- About
- Editorial board
- Articles
- Special issues
- Highlight articles
- Manuscript tracking
- Subscribe to alerts
- Peer review
- For authors
- For reviewers
- EGU publications

Journal cover
Journal topic
**Atmospheric Chemistry and Physics**
An interactive open-access journal of the European Geosciences Union

Journal topic

- About
- Editorial board
- Articles
- Special issues
- Highlight articles
- Manuscript tracking
- Subscribe to alerts
- Peer review
- For authors
- For reviewers
- EGU publications

**Research article**
13 Jun 2018

**Research article** | 13 Jun 2018

Assessing the capability of different satellite observing configurations to resolve the distribution of methane emissions at kilometer scales

^{1}College of Chemistry/Department of Earth and Planetary Sciences, University of California, Berkeley, CA, USA^{2}School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA^{3}ExxonMobil Research and Engineering Company, Annandale, NJ, USA

^{1}College of Chemistry/Department of Earth and Planetary Sciences, University of California, Berkeley, CA, USA^{2}School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA^{3}ExxonMobil Research and Engineering Company, Annandale, NJ, USA

**Correspondence**: Alexander J. Turner (alexjturner@berkeley.edu)

**Correspondence**: Alexander J. Turner (alexjturner@berkeley.edu)

Abstract

Back to toptop
Anthropogenic methane emissions originate from a large number of fine-scale
and often transient point sources. Satellite observations of atmospheric
methane columns are an attractive approach for monitoring these emissions but
have limitations from instrument precision, pixel resolution, and measurement
frequency. Dense observations will soon be available in both low-Earth and
geostationary orbits, but the extent to which they can provide fine-scale
information on methane sources has yet to be explored. Here we present an
observation system simulation experiment (OSSE) to assess the capabilities of
different satellite observing system configurations. We conduct a 1-week
WRF-STILT simulation to generate methane column footprints at
1.3 × 1.3 km^{2} spatial resolution and hourly temporal resolution
over a 290 × 235 km^{2} domain in the Barnett Shale, a major
oil and gas field in Texas with a large number of point sources. We sub-sample
these footprints to match the observing characteristics of the recently
launched TROPOMI instrument (7 × 7 km^{2} pixels, 11 ppb
precision, daily frequency), the planned GeoCARB instrument
(2.7 × 3.0 km^{2} pixels, 4 ppb precision, nominal twice-daily
frequency), and other proposed observing configurations. The information
content of the various observing systems is evaluated using the Fisher
information matrix and its eigenvalues. We find that a week of TROPOMI
observations should provide information on temporally invariant emissions at
∼ 30 km spatial resolution. GeoCARB should provide information
available on temporally invariant emissions ∼ 2–7 km spatial
resolution depending on sampling frequency (hourly to daily). Improvements to
the instrument precision yield greater increases in information content than
improved sampling frequency. A precision better than 6 ppb is critical for
GeoCARB to achieve fine resolution of emissions. Transient emissions would be
missed with either TROPOMI or GeoCARB. An aspirational high-resolution
geostationary instrument with 1.3 × 1.3 km^{2} pixel resolution,
hourly return time, and 1 ppb precision would effectively constrain the
temporally invariant emissions in the Barnett Shale at the kilometer scale
and provide some information on hourly variability of sources.

Download & links

How to cite

Back to top
top
How to cite.

Turner, A. J., Jacob, D. J., Benmergui, J., Brandman, J., White, L., and Randles, C. A.: Assessing the capability of different satellite observing configurations to resolve the distribution of methane emissions at kilometer scales, Atmos. Chem. Phys., 18, 8265–8278, https://doi.org/10.5194/acp-18-8265-2018, 2018.

1 Introduction

Back to toptop
Methane is a greenhouse gas emitted by a range of natural and anthropogenic sources (Kirschke et al., 2013; Saunois et al., 2016; Turner et al., 2017). Anthropogenic methane emissions are difficult to quantify because they tend to originate from a large number of potentially transient point sources such as livestock operations, oil or gas leaks, landfills, and coal mine ventilation. Atmospheric methane observations from surface and aircraft have been used to quantify emissions (e.g., Miller et al., 2013; Caulton et al., 2014; Karion et al., 2013, 2015; Lavoie et al., 2015; Conley et al., 2016; Peischl et al., 2015, 2016; Houweling et al., 2016) but are limited in spatial and temporal coverage. Satellite measurements have dense and continuous coverage but limitations from observational errors and pixel resolution need to be understood. Here we perform an observing system simulation experiment (OSSE) to investigate the information content of different configurations of satellite instruments for observing fine-scale and transient methane sources, taking as a test case the oil and gas production sector.

Low-Earth orbit satellite observations of methane by solar backscatter in the
shortwave infrared (SWIR) have been available since 2003 from the SCIAMACHY
instrument (2003–2012; Frankenberg et al., 2005) and from the GOSAT
instrument (2009–present; Kuze et al., 2009, 2016). SWIR instruments measure
the atmospheric column of methane with near-unit sensitivity throughout the
troposphere. SCIAMACHY and GOSAT demonstrated the capability for
high-precision (<1 %) measurements of methane from
space (Buchwitz et al., 2015), but SCIAMACHY had coarse pixels
(30 × 60 km^{2} in nadir) and GOSAT has sparse coverage (10 km
diameter pixels separated by 250 km). Inverse analyses have used
observations from these satellite-based instruments to estimate methane
emissions at ∼ 100–1000 km spatial resolution
(e.g., Bergamaschi et al., 2009, 2013; Fraser et al., 2013; Monteil et al., 2013; Wecht et al., 2014a; Cressot et al., 2014; Kort et al., 2014; Turner et al., 2015, 2016a; Alexe et al., 2015; Tan et al., 2016; Buchwitz et al., 2017; Sheng et al., 2018a, b).
But such coarse resolution makes it difficult to resolve individual source
types because of spatial overlap (Maasakkers et al., 2016).

Improved observations of methane from space are expected in the near
future (Jacob et al., 2016). The TROPOMI
instrument (Veefkind et al., 2012; Butz et al., 2012; Hu et al., 2016, 2018), launched in October 2017,
will provide global mapping at 7 × 7 km^{2} nadir resolution once per
day. The GeoCARB geostationary instrument (Polonsky et al., 2014; O'Brien et al., 2016) will be
launched in the early 2020s with current design values of 3 × 3 km^{2} pixel resolution and twice-daily return time. Additional instruments are
presently in the proposal stage with improved combinations of pixel
resolution, return time, and instrument
precision (Fishman et al., 2012; Butz et al., 2015; Xi et al., 2015).

An OSSE simulates the atmosphere as it would be observed by an instrument
with a given observing configuration and error specification. Several OSSEs
have been conducted to evaluate the potential of satellite observations to
quantify methane sources, but they have been conducted at either coarse
(∼ 50 × 50 km^{2}) spatial resolution (Wecht et al., 2014b; Bousserez et al., 2016)
or assumed idealized flow conditions (Bovensmann et al., 2010; Rayner et al., 2014). Here we
use a 1-week simulation of atmospheric methane with 1.3 × 1.3 km^{2}
resolution over a 290 × 235 km^{2} domain to simulate continuous and
transient emissions in the Barnett Shale region of Texas, and from there we
quantify the capability of different satellite instrument configurations to
resolve and quantify these sources at the kilometer and hourly scales. Our
choice of scales is guided by the resolution of the planned satellite
observations, and our choice of the Barnett Shale is guided by the
availability of a high-resolution emission inventory for the
region (Lyon et al., 2015). The pattern and density of methane emissions in
the Barnett Shale is typical of other source regions in the
US (Maasakkers et al., 2016).

2 High-resolution OSSE environment

Back to toptop
We simulate atmospheric methane concentrations over the Barnett Shale in
Texas at 1.3 × 1.3 km^{2} horizontal resolution for the period of
19–25 October 2013 using a framework similar to that of Turner et al. (2016b).
The simulation uses version 3.5 of the Weather Research and Forecasting (WRF)
model (Skamarock et al., 2008) over a succession of nested domains (left panel in
Fig. 1) with 1.3 × 1.3 km^{2} spatial resolution in
the innermost domain covering 290 × 235 km^{2}. There are 50
vertical layers up to 100 hPa. Boundary-layer physics are represented with
the Mellor–Yamada–Janjíc scheme and the land surface is represented
with the five-layer slab model (Skamarock et al., 2008). The simulation is
initialized with assimilated meteorological observations from the North
American Regional Reanalysis
(https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/north-american-regional-reanalysis-narr,
last access: 4 May 2018).
Overlapping 30 h forecasts were initialized every 24 h at
00:00 UTC and the first 6 h of each forecast were discarded to allow for
model spinup. Grid nudging was used in the outermost domain.

WRF meteorology is used to drive the Stochastic Time-Inverted Lagrangian
Transport (STILT) model (Lin et al., 2003). STILT is a Lagrangian particle
dispersion model. It advects an ensemble of particles backward in time from
selected receptor locations, using the archived hourly WRF wind fields and
boundary-layer heights. STILT calculates the footprint for the receptors; a
spatiotemporal map of the sensitivity of observations to emissions
contributing to the concentration at each selected receptor location and
time. We use STILT to calculate 10-day footprints for hourly column
concentrations at 1.3 × 1.3 km^{2} resolution over a
70 × 70 km^{2} domain in the innermost WRF nest, tracking the
resulting footprints over a 290 × 235 km^{2} domain (right panel in
Fig. 1). With this system we examine the constraints on
emissions over the 290 × 235 km^{2} domain provided by dense SWIR
satellite observations (over the 70 × 70 km^{2} domain) that have
up to 1.3 km pixel resolution and hourly daytime frequency. Footprints for
each column are obtained by releasing 100 STILT particles from vertical
levels centered at 28, 97, 190, and 300 m above the surface and 8 additional
levels up to 14 km altitude spaced evenly on a pressure grid. The column
footprints are then constructed by summing the pressure-weighted
contributions from individual levels, using a typical SWIR averaging kernel
taken from Worden et al. (2015) with near-uniformity in the troposphere and
correcting for water vapor (see Appendix A in O'Dell et al., 2012).

The footprint for the *i*^{th} receptor location and time can be
expressed as a vector ${\mathit{h}}_{i}={\left(\partial {y}_{i}/\partial \mathit{x}\right)}^{T}$ describing the sensitivity
of the column concentration *y* at that receptor location and time to the
emission fluxes ** x** over the 290 × 235 km

$$\begin{array}{}\text{(1)}& {y}_{i}={\mathit{h}}_{i}\mathit{x}+{b}_{i},\end{array}$$

where *b*_{i} is the background column concentration upwind of the
290 × 235 km^{2} domain. We can then write the full set of observations
as a vector ** y** of length

$$\begin{array}{}\text{(2)}& \mathit{y}=\mathbf{H}\mathit{x}+\mathit{b},\end{array}$$

where ** b** is the background vector with elements

Figure 2 shows the sum of all column footprints produced on
individual days for the 70 × 70 km^{2} observation domain. Computing
these high-resolution footprints was a non-trivial computational task and
ultimately yielded more than 4 Tb of footprints for the week of
pseudo-satellite observations in the Barnett Shale. The footprints show large
variability from day to day over the course of the week, reflecting
meteorological variability. For example, winds are from the north on 19 October and from the south on 20 October.
The winds are weak on 24 October, resulting in a strong local contribution to the footprint. Summing the
footprints over the course of the week (bottom right panel of
Fig. 2), we find that the observations are mainly sensitive
to the core 70 × 70 km^{2} domain where they are made, with a diffuse
sensitivity over the outer 290 × 235 km^{2} domain. Additional
observations within the outer domain would need to be considered to constrain
emissions in that domain. However, information on emissions in the
70 × 70 km^{2} core domain is mainly contributed by observations within
the domain. Thus our focus will be to determine the capability of the
observations in the 70 × 70 km^{2} domain to constrain emissions within
that same domain, but we include the outer 290 × 235 km^{2} domain in
our footprint analysis for completeness in accounting of information.
Previous work Turner et al. (2016b, Supplement Sect. 6.1) investigated
the impact of domain size on error reduction for WRF-STILT inversions in
California's Bay Area and found that it had a negligible impact

The footprint information can be combined with an emission inventory for the
290 × 235 km^{2} domain to generate a field of column concentrations
over the 70 × 70 km^{2} domain as would be observed from satellite. For this purpose we
use the Environmental Defense Fund (EDF) inventory for the
Barnett Shale in October 2013 at 4 × 4 km^{2} resolution compiled by
Lyon et al. (2015). We downscale the EDF inventory by uniform attribution from
4 × 4 km^{2} to 1.3 × 1.3 km^{2} spatial resolution. The
inventory is shown in Fig. 3 and includes contributions
from oil and gas production, livestock operations, landfills, and urban emissions
from the Dallas–Fort Worth area. It provides mean monthly values with no
temporal resolution, but presumes that some sources will behave as sporadic
large transients (Zavala-Araiza et al., 2015). Figure 4 shows an example of
the methane column enhancements above background (**H**** x**)
computed at 09:00 local time on 23 October. We find enhancements in the range of
0–10 ppb due to emissions within the 290 × 235 km

3 Information content of different satellite observing systems

Back to toptop
^{a} Hourly observations are 10
times per day at 08:00–17:00 LT,
twice-daily observations are at 10:00 and 14:00 LT, and daily observations are at 13:00 LT.^{b} Aspirational instrument with the highest observation
frequency and pixel resolution that can be simulated within our OSSE
framework.

We aim to determine the information content from different satellite-based
observing systems regarding the spatial and temporal distribution of
emissions in the Barnett Shale. We consider both steady and potentially
transient emissions with five different satellite observing configurations
(Table 1). TROPOMI (global daily mapping,
7 × 7 km^{2} nadir pixel resolution, 11 ppb precision; Veefkind et al., 2012)
was launched in October 2017 and is expected to provide an operational data
stream by the end of 2018. GeoCARB (geostationary, 2.7 × 3.0 km^{2} pixel
resolution, 4 ppb precision; O'Brien et al., 2016) is planned for launch
in the early 2020s and its observation schedule is still under discussion
with a tentative design for observations twice daily; here we examine
different return frequencies of hourly, twice daily, and daily. Finally, the
hypothetical “hi-res” configuration assumes geostationary hourly
observations at the 1.3 × 1.3 km^{2} pixel resolution of our WRF
simulation and with 1 ppb precision; it represents an aspirational system
that combines the frequent return time, fine pixel resolution, and high
precision of instruments presently at the proposal
stage (Bovensmann et al., 2010; Fishman et al., 2012; Xi et al., 2015). All configurations are filtered
for cloudy scenes.

The various satellite observing configurations of
Table 1 differ in their return frequency, pixel
resolution, and instrument precision. The benefit of improving any of these
attributes may be limited by error in the forward model used in the inverse
analysis (i.e., the Jacobian matrix **H**) and by spatial or temporal
correlation of the errors. These limitations are described by the model–data
mismatch error covariance matrix (**R**) including summed
contributions from the instrument, forward model, and representation
errors (Turner and Jacob, 2015; Brasseur and Jacob, 2017). Representation errors are negligible
here because the instrument pixels are commensurate or coarser than the model
grid resolution. Instrument error (i.e., precision) is listed in
Table 1. Forward model error is estimated by computing
STILT footprints for a subset of the meteorological period using the Global
Data Assimilation System (GDAS;
https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/global-data-assimilation-system-gdas,
last access: 4 May 2018) applying the two sets of footprints to either the
EDF methane inventory (Fig. 3; Lyon et al., 2015) or the
gridded EPA inventory (Maasakkers et al., 2016), and computing semivariograms of
differences in column concentrations. From this we obtain a forward model
error standard deviation of 4 ppb with an error correlation length scale of
40 km. We assume a temporal model error correlation length of 2 h.
Sheng et al. (2018b) previously derived a temporal model error correlation length
of 5 h in simulation of TCCON methane column observations at
25 km resolution, and we expect our correlation length to be shorter
because of the finer resolution.

Bayesian inference is commonly used when estimating methane emissions with atmospheric observations, allowing for errors in the observations and in the prior estimates:

$$\begin{array}{}\text{(3)}& P\left(\mathit{x}\right|\mathit{y})\propto P(\mathit{y}\left|\mathit{x}\right)P\left(\mathit{x}\right),\end{array}$$

where *P*(** x**|

$$\begin{array}{ll}\text{(4)}& {\displaystyle}P\left(\mathit{x}\right|\mathit{y})\propto & {\displaystyle}\mathrm{exp}\left\{-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left(\mathit{y}-\mathbf{H}\mathit{x}\right)}^{T}{\mathbf{R}}^{-\mathrm{1}}\left(\mathit{y}-\mathbf{H}\mathit{x}\right)\right.{\displaystyle}& {\displaystyle}\left.-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left(\mathit{x}-{\mathit{x}}_{a}\right)}^{T}{\mathbf{B}}^{-\mathrm{1}}\left(\mathit{x}-{\mathit{x}}_{a}\right)\right\},\end{array}$$

where **B** is the *n*×*n* prior error covariance matrix and
*x*_{a} is the *n*×1 vector of prior fluxes. The most probable
solution is obtained by minimizing the cost function:

$$\begin{array}{ll}\text{(5)}& {\displaystyle}\mathcal{J}\left(\mathit{x}\right)=& {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left(\mathit{y}-\mathbf{H}\mathit{x}\right)}^{T}{\mathbf{R}}^{-\mathrm{1}}\left(\mathit{y}-\mathbf{H}\mathit{x}\right){\displaystyle}& {\displaystyle}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left(\mathit{x}-{\mathit{x}}_{a}\right)}^{T}{\mathbf{B}}^{-\mathrm{1}}\left(\mathit{x}-{\mathit{x}}_{a}\right),\end{array}$$

yielding the posterior estimate ($\widehat{\mathit{x}}$):

$$\begin{array}{}\text{(6)}& \widehat{\mathit{x}}={\mathit{x}}_{a}+\underset{\text{posterior error covariance matrix}}{\underbrace{{\left({\mathbf{H}}^{T}{\mathbf{R}}^{-\mathrm{1}}\mathbf{H}+{\mathbf{B}}^{-\mathrm{1}}\right)}^{-\mathrm{1}}}}{\mathbf{H}}^{T}{\mathbf{R}}^{-\mathrm{1}}\left(\mathit{y}-\mathbf{H}\mathit{x}\right)\end{array}$$

with an *n*×*n* posterior error covariance matrix:

$$\begin{array}{}\text{(7)}& \mathbf{Q}=(\underset{\text{observations}}{\underbrace{{\mathbf{H}}^{T}{\mathbf{R}}^{-\mathrm{1}}\mathbf{H}}}+\underset{\text{prior}}{\underbrace{{\mathbf{B}}^{-\mathrm{1}}}}{)}^{-\mathrm{1}}\end{array}$$

that characterizes the uncertainty in the solution. The first term in the posterior covariance matrix is known as the Fisher information matrix: $\mathcal{F}={\mathbf{H}}^{T}{\mathbf{R}}^{-\mathrm{1}}\mathbf{H}$ (see, for example, Rodgers, 2000; Tarantola, 2004).

Comparison between 𝓕 and **B**^{−1} identifies the
extent to which the observations reduce the uncertainty in the fluxes.
Specifically, the number of pieces of information on emissions acquired to
better than measurement error is the number of eigenvalues of
${\mathbf{B}}^{\mathrm{1}/\mathrm{2}}\mathcal{F}{\mathbf{B}}^{\mathrm{1}/\mathrm{2}}$ that are greater than
unity (Rodgers, 2000). As such, the Fisher information matrix and prior
error covariance matrix can quantify the effective rank of the observing
system.

A drawback with this formulation of the information content is that it relies on the assumption of a Gaussian prior pdf. A number of papers have suggested that the pdf of methane emissions from a given source may be skewed, with a “fat tail” of transient high emissions (e.g., Brandt et al., 2014; Zavala-Araiza et al., 2015; Frankenberg et al., 2016). Alternate formulations for the cost function to be minimized may include no prior information (least-squares regression), a prior constraint that promotes a sparse solution (e.g., Candes and Wakin, 2008), a prior constraint based on frequentist regularization approaches (such as LASSO regression or Tikhonov regularization), or a prior constraint based on the spatial patterns of emissions rather than their magnitudes (geostatistical inversion). Table 2 lists the corresponding formulations. From Table 2 we see that the observation term is the same in all cases. Thus the Fisher information matrix provides a general measure of the information content provided by an observing system, independent of the form of the prior constraint, and we use it in what follows as a measure of the information content.

^{a} *γ* is the
regularization parameter for LASSO regression and Tikhonov regularization.
**G** is a matrix with columns corresponding to different spatial
datasets and ** β** is a vector of drift coefficients for the spatial
datasets. Other variables defined in the text.

The Fisher information matrix is an *n*×*n* matrix. Each of its *n*
eigenvectors represent an independent normalized emission flux pattern and
the corresponding eigenvalues are the inverses of the error variances
associated with that pattern. A more useful way of stating this is that the
inverse square root of the *i*^{th} eigenvalue of
𝓕 represents the flux threshold *f*_{i} needed for the
observations to be able to constrain the emission flux pattern represented by
the *i*^{th} eigenvector. Whether that flux threshold is useful
depends on the magnitude of the emissions, and this can be assessed for the
problem at hand. Thus the eigenanalysis of the Fisher information matrix
gives us a general estimate of the capability of an observing system to
quantify emissions, which can then be applied to any actual *n*×*n*
emission field.

For a given emission field, we may expect that some of the *n* emission flux
patterns will be usefully constrained by the observing system while others
are not. The number of patterns that are usefully constrained represents the
number ℐ≤*n* pieces of information on emissions provided by
the observing system. We will equivalently refer to it as the rank of the
Fisher information matrix. This is determined by comparing the eigenvalues of
an emission inventory (*e*_{i}) to the flux thresholds. The number of *e*_{i}
larger than the corresponding *f*_{i} provides a cut-off to estimate
ℐ:

$$\begin{array}{}\text{(8)}& \mathcal{I}=\sum _{i}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\left\{\begin{array}{ll}\mathrm{1},& {e}_{i}>{f}_{i}\\ \mathrm{0},& {e}_{i}\le {f}_{i}\end{array}\right.\end{array}$$

In the case of Bayesian inference, this is roughly equivalent to the degrees of freedom for signal with a diagonal prior error covariance matrix and a relative uncertainty of 100 %. But the eigenanalysis of the Fisher information matrix provides a more general approach of the capability of an observing system that can be confronted to any prior constraint and allows intercomparison of different observing system configurations.

There is an inconsistency in this formulation of ℐ:
𝓕 and **B**^{−1} have different eigenspaces. In this
work we have chosen to treat these matrices separately because, in practice,
it is computationally infeasible to directly compute the eigenvalues of the
matrix product if *n* is large, as in the case here of constraining hourly
emissions of the spatially distributed inventory. This inconsistency results
in our estimate of ℐ likely being an upper bound on the
information content (see Appendix for details).

4 Comparing different satellite configurations

Back to toptop
The eigenanalysis of Sect. 3 allows us to intercompare the
value of different satellite configurations for resolving the fine-scale
patterns of methane emissions within a given domain. Here we apply it to the
Barnett Shale domain of Sect. 2. We consider two limiting cases: Case 1
assumes the emissions to be temporally invariant and Case 2 assumes the
emissions to vary hourly with no temporal correlation. In Case 1 the
problem is typically overdetermined (*m*>*n*), depending on the satellite
configuration, and the maximum rank of 𝓕 is *n* (the number
of emission grid cells). In Case 2 the problem is underdetermined (*m*<*n*) and the maximum rank of 𝓕 is *m* (the number of
observations).

In both Case 1 and 2, the observations only provide useful
information (as defined by Eq. 8) if the signal is larger than
the noise, as diagnosed by the *e*_{i}>*f*_{i} criterion of Eq. 8.
Here the emissions are the downscaled EDF inventory, which includes 40 140
grid cells in the 290 × 235 km^{2} inversion domain (*n*= 40 140 in
Case 1 with temporally invariant emissions) but only 2 601 of those grid
cells are within the 70 × 70 km^{2} observation domain (dashed orange
box in Fig. 1), where we might expect the observations to
provide the strongest constraints. In Case 2 with temporally variable
emissions we have $n=\mathrm{40}\phantom{\rule{0.125em}{0ex}}\mathrm{140}\times \mathrm{24}=\mathrm{963}\phantom{\rule{0.125em}{0ex}}\mathrm{360}$ grid cells for a single
day.

Figure 5 shows the ensemble of flux thresholds for the five satellite configurations, assuming temporally invariant emissions. The ranked flux patterns are on the abscissa; leading flux patterns correspond to larger patterns of variability (e.g., regional-scale emissions), and the trailing flux patterns correspond to fine-scale variability. The corresponding flux thresholds are on the ordinate. The flux threshold is lowest for the leading flux patterns and largest for the trailing flux patterns. This means that the regional-scale emissions are easiest to quantify and the finer-scale emissions are increasingly difficult to quantify. The information content (ℐ) is obtained from the intersection of the flux thresholds (colored lines) with the eigenvalues from the emission inventory (black line). A higher information content means that finer scales of emission variability can be detected.

From Fig. 5, we see that a week of TROPOMI observations
provides five pieces of information on emissions for the 70 × 70 km^{2}
core domain out of a possible 2601 pieces of information describing the
emissions on the 1.3 × 1.3 km^{2} grid. The actual pieces of information
are the eigenvectors of the Fisher information matrix, and the ranked
eigenvectors describe gradually finer patterns of variability from
70 × 70 to 1.3 × 1.3 km^{2}. The *k*^{th} ranked eigenvector
may be assumed to describe an emission pattern of dimension 70$/\sqrt{k}$,
implying that TROPOMI can resolve emissions on a 30 km scale.

The three GeoCARB configurations provide 98–961 pieces of information
dependent on whether the observations are daily, twice daily, or hourly.
Following the above assumption, this corresponds to resolving emissions on a
∼ 2–7 km scale. Hourly observations provide 10 times more information (as
defined by Eq. 8) on emission patterns than daily observations,
and 3 times more than twice-daily observations (the default configuration of
GeoCARB). Remarkably, more is gained by going from daily to twice daily
(factor of 3.4) than going from twice daily to hourly (factor of 2.9)
because of the temporal error correlation in the transport model. The
aspirational hi-res satellite configuration provides 2 221 pieces of
information on temporally invariant sources, corresponding to 85 % of the
flux patterns in the 70 × 70 km^{2} observation region, which means that
much of the spatial variability in the 1.3 × 1.3 km^{2} emissions in the
Barnett Shale is resolved.

Figure 6 further quantifies the importance of instrument
precision and return frequency for the GeoCARB pixel resolution of
2.7 × 3.0 km^{2}. It shows the flux thresholds for a set of
configurations where the instrument precision is varied from 0 to 14 ppb and
the return frequency is varied from 1 to 10 returns per day. We find that
instrument precision is more important than return frequency for increasing
the information content from the observations.

In Case 2 we assume that the methane sources in individual pixels vary in
time on an hourly basis with no correlation from one hour to the next, making
the problem generally underdetermined (*m*<*n*) for all satellite
configurations. Here we aim to determine the ability of the satellite
observations to quantify the hourly emissions over the spatial patterns
defined by the eigenvectors of 𝓕 and making no assumption as
to the persistence of those emissions. We treat each day independently and
compute the eigenvalues of the Fisher information matrix for each day.
Figure 7 shows the flux thresholds for the five
satellite configurations on a representative day. From
Fig. 7, we see that TROPOMI is unable to provide any
information on hourly emissions in the Barnett Shale. The three GeoCARB
configurations provide 2–54 pieces of information.
Figure 8 evaluates the impact of sampling frequency and
instrument precision for the GeoCARB configurations. As with the temporally
invariant case, we find that instrument precision is more important for
increasing the information content. The aspirational “hi-res” configuration
(shown in Fig. 7) is the only configuration that is able
to provide substantial information (458 pieces of information) on temporally
variable emissions.

Figure 9 summarizes the findings from
Figs. 6 and 8. It compares the
information content ℐ from configurations with
2.7 × 3.0 km^{2} spatial resolution (GeoCARB) as the instrument
precision and return frequency are varied from 0 to 14 ppb and 1 to 10
returns per day, respectively, for both temporally variable and constant
sources. Uncertainty of ℐ is estimated by randomly sampling *e*_{i}
from the ensemble of emission inventory eigenvalues and comparing to *f*_{i} in
Eq. 8. For the temporally invariant sources (Case 1), we find
considerable increases in information content for instrument precisions
better than 6 ppb (top left panel in Fig. 9) and an
approximately linear relationship between information content and return
frequency (top right panel in Fig. 9). The satellite
configurations provide considerably less information for the temporally
variable sources (Case 2). We find that satellite configurations with
instrument precision worse than 6 ppb provide no information on temporally
variable sources (bottom left panel in Fig. 9). As with the
temporally invariant case, we find an approximately linear relationship
between information content and return frequency (bottom right panel in
Fig. 9). From this, we conclude that a GeoCARB-like
instrument would greatly benefit from having an instrument precision better
than 6 ppb.

5 Conclusions

Back to toptop
We conducted an observing system simulation experiment (OSSE) to evaluate the
potential of different satellite observation systems for atmospheric methane
to quantify methane emissions at kilometer scale. This involved a 1-week
WRF-STILT simulation of atmospheric methane columns with 1.3 × 1.3 km^{2}
spatial resolution over the 290 × 235 km^{2} Barnett Shale domain
to quantify the information content of different satellite instrument
configurations for resolving the kilometer-scale distribution of methane
emissions within that domain. We evaluated the information content of the
different satellite observing systems through an eigenanalysis of the Fisher
information matrix 𝓕, which characterizes the capability of
an observing system independently of the form of the prior information. The
eigenvalues of 𝓕 define the emission flux thresholds for
detection of emission patterns down to 1.3 km in scale as defined by the
eigenvectors. Here we put these flux thresholds in context of the
high-resolution EDF emission inventory for the Barnett Shale to quantify the
information content from different satellite observing configurations. The
same approach could be readily used for different observation domains and
different prior inventories.

We find from this analysis that the recently launched TROPOMI satellite
instrument (low-Earth orbit, 7 × 7 km^{2} pixels, daily return time,
11 ppb precision) should be able to constrain the mean emissions in the Barnett
Shale and provide some coarse-resolution information on the distribution of
temporally invariant emissions at ∼ 30 km scales. The planned GeoCARB
instrument (geostationary orbit, 2.7 × 3.0 km^{2} pixels, twice-daily
return time, 4 ppb precision) will provide 50 times more information than
TROPOMI. The observing frequency of GeoCARB is still under discussion; we
find that twice-daily observations triple the information content relative to
daily observations, while hourly observations allow another tripling. The 4
ppb precision of GeoCARB is well adapted to the magnitude of methane sources;
we find that a precision larger than 6 ppb would considerably decrease the
information content. An aspirational “hi-res” instrument using attributes
of currently proposed instruments (geostationary orbit, 1.3 × 1.3 km^{2} pixels,
hourly return time, 1 ppb precision) can resolve much of the
kilometer-scale spatial distribution in the EDF inventory. This assumes that
the emissions are constant in time or that their temporal variability is
known. Resolving hourly variable emissions at the kilometer scale will be
very limited even with the aspirational “hi-res” instrument.

Data availability

Back to toptop
Data availability.

The source code for all models is publicly available through the cited references.

Appendix A: Computing the information content

Back to toptop
We treat 𝓕 and **B**^{−1} separately because
it is computationally infeasible to compute the eigenvalues of the matrix
product when we attempt to resolve hourly emissions as *n*>10^{6} and both
𝓕 and **B**^{−1} are *n*×*n* matrices.
This separation of 𝓕 and **B**^{−1} results
in our estimate of ℐ likely being an upper bound on the
information content. This follows from Bhatia (1997) who prove that
$\mathit{\lambda}\left(\mathbf{CD}\right){\prec}_{w}{\mathit{\lambda}}^{\downarrow}\left(\mathbf{C}\right)\cdot {\mathit{\lambda}}^{\downarrow}\left(\mathbf{D}\right)$, where **C** and
**D** are Hermitian positive definite matrices,
*λ*^{↓}(X) denotes the vector of eigenvalues
of **X** in decreasing order, ≺_{w} is the weak majorization
preorder, and $\mathbf{p}\times \mathbf{q}=\left({p}_{\mathrm{1}}{q}_{\mathrm{1}},\mathrm{\dots},{p}_{n}{q}_{n}\right)$. Therefore, directly computing the eigenvalues of
${\mathbf{B}}^{\mathrm{1}/\mathrm{2}}\mathcal{F}{\mathbf{B}}^{\mathrm{1}/\mathrm{2}}$, as
Rodgers (2000) suggests for the Bayesian inference case with Gaussian
errors, would likely yield fewer eigenvalues larger than unity than our
estimate.

In the case of temporally variable emissions, the system is generally
underdetermined (*m*<*n*) and we can use a singular value decomposition to
efficiently compute the eigenvalues of 𝓕. For an
*m*×*n* real matrix **A**, the non-zero singular values of
**A**^{T}**A** and **AA**^{T} are identical even
though the singular vectors are different (see, for
example, Rodgers, 2000) but the dimensions of these two matrices are
*n*×*n* and *m*×*m*, respectively, and the eigenvalues can be
computed from the square root of the non-zero singular values. We can write
$\mathcal{F}={\widehat{\mathbf{H}}}^{T}\widehat{\mathbf{H}}$, where
$\widehat{\mathbf{H}}={\mathbf{L}}^{-\mathrm{1}}\mathbf{H}$ is the pre-whitened Jacobian
and **L** is a lower triangular matrix from a Cholesky decomposition
of **R** (such that **R**=**LL**^{T}). Thus, the
eigenvalues of 𝓕 can be obtained by analysis of either
${\widehat{\mathbf{H}}}^{T}\widehat{\mathbf{H}}$ (an *n*×*n* matrix) or
$\widehat{\mathbf{H}}{\widehat{\mathbf{H}}}^{T}$ (an *m*×*m* matrix).

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

Back to toptop
Acknowledgements.

This work was supported by the ExxonMobil Research and Engineering Company
and the US Department of Energy (DOE) Advanced Research Projects Agency –
Energy (ARPA-E). A. J. Turner is supported as a Miller Fellow with the Miller
Institute for Basic Research in Science at UC Berkeley. This research used
the Savio computational cluster resource provided by the Berkeley Research
Computing program at the University of California, Berkeley (supported by the
UC Berkeley Chancellor, Vice Chancellor for Res., and Chief Information
Officer). This research also used resources from the National Energy Research
Scientific Computing Center, which is supported by the Office of Science of
the DOE under contract no. DE-AC02-05CH11231. We also
acknowledge high-performance computing support from Cheyenne
(doi:10.5065/D6RX99HX) provided by NCAR's Computational and Information
Systems Laboratory, sponsored by the National Science
Foundation.

Edited by: Martin
Heimann

Reviewed by: two anonymous referees

References

Back to toptop
Alexe, 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, https://doi.org/10.5194/acp-15-113-2015, 2015. a

Bergamaschi, P., Frankenberg, C., Meirink, J. F., Krol, M., Villani, M. G.,
Houweling, S., Dentener, F., Dlugokencky, E. J., Miller, J. B., Gatti, L. V.,
Engel, A., and Levin, I.: Inverse modeling of global and regional CH_{4}
emissions using SCIAMACHY satellite retrievals, J. Geophys.
Res., 114, https://doi.org/10.1029/2009jd012287, 2009. a

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 CH_{4} in the first decade of the 21st century: Inverse modeling
analysis using SCIAMACHY satellite retrievals and NOAA surface measurements,
J. Geophys. Res.-Atmos., 118, 7350–7369,
https://doi.org/10.1002/jgrd.50480, 2013. a

Bhatia, R.: Matrix Analysis, Graduate Texts in Mathematics, Springer, New York, 1997. a

Bousserez, N., Henze, D. K., Rooney, B., Perkins, A., Wecht, K. J., Turner, A. J., Natraj, V., and Worden, J. R.: Constraints on methane emissions in North America from future geostationary remote-sensing measurements, Atmos. Chem. Phys., 16, 6175–6190, https://doi.org/10.5194/acp-16-6175-2016, 2016. a

Bovensmann, H., Buchwitz, M., Burrows, J. P., Reuter, M., Krings, T., Gerilowski, K.,
Schneising, O., Heymann, J., Tretner, A., and Erzinger, J.: A remote sensing technique
for global monitoring of power plant CO_{2} emissions from space and related applications,
Atmos. Meas. Tech., 3, 781–811, https://doi.org/10.5194/amt-3-781-2010, 2010. a, b

Brandt, A. R., Heath, G. A., Kort, E. A., O'Sullivan, F., Petron, G., Jordaan, S. M., Tans, P., Wilcox, J., Gopstein, A. M., Arent, D., Wofsy, S., Brown, N. J., Bradley, R., Stucky, G. D., Eardley, D., and Harriss, R.: Energy and environment. Methane leaks from North American natural gas systems, Science, 343, 733–735, https://doi.org/10.1126/science.1247045, 2014. a

Brasseur, G. P. and Jacob, D. J.: Modeling of Atmospheric Chemistry, Princeton University Press, Princeton, NJ, 2017. a

Buchwitz, M., Reuter, M., Schneising, O., Boesch, H., Guerlet, S., Dils, B.,
Aben, I., Armante, R., Bergamaschi, P., Blumenstock, T., Bovensmann, H.,
Brunner, D., Buchmann, B., Burrows, J. P., Butz, A., Chédin, A., Chevallier,
F., Crevoisier, C. D., Deutscher, N. M., Frankenberg, C., Hase, F., Hasekamp,
O. P., Heymann, J., Kaminski, T., Laeng, A., Lichtenberg, G., De Maziére,
M., Noël, S., Notholt, J., Orphal, J., Popp, C., Parker, R., Scholze, M.,
Sussmann, R., Stiller, G. P., Warneke, T., Zehner, C., Bril, A., Crisp, D.,
Griffith, D. W. T., Kuze, A., O'Dell, C., Oshchepkov, S., Sherlock, V., Suto,
H., Wennberg, P., Wunch, D., Yokota, T., and Yoshida, Y.: The Greenhouse Gas
Climate Change Initiative (GHG-CCI): Comparison and quality assessment of
near-surface-sensitive satellite-derived CO_{2} and CH_{4} global data sets,
Remote Sens. Environ., 162, 344–362,
https://doi.org/10.1016/j.rse.2013.04.024, 2015. a

Buchwitz, M., Schneising, O., Reuter, M., Heymann, J., Krautwurst, S., Bovensmann, H., Burrows, J. P., Boesch, H., Parker, R. J., Somkuti, P., Detmers, R. G., Hasekamp, O. P., Aben, I., Butz, A., Frankenberg, C., and Turner, A. J.: Satellite-derived methane hotspot emission estimates using a fast data-driven method, Atmos. Chem. Phys., 17, 5751–5774, https://doi.org/10.5194/acp-17-5751-2017, 2017. a

Butz, A., Galli, A., Hasekamp, O., Landgraf, J., Tol, P., and Aben, I.: TROPOMI
aboard Sentinel-5 Precursor: Prospective performance of CH_{4} retrievals for
aerosol and cirrus loaded atmospheres, Remote Sens. Environ., 120,
267–276, https://doi.org/10.1016/j.rse.2011.05.030, 2012. a

Butz, A., Orphal, J., Checa-Garcia, R., Friedl-Vallon, F., von Clarmann, T., Bovensmann, H., Hasekamp, O., Landgraf, J., Knigge, T., Weise, D., Sqalli-Houssini, O., and Kemper, D.: Geostationary Emission Explorer for Europe (G3E): mission concept and initial performance assessment, Atmos. Meas. Tech., 8, 4719–4734, https://doi.org/10.5194/amt-8-4719-2015, 2015. a

Candes, E. J. and Wakin, M. B.: An introduction to compressive sampling, IEEE Signal Processing Magazine, 25, 21–30, https://doi.org/10.1109/Msp.2007.914731, 2008. a

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, https://doi.org/10.1073/pnas.1316546111, 2014. a

Conley, S., Franco, G., Faloona, I., Blake, D. R., Peischl, J., and Ryerson, T. B.: Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA, Science, 351, 1317–20, https://doi.org/10.1126/science.aaf2348, 2016. a

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, https://doi.org/10.5194/acp-14-577-2014, 2014. a

Fishman, J., Iraci, L. T., Al-Saadi, J., Chance, K., Chavez, F., Chin, M., Coble, P., Davis, C., DiGiacomo, P. M., Edwards, D., Eldering, A., 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., Newchurch, 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, https://doi.org/10.1175/bams-d-11-00201.1, 2012. a, b

Frankenberg, C., Meirink, J. F., van Weele, M., Platt, U., and Wagner, T.: Assessing methane emissions from global space-borne observations, Science, 308, 1010–1014, https://doi.org/10.1126/science.1106644, 2005. a

Frankenberg, C., Thorpe, A. K., Thompson, D. R., Hulley, G., Kort, E. A., Vance, N., Borchardt, J., Krings, T., Gerilowski, K., Sweeney, C., Conley, S., Bue, B. D., Aubrey, A. D., Hook, S., and Green, R. O.: Airborne methane remote measurements reveal heavy-tail flux distribution in Four Corners region, P. Natl. Acad. Sci. USA, 113, 9734–9739, https://doi.org/10.1073/pnas.1605617113, 2016. a

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, https://doi.org/10.5194/acp-13-5697-2013, 2013. a

Houweling, S., Bergamaschi, P., Chevallier, F., Heimann, M., Kaminski, T., Krol, M., Michalak,
A. M., and Patra, P.: Global inverse modeling of CH_{4} sources and sinks: an overview of methods,
Atmos. Chem. Phys., 17, 235–256, https://doi.org/10.5194/acp-17-235-2017, 2017. a

Hu, H., Hasekamp, O., Butz, A., Galli, A., Landgraf, J., Aan de Brugh, J., Borsdorff, T., Scheepmaker, R., and Aben, I.: The operational methane retrieval algorithm for TROPOMI, Atmos. Meas. Tech., 9, 5423–5440, https://doi.org/10.5194/amt-9-5423-2016, 2016. a

Hu, H., Landgraf, J., Detmers, R., Borsdorff, T., Aan de Brugh, J., Aben, I., Butz, A., and Hasekamp, O.: Toward Global Mapping of Methane With TROPOMI: First Results and Intersatellite Comparison to GOSAT, Geophys. Res. Lett., 45, https://doi.org/10.1002/2018gl077259, 2018. a

Jacob, D. J., Turner, A. J., Maasakkers, J. D., Sheng, J., Sun, K., Liu, X., Chance, K., Aben, I., McKeever, J., and Frankenberg, C.: Satellite observations of atmospheric methane and their value for quantifying methane emissions, Atmos. Chem. Phys., 16, 14371–14396, https://doi.org/10.5194/acp-16-14371-2016, 2016. a, b

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, https://doi.org/10.1002/grl.50811, 2013. a

Karion, A., Sweeney, C., Kort, E. A., Shepson, P. B., Brewer, A., Cambaliza, M., Conley, S. A., Davis, K., Deng, A., Hardesty, M., Herndon, S. C., Lauvaux, T., Lavoie, T., Lyon, D., Newberger, T., Petron, G., Rella, C., Smith, M., Wolter, S., Yacovitch, T. I., and Tans, P.: Aircraft-Based Estimate of Total Methane Emissions from the Barnett Shale Region, Environ. Sci. Technol., 49, 8124–31, https://doi.org/10.1021/acs.est.5b00217, 2015. a

Kirschke, S., Bousquet, P., Ciais, P., Saunois, M., Canadell, J. G., Dlugokencky, E. J., Bergamaschi, P., Bergmann, D., Blake, D. R., Bruhwiler, L., Cameron-Smith, P., Castaldi, S., 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 Quéré, 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 Zeng, G.: Three decades of global methane sources and sinks, Nat. Geosci., 6, 813–823, https://doi.org/10.1038/ngeo1955, 2013. a

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, https://doi.org/10.1002/2014gl061503, 2014. a

Kuze, A., Suto, H., Nakajima, M., and Hamazaki, T.: Thermal and near infrared sensor for carbon observation Fourier-transform spectrometer on the Greenhouse Gases Observing Satellite for greenhouse gases monitoring, Appl. Opt., 48, 6716–6733, https://doi.org/10.1364/AO.48.006716, 2009. a

Kuze, A., Suto, H., Shiomi, K., Kawakami, S., Tanaka, M., Ueda, Y., Deguchi, A., Yoshida, J., Yamamoto, Y., Kataoka, F., Taylor, T. E., and Buijs, H. L.: Update on GOSAT TANSO-FTS performance, operations, and data products after more than 6 years in space, Atmos. Meas. Tech., 9, 2445–2461, https://doi.org/10.5194/amt-9-2445-2016, 2016. a

Lavoie, T. N., Shepson, P. B., Cambaliza, M. O., Stirm, B. H., Karion, A., Sweeney, C., Yacovitch, T. I., Herndon, S. C., Lan, X., and Lyon, D.: Aircraft-Based Measurements of Point Source Methane Emissions in the Barnett Shale Basin, Environ. Sci. Technol., 49, 7904–7913, https://doi.org/10.1021/acs.est.5b00410, 2015. a

Lin, J. C., Gerbig, C., Wofsy, S. C., Andrews, A. E., Daube, B. C., Davis, K. J., and Grainger, C. A.: A near-field tool for simulating the upstream influence of atmospheric observations: The Stochastic Time-Inverted Lagrangian Transport (STILT) model, J. Geophys. Res.-Atmos., 108, ACH 2–1–ACH 2–17, https://doi.org/10.1029/2002jd003161, 2003. a

Lyon, D. R., Zavala-Araiza, D., Alvarez, R. A., Harriss, R., Palacios, V., Lan, X., Talbot, R., Lavoie, T., Shepson, P., Yacovitch, T. I., Herndon, S. C., Marchese, A. J., Zimmerle, D., Robinson, A. L., and Hamburg, S. P.: Constructing a Spatially Resolved Methane Emission Inventory for the Barnett Shale Region, Environ. Sci. Tech., 49, 8147–8157, https://doi.org/10.1021/es506359c, 2015. a, b, c, d, e, f

Maasakkers, J. D., Jacob, D. J., Sulprizio, M. P., Turner, A. J., Weitz, M., Wirth, T., Hight, C., DeFigueiredo, M., Desai, M., Schmeltz, R., Hockstad, L., Bloom, A. A., Bowman, K. W., Jeong, S., and Fischer, M. L.: Gridded National Inventory of U.S. Methane Emissions, Environ. Sci. Tech., 50, 13123–13133, https://doi.org/10.1021/acs.est.6b02878, 2016. a, b, c

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, P. Natl. Acad. Sci. USA, 110, 20018–20022, https://doi.org/10.1073/pnas.1314392110, 2013. a

Monteil, G., Houweling, S., Butz, A., Guerlet, S., Schepers, D., Hasekamp, O.,
Frankenberg, C., Scheepmaker, R., Aben, I., and Röckmann, T.: Comparison of
CH_{4} inversions based on 15 months of GOSAT and SCIAMACHY observations,
J. Geophys. Res.-Atmos., 118, 11807–11823,
https://doi.org/10.1002/2013jd019760, 2013. a

O'Brien, D. M., Polonsky, I. N., Utembe, S. R., and Rayner, P. J.: Potential of a
geostationary geoCARB mission to estimate surface emissions of CO_{2}, CH_{4} and CO in a
polluted urban environment: case study Shanghai, Atmos. Meas. Tech., 9, 4633–4654, https://doi.org/10.5194/amt-9-4633-2016, 2016. a, b

O'Dell, C. W., Connor, B., Bösch, H., O'Brien, D., Frankenberg, C., Castano, R.,
Christi, M., Eldering, D., Fisher, B., Gunson, M., McDuffie, J., Miller, C. E.,
Natraj, V., Oyafuso, F., Polonsky, I., Smyth, M., Taylor, T., Toon, G. C., Wennberg,
P. O., and Wunch, D.: The ACOS CO_{2} retrieval algorithm – Part 1: Description and
validation against synthetic observations, Atmos. Meas. Tech., 5, 99–121,
https://doi.org/10.5194/amt-5-99-2012, 2012. a

Peischl, J., Ryerson, T. B., Aikin, K. C., de Gouw, J. A., Gilman, J. B., Holloway, J. S., Lerner, B. M., Nadkarni, R., Neuman, J. A., Nowak, J. B., Trainer, M., Warneke, C., and Parrish, D. D.: Quantifying atmospheric methane emissions from the Haynesville, Fayetteville, and northeastern Marcellus shale gas production regions, J. Geophys. Res.-Atmos., 120, 2119–2139, https://doi.org/10.1002/2014JD022697, 2015. a

Peischl, J., Karion, A., Sweeney, C., Kort, E. A., Smith, M. L., Brandt, A. R., Yeskoo, T., Aikin, K. C., Conley, S. A., Gvakharia, A., Trainer, M., Wolter, S., and Ryerson, T. B.: Quantifying atmospheric methane emissions from oil and natural gas production in the Bakken shale region of North Dakota, J. Geophys. Res.-Atmos., 121, 6101–6111, https://doi.org/10.1002/2015jd024631, 2016. a

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, https://doi.org/10.5194/amt-7-959-2014, 2014. a

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, https://doi.org/10.5194/amt-7-3285-2014, 2014. a

Rodgers, C. D.: Inverse Methods for Atmospheric Sounding, World Scientific, Singapore, 2000. a, b, c, d

Saunois, M., Bousquet, P., Poulter, B., Peregon, A., Ciais, P., Canadell, J. G., Dlugokencky, E. J., Etiope, G., Bastviken, D., Houweling, S., Janssens-Maenhout, G., Tubiello, F. N., Castaldi, S., Jackson, R. B., Alexe, M., Arora, V. K., Beerling, D. J., Bergamaschi, P., Blake, D. R., Brailsford, G., Brovkin, V., Bruhwiler, L., Crevoisier, C., Crill, P., Covey, K., Curry, C., Frankenberg, C., Gedney, N., Höglund-Isaksson, L., Ishizawa, M., Ito, A., Joos, F., Kim, H.-S., Kleinen, T., Krummel, P., Lamarque, J.-F., Langenfelds, R., Locatelli, R., Machida, T., Maksyutov, S., McDonald, K. C., Marshall, J., Melton, J. R., Morino, I., Naik, V., O'Doherty, S., Parmentier, F.-J. W., Patra, P. K., Peng, C., Peng, S., Peters, G. P., Pison, I., Prigent, C., Prinn, R., Ramonet, M., Riley, W. J., Saito, M., Santini, M., Schroeder, R., Simpson, I. J., Spahni, R., Steele, P., Takizawa, A., Thornton, B. F., Tian, H., Tohjima, Y., Viovy, N., Voulgarakis, A., van Weele, M., van der Werf, G. R., Weiss, R., Wiedinmyer, C., Wilton, D. J., Wiltshire, A., Worthy, D., Wunch, D., Xu, X., Yoshida, Y., Zhang, B., Zhang, Z., and Zhu, Q.: The global methane budget 2000–2012, Earth Syst. Sci. Data, 8, 697–751, https://doi.org/10.5194/essd-8-697-2016, 2016. a

Sheng, J.-X., Jacob, D. J., Turner, A. J., Maasakkers, J. D., Benmergui, J., Bloom, A. A., Arndt, C., Gautam, R., Zavala-Araiza, D., Boesch, H., and Parker, R. J.: 2010–2015 methane trends over Canada, the United States, and Mexico observed by the GOSAT satellite: contributions from different source sectors, Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2017-1110, in review, 2018a. a

Sheng, J.-X., Jacob, D. J., Turner, A. J., Maasakkers, J. D., Sulprizio, M. P., Bloom, A. A., Andrews, A. E., and Wunch, D.: High-resolution inversion of methane emissions in the Southeast US using SEAC4RS aircraft observations of atmospheric methane: anthropogenic and wetland sources, Atmos. Chem. Phys., 18, 6483–6491, https://doi.org/10.5194/acp-18-6483-2018, 2018b. a, b

Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Duda, M. G., Huang, X.-Y., Wang, W., and Powers, J. G.: A Description of the Advanced Research WRF Version 3, Tech. rep., National Center for Atmospheric Res., https://doi.org/10.5065/D68S4MVH, 2008. a, b

Tan, Z., Zhuang, Q., Henze, D. K., Frankenberg, C., Dlugokencky, E., Sweeney, C., Turner, A. J., Sasakawa, M., and Machida, T.: Inverse modeling of pan-Arctic methane emissions at high spatial resolution: what can we learn from assimilating satellite retrievals and using different process-based wetland and lake biogeochemical models?, Atmos. Chem. Phys., 16, 12649–12666, https://doi.org/10.5194/acp-16-12649-2016, 2016. a

Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2004. a

Turner, A. J. and Jacob, D. J.: Balancing aggregation and smoothing errors in inverse models, Atmos. Chem. Phys., 15, 7039–7048, https://doi.org/10.5194/acp-15-7039-2015, 2015. a

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, https://doi.org/10.5194/acp-15-7049-2015, 2015. a

Turner, A. J., Jacob, D. J., Benmergui, J., Wofsy, S. C., Maasakkers, J. D., Butz, A., Hasekamp, O., and Biraud, S. C.: A large increase in U.S. methane emissions over the past decade inferred from satellite data and surface observations, Geophys. Res. Lett., 2218–2224, https://doi.org/10.1002/2016gl067987, 2016a. a

Turner, A. J., Shusterman, A. A., McDonald, B. C., Teige, V., Harley, R. A.,
and Cohen, R. C.: Network design for quantifying urban CO_{2} emissions:
assessing trade-offs between precision and network density, Atmos. Chem.
Phys., 16, 13465–13475, https://doi.org/10.5194/acp-16-13465-2016, 2016b. a, b

Turner, A. J., Frankenberg, C., Wennberg, P. O., and Jacob, D. J.: Ambiguity in the causes for decadal trends in atmospheric methane and hydroxyl, P. Natl. Acad. Sci. USA, 114, 5367–5372, https://doi.org/10.1073/pnas.1616020114, 2017. a

Veefkind, J. P., Aben, I., McMullan, K., Förster, H., de Vries, J., Otter, G., Claas, J., Eskes, H. J., de Haan, J. F., Kleipool, Q., van Weele, M., Hasekamp, O., Hoogeveen, R., Landgraf, J., Snel, R., Tol, P., Ingmann, P., Voors, R., Kruizinga, B., Vink, R., Visser, H., and Levelt, P. F.: TROPOMI on the ESA Sentinel-5 Precursor: A GMES mission for global observations of the atmospheric composition for climate, air quality and ozone layer applications, Remote Sens. Environ., 120, 70–83, https://doi.org/10.1016/j.rse.2011.09.027, 2012. a, b

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, https://doi.org/10.1002/2014jd021551, 2014a. a

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, https://doi.org/10.5194/acp-14-8173-2014, 2014b. a

Worden, J. R., Turner, A. J., Bloom, A., Kulawik, S. S., Liu, J., Lee, M., Weidner, R., Bowman, K., Frankenberg, C., Parker, R., and Payne, V. H.: Quantifying lower tropospheric methane concentrations using GOSAT near-IR and TES thermal IR measurements, Atmos. Meas. Tech., 8, 3433–3445, https://doi.org/10.5194/amt-8-3433-2015, 2015. a

Xi, X., Natraj, V., Shia, R. L., Luo, M., Zhang, Q., Newman, S., Sander, S. P., and Yung,
Y. L.: Simulated retrievals for the remote sensing of CO_{2}, CH_{4}, CO, and H_{2}O from
geostationary orbit, Atmos. Meas. Tech., 8, 4817–4830, https://doi.org/10.5194/amt-8-4817-2015, 2015 a, b

Zavala-Araiza, D., Lyon, D. R., Alvarez, R. A., Davis, K. J., Harriss, R., Herndon, S. C., Karion, A., Kort, E. A., Lamb, B. K., Lan, X., Marchese, A. J., Pacala, S. W., Robinson, A. L., Shepson, P. B., Sweeney, C., Talbot, R., Townsend-Small, A., Yacovitch, T. I., Zimmerle, D. J., and Hamburg, S. P.: Reconciling divergent estimates of oil and gas methane emissions, P. Natl. Acad. Sci. USA, 112, 15597–155602, https://doi.org/10.1073/pnas.1522126112, 2015. a, b

Short summary

We conduct a 1-week WRF-STILT simulation to generate methane column footprints at 1.3 km spatial resolution and hourly temporal resolution over the Barnett Shale. We find that a week of TROPOMI observations should provide regional (~30 km) information on temporally invariant sources and GeoCARB should provide information on temporally invariant sources at 2–7 km spatial resolution. An instrument precision better than 6 ppb is an important threshold for achieving fine resolution of emissions.

We conduct a 1-week WRF-STILT simulation to generate methane column footprints at 1.3 km spatial...

Atmospheric Chemistry and Physics

An interactive open-access journal of the European Geosciences Union