Introduction
Although the total CO2 emissions of developed countries
may be well constrained from the total consumption of fossil fuel, their
spatial and temporal distribution are not known with the same level of
accuracy. In so-called bottom-up emission estimates, CO2 emission is
calculated as a combination of geo-referenced activity proxies (e.g. road
traffic data, or number and type of buildings that relate to residential
emissions; Gurney et al., 2012) multiplied by emission factors, accounting
for the disaggregation of national annual budgets when dealing with regional
or city inventories. The accuracy of the bottom-up inventories is seldom
assessed and mostly relies on the difference between various estimates and on
expert knowledge.
Due to the high population density associated with ground transportation,
residence and industry, anthropogenic CO2 emissions are large within
cities (Pataki et al., 2006). The emitted CO2 is transported in the
atmosphere and results in elevated CO2 concentration above and downwind
of cities. There is therefore a potential to estimate the net CO2 flux
of a city from a few atmospheric concentration measurements located within or
in the vicinity of the city (McKain et al., 2012). Over a very dense urban
area, the net CO2 flux is dominated by fossil fuel emissions, but over
less dense urban structures, the net ecosystem exchange (NEE) becomes
significant and can partly offset fossil CO2 emissions during the
growing season (Nordbo et al., 2012). Top-down net CO2 flux estimates,
constrained by independent atmospheric measurements, could come in complement
to, or for the assessment of, current estimates that rely on bottom-up
inventories.
The technique of estimating surface CO2 fluxes from atmospheric
composition measurements – and potentially from prior information – is
relatively mature. It has been used for many years to estimate the biogenic
fluxes on the global (Gurney et al., 2002; Chevallier et al., 2010),
continental (Broquet et al., 2013; Peylin et al., 2005) and regional (Lauvaux
et al., 2009, 2012) scales. However, because of uncertainties in the
atmospheric transport, insufficient measurement sampling, and inconsistencies
between the mathematical framework hypothesis of most inversions (e.g. no
biases, Gaussian distribution of errors, uncorrelated observation errors) and
the reality, the results are not always consistent, in particular on the
regional scale, as shown for instance through the recent comparison of
global- and continental-scale biogenic flux estimates by several global
inversions (Peylin et al., 2013).
Estimating the net CO2 flux of a city using similar mathematical and
modelling tools amplifies the difficulties inherent to the atmospheric
inversion. The spatial heterogeneity of the source and the possibility of
having very high emissions locally (e.g. a power plant) make the structure of
the prior error statistics complex and the concentration plume highly
variable. Relating mole fractions to city sources furthermore requires
accurate atmospheric transport modelling on a fine scale. Atmospheric
transport in urban areas is influenced by specific meteorological processes
such as higher roughness of urban canopies (Zhao et al., 2014) and urban heat
island effects (Nehrkorn et al., 2013). For instance, Pal et al. (2012)
reported significantly thicker boundary layer over the city of Paris than in
the surrounding rural area during a 4-day campaign that took place in March
2011, which was interpreted as a consequence of the urban heat island effect.
Another difficulty, shared with the inversion of biogenic fluxes, lay in the
temporal variability of the fossil fuel emissions, which have a strong daily
cycle but also day-to-day variability resulting from, for instance,
temperature changes (through heating) or activity (e.g. traffic) variability.
Last, measurements in and around a target city collect CO2 molecules of
various origins that must be separated into city sources and remote sources
and sinks through the inversion.
This challenge has been addressed recently by several research projects, e.g.
INFLUX (sites.psu.edu/influx; Turnbull et al., 2014) over Indianapolis or
Megacities (http://megacities.jpl.nasa.gov; Duren and Miller, 2012)
over Los Angeles, which have set up a network of surface, tower and airborne
measurements of the atmospheric CO2 mole fractions. Satellite data may
also provide valuable information as shown by Kort et al. (2012). The results
from the ongoing urban CO2 measurement project at Salt Lake City
indicated that monthly emission relative changes of 15 % could be
detected at the 95 % confidence level with the current monitoring system
(McKain et al., 2012) even though this study concluded on the inability to
derive absolute estimates for a given month.
The CO2-Megaparis project has a similar objective for the Paris area.
This is a potentially favourable case as the city is very dense and the
emissions intense over a limited surface, with a fairly flat topography in
the surroundings, which makes the atmospheric transport modelling easier. A
pilot campaign in early 2010 was conducted in the framework of the MEGAPOLI
project. Measurements of the mole fraction of CO2 and its isotopes have
been used to estimate the relative contribution of fossil and biogenic
emissions in the concentration gradients (Lopez et al., 2013). The main
campaign started in August 2010 with the installation of three CO2 and
CO monitoring stations within the city and its surroundings that provided
near-continuous measurements until July 2011. These three stations complement
two stations of the ICOS France network located in the Paris region outside
the city that have been operational for several years. Lac et al. (2013) made
a first analysis of the measurements and a comparison against atmospheric
modelling using the Meso-NH mesoscale transport model, combined with a
surface scheme that accounts for the urban environment, for a period of 5
days in March 2011. They demonstrated the ability of the modelling framework
to reproduce several features of the mixing layer height, as reported in Pal
et al. (2012), and of the mole fraction daily cycle.
Information about the CO2 measuring stations that are used in
this paper.
Location
Acronym
Latitude
Longitude
Height
Distance
(∘)
(∘)
a.g.l.
from Paris
(m)
centre (km)
Eiffel Tower
EIF
48.8582
2.2946
300
4 (W)
Montgé-en-Goële
MON
49.0284
2.7489
9
35 (NE)
Gonesse
GON
48.9908
2.4446
4
16 (N)
Gif-sur-Yvette
GIF
48.7100
2.1475
7
23 (SW)
Trainou forest
TRN
47.9647
2.1125
180
101 (S)
Map of the study area showing the location of the continuous
CO2 measurement stations that are used in this paper (red dots). The
black lines show the model grid with a 2 km resolution at the centre, and
10 km on the sides. The red line shows the limits of the Île-de-France
region.
Large efforts have been made by AirParif, the air quality agency for the
Paris area, to generate an inventory of the Paris area emissions, for various
pollutants and for CO2 as well. The AirParif emission inventory,
detailed in Sect. 2.2, provides an hourly description of the CO2
emissions at ≈1 km resolution for representative weekdays and
months. We use this inventory as an input to the atmospheric transport
simulations and compare the results to the atmospheric concentration
measurements from the five sites. We then attempt a correction of the
inventory based on the differences between the observed and modelled mole
fractions. With only five stations in the vicinity of the city, there is
likely not enough information to constrain the spatial distribution of the
emissions. We therefore only rescale the emissions, relying on the spatial
distribution provided by the Airparif inventory. For the inversion, NEE and
fossil fuel emissions are optimised separately. We focus on two 30-day
periods in the autumn of 2010. This choice is driven by the expectation of
rather small biogenic fluxes during this time period, which makes easier the
interpretation of the measurements in terms of anthropogenic fluxes. Our
objective is to assess whether a reliable estimate of the emissions on the
daily to monthly timescales can be derived from the combination of
atmospheric measurements, available inventories and information on the
atmospheric transport. A forthcoming paper will apply the methodology to a
full year of observations and analyse the result for the spring and summer
periods, when CO2 uptake by NEE can partially offset fossil fuel
emissions (Pataki et al., 2007). In the following, Sect. 2 analyses the time
series of measured and modelled CO2 mole fractions; Sect. 3 describes
the methodology to correct the inventory based on the measurement–model
mismatches. The results are shown in Sect. 4, while Sect. 5 discusses the
results and provides conclusions.
Measurements and direct simulations
CO2 concentration measurements
In this paper, we use CO2 mole fraction measurements that have been
acquired continuously in the framework of the CO2-Megaparis and
ICOS-France projects. Three stations have been equipped with high-precision
CO2/CO analysers (Picarro G1302) specifically for the project
objectives. One is located in the heart of Paris, at the summit of the Eiffel
Tower, 300 m above the surface. Two are located to the north and north-east
of the Paris area in a mixed urban–rural environment. They are complemented
by two ICOS-France stations that were operational before the start of the
project. One is located in the south-west, about 20 km from the centre of
Paris, while the other is a tall tower located further south by about
100 km. Both use gas chromatograph analysers (Agilent HP6890). The locations
of the stations are given in Table 1 and are shown in Fig. 1. They are very
roughly located along a NE–SW direction, which defines the dominant wind
directions, thus favourable for the monitoring of the CO2 increase due
to the emissions of the Paris area, with a station at the edge of the urban
area in both directions. The measurements are quality controlled and binned
at a temporal resolution of 1 h. They have been regularly calibrated against
the WMO mole fraction scale (Zhao and Tans, 2006) so that measurement
accuracy to the WMO-X2007 scale is estimated to be better than 0.38 ppm. The
instrumental reproducibility is better than 0.17 ppm on the 5 min average
measurements available from the CO2-Megaparis stations, and the temporal
averaging to the hourly mean values used in this paper leads to precision
much better than the accuracy (Zhao and Tans, 2006).
Typical day-total CO2 emissions of Île-de-France, according
to the AirParif year 2008 inventory, for a weekday in October. The point
sources are not included in this map. The emissions are provided for the area
outlined in red in Fig. 1. The resolution is 1 km. The grid is 0.2∘
in latitude and 0.4∘ in longitude.
Atmospheric transport modelling
Atmospheric transport modelling provides the link between the surface fluxes
and the atmospheric mole fractions. Here, we use the Chimere transport model
(Menut et al., 2013) with a resolution of 2 km around the city of Paris, and
10 km for the surroundings of the modelling domain (see Fig. 1). There are
118 × 118 pixels in the modelling grid that covers an area of
approximately 500 × 500 km2. There are 19 layers on the
vertical, from the surface to 500 hPa. The Chimere transport model is driven
by ECMWF-analysed meteorology at 15 km resolution. There is no urban scheme
in the atmospheric modelling that is used here, which may be seen as a
significant limitation to our inversion set-up. However, we conducted forward
simulation comparisons between our modelling and that used in Lac et al.
(2013), which includes specific surface parameterisation to account for the
urban area, and we did not find significant differences in the simulated
CO2 mole fractions.
The model simulates the mole fractions that are driven by the surface fluxes
and the boundary conditions. The surface fluxes that are accounted for in the
simulations are the sum of the following.
Anthropogenic fossil fuel CO2 emissions within the Île-de-France region, from the AirParif inventory, as described in Sect. 2.3 and shown in Fig. 2. Île-de-France is the administrative region spreading typically within 60 km around the city of Paris, the boundaries of which are shown in Fig. 1.
Anthropogenic fossil fuel CO2 emissions outside the Île-de-France region, according to the Edgar database (Janssens-Maenhout, 2012) available at 10 km resolution. These are only annual mean fluxes, and there is no description of the diurnal or seasonal cycle in this
inventory.
Biogenic fluxes from the C-TESSEL land surface model as described in Sect. 2.4
The CO2 boundary conditions prescribed at the lateral and top edges of
the simulation domain, and transported inside the domain by Chimere, are
obtained from the Monitoring Atmospheric Composition and Climate (MACC)
global inversion, v10.2 (http://www.copernicus-atmosphere.eu/). In this
simulation, the global distribution of surface CO2 fluxes has been
optimised to fit the mole fractions measured at a number of stations
distributed over the world, given their assigned uncertainty and prior
information of the surface fluxes. Given the relatively coarse spatial
resolution of the transport model used in the MACC inversion, CO2
boundary conditions here are temporally and spatially very smooth and have
little impact on the spatial gradients simulated within the domain area.
AirParif inventory
The AirParif air quality agency
(http://www.airparif.asso.fr/en/index/index) has developed an inventory
of emissions (for greenhouse gases such as CO2 but also for air
pollutants) at 1 km spatial resolution and an hourly time step for the
Île-de-France region. The emissions are quantified by activity sectors.
The improvement in methodologies and emission factors leads to frequent
updates of the emission estimates.
Nearly 80 different source types are included in the inventory with three
main classes: point, linear and diffuse sources. Point sources correspond to
large industries, power plants, and waste burning; linear sources are related
to transportation, while diffuse sources are mostly associated with the
residential and commercial sectors. The road traffic emission estimates use a
traffic model and vehicle-counting devices that report the number of vehicles
and their average speed over almost 40 000 km portions of roadways. Large
industries are requested to report their CO2 emissions and these are
used in the inventory. For smaller industrial sources that are not required
to report their emissions, a disaggregation of the regional fuel consumption
is made based on the number of employees, leading to larger uncertainties. We
have used the latest available version of the inventory, corresponding to the
year 2008, which has been developed for five typical months (January, April,
July, August, and October) and three typical days (a weekday, Saturday and
Sunday) to account for the seasonal and weekly cycles of the emissions.
Therefore, this inventory estimates typical emissions but does not attempt to
reproduce the daily variations resulting from specific meteorological
conditions, or specific events such as public holidays.
Temporal variation of the main CO2 emission sectors according
to the AirParif inventory for the whole Île-de-France region. The figure
shows, for 5 typical months and 3 typical days (weekday, Saturday, Sunday),
the hourly CO2 emissions. The black line is the total emission (left
scale), while the four coloured lines are for different sectors (right
scale).
Figure 2 shows an example of the spatial distribution of the total emissions
for a weekday in October. Typical values are a few hundred
gCO2 m-2 day-1 within the city and a few tens of
gCO2 m-2 day-1 in the suburbs. The main roads are clearly
shown with flux enhancements of a few tens of
gCO2 m-2 day-1 at the 1 km2 resolution of the
inventory. Further processing of this map shows that one-third of the
Île-de-France emissions are within 10 km of the Paris centre, and that
61 % are within 20 km.
There is a large temporal variation in emissions, as shown in Fig. 3, mostly
on the daily scale, but also on the weekly and seasonal scales. Most
components show a large daily cycle with minimum emissions at night. During
the day, the traffic-related emissions show several maxima in the morning,
midday, and late afternoon. The daily cycles of the other activities are less
pronounced but nevertheless significant. Point sources have the smallest
daily cycle amplitude due to the industrial temporal profile that is
relatively flat. The Paris area has few point sources, and they contribute
typically 20 % of the total emissions. The seasonal cycle is most
pronounced for the residential emissions related to heating and cooking. One
notes that residential CO2 emissions do not go to zero during the summer
months, because energy is still consumed for cooking and for heating water in
summer.
In the following, the AirParif inventory for the year 2008 is used as a prior
estimate of the fossil fuel emissions within the Île-de-France region,
both for the direct transport simulations (Sect. 2.5) and for the flux
inversion (Sect. 3). Note that the inventory of point source emissions
provides injection heights that have been used in the source term of the
simulations. The AirParif inventory is provided as a function of legal time,
and we have accounted for the time shift between legal time and UTC time,
including the impact of daylight saving. Note that, due to the longitude of
Paris, UT time and solar times are very similar.
Mean diurnal cycle of the biogenic flux (net ecosystem exchange) for
the 12 calendar months and for the same area as in Figs. 2 and 3 which is
outlined in red in Fig. 1. The values were derived from an average of the
C-Tessel simulations.
Biogenic fluxes
The NEE fluxes used here are provided by the land surface component of the
ECMWF forecasting system, C-TESSEL (Boussetta et al., 2013). They are
extracted from the ECMWF operational archives at the highest available
resolutions, 15 km and 3 h. These data are interpolated in space (2 to
10 km) and time (1 h) to be consistent with our atmospheric transport model
grid and temporal resolution.
Figure 4 shows the mean daily cycle of NEE for the Île-de-France area and
for the 12 calendar months. There are large diurnal and seasonal NEE cycles.
The flux is positive (emission) during the night and negative (uptake) during
the day, even during the winter months, given the rather mild winter
temperature prevailing over the Paris area. Nevertheless, the amplitude of
the daily cycle of NEE is much larger in summer than it is in winter. The NEE
values are of similar magnitude than the anthropogenic emissions with a
strong anti-correlation in the daily cycle (negative NEE vs. large
anthropogenic emissions during daytime; positive NEE and smaller
anthropogenic emissions during the night). During the winter, NEE is
relatively small and the anthropogenic emissions clearly dominate, but
daytime NEE still offsets on average ∼ 20 % of the emissions,
according to the C-TESSEL model simulations. During spring and summer,
however, the daytime NEE uptake is larger in absolute value than the
anthropogenic emissions, as shown through a comparison of Figs. 3 and 4.
As our main interest is in the anthropogenic emissions, we chose to analyse a
period when the biogenic flux is small, i.e. during
autumn and winter. The present paper focuses on
two 30-day periods that start on 21 October and 27 November 2010. During
these periods, the monthly mean hourly NEE fluxes are less than
3 ktCO2 h-1 over the Île-de-France area. NEE is then small,
but not negligible, compared to anthropogenic emissions during the chosen
inversion periods.
Direct CO2 transport simulations
Figure 5, together with Fig. S1 in the Supplement, shows the time series of
the CO2 mole fractions together with an indication of the modelled wind
speed and direction to help the interpretation of the results. These time
series are derived from observations and direct atmospheric modelling as
described in Sect. 2.2.
The Trainou (TRN) station (bottom row) is far from the Paris agglomeration.
In addition, the measurement inlet is 180 m from the surface. It shows a
diurnal cycle amplitude that is much smaller than at the other sites. In
addition, the modelled contribution from both anthropogenic and biogenic
fluxes within the simulation domains is limited to a few ppm, as shown by the
difference between the black and green curves. There are a few exceptions
however, essentially when the wind blows from the north, i.e. from the
direction of the city of Paris, and transports fossil CO2 from the urban
area to the TRN rural site. The best examples are around 8 and 23 December.
For these particular cases, the measurements at TRN are significantly larger
than the model results. The underestimate by the model is not limited to
these dates and there are significant discrepancies between the model and the
measurements at this remote background site, in particular at the end of
November and at the beginning of December.
The other sites are much closer to Paris and are then more affected by the
fossil CO2 emissions. At Gif-sur-Yvette (GIF), the largest mole
fractions are observed when the wind is from the north-east, which is
expected as the city of Paris is in that direction. There is also an impact
of the wind, as the largest mole fractions are measured under low wind speed
conditions. During the October–November period (Fig. S1), the wind is mostly
from the south and southwest, thus not from the city, and there is a
relatively good agreement between the modelled and measured mole fractions.
In December, the wind direction is more variable, the fossil CO2 signal
appears much larger, and there are very significant differences between the
measurements and the model estimates.
Gonesse (GON) is located to the north of the city, while
Montgé-en-Goële (MON) is further away, to the north-east. The shorter
distance to the main source may explain the larger signal at the former
station. The only cases when the modelled anthropogenic contribution is small
at GON (small difference between the black and green curves) is when the wind
is from the north. For other wind directions, the modelled signal is strong
– more than 10 ppm – and there are large differences between the
measurements and the modelling results. During December, the measurements are
most often larger than the model estimates. A similar observation can be made
at MON. Surprisingly, the measurements are significantly larger than the
modelling results, even when the wind blows from the north or north-east,
i.e. when the Paris agglomeration contribution is negligible (3 December,
6–9 December, 22–23 December). For these cases, the most likely explanation
is an underestimate of modelled CO2 from the boundary conditions or from
emissions within the modelling domain outside of Île-de-France.
Hereafter, we shall denote this contribution as that from “remote fluxes”.
Note that this impact from remote fluxes shows a large increase in the mole
fraction for the periods discussed above. We may then hypothesise that this
increase is underestimated. The interpretation is that anthropogenic
emissions from the Benelux area generate high concentrations that are
underestimated in the boundary condition field that is used in our
simulations.
The EIF site is at the top of the Eiffel Tower, 300 m above the city of
Paris. The wind speed for this station is larger than for the other one,
simply because it is higher in altitude. One expects atmospheric mixing
between the surface emissions and the inlet, so that the measurements are
representative of a larger area than e.g. MON and GON. Nevertheless, there
are some very significant differences between the modelled and observed mole
fractions at EIF. The differences may be huge, larger than 30 ppm, even
during the afternoon, e.g on 24 October, 7 November, 3 December, and 12
December. Clearly, our atmospheric modelling framework cannot properly
represent the mole fraction time series at the EIF station, either because of
strong local (sub-grid-cell) emissions, or because of atmospheric transport
processes that are not properly represented, in particular concerning the
vertical transport above the city. Further analysis of the model–measurement
mismatch is shown in Fig. S3. The largest mismatches are preferentially
observed during the morning and for low wind speeds, but are observed at all
hours of the day and for all wind speeds and directions, which prevents us
from attributing these mismatches to a specific bias in the transport model
or to a bias in the estimate of the emissions for a specific area.
The curves in Figs. 5 and S1 show very large temporal variations of CO2
within a day at all stations. Further analysis confirms that the largest
variations are observed during the night, when the mixing layer is shallow.
During the night and morning, the atmosphere is often very stable, so that
surface emissions accumulate within the lowest atmospheric layers, the
thickness of which ranges from a few metres to tens of
metres. The atmospheric mole fraction
is then mostly sensitive to local fluxes and vertical mixing – an
atmospheric process that is difficult to model – so that there is a large
uncertainty about the modelled link between the emissions and the atmospheric
mole fraction. The nighttime and morning measurements are thus not
appropriate for our flux inversion, as inverting them would be too sensitive
to atmospheric transport biases. As a consequence, we focus on the
concentration measurements acquired during the afternoon only, from noon to
4 p.m., when the mixing layer is usually well developed. The daily averages
of these afternoon measured and modelled values are shown in Fig. 5 as
diamond symbols.
Figure 6 shows a scatter plot of the measured and modelled mole fractions at
the five sites together with the statistics of their comparison. The scatter
plots confirm the visual impression of Fig. 5: there is a significant
correlation between the measured and modelled mole fractions, which
demonstrates the model skill. There are also significant discrepancies and a
large bias, in particular at the EIF station. The smallest errors (both
biases and standard deviations) are found at TRN, which is the site furthest
from Paris.
Time series of the measured (red) and modelled (green) CO2 mole
fractions (ppm) for the five sites used in this paper (see Table 1). The
black line is the modelled mole fraction that is transported from the domain
boundaries, with an additional contribution from anthropogenic emissions
outside the Île-de-France region (Edgar fluxes). The green line shows the
modelled mole fraction that includes the same contributions, plus the
biogenic fluxes within the modelling domain and the anthropogenic emissions
within the Île-de-France region. Red are the observations. Note that
there are some time periods when no measurements are available due to either
calibration processes or, more rarely, failure of the monitoring
instrumentation. For such periods, modelling results are not shown. The
symbols show the mean of the afternoon measurement–model values that are
used for the inversion. The blue arrows indicate the wind speed and direction
at noon. A length equivalent to 1 day on the x axis is for a wind speed of
10 m s-1. Grey shaded areas indicate Sundays. This figure is for the
30-day period starting on 27 November 2010. Figure S1 in the Supplement shows
the same figure for the other period.
Analyses and insight for the inverse modelling configuration
Both the measurements and the modelling results show some impact of the Paris
area anthropogenic emissions on the CO2 mole fractions at the five sites
analysed here. The mole fraction increases over the modelled large-scale
value depend on the wind speed and direction, and a typical order of
magnitude is 10 ppm. As expected, the signal is smaller for the rural
station of TRN, which is further away from the city than the other sites.
Many of the features in the measured time series are well reproduced by the
modelling framework, which gives some confidence in its usefulness to improve
the emission estimates.
Scatter plot of the measured and modelled CO2 mole fractions at
the five monitoring stations within and in the vicinity of the city of Paris.
The model vs. measurement bias, standard deviation and correlations are
provided within each subplot. This figure is for the 30-day period starting
on 27 November 2010. Figure S2 in the Supplement shows the same figure for
the other period.
There are also some significant differences between the measured and modelled
mole fractions that cannot be justified by inaccurate emission inventories in
the Paris area. The most obvious such feature is the mole fraction
underestimate at MON and GON under northerly wind conditions when these sites
have low sensitivity to the Île-de-France emissions. This feature
strongly suggests that remote fluxes lead to mole fraction increases that
have biases with typical magnitudes that are similar to the impacts of the
Paris area emissions. On the other hand, as the impact from remote fluxes is
large scale, one may expect that this impact will be similar for monitoring
stations upwind and downwind from the Paris urban area. The
model–measurement error may then be strongly reduced when analysing the
difference in mole fractions between two stations that are located upwind and
downwind from the Paris urban area, respectively. On the other hand, the mole
fraction difference between such stations that are close to the Paris area
should contain a clear signature of the emissions from this area, and a
relatively weak signature from other fluxes. It then suggests the use of
downwind–upwind gradients in the CO2 mole fractions rather than the
absolute value of CO2 measurements in the inversion procedure.
The other significant feature in the comparison of the modelled and measured
CO2 mole fractions is much larger errors at the EIF site than at the
other stations. These results illustrate the difficulty in modelling the
CO2 mole fraction within cities, even with a measurement inlet in
altitude, well above the sources. Note that McKain et al. (2012) also find
very large (> 30 ppm) model–measurement mismatches within the
urban area of Salt Lake City, even when using a high-resolution model.
Similarly, Lac et al. (2013) find large model–measurement differences at EIF
despite the use of an urban parameterisation in the modelling. The inability
to model the CO2 signal at EIF properly may have a detrimental impact on
the emission estimates derived from atmospheric inversion. Conversely, the
forward simulations show that the TRN site has low sensitivity to the Paris
area emissions due to its location further away from the city than the other
sites. Consequently, it cannot be used as a “downwind” site; in addition,
GIF is better suited as an “upwind site” for southerly conditions, as it is
closer to the urban area and therefore provides better information on the air
composition as it enters the city. These features suggest not to use EIF and
TRN and rather to focus on MON, GON and GIF to estimate the Paris area
emission from their measured mole fractions.
The main objective of the “gradient” inversion method is thus to focus on
the monitoring stations that are at the edge of the urban area and to
estimate the city-scale emissions by removing most of the upwind signal from
the measured and modelled concentrations. The upwind signal is driven by
remote fluxes both from the boundary conditions and by fluxes within the
model domain but outside the city whose estimates bear very large
uncertainties. The inversion method also attempts to select the downwind
measurements that are affected by the emissions from a large part of the
city, in an attempt to minimise the
impact of aggregation errors. Ideally, we would select only the wind
direction when one station lies directly downwind from another, with the city
of Paris in between. However, given the very limited network of stations
surrounding Paris, we have to broaden significantly the range of acceptable
wind directions.
Based on this analysis, the emission estimate procedure only uses the
measurements from GON, MON and GIF, and is based on the CO2 mole
fraction gradients between the upwind and downwind stations, a method which
requires the selection of favourable wind conditions. The mathematical
framework is described in the next section, while the inversion results are
presented in Sect. 4.
Flux inversion
Principles
We follow a linear Bayesian inversion approach with Gaussian error statistics
to determine the optimal surface fluxes (anthropogenic emissions and biogenic
fluxes) and their uncertainties from a prior estimate of the fluxes and their
uncertainties and from the mole fraction measurements.
We call x the state vector that gathers the scaling factors for the
6-hourly flux maps, xB its prior estimate, H
the matrix operator that relates state parameters and mole fraction gradients
according to the atmospheric transport model, y the observed mole
fraction gradients, yF the simulated impact on these
mole fraction gradients of the lateral boundary conditions and of the fluxes
that are not accounted for in the state vector, B the uncertainty
covariance matrix of xB, and R the error
covariance matrix of y. These components are detailed in the next
section.
The optimal solution is given by Tarantola (2005):
xA=xB+B-1+HTR-1H-1HTR-1y-yF-HxB
and its posterior error covariance matrix is
A=B-1+HTR-1H-1.
Note that A does not depend on the actual measurement values, but
varies, among other factors, with their temporal and spatial sampling.
State vector: x
Both the anthropogenic and biogenic prior fluxes described in Sect. 2 show a
large diurnal cycle that impacts the model simulations of CO2, and that
is uncertain. It then appears useful to invert this cycle together with the
flux daily mean values. However, as discussed earlier, only CO2
measurements during the early afternoon can reliably be used to estimate the
fluxes, and their information about the daily cycle is rather poor. We limit
the number of independent periods to four, corresponding to the local times
between 0 and 6, 6 and 12, 12 and 18, and 18 and 24 h, respectively.
For the fossil fluxes, we use a scaling factor for each individual day in the
state vector, which makes the number of corresponding variables amount to
30 × 4 = 120 for the 30-day period of the inversion. These
scaling factors apply to the prior flux estimates derived from the AirParif
inventory and are denoted λ0-6i,λ6-12i,λ12-18i,λ18-24i, with i between 1 and 30.
Similarly, we optimise scaling factors of the prior NEE flux from C-TESSEL.
The simulation domain shown in Fig. 1 is split into 3 × 3 large
boxes, and we choose the same 6 h periods as for the anthropogenic fluxes to
optimise scaling factors of NEE. However, we do not attempt a daily retrieval
of NEE, and considered a single scaling factor for optimising monthly NEE for
each 6 h window over a 30-day inversion period. The number of variables to
optimise NEE is therefore 3 × 3 × 4 = 36. In the
following, these NEE scaling factors are shown as α0-6X,α6-12X,α12-18X,α18-24X, where X is one of the
nine large boxes. One of the nine boxes covers the Île-de-France region,
while the other ones are in the surrounding area. In the Inversion results
sections, we analyse the inversion of NEE for the centre box (X = C)
together with those for the anthropogenic emissions. The surrounding boxes
provide some ability to the inversion system to control part of the errors
from remote NEE, but one cannot expect to get a reliable estimate of the NEE
in these areas given the weak observational constraint on this remote NEE.
The state vector x for the linear inversion has therefore
120 +36 = 156 variables that represent the scaling factors to the
modelled fluxes. The prior value of each of these scaling factors in
xB is 1.
Measurements gradients: y
y contains the measurement gradients that are used to constrain the
flux inversion. As explained above, we only use hourly measurements that have
been acquired during the afternoon from noon to 4 p.m. local time. In
addition, the corresponding measurements need to have a sensitivity to local,
unresolved, fluxes that is insignificant in comparison to that of
larger-scale fluxes. This condition is not met when the wind speed is low. We
therefore use for the inversion only the measurements filtered for wind
speeds larger than a given threshold at both sites used to compute the
gradient. The results presented in this study are obtained with a threshold
of 2 m s-1. The wind speed estimate used for such a selection is the
one analysed by the ECMWF at the location, height, and time of the
observation. This criterion retains about 70 % of the potential
measurements.
In Eq. (1), the downwind–upwind differences in mole fraction measurements
y are corrected for the contributions that are not accounted for in
the state vector (yF). yF are the
modelled mole fractions accounting for the boundary conditions and
anthropogenic fluxes outside Île-de-France (prescribed from the Edgar
database). This contribution is shown as a blue line in Fig. 5 and
Fig. S1 (in the Supplement).
When the wind is from the south-west (upwind direction between 160∘
and 260∘), GIF is considered upwind from the urban area, and the
corresponding y elements are the differences between the mole
fractions measured at either MON or GON and that measured at GIF. Similarly,
when the wind is from the north-east (upwind direction between 0∘ and
135∘), MON is used as an upwind reference to the GIF or GON mole
fraction measurements. For other wind directions, the measurements are not
assimilated.
Prior flux uncertainties and error correlations: B
Although we invert the scaling factors of fossil CO2 emissions for each
day and each 6 h period, the uncertainties in these factors are correlated.
We therefore attempt to assign correlations for the prior uncertainties based
on several considerations: (i) the monthly budget for the AirParif inventory
is generally stated to have an uncertainty of 20 %, which is used here;
(ii) we assume small positive correlations between the different 6 h
windows; (iii) we assume stronger correlations from day to day for a given
6 h window; and (iv) the a priori uncertainty of individual 6 h emissions
should have a typical order of 50 %.
Based on these considerations, we set, rather arbitrarily, prior error
correlations to 0.4 for two adjacent time periods (e.g. 12–18 and 18–24)
and to 0.2 for non-adjacent time periods (e.g. 6–12 and 18–24). For
successive days, we use an exponential decorrelation with a characteristic
time Tcor. The correlation between the prior uncertainties of the
fossil CO2 emission scaling factors is then the product of this
exponential and the time periods' correlation. For instance, the correlation
between λ0-65 and λ6-129 is
0.4 exp (-4/Tcor).
The results shown in this paper have mostly been obtained with a temporal
correlation Tcor of 7 days, but other values, from 1 to 30 days,
have also been tested. We have
verified that such a B matrix is positive-definite. The
desegregation of the assumed 20 % uncertainty for the monthly emission
totals, based on these temporal correlations, results in standard deviations
of uncertainties for individual 6 h periods of
33 % (Tcor= 30 days) to
50 % (Tcor= 7 days).
For the biogenic flux scaling factors, we set a relative prior uncertainty
(standard deviation) close to 0.70 with some variations according to the box
size (the variance varies inversely to the surface of the box), based on the
numbers derived at 0.5∘ resolution in Broquet et al. (2011). We do
not assign any spatio-temporal correlation between the various biogenic
scaling factors, i.e. between the nine boxes or the four time periods.
Similarly, there is no correlation in B between the prior
uncertainties in the biogenic and anthropogenic fluxes.
Operator matrix: H
The operator matrix H provides the link between the surface fluxes
and the mole fraction measurements. It combines the spatio-temporal
distributions of the fluxes, both for the AirParif inventory and the C-Tessel
biogenic fluxes, that are assumed and not modified through the inversion, the
atmospheric transport by the Chimere model, the sampling of the atmosphere at
the instrument locations, and the selection of gradients according to the
criteria developed in Sect. 3.3. Note that the AirParif inventory has a 1 h
temporal resolution. The direct simulation (Hx) uses the
description of the emissions at this temporal resolution. Each element of the
state vector corresponds to a natural or anthropogenic surface flux for a
longer time period. We use the atmospheric transport model to compute the
impact on the mole fraction of each surface flux (156 in total) corresponding
to an element of the control vector. The 4-D mole fraction fields from each
of these simulations are then sampled at the place and time of the
atmospheric observations used to compute the downwind–upwind gradients
corresponding to the observation vector. These simulated mole fraction
gradients provide the elements of each column of the H matrix.
Observation error: R
The measurements provided by the instrument are precise, certainly better
than 0.3 ppm. However, the observation error in R also includes any
source of misfit between the model and the data that is not accounted for in
the state vector, such as the representation error, the impact of the error
on the spatial distribution of the fluxes, and the atmospheric transport
modelling error. These are difficult to assess (Broquet et al., 2013),
although one expects significant values given the very heterogeneous urban
environment that is discussed here.
Due to the complexity and misunderstanding of the processes underlying the
observation error, which may lead to positive or negative correlations, we
ignore observation error correlations in the construction of R,
which is thus diagonal.
We use two statistical diagnostics of the misfits in the observation space
described by Desroziers et al. (2005) to infer typical observation error
variances: (i) the agreement between the sum of the uncertainty from the
prior estimate of the control parameters and of the observation error with
the RMS Root Mean Square of the prior
misfits to the assimilated data; and (ii) the agreement between the
observation error with the mean of the product of prior and posterior misfits
to the assimilated data. Based on this analysis, we set a 3 ppm observation
error for the mole fraction gradients that are used for the inversion.
We can note that this value is significantly smaller than the
model–measurement differences as shown in Fig. 5. This is due to the fact
that the observation errors related to uncertainties in the large-scale
impact of the remote fluxes are strongly correlated between the measurement
sites at a given time. Therefore, they vanish when considering gradients in
the model fractions rather than values at individual sites such as in Fig. 5.
This is further discussed in Sect. 4.2.
Inversion results
In the following, we present the result of the inversion described in the
previous section. We first analyse the modelled mole fractions, prior and
posterior, against the measurements. We then analyse the retrieved fluxes,
both NEE and fossil fuel.
Time series of the mole fraction differences between a station
(y axis label) and another one used as a reference (either GIF or GON) and
selected based on the wind direction (see Sect. 3.3). The symbols show the
mean afternoon concentrations (12 a.m.–4 p.m.) for the measurements (red),
and the prior (green) and posterior (blue) estimates. As in Fig. 5, the
arrows indicate the wind speed and direction. A similar figure for the other
time period is shown in the Supplement.
Mole fraction gradients
Figures 7 and S4 show the time series of the afternoon-mean mole fraction
gradients. Some days are missing, either because either station is
unavailable or because the wind direction does not fulfil the selection
criteria developed in Sect. 3.3. The prior value is almost always positive,
because the reference is chosen upwind of the Paris agglomeration. There are
a few exceptions, like on 22 December at GON, MON being used at the upwind
reference according to the wind direction. As GON is in the northern part of
the Paris agglomeration, one expects a smaller signal than for southerly wind
conditions. Further investigation demonstrated that this unexpected behaviour
is linked to a large spatial gradient of the CO2 concentration generated
by anthropogenic emissions over the Benelux accounted for in the Edgar
inventory and transported by the Chimere model (yF in
Eq. 1). Interestingly, the observations confirm the sign and the order of
magnitude of the gradient that is modelled with our set-up that uses crude
anthropogenic emissions outside Île-de-France.
Another negative gradient is observed at GIF-MON for northerly wind
conditions on 3 December. This is very unexpected, and we could not find a
valid explanation for this particular case.
In general, the observations are smaller than the prior, and the posterior is
in between. Indeed, the inversion result leads to concentration gradients
that are closer to the observations. As a result, some of the posterior
gradients are negative (see the end of the period at GIF in Fig. 7).
Figures 8 and S4 show scatter plots of measured vs. modelled mole fraction gradients. The
first row of the plots in each of these figures shows the modelled mole
fractions from the domain boundaries and the fossil CO2 emission outside
Île-de-France (black lines in Fig. 5, yF in Eq. 1)
against the measurement. This constitutes the modelled contribution to the
mole fraction that is not optimised by the inversion. The values on the
y axis show the modelled impact of the remote fluxes on the
upwind–downwind mole fraction gradient. As expected, this impact is small
compared to the measured gradient shown on the x axis.
The second row shows simulated CO2 induced by prior NEE and fossil
CO2 fluxes (i.e. those that are optimised through the inversion) against
measured mole fractions corrected for the large-scale values (i.e.
yF, shown on the y axis of the first row). Although
there is a large spread, the correlation is significant, which shows that the
transport model and the prior flux set-up have altogether some ability to
reproduce the observed CO2 mole fraction variability. For the
October–November period (in the Supplement), the biases are large for all
site gradients (2.1 to 4.8 ppm), whereas, for the November–December period,
they are even larger at GIF-MON (7.1 ppm) but rather small in comparison at
both other sites. The standard deviation of the measurement–model difference
varies with the sites and period, between 2.0 and 5.8 ppm. This is
significantly smaller than the standard deviation for the mole fractions
(Figs. 6 and S2) that vary between 3.6 and 6.6 ppm. These smaller values
confirm the choice made of attempting an inversion based on the mole fraction
gradient rather than the individual observations.
After the inversion, the agreement is significantly improved, as shown in the
third row. Note however that the standard deviation for the MON site (when
GIF is used as a reference) is slightly degraded from the prior value of
2.0 ppm. After the inversion, the correlation between optimised and observed
CO2 gradients for all three stations is larger than 0.90. For the other
time period shown in the Supplement (Fig. S5), the correlation statistics are
not as good. However, this is due to a lower variability of the gradients,
and the posterior standard deviations are 2.3, 2.7 and 2.3 ppm for the three
sites, and are then similar to the values shown in Fig. 7.
Scatter plot of the measured and modelled concentration gradients
for three downwind stations; either GIF or MON is used as an upwind
reference. The first row shows the mole fraction simulated using the boundary
conditions and the anthropogenic emissions outside Île-de-France
(yF in Eq. 1) against the measurements. The second row
shows the concentration estimates derived from the prior values for the
biogenic fluxes and anthropogenic fluxes against the corrected measurements
(i.e. y–yF in Eq. 1). The last row is the same
but uses the posterior estimates. This figure is for the November–December
period. A similar figure for the other time period is shown in the
Supplement.
Overall, the statistics improve significantly between the prior and the
posterior, and there is a good agreement between the measured and modelled
mole fraction gradients. This raises confidence in our ability to model the
impact of the Paris CO2 emissions on the atmospheric concentrations for
various wind conditions.
Daily flux estimates
Figure 9 shows the daily anthropogenic fluxes inferred by the inversion
procedure. Here, we have aggregated the four 6 h periods as well as their
uncertainty, accounting for the error correlations between the periods.
Although the inversion controls scaling factors, we show here the resulting
fluxes expressed in MtCO2 per day. There is a clear weekly cycle in the
prior emissions that are smaller during the weekends. One may also note a
shift in prior emission between 29 October and 1 November that corresponds to
a change in month and therefore the switch to a different data set in the
AirParif inventory. The Airparif inventory includes a profile for October.
For November and December, Airparif recommends the use of the January
emission profile.
Daily flux estimates of the anthropogenic emission for the 30 days
of the period. The blue line and shading show the prior flux according to the
AirParif inventory together with its assumed uncertainty. Yellow shading
indicates Sundays; note the weekly cycle with lower values during Saturdays
and Sundays. The red symbols and bars show the posterior estimates with their
uncertainty range. Both 30-day periods are shown.
The uncertainty reduction is significant for all the days of the two time
periods and a typical order of magnitude is a factor of 2. The emission
uncertainty is reduced even for days with no usable measurements, when the
wind direction is not within any of the two ranges defined in Sect. 3.3, due
to the temporal correlation of the uncertainties and thus of the corrections
applied to the prior (Sect. 3.4). The deviations of the flux estimate from
the prior follow the gradient observation deviation from the model (see
Fig. 7). These deviations are mostly negative, although they are positive for
a few days during both time periods. For the November–December period, the
posterior emission estimates are within the bounds of the prior uncertainty
range. On the other hand, the posterior estimate is much lower than the prior
flux during the second half of the October–November period (Fig. 9, top).
Interestingly, this period (1 to 20 November 2010) was very mild
(MeteoFrance, 2010), which suggests that the heating sector emissions were
well below the AirParif inventory values for that period. During this season,
according to the AirParif inventory, the heating sector, commercial and
residential, amounts to more than 50 % of the emission, so that the total
emission is highly sensitive to temperature. Note that AirParif recommends
the use of the January inventory for both November and December. As the
temperatures are generally milder during October than January, one may expect
that the inventory will be larger than the true fluxes during October, which
is then consistent with the negative correction to the fluxes during that
period.
Total flux estimates over the full 30-day period, for the four 6 h
periods. Red is for the anthropogenic emissions, green is for the biogenic
fluxes, while blue is for the total. The prior estimates are shown as open
rectangles, while the posterior is shown as filled rectangles. Both 30-day
periods are shown independently.
Figure 9 was generated using a 7-day correlation time for the emission
uncertainties. We also tested similar inversions using different error
correlation times (Tcor) in the range of the synoptic to seasonal
timescales that drives the emission variability to assess the result
sensitivity to this parameter. With a 1-day error correlation time, rather
than the 7 days used in our standard configuration, there are days with
little or no flux constraint by the observations, while there is no smoothing
of the day-to-day variability correction, resulting in an even larger spread
of the retrieved fluxes (not shown). At the other extreme, a 30-day
correlation time leads to much smoother results. Most of the daily optimised
flux estimates remain within the prior uncertainty range.
Monthly budgets
Figure 10 shows the monthly mean flux estimates for the Île-de-France
region for the various 6 h periods. It shows the results of the inversion
for the anthropogenic emissions, the NEE of the central box that covers
Île-de-France, as well as the total. Note that the total estimate is
necessarily the sum of the biogenic and anthropogenic fluxes. Conversely, the
uncertainty range of the total is not a simple sum, as it accounts for the
correlations between NEE and fossil CO2 emission errors in the
A matrix linked to the difficulty in distinguishing NEE and fossil
fluxes from the measurements.
The inversion has little impact on the fluxes for the 0–6 h and 18–24 h
periods. On the other hand, the impact is strong for the 6–12 h and
12–18 h periods. This is because we only use afternoon observations that
are sensitive to the emissions from the morning and afternoon periods only.
The assigned correlations in the set-up of the B matrix transport
some constraint to the other time windows. Although the inversion based on
the mole fraction gradients uses few independent observations, because of the
additional data selection based on the wind direction, the impact on the flux
estimates is significant.
Figure 10 shows that the uncertainty reduction is much larger for the fossil
fuel than for the NEE. This is the result of the inversion based on the
gradients downwind–upwind from the city which are mostly sensitive to the
fluxes in between. The contribution from the NEE to the measurement is then
small. Nevertheless, the correlations in the anthropogenic and NEE
uncertainties are small (±0.15 or less). These numbers indicate that the
observation sampling provides significant information to distinguish NEE from
fossil CO2 fluxes in the inversion. Although a given measurement cannot
trace the origin of the mole fraction excess, the assigned biogenic and
anthropogenic flux errors have different spatial and temporal patterns which
are exploited by the inversion system to attribute the mole fraction signal
to specific sectors. However, this attribution relies on the a
priori spatial and temporal distribution of the fluxes that are
affected by uncertainties. Thus, the theoretical ability of the system to
disentangle natural and anthropogenic fluxes may not be realised in practice.
Discussion and conclusions
This paper is a first attempt at estimating the Paris area emissions from
measurements of atmospheric CO2 mole fractions and prior flux knowledge.
There is obviously room for improvement in several aspects of the inversion
system: the number and spatial distribution of the monitoring stations, the
atmospheric transport model including the use of an urban scheme, the
modelling of concentrations at the simulation domain boundaries, the
definition of the emissions outside Île-de-France, the definition of the
control vector, etc. However, first conclusions of broad implications beyond
this first attempt can be drawn that should guide further inverse modelling
developments for Paris and other cities.
The analysis of the CO2 time series shows significant differences
between the measured and modelled mole fractions upwind of the city of Paris.
These differences indicate that the simulated mole fractions at the domain
boundaries may be off by several ppm. The errors in this simulation are of
similar magnitudes as the signals from the Paris area emissions. Although the
number of cases is limited, it seems that the boundary concentrations are
significantly underestimated when the wind is from the north or
north-east (Benelux). These uncertainties on the domain boundaries generate
large-scale errors in the modelled mole fraction and suggest applying the
inversion not to the measurements themselves, but rather to upwind–downwind
gradients, as was done in this paper. Indeed, the measurement–model
agreement is much better for the gradients than it is for the direct values.
It confirms that the large-scale pattern of the CO2 mole fraction, which
is not related to the Île-de-France fluxes, is not properly modelled. The
information provided by our five-site network does not allow optimisation of
the structure of the CO2 boundary conditions, which is directly
prescribed by a coarse-scale global inversion. Exploiting the distant sites
currently operational in Europe would be unlikely to improve this situation.
In this context, the inversion based upon gradients as presented in Sect. 4
appears necessary. It relies on the assumption that, due to atmospheric
diffusion, the signature of remote fluxes upwind of the city is sufficiently
homogeneous in space, horizontally and vertically, and time over the path
through the city from upwind to downwind sites both located within the
afternoon PBL. As a consequence, the main part of such a large-scale signal
is removed through the differences between two sites. The validity of this
hypothesis is confirmed by the much better agreement between measured and
modelled mole fractions as shown through the comparison of Figs. 6 and 8.
Both measurements and atmospheric transport simulations indicate, however,
that the CO2 mole fraction signal generated by distant sources outside
the Chimere model domain has some spatial structures (see e.g. the
variability of modelled values in Fig. 8, top) which need to be accounted
for.
The drawback of using the gradient-based inversion method is a reduction in
the number of observations, in particular with the current monitoring network
that only samples a fraction of possible wind directions. Nevertheless,
although the number of observations is very much reduced, our inversion
system based on the gradient reports significant uncertainty reductions. It
must also be noted that we assumed a 7-day error correlation time for the
anthropogenic emissions, so that our system shows flux uncertainty
reductions, even on days with no valid observation, as the flux is
constrained by observation of the previous or following days.
The setting of temporal error correlation in prior fluxes is therefore
essential for the inversion. Although the results in this paper are mostly
derived with a 7-day correlation length, this is a somewhat arbitrary choice,
and the results are significantly affected when using different values. In
particular, a much shorter value (1 day) leads to very large variations in
the posterior daily emissions. Further work should be devoted to the
assignment of objective correlation lengths based on the processes that lead
to emission uncertainties. Climatic conditions in general, and more
specifically temperature during the cold season, influence the emission with
a timescale that is consistent with synoptic events, i.e. close to a week;
the impacts of specific events such as holidays, commemorations or strikes
have a much shorter timescale, while inventory biases linked to e.g. the
emission factors have an impact on the fluxes on timescales of months or even
longer.
Our analysis also indicates model–measurement discrepancies at the EIF site
that are much larger than at other sites. On the one hand, this is somewhat
surprising, as a measurement inlet at altitude should ensure a larger spatial
representativeness than at the surface sites and less sensitivity to local,
poorly represented, emissions. Usually, tall tower-based measurements are
preferred to those at the surface for the estimate of biogenic fluxes. On the
other hand, EIF is located close to the centre of the city of Paris, and is
therefore affected by stronger local emissions than the other sites used in
this paper. City fluxes are highly heterogeneous, while the model used in
this paper has a 2 km spatial resolution, does not include information on
the 3-D structure of the urban canopy, and uses limited information on the
CO2 source injection heights. Such a model may then be insufficient to
account properly for atmospheric processes that link the local surface fluxes
to the concentrations at the top of the Eiffel Tower. Previous results
obtained at MeteoFrance by Lac et al. (2013) using a high-resolution (2 km)
meteorological model that includes urban parameterisations, and validated
against local meteorological measurements, also show high model–data misfits
at EIF similar to those found in the present paper. McKain et al. (2012) also
show poor skill in representing the mole fraction at urban sites, so that the
information content of the measurements is not applied for an estimate of the
absolute emissions, but rather for a long-term relative change. These
findings can be related to our difficulties in modelling urban CO2 at
EIF using a 2 km resolution transport model that are typical of the current
generation of models. The use of urban sites such as EIF for atmospheric
inversion will likely necessitate long-term research by the inverse modelling
and transport modelling communities.
At present, our mesoscale atmospheric transport model cannot reconcile the
measurements at the top of the tower with those at the surface in the
vicinity of the city, given our set of surface fluxes and inversion settings.
This cast doubts on the quality of the modelling at the other sites. Indeed,
if the atmospheric transport model does not properly simulate the atmospheric
vertical transport between the surface and an inlet at 300 m in altitude, it
likely misrepresents the link between surface fluxes and atmospheric mole
fractions. Conversely, the large modelling errors at EIF may be related to
its urban location (and to the strong influence of local urban sources), and
this would raise concerns regarding the ability to exploit urban
measurements, and therefore to solve for the spatial distribution of the
fluxes within the urban area.
The largest differences between the measured and modelled concentrations
occur for low wind speeds. For this reason, we have chosen a 2 m s-1
wind speed threshold below which the measurements are not used in the
inversion. A larger threshold rejects further observations, and reduces the
range of flux corrections through the inversion. The choice of the threshold
is somewhat arbitrary and we have refrained from using a large one to clearly
demonstrate the impact of a few situations with low wind speed. There are
several hypotheses for the poor modelling at low wind speed, including larger
representativity errors of subgrid patterns, or larger errors in vertical
mixing modelling. However, such issues are continuous and there is no
indication that the modelling errors disappear between e.g. 2 and
3 m s-1. Thus, further rejection of low wind speed observations may hide the deficiencies in
the atmospheric transport without improving the flux inversion.
We also stress that our analysis is based on measurements during the late
autumn period. This is a favourable case for the inversion of fossil fuel
CO2 emissions, as there is less interference with the biogenic fluxes
(Pataki et al., 2007). During spring and summer, the NEE is much larger (in
absolute value) and also more uncertain. In fact, during May, the biogenic
sink is likely larger than the anthropogenic emissions within
Île-de-France, as shown by Figs. 3 and S4. The gradient inversion method
is designed also to minimise this interference of biogenic flux with the
constraint on anthropogenic fluxes. Indeed, the theoretical posterior
uncertainties indicate few correlations between the retrieved NEE and
anthropogenic emissions. There is however vegetation within the urban area
that may generate a significant sink during the growing season. A successful
anthropogenic emission inversion would benefit from additional efforts to
describe the biogenic fluxes and the use of additional tracers such as
14C to separate the signature of fossil fluxes and biogenic emissions.
One future direction is thus to use a more realistic NEE model over the Paris
area that could be calibrated upon local eddy covariance observations (e.g.
the method used in Gerbig et al., 2003) and satellite land cover and
vegetation activity.
The prior estimate of the Île-de-France CO2 emissions does not
account for human respiration. Yet, within dense urban areas, human
respiration can be a significant fraction of the fossil fuel emissions (Ciais
et al., 2007; Widory and Javoy, 2003). Respiration by human beings is a
source of CO2 of typically 1 kgCO2 day-1 (Prairie and
Duarte, 2007), which, assuming a total population of 11.7 million for the
Île-de-France, leads to 4.2 MtCO2 per year, or 8 % of the
AirParif fossil fuel inventory. Although small, this flux is far from
negligible compared to fossil fuel emissions. While the CO2 mole
fraction measurements are sensitive to the human respiration flux, our
control vector only accounts for the fossil fuel emissions and NEE fluxes.
Although it does not have point sources, the spatial distribution of the
human respiration is broadly similar to that of the fossil fuel emissions, so
that the inversion will attribute the human respiration mole fraction signal
to the fossil fuel rather than to the NEE fluxes. We therefore expect an
overestimate of the fossil fuel emission by typically 8 % in our
inversion that neglects human respiration. A larger percentage may be
expected in summer and a smaller one in winter due to the seasonal cycle of
the fossil fuel emissions that has a larger relative amplitude than that of
the human respiration. Improvement in our inversion system should explicitly
account for the human respiration, based on the spatial distribution of the
population.
One often stated objective of the top-down inversion of fossil fuel CO2
emissions is to provide an independent verification of the bottom-up
estimates, i.e. the inventories (Levin et al., 2011; McKain et al., 2012;
Duren and Miller, 2012). However, information about the spatial and temporal
distribution of the emissions has to be used for inverse modelling to limit
aggregation errors in the overall budget. In our case, the number of
monitoring stations is far too small to invert the spatial distribution of
the emissions independently. We have been able to rely on the comprehensive
distribution from AirParif. With a larger number of monitoring stations, it
may be possible to estimate some information about the flux spatial
distribution, but atmospheric transport is not a reversible process, and some
accurate information about the spatial distribution will likely be needed, so
that the atmospheric inversion cannot be seen as independent of the
inventories, but rather as a means of verifying or refining them. In
addition, as long as the accuracy in the atmospheric transport does not allow
the use of nighttime or morning measurements, it will not be possible to
monitor the daily cycle of the emissions. Thus, the computation of daily or
monthly fluxes requires some robust information about the daily cycle that
should rely on inventories. Thus, again, our top-down emission estimate is
far from being independent of the bottom-up inventory.
Although the inversion procedure provides a posterior uncertainty estimate,
one should interpret this uncertainty with caution. Indeed, the mathematical
framework used here relies on a number of hypotheses, some of which are crude
approximations of the reality, such as the spatial and temporal correlations
in the flux uncertainties or the unbiased atmospheric transport modelling.
The impact of these assumptions has not been quantified. Although we have no
“truth” with which to benchmark the inversion results, and there are not
even enough measurement sites to perform “leave-one-out” tests, one can
perform some sanity checks on the results. One sanity check is the comparison
of the measured and modelled mole fractions (Figs. 8 and S4). The analysis of
these figures confirms the ability of our inversion to improve the
measurement–model agreement. Nevertheless, we note that the posterior misfit
(≈ 2.5 ppm) is still a significant fraction of the signal that is
analysed (10–20 ppm). The crucial question is whether the atmospheric
modelling error is random or a bias, and we have no element to answer that
question. The other sanity check consists in analysing the validity of the
retrieved daily fluxes (Fig. 9). In this respect, the daily fluxes show
day-to-day variations that are suspicious although not refutable at this
stage. A result that points in favour of the flux inversions shown here is
the significant reduction from the prior during a period with temperatures
above the seasonal normal, and the negative correction of the emissions
during November from the prior value that is based on an inventory simulating
January emissions. A single such event is certainly not sufficient to
validate the inversion system, however. We shall apply the same inversion
set-up to more than a year of measurements and analyse the results with
respect to the temperature anomaly or another short-term event that may have
a significant influence on the Île-de-France CO2 emissions. More
measurement sites are needed to evaluate the skill of the inversion better.
The deployment of a network of five sites around Paris within the framework
of the CarboCount-City project will help in this direction. In addition,
inlets at different altitudes will be installed at the Eiffel Tower station
for a better assessment of the CO2 vertical distribution and transport
within the urban area. These will be most useful for the longer-term
objective of improving the atmospheric transport modelling within the city,
which may allow the EIF measurements to be used by the inversion system.