This study assesses the potential of satellite imagery of vertically integrated columns of dry-air mole fractions of

Cities, thermal power plants and industrial factories cover a very small fraction of the land surface but are emitting a large amount of

Measurements of

The main approach currently investigated for the estimate of

Broquet et al. (2018) showed that the part of the

Previous studies on the potential of the satellite

Therefore, in this study, we develop a Plume Monitoring Inversion Framework
(PMIF) and conduct a set of observing system simulation experiments (OSSEs)
to assess, for the first time, the performance of a satellite instrument to
monitor the emissions of all the clumps across the globe and over a whole
year. The imager studied has the foreseen characteristics of the individual
satellites of the forthcoming CO2M mission. It would be a high-resolution
spectrometer, with

This PMIF system provides an indication of the satellite system capabilities
for the full range of cities and power plants varying in topography,
emission budget and spread, proximity to other major sources, and for a
large range of meteorological conditions. It complements other systems that
focus on specific regions with more complex (but area-limited) models and
consideration of diffuse sources and natural fluxes, allowing for
extrapolating and up-scaling results of those more complex systems to get a
more systematic understanding of their implications for the monitoring of

The PMIF system and the OSSEs analyzed in this first study are described in Sect. 2. The results obtained with the PMIF for the city of Paris are compared with those of Broquet et al. (2018) in Sect. 3.1. The uncertainty in the retrieved emissions of individual clumps with one imaging satellite for 3 h time windows, for daily emissions and for annual emissions is assessed in Sect. 3.2–3.4. Section 4 discusses the drivers of the spatial variations of the uncertainty in the retrieved emissions, the limitations of PMIF and the implications for a future operational observing system.

The theoretical framework of the inversion system developed in this study is
the same as the traditional atmospheric inversions. The inversion derives a
statistical estimate for a set of control variables

Equation (1) shows that A only depends on prior and observation error
covariance matrices, on the observation operator, and implicitly on the
structure of the observation vector (i.e., on the time, location and
representation of the observations in

We characterize

We use a Gaussian plume model (Sect. 2.4) to simulate the atmospheric
transport at a spatial resolution consistent with that of the

The configuration of the PMIF-Paris inversion.

The different options for the configuration of PMIF-Globe inversions.

In this study, we consider the samplings from two different virtual

The first sampling used in PMIF-Paris (Table 1 and Sect. 2.7.1) is the
simulation of the sampling for CarbonSat by Buchwitz et al. (2013)
exactly as in Broquet et al. (2018).

The second sampling is global and is used for all the other experiments of PMIF-Globe (Table 2 and Sect. 2.7.2). It corresponds to that of a single CO2M satellite with a 300 km swath and 2 km spatial resolution. CO2M is similar to CarbonSat for sampling but has a larger swath and better precision (Sect. 2.5). The simulation is based on the method and model described by Buchwitz et al. (2013) but uses different values for the parameters in the model.

In the PMIF-Paris inversion, the satellite observations are sampled at 11:00
local time, in line with the experiments from Broquet et al. (2018). The inversion solves for the mean emissions for the 6 h before 11:00 local time. Broquet et al. (2018) solved for the hourly emissions during this 6 h period but PMIF can only solve for the mean emissions during the 6 h period due to the fact that the Gaussian plume model cannot be used to compute the signatures in the

In the PMIF-Globe inversion, the satellite observations are sampled at a
local time of approximately 11:30 over all the clumps. The inversion solves
for a scaling factor for 3 h mean emissions between 08:30 and 11:30 and a
scaling factor for the emissions during of the rest of the day (00:00–08:30
plus 11:30–24:00) for each day over 1 year and for all the clumps over the
globe:

In both types of experiments, we do not include the diffuse emissions
outside the selected clumps and the natural fluxes (more generally, any
parameter of the “background concentrations”, Kuhlmann et al., 2019) in
the control vector. The setup of the

The observation operator in PMIF (which is used in Eq. 1) is composed of two
sub-operators. The first operator (

The size of the full theoretical control vector corresponds to 11 314
emission clumps times 2 time windows for each day times 366 d. The size
of this full theoretical observation vector over the year is thus more than
30 000 000. Building matrices and applying Eq. (1) with such spaces is, in
practice, not computationally affordable. Therefore, we divide the globe
into 5400 spatial inversion windows (from 180

We evaluate the projection of the measurement noise of the satellite
observation and ignore uncertainties in the observation operator. The
measurement noise is derived from the simulations of random measurement
errors from Buchwitz et al. (2013), and the impact of the systematic measurement errors is ignored. The random measurement errors are simulated as a function of geographic location (e.g., solar zenith angle, SZA), surface (e.g., albedo) and atmosphere characteristics (e.g., AOD). The random measurement error is 1.4 ppm for vegetation albedo and SZA 50

Two configurations for the prior uncertainty are used in the OSSEs (Sect. 2.7). In the PMIF-Paris inversion, the prior uncertainty is 22.4 % for the each of the scaling factors for 6 h mean emission, the choice of this value being consistent with the configuration used by Broquet et al. (2018).

In the PMIF-Globe inversions, the prior uncertainty is downscaled from its
estimate for the annual budget of emissions of each clump. A prior
uncertainty in annual emission of 30 % is assumed for all clumps. This
value is chosen to be of the same order of magnitude as the typical
difference between emission inventories for a single point source and city.
For example, Gurney et al. (2016) found that one-fifth of the power plants had monthly emission differences larger than 13 % between the estimates by two different US agencies. Gurney et al. (2019) compared the emission maps from ODIAC and Hestia for four US cities and found the whole-city differences are between

The hourly emissions in inventories are usually derived from the periodic
typical temporal profiles to annual emissions (Andres et al., 2011; Nassar et al., 2013). There are large variations in actual emissions from hour to hour and from day to day, resulting in large differences between the emission
estimates derived based on typical temporal profiles and actual emissions.
These differences are sources of uncertainties in the emission inventories
which are used in the inversion as prior information. However, there is no
consensus regarding the uncertainty in emission inventories and their error
structures (Gurney et al., 2019). We compare the typical temporal profiles of transport emissions and energy sector from the TIMES product with the TOMTOM traffic index (

In some scenarios, we consider an “annual component” that is fully
correlated in time over 1 year. We also consider “uncorrelated” components
whose temporal auto-correlations are null and “sub-annual” components
whose temporal auto-correlations follow the exponential decaying model with
a correlation length smaller than 1 year. Specifically, we assume that the
correlation between two instants of the sub-annual component at hourly scale
is described by the following:

The detailed configuration of the different scenarios for the decomposition
of the prior uncertainty are listed below:

The prior uncertainty in the 3 h mean emissions between 08:30 and 11:30 is
close to or larger than 100 % in scenarios SCS and MCS, and it even reaches an abnormally huge value of 1623 % in NoCor. Andres et al. (2016) estimated the uncertainty in the widely used emission map CDIAC (Carbon Dioxide Information Analysis Center). They found that the average uncertainty in monthly emissions for one

Two sets of OSSEs are conducted under different configurations adapted to different purposes, as described below. Tables 1 and 2 summarize the different configurations of the OSSEs.

In the first OSSE PMIF-Paris, the configuration of the control vector, observation sampling and errors, and prior uncertainties are made such that they resemble those in the MC-2 experiments from Broquet et al. (2018): (1) the inversion controls the 6 h mean emissions from Paris before the satellite overpasses on single days; (2) the observation sampling and errors are obtained from CarbonSat mission simulation (Buchwitz et al., 2013). We ignore temporal auto-correlation of the uncertainty in scaling factors for 6 h mean emissions between different days. We select the same 69 satellite CarbonSat overpasses over Paris during 1 year as Broquet et al. (2018). The 31 d of October 2010 are used to provide a wide sample of atmospheric transport conditions, i.e., 31 wind fields. These atmospheric transport conditions are combined with the 69 sets of CarbonSat overpasses (with various cloud and aerosol coverage) to form 2139 inversion samples. The results for different overpasses using the same wind field of a single day are ranked according to the uncertainty reductions and are compared to those obtained in Broquet et al. (2018).

In this second set of OSSEs, PMIF-Globe, we conduct inversions for all the
clumps over 1 year. However, the large sizes of the control vector, of the
observation vector and of the associated covariance matrices prevent the
derivation of a full A for all the clumps and all the time windows using Eq. (1). In PMIF, we thus propose and apply a two-step computation that
approximates Eq. (1). This computation assumes that the system has a limited
capability to improve the separation between plumes from distinct clumps on
a given day by crossing the information obtained from different days. In
that sense, the inversion considers the uncertainty reduction obtained for
individual days when considering all the clumps together (first step, see
below) before focusing on individual clumps to account for temporal
correlations in the prior uncertainty (the second step, see below). In other
words, we assume that when crossing information between different time
windows for a given clump, the impact of filtering information from
different spatial overlaps of plumes on different days is relatively smaller
than that of temporal auto-correlation in the prior uncertainty. It is shown
that this method provides a good approximation of

In a first step, Eq. (1) is applied to each

In the second step, the inversion is conducted for each clump

In PMIF-Globe, we first conduct the inversion in which the prior uncertainty
has no temporal auto-correlation (Exp-NoCor). This is made by applying step 1 to all the

The comparison of the results from the PMIF-Paris experiment to that of
Broquet et al. (2018) is used to demonstrate that the PMIF produces meaningful statistics for other clumps despite its relative simplicity at the local scale (its complexity being linked to its global and annual coverage). Figure 1 shows the theoretical uncertainty reduction for the 6 h mean emissions obtained in PMIF-Paris inversions with the 1st, 5th, 10th, 15th, 19th and 25th best observation sampling from CarbonSat over 31 inversion days (Sect. 2.7.1), each day being characterized by the average wind speed over Paris. We compare these results with the Fig. 6 from Broquet et al. (2018). Like Broquet et al. (2018), Fig. 1 illustrates the strong correlation between the uncertainty reduction and the average wind speed, indicating that lower wind speed results in a larger signal close to the city that is easier to assimilate than elongated plumes under large wind speeds. For the best observation sampling, the uncertainty reduction remains smaller than 40 % when the wind speed is larger than 13 m s

Some differences are seen in Fig. S3, between the results obtained by PMIF
and by Broquet et al. (2018). For example, the PMIF-Paris inversion slightly overestimates the uncertainty reduction under high wind speed (

Figure 1 shows that the uncertainty reduction on 6-hourly emissions from
Paris before the satellite overpass can be up to 74 % under calm wind
conditions (wind speed

Theoretical uncertainty reduction for the 6 h mean emissions in the PMIF-Paris experiments using the 1st (red), 5th (orange), 10th (light green), 15th (purple), 19th (blue) and 25th (green) best observation sampling from the CarbonSat simulation. The results from the 31 inversion days are given as a function of the average wind speed over the Paris clump. A comparison with the results from Broquet et al. (2018) is given in Fig. S3.

Figure 2a shows the distribution of the number of 08:30–11:30 time windows per
clump for which the posterior uncertainty of 3 h mean emissions is smaller
than 20 % (this number is called N20) in Exp-NoCor. Clumps with small emission budgets tend to have lower N20 values than those with large budgets, due to the fact that the atmospheric plume generated by small
emission clumps is difficult to distinguish from the measurement noise.
Typically, N20 is smaller than 5 d for clumps emitting less than 2 MtC yr

We also show the numbers of 08:30–11:30 time windows per clump being labeled as “well-constrained” when the posterior uncertainty of 3 h mean emission is smaller than other thresholds, e.g., 10 % and 30 % (Fig. 2b). In general, using a posterior uncertainty larger than 20 % as a threshold, we could expect more “well-constrained” cases. But for a given threshold, we still find the number of well-constrained cases increases with the emission budgets.

Figure 3 shows the posterior uncertainty in the clump emissions for the
“well constrained” 08:30–11:30 time windows (identified in Exp-NoCor) from
different OSSEs. It confirms that in all OSSEs, the posterior uncertainties
for clumps with larger emissions are smaller than those with lower
emissions. Within a given bin of clump annual emission, the posterior
uncertainties from the various OSSEs are very similar, even though they are
obtained with different hypotheses regarding the temporal auto-correlation
in the prior uncertainty. The interpretation is that, for the inversion of
the 3 h emissions before a given satellite overpass, most of the constraint
is imposed by the direct satellite observations during this overpass. These
observations are independent on different days, and the constraints on
different days are not strongly crossed even when errors in the prior
estimate are highly correlated in time. However, although small, the impact
of temporal auto-correlations in the prior uncertainties can be seen. For
example, the posterior uncertainties in ASS (SCS) are systematically smaller
than those in AMS (MCS), which confirms that the capability of the inversion
system to use the information from observations from previous or subsequent
days to reduce the posterior uncertainties increases with the temporal
auto-correlations. In SectCS, the posterior uncertainties are smaller than
those in MCS and SCS in most regions (Fig. S5), due to the fact that the
uncertainty in industrial emissions has a long temporal auto-correlation
(

Distribution of the posterior uncertainty in the 3 h mean emissions during the 08:30–11:30 time windows (for which the posterior uncertainty in 3 h mean emissions are smaller than 20 % in Exp-NoCor) obtained with
different OSSEs. Dots and error bars are the median and interquartile range.
The results are binned according to the clump annual emission with bin
limits given on the

In previous sections, we analyzed the uncertainty reduction and the
posterior uncertainty for the 3 h emissions that generate the atmospheric
plume observed from space at 11:30. We now analyze the potential to monitor
the daily emission, relying on the extrapolation of constraints on emissions
between 08:30 and 11:30 using temporal auto-correlation of the prior
uncertainties in step 2 of the inversion (Sect. 2.7.2). Figure 4 shows the distribution of the number of days when the posterior uncertainties in daily emissions are smaller than 20 % (D20) for the same bins of emission clumps as in the previous section. Similar to the distribution of N20, clumps with small emission budgets tend to have lower D20 values than those with large budgets, due to having smaller signal-to-noise ratios for clumps with smaller emissions. The D20 values also strongly depend on the temporal auto-correlation in the prior uncertainty. When no correlation (Exp-NoCor) or short correlation (MCS) are assumed, D20 remains zero even for the largest clumps, since most of the daily emissions are disconnected from the 3 h emissions that are constrained by the satellite observation and keep
on bearing the large prior uncertainties associated with the Exp-NoCor and
MCS scenarios. When significant temporal auto-correlations (e.g., in the case
of AMS, ASS and SCS) are assumed, the results get better and the posterior
uncertainties for the daily emissions become less than 20 % for more than
100 d for clumps emitting more than 5 MtC yr

Number of days within the year when the posterior uncertainty of daily emissions is smaller than 20 % (D20). The results are binned according to the clump annual emission with bin limits given on the

We now analyze the results for the annual emissions, allowed again by the
derivation of the posterior uncertainty covariance matrix

Distribution of the posterior uncertainties in annual

PMIF provides information on the potential of space-borne imagery to constrain

In this study, we focused on the projection of uncertainties in satellite
observations on the uncertainty of inverted emissions. Some sources of
uncertainties that could have some impacts on the inversions when dealing
with real data are ignored. Firstly, the plumes generated by the Gaussian
plume model are straight along the wind direction at the source pixel. As a
result, we allow the plumes from nearby clumps to potentially cross each
other, but these plumes will systematically diverge over long distances. The
Gaussian plume model cannot reproduce plumes overlapping along the
atmospheric circulation like Eulerian transport models. In this sense, the
overlapping effect of plumes can be underestimated in PMIF. In a realistic
situation of atmospheric transport, if plumes from multiple clumps overlap
very often, the inversion performance for individual clumps will be degraded
since it will have difficulties accurately attributing the

Although it ignores the sources of uncertainties listed above, the current PMIF can still be used to investigate the impacts of some key parameters of the inversion problem and to allow, for the first time, a first-order extrapolation of the results from single-city studies to all significant emission clumps over the globe and under a full range of meteorological conditions during a year.

The key result summarized in Fig. 2 is that using a single CO2M satellite,
only the clumps with annual budget higher than 2 MtC yr

Number of observations in

We showed that one CO2M imager can provide a direct constraint for the
estimate of emissions from clumps with emissions larger than 2 MtC yr

We also investigated the possibility of extrapolating the information
obtained from the time windows for which the emissions are constrained by
satellite observations to estimate emissions on other hours, days and
throughout a year. Such an extrapolation relies on the model of the emission
inventories used as a prior of PMIF, that is, in the framework of PMIF, the
temporal auto-correlation of the uncertainty of prior emissions. The
analysis of posterior uncertainties in the 3 h mean emissions, in daily
emissions and in annual emissions all show that the configuration of this
temporal auto-correlation has a large impact on the inversion results. For
example, posterior uncertainties in annual emissions range from less than
10 % with strong auto-correlation (ASS) to 25 % with medium
auto-correlation (MCS) for clumps with emissions higher than 2 MtC yr

Even if emissions can be effectively constrained by CO2M for clumps whose
emissions are larger than 2 MtC yr

The source code for PMIFv1.0 is included in the Supplement. To run PMIF, some input files are needed. The ODIAC inventory is available at

The supplement related to this article is available online at:

PC, GB and FMB designed the research. YW and FL developed the PMIF code and performed the analysis. MB and MR simulated the satellite sampling and random measurement noise for CarbonSat and CO2M imagers. YW, GB, FMB, FL, MB, MR, YM, AL, GLM, BZ and PC wrote the paper.

The authors declare that they have no conflict of interest.

This work was mainly conducted and funded in the frame of the ESA. It also received support from the French National Research Agency (ANR). Yilong Wang also acknowledges support from National Key Research and Development Program of China. We would like to thank Bernard Pinty for providing the vision of a

This research has been supported by the ESA (project no. 4000120184/17/NL/FF/mg), the French National Research Agency (ANR)'s program “Chaires Industrielles 2017” through the TRACE Industrial Chair (UVSQ/CEA/CNRS/Thales Alenia Space/TOTAL/SUEZ) (grant no. ANR-17-CHIN-0004), and the National Key Research and Development Program of China (grant no. 2017YFA0605303).

This paper was edited by Havala Pye and reviewed by two anonymous referees.