret,
which is the one that should be used when applying Eq. () to
proxy XCH4 retrievals. In a ratio inversion, Eq. () is
applied separately to the modeled profiles of CO2 and CH4, after which
the ratio of the modeled total columns is taken.
The use of averaging kernels could in theory be avoided by including the
radiative transfer model in the inversion, so that the model yields the
satellite-observed spectral radiances instead of retrieved mixing ratios.
However, for practical reasons this has not been done so far. This approach
would avoid inconsistencies between the a priori profile and its
uncertainty as used in the retrieval and as generated by the a priori
transport model. For further discussion about the statistical consequences of
this inconsistency see .
A major challenge in the use of satellite data in inversions is to
realistically account for uncertainty. Satellite retrievals are influenced by
various physical and chemical conditions along the light path that is being
measured. Inaccuracies in the capability of the retrieval to take these into
account vary at the same spatiotemporal scales as these conditions
themselves. They may even correlate with the retrieved variable, like water
vapor in the case of SCIAMACHY XCH4 retrievals ,
which makes it difficult to distinguish signal from error. Errors that behave
quasi-random and affect neighboring retrievals in a coherent way can in
theory be accounted for by specifying the off-diagonal terms in the data
error covariance matrix. In practice, there are many ways to do this, but
quantitative information to justify a specific choice is lacking. In general,
correlated uncertainty reduces the number of independent measurements, which
justifies averaging retrievals within a certain distance of each
other. Usually the uncertainty of the mean is calculated using a lower bound
representing the contribution of purely systematic error. An alternative
approach, referred to as ”error inflation”, is to increase the error of
individually assimilated retrievals such that the uncertainty of a mean of
surrounding retrievals does not drop below this minimum level
. The advantage of this approach is that it avoids subjective
decisions about which samples to combine into an average. Error inflation, or
similar methods that compensate the neglect of off diagonals in the data
error covariance matrix by increasing the (diagonal) uncertainty, lead to a
χ2 below 1. Although this may seem suboptimal from a statistical point
of view, demonstrated that this de-weighing of data
nevertheless leads to uncertainty reductions that are closer to those
obtained when off diagonals in R had been accounted for.
Therefore, this approach avoids over constraining the problem by neglecting
the contribution of data error covariance.
As the inversion formalism assumes all errors to be random, measurement bias
must be either corrected prior to use in the inversion or be estimated as
state vector elements. Both cases require knowledge of the spatiotemporal
pattern of the bias. Given a model representation of the bias H′, the
model-simulated measurements can be reformulated as
zf=HMx+H′(x′),
where systematic errors are accounted for using a set of extended state
vector elements x′. Different formulations of H′(x′) have been used in CH4 inversions using satellite retrievals
from GOSAT and SCIAMACHY. used simple polynomials of latitude
and season to account for inconsistencies arising from the combined use of
surface and satellite measurements at large scales. The motivation is that
surface measurements are best suited to constrain the large scales, whereas
satellite data can be used to fill in regional detail, which the surface
network is unable to resolve. An alternative approach is to
assess potential causes of systematic error in satellite retrievals, identify
the main drivers – or variables that can serve as proxies of their
spatiotemporal variation – and optimize the magnitude of the corresponding
error contribution in the inversion. It should be noted that the
inversion-optimized x′a has contributions from the measurements as
well as systematic errors in the transport model. In addition, if the bias
variables co-vary with the XCH4 signal of uncertainties in the surface
fluxes, then the inversion will have limited skill in resolving their
contributions. To avoid this problem, the TCCON network can be used to
optimize the bias model . However, because of its
sparse global coverage and uncertainties in the TCCON measurements
themselves, uncertainties will remain that can be further optimized in the
inversion.
The importance of transport model uncertainties
An important assumption in inverse modeling is that the influence of
atmospheric transport model uncertainties is small compared with the
uncertainty of the a priori fluxes. Formally, there are ways to account for
transport model uncertainty in the optimization; however, in practice they
are difficult to implement when lacking the information required to characterize
the statistics of transport model uncertainties in a realistic manner. In
addition, there is the fundamental problem that the transport model
uncertainty has a significant and poorly quantified systematic component.
assess the importance of transport model uncertainties based
on the results of the TransCom-CH4 model intercomparison. The results
highlight the importance of specific aspects of atmospheric transport that
are critical for the simulation of atmospheric methane, as will be discussed
further in this section. Quantifying the impact of transport model
differences on inversion-estimated surface fluxes requires an inversion
intercomparison. Attempts in this direction have been made, for example by
. However, in that study inversions were compared without a
protocol to standardize the setups. Although useful for an assessment of
global CH4 emissions and uncertainties, isolating the role of transport
model uncertainties requires a dedicated experiment. used the
output of 10 models participating in the TransCom-CH4 experiment to
generate “pseudo measurements” that were inverted in the LMDz model. The
results confirm the importance of transport model uncertainties, with
estimated annual fluxes on subcontinental scales varying by 23–48 %.
Uncertainty in XCH4 due to transport model differences for
January (left) and July (right). The middle and bottom panels show the
percent contribution from the troposphere (1000–200 hPa) and the
stratosphere (200–0 hPa) to the total column variability shown in the top
panel. Results are obtained using the submissions to the TransCom-CH4
experiment (Control (CTL) tracer for the year 2000).
Several studies have highlighted the large contribution of atmospheric
transport, including intra and interannual variability, to the observed
variability in CH4. Because of this, studies
that directly relate mixing ratio variations to source variations should be
treated with care see, e.g.,. For CH4 inversions
the observed interhemispheric gradient is of particular importance since it is
the dominant mode of variation in background CH4 mixing ratios. The
results of point to a ∼ 50 ppb (40 %) difference in
the simulation of this gradient due to differences in model-simulated
interhemispheric exchange times. Uncertainty in interhemispheric exchange
not only affects the inversion-derived latitudinal distribution of emissions,
but also their seasonal cycle in the tropics. The latter is caused by the
seasonal dynamics of the intertropical convergence zone (ITCZ). The observed
seasonal cycles at tropical measurement sites, such as Samoa and Seychelles,
are largely determined by the seasonally varying position of the ITCZ in
combination with the size of the north–south gradient of CH4. To assess
and improve the interhemispheric exchange in models, SF6 measurements
were used . Despite sizable uncertainties in the
emission inventory of SF6, it nevertheless provides an
important constraint on interhemispheric exchange. So far, transport and
methane fluxes have been optimized in separate steps, although they could in
theory be combined into a single inversion.
Large CH4 gradients are also found in the stratosphere, owing to the long
timescale of stratosphere–troposphere exchange in combination with the
chemical degradation of CH4 in the stratosphere. The modeling of
stratospheric CH4 is gaining importance with the increasing use of
satellite data in source–sink inversions. The offline atmospheric transport
models that are used for inverse modeling tend to underestimate the residence
time (or “age”) of stratospheric air . As a
consequence of this, models that accurately reproduce the surface
concentrations as observed by the global networks (e.g., after optimization
using those data) are expected to overestimate satellite-observed total
column CH4. Since the mean age of stratospheric air varies
latitudinally and seasonally, the transport bias varies accordingly. Indeed,
the TransCom-CH4 simulations show large differences between
models, increasing towards higher latitudes in the stratosphere. Although the
averaging kernel of SWIR XCH4 retrievals decreases with altitude in the
stratosphere, transport model differences are large enough to be important
for emission quantification. Satellite instruments capable of measuring
stratospheric CH4, such as MIPAS and ACE-FTS, are useful for testing
models. However, the accuracy of those measurements is also limited
. A promising development is the use of air core to measure the
stratospheric profile of CH4 at high accuracy , not only to
evaluate the accuracy of total column FTS measurements from the TTCON network
but also atmospheric transport models. However, because of the observed local
variability, which coarse grid models have difficulty reproducing, many
balloon flights will be needed to assess and improve, or bias correct, the
models.
Using continuous measurements from dense regional networks within Europe and
the USA, the large-scale transport problems discussed above are less
important. In this case, the observed variability is determined mostly by the
passage of fronts of synoptic weather systems and planetary boundary
layer (PBL) dynamics. Although the emissions of methane from energy use have
some diurnal variation, PBL dynamics are more important especially during
summer. Unfortunately, the representation of the nocturnal boundary layer in
transport models is too poor to make use of the observed diurnal variability.
Instead, measurements are used only during the afternoon when the planetary
boundary layer is well developed. Nevertheless, mixing within the PBL and
trace gas exchange with the free troposphere is an important source of
uncertainty . Since satellite data from sensors
operating in the SWIR are only weakly sensitive to the vertical distribution
of CH4 in the troposphere, their use may be less sensitive to such errors.
The increased coverage and spatial resolution of the new generation of
satellite sensors, such as Sentinel 5 precursor TROPOMI , will
increase the relevance of satellites for regional-scale emission assessment.
These data are highly complementary to surface measurements in the sense that
they have a different sensitivity to critical aspects of transport model
uncertainty. To bring together regional emission estimates from satellites
and surface data is both a major challenge and a great opportunity for
testing atmospheric transport.
To assess transport model uncertainties in the simulation of XCH4 we
analyzed the archived output of the TransCom-CH4 experiment
(see Fig. ). XCH4 fields were calculated from monthly
mean mixing ratio output on pressure levels for the year 2000, interpolated
to a common horizontal resolution of 2∘× 2∘. To
account for the vertical sensitivity of satellite-retrieved XCH4, we
apply averaging kernels from the RemoTeC GOSAT full physics retrieval
. Finally, standard deviations were calculated for each
vertical column using results from seven models: ACTM, GEOS-CHEM, MOZART, NIES,
PCTM, TM5, and TOMCAT. Figure shows 1-σ differences
between the models for the total column, as well as the percentage
contribution of stratospheric and tropospheric sub-columns. Results for the
total column show σ values up to ∼ 2 % (or 35 ppb),
associated mostly with steep orography, see, e.g., the Andes, the Himalayas,
and most notably the ice caps. The contribution from the troposphere is low
in the Southern Hemisphere compared with the Northern Hemisphere because a
global offset between the models has been removed at the South Pole.
Therefore, the impact of differences in interhemispheric mixing is seen
mostly in the Arctic, contributing ∼ 10 ppb in XCH4. The
tropospheric contribution to transport model uncertainty also highlights the
centers of tropical convection. The contribution of the stratospheric column
to the variation in XCH4 is sizable, and increases towards the poles.
The asymmetry between the North and South poles is mainly because of the South
Pole correction, taking out offsets in the SH lower troposphere. It means
that the large uncertainties in XCH4 over Antarctica are caused mainly
by the stratosphere. They follow the orography of the ice cap because the
impact of the stratospheric sub-column increases as the thickness of the
tropospheric sub-column reduces. Towards northern latitudes differences
increase up to 50–60 %, highlighting the importance of uncertainty in
stratospheric transport when inverting satellite-retrieved total columns.
New directions
Compared with the 1990s, when the first inverse modeling studies on CH4
were published, many things have changed, most notably the availability of
data and computer power. Inverse modeling techniques have been developing
further to make use of these advances. Studies used to concentrate on the use of
specific data sets, for example, to investigate the use of remote sensing or
tall tower networks. Other types of measurements were used to further
constrain specific processes, such as the use of MCF to constrain OH or
satellite-observed inundation to improve the representation of wetland
dynamics. Despite these efforts, the robustness of inverse-modeling-derived
estimates is still limited for scales smaller than broad latitudinal bands
. Because of this, it remains difficult to attribute the
significant changes in the global growth rate that have been observed in the
past decades to specific processes. Aside from important efforts to further
improve the quality of data and models, there is scope to further explore the
combined use of different data sets to further constrain the inverse problem
from different directions.
Conceptual diagram of ways to extend the use of measurements in
CH4 flux inversions. Square boxes represent models, ovals represent measurements,
and the rounded box represents the target variable of the CH4 inversion.
Call outs provide examples of the kind of measurements that are meant by the
ovals (without attempting to be complete). Black arrows: coupled and assimilated into inversions already; dashed arrows: not (yet) coupled or assimilated.
To improve our understanding of what drives the interannual variability in
the CH4 growth rate, it is critical to be able to separate influences from
varying sources and sinks. To this end, further effort is needed to constrain
the atmospheric oxidation of CH4. Since the CH4 and
δ13C-CH4 data provide limited constraints on the sink, other
data will be needed. The problem with the MCF optimization method is that the
two measurement networks, NOAA and AGAGE, lead to different answers, which
again differ from chemistry transport model simulations, as demonstrated
nicely by . A better understanding of what causes
these differences, including the role of the sparse network for measuring MCF
and remaining questions regarding radical recycling in CTMs, is needed . A
promising direction is the use of measurements of other key compounds in
photochemistry, such as CO, O3, CH2O, and NOx, to bring the
photochemical models into better agreement with the actual observed state
.
Measurements of the vertical profile of CH4 may further improve the
separation between surface sources and atmospheric sinks. For this purpose,
aircraft measurements are available, as well as satellites that are sensitive
to specific altitude ranges, such as IASI and TES
. As discussed in , applying a uniform scaling of
the CH4 lifetime in a transport model influences mostly the
interhemispheric gradient and the gradient between stratosphere and
troposphere. The transport across these gradients leads to a detectable
signal in the upper troposphere, despite the fast vertical mixing within the
troposphere. However, because these gradients are small and
sensitive to uncertainties in the sub grid parameterization of vertical
transport in transport models, it is still a question how effective aircraft
profile measurements can be. In the stratosphere the prospects for
independent measurement constraints on the sinks are better since the
gradients are much larger. It will still require the combined use of CH4
and a chemically inert tracer such as SF6 or CO2 to distinguish between
uncertainties in stratospheric transport and chemistry.
Another approach to separate the influences of sources and sinks is to limit
the domain of the inversion to important source regions. In such regions, the
concentration signal of the sources varies much more than that of the
sink because of the high spatial heterogeneity of CH4 emissions. The sink
scales with the total CH4 abundance, which is still dominated by the
background. The sources can be quantified, independent of the sink, using
short-term departures from the background due to fresh emissions. The
influence of the sink on those departures can be neglected because the
regional transport times are much shorter than the lifetime of CH4.
Meanwhile, several successful attempts have been made to quantify regional
CH4 emissions using this approach, for example, using the tall tower
networks in Europe and the USA .
Continuous measurements from tall towers record highly variable CH4
concentrations providing much information about regional sources, challenging
the performance of high-resolution mesoscale transport models. Despite the
challenges, the results demonstrate the potential of this approach for supporting country-scale emission verification.
The use of land surface models to provide a priori emission estimates
for use in inverse modeling implies that the concept of carbon cycle data
assimilation (CCDAS), which has only been applied to CO2 so far, may also be
beneficial for CH4. Aside from the advantage of gaining actual process
understanding, which is needed for improved projections of future CH4
concentrations, optimization at process level facilitates the combined use of
different types of measurements. In the case of wetland emissions,
hydrological conditions are an important driver, particularly in the tropics
. Satellite-observed inundation is already used to prescribe
the dynamics of the wetland extent . In combination with
hydrological modeling, some limitations of the measurements could be
addressed, such as the difficulty to measure water underneath dense
vegetation and the fact that wetland soils may be partially saturated but are
not necessarily inundated. Improving the representation of wetland emissions
in process models will also require extension of the flux measurement
network. These measurements would be an essential component of a multi-stream
data assimilation system for methane (or MDAS), but the coverage of the
network should be more comparable to that of FLUXNET CO2.
In particular, the model parameterization of methane emissions from tropical
wetlands is severely limited by the availability of flux measurements. Such
limitations are important to address, but in the meantime the concepts and
methods for MDAS should already be developed using the existing data.
Aside from the use of satellites to improve the representation of wetland
hydrology, several other kinds of measurements can provide process-specific
information. For example, atmospheric tracers such as ethane and carbon
monoxide provide useful information about emissions from fossil fuel mining
and biomass burning , which
could be combined with methane measurements in a data assimilation framework.
Figure shows a conceptual diagram of how current inversion
setups could evolve in order to further increase the constraints on the
source and sink processes by using various types of measurements.
Closing remarks
In the past 3 decades of CH4 inverse modeling, important progress has
been made in developing atmospheric transport models and inversion methods
for the use of various kinds of measurements. Despite this progress, it
remains a challenge to identify the dominant drivers of the large global
growth rate variations that have been observed during this period. This is
caused in part by the difficulty of separating the influence of surface
emissions and atmospheric sinks. Breaking up global estimates into regional
contributions, the robustness of the estimates decreases further, except in
regions where tall tower networks support regional flux estimation. There is
no single solution to this problem since every new approach, such as the use
of methane isotopologues or satellite data, brings new information as well as
additional unknowns. Making optimal use of the improving observational
constraints on atmospheric methane puts increasing demands on the quality of
atmospheric transport models. We demonstrated that the use of satellite-retrieved XCH4 calls for an improved model representation of
stratospheric methane.
Aside from the ongoing developments to improve models and measurement data sets,
the combined use of different data sets in a single optimization framework is
still left largely unexplored. As discussed, the methane budget offers
several directions for applying the CCDAS concept to CH4, on the side of
the sources, the sinks, or ideally both. It will be a challenge to combine
different data sets in a consistent manner, but inconsistencies will also help
identify new directions for improvement. The use of isotopic measurements was
discussed as well as how the initial condition can be set up to avoid influences of
long isotopic equilibration times.
The COP21 climate agreement offers a great opportunity for inverse modeling
to support international efforts to reduce emissions by providing
independent estimates to verify if intended reduction targets are being
achieved. However, the steps that are needed to become relevant in this
process are still sizable. Compared with the achievements of the past 3 decades, it is clear that the overall progress will have to accelerate. To
achieve this will require closer international collaboration to make more
efficient use of the collective effort that is spent by different research
groups already. The annual assessments of GCP-CH4 are an
important first step in this direction.
Isotopic equation in delta notation
To derive Eq. () from Eq. () we first
subtract Eq. (), multiplied with a reference isotopic ration
Rref, from Eq. () resulting in
Rz-Rrefzf=HMeRe-Rrefxe-HMsα12,s13Rz-RrefZxs+HM0R0-RrefZ0x0.
To transfer to delta notation we substitute R in
Eq. () using
Rx=(I+αx)RVPDB,
where subscript x refers to any specific occurrence of R in
Eq. () and RVPDB is the isotopic ratio of the
Vienna Pee Dee Belemnite international reference standard. Note that since we
are using matrix notation R represents a diagonal matrix of
isotopic ratios (the same applies to α). After
substitution and dividing by RVPDB, we obtain
(αz-αref)zf=HM0(αe-αref)xe-HMsα12,s13αz+α12,s13-(αref+I)Zxs+HM0(α0-αref)Z0x0.
Depending on the choice of αref, different
formulations can be derived. Equation () is derived using
αref=0.
Notation
Table of notation, taken from Table 1, page
4. Basic notationsymbolDescriptionBOLDMatrixboldVectorxTarget variables for assimilationzModel state variablesyVector of observationsJCost functionU(x,xt)Uncertainty covariance of x around some reference point xtC(x)Uncertainty correlation of xp(x)Probability density function evaluated at xG(x,μ,U)Multivariate normal (Gaussian) distribution with mean μ and covariance UHObservation operator mapping model state onto observablesHJacobian of H, often used in its place, especially for linear problemsMModel to evolve state vector from one timestep to the nextMJacobian of M(⋅)aPosterior or analysis(⋅)bBackground or prior(⋅)fForecast(⋅)g(First) guess in iteration(⋅)tTrueδIncrementUseful shortcutsymbolsDescriptiondy-H(x) (Innovation)U(x)Uncertainty covariance of x about its own mean, i.e., the true uncertainty covarianceBU(xb) (Prior uncertainty covariance)QU(xf,xt) (Forecast uncertainty covariance)RU(y-H(xt)) (Innovation uncertainty covariance)AU(xa) (Posterior uncertainty covariance)
Acknowledgements
We acknowledge the support from the International Space Science Institute
(ISSI). This publication is an outcome of the ISSI's Working Group on
“Carbon Cycle Data Assimilation: How to consistently assimilate multiple
data streams”.
Edited by: M. Scholze
Reviewed by: three anonymous referees
ReferencesAlexe, M., Bergamaschi, P., Segers, A., Detmers, R., Butz, A., Hasekamp, O.,
Guerlet, S., Parker, R., Boesch, H., Frankenberg, C., Scheepmaker, R. A.,
Dlugokencky, E., Sweeney, C., Wofsy, S. C., and Kort, E. A.: Inverse
modelling of CH4 emissions for 2010–2011 using different satellite
retrieval products from GOSAT and SCIAMACHY, Atmos. Chem. Phys., 15,
113–133, 10.5194/acp–15–113–2015, 2015.Allan, W., Lowe, D. C., Gomez, A. J., Struthers, H., and Brailsford, G. W.:
Interannual variation of 13C in tropospheric methane: Implications for
a possible atomic chlorine sink in the marine boundary layer, J. Geophys.
Res., 110, 10.1029/2004JD005650, 2005.Aydin, M., Verhulst, K. R., Saltzman, E. S., Battle, M. O., Montzka, S. A.,
Blake, D. R., Tang, Q., and Prather, M. J.: Recent decreases in fossil-fuel
emissions of ethane and methane derived from firn air, Nature, 476,
198–201,
10.1038/nature10352, 2011.Baker, D. F., Doney, S. D., and Schimel, D. S.: Variational data assimilation
for atmospheric CO2, Tellus B, 58, 359–365, 2006.Baldocchi, D., Falge, E., Gu, L. H., Olson, R., Hollinger, D. et al.:
FLUXNET: A new
tool to study the temporal and spatial variability of ecosystem-scale carbon
dioxide, water vapor, and energy flux densities, Bull. Am. Met. Soc., 82,
2415–2434, 10.1175/1520-0477, 2001.Bastos, A., Running, S. W., Gouveia, C., and Trigo, R. M.: The global NPP
dependence on ENSO: La Niña and the extraordinary year of 2011, J.
Geophys. Res., 118, 1247–1255, 10.1002/jgrg.20100, 1995.Beck, V., Chen, H., Gerbig, C., Bergamaschi, P., Bruhwiler, L., Houweling, S.,
Röckmann, T., Kolle, O., Steinbach, J., Koch, T., Sapart, C. J., van
der Veen, C., Frankenberg, C., Andreae, M. O., Artaxo, P., Longo, K. M., and
Wofsy, S. C.: Methane airborne measurements and comparison to global models
during BARCA, J. Geophys. Res., 117, D15310, 10.1029/2011JD017345,
2012.
Bergamaschi, P., Bräunlich, M., Marik, T., and Brenninkmeijer, C. A. M.:
Measurements of the carbon and hydrogen isotopes of atmospheric methane at
Izãna, Tenerife: Seasonal cycles and synoptic-scale variations, J.
Geophys. Res., 105, 14531–14546, 2000.Bergamaschi, P., Frankenberg, C., Meirink, J. F., Krol, M., Dentener, F.,
Wagner, T., Platt, U., Kaplan, J. O., Körner, S., Heimann, M.,
Dlugokencky, E. J., and Goede, A.: Satellite chartography of atmospheric
methane from SCIAMACHY on board ENVISAT: 2. Evaluation based on inverse
model simulations, J. Geophys. Res., 112, 10.1029/2006JD007268, 2007.Bergamaschi, P., Frankenberg, C., Meirink, J.-F., Krol, M., Gabriella
Villani, M., Houweling, S., Dentener, F., Dlugokencky, E. J., Miller, J. B.,
Gatti, L. V., Engel, A., and Levin, I.: Inverse modeling of global and
regional CH4 emissions using SCIAMACHY satellite retrievals, J.
Geophys. Res., 114, D22301, 10.1029/2009JD012287, 2009.Bergamaschi, P., Krol, M., Meirink, J. F., Dentener, F., Segers, A., van
Aardenne, J., Monni, S., Vermeulen, A. T., Schmidt, M., Ramonet, M., Yver,
C., Meinhardt, F., Nisbet, E. G., Fisher, R. E., O'Doherty, S., and
Dlugokencky, E. J.: Inverse modeling of European CH4 emissions
2001–2006, J. Geophys. Res., 115, D22309, 10.1029/2010JD014180,
2010.Bergamaschi, P., Houweling, S., Segers, A., Krol, M., Frankenberg, C.,
Scheepmaker, R. A., Dlugokencky, E., Wofsy, S. C., Kort, E. A., Sweeney, C.,
Schuck, T., Brenninkmeijer, C., Chen, H., Beck, V., and Gerbig, C.:
Atmospheric CH4 in the first decade of the 21st century: Inverse
modeling analysis using SCIAMACHY satellite retrievals and NOAA surface
measurements, J. Geophys. Res., 118, 7350–7369, 10.1002/jgrd.50480,
2013.Bergamaschi, P., Corazza, M., Karstens, U., Athanassiadou, M., Thompson, R. L.,
Pison, I., Manning, A. J., Bousquet, P., Segers, A., Vermeulen, A. T.,
Janssens-Maenhout, G., Schmidt, M., Ramonet, M., Meinhardt, F., Aalto, T.,
Haszpra, L., Moncrieff, J., Popa, M. E., Lowry, D., Steinbacher, M., Jordan,
A., O'Doherty, S., Piacentino, S., and Dlugokencky, E.: Top-down estimates
of European CH4 and N2O emissions based on four different
inverse models, Atmos. Chem. Phys., 15, 715–736,
10.5194/acp-15-715-2015, 2015.
Bloom, A., Palmer, P. I., Fraser, A., Reay, D. S., and Frankenberg, C.:
Large-scale controls methanogenesis inferred from methane and gravity
spaceborne data, Science, 327, 322–325, 2010.Borsdorff, T., Hasekamp, O. P., Wassmann, A., and Landgraf, J.: Remote sensing
of atmospheric trace gas columns: An efficient approach for regularization
and calculation of total column averaging kernels, Atmos. Meas. Tech., 7, 523–535, 10.5194/amt-7-523-2014, 2014.Bousquet, P., Ciais, P., Miller, J. B., Dlugokencky, E. J., Hauglustaine,
D. A., Prigent, C., Van der Werf, G. R., Peylin, P., Brunke, E.-G.,
Carouge, C., Langenfelds, R. L., Lathière, J., Papa, F., Ramonet, M.,
Schmidt, M., Steele, L. P., Tyler, S. C., and White, J.: Contribution of
anthropogenic and natural sources to atmospheric methane variability, Nature,
443, 439–443, 10.1038/nature05132, 2006.Bousquet, P., Ringeval, B., Pison, I., Dlugokencky, E. J., Brunke, E.-G.,
Carouge, C., Chevallier, F., Fortems-Cheiney, A., Frankenberg, C.,
Hauglustaine, D. A., Krummel, P. B., Langenfelds, R. L., Ramonet, M.,
Schmidt, M., Steele, L. P., Szopa, S., Yver, C., Viovy, N., and Ciais, P.:
Source attribution of the changes in atmospheric methane for 2006–2008,
Atmos. Chem. Phys., 11, 3689–3700, 10.5194/acp-11-3689-2011, 2011.
Bovensmann, H., Burrows, J. P., Buchwitz, M., Frerick, J., Noël, S.,
Rozanov, V. V., Chance, K. V., and Goede, A. P. H.: SCIAMACHY: Mission
objectives and measurement modes, J. Atmos. Sci., 56, 127–150, 1999.Bregman, B., Meijer, E., and Scheele, R.: Key aspects of stratospheric tracer modeling using assimilated winds, Atmos. Chem. Phys., 6, 4529–4543, 10.5194/acp-6-4529-2006, 2006.
Brown, M.: Deduction of emissions of source gases using an objective inversion
algorithm and a chemical transport model, J. Geophys. Res., 98,
12639–12660, 1993.
Brown, M.: The singular value decomposition method applied to the deduction of
the emissions and the isotopic composition of atmospheric methane, J.
Geophys. Res., 100, 11425–11446, 1995.
Bruhwiler, L., Tans, P., and Ramonet, M.: A time-dependent assimilation and
source retrieval technique for atmospheric tracers, in: Inverse Methods in
Global Biogeochemical Cycles, edited by: Kasibhatla, P. , AGU, Washington, DC,
Geophys. Monogr. Ser., 114, 265–277, 2000.Bruhwiler, L., Dlugokencky, E., Masarie, K., Ishizawa, M., Andrews, A., Miller,
J., Sweeney, C., Tans, P., and Worthy, D.: CarbonTracker-CH4: an
assimilation system for estimating emissions of atmospheric methane, Atmos.
Chem. Phys., 14, 8269–8293, 10.5194/acp–14–8269–2014, 2014.Butz, A., Guerlet, S., Hasekamp, O., Schepers, D., Galli, A., Aben, I.,
Frankenberg, C., Hartmann, J. M., Tran, H., Kuze, A., Keppel-Aleks, G.,
Toon, G., Wunch, D., Wennberg, P., Deutscher, N., Griffith, D., Macatangay,
R., Messerschmidt, J., Notholt, J., and Warneke, T.: Toward accurate CO2
and CH4 observations from GOSAT, Geophys. Res. Lett., 38, L14812,
10.1029/2011GL047888, 2011.Chen, Y. and Prinn, R. G.: Estimation of atmospheric methane emissions between 1996 and 2001 using a three-dimensional global chemical transport
model, J. Geophys. Res., 111, JD006058, 10.1029/2005JD006058, 2006.Chevallier, F.: Impact of correlated observation errors on inverted CO2
surface fluxes from OCO measurements, Geophys. Res. Lett., 34, L24804,
10.1029/2007GL030463, 2007.Chevallier, F.: On the statistical optimality of CO2 atmospheric
inversions assimilating CO2 column retrievals, Atmos. Chem. Phys., 15, 11133–11145, 10.5194/acp-15-11133-2015, 2015.Chevallier, F., Fisher, M., Peylin, P., Serrar, S., Bousquet, P., Breon, F. M.,
Chedin, A., and Ciais, P.: Inferring CO2 sources and sinks from
satellite observations: Method and application to TOVS data, J. Geophys.
Res., 110, D24309, 10.1029/2005JD006390, 2005.Chevallier, F., Bréon, F.-M., and Rayner, P. J.: Contribution of the
Orbiting Carbon Observatory to the estimation of CO2 sources and sinks:
Theoretical study in a variational data assimilation framework, J. Geophys.
Res., 112, D09307, 10.1029/2006JD007375, 2007.Cressot, C., Chevallier, F., Bousquet, P., Crevoisier, C., Dlugokencky, E. J.,
Fortems-Cheiney, A., Frankenberg, C., Parker, R., Pison, I., Scheepmaker,
R. A., Montzka, S. A., Krummel, P. B., Steele, L. P., and Langenfelds, R. L.:
On the consistency between global and regional methane emissions inferred
from SCIAMACHY, TANSO-FTS, IASI and surface measurements, Atmos. Chem.
Phys., 14, 577–592, 10.5194/acp–14–577–2014, 2014.Deeter, M. N., Edwards, D. P., Gille, J. C., and Drummond, J. R.: Sensitivity
of MOPITT observations to carbon monoxide in the lower troposphere, J.
Geophys. Res., 112, 10.1029/2007JD008929, 2007.Desroziers, G. and Berre, L.: Accelerating and parallelizing minimizations in
ensemble and deterministic variational assimilations, Q. J. R. Meteorol.
Soc., 138, 1599–1610, 10.1002/qj.1886, 2012.Dlugokencky, E. J., Bruhwiler, L., White, J. W. C., Emmons, L. K., Novelli,
P. C., Montzka, S. A., Masarie, K. A., Lang, P. M., Crotwell, A. M., Miller,
J. B., and Gatti, L. V.: Observational constraints on recent increases in the
atmospheric CH4 burden, Geophys. Res. Lett., 36, L18803,
10.1029/2009GL039780, 2009.Douglass, A. R., Schoeberl, M. R., and Rood, R. B.: Evaluation of transport in
the lower tropical stratosphere in a global chemistry and transport model, J.
Geophys. Res., 108, 4259, 10.1029/2002JD002696, 2003.Ehret, G., Kiemle, C., Wirth, M., Amediek, A., Fix, A., and Houweling, S.:
Space-borne remote sensing of CO2, CH4, and N2O by integrated path
differential absorption lidar: a sensitivity analysis, Appl. Phys.
B, 90, 593–608,
10.1007/s00340-007-2892-3, 2008.
Enting, I. G.: A classification of some inverse problems in geochemical
modeling, Tellus B, 37, 216–229, 1985.
Enting, I. G.: Inverse problems in atmospheric constituent studies, III.
Estimating errors in surface sources, Inverse problems, 9, 649–665, 1993.Enting, I. G. and Mansbridge, J. V.: Seasonal sources and sinks of atmospheric
CO2; direct inversion of filtered data, Tellus B, 41, 111–126,
1989.
Enting, I. G. and Newsam, G. N.: Atmospheric constituent inversion problems:
Implications for baseline monitoring, J. Atmos. Chem., 11, 69–87, 1990.Eyer, S., Tuzson, B., Popa, M. E., van der Veen, C., Röckmann, T.,
Rothe, M., Brand, W. A., Fisher, R., Lowry, D., Nisbet, E. G., Brennwald,
M. S., Harris, E., Zellweger, C., Emmenegger, L., Fischer, H., and Mohn, J.:
Real-time analysis of δ13C and δD-CH4 in ambient air
with laser spectroscopy: method development and first intercomparison
results, Atmos. Meas. Tech., 9, 263–280, 10.5194/amt-9-263-2016, 2016.Feng, L., Palmer, P. I., Bösch, H., and Dance, S.: Estimating surface
CO2 fluxes from space-borne CO2 dry air mole fraction observations
using an ensemble Kalman Filter, Atmos. Chem. Phys., 9, 2619–2633, 10.5194/acp-9-2619-2009, 2009.Fischer, H., Behrens, M., Bock, M., Richter, U., Schmitt, J., Loulergue, L.,
Chappellaz, J., Spahni, R., Blunier, T., Leuenberger, M., and Stocker, T. F.:
Changing boreal methane sources and constant biomass burning during the last
termination, Nature, 452, 864–867, 10.1038/nature06825, 2008.Franco, B., Mahieu, E., Emmons, L. K., Tzompa-Sosa, Z. A., Fischer, E. V.,
Sudo, K., Bovy, B., Conway, S., Griffin, D., Hannigan, J. W., Strong, K., and
Walker, K. A.: Evaluating ethane and methane emissions associated with the
development of oil and natural gas extraction in North America, Environ. Res.
Lett., 11, 10.1088/1748-9326/11/4/044010, 2016.
Frankenberg, C., Meirink, J. F., van Weele, M., Platt, U., and Wagner, T.:
Assessing Methane Emissions from Global Space-Borne Observations, Science,
3008, 1010–1014, 2005.Frankenberg, C., Bergamaschi, P., Butz, A., Houweling, S., Meirink, J.-F.,
Notholt, J., Petersen, A. K., Schrijver, H., Warneke, T., and Aben, I.:
Tropical methane emissions: A revised view from SCIAMACHY onboard ENVISAT,
Geophys. Res. Lett., 35, L15811, 10.1029/2008GL034300, 2008.Fraser, A., Palmer, P. I., Feng, L., Boesch, H., Cogan, A., Parker, R.,
Dlugokencky, E. J., Fraser, P. J., Krummel, P. B., Langenfelds, R. L.,
O'Doherty, S., Prinn, R. G., Steele, L. P., van der Schoot, M., and
Weiss, R. F.: Estimating regional methane surface fluxes: the relative
importance of surface and GOSAT mole fraction measurements, Atmos. Chem.
Phys., 13, 5697–5713, 10.5194/acp-13-5697-2013, 2013.
Fung, I., John, J., Lerner, J., Matthews, E., Prather, M., Steele, L. P., and
Fraser, P. J.: Three-dimensional model synthesis of the global methane cycle,
J. Geophys. Res., 96, 13033–13065, 1991.Hausmann, P., Sussmann, R., and Smale, D.: Contribution of oil and natural gas
production to renewed increase in atmospheric methane (2007–2014): top–down
estimate from ethane and methane column observations, Atmos. Chem. Phys., 16,
3227–3244, 10.5194/acp-16-3227-2016, 2016.
Hein, R., Crutzen, P. J., and Heimann, M.: An inverse modeling approach to
investigate the global atmospheric methane cycle, Global Biogeochem. Cy.,
11, 43–76, 1997.Holmes, C. D., Prather, M. J., Sövde, O. A., and Myhre, G.: Future
methane, hydroxyl, and their uncertainties: key climate and emission
parameters for future predictions, Atmos. Chem. Phys., 13, 285–302, 10.5194/acp-13-285-2013, 2013.
Houweling, S., Kaminski, T., Dentener, F. J., Lelieveld, J., and Heimann, M.:
Inverse modeling of methane sources and sinks using the adjoint of a global
transport model, J. Geophys. Res., 104, 26137–26160, 1999.Houweling, S., Hartmann, W., Aben, I., Schrijver, H., Skidmore, J., and
Roelofs, G.-J.: Evidence of systematic errors in SCIAMACHY-observed
CO2 due to aerosols, Atmos. Chem. Phys., 5, 3003–3013, 10.5194/acp-5-3003-2005, 2005.Houweling, S., Krol, M., Bergamaschi, P., Frankenberg, C., Dlugokencky, E. J.,
Morino, I., Notholt, J., Sherlock, V., Wunch, D., Beck, V., Gerbig, C., Chen,
H., Kort, E. A., Röckmann, T., and Aben, I.: A multi-year methane
inversion using SCIAMACHY, accounting for systematic errors using TCCON
measurements, Atmos. Chem. Phys., 14, 3991–4012,
10.5194/acp–14–3991–2014, 2014.Hungershoefer, K., Breon, F.-M., Peylin, P., Chevallier, F., Rayner, P.,
Klonecki, A., Houweling, S., and Marshall, J.: Evaluation of various
observing systems for the global monitoring of CO2 surface fluxes,
Atmos. Chem. Phys., 10, 10503–10520, 10.5194/acp-10-10503-2010, 2010.Kai, F. M., Tyler, S. C., Randerson, J. T., and Blake, D. R.: Reduced methane
growth rate explained by decreased Northern Hemisphere microbial sources,
Nature, 476, 194–197, 10.1038/nature10259, 2011.Kaminski, T., Heimann, M., and Giering, R.: Sensitivity of the seasonal cycle
of CO2 at remote monitoring stations with respect to seasonal surface
exchange fluxes determined with the adjoint of an atmospheric transport
model, Phys. Chem. Earth, 21, 457–462, 1996.Karion, A., Sweeney, C., Tans, P., and Newberger, T.: AirCore: An
Innovative Atmospheric Sampling System, J. Atmos. Oceanic Technol., 27,
1839–1853, 10.1175/2010JTECHA1448.1, 2010.Kirschke, S., Bousquet, P., Ciais, P., Saunois, M., Canadell, J. G. et al.:
Three decades of global methane sources and sinks, Nat. Geosci., 6,
813–823, 10.1038/ngeo1955, 2013.Koffi, E. N., Bergamaschi, P., Karstens, U., Krol, M., Segers, A., Schmidt,
M., Levin, I., Vermeulen, A. T., Fisher, R. E., Kazan, V., Klein Baltink, H.,
Lowry, D., Manca, G., Meijer, H. A. J., Moncrieff, J., Pal, S., Ramonet, M.,
Scheeren, H. A., and Williams, A. G.: Evaluation of the boundary layer
dynamics of the TM5 model over Europe, Geosci. Model Dev., 9, 3137–3160,
10.5194/gmd-9-3137-2016, 2016.Kort, E. A., Frankenberg, C., Costigan, K. R., Lindenmaier, R., Dubey, M. K.,
and Wunch, D.: Four corners: The largest US methane anomaly viewed from
space, Geophys. Res. Lett., 41, 6898–6903, 10.1002/2014GL061503, 2014.Kretschmer, R., Koch, F.-T., Feist, D. G., Biavati, G., Karstens, U., and
Gerbig, C.: Toward Assimilation of Observation-Derived Mixing Heights to
Improve Atmospheric Tracer Transport Models, in: Lagrangian Modeling of the
Atmosphere, edited by: Lin, J., Brunner, D., Gerbig, C., Stohl, A., Luhar, A.,
and Webley, P., American Geophysical Union, Washington DC,
10.1029/2012GM001255, 2012.Landgraf, J., aan de Brugh, J., Scheepmaker, R., Borsdorff, T., Hu, H.,
Houweling, S., Butz, A., Aben, I., and Hasekamp, O.: Carbon monoxide total
column retrievals from TROPOMI shortwave infrared measurements, Atmos. Meas.
Tech., 9, 4955–4975, 10.5194/amt-9-4955-2016, 2016.Lassey, K. R., Lowe, D. C., and Manning, M. R.: The trend in atmospheric
methane δ13C and implications for isotopic constraints on the
global methane budget, Global Biogeochem. Cy., 14, 41–49,
10.1029/1999GB900094, 2000.
Lelieveld, J., Brenninkmeijer, C. A. M., Jöckel, P., Isaksen, I. S. A.,
Krol, M. C., Mak, J. E., Dlugokencky, E., Montzka, S. A., Novelli, P. C.,
Peters, W., and Tans, P. P.: New Directions: Watching over tropospheric
hydroxyl (OH), Atmos. Environ., 40, 5741–5743, 2006.Lelieveld, J., Gromov, S., Pozzer, A., and Taraborrelli, D.: Global
tropospheric hydroxyl distribution, budget and reactivity, Atmos. Chem.
Phys., 16, 12477–12493, 10.5194/acp-16-12477-2016, 2016.Levin, I., Naegler, T., Heinz, R., Osusko, D., Cuevas, E., Engel, A.,
Ilmberger, J., Langenfelds, R. L., Neininger, B., v. Rohden, C., Steele,
L. P., Weller, R., Worthy, D. E., and Zimov, S. A.: The global SF6
source inferred from long-term high precision atmospheric measurements and
its comparison with emission inventories, Atmos. Chem. Phys., 10, 2655–2662,
10.5194/acp-10-2655-2010, 2010.Levin, I., Veidt, C., Vaughn, B. H., Brailsford, G., Bromley, T., Heinz, R.,
Lowe, D., Miller, J. B., Poss, C., and White, J. W. C.: No inter-hemispheric
d13CH4 trend observed, Nature, 486, E3–E4, 10.1038/nature11175, 2012.Locatelli, R., Bousquet, P., Chevallier, F., Fortems-Cheney, A., Szopa, S.,
Saunois, M., Agusti-Panareda, A., Bergmann, D., Bian, H., Cameron-Smith,
P., Chipperfield, M. P., Gloor, E., Houweling, S., Kawa, S. R., Krol, M.,
Patra, P. K., Prinn, R. G., Rigby, M., Saito, R., and Wilson, C.: Impact of
transport model errors on the global and regional methane emissions estimated
by inverse modelling, Atmos. Chem. Phys., 13, 9917–9937, 10.5194/acp-13-9917-2013, 2013.Locatelli, R., Bousquet, P., Saunois, M., Chevallier, F., and Cressot, C.:
Sensitivity of the recent methane budget to LMDz sub-grid-scale physical
parameterizations, Atmos. Chem. Phys., 15, 9765–9780,
10.5194/acp-15-9765-2015, 2015.Meirink, J.-F., Bergamaschi, P., Frankenberg, C., d'Amelio, M. T. S.,
Dlugokencky, E. J., Gatti, L. V., Houweling, S., Miller, J. B.,
Röckmann, T., Villani, M. G., and Krol, M. C.: Four-dimensional
variational data assimilation for inverse modeling of atmospheric methane
emissions: Analysis of SCIAMACHY observations, J. Geophys. Res., 113,
D17301, 10.1029/2007JD009740, 2008a.Meirink, J. F., Bergamaschi, P., and Krol, M. C.: Four-dimensional variational
data assimilation for inverse modelling of atmospheric methane emissions:
Method and comparison with synthesis inversion, Atmos. Chem. Phys., 8, 6341–6353, 10.5194/acp-8-6341-2008, 2008b.Mikaloff Fletcher, S. E., Tans, P. P., Bruhwiler, L. M., Miller, J. B., and
Heimann, M.: CH4 sources estimated from atmospheric observations of
CH4 and its 13C /12C isotopic ratios: 1. Inverse modeling of
source processes, Global Biogeochem. Cy., 18, 1–17, 10.1029/2004GB002223,
2004a.Mikaloff Fletcher, S. E., Tans, P. P., Bruhwiler, L. M., Miller, J. B., and
Heimann, M.: CH4 sources estimated from atmospheric observations of
CH4 and its 13C /12C isotopic ratios: 2. Inverse modeling of
CH4 fluxes from geographical regions, Global Biogeochem. Cy., 18,
1–15,
10.1029/2004GB002224, 2004b.Miller, J. B., Gatti, L. V., d'Amelio, M. T. S., Crotwell, A. M.,
Dlugokencky, E. J., Bakwin, P., Artaxo, P., and Tans, P. P.: Airborne
measurements indicate large methane emissions from the eastern Amazon
basin, Geophys. Res. Lett., 34, 1–5, 10.1029/2006GL029213, 2007.
Miller, S. M., Wofsy, S. C., Michalak, A. M., Kort, E. A., Andrews, A. E.,
Biraud, S. C., Dlugokencky, E. J., Eluszkiewicz, J., Fischer, M. L.,
Janssens-Maenhout, G., Miller, B. R., Miller, J. B., Montzka, S. A.,
Nehrkorn, T., and Sweeney, C.: Anthropogenic emissions of methane in the
United States, PNAS, 110, 20018–20022, 2013.Miyazaki, K., Eskes, H. J., Sudo, K., Takigawa, M., van Weele, M., and
Boersma, K. F.: Simultaneous assimilation of satellite NO2, O3,
CO, and HNO3 data for the analysis of tropospheric chemical
composition and emissions, Atmos. Chem. Phys., 12, 9545–9579,
10.5194/acp-12-9545-2012, 2012.Monteil, G., Houweling, S., Dlugockenky, E. J., Maenhout, G., Vaughn, B. H.,
White, J. W. C., and Röckmann, T.: Interpreting methane variations in
the past two decades using measurements of CH4 mixing ratio and isotopic
composition, Atmos. Chem. Phys., 11, 9141–9153, 10.5194/acp-11-9141-2011, 2011.Monteil, G., Houweling, S., Guerlet, S., Schepers, D., Frankenberg, C.,
Scheepmaker, R., Aben, I., Butz, A., Hasekamp, O., Landgraf, J., Wofsy,
S. C., and Röckmann, T.: Intercomparison of 15 months inversions of
GOSAT and SCIAMACHY CH4 retrievals, J. Geophys. Res., 118,
11807–11823, 10.1002/2013JD019760, 2013.
Montzka, S. A., Krol, M., Dlugokencky, E. J., Hall, B., Joeckel, P., and
Lelieveld, J.: Small Interannual Variability of Global Atmospheric Hydroxyl,
Science, 331, 67–69, 2011.Naik, V., Voulgarakis, A., Fiore, A. M., Horowitz, L. W., Lamarque, J.-F. et
al.: Preindustrial to present-day changes in tropospheric
hydroxyl radical and methane lifetime from the Atmospheric Chemistry and
Climate Model Intercomparison Project (ACCMIP), Atmos. Chem. Phys., 13,
5277–5298, 10.5194/acp-13-5277-2013, 2013.Nassar, R., Sioris, C. E., Jones, D. B. A., and McConnell, J. C.: Satellite
observations of CO2 from a highly elliptical orbit for studies of the
Arctic and boreal carbon cycle, J. Geophys. Res., 119, 2654–2673,
10.1002/2013JD020337, 2014.Neef, L., van Weele, M., and van Velthoven, P.: Optimal estimation of the
present-day global methane budget, Global Biogeochem. Cy., 24,
10.1029/2009GB003661, 2010.
Newsam, G. N. and Enting, I. G.: Inverse problems in atmospheric constituent
studies, I., Determination of surface sources under a diffusive transport
approximation, Inverse Prob., 4, 1037–1054, 1988.Ostler, A., Sussmann, R., Patra, P. K., Houweling, S., De Bruine, M.,
Stiller, G. P., Haenel, F. J., Plieninger, J., Bousquet, P., Yin, Y.,
Saunois, M., Walker, K. A., Deutscher, N. M., Griffith, D. W. T.,
Blumenstock, T., Hase, F., Warneke, T., Wang, Z., Kivi, R., and Robinson, J.:
Evaluation of column-averaged methane in models and TCCON with a focus on the
stratosphere, Atmos. Meas. Tech., 9, 4843–4859,
10.5194/amt-9-4843-2016, 2016.Pandey, S., Houweling, S., Krol, M., Aben, I., and Röckmann, T.: On the
use of satellite-derived CH4 : CO2 columns in a joint inversion
of CH4 and CO2 fluxes, Atmos. Chem. Phys., 15,
8615–8629, 10.5194/acp-15-8615-2015, 2015.Pandey, S., Houweling, S., Krol, M., Aben, I., Chevallier, F., Dlugokencky,
E. J., Gatti, L. V., Gloor, E., Miller, J. B., Detmers, R., Machida, T., and
Röckmann, T.: Inverse modeling of GOSAT-retrieved ratios of total
column CH4 and CO2 for 2009 and 2010, Atmos. Chem. Phys., 16,
5043–5062, 10.5194/acp-16-5043-2016, 2016.Parker, R. J., Boesch, H., Byckling, K., Webb, A. J., Palmer, P. I., Feng, L.,
Bergamaschi, P., Chevallier, F., Notholt, J., Deutscher, N., Warneke, T.,
Hase, F., Sussmann, R., Kawakami, S., Kivi, R., T., D. W., Griffith, and
Velazco, V.: Assessing 5 years of GOSAT Proxy XCH4 data and
associated uncertainties, Atmos. Meas. Tech., 8, 4785–4801,
10.5194/amt-8-4785-2015, 2015.Patra, P. K., M, T., Ishijima, K., Choi, B. C., a.D Cunnold, Dlugokencky,
E. J., Fraser, P., Gomez-Pelaez, A. J., Goo, T. Y., Kim, J. S., Krummel,
P., Langenfelds, R., Mukai, H., O'Doherty, S., Prinn, R. G., Simmonds, P.,
Steele, P., Tohjima, Y., Tsuboi, K., Uhse, K., Weiss, R., Worthy, D., and
Nakazawa, T.: Growth Rate, Seasonal, Synoptic, Diurnal Variations and Budget
of Methane in the Lower Atmosphere, J. Met. Soc. Japan, 87, 635–663,
10.2151/jmsj.87.635, 2009.Patra, P. K., Houweling, S., Krol, M., Bousquet, P., Belikov, D., Bergmann,
D., Bian, H., Cameron-Smith, P., Chipperfield, M. P., Corbin, K.,
Fortems-Cheiney, A., Fraser, A., Gloor, E., Hess, P., Ito, A., Kawa, S. R.,
Law, R. M., Loh, Z., Maksyutov, S., Meng, L., Palmer, P. I., Prinn, R. G.,
Rigby, M., Saito, R., and Wilson, C.: TransCom model simulations of CH4
and related species: linking transport, surface flux and chemical loss with
CH4 variability in the troposphere and lower stratosphere, Atmos. Chem.
Phys., 11, 12813–12837, 10.5194/acp-11-12813-2011, 2011.Patra, P. K., Saeki, T., Dlugokencky, E. J., Ishijima, K., Umezawa, T., Ito,
A., Aoki, S., Morimoto, S., Kort, E. A., Crotwell, A., Ravi Kumar, K., and
Nakazawa, T.: Regional Methane Emission Estimation Based on Observed
Atmospheric Concentrations (2002–2012), J. Met. Soc. Jap., 94, 91–112,
10.2151/jmsj.2016-006, 2016.Peters, W., Miller, J. B., Whitaker, J., Denning, A. S., Hirsch, A., Krol,
M. C., Zupanski, D., Bruhwiler, L., and Tans, P. P.: An ensemble data
assimilation system to estimate CO2 surface fluxes from atmospheric
trace gas observations, J. Geophys. Res., 110, 10.1029/2005JD006157,
2005.
Peters, W., Jacobson, A. R., Sweeney, C., Andrews, A. E., Conway, T. J.,
Masarie, K., Miller, J. B., Bruhwiler, L. M. P., Petron, G., Hirsch, A. I.,
Worthy, D. E. J., van der Werf, G. R., Randerson, J. T., Wennberg, P. O.,
Krol, M. C., and Tans, P. P.: An atmospheric perspective on North American
carbon dioxide exchange: CarbonTracker, Proc. Natl. Acad. Sci., 104,
18925–18930, 2007.Pison, I., Bousquet, P., Chevallier, F., Szopa, S., and Hauglustaine, D.:
Multi-species inversion of CH4, CO and H2 emissions from surface
measurements, Atmos. Chem. Phys., 9, 5281–5297, 10.5194/acp-9-5281-2009, 2009.Pison, I., Ringeval, B., Bousquet, P., Prigent, C., and Papa, F.: Stable
atmospheric methane in the 2000s: key-role of emissions from natural
wetlands, Atmos. Chem. Phys., 13, 11609–11623, 10.5194/acp-13-11609-2013, 2013.
Prinn, R. G., Weiss, R. F., Fraser, P. J., Simmonds, P. G., Cunnold, D. M.,
Alyea, F. N., O'Doherty, S., Salameh, P., Miller, B. R., Huang, J., Wang,
R. H. J., Hartley, D. E., Harth, C., Steele, L. P., Sturrock, G., Midgley,
P. M., and McCulloch, A.: A history of chemically and radiatively important
gases in air deduced from ALE/GAGE/AGAGE, J. Geophys. Res., 105,
17751–17792, 2000.Rayner, P., Michalak, A. M., and Chevallier, F.: Fundamentals of Data
Assimilation, Geosci. Model Dev. Discuss., 10.5194/gmd-2016-148, in review, 2016.Rigby, M., Prinn, R. G., Fraser, P. J., Simmonds, P. G., Langenfelds, R. L.,
Huang, J., Cunnold, D. M., Steele, L. P., Krummel, P. B., Weiss, R. F.,
O'Doherty, S., Salameh, P. K., Wang, H. J., Harth, C. M., Mühle, J.,
and Porter, L. W.: Renewed growth of atmospheric methane, Geophys. Res.
Lett., 35, 10.1029/2008GL036037, 2008.Ringeval, B., de Noblet-Ducoudré, N., Ciais, P., Bousquet, P., Prigent,
C., Papa, F., and Rossow, W. B.: An attempt to quantify the impact of changes
in wetland extent on methane emissions on the seasonal and interannual time
scales, Global Biogeochem. Cy., 24, 10.1029/2008GB003354, 2010.Ringeval, B., Houweling, S., van Bodegom, P. M., Spahni, R., van Beek, R.,
Joos, F., and Röckmann, T.: Methane emissions from floodplains in the
Amazon basin: Challenges in developing a process-based model for global
applications, Biogeosciences, 11, 1519–1558, 10.5194/bg-11-1519-2014, 2014.Röckmann, T., Eyer, S., van der Veen, C., Popa, M. E., Tuzson, B.,
Monteil, G., Houweling, S., Harris, E., Brunner, D., Fischer, H., Zazzeri,
G., Lowry, D., Nisbet, E. G., Brand, W. A., Necki, J. M., Emmenegger, L., and
Mohn, J.: In situ observations of the isotopic composition of methane at the
Cabauw tall tower site, Atmos. Chem. Phys., 16, 10469–10487,
10.5194/acp-16-10469-2016, 2016.Rödenbeck, C.: Estimating CO2 sources and sinks from atmospheric
mixing ratio measurements using a global inversion of atmospheric transport,
Tech. Rep. 6 ISSN 1615-7400, Max-Planck-Institut für Biogeochemie,
Jena, Germany, 2005.Saunois, M., Bousquet, P., Poulter, B., Peregon, A., Ciais, P. et al.: The
global methane budget 2000–2012, Earth Syst. Sci. Data, 8, 697–751,
10.5194/essd-8-697-2016, 2016.Schaefer, H., Mikaloff Fletcher, S. E., Veidt, C., Lassey, K. R., Brailsford,
G. W., Bromley, T. M., Dlugokencky, E. J., Michel, S. E., Miller, J. B.,
Levin, I., Lowe, D. C., Martin, R. J., Vaughn, B. H., and White, J. W. C.: A
21st-century shift from fossil-fuel to biogenic methane emissions indicated
by 13CH4, Science, 352, 80–84, 2016.Simpson, O. J., Sulbaek, M. P., Meinardi, A. S., Bruhwiler, L., Blake, N. J.,
Helmig, D., Sherwood Rowland, F., and Blake, D. R.: Long-term decline of
global atmospheric ethane concentrations and implications for methane,
Nature, 491, 10.1038/nature11342, 2012.Spivakovsky, C. M., Yevich, J. A., Logan, A., Wofsy, S. C., McElroy, M. B., and
Prather, M. J.: Tropospheric OH in a three dimensional chemical tracer
model: an assessment based on observations of CH3CCl3, J. Geophys.
Res., 95, 18411–18471, 1990.
Tans, P. P.: A note on isotopic ratios and the global atmospheric methane
budget, Global Biogeochem. Cy., 11, 77–81, 1997.
Tarantola, A.: Inverse problem theory, and methods for model parameter
estimation, Society for Industrial and Applied Mathematics, Philadelphia,
2005.Terao, Y., Mukai, H., Nojiri, Y., Machida, T., Tohjima, Y., Saeki, T., and
Maksyutov, S.: Interannual variability and trends in atmospheric methane over
the western Pacific from 1994 to 2010, J. Geophys. Res., 116, D14303,
10.1029/2010JD015467, 2011.Turner, A. J., Jacob, D. J., Wecht, K. J., Maasakkers, J. D., Lundgren, E.,
Andrews, A. E., Biraud, S. C., Boesch, H., Bowman, K. W., Deutscher, N. M.,
Dubey, M. K., Griffith, D. W. T., Hase, F., Kuze, A.,
Notholt, J., Ohyama, H., Parker, R., Payne, V. H., Sussmann, R., Sweeney, C., Velazco, V. A., Warneke, T., Wennberg,
P. O., and Wunch, D.: Estimating global and North American methane emissions with high spatial resolution using GOSAT satellite
data, Atmos. Chem. Phys., 15, 7049–7069, 10.5194/acp-15-7049-2015,
2015.Turner, A. J., Jacob, D. J., Benmergui, J., Wofsy, S. C., Maasakkers, J. D.,
Butz, A., Hasekamp, O., Biraud, S. C., and Dlugokencky, E.: A large increase
in US methane emissions over the past decade inferred from satellite data
and surface observations, Geophys. Res. Lett., 43, 2218–2224,
10.1002/2016GL067987, 2016.Voulgarakis, A., Naik, V., Lamarque, J.-F., Shindell, D. T., Young, P. J.,
Prather, M. J., Wild, O., Field, R. D., Bergmann, D., Cameron-Smith, P.,
Cionni, I., Collins, W. J., Dalsøren, S. B., Doherty, R. M., Eyring, V.,
Faluvegi, G., Folberth, G. A., Horowitz, L. W., Josse, B., MacKenzie, I. A.,
Nagashima, T., Plummer, D. A., Righi, M., Rumbold, S. T., Stevenson, D. S.,
Strode, S. A., Sudo, K., Szopa, S., and Zeng, G.: Analysis of present day and
future OH and methane lifetime in the ACCMIP simulations, Atmos. Chem.
Phys., 13, 2563–2587, 10.5194/acp-13-2563-2013, 2013.Wang, J. S., Logan, J. A., McElroy, M. B., Duncan, B. N., Megretskaia, I. A.,
and Yantosca, R. M.: A 3-D model analysis of the slowdown and interannual
variability in the methane growth rate from 1988 to 1997, Global Biogeochem.
Cy., 18, GB3011, 10.1029/2003GB002180, 2004.Warwick, N. J., Bekki, S., Law, K. S., Nisbet, E. G., and Pyle, J. A.: The
impact of meteorology on the interannual growth rate of atmospheric methane,
Geophys. Res. Lett., 29, 10.1029/2002GL015282, 2002.Wecht, K. J., Jacob, D. J., Frankenberg, C., Jiang, Z., and Blake, D. R.:
Mapping of North American methane emissions with high spatial resolution by
inversion of SCIAMACHY satellite data, J. Geophys. Res., 119, 7741–7756,
10.1002/2014JD021551, 2014.Wilson, C., Gloor, M., Gatti, L. V., Miller, J. B., Monks, S. A., McNorton,
J., Bloom, A. A., Basso, L. S., and Chipperfield, M. P.: Contribution of
regional sources to atmospheric methane over the Amazon Basin in 2010 and
2011, Global Biogeochem. Cy., 30, 400–420, 10.1002/2015GB005300,
2016.Worden, J., Kulawik, S., Frankenberg, C., Payne, V., Bowman, K.,
Cady-Peirara, K., Wecht, K., Lee, J.-E., and Noone, D.: Profiles of
CH4, HDO, H2O, and N2O with improved lower tropospheric
vertical resolution from Aura TES radiances, Atmos. Meas. Tech., 5,
397–411, 10.5194/amt-5-397-2012, 2012.
Wunch, D., Toon, G. C., Blavier, J.-F. L., Washenfelder, R. A., Notholt, J.,
Connor, B. J., Griffith, D. W. T., Sherlock, V., and Wennberg, P. O.: The
total carbon column observing network, Phil. Trans. R. Soc., 369, 2087–2112,
10.1098/rsta.2010.0240, 2011a.Wunch, D., Wennberg, P. O., Toon, G. C. et al.: A method for evaluating bias
in global measurements of CO2 total columns from space, Atmos. Chem. Phys.,
11, 12317–12337, 2011b.Zazzeri, G., Lowry, D., Fisher, R. E., France, J. L., Lanoisellé, M., and
Nisbet, E. G.: Plume mapping and isotopic characterisation of anthropogenic
methane sources, Atmos. Environ., 110, 151–162,
10.1016/j.atmosenv.2015.03.029, 2015.