We present a novel high-resolution inverse modelling
system (“FLEXVAR”) based on FLEXPART-COSMO back trajectories driven by COSMO
meteorological fields at
Atmospheric methane (CH
Reducing CH
The development of emission reduction pathways as well as the control of
international climate agreements requires the accurate quantification of
current (and past) GHG emissions. For CH
In order to analyse regional emissions in more detail (and more accurately),
specific regional inversions have been performed, employing regional
atmospheric transport models at higher horizontal resolution (typically in
the range of
In order to further improve the atmospheric modelling, it is essential to
further increase the spatial resolution, aiming at further improving the
simulation of regional monitoring stations. A pioneering high-resolution
study has been reported by Henne et al. (2016), using the
FLEXPART-COSMO back trajectories driven by meteorological fields from the
Swiss national weather service (MeteoSwiss) at horizontal resolution of
approximately
Aiming at high-resolution inversions of larger regions (such as the European
domain), we have therefore developed a novel inversion framework (denoted
“FLEXVAR”) based on the four-dimensional variational (4DVAR) data
assimilation technique (Meirink et al., 2008;
Talagrand and Courtier, 1987), which allows for the optimization of a much
larger number of parameters and therefore also avoids the need to apply
reduced grids. As in the Henne et al. (2016) study, the new system
uses FLEXPART-COSMO back trajectories driven by COSMO meteorological fields
at
The objective of this paper is to present the new FLEXVAR system and its
application to the inversion of European CH
FLEXPART is a Lagrangian atmospheric transport model that simulates the advective, turbulent, and convective transport by tracking the positions of a large number of infinitesimally small air parcels, so-called particles, either forward or backward in time (Pisso et al., 2019; Stohl et al., 2005). FLEXPART is an offline model that requires meteorological fields such as 3D wind fields from a numerical weather prediction (NWP) model as input. FLEXPART-COSMO is a version of the model that is driven by the output of the NWP model COSMO, which was jointly developed by a consortium of European weather services under the lead of the German meteorological service DWD (Baldauf et al., 2011). Different from all other FLEXPART versions, FLEXPART-COSMO operates on the native vertical grid of the driving model COSMO, which avoids potential loss of information and inaccuracies associated with the interpolation onto a different grid. More details on the model are provided in Henne et al. (2016) and Pisso et al. (2019).
In the backward mode, particles are released at the locations of individual
observations and followed backwards in time over typically a few days. By
sampling the near-surface residence times of the particles along their
paths, a so-called source–receptor sensitivity matrix or “footprint” is
computed, which describes the relationship between the change in mole
fraction at the observation site and the fluxes discretized in space and
time (Seibert and Frank, 2004). A time series of simulated
mole fractions can be obtained by integrating the time series of
source–receptor matrices with a discretized flux estimate. The simulations
were driven by hourly output from the operational COSMO-7 analyses of the
Swiss weather service MeteoSwiss at a horizontal spatial resolution of about
The new coupled FLEXPART-COSMO TM5 4DVAR inverse modelling system, denoted
FLEXVAR, allows for the optimization of emissions at grid scale using the
four-dimensional variational (4DVAR) data assimilation technique
(Meirink et al., 2008; Talagrand and Courtier,
1987), the FLEXPART-COSMO back trajectories described in Sect. 2.1, and
background mole fractions (“baselines”) from TM5-4DVAR (described in Sect. 2.2.2 and 2.4). The system follows the classical Bayesian approach
minimizing the cost function
The observation error covariance matrix
The observation operator
The minimization of the cost function Eq. (1) requires the evaluation of the
gradient of the cost function with respect to the state vector:
In order to achieve better convergence of the minimization algorithm,
pre-conditioning is applied, transforming the state vector
For the regular inversions, we use the limited memory quasi-Newton algorithm
m1qn3 developed by Gilbert and Lemaréchal (1989), which also allows
for the optimization of non-linear problems (as the semi-lognormal pdf (Eq. 2) introduces non-linearity to our optimization problem). In order to
evaluate the posterior uncertainties, additional inversions are performed
using a conjugate gradient algorithm (Fisher and Courtier, 1995; Lanczos,
1950; Meirink et al., 2008) for minimization and the linear expansion of the
emission deviation factors (Eq. 3). The posterior covariance is then
computed from the leading eigenvalues of the Hessian of the cost function:
Since FLEXPART-COSMO is a limited domain model, providing the
source–receptor relationship due to emissions in the European COSMO-7
domain, it requires the provision of background mole fractions
(baselines), representing the CH
We applied two different approaches to estimate the model representation
error. The first approach, denoted “OBS”, is similar to the method described
by Henne et al. (2016), evaluating the residuals (difference between
observations and model simulations) as a function of CH
As alternative to the model representation error OBS described above, a
second approach, denoted “METEO”, has been developed, parameterizing the
model representation error as a function of wind speed:
FLExKF is an inverse modelling system based on an extended Kalman filter as described in detail in Brunner et al. (2012, 2017). Observations are assimilated sequentially (here day by day) to provide the best linear unbiased estimate of the emissions and their uncertainties based on measurements up to the present time of the assimilation. Rather than estimating monthly or annual mean emissions, the system adjusts the emissions continuously as the assimilation proceeds and in this way creates a smoothly varying emission field that later can be averaged to monthly or annual means. The filter includes a forecast step, which predicts the evolution of the emissions from one assimilation time step to the next. The simplest assumption is persistence (i.e. no change with time), but to incorporate seasonally varying prior emissions, a non-zero forecast update was implemented that follows the linear change in prior emissions from 1 month to the next. Since the forecast step is associated with an uncertainty, the posterior uncertainty can become larger than the prior uncertainty in regions that are poorly constrained by observations. In order to avoid an unrealistic growth of the uncertainties in these regions, the posterior uncertainties are reset to the prior uncertainty whenever they become larger.
The state vector consists of two components: (i) emissions on a reduced grid
with a total of 3608 elements for inversions with observation data set O1
and 6497 elements for inversions with observation data set O2 (Sect. 3.1 and
Table 1) and (ii) coefficients of an AR(1) autoregressive process describing
temporal correlations in the residuals at each individual site. As described
in Brunner et al. (2012), the reduced grid has high
spatial resolution near the measurement sites and lower resolution further
away, reflecting the reduced contribution of emissions at larger distance to
observed CH
Another option in FLExKF is to optimize baseline mole fractions at each
observation site in addition to the gridded emission field. However, in the
configuration used here, the baselines (Rödenbeck baselines) described
in Sect. 2.2.2 were used directly without optimization. The results of
FLExKF should be readily comparable to those of FLEXVAR, since the same
FLEXPART-COSMO back trajectories, baselines, and observations were used.
Spatial correlations in the prior emission uncertainties were represented in
the prior error covariance matrix with a correlation length scale of 200 km
(exponential decay as in Eq. 8). The matrix was scaled such that the prior
uncertainty of the total domain emissions was 20 % (1
TM5-4DVAR is a global inverse modelling system based on the 4DVAR data
assimilation technique and has been described in detail by Meirink et al. (2008), while subsequent updates have been reported in
Bergamaschi et al. (2018a, 2010). TM5-4DVAR uses the Eulerian atmospheric
chemistry transport model TM5 (Krol et al., 2005), a
two-way nested zoom model, which allows the system to zoom in over specific
regions of interest. Here, we apply the
As for the regular FLEXVAR inversions, a semi-lognormal pdf has been used
(Eq. 2). Minimization of the cost function Eq. (1) is performed using the
m1qn3 algorithm (Gilbert and Lemaréchal, 1989) and the adjoint of
the tangent linear TM5 model (Krol et al., 2008; Meirink et al., 2008)
for evaluation of the gradient of the cost function Eq. (11). Four groups of
CH
The atmospheric observations used in this study (within the COSMO-7 domain)
include ground-based CH
The atmospheric CH
European monitoring stations used in this study. “Alt” is the surface altitude (m above sea level), “SH” is the sampling height (m) above ground, “ST” specifies the sampling type (“I”: in situ measurements; “D”: discrete air sample measurements). “FLEX” is the release height (m) used for calculation of the FLEXPART-COSMO back trajectories (“a.g.l.”: release height above model surface; “a.s.l.”: release height above sea level). The column “M” indicates the stations which have been classified as mountain stations. The last two columns indicate the use of the corresponding station data in the observation data sets O1 and O2.
For the in situ measurements (which are available quasi-continuously in
time), we assimilate only early afternoon data for stations in the boundary
layer and night-time data for mountain stations
(Bergamaschi et al., 2015),
selecting the 3 h time interval of the FLEXPART back trajectories (which
are provided for [00:00–03:00, 03:00–06:00, …] UTC), which is closest to
the time interval [12:00–15:00] LT for the stations in the boundary layer
and [00:00–03:00] LT for the mountain stations (indicated in Table 1 by
column “M”), respectively. This procedure ensures consistent averaging of
the FLEXPART back trajectories and the assimilated observations over the
same 3 h time intervals. Discrete air samples were taken as available,
i.e. without any temporal selection. The measurement uncertainty is set to
3 ppb for all observations (for observational part
In this study, we investigate two observation data sets (Table 1). The first data set, denoted O1, is considered the observational base data set and uses only the ICOS and NOAA data, while the second data set, O2, also includes all additional in situ measurements. The largest difference between the two data sets is the much better observational coverage of the British Isles in O2 with six in situ measurement stations located in that area, compared to only one station with discrete air sampling (MHD/NOAA) in O1.
Three different emission inventories are used alternatively as prior
estimates of the major anthropogenic CH
Natural CH
Using the above emission inventories, we have assembled the emission data sets E1, E2, and E3 as compiled in Table 2 and used as prior estimates for the different inversions described in Sect. 3.4. All emission data sets have been mapped on the COSMO-7 grid, using the Python package “emiproc” (Jähn et al., 2020), which has been integrated into the FLEXVAR inverse modelling system.
Emission inventories used in this study. The second column
(“Total”) lists the total CH
In order to extract from gridded emission data (on COSMO-7 grid) total
emissions of countries (or group of countries), country masks have been
generated using the “Natural Earth dataset”
(
Since the COSMO-7 domain does not cover the upper northern part of the UK, a
correction factor of 1.057 is applied to estimate the total emissions of the
country region “UK
Table 3 compiles the different FLEXVAR inversions presented in this paper.
INV-E1-O1 represents the base inversion, using the emission data set E1 as
prior estimates, the observation data set O1, the METEO model representation error
(Sect. 2.2.3), the Rödenbeck baselines (Sect. 2.2.2), and our default
settings for the prior error covariance. A first set of sensitivity
inversions investigates the impact of using alternatively the particle position baselines and the alternative parameterization OBS of the model
representation error (and the combination of both). In a further inversion
series, we analyse the sensitivity of the inversions to the main settings of
the prior error covariance matrix, i.e. for the spatial correlation length
constant,
In addition to the FLEXVAR inversions compiled in Table 3, inversions with the FLExKF system (described in Sect. 2.3) and with TM5-4DVAR (described in Sect. 2.4) have been performed for comparison with FLEXVAR (and will be discussed in Sect. 4.3). These inversions have been made for both observational data sets, O1 and O2, using the emission inventory E3 as prior estimates. Furthermore, additional FLExKF inversions have been performed using alternatively E1 as prior estimates.
FLEXVAR sensitivity inversions. The column “Prior” lists the
emission data set used (Table 2) and column “Obs” the observation data set
(Table 1). “MRE” is the applied model representation error (Sect. 2.2.3), and
“Baseline” lists the applied approach to calculate the baselines (Sect. 2.2.2). “
Figure 1 shows maps of European CH
Sensitivity of FLEXVAR inversions to different approaches to
calculate the baselines and to parameterize the model representation error.
Total CH
Time series of simulated and observed CH
Figure 3 illustrates the two different baselines at some example stations
during the 3-month period from 1 April until 1 July 2018. In general, both
baselines are rather similar, including their synoptic variability. However,
there are certain periods during which the particle position baselines
are somewhat higher than the Rödenbeck baselines, for example, at KIT, SAC,
and OPE during the period between day 140 and day 162. Consequently, the
observational forcing (i.e. the enhancement of the observations above
baseline) is lower during such periods for the particle position baselines, resulting in lower derived emissions. One major difference
between both approaches is that in the case of the Rödenbeck baselines, the
background mole fractions are transported to the stations by TM5, while in
the case of the particle position baselines, they are transported by FLEXPART.
In order to further investigate which baselines are more realistic, we have
compared model simulations and observations for “background conditions”,
defined as events when the contribution of European emissions (evaluated by
Eq. 10) is lower than a certain threshold (here set to 5 ppb). Figure S2
shows the comparison for eight stations, for which a sufficient number
(
Figure 1 illustrates the sensitivity of the derived emissions to the applied
parameterization of the model representation error. Inversion
INV-E1-O1-S2.1, for which the OBS model representation error has been
used, results in overall lower CH
The OBS model representation error increases with increasing observed
CH
Given the relatively large impact of the parameterization of the model representation error and the baselines, we have also performed an inversion combining the OBS model representation error and the particle position baselines (inversion INV-E1-O1-S2.2), which yields further reduced country total emissions compared to INV-E1-O1-S2.1 and INV-E1-O1-S1 (Fig. 2).
In the following, the sensitivity of the FLEXVAR inversions to the main
parameters of the prior covariance is investigated, i.e. horizontal
correlation length constant, temporal correlation scale constant, and
assumed uncertainties of emissions per grid cell and emission time step.
Figure S4 shows inversions for horizontal correlation length constants
Figure S5 shows the dependence of the inversions on the assumed uncertainties of prior emissions per grid cell and month for values of 50 % (INV-E1-O1-S4.1), 100 % (default value; INV-E1-O1), and 200 % (INV-E1-O1-S4.2). The increase of the assumed prior uncertainty leads to a significant increase of the derived regional inversion increments. This effect is most pronounced at larger distances from the monitoring stations, where observational constraints are relatively weak. Especially the large inversion increments visible in INV-E1-O1-S4.2 at the eastern domain boundary are probably an artefact, since the inversion may generate such patterns in regions far from the observations to compensate for systematic errors, for example, in model transport and with little penalty in the cost function in the case of prior uncertainties that are assumed very high.
Despite the dependence of the smaller-scale regional inversion increments on the assumed prior uncertainties, the impact on the derived annual total emissions remains again very small for the country regions shown in Fig. 2, since their emissions are relatively well constrained by the available observations and since differences in the smaller-scale inversion increments are averaged out over larger areas.
Sensitivity of FLEXVAR inversions to applied prior emission
inventories.
Figure 4 shows maps of the European CH
While the base observation data set O1 uses only the ICOS in situ stations,
complemented by the NOAA discrete air sampling sites, nine further in situ
stations from other networks/institutions are added in observation data
set O2 (Table 1). Six of the additional stations are located on the British
Isles, two in Switzerland, and one in the Netherlands. Figure 5 displays the
inversions INV-E1-O1 and INV-E1-O2 using the two different observation data
sets. As expected, the largest differences are visible in the regions around
the additional stations. For UK
Using the extended observation data set O2, we have performed additional inversions, using alternatively the prior emission data sets E2 or E3 instead of E1. As for observation data set O1 (discussed in Sect. 4.2.1), the sensitivity of derived annual total emissions to the applied prior emission data set is relatively small (Fig. 2).
Sensitivity of FLEXVAR inversions to assimilated observations.
Furthermore, additional inversions (of observation data set O2) have been performed using alternatively the particle position baselines (INV-E1-O2-S1) or the alternative parameterization OBS of the model representation error (INV-E1-O2-S2.1). In a similar way, as shown with observation data set O1 (discussed in Sect. 4.1.1. and 4.1.2.), the use of these alternative parameterizations results in generally lower posterior emissions, with lowest posterior emission calculated in inversion INV-E1-O2-S2.2 (combining the OBS model representation error and the particle position baselines).
In the following we compare the FLEXVAR inversions with inversions using the
extended Kalman filter (FLExKF) system (Sect. 2.3) and TM5-4DVAR (Sect. 2.4). Figure 6 shows the results of these three models using the emission
data set E3 as prior and the observation data set O2. Overall, all three
inverse models show relatively good consistency of the major spatial
patterns of the derived inversion increments, for example, the increase of
emissions over the BENELUX region and north-western France, the decrease of
emissions around Paris, and the decrease of offshore emissions over the
North Sea compared to the prior emissions. Since FLExKF uses the same
atmospheric transport as FLEXVAR, it is to be expected that the inversions
of these two models should give similar results. Nevertheless, there are
also some significant differences visible between the two models, especially
for the southern part of France, for which FLExKF yields overall lower
emissions than FLEXVAR. This difference is also clearly visible in the
derived country total emissions (Fig. 7; Table S4), with 10.3 % lower
annual total CH
The spatial emission patterns derived by TM5-4DVAR are in general similar to
those calculated by FLEXVAR and FLExKF (Fig. 6) but show also some
differences, for example, around the stations PUY and HPB, where TM5-4DVAR
calculates higher emissions than FLEXVAR and FLExKF, probably related to the
particular challenge to simulate mountain sites and sites in complex
topography. Further differences between the models are the different derived
seasonal variations of emissions, with larger variations calculated by
TM5-4DVAR for Germany, France, and UK
Annual average CH
Total CH
Nevertheless, the differences in the annual total emissions for the country
regions are only moderate. For Germany, somewhat higher emissions are
calculated by TM5-4DVAR compared to FLEXVAR and FLExKF, while the posterior
emissions for France, BENELUX, and UK
Figure 7 also includes inversions of the three models using the base
observation data set O1. As discussed for FLEXVAR in Sect. 4.2.2.,
FLExKF and TM5-4DVAR also show higher emissions for UK
In order to evaluate the quality of the derived emissions, it is useful to
analyse how well the observations are reproduced by the models. Figure S6
compares the statistics (correlation coefficient and rms difference) for the
three models (using prior emission data set E3 and observation data set O2).
At most stations relatively high correlation coefficients and low rms
differences are obtained by all three models. However, stations with larger
regional emissions (e.g. LUT, CBW, BRM, IPR) or complex topography (e.g.
OXK, IPR) show generally poorer statistical performance. Figure S6 also
shows that the best statistical performance is achieved by FLEXVAR with a
mean correlation coefficient of
Figure S7 shows the time series of observed and simulated CH
In the following, we compare the annual total CH
Figure 7 shows that the CH
We have presented the novel inverse modelling system FLEXVAR based on the
4DVAR assimilation technique and FLEXPART-COSMO back trajectories driven by
COSMO meteorological fields at
We have investigated the sensitivity of the FLEXVAR inversions to internal
parameterizations, model settings, and main model input data. Using the
particle position baselines yields in general lower derived emissions
compared to inversions which apply the Rödenbeck baselines, resulting
in differences in the annual total emissions of 5 %–14 % for the analysed
country regions (Germany, France, BENELUX, and UK
The FLEXVAR and FLExKF inversions at high spatial resolution of
The inverse models derive higher annual total CH
Our study demonstrates that the new FLEXVAR system can be applied for
verification of reported emissions, as planned, for example, by Empa for its
quasi-operational system to estimate Switzerland's annual CH
While the relatively good agreement among the three models used in this study gives some confidence in the robustness of the inverse modelling results, further specific studies should be performed to assess the quality of the top-down estimates independently. Such assessments should include the comparison with further inverse models, comparison with independent regional emission estimates (e.g. based on aircraft or satellite measurements), and a more detailed validation of the applied atmospheric transport models (especially regarding the simulation of boundary layer height dynamics and vertical transport).
The code of the FLEXVAR inverse modelling system is available upon request.
The atmospheric observations from ICOS are available at
The supplement related to this article is available online at:
PB led the FLEXVAR development. AS designed the FLEXVAR concept and performed the technical implementation of the FLEXVAR code. PB performed the FLEXVAR and TM5-4DVAR inversions. DB performed the FLExKF inversions and contributed to the integration of the FLEXPART-COSMO back trajectories into FLEXVAR. JMH generated the FLEXPART-COSMO back trajectories and contributed to the development of the FLEXVAR emission preprocessing. SH contributed to the development of the FLEXPART-COSMO modelling system. PB prepared the paper and figures with contributions from DB, AS, and JMH. SH, MR, TA, TB, HC, SC, MD, GF, AF, DK, XL, MLe, MLi, MLo, GM, JMW, SOD, BS, MS, PT, GV, and CYK provided atmospheric observation data.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The VERIFY project has received funding from the European Union's Horizon
2020 Research and Innovation programme under grant agreement no. 776810. We
are grateful to ECMWF for providing computing resources under the special
projects “Improve European and global CH
This research has been supported by Horizon 2020 (grant no. VERIFY (776810)).
This paper was edited by Ilse Aben and reviewed by two anonymous referees.