ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-6175-2016Constraints on methane emissions in North America from future geostationary remote-sensing measurementsBousserezNicolasnicolas.bousserez@colorado.eduHenzeDaven K.RooneyBrigittePerkinsAndreWechtKevin J.TurnerAlexander J.https://orcid.org/0000-0003-1406-7372NatrajVijayWordenJohn R.Department of Mechanical Engineering, University of Colorado, Boulder, CO, USAJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USASchool of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USAnow at: Department of Atmospheric Sciences, University of Washington, Seattle, WA, USANicolas Bousserez (nicolas.bousserez@colorado.edu)20May201616106175619021April201510July201525March201615April2016This 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/16/6175/2016/acp-16-6175-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/6175/2016/acp-16-6175-2016.pdf
The success of future geostationary (GEO) satellite observation missions
depends on our ability to design instruments that address their key
scientific objectives. In this study, an Observation System Simulation
Experiment (OSSE) is
performed to quantify the constraints on methane (CH4) emissions in North
America obtained from shortwave infrared (SWIR), thermal infrared (TIR), and
multi-spectral (SWIR+TIR) measurements in geostationary orbit and from
future SWIR low-Earth orbit (LEO) measurements. An efficient stochastic
algorithm is used to compute the information content of the inverted
emissions at high spatial resolution (0.5∘× 0.7∘)
in a variational framework using the GEOS-Chem chemistry-transport model and
its adjoint. Our results show that at sub-weekly timescales, SWIR
measurements in GEO orbit can constrain about twice as many independent flux
patterns than in LEO orbit, with a degree of freedom for signal (DOF) for the
inversion of 266 and 115, respectively. Comparisons between TIR GEO and SWIR
LEO configurations reveal that poor boundary layer sensitivities for the TIR
measurements cannot be compensated for by the high spatiotemporal sampling of
a GEO orbit. The benefit of a multi-spectral instrument compared to current
SWIR products in a GEO context is shown for sub-weekly timescale constraints,
with an increase in the DOF of about 50 % for a 3-day inversion. Our
results further suggest that both the SWIR and multi-spectral measurements on
GEO orbits could almost fully resolve CH4 fluxes at a spatial resolution
of at least 100 km × 100 km over source hotspots (emissions
> 4 × 105 kg day-1). The sensitivity of the optimized
emission scaling factors to typical errors in boundary and initial conditions
can reach 30 and 50 % for the SWIR GEO or SWIR LEO configurations,
respectively, while it is smaller than 5 % in the case of a multi-spectral
GEO system. Overall, our results demonstrate that multi-spectral measurements
from a geostationary satellite platform would address the need for higher
spatiotemporal constraints on CH4 emissions while greatly mitigating the
impact of inherent uncertainties in source inversion methods on the inferred
fluxes.
Introduction
Methane (CH4) plays a key role in both atmospheric chemistry
composition and climate. With a radiative forcing relative to preindustrial
times that is one-third that of carbon dioxide, CH4 is the second
most important greenhouse gas . Furthermore, as
a precursor to tropospheric ozone, CH4 also impacts surface-level air
quality and
crops e.g.,, and contributes to ozone
radiative forcing e.g.,. Considerable
uncertainty remains in our understanding of CH4 sources
e.g.,, which include
emissions from coal, wetlands, livestock, landfills, biomass burning,
geologic seepage, and leaks from the production and distribution of natural
gas.
Although there is a growing interest in using CH4 emission
regulations as an efficient lever to simultaneously address current air
quality and global warming challenges e.g.,, the
lack of confidence in the available CH4 emission estimates remains
a problematic limitation to the design of efficient environmental policies.
Indeed, recent studies showed discrepancies of up to a factor of 2 between
bottom-up inventories and top-down inversions using atmospheric CH4
concentration observations . Extrapolation of local emission characteristics to larger areas
and/or the use of proxy data (e.g., energy consumption, emission ratios
applied to co-emitted species) are the main sources of error in bottom-up
methods. On the other hand, top-down approaches using space-based
measurements of CH4 from low-Earth orbit (LEO) platforms allow
a global spatial coverage within 1 to 6 days but at the same local time.
However, as CH4 emissions can exhibit significant diurnal cycles,
e.g., over wetland or boreal peatland , such
temporal undersampling may affect our ability to accurately quantify those
fluxes. More generally, insufficient observational coverage and the diffusive
nature of transport considerably reduce our ability to spatially resolve
grid-scale emissions from space.
Geostationary (GEO) remote-sensing measurements would alleviate the
above-mentioned shortcomings by providing an almost continuous monitoring and
complete spatial coverage of CH4 concentrations within the field of
view. Previous studies have already demonstrated the potential of
column-integrated trace gas measurements from geostationary satellites to
constrain surface fluxes at regional scale, from single mega-city emissions
down to power plant sources . The
GEOstationary Coastal and Air Pollution Events (GEO-CAPE) mission
was recommended by the National Research Council's Earth
Science Decadal Survey in order to improve our understanding of both coastal
ecosystems and air quality from regional to continental scale. Its aim is to
enable multiple daily observations of key atmospheric and oceanic
constituents over North and South America from a GEO platform. For
air-quality applications, such high-spatial and high-temporal-resolution
measurements would enable source estimates of air-quality pollutants and
climate forcers and development of effective emission-control strategies at
an unprecedented level of confidence. In order to provide more flexibility
and to minimize the cost and risk of the mission, the concept of a phased
implementation that would launch remote-sensing instruments separately on
commercial host spacecrafts has been adopted. The first phase will consist of
the launching of the Tropospheric Emissions: Monitoring of Pollution (TEMPO)
instrument circa 2019 , which will provide GEO hourly
measurements of ozone and precursors as well as aerosols over greater North
America (from Mexico City to the Canadian tar sands, and from the Atlantic to
Pacific oceans). For the second phase, which aims at completing GEO-CAPE's
mission requirements by including measurements of important drivers of
climate and air quality such as CH4, CO, and ammonia
, a rigorous instrument design study is critical to achieve
the mission's scientific objectives within its budget constraints.
In this study we perform an Observation System Simulation Experiment (OSSE)
in order to characterize the constraints on grid-scale CH4 emissions
over North America provided by different potential GEO-CAPE instrument
configurations. The simulation consists of a 4D-Var inversion of CH4
emissions using the GEOS-Chem chemical-transport
model (CTM) over a 0.5∘× 0.7∘ horizontal grid
resolution covering North America. In practice, quantifying the information
content of such a high-dimensional problem requires either Monte Carlo
simulations or, for linear models, a numerical approximation of the inverse
Hessian matrix of the 4D-Var cost function .
Although previous studies have used Monte Carlo estimates
e.g.,, their computational
cost can be extremely high. Indeed, many perturbed inversions (typically
about 50) are needed, each of them requiring numerous forward and adjoint
model integrations (iterations) in case the problem is not well conditioned
(about 50 iterations for our methane inversion). Alternatively, inverse
Hessian approximations based on information from the minimization itself can
be employed, but are usually of very low rank e.g.,. Therefore, most information content analyses in previous
trace-gas Bayesian inversion studies have relied on explicit calculations of
the inverse Hessian matrix, by either considering a regional domain
e.g., or performing a prior dimension reduction of the
control vector e.g.,. However, thus far
dimension reduction methods for high-dimensional problems have relied on
suboptimal choices for the reduced space, which preclude an accurate and
objective quantification of the spatiotemporal constraints on the optimized
emissions.
In this study we use a gradient-based randomization algorithm to approximate
the inverse Hessian of the cost function , which allows
us to calculate the posterior errors as well as the model resolution matrix
(or averaging kernel) of our CH4 emission inversion at grid-scale
resolution. Such information is used to evaluate the impact of different
instrumental designs (spatiotemporal sampling, vertical sensitivity of the
measurements) on CH4 emission constraints. In particular, the
potential of CH4 retrievals from the future TROPOspheric Monitoring
Instrument (TROPOMI) shortwave infrared (SWIR) measurements in a LEO orbit as
well as from a hypothetical multi-spectral instrument in a geostationary
orbit are examined. Section 2 describes the OSSE framework considered in this
study, which comprises the 4D-Var method, the forward model, as well as the
observations and prior information used. Section 3 presents the results of
our experiments, where the information content of the inversion is analyzed
in detail. A conclusion to this work is presented in the last section of the
paper.
Inverse method4D-Var system and information content
The variational approach to Bayesian inference is the method of choice for
high-dimensional problems, since the solution can be computed by iteratively
minimizing a cost function instead of algebraically solving for the minimum,
which becomes computationally intractable for high-dimensional systems.
Provided the error statistics are all Gaussian, finding the maximum
likelihood entails solving the following problem:
argminxJ(x)J(x)=12(H(x)-y)TR-1(H(x)-y)+12(x-xb)TB-1(x-xb),
where xb is the prior vector, defined in the control
space E of dimension n, x belongs to E, y is the
observation vector, defined in the observations vector space F of dimension
p, H:E→F is the forward model operator (also called the
observational operator), which associates with any vector in E its
corresponding observation in F, and R and B are the
covariance matrices of the observation and prior errors with dimension
(p×p) and (n×n), respectively. The argument of the minimum of
Eq. () is called the analysis and is referred to as
xa.
When the adjoint of the forward model (HT) is available, the
minimum of the cost function J can be found iteratively using
a gradient-based minimization algorithm . The gradient of the
cost function with respect to the control vector x can be written as
∇J(x)=HTR-1(H(x)-y)+B-1(x-xb).
An important result is that if the forward model is approximately linear, the
posterior error covariance matrix Pa is equal to the
inverse of the Hessian of the cost function:
Pa=(∇2J)-1(xa)=(B-1+HTR-1H)-1.
This equivalence can be used to compute information content diagnostics prior
to performing the inversion. In this study, following ,
the diagonal elements of Pa (error variances) are
computed using a randomization estimate of
HTR-1H. Here an ensemble of 500 random
gradients of the cost function are used, based on the convergence of the
uniform norm (‖.‖∞) of the inverse Hessian approximation.
showed that good approximation of both the error
variances and the error correlations can be obtained using this approach. For
the present study we further validated our method by comparing direct
finite-difference estimates of selected diagonal elements of
Pa to their stochastic approximations, and found
a relative error standard deviation smaller than 10 %.
The model resolution matrix (or averaging kernel A) is defined as
the sensitivity of the analysis xa (optimized CH4
emissions) to the truth xt (true emissions):
A≡∂xa∂xt.
The model resolution matrix in Eq. () can be rewritten
in matrix form:
A=I-PaB-1.
Since B is diagonal in our experiments,
Eq. () allows us to calculate any element of
A using
Ai,j=δij-Pi,jaBj,j.
Finally, the degree of freedom for signal (DOF) of the inversion is defined
as the trace of A, that is, DOF=∑iAi,i.
Forward model and prior emissions
The forward model in Eq. () includes the GEOS-Chem
chemistry-transport model, which relates the CH4 emissions to the 3-D
concentration field of atmospheric CH4, and the satellite observation
operator that transforms the CH4 concentration profiles into their
corresponding retrieved profile or columns. The GEOS-Chem simulation used in
our experiment is described in and . It
consists of a nested simulation over North America at 0.5∘×0.7∘ horizontal resolution and 72 vertical levels, driven by offline
meteorological data provided by GEOS-5 reanalysis from the NASA Global
Modeling and Assimilation Office (GMAO). Boundary conditions for the nested
domain are used every 3 h from a global 4∘×5∘
GEOS-Chem simulation. In the case of profile assimilation (multi-spectral
instrument), the application of the measurement averaging kernels to the
model profiles can be written as follows:
lnzretr=lnza+A(lnzmod-lnza),
where zretr is the profile that would be retrieved if the
modeled profile concentrations (zmod) were sounded, and
za represents the prior profile concentrations. In the
case of XCH4 columns assimilation, we obtain
XCH4=XCO2ΩCO2(Ωa+aT(ωmod-ωa)),
where ωmod is the modeled
vertical profile of methane, ωa
is the a priori profile, Ωa is the corresponding a
priori column concentration of methane, a is a column averaging
kernel vector that describes the sensitivity as a function of altitude,
ΩCO2 is the measured vertical column concentration of
CO2, and XCO2 is a modeled column mixing ratio of
CO2. For simplicity, we use a single averaging kernel for each
instrument. A larger ensemble of averaging kernels describing a potential
range of sensitivities is beyond the scope of this study given the
computational cost. However, based on knowledge of thermal IR (e.g., TES) and
total column (e.g., TROPOMI) retrievals, use of a single averaging kernel is
a reasonable approximation as our study is constrained to Northern Hemisphere
summertime where the temperature and sunlight conditions provide a sufficient
signal for the present evaluation, and because our study looks at the
relative merits of different observing approaches.
The prior methane emissions we use are from the EDGARv4.2 anthropogenic
methane inventory (), the wetland model from as
implemented by , the GFED3 biomass burning
inventory , a termite inventory and soil absorption from
, and a biofuel inventory from
. Figure shows the total
average daily prior methane emissions for the entire North America nested
domain. Strong hotspots of CH4 sources clearly appear over the
Canadian wetlands, the Appalachian Mountains (an extensive coal mining area)
and densely urbanized areas (e.g., southern California and the eastern
coast). Following previous assessments of the range of the prior error
, we assume a relative prior standard error of
40 % for our bottom-up emission inventory in every grid cell. This results
in a 2.9 Tg month-1
uncertainty in the total emission budget over North America, a magnitude
comparable to the correction to the prior budget found in the inversion of
of 2.3 Tg month-1. We assume no prior spatial error
correlations, which means that the matrix B in
Eq. () is diagonal. Accurately defining error correlations in
bottom-up inventories is a challenging problem due to the sparsity of
available flux measurements, and is beyond the scope of our study. However,
it is likely that the diagonal B assumption made in our study is
overly optimistic, which may result in an overestimation of the spatial
resolution of the constraints afforded by the satellite measurements. Note
that in our setup one emission scaling factor is optimized per grid cell;
therefore, the temporal variability of the emissions is assumed to be a hard
constraint at scales smaller than the assimilation window.
Total daily average prior methane emissions for the nested
North America domain (0.5∘×0.7∘).
Observations and model uncertainties
We consider several instrument configurations for our study, which are
associated with different vertical sensitivities: the future TROPOMI
instrument (2016 launch), which will measure in the shortwave infrared
(SWIR); the Tropospheric Emission Spectrometer (TES) V005 Lite product
(http://tes.jpl.nasa.gov/data/), which
consists of CH4 vertical profile retrievals from thermal infrared
(TIR) measurements at 7.58–8.55 µm; and a hypothetical
multi-spectral CH4 profile retrieval, which allows us to capture a
signal in the boundary layer. Since the DOF for the TES retrievals is less
than 2, we use a pressure-weighted TES XCH4 column instead of
the retrieved CH4 profiles. The averaging kernel for the TROPOMI
configuration is taken from the Greenhouse gases Observing SATellite (GOSAT)
Proxy XCH4 v3.2 retrieval described by (available
from http://www.leos.le.ac.uk/GHG/data/), which consists of CH4
column mixing ratios (XCH4) obtained from SWIR measurements near
1.6 µm. As noted in
, the difference between the TROPOMI and GOSAT retrievals
are of little consequence, as the averaging kernel for SWIR observations is
near unity in the troposphere in any case. The multi-spectral averaging
kernel is derived by first combining the Jacobians (or sensitivities) of the
modeled radiances to methane concentrations from the 1.6 and 8 µm
bands. Both the TES and GOSAT retrievals also simultaneously estimate
interferences such as clouds, albedo, emissivity, temperature, and
H2O. The effects of these interferences can be included by further
combining their corresponding Jacobians with the methane Jacobians
e.g.,. Constraints for methane and
the other radiative interferences are described in
and . The combination of these Jacobians and
constraints are then used to calculate the averaging kernel. The methane
component of the resulting multi-spectral, multi-species averaging kernel is
then used for this study. The effect of the interferences with this
simultaneous retrieval approach is to reduce the overall sensitivity to
methane but improve the posteriori errors. A proof of concept for combining
near-IR and IR-based methane estimates to derive a lower tropospheric
estimate is discussed in using GOSAT and TES profile
retrievals.
Averaging kernels for the different instrument configurations:
(a) TROPOMI column averaging kernel; (b) TES column
averaging kernel; (c) multi-spectral averaging kernels at three
pressure levels: 908, 562 and 383 hPa.
Figure shows the column averaging kernel for the TROPOMI
and TES XCH4 retrievals as well as the averaging kernels at
three different levels for the multi-spectral retrieval. The TROPOMI
retrieval sensitivity is nearly uniform throughout the troposphere, with
averaging kernel values close to 1. The TES retrieval is mostly sensitive to
CH4 concentrations in the upper troposphere, with a peak of the
column averaging kernel around 300 hPa. The multi-spectral profile
retrieval shows a distinct signal in the boundary layer, with weaker
sensitivities above.
Observation and model transport errors are assumed to be independent and
therefore added in quadrature to define the error covariance matrix
R in Eq. (). Observational error standard
deviations for TROPOMI XCH4 columns are uniformly set to
12 ppb, within the range of values reported for GOSAT in
. For the TES retrievals, the profile error
covariance matrix is averaged vertically using pressure-weighted functions to
obtain XCH4 column errors, as described in .
This results in a 0.5–2 % (or 10–40 ppb) standard error deviation for
the TES columns . For the multi-spectral
retrievals, a vertically resolved error covariance matrix is used. The error
covariance for the multi-spectral retrieval is derived along with the
averaging kernel using the approach described in and
references therein. The Jacobians for CH4 and other trace gases
affecting the observed radiances, from the near-IR and thermal IR, are
combined along with noise estimates for both spectral regions that are based
on TES and GOSAT radiances. Because we assume that interferences such as
albedo, emissivity, and H2O are jointly estimated, the
uncertainties from these interferences are also included in the resulting
observation error matrix. The resulting pressure-weighted column
XCH4 error standard deviation is similar to the one obtained for
GOSAT retrievals (∼ 12 ppb).
As shown by , taking into account transport errors is
critical in order to mitigate uncertainties in the inversion, since
neglecting them can lead to discrepancies in the posterior estimates of more
than 150 % of the prior flux at model grid scale. We estimate model
transport error using model–data comparison statistics for North American in
situ observations from the NOAA/ESRL surface, tower, and flask network as
well as observations from the HIPPO and CalNex measurement campaigns
. Model error standard deviations are set to 46 ppb in
the boundary layer and 22 ppb in the free troposphere.
Vertical error correlations between simulated concentrations
are difficult to quantify with the limited observational sampling available in situ.
Transport error correlations between the boundary layer and the free
troposphere
are assumed to be negligible due to the decoupling of the physical processes
between those two regions. However, within both the boundary layer and the
free troposphere,
a model error correlation of one is assumed between all altitude levels, which is a conservative
(pessimistic) assumption. Our gradient-based estimates of the inverse Hessian matrix
involve generating random perturbations that follow the observational error statistics
(see Sect. ). For the multi-spectral configuration, a
singular value decomposition (SVD) is first performed on the vertically
resolved matrix R in order to generate independent perturbations
e.g.,.
Density of satellite observations (grid cell-1 week-1) for LEO (left) and GEO
(right) orbits for the nested North America domain
(0.5∘×0.7∘) and for the period 1–8 July 2008.
In order to assess the relative impact of measurement sensitivity versus
spatiotemporal sampling on the CH4 emission constraints, both LEO and
GEO orbit configurations are considered in our study. The LEO orbit
configuration approximately follows TROPOMI's sun-synchronous polar orbit
with an Equator overpass local time of 14:00 and daily global coverage with a
footprint area of ∼7×7 km2. The GEO configuration corresponds
to hourly observations over North America from 10 to 60∘ N. The GEO
footprint considered is ∼4km, i.e., much finer than the
GEOS-Chem resolution used (∼50km). For both LEO and GEO
configurations, observations are therefore averaged together within each
GEOS-Chem grid cell and the instrument error standard deviation is reduced by
multiplying it by the square root of the number of observations.
Finally, contamination by clouds is taken into account for each grid cell by
removing a fraction of the total number of observations within that cell that
corresponds to the GEOS-5 cloud fraction. The resulting spatial distribution
of the observational data density for each satellite configuration (LEO or
GEO) is shown in Fig. .
Results
In the following experiments, we consider the inversion of 30-, 7-, and 3-day
grid-scale emission scaling factors over North America. In particular, this
means that the spatiotemporal variability of the methane fluxes (e.g.,
diurnal cycle and spatial distribution) within each time window is assumed to
be known, and only its magnitude is adjusted. The information content of the
inversion is analyzed for four different observational systems:
a TROPOMI instrument onboard a low-Earth orbit platform
(TROPOMI_LEO);
a TROPOMI instrument onboard a geostationary orbit platform
(TROPOMI_GEO);
a TES-like instrument onboard a geostationary orbit platform
(TES_GEO);
a multi-spectral instrument onboard a geostationary orbit
platform (MULTI_GEO).
Relative error variance reduction for a 30-day methane emission
optimization (1–30 July 2008) using (a) TROPOMI low-Earth orbit
observations (TROPOMI_LEO); (b) GEO-CAPE
observations with a TES-like instrument (TES_GEO); (c) GEO-CAPE observations with a TROPOMI-like instrument (TROPOMI_GEO);
and (d) GEO-CAPE observations with a multi-spectral instrument
(MULTI_GEO). Zero values correspond to emissions with no constraints from
observations, while values of one correspond to emissions entirely
constrained by observations. The DOF for each inversion, which is the sum of
all diagonal elements of the model resolution matrix, is also indicated.
Error reduction of optimized methane emissions
Figures , , and
show the relative error variance reduction in the
emission scaling factors for 30-, 7-, and 3-day inversions, respectively, for
each of the observational configurations described above. The DOF, which
quantifies the number of pieces of information independently constrained by
the observations, is also indicated. For the monthly inversion, the
TROPOMI_LEO, TROPOMI_GEO, and MULTI_GEO configurations show error variance
reductions close to 100 % for sparse hotspots over the continent, in
particular in the Los Angeles basin, the central US, the Toronto urban area,
the Appalachian Mountains, and the northeastern US. The TES_GEO
configuration still shows significant observational constraints in those
locations, with error variance reductions > 70 %. However, overall the
error variance reductions afforded by using a TES-like instrument in
geostationary orbit are much smaller than the one obtained from a
TROPOMI-like or multi-spectral instrument. In particular, the DOF for the
TES_GEO configuration (164) is about half that of the TROPOMI_LEO
configuration (298). This demonstrates that using measurements with
significant sensitivities to lower-tropospheric concentrations is critical to
obtaining surface flux information, even in a geostationary framework with
high-frequency temporal sampling. The advantage of the GEO over the LEO
configuration is more pronounced when smaller emission timescales are
constrained (weekly, 3-day). In particular, the DOF for TROPOMI_LEO varies
from 88 to 43 % of the DOF for TROPOMI_GEO between the monthly and 3-day
inversions. Similarly, but to a lesser extent, the benefit of a
multi-spectral profile observation compared to a TROPOMI-like column
measurement is most evident when the temporal resolution of the flux
inversion is increased, with a DOF ratio between TROPOMI_GEO and MULTI_GEO
varying from 84 to 67 % between the monthly and 3-day inversions.
These results are synthesized in Fig. ,
which shows the relative error variance reduction as a function of emission magnitude,
for each observational system and inversion time window. The convergence of
the
flux constraints provided by the TROPOMI (LEO or GEO) and the multi-spectral GEO
instruments is well illustrated by the convergence of the corresponding curves as the temporal scale
of the optimization increases from 3 days to 1 month. These results also show
that for grid cells with high CH4 emissions (>4×105kgday-1grid-1), a multi-spectral instrument in
geostationary orbit would reduce prior flux error variances by more than
80 % at timescales as small as 3 days. In particular, this could provide
valuable information
to monitor the variation of CH4 emission hotspot activities between workweek and weekend.
Finally, we note that obtained a DOF of 39 for a multi-year CH4
flux inversion over North America using GOSAT LEO observations.
The much higher DOF (298) obtained for our monthly TROPOMI_LEO inversion
clearly
demonstrates the impact of spatial sampling when using a TROPOMI LEO configuration, which will
provide roughly 2 orders of magnitude more observations than GOSAT. We also note that in
, a prior dimension reduction of the inverse problem was
performed to enable an analytical computation of the solution with only 369
control vector elements. Although it is claimed that the aggregation scheme
used to define the reduced space is designed to account for prior error
correlations, the results obtained in indicate the
reduction method is suboptimal (see the interactive discussion of
, for more details), which could result in an
underestimation of the DOF. On the other hand, in our case neglecting error
correlations in the prior inventory may result in an overestimation of the
DOF. In the absence of a rigorous methodology to accurately estimate the
prior error correlations, the DOFs we derived should therefore be interpreted
with caution, but can provide useful insights into the relative magnitude of
the constraints afforded by different instruments and orbit configurations.
These results also correspond to the limit to which the observational
constraints would tend as the effective spatial resolutions of the bottom-up
CH4 inventories are increased. In relation to previous works by
and , it should also be noted that the gradient-based algorithm
used in our study allows us to estimate the DOF of the inversion prior to
optimization; this information could therefore be used to objectively
determine an appropriate dimension for the inverse problem, upon which
specific dimension reduction methods could be devised.
Coordinates of the five locations considered for the rows of the
model resolution matrix, with their corresponding emission rate.
RegionCoordinatesEmissionEmission(lon, lat (∘))(105kgday-1(gridcell)-1)(105kgday-1km-2)Eastern US(-82, 38)3990.12Central US(-104, 40)8300.26California(-117.3, 34.5)8950.26Western Canadian wetlands(-120, 61.5)5750.29Eastern Canadian wetlands(-84.6, 52.5)2050.08
Relative error variance reduction for a 7-day methane emission
optimization (1–8 July 2008) using (a) TROPOMI low-Earth orbit
observations (TROPOMI_LEO); (b) GEO-CAPE observations with
a TES-like instrument (TES_GEO); (c) GEO-CAPE observations with
a TROPOMI-like instrument (TROPOMI_GEO); and (d) GEO-CAPE
observations with a multi-spectral instrument (MULTI_GEO). Zero values
correspond to emissions with no constraints from observations, while values
of one correspond to emissions entirely constrained by observations. The DOF
for each inversion, which is the sum of all diagonal elements of the model
resolution matrix, is also indicated.
Relative error variance reduction for a 3-day methane emission
optimization (1–3 July 2008) using (a) TROPOMI low-Earth orbit
observations (TROPOMI_LEO); (b) GEO-CAPE observations with
a TES-like instrument (TES_GEO); (c) GEO-CAPE observations with
a TROPOMI-like instrument (TROPOMI_GEO); and (d) GEO-CAPE
observations with a multi-spectral instrument (MULTI_GEO). Zero values
correspond to emissions with no constraints from observations, while values
of one correspond to emissions entirely constrained by observations. The DOF
for each inversion, which is the sum of all diagonal elements of the model
resolution matrix, is also indicated.
Spatial resolution of the inversion
An objective measure of the spatial resolution of the inversion, i.e., the
ability of the observational system to constrain grid-scale emissions
independently of each other, is provided by the rows of the model resolution
matrix (see Eq. ). Figure
shows the model resolution matrix rows of the weekly inversion corresponding
to five different locations, chosen to span a range of characteristics, in
terms of emissions magnitude and error reduction. For readability, only grid
cells included within the largest circle centered on each location and
containing values greater than 0.05 are shown. Table
summarizes the coordinates and CH4 emissions corresponding to each
location. Since the model grid-cell area depends on the latitude, the
radiuses of each of the structures shown in Fig.
are also summarized in Table . Note that the 3-day
inversion results (not shown) gave similar results to the 1-week inversion.
The gain in spatial resolution of the optimized fluxes when a GEO orbit is
used is evident when comparing the TROPOMI_LEO and TROPOMI_GEO results. In
particular, Table suggests that for the central US
and California regions, the spatial resolution of the independently
constrained flux patterns is about 2 times higher in the case of a GEO
configuration (radius ∼ 80 km) compared to a LEO configuration (radius
∼ 160 km). Based on the comparison between the TROPOMI_GEO and
MULTI_GEO configurations, the gain in spatial resolution afforded by the use
of a multi-spectral instrument appears significant (factor of 2) only over
the eastern US region. Note that although the sizes of the flux structures
are similar between the TES_GEO and TROPOMI_LEO configurations, the average
values of the model resolution matrix row within each structure are
significantly higher in the case of TROPOMI_LEO.
Coordinates of the five locations considered for the rows of the
model resolution matrix and approximate radius of influence of neighboring
grid cells (see text), for each satellite configuration and a weekly methane
flux inversion.
RegionCoordinatesTES_GEOTROPOMI_LEOTROPOMI_GEOMULTI_GEO(lon, lat (∘))Radius (km)Radius (km)Radius (km)Radius (km)Eastern US(-82, 38)16016016080Central US(-104, 40)791587979California(-117.3, 34.5)1641648282Western Canadian wetlands(-120, 61.5)130196131196Eastern Canadian wetlands(-84.6, 52.5)283213142142
Relative error variance reduction as a function of methane emission
magnitude for a (a) 30-day (1–30 July 2008), (b) 7-day
(1–8 July 2008), and (c) 3-day (1–4 July 2008) inversion. Blue:
TROPOMI
low-Earth orbit observations (TROPOMI_LEO); green: GEO-CAPE
observations with a TES-like instrument (TES_GEO); red: GEO-CAPE
observations with a TROPOMI-like instrument (TROPOMI_GEO); black:
GEO-CAPE observations with a multi-spectral instrument
(MULTI_GEO). Results for a 3-day MULTI_GEO inversion are also
shown in purple (top). The vertical bars indicate the standard
deviation of observational constraints within each bin.
Rows of the model resolution matrix (unitless) for five locations
for a 7-day inversion (1–8 July 2008), using (a) TROPOMI low-Earth
orbit observations (TROPOMI_LEO);
(b) GEO-CAPE observations with a TES-like instrument
(TES_GEO); (c) GEO-CAPE observations with a TROPOMI-like
instrument (TROPOMI_GEO); and (d) GEO-CAPE observations with
a multi-spectral instrument (MULTI_GEO). Coordinates of the five
locations considered are reported in Table
and approximately correspond to the peak value of each structure on the maps.
Sensitivity of the optimized emission scaling factors to
uncertainties in boundary conditions for a 7-day inversion (1–8 July 2008),
using (a) TROPOMI low-Earth orbit observations (TROPOMI_LEO);
(b) GEO-CAPE observations with a TES-like instrument (TES_GEO);
(c) GEO-CAPE observations with a TROPOMI-like instrument
(TROPOMI_GEO); and (d) GEO-CAPE observations with a multi-spectral
instrument (MULTI_GEO). Shown is the impact of perturbations of the boundary
condition concentrations with Gaussian distribution
N(0.16 ppb) on the
optimized scaling factors. Note the different color scale for the MULTI_GEO
configuration.
Sensitivity of the optimized emission scaling factors to
uncertainties in initial condition concentrations for a 7-day inversion
(1–8 July 2008), using (a) TROPOMI low-Earth orbit observations
(TROPOMI_LEO); (b) GEO-CAPE observations with a TES-like instrument
(TES_GEO); (c) GEO-CAPE observations with a TROPOMI-like instrument
(TROPOMI_GEO); and (d) GEO-CAPE observations with a multi-spectral
instrument (MULTI_GEO). Shown is the impact on the optimized emission
scaling factors of perturbations of the boundary layer and free troposphere
initial CH4 concentrations with Gaussian distributions
N(0.22 ppb) and
N(0.46 ppb), respectively.
Note the different color scale for the MULTI_GEO configuration.
Impact of boundary and initial conditions uncertainties
Boundary and initial conditions used in the forward transport model contain
errors. Therefore, any consistent flux inversion system should jointly
optimize the fluxes, initial state and boundary conditions. However, in
practice, many studies overlook this issue and optimize those quantities
separately e.g.,. In the latter case, a
flux-only inversion is performed with initial and boundary conditions that
are effectively assumed perfectly known. It is therefore of interest to
estimate the impact of errors in the initial and boundary conditions on the
optimized fluxes. Figure shows the perturbations in the
optimized emission scaling factors for the weekly inversion resulting from
random Gaussian perturbations of the boundary conditions with standard
deviation 16 ppb. The choice for the standard error of the noise is based on
model–data comparisons from the HIAPER Pole-to-Pole
Observations (HIPPO) experiment
, which consists in extensive aircraft measurements
throughout the troposphere over the Pacific Ocean. Only weekly inversion
results are shown here, so that enough constraints are obtained for all
observational configurations while keeping the computational cost of the
inversions manageable.
For all configurations, the results show
scaling factor perturbations throughout the North America domain, although
they are less pronounced over the eastern US due to the dominant westerly
propagation
of the boundary condition perturbations into the domain.
The TES_GEO and TROPOMI_GEO configurations show similar sensitivities
of the optimized scaling factors to boundary conditions, with large areas characterized
by perturbations between 10 and 50 %, and with impacts greater than 50 % locally.
In comparison, the TROPOMI_GEO configuration shows smaller sensitivities to boundary conditions, with perturbations generally smaller than 30 %. The MULTI_GEO results are
in contrast to the other configurations, with most scaling factor
perturbations being smaller than 5 %.
The differences between the sensitivities of the optimized fluxes to boundary
conditions for different observational systems are driven by two factors:
(1) the sensitivity of the observations to the underlying fluxes (defined by
the operator H) and (2) the model–data mismatch (i.e.,
H(x)-y)). This can be seen, e.g., by considering the
observational term in the gradient formula of Eq. (). Formally,
a perturbation of the boundary conditions will translate into a corresponding
perturbation of the observations (y) in the model–data mismatch,
which is propagated into flux scaling factor perturbations through the
adjoint matrix of sensitivities (HT). The effect of (1) is
clearly seen when comparing the TROPOMI_GEO and TROPOMI_LEO results, the
higher temporal frequency of the geostationary observations providing higher
sensitivity to the fluxes. The effect of (2) is best illustrated by comparing
the TROPOMI_GEO and MULTI_GEO results. Indeed, since the multi-spectral
measurements allow for distinguishing boundary layer from free tropospheric
CH4 concentrations, and given the uniform (∼ 1) sensitivity of
the TROPOMI column measurements throughout the troposphere (see
Fig. ), the boundary layer model–data mismatch
(MULTI_GEO) is much smaller than the column model–data mismatch
(TROPOMI_GEO), which results in much higher flux adjustments for the
TROPOMI_GEO configuration.
The same analysis applies to the sensitivities of the optimized fluxes to
initial conditions, which are shown in Fig. . Here the
CH4 3-D initial concentrations were perturbed with random Gaussian
noises of standard deviation 46 and 22 ppb in the boundary layer and the
free troposphere, respectively, based on model–data comparisons with NOAA
flasks, tall tower, and aircraft measurements over North America
. In the case of initial conditions, as opposed to
boundary conditions, the forcing perturbations are applied only once at the
beginning of the inversion window, which results in the signal being quickly
diluted and therefore in smaller impacts on the optimized fluxes. The
TROPOMI_GEO configuration, which combines significant sensitivities to
CH4 concentrations throughout the troposphere with high-frequency
measurements, is most sensitive to initial condition perturbations, with up
to 30 % variability in the optimized scaling factors. The TROPOMI_LEO and
TES_GEO configurations show comparable sensitivities, with scaling factor
perturbations generally smaller than 10 %. Similarly to the boundary
condition case, initial condition sensitivities associated with the
MULTI_GEO configuration are about 1 order of magnitude smaller than other
configurations, with scaling factor perturbations generally smaller than
3 %. These results show that although the advantage of a multi-spectral
instrument in terms of spatiotemporal constraints on the fluxes becomes
significant only for timescales smaller than a week, there is still a clear
benefit in using this configuration to mitigate the impact of uncertainties
in boundary and initial conditions on the inversion, even when optimizing
fluxes at coarser temporal resolution (e.g., weekly or monthly).
Conclusions
In this paper we evaluated top-down constraints on methane emissions in North
America provided by future potential geostationary (GEO-CAPE) and planned
low-Earth orbit (TROPOMI) remote-sensing observation missions. For the first
time, a grid-scale estimate of the information content of a high resolution
inversion (0.5∘×0.7∘ over North America) in a 4D-Var
inversion framework has been performed using an efficient stochastic
algorithm. In particular, this allowed us to compute both the relative error
reductions and the spatial correlations between observational constraints in
the inversion. Instrument configurations corresponding to TIR and SWIR
methane retrievals (TES-like and TROPOMI, respectively), as well as
a potential future multi-spectral retrieval, were considered. This allowed us
to assess the relative importance of the vertical sensitivity of the
measurement versus the spatiotemporal resolution of the sampling (GEO versus
LEO) in methane flux inversions.
We found that a GEO configuration provides significant benefits over the
future TROPOMI LEO products in terms of error reductions in the optimized
fluxes when the targeted timescales are about a week or less. For a 3-day
inversion, the number of pieces of information (DOF) independently
constrained by the GEO observations is about twice as many as in the case of
a LEO configuration (DOF of 266 and 115, respectively). Experiments with TIR
GEO and SWIR LEO configurations demonstrated that the high temporal frequency
of GEO observations cannot compensate for weak sensitivities of the satellite
measurement to boundary layer concentrations, since constraints from a
TES-like instrument in GEO orbit correspond to only about half of the
information content afforded by a TROPOMI instrument in LEO orbit for a
monthly inversion (DOF of 164 and 298, respectively). In a GEO orbit, the
benefit of using a multi-spectral instrument compared to a SWIR instrument
has been demonstrated for weekly to sub-weekly scale flux constraints, with
an increase in the DOF of about 50 % for a 3-day inversion. For the
multi-spectral GEO configuration, the information content is similar for a
3-day or a 1-month optimization (DOF of 397 and 398, respectively). Moreover,
comparison of our results with those from a recent CH4 inversion
study by suggests that TROPOMI or GEO-CAPE could improve
monthly-scale constraints on emissions by about an order of magnitude
relative to GOSAT.
Over some local CH4 source hotspots (emissions
> 4 × 105 kg day-1) in the central US, California and
eastern US, both SWIR and multi-spectral GEO configurations allow for nearly
complete constraints on emissions (error reduction close to 100 %) at a
spatial resolution smaller than 100 km × 100 km. These estimates
are optimistic, given the lack of spatial error correlation considered in our
prior emissions, which should be addressed in future work, but do reveal the
potential spatial resolution provided by the measurements alone.
The sensitivity of the optimized emission scaling factors to uncertainties in
initial and boundary conditions has also been assessed by propagating random
perturbations of these forcings into the flux estimates. While the flux
responses to the boundary and initial condition perturbations can reach 50
and 30 %, respectively, in the case of TROPOMI column constraints, they
were an order of magnitude lower (< 5 %) in the case of multi-spectral
profile observations.
With growing concerns about the environmental impacts of CH4
emissions from the oil and gas industry and the urge for better monitoring of
the US' CH4 budget, a multi-spectral instrument onboard geostationary
orbit would provide a key tool to characterize the variability of the
CH4 fluxes at a weekly to sub-weekly timescale, while greatly
mitigating the impact of inverse method uncertainties on the optimized
fluxes. Moreover, such an observational system would allow for better
understanding of the critical role of wetlands in the global methane budget
and their impact on climate change e.g.,. Further investigations would be needed to quantify
the sensitivity of these results to the choice of the reference CH4
emission inventory, since significant discrepancies in the magnitude and
spatiotemporal distributions of CH4 sources exist between current
bottom-up inventories .
In our study we have neglected prior error correlations in the absence of
robust data and methodology to rigorously estimate them. Since error
correlations in prior bottom-up inventories nevertheless exist, additional
experiments should be performed to test the sensitivity of our information
content analysis to different error correlation structures. Likewise,
horizontal spatial correlations associated with model and observations errors
should be included in future OSSEs in order to obtain more reliable error
reduction estimates. We have also performed the inversion using emission
scaling factors, which effectively places a hard constraint on the spatial
distribution of the emissions – an assumption that warrants further
investigations. The robustness of our results against model and observational
biases should also be investigated. Finally, following recent studies
investigating regional to urban constraints from geostationary remote-sensing
instruments , it would be interesting to apply
the present methodological framework to inversions at much higher
spatiotemporal resolution in order to analyze the ability of such
observational systems to extract information at spatial scales of only a few
km2.
Acknowledgements
This project was supported by NASA GEO-CAPE Science Team grant NNX14AH02G and
NOAA grant NA14OAR4310136. This work utilized the Janus supercomputer, which
is supported by the National Science Foundation (award number
CNS-0 821 794) and the University of Colorado Boulder. The Janus
supercomputer is a joint effort of the University of Colorado Boulder, the
University of Colorado Denver and the National Center for Atmospheric
Research. Alexander J. Turner was supported by a Department of Energy (DOE)
Computational Science Graduate Fellowship (CSGF). Part of this research was
carried out at the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with the National Aeronautics and Space
Administration. Edited by: M. Palm
ReferencesBasu, S., Guerlet, S., Butz, A., Houweling, S., Hasekamp, O., Aben, I.,
Krummel, P., Steele, P., Langenfelds, R., Torn, M., Biraud, S., Stephens, B.,
Andrews, A., and Worthy, D.: Global CO2 fluxes estimated from GOSAT
retrievals of total column CO2, Atmos. Chem. Phys., 13, 8695–8717,
doi:10.5194/acp-13-8695-2013,
2013.Bloom, A. A., Palmer, P. I., Fraser, A., and Reay, D. S.: Seasonal
variability of tropical wetland CH4 emissions: the role of the
methanogen-available carbon pool, Biogeosciences, 9, 2821–2830,
doi:10.5194/bg-9-2821-2012,
2012.Bocquet, M., Wu, L., and Chevallier, F.: Bayesian design of control space for
optimal assimilation of observations. Part I: Consistent multiscale formalism, Q. J. Roy. Meteor. Soc., 137, 1340–1356,
10.1002/qj.837, 2011.Bousserez, N., Henze, D. K., Perkins, A., Bowman, K. W., Lee, M., Liu, J.,
Deng, F., and Jones, D. B. A.: Improved analysis-error covariance matrix for
high-dimensional variational inversions: application to source estimation
using a 3-D atmospheric transport model, Q. J. Roy. Meteor. Soc., 141,
1906–1921, doi:10.1002/qj.2495,
2015.Butz, A., Hasekamp, O. P., Frankenberg, C., Vidot, J., and Aben, I.:
CH4 retrievals from space-based solar backscatter measurements:
Performance evaluation against simulated aerosol and cirrus loaded scenes, J.
Geophys. Res., 115, D24302, 10.1029/2010JD014514, 2010.
Caulton, D. R., Shepson, P. B., Santoro, R. L., Sparks, J. P.,
Howarth, R. W., Ingraffea, A. R., Cambaliza, M. O., Sweeney, C., Karion, A.,
Davis, K. J., Stirm, B. H., Montzka, S. A., and Miller, B. R.: Toward
a better understanding and quantification of methane emissions from shale gas
development, P. Natl. Acad. Sci. USA, 111, 6237–6242, 2014.Chance, K., Liu, X., Suleiman, R. M., Flittner, D. E., Al-Saadi, J., and
Janz, S. J.: Tropospheric emissions: monitoring of pollution (TEMPO), Proc. SPIE 8866, Earth Observing Systems XVIII, 88660D (23 September 2013),
10.1117/12.2024479, 2013.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.-Atmos., 112, 2156–2202, 2007.Connor, B. J., Boesch, H., Toon, G., Sen, B., Miller, C., and Crisp, D.:
Orbiting Carbon Observatory: Inverse method and prospective error analysis,
J. Geophys. Res.-Atmos., 113, D05305, 10.1029/2006JD008336, 2008.Cressot, C., Chevallier, F., Bousquet, P., Crevoisier, C.,
Dlugokencky, E. J., A., Fortems-Cheiney, A., Frankenberg, C., Parker, R.,
Pison, I., Scheepmaker, R. A., Montzka, S. 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,
doi:10.5194/acp-14-577-2014,
2014.Deng, F., Jones, D. B. A., Henze, D. K., Bousserez, N., Bowman, K. W.,
Fisher, J. B., Nassar, R., O'Dell, C., Wunch, D., Wennberg, P. O., Kort, E.
A., Wofsy, S. C., Blumenstock, T., Deutscher, N. M., Griffith, D. W. T.,
Hase, F., Heikkinen, P., Sherlock, V., Strong, K., Sussmann, R., and Warneke,
T.: Inferring regional sources and sinks of atmospheric CO2 from GOSAT
XCO2 data, Atmos. Chem. Phys., 14, 3703–3727,
10.5194/acp-14-3703-2014, 2014.
Dlugokencky, E. J., Nisbet, E. G., Fisher, R., and Lowry, D.: Global
atmospheric methane: budget, changes and dangers, Philos. T. R. Soc. A, 369,
2058–2072, 2011.European Commission: Emission Database for Global Atmospheric Research (EDGAR),
release version 4.2, Tech. rep., Joint Research Centre (JRC)/Netherlands Environmental
Assessment Agency (PBL), available at: http://edgar.jrc.ec.europa.eu (last access: 1 December 2014), 2011.
Fiore, A. M., Jacob, D. J., Field, B. D., Streets, D. G., Fernandes, S. D.,
and Jang, C.: Linking ozone pollution and climate change: the case for
controlling methane, Geophys. Res. Lett., 29, 25–1, 2002.
Fiore, A. M., West, J. J., Horowitz, L. W., Naik, V., and Schwarzkopf, M. D.:
Characterizing the tropospheric ozone response to methane emission controls
and the benefits to climate and air quality, J. Geophys. Res.-Atmos., 113,
1984–2012, 2008.
Fishman, J., Iraci, L., Al-Saadi, J., Chance, K., Chavez, F., Chin, M.,
Coble, P., Davis, C., DiGiacomo, P., Edwards, D., Eldering, L., Goes, J.,
Herman, J., Hu, C., Jacob, D. J., Jordan, C., Kawa, S. R., Key, R., Liu, X.,
Lohrenz, S., Mannino, A., Natraj, V., Neil, D., Neu, J., Newchruch, M.,
Pickering, K., Salisbury, J., Sosik, H., Subramaniam, A., Tzortziou, M.,
Wang, J., and Wang, M.: The United States' next generation of atmospheric
composition and coastal ecosystem measurements: NASA's Geostationary Coastal
and Air Pollution Events (GEO-CAPE) Mission, B. Am. Meteorol. Soc., 93,
1547–1566, 2012.Fu, D., Worden, J. R., Liu, X., Kulawik, S. S., Bowman, K. W., and Natraj,
V.: Characterization of ozone profiles derived from Aura TES and OMI
radiances, Atmos. Chem. Phys., 13, 3445–3462, 10.5194/acp-13-3445-2013,
2013.
Fung, I., John, J., Lerner, J., Matthews, E., Prather, M., Steele, L., and
Fraser, P.: Three-dimensional model synthesis of the global methane cycle, J.
Geophys. Res.-Atmos., 96, 13033–13065, 1991.Gazovic, M., Kutzbach, L., Schreiber, P., Wille, C., and Wilmking, M.:
Diurnal dynamics of CH4 from a boreal peatland during snowmelt, Tellus B,
62, 133–139, 2010.Kaplan, J. O.: Wetlands at the Last Glacial Maximum: distribution and methane
emissions, Geophys. Res. Lett., 29, 3-1–3-4, 10.1029/2001GL013366, 2002.
Karion, A., Sweeney, C., Pétron, G., Frost, G., Michael Hardesty, R.,
Kofler, J., Miller, B. R., Newberger, T., Wolter, S., Banta, R., Brewer, A.,
Dlugokencky, E., Lang, P., Montzka, S. A., Schnell, R., Tans, P.,
Trainer, M., Zamora, R., and Conley, S.: Methane emissions estimate from
airborne measurements over a western United States natural gas field,
Geophys. Res. Lett., 40, 4393–4397, 2013.
Katzenstein, A. S., Doezema, L. A., Simpson, I. J., Blake, D. R., and
Rowland, F. S.: Extensive regional atmospheric hydrocarbon pollution in the
southwestern United States, P. Natl. Acad. Sci. USA, 100, 11975–11979, 2003.
Kirschke, S., Bousquet, P., Ciais, P., Saunois, M., Canadell, J. G.,
Dlugokencky, E. J., Bergamaschi, P., Bergmann, D., Blake, D. P.,
Bruhwiler, L., Cameron-Smith, P., Castaldi, P., Chevallier, F., Feng, L.,
Fraser, A., Heimann, M., Hodson, E. L., Houweling, S., Josse, B.,
Fraser, P. J., Krummel, P. B., Lamarque, J. F., Langenfelds, R. L., Le
Quere, C., Naik, V., O'Doherty, S., Palmer, P. I., Pison, I., Plummer, D.,
Poulter, B., Prinn, R. G., Rigby, M., Ringeval, B., Santini, M., Schmidt, M.,
Shindell, D. T., Simpson, I. J., Spahni, R., Steele, L. P., Strode, S. A.,
Sudo, K., Szopa, S., van der Werf, G. R., Voulgarakis, A., van Weele, M.,
Weiss, R. F., Williams, J. E., and Zen, G.: Three decades of global methane
sources and sinks, Nat. Geosci., 6, 813–823, 2013.Kort, E. A., Eluszkiewicz, J., Stephens, B. B., Miller, J. B., Gerbig, C.,
Nehrkorn, T., Daube, B. C., Kaplan, J. O., Houweling, S., and Wofsy, S. C.:
Emissions of CH4 and N2O over the United States and Canada
based on a receptor-oriented modeling framework and COBRA-NA atmospheric
observations, Geophys. Res. Lett., 35, L18808, 10.1029/2008GL034031, 2008.Kulawik, S. S., Worden, J., Eldering, A., Bowman, K., Gunson, M.,
Osterman, G. B., Zhang, L., Clough, S., Shephard, M. W., and Beer, R.:
Implementation of cloud retrievals for Tropospheric Emission Spectrometer
(TES) atmospheric retrievals: part 1. Description and characterization of
errors on trace gas retrievals, J. Geophys. Res., 111, D24204,
10.1029/2005JD006733, 2006.
Lions, J. L.: Optimal Control of Systems Governed by Partial Differential
Equations, Springer-Verlag, Berlin, 1971.Liu, J., Bowman, K., Lee, M., Henze, D. K., Bousserez, N., Brix, H.,
Collatz, G., Menemenlis, D., Ott, L., Pawson, S., Jones, D., and Nassar, R.:
Carbon monitoring system flux estimation and attribution: impact of
ACOS-GOSAT XCO2 sampling on the inference of terrestrial biospheric
sources and sinks, Tellus B, 66, 22486, 10.3402/tellusb.v66.22486, 2014.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,
doi:10.5194/acp-13-9917-2013,
2013.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, 2008.
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., Montzkad, S. A.,
Nehrkornf, T., and Sweene, C.: Anthropogenic emissions of methane in the
United States, P. Natl. Acad. Sci. USA, 110, 20018–20022, 2013.
Miller, S. M., Worthy, D. E., Michalak, A. M., Wofsy, S. C., Kort, E. A.,
Havice, T. C., Andrews, A. E., Dlugokencky, E. J., Kaplan, J. O.,
Levi, P. J., Tian, H., and Zhang, B.: Observational constraints on the
distribution, seasonality, and environmental predictors of North American
boreal methane emissions, Global Biogeochem. Cy., 28, 146–160, 2014.
Morin, T. H., Bohrer, G., Naor-Azrieli, L., Mesi, S., Kenny, W. T.,
Mitsch, W. J., and Schaefer, K. V. R.: The seasonal and diurnal dynamics of
methane flux at a created urban wetland, Ecol. Eng., 72, 74–83, 2014.
Myhre, G. and Shindell, D.: Climate Change 2013: The Physical Science Basis,
Intergovernmental Panel on Climate Change (IPCC), Chap. 8, Cambridge University
Press,
2013.Parker, R., Boesch, H., Cogan, A., Fraser, A., Feng, L., Palmer, P. I.,
Messerschmidt, J., Deutscher, N., Griffith, D. W., Notholt, J.,
Wennberg, P. O., and Wunch, D.: Methane observations from the Greenhouse
Gases Observing SATellite: comparisonn to ground-based TCCON data and model
calculations, Geophys. Res. Lett., 38, L15807, 10.1029/2011GL047871,
2011.Pickett-Heaps, C. A., Jacob, D. J., Wecht, K. J., Kort, E. A., Wofsy, S. C.,
Diskin, G. S., Worthy, D. E. J., Kaplan, J. O., Bey, I., and Drevet, J.:
Magnitude and seasonality of wetland methane emissions from the Hudson Bay
Lowlands (Canada), Atmos. Chem. Phys., 11, 3773–3779,
doi:10.5194/acp-11-3773-2011,
2011.Polonsky, I. N., O'Brien, D. M., Kumer, J. B., O'Dell, C. W., and the geoCARB
Team: Performance of a geostationary mission, geoCARB, to measure CO2,
CH4 and CO column-averaged concentrations, Atmos. Meas. Tech., 7,
959–981, 10.5194/amt-7-959-2014, 2014.Rayner, P. J., Utembe, S. R., and Crowell, S.: Constraining regional
greenhouse gas emissions using geostationary concentration measurements: a
theoretical study, Atmos. Meas. Tech., 7, 3285–3293,
doi:10.5194/amt-7-3285-2014,
2014.
Shindell, D., Kuylenstierna, J. C., Vignati, E., van Dingenen, R., Amann, M.,
Klimont, Z., Anenberg, S. C., Muller, N., Janssens-Maenhout, G., Raes, F.,
Schwartz, J., Faluvegi, G., Pozzoli, L., Kupiainen, K., Hoglund-Isaksson, L.,
Emberson, L., Streets, D., Ramanathan, V., Hicks, K., Oanh, N., Milly, G.,
Williams, M., Demkine, V., and Fowler, D.: Simultaneously mitigating
near-term climate change and improving human health and food security,
Science, 335, 183–189, 2012.Tarantola, A.: Inverse problem theory and methods for model parameter
estimation, SIAM, 10.1137/1.9780898717921, 2005.Turner, A. J. and Jacob, D. J.: Balancing aggregation and smoothing errors in
inverse models, Atmos. Chem. Phys., 15, 7039–7048,
10.5194/acp-15-7039-2015, 2015.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.van der Werf, G. R., Randerson, J. T., Giglio, L., Collatz, G. J., Mu, M.,
Kasibhatla, P. S., Morton, D. C., DeFries, R. S., Jin, Y., and
van Leeuwen, T. T.: Global fire emissions and the contribution of
deforestation, savanna, forest, agricultural, and peat fires (1997–2009),
Atmos. Chem. Phys., 10, 11707–11735,
doi:10.5194/acp-10-11707-2010,
2010.Wecht, K. J., Jacob, D. J., Wofsy, S. C., Kort, E. A., Worden, J. R.,
Kulawik, S. S., Henze, D. K., Kopacz, M., and Payne, V. H.: Validation of TES
methane with HIPPO aircraft observations: implications for inverse modeling
of methane sources, Atmos. Chem. Phys., 12, 1823–1832,
doi:10.5194/acp-12-1823-2012,
2012.
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.-Atmos., 119,
7741–7756, 2014a.Wecht, K. J., Jacob, D. J., Sulprizio, M. P., Santoni, G. W., Wofsy, S. C.,
Parker, R., Bösch, H., and Worden, J.: Spatially resolving methane
emissions in California: constraints from the CalNex aircraft campaign and
from present (GOSAT, TES) and future (TROPOMI, geostationary) satellite
observations, Atmos. Chem. Phys., 14, 8173–8184,
doi:10.5194/acp-14-8173-2014,
2014b.
West, J. J. and Fiore, A. M.: Management of tropospheric ozone by reducing methane emissions, Environ. Sci. Technol., 39, 4685–4691, 2005.West, J. J., Fiore, A. M., Horowitz, L. W., and Mauzerall, D. L.: Global
health benefits of mitigating ozone pollution with methane emission controls,
P. Natl. Acad. Sci. USA, 103, 3988–3993, 2006.
West, J. J., Fiore, A. M., and Horowitz, L. W.: Scenarios of methane emission
reductions to 2030: abatement costs and co-benefits to ozone air quality and
human mortality, Climatic Change, 114, 441–461, 2012.Worden, J., Kulawik, S., Shephard, M. W., Clough, S. A., Worden, H.,
Bowman, K., and Goldman, A.: Predicted errors of tropospheric emission
spectrometer nadir retrievals from spectral window selection, J. Geophys.
Res., 109, D09308, 10.1029/2004JD004522, 2004.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,
doi:10.5194/amt-5-397-2012,
2012.Worden, J. R., Turner, A. J., Bloom, A., Kulawik, S. S., Liu, J., Lee, M.,
Weidner, R., Bowman, K., Frankenberg, C., Parker, R., Payne, V. H.:
Quantifying lower tropospheric methane concentrations using GOSAT near-IR and
TES thermal IR measurements, Atmos. Meas. Tech., 8, 3433–3445,
doi:10.5194/amt-8-3433-2015,
2015.Xiao, Y., Logan, J. A., Jacob, D. J., Hudman, R. C., Yantosca, R., and
Blake, D. R.: Global budget of ethane and regional constraints on US sources,
J. Geophys. Res.-Atmos., 113, D21306,
doi:10.1029/2007JD009415,
2008.Yevich, R. and Logan, J. A.: An assessment of biofuel use and burning of
agricultural waste in the developing world, Global Biogeochem. Cy., 17, 1095,
doi:10.1029/2002GB001952,
2003.Zhu, L., Henze, D., Bash, J. O., Cady-Pereira, K. E., Shephard, M. W.,
Luo, M., and Capps, S. L.: Sources and impacts of atmospheric NH3:
Current understanding and frontiers for modeling, measurements, and remote
sensing in North America, Current Pollution Reports, 1, 95–116, 2015.