Combining measurements of atmospheric CO
CO
Atmospheric inversions exploit the observed variability in atmospheric mixing
ratios of CO
In all these pioneer studies, the actual spatial scale of the areas emitting
FFCO
In recent years, as part of the ICOS project, a rather dense network of
standardized, long-term and high-precision atmospheric measurements of
CO
In this study, we study the potential of an atmospheric inversion system to
quantify FFCO
Our inversion system solves for monthly FFCO
Although the results are presented only over Europe, we use a global
inversion system and the global transport model LMDZv4 to ensure that
uncertainties in FFCO
The presentation of the results first focuses on regional FFCO
The paper is organized as follows. Section 2 gives a full description of the
inversion and framework of Observing System Simulation Experiments (OSSEs). Section 3 analyzes the statistics of the
posterior uncertainties and misfits from inversions using different
observation networks. Section 4 evaluates the potential of atmospheric
inversion for the monitoring of decadal changes and discusses the relevance
of using a coarse-resolution transport model in the inversion system to
quantify regional FFCO
We consider three different observation networks, in which the number of the
stations ranges from 17 to 233. The minimum network (NE17) includes 17 sites,
based on existing European ICOS
Site locations for the three continental network configurations
used in this study:
The high-altitude station Jungfraujoch (JFJ) at 3450 m a.s.l. (meters above sea level)
in Switzerland samples free tropospheric air over Europe, assumed to
be representative of the “background” concentration. In all the three
configurations of the observation network, JFJ is chosen as the reference
station. In this study, we assimilate gradients of FFCO
Wang et al. (2017) have already made a detailed characterization of the
distributions of representation errors at the sites considered here and
characterized two types of stations based on the population density of the
grid cells within which a station is located and on the locations of large
point sources (e.g., large power plants). All the sites in different networks
are thus categorized as “urban” or “rural” sites according to their
results. In the NET233 network, the two sites in each land pixel of the
transport model are assumed to be one urban and one rural, distanced by more
than 200 km in order to combine data for the structures of representation
errors that are different (i.e., which have a different view in terms of the scale
of FFCO
The assessment of the potential of different networks to constrain fossil fuel emissions is based on the inversion framework presented by Wang et al. (2017). In this section we summarize the main elements of this framework for which the details can be found in Wang et al. (2017).
The inversion relies on a Bayesian statistical framework. The estimate of the
fossil fuel emission budgets at monthly and regional scales over 1 year,
called hereafter the control variables
Equation (1) shows that
A common performance indicator is the theoretical uncertainty reduction (UR)
for specific budgets of the fossil fuel emissions (at control or larger
space and timescales), defined by
However, if the modeling of
We focus on uncertainties and misfits at both monthly and annual scales.
However, we can have only one practical realization for
The inversion system has a global coverage and controls monthly budgets of
FFCO
Current atmospheric
The atmospheric FFCO
We use the high-resolution (0.1
The offline version of the general circulation model of LMDZv4 forms
The sampling of FFCO
In sum, the observation operator used in the practical configuration of the
inversion system is defined by
Emission estimates from inventories are limited to annual and national
scales and rarely provide systematic assessments of uncertainties. There are
a limited number of datasets providing emission maps at higher
spatial–temporal resolutions. Although there have been some efforts to
compare such FFCO
The first configuration of the
The second configuration of the
Wang et al. (2017) derived estimates of the observation errors in FFCO The measurement error The representation error The transport error The aggregation error
In this study, we use the estimates of the standard deviations and of the
correlation functions for these different types of observation errors from
Wang et al. (2017) to set up the
A simpler account of the spatial correlations in the observation errors is
derived from the diagnostics of Wang et al. (2017). We do not account for the
spatial correlation in the representation error, as the scale of the spatial
correlation according to Wang et al. (2017), i.e., 55–89 km, is much smaller
than the size of the grid cells of the global transport model
Assuming that all these sources of errors are independent from each other
and have Gaussian and unbiased distributions, i.e.,
In this study, we consider two types of OSSEs corresponding to the two
configurations of prior error covariance matrix
In the OSSEs, the synthetic prior estimate of the regional–monthly emissions
Schematic of the OSSEs.
Setup and performance indicators of the two types of inversions.
The parameters of the two inversion configurations are summarized in Table 1 and Fig. 3. All the combinations of networks and data temporal sampling described in Sect. 2.1 and 2.2.2 are tested with the two configurations of OSSEs. The resulting eight OSSEs are listed in Table 2.
Notations for the eight OSSEs.
Average monthly uncertainty reductions and misfit reductions in
FFCO
Average monthly relative prior and posterior uncertainties and
misfits of FFCO
Figure 4 shows the URs of monthly emissions using the NET17 and NET43 networks and 2-week sampling (N-17W, E-17W, N-43W and E-43W in Table 2). With NET17, INV-N and INV-E inversions show similar spatial patterns of UR scores. The largest UR occurs in the region of western Germany, being 34 % for inversion N-17W and 38 % for E-17W. The URs are also significant in eastern Germany for both inversions. This stems from the fact that several stations are located around and within these regions and that the emission in these regions are higher than those in other regions. Moderate UR values are found for Benelux (12 %) and eastern France (15 %) in inversion E-17W and the UR values elsewhere are marginal. Going from NET17 to NET43 adds a significant increase (improvement) of the UR for southern UK (from 3 to 23 %), northern Italy (from 3 to 18 %) and eastern Europe (from 2 to 15 %) in INV-N (Fig. 4e). The increase of UR in E-43W, compared with the UR in E-17W, mainly occurs in eastern France (from 16 to 33 %) and the Balkans (from 3 to 13 %). Because the added stations in NET43, compared to NET17, are mostly located outside Germany, the URs over western and eastern Germany are not significantly improved (Fig. 4e and g). Despite their different URs for specific regions, both types of inversions highlight the overall increase in the UR for western European regions by increasing the number of sites from NET17 to NET43.
The differences in the spatial patterns of UR between INV-N and INV-E
inversions shown in Fig. 4 reveal the high sensitivity of UR to the
configuration of the prior uncertainties. Figure 5a and b show the prior
uncertainties associated with the two configurations of
Complementing the uncertainty reduction, Fig. 5 shows the prior and posterior
uncertainties and provides insight into the precision of the estimates of
monthly FFCO
The correlation structure in the prior (first row) and posterior
(second row) uncertainties in monthly regional FFCO
The scores of the MR and misfits of monthly emissions in both inversions
using NET17 and NET43 and 2-week sampling are shown in Fig. 4 (b, d, f, h)
and Fig. 5 (b, d, f, h, j, l). In INV-E, there are slight differences between
posterior misfits and uncertainties and between MR and UR. For example, for
E-43W, the MR (21 %) for Iberian Peninsula is larger than the UR
(5 %), while the MR (40 %) for western Germany is slightly smaller
than the UR (47 %). Despite such differences, the spatial patterns of the
MRs in Fig. 4 and posterior misfits in Fig. 5 are close to those of the URs
and posterior uncertainties. In contrast, there are large differences
between the statistics of posterior misfits and posterior uncertainties and
between MRs and URs in INV-N. In some regions, such as southern UK
(MR
Uncertainty reduction (UR) and misfit reduction (MR) of annual
FFCO
Figure 6 shows the correlations in the prior and posterior uncertainties in
monthly emissions from different regions, and their differences in inversions
N-43W and E-43W. After assimilating the observations, the change of
correlations mainly occurs among regions that have large URs. In both
inversions, there are negative correlations between the posterior
uncertainties in monthly emissions from some neighboring regions, in
particular between western Germany and eastern Germany (from
We compare the performance of different inversions to constrain annual mean
FFCO
Both the spatial spread and the magnitude of the MR of annual emissions in INV-E (Fig. 7d and h) are larger than those of the UR. The differences between MR and UR are much larger at annual than at monthly scale (when comparing Figs. 4 and 7). The cause of the discrepancy between UR and MR was presented in Sect. 2.2.1, and it may have a larger impact at the annual scale than at the monthly scale due to the evaluation of annual UR scores to annual MR values corresponding to single realizations of the misfits. In INV-N, the spatial spread and the magnitude of the MR are still significantly different from those of the UR and the MRs for some regions are still negative and far below zero.
Average uncertainty and misfit reductions in the monthly FFCO
Figure 8 shows the URs and MRs of monthly emissions from inversions using
NET43 and daily sampling and from inversions using NET233 network and 2-week
sampling (N-43D, E-43D, N-233W and E-233W in Table 2). When using NET43 and
daily sampling, the URs of monthly emissions are generally larger (improved)
than when using 2-week sampling for all regions. The differences between the
UR values of monthly emissions with daily and with 2-week sampling are larger
(meaning more improvement with daily sampling) over the regions where the
network is dense and the emissions are high. For instance, the URs of monthly
emissions for western Germany are as high as 62 % (or 67 %) in INV-N
(or INV-E). When using the much denser NET233 network but with a lower 2-week
sampling (Fig. 8d–f), we found that URs of monthly emissions in some regions
that were poorly sampled by networks NET17 and NET43 are largely improved.
For instance, the UR value in eastern Europe is 36 % in N-233W (compared with
15 % in N-43W) and is 73 % in the Balkans in E-233W (compared with
13 % in E-43W). In principle, large regions tend to encompass more sites
and to be surrounded by more sites than small regions and thus may have more
observations to improve their estimates of emissions. However, in both N-233W
and E-233W, the URs for regions with a large area like northern Europe are
still limited to below 5 %. Large URs are identified over the regions
whose absolute uncertainties are high, revealing the important roles of the
absolute prior uncertainties when using the coarse-resolution transport model
in the inversion of FFCO
In the Copenhagen conference of parties, the European Union (EU) set up the
goal to decrease its emissions (in CO
The uncertainty in the trend of FFCO
Uncertainties in the regressed linear trends as a function of the posterior uncertainty in annual emissions. The uncertainties in the trends are defined as the ratio between the uncertainties in the linear regression slope of absolute annual emissions and the annual emission budget in the base year.
Our assumption that the posterior uncertainties in annual emissions have the
same amplitude from year to year should not strongly drive the results, so
the results here give a good indication of the level of uncertainty in the
trend detection for a typical level of uncertainty at the annual scale.
However, changes of the transport from year to year or on decadal scales
(Aulagnier et al., 2009; Ramonet et al., 2010) may change the level of the
sensitivity of the observations to the emissions, i.e., the level of the
atmospheric constraint of the inversions which leads to uncertainty
reduction, and thus the level of posterior uncertainties on the same
timescales. A more complex model accounting for varying levels of annual
posterior uncertainties may thus be useful to refine the quantification of
the uncertainty in the trends. Of note is that the level of uncertainties in
the trends could be increased if the modeling framework accounts for the
trends in the transport or in the sources of
In this study, we showed that given the NET17
We made sure (as compared to previous OSSEs published for the USA) to
account for aggregation and representation errors, which is the reason why
our inversions do not provide as impressive error reductions (uncertainty and
misfit) as the misfit reduction of Ray et al. (2014) and Basu et al. (2016).
However, we still did not account for all sources of uncertainty. Indeed, we
assumed that atmospheric FFCO
In Sect. 3.3, we explored the concept of having more observations assimilated
in the inversion system by increasing the sampling frequency and expanding
the observational network. Wang et al. (2017) showed that because the
representation error, aggregation error and the prior FFCO
This study provides understanding of the inversion behavior and sensitivity
to network density, but the precise quantification of the performance of the
inversion is largely dependent on the spatial resolution of the transport
model. Wang et al. (2017) showed that the representation error contributes
the most to the observation errors, followed by the transport and measurement
errors. Following the definition of the observation errors in Wang et
al. (2017) and in this study, both the representation and the transport error are
highly dependent on the transport model resolution. Increasing the transport
model resolution will reduce the representation errors and (potentially)
reduce the transport error if topography effects and synoptic variations are
better simulated by finer-resolution models. We thus assume that using a
regional mesoscale transport model with higher resolution than LMDZv4 (like
for the regional-scale natural flux inversions in Kadygrov et al., 2015;
Broquet et al., 2013; Gourdji et al., 2012; Lauvaux et al., 2008) should be
the most efficient way to improve the results from atmospheric inversion of
FFCO
However, unlike such regional transport models, a global transport model can
propagate uncertainties in emissions in other continents to Europe and thus
allow one to account for them when estimating the European emissions. To quantify
the impact of the uncertainties in emissions from other continents, we
conducted additional inversions that only solve for emissions in European
regions, ignoring those of other continents. The results show that fossil fuel
emissions from other continents have negligible impacts on UR, MR and
posterior emission budgets of European regions (the relative differences
between these estimates being smaller than 1 %; not shown). This
indicates that the inversion system mainly exploits the signals of the
gradients between the European sites to constrain the European emissions, and
the incoming FFCO
The inconsistencies between the posterior misfits and the theoretical
computation of posterior uncertainties and between the scores of MR and UR
in INV-N inversions indicate that the theoretical computation of posterior
uncertainty is not sufficient to characterize the actual performance of the
inversion, especially when the prior uncertainty covariance matrix does not
capture the actual error statistics of the prior estimate of the emissions.
Moreover, in INV-N, there is a degradation of the emission estimates for many
regions, characterized by negative and far-below-zero MRs in Sect. 3. This
degradation occurs even when using daily measurements or the network NET233.
A first explanation is that the signature of the errors in the prior emission
estimates in the FFCO
In such a situation, only a precise configuration of the prior uncertainty
covariance matrix can support the filtering of the prior errors.
Consequently, even though both
In real applications, having such a good fit between the configuration of the
prior uncertainty covariance matrix in the inversion system as between
In this study, we present the application of a global atmospheric inversion
method to quantify FFCO
Increasing the number of observations assimilated in the inversion system by
using daily sampling or a very dense observational network could potentially
increase the UR over European regions. However, even though the inverse
modeling framework used here can be assumed to be optimistic, e.g., regarding
the assumption of the FFCO
The inversion system is available upon request from Yilong Wang (yilong.wang@lsce.ipsl.fr).
The
The
Assuming the linear trend of the FFCO
Since
Annual FFCO
In this study, based on the time series of national annual emissions from IER-EDG, we assume a 5 % IAV in the annual fossil fuel emissions for European countries. In general, this 5 % IAV is the upper limit of the typical values for European countries (Levin and Rödenbeck, 2007). Ballantyne et al. (2015) assumed that in the self-reported fossil fuel emission inventories, the emission error in 1 year could be highly correlated with the error from the previous year by an autoregressive coefficient of 0.95 due to potential errors that are not corrected retroactively after about 20 years. However, we do not conduct a multi-year inversion to get a typical estimate of the correlations in the posterior uncertainties in annual emissions and assume that there is no correlations between the posterior uncertainties in annual emissions. This assumption is fairly conservative, since Eq. (C4) implies that the larger (either positive or negative) the correlations between the estimation of fossil fuel emissions from different years, the smaller the uncertainties in the regressed trends.
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
The authors acknowledge the support of the French Commissariat à
l'énergie atomique et aux énergies alternatives (CEA). This study is
co-funded by the European Commission under the EU Seventh Research Framework
Programme (grant agreement no. 283080, geocarbon project). Grégoire Broquet and Frédéric
Vogel acknowledge funding from the industrial chair BridGES (supported by the
Université de Versailles Saint-Quentin-en-Yvelines, the CEA, the Centre National
de la Recherche Scientifique, Thales Alenia Space and Veolia). We are also
grateful to Ingeborg Levin for the useful discussions on this topic. We also
would like to thank the partners of the ICOS infrastructure for details of
radiocarbon samplings and FFCO