Introduction
At the 2010 Cancun summit, parties from the United Nations Framework
Convention on Climate Change (UNFCCC) agreed to set up a target of keeping
global warming under 2 ∘C compared to pre-industrial levels
(UNFCCC, 2011; Meinshausen et al., 2009; Ciais et al., 2013). Shah et al. (2013) showed that this 2 ∘C global warming target is economically
and technically feasible, albeit demanding a mitigation of the greenhouse
gas (GHG) emissions across all sectors of anthropogenic activities. Many
developed and developing countries consequently have made commitments to
reduce their emissions under the UNFCCC. National commitments focus on the
land use sector or on economy-wide activities such as electricity production
and industrial processes. There is, however, a gap between these commitments
and the requirements on emission reductions (often referred to as “emission
gap”) for achieving the 2 ∘C global warming target (UNEP, 2013).
Cities occupy less than 3 % of the world's land surface (Liu et al.,
2014), but directly release about 44 % of the global energy-related
CO2 and are responsible for 71–76 % of CO2 emissions from global
final energy use (Seto et al., 2014). This urban share of the anthropogenic
emissions will continue to increase in the context of an accelerating
urbanization process (IEA, 2008). The global urban population has grown from
746 million in 1950 to 3.9 billion in 2014, and it is expected to grow by
2.5 billion people by 2050, with nearly 90 % of them living in Asia and
Africa (UN, 2014).
City mitigation options, such as the improvement of public transportation
infrastructures using mass and rapid transit systems, of building
retrofits, and of energy/waste recycling, and the development of district
heating/cooling plants (Sugar and Kennedy, 2013; Erickson and Tempest,
2014) can significantly contribute to bridging the emission gap. This
plausible additional city contribution could cover ∼ 15 % of
the total emission reduction required to reach the 2 ∘C global
warming target and represents up to two-thirds of the level of emission
reduction covered by the national commitments (Erickson and Tempest, 2014).
Large urban areas have a strong potential to decrease per capita CO2
emissions for some important sectors (e.g., transportation and heating) where
clusters of population and economic activities can share common
infrastructures (Bettencourt et al., 2007; Dodman, 2009; Glaeser and Kahn,
2010; CDP, 2012).
Thousands of cities declared to be willing to take actions to report and
reduce their CO2 emissions (Rosenzweig et al., 2010; Reckien et al.,
2013). Such efforts can decrease their climate vulnerability and foster
co-benefits in terms of air quality, energy access, public health, and city
livability (Seto et al., 2014). They may also foster significant local
economic development through advances in green technology. For instance, the
London low-carbon environmental goods and services sector is estimated to
have generated more than USD 25 billion revenue for 2011/12 (BIS,
2013).
To check whether claimed reduction targets are fulfilled, the present-day
city emissions have to be known accurately to define a baseline upon which
reductions are defined, and these emissions will have to be monitored over
time during the agreed-upon reduction period. Such quantification of
emissions and emission reduction echoes the concept of monitoring,
reporting, and verification (MRV) that is the cornerstone of most market- or
policy-based mechanisms in climate economy (Bellassen and Stephan, 2015). It
ensures that the mitigation actions are properly monitored and reported and
that the mitigation outcomes can be verified. The MRV has been widely
applied in many contexts such as projects, organizations, policies, sectors,
or activities within territories (see Bellassen and Stephan, 2015, and
references therein). For diverse applications, MRV can rely upon different
standards but requires transparency, quality, and comparability of
information about emission accounting and the mitigation action
implementations.
The first urban mitigation actions relevant for MRV are those whose impacts
are relatively easy to measure, e.g., projects and Programmes of Activities
under the Clean Development Mechanism as well as efforts on
emission reductions for large factories and buildings under the Tokyo
Emission Trading Scheme (ETS) (Clapp et al., 2010; IGES, 2012; Marr and
Wehner, 2012; UNEP, 2014). However, there is a lack of technical capacity
for accurate accounting of diffuse sources, e.g., transportation and
residential buildings. This lack of capacity makes MRV for citywide
emissions challenging (Wang-Helmreich et al., 2012; UNEP, 2014) and may
hinder citywide mitigation implementation in the absence of strong political
will, sufficient institutional governance and financial support. Hitherto
MRV practices for urban mitigation actions are still limited and the
majority of sources within the city territory remain uncovered. For
instance, the Tokyo ETS – the most advanced urban ETS scheme – only
regulates less than 20 % of the city total emissions (TMG, 2010). In this
context, there is a keen need to scale up policy instruments and market
mechanisms to better support citywide mitigation actions (World Bank, 2010;
Wang-Helmreich et al., 2012; The Gold Standard, 2014). This gap may be
reduced by new mechanisms such as the Nationally Appropriate Mitigation
Actions (NAMAs; recent move to raise pre-2020 emission reduction ambitions
by increasing access to climate financing) and the new market-based
mechanism (NMM; currently in negotiation for post-2020 carbon financing
about crediting and trading of mitigation outcomes). Both mechanisms are
designed under UNFCCC to increase the flexibility of mitigation actions so
that broader segments of economy or policy-making can be included in
developed and developing countries (Howard, 2014; UNEP, 2014). Based on
estimates of emissions from the major sectors, a conceivable approach would
be to set up overall city mitigation targets and then negotiate specific
targets for individual sectors or groups of sources. Empowered by city-scale
MRV (see UNEP, 2014, for current developments), city mitigation
implementation could be (1) credited or traded under designed mechanisms
and (2) registered for receiving international aide through climate finance.
However, ultimately, all these provisions for citywide mitigation actions
and their MRV necessitate the availability of accurate emission accounting
methods.
The emission accounting methods that are usually suggested are inventories
based on statistical data (World Bank, 2010; Wang-Helmreich et al., 2012).
Developing city-scale inventories, and updating them over time, involves
extensive collection of consistent and comparable emissions data, which
measure the level of activities (e.g., energy use statistics or, in a more
sector-specific manner, kilometers driven by vehicles and volume of waste
provided to landfill) and the activity-to-carbon conversion rates (i.e.,
emission factor). In the past, cities have followed diverse guidelines or
protocols for emission inventory compilation, and recently there is a trend
of centralization, e.g., with the newly proposed Global Protocol for
Community-Scale Greenhouse Gas Emission Inventories (GPC; Fong et al., 2014) and the UNFCCC reporting platform NAZCA (climateaction.unfccc.int).
Admittedly, inventories of city emissions are known to suffer from
incomplete and uncertain data (see Appendix A for a brief review of city
inventories). For instance, there is usually a lack of precise statistics
regarding the total amount of fossil fuel that has been consumed within the
cities. This limitation impedes the practical use of city inventories in
climate economy.
An improved emission accounting could rely on continuous atmospheric
measurements of CO2 concentrations by networks of stations around and
within cities. Indeed, accurate measurement of the atmospheric signals, e.g.,
the CO2 concentration gradients, provides information about the
emissions that is independent from the inventories. The statistical method
known as atmospheric inversion, which has been used for decades for
improving the knowledge of global and continental scale natural CO2
fluxes (Enting, 2002; Bousquet et al., 2000; Gurney et al., 2002; Peters et
al., 2007; Chevallier et al., 2010; Broquet et al., 2013), can be used to
exploit atmospheric measurements for quantifying CO2 emissions at the
city scale (McKain et al., 2012; Kort et al., 2013; Lauvaux et al., 2013;
Hutyra et al., 2014; Bréon et al., 2015). The principle of an inversion
is to combine information from inventory data with atmospheric CO2
measurements to deliver improved emission estimates, i.e., estimates with a
reduced uncertainty, compared to the prior inventory. An inversion generally
uses a 3-D model of atmospheric transport to relate emissions to
observations. In just a few years, a number of city atmospheric CO2
measurement networks have been deployed for pilot studies. Examples of
cities where such networks have been deployed are Toronto (with 3 sites),
Paris (with 5 sites), Recife (with 2 sites), Sao-Paulo (with 2 sites), Salt
Lake City (∼ 7 sites), Los Angeles (∼ 10 sites),
and Indianapolis (with 12 sites). This creates a need to better document the
theoretical potential of atmospheric inversions to monitor emissions and
their changes or to independently verify inventories, with a quality
relevant for city MRV applications. Urban emissions are mainly connected to
emissions from fossil fuel combustion, as other sources of urban emissions
such as biofuel uses are usually very limited. Hence, for simplicity, we
assume that urban emissions are all from fossil fuel combustion in our
study.
Bréon et al. (2015), hereafter referred to as B15, used CO2
measurements from three stations in the Paris area and a Bayesian inversion
methodology to estimate CO2 fossil fuel emissions in the Paris
metropolitan area (the Île-de-France – IDF – region, which has
∼ 12 million inhabitants) in winter 2010. The most resolved
regional bottom-up inventory estimates that this area emitted 11.4 TgC in
2010 (AIRPARIF, 2013), an amount equivalent to ∼ 12 % of the
CO2 fossil fuel emissions from the whole of France (Boden et al., 2013).
B15 did not attempt to estimate sectoral emissions separately due to the
very limited size of the measurement network they used. They focused rather
on quantifying total CO2 emissions from the Paris urban area. Staufer
et al. (2016) refined the configuration of the inversion system of B15 and
applied it for a 1-year inversion of the Paris emissions.
In this paper, we assess the performance of atmospheric inversion for the
monitoring of total and sectoral fossil fuel emissions in the Paris
metropolitan area when using denser networks, based on observing system
simulation experiments (OSSEs). The objective is to analyze the sensitivity
of this performance to the size and design (i.e., the location of the
stations) of such networks and thus to derive requirements on the
configuration of the atmospheric inversion to provide different levels of
accuracy on the estimates of the total and sectoral city emissions. We base
our inversion methodology and the configuration of the OSSEs – notably the
assimilation of concentration gradients and the practical configuration of
the inversion parameters – on the system, expertise, and diagnostics
documented in B15 and Staufer et al. (2016). The use of much larger
measurement networks still necessitates some assumptions regarding the
inversion framework and the characterization of the sources of errors.
Diagram of the principle of the city CO2 emissions inversion
system and of the computation of uncertainties in the inverted emission
budgets. Note that there is no computation of x and y vectors in
this OSSE study.
The CO2 measurement instruments presently used for atmospheric
inversion in the scientific community are rather expensive (typically
∼ EUR 50 k per sensor), which explains the limited size of
the existing city networks. To bridge this data gap, national and European
innovation projects (e.g.,
http://www.climate-kic-centre-hessen.org/miriade.html, MIRIADE-ANR:
ANR-11-ECOT-0004) have been proposed to test lower-cost (typically
∼ EUR 1 k per unit) sensors (called hereafter low-cost
medium precision – LCMP – sensors) and to develop a corresponding
calibration strategy which would enable the measurement of CO2
concentrations with a precision and an accuracy that would be acceptable for
city-scale inversions (but maybe not for other scales, for which more
expensive instruments may still be needed for the foreseeable future). This
motivates our tests, in this study, of networks with up to 70 sensors.
The principle of the inversion performance assessment, the inversion
methodology and the OSSE setup are described in Sect. 2. The inversion
results are analyzed in Sect. 3. Based on these results, Sect. 4 discusses
requirements on the configuration of the observation network for achieving
different targets of accuracy in the estimates of total and sectoral
CO2 emissions from the Paris area. Conclusions are drawn in Sect. 4.
Methodology
The principle and the configuration of our atmospheric inversion system are
close to those of B15. The general principle is to estimate the emission
budgets for different sectors of anthropogenic activity, areas, and time
windows, which altogether constitute the total emissions of IDF for the
month of January 2011. It corrects a prior estimate of these emission
budgets given by an inventory to better fit observed concentration gradients
between pairs of sites along the wind direction, in and around the Paris
area, since such gradients characterize the enhancement of atmospheric
CO2 due to the Paris emissions. An atmospheric transport model is used
to simulate the gradients corresponding to a given estimate of the
emissions.
The atmospheric inversion theory relies on a statistical framework which
accounts for the uncertainties in the prior estimate of the emissions, in
the transport model and in the measurements, and which diagnoses the
uncertainty in the estimate of the inverted (“posterior”) emissions as a
function of the observation location and time, of the atmospheric transport,
and of these prior model and measurement uncertainties. This diagnostic is
used in this study as a natural indicator of the inversion performance.
Since it depends neither on the actual value of the observations that are
assimilated nor on the actual value of the prior estimate of the emissions or the actual value of the corrections applied by the inversion on the
prior emission estimates, it allows conducting OSSEs without generating
synthetic gradient observations for the hypothetical networks that are
tested and without conducting practical emission estimates.
Theoretical framework of the Bayesian inversion
By Bayesian inversion, the information from an observation vector
y of CO2 concentration gradients is combined with a
prior estimate xb of the CO2 emissions
budget for various sectors, areas, and time windows (i.e., of the vector of
parameters controlled by the inversion x, or “control
vector” hereafter) to provide an updated estimate of the control vector
xa (Enting, 2002):
xa=xb+BHT(R+HBHT)-1y-Hxb,
where H is a linear matrix operator linking
y with x based on the modeling
of the spatial and temporal distribution of the emissions at high resolution
and the modeling of the atmospheric transport at high resolution. The
uncertainties in y,H and
xb are assumed to have statistical
distributions that are Gaussian, unbiased, and independent of each other. The
linking of y with x in general
suffers from some deficiencies in the measuring instruments and the
atmospheric modeling. The sum of the measurement and model errors is called
the observation error, the covariance matrix of which is denoted R. We denote B the error covariance matrix for the
prior estimate of the control parameters. The uncertainty in the estimate
xa given by Eq. (1) is Gaussian and
unbiased and its covariance matrix (which is “smaller” than
B) is
A=(B-1+HTR-1H)-1.
The comparison between this posterior error covariance matrix and the prior
one, starting from realistic prior and observation error statistics, allows
us to quantify the inversion performance. We pay specific attention to the
diagnostic of the relative difference between the posterior and the prior
uncertainties for the total and sectoral budgets of the emissions during the
month of January 2011.
In the following sections, we detail each component of our inversion system
underlying Eq. (2) (see Fig. 1).
Control vector
Our control vector x does not directly include emission
budgets, but rather scaling factors that are to be applied to the emission
budgets which are included in the observation operator
H. For the sake of simplicity, Fig. 1 presents the
inversion framework as if the emission budgets themselves were controlled,
which is quite equivalent to the strict implementation of the inversion
system. Each scaling factor in x corresponds to the
emission budget of a given spatial area of the IDF domain, a given temporal
window, and a given sector or group of sectors of CO2-emitting
activity. The corresponding ensemble of areas, temporal windows, and sectors
partitions the IDF domain, the month of January 2011, and the full range of
emitting activities, respectively. Hereafter, we will call “control tile”
the combination of an area, a temporal window, and a sector (or group of
sectors) associated with a control parameter.
While it is desirable to solve for the emissions at high spatial, temporal,
and sectoral resolution, computational constraints, such as the inversion of
B and
(B-1+HTR-1H) in Eq. (2) and the computation of H which
requires in principle as many transport simulations as control
parameters, limit the size of the control vector x. We
group the various sectors provided by inventories (detailed in Sect. 2.4.1)
into seven groups of sectors (see Appendix A for details), namely (1) commercial and residential building heating/cooling, (2) road transport, (3) energy
production (power plants), (4) combustion and production processes in
industries, (5) combustions from agricultural activities, (6) airline traffic,
and (7) the remainder of all other sectors with smaller emission budgets
(e.g., railway, navigation, fugitive emissions, and several minor production
processes). These seven sectors are labeled for short as building, road,
energy, production, agriculture, airline, and remainder, respectively.
In order to save computations, for the less important sectors (isolated
energy and production point sources, agriculture, airline, and remainder), we
consider that the spatial area of control for the inversion is the whole IDF
area. However, for building and road emissions, we spatially partition IDF
into five zones for which the fluxes can be optimized: a central zone
(approximately the administrative definition of the city of Paris, which is
very densely populated) and four surrounding areas (the northwestern,
southwestern, northeastern, and southeastern areas of the remaining IDF region,
with borders adapted to the distribution of the building and road emissions;
see Fig. 2).
Sectoral budgets of fossil fuel CO2 emissions from the IER
inventory for the five “control” zones (central Paris in dark blue and
four other surrounding areas in light blue) partitioning the IDF region and
for the month of January in 2011 (see the first seven rows in Table 1 for
sector specifications). The circle area is proportional to the emission
budge. The upper right largest circle shows the total sectoral budgets for
all the five areas of IDF. The red pentagons shows the two airports CDG and
Orly, and the purple triangles show several large point emissions such as
three EDF power plants and the TOTAL Grandpuits refinery. Note that these
five zones in blue mark out the IDF region, but do not strictly follow the
administrative borders (black lines) within IDF.
Spatiotemporal resolutions of the sectoral control factors for
inversions over 30-day periods (see the main text and Table A1 for more
information on aggregate sectors).
Control factors
Spatial resolution
Time resolution
Number of factors
Building
Five zone
Daily daytime and nighttime
300
Road
Five zones
Daily daytime and nighttime
300
Energy
One zone
Daily daytime and nighttime
60
Production
One zone
Daily daytime and nighttime
60
Agriculture
One zone
Daily
30
Airline
One zone
Daily
30
Rest
One zone
Daily
30
NEE
One zone
5-day period with four daily 6 h windows
24
–
–
–
834 (total)
Regarding the temporal partitioning, for the three sectors which have the
smallest budgets of emissions (agriculture, airline, and remainder), the
temporal resolution of the control vector is daily. For the four other
sectors (building, road, energy, and production), we refine the temporal
resolution to 12 h and control separately the daytime (7–19 h) and nighttime
(19–7 h) emissions for each day in order to account for the large diurnal
variations in the emissions.
Atmospheric CO2 observations are sensitive to vegetation–atmosphere
CO2 fluxes in addition to fossil fuel CO2 emissions. For cities
surrounded by vegetation or containing green areas, the impact of
vegetation–atmosphere CO2 fluxes on city carbon balance can be
significant. For instance, Nordbo et al. (2012) extrapolated from their
measurements, that an 80 % green-area fraction would approximately make
cities carbon-neutral. In our inversions, we account for the influence of
the natural vegetation and soil CO2 fluxes (or net ecosystem exchange,
NEE) by including, in the control vector, the scaling factors for the
budgets of NEE in the full modeling domain (see Sect. 2.4) and for the four
different 6 h windows of the day (i.e., 0–6 h, 6–12 h, 12–18 h, and 18–24 h
local time) over different 5-day periods during January 2011. The number of
NEE scaling factors included in the control vector is thus 24, and the total
number of scaling factors is 834 (see Table 1 for details).
Observations
We use an inversion system similar to that of B15, in which observations are
taken to be CO2 atmospheric concentration gradients between upwind and
downwind stations (see Sect. 2.4.3 for details). The use of concentration
gradients rather than concentrations cancels out the pervasive large-scale influence from remote fluxes outside of the city domain well and informs
about the local emissions between upwind and downwind stations. B15 also
suggested assimilating only afternoon gradients when the wind speed is above
a given threshold. By selecting afternoon gradients, we avoid biases in the
vertical mixing during nighttime, mornings, and evenings when mesoscale
transport models have difficulties in representing the planetary boundary
layer (Seibert et al., 2000; Steeneveld et al., 2008). Selecting data for
high wind speed limits the signature in the atmospheric measurements of
local sources that are in the vicinity of the measurement sites and that
cannot be represented correctly by the transport model.
Locations for the elliptical (E), random-even (R), and uniform (U)
networks over IDF. The brown area marks out where the population density is
larger than 1250 people per km2. The E network (green dots) consists of
three rings surrounding the densely populated urban area in brown. The U
network (red crosses) extends to the regular grid points of the IDF domain.
The site locations of the R network are randomly selected, respectively, in
three concentric areas: (1) the city center (the administrative “city of
Paris”) within the peripheral ring (coinciding with the smallest green
ring), (2) the suburban area (in brown) with central Paris clipped out, and
(3) the rest of IDF.
For investigating the potential of the inversion as a function of the
observation network, we consider three strategies to deploy a given number
of stations. These strategies define three corresponding types of networks:
the elliptical (E), uniform (U), and random-even (R) networks (Fig. 3). The E
networks surround emissions in the city center and appear suitable to the
assimilation of city downwind–upwind gradients. The E networks consist in
three concentric ellipses or rings of stations around the main part of the
Paris urban area (the Paris administrative city and its three surrounding
administrative circumscriptions), encompassing almost the whole urban area
of IDF. The U networks position the stations on a regular grid. The R
networks aim to balance the position of stations near the city center and
in the surrounding areas. The R networks thus have denser coverage over the
city center and fewer stations in the surrounding zones than the U networks,
but they still cover the whole IDF domain. Apart from the E networks, the U
and R networks have stations both close to the emissions in the Paris urban
area and in rural areas in its vicinity.
Selection of a subset of 10 sites (red triangles) from a cloud of
candidate locations for the R network to form smaller networks. The blue
circles show the sites that are not selected from available locations. The
open circles/triangles present rural sites, and the filled circles/triangles
present urban sites. This figure also shows how the wind direction selects
candidates of upwind sites for concentration gradient computations at a
downwind station. The blue arrow indicates the wind direction at that
downwind station. The two red triangles covered in the shadow area are
candidate upwind sites according to the selection procedure detailed in
Sect. 2.4.3.
We assess the potential of the inversion when using these networks of either
10, 30, 50, or 70 stations. For a given network, the station locations are
chosen as a subset of a predefined set of 90 candidate locations, depending
on the type of network. For example, 14, 24, and 52 of the 90 candidate
stations for R networks are located in the urban center, the suburban area,
and the rural area, respectively. For a given number of stations n, 10
networks are selected for the inversion out of an ensemble of 100 networks
that are generated by randomly selecting n stations from the set of 90
candidate locations. The selection of such sets of 10 networks is based on
ad hoc verifications that the station locations should be evenly distributed
in the urban, suburban, and rural areas as would have been done for the
design of real networks. This selection limits the range of the random
generation of networks to a set of sensible networks for which a further
discrimination should rely on the type of network performance assessment
that is conducted in this study. Figure 4 shows an example of an R network of
10 stations resulting from the above selection procedure. The design of
current real city networks is much influenced by administrative and
technical issues (e.g., agreements with potential hosts of the site and
ability to fix inlets at desired height). Here, as discussed in more detail
in Sect. 2.4.3, we assume that the measurements are taken at 25 m a.g.l. at all stations. This simplifies these
considerations for our practical inversion framework since 25 m a.g.l. is a
common height of private and public buildings in the Paris region. However,
for many cities, the number of buildings higher than 25 m a.g.l. is
limited,
which could raise critical logistical issues for the deployment of networks
with a large number of sensors.
The strategy to properly combine stations from the different selected
networks for city downwind–upwind gradient computation (and thus for the
precise definition of the observation vector) is detailed in Sect. 2.4.3 as
part of the description of the observation operator.
Observation operator
The observation operator H that links the scaling of
surface emission budgets to CO2 concentration gradients in the
atmosphere can be decomposed into a chain of three operators
(H=H1H2H3; Fig. 1): the spatial and temporal distribution of the CO2 fluxes
within a corresponding control tile H1, the atmospheric transport
of CO2 given these spatial and temporal distributions of the fluxes
H2, and a sampling of the resulting simulated
CO2 to be compared with the observations H3.
H1 maps the scaling factors in the control vector to the CO2
fluxes on the transport modeling grid. It uses an emission inventory and an
ecosystem model simulation to prescribe the small-scale spatiotemporal
distribution of the gridded CO2 fluxes. Applying
H1 to a scaling factor uniformly rescales the
prescribed CO2 fluxes within each control tile and thus adjusts the
emission budget of that control tile. H2 is the
mesoscale atmospheric transport model that maps the gridded fluxes generated
by H1 to simulations of the CO2 concentration
fields on the transport model grid (at 2 to 10 km horizontal resolution and
1h temporal resolution for a northern France area encompassing the IDF
region). H3 is a linear algorithm that computes Paris
downwind–upwind CO2 gradients between measurement stations, extracting
the observations from the CO2 field simulated by
H2.
H1
The NEE simulations from C-TESSEL – the land surface model of the
short-range forecasts of the European Centre for Medium range Weather
Forecasts (ECMWF) at a spatiotemporal resolution of 15 km and 3 h (Boussetta
et al., 2013) – are interpolated to derive the distribution of NEE at the
spatiotemporal resolution of the atmospheric transport model.
We rely on an inventory of the French emissions from the Institute of Energy
Economics and the Rational Use of Energy (IER) at the University of
Stuttgart to derive the distribution of sectoral fossil fuel CO2
emissions in IDF at a high spatial resolution of 1 km × 1 km
(Latoska, 2009). It disaggregates the annual emissions of France in 2005
(according to the national inventory submissions 2007 from UNFCCC,
http://www.unfccc.int), making use of extensive data from diverse databases
for point, line, and area emissions and of proxy information such as
population and land cover maps. As for the temporal distribution of the
emissions, we apply monthly, weekly, and hourly temporal profiles also
produced by IER to derive hourly emission maps. These temporal profiles are
defined for France as functions of each sector but not of the spatial
location.
There are 51 sectors indexed by NFR code in the IER inventory. We compute
the emission budgets for all these 51 NFR sectors and re-aggregate them
into the seven groups of sectors defined in Sect. 2.2 (see Table A1). The
emission budget of the three major sectors (energy, road, and building) represents
∼ 84.4 % of total fossil fuel CO2 emissions over IDF
according to the IER inventory. Figure 2 shows, for the seven sectors, the
spatial distribution of the emissions among the five distinct geographic zones
of IDF that are used to define the control tiles. The northwestern and
southeastern zones have more emissions than the other three zones, mainly due
to the presence of large point sources, e.g., the EDF power plants and the
TOTAL Grandpuits refinery (see Figs. 2 and 5c). Building and road
emissions, however, are distributed rather evenly in space over
the five zones. The budgets of the emissions related to production (7.4 %
of total), agriculture (3.7 %), airline (3.3 %), and remainder sectors
(1.2 %) are relatively small compared to that of the first three sectors.
Figure 5 shows the spatial distributions of the emissions from the seven
sectors derived for January based on the IER inventory and on the temporal
profiles from IER. The IER inventory is not fully faithful to the actual
emissions from IDF but, in principle, this has very limited impact on the
theoretical computation in our OSSE framework of inversion.
Sectoral and spatial distribution of the IER inventory over IDF for
January 2011.
H2
Following B15, we use the mesoscale atmospheric chemistry-transport model
CHIMERE (Menut et al., 2013) to simulate the signature of CO2 fluxes in
the atmosphere over the IDF area. This model has successfully served for air
quality applications in megacities (Couvidat et al., 2013; Zhang et al.,
2013). The CHIMERE model domain in this study, which is the same as that in
B15, covers an area of about 500 × 500 km2 in northern France that is
centered on IDF. Its horizontal resolution is 2 km × 2 km over IDF
and its vicinity and 2 km × 10 km to 10 km × 10 km over
the rest of the domain (see Supplement Fig. S1). In total, there are 118 × 118 cells in the model horizontal grid. Vertically there are 19
sigma-pressure (terrain-following) layers from the surface up to 500 hPa.
The top level of the first layer is at about 25 m a.g.l., and there are at least
six layers below 250 m a.g.l. The meteorological fields driving the CHIMERE
simulations come from the ECMWF analyses at 15 km resolution. The CHIMERE
modeling system prepares meteorological data on its model grid by diagnosing
sub-grid processes, such as turbulent mixing and convection (Menut et al.,
2013). We use Global Land Cover Facility (GLCF) land use data at 1 km × 1 km
resolution for this diagnosis. Simple urban parameterization is adopted to
correct wind speed in the surface layer taking into account the increased
roughness in the urban area (Menut et al., 2013), since B15 found no
significant differences in the simulation of CO2 mole fractions when
advanced urban scheme is used.
The exchange of CO2 between the CHIMERE 3-D regional domain and the
surrounding atmosphere depends on the wind conditions from the ECMWF product
and the CO2 concentrations at the domain boundaries. These exchanges
characterize the signature of remote fluxes outside the modeling domain that
impact the observed and simulated atmospheric CO2 in IDF. We need to
account for these CO2 boundary concentrations and for the CO2
concentration field at the initial date of the simulations (i.e., the
CO2 initial condition) when simulating concentrations, which is not the
case when applying the analytical computation of the uncertainties in the
inverted emissions budgets through Eq. (2). When simulating CO2
concentration fields for the preliminary illustration of the CO2
variations in IDF in Sect. 2.4.3, the boundary conditions are derived from
the interpolation of the global inversion product of Chevallier et al. (2010). This product has a resolution of 3.75∘ (longitude) × 2.5∘ (latitude), which gives about 2–3 cells at each
CHIMERE domain lateral boundaries, yielding a smooth influence in both space
and time from the CO2 boundary conditions. The CO2 initial
condition is built from the interpolation of CO2 given by that global
inversion product. We do not control these CO2 boundary and initial
concentrations in our inversion system, which explains why these components
do not appear in the computation of the posterior uncertainties given by Eq. (2). However, as detailed in Sect. 2.5.2, uncertainties in these conditions
still impact the accuracy of the inversion and have to be accounted for in
the model uncertainty. Anthropogenic emissions within the modeling domain
but outside IDF are not estimated in our inversions.
H3
For a given network, the operator H3
consists in a combination of three operations: the linear interpolation of
concentrations from the transport model grid to the actual point at which
CO2 measurements are collected, the selection of afternoon CO2
concentration data (12–17 h) at each station (upwind or downwind) when the
wind speed from the transport model is higher than 3 m s-1 at the
downwind station, and the CO2 city downwind–upwind gradient
computation. While B15 consider gradients between pairs of stations downwind
and upwind the full Paris urban area, this study assesses the potential of
assimilating gradients between stations that are located within either urban
or rural area. The gradients are thus representative of local urban
emissions and not necessarily of the citywide emissions as in B15. The
assimilation of all gradients should help better constrain the spatial and
sectoral distribution of the emissions.
In this synthetic study, we assume that the measurements are taken
continuously at the height of 25 m a.g.l. at all stations during the month of
January 2011. This height can correspond to the setup of these stations at
the top of existing buildings for which 25 m a.g.l. is a common height in the
Paris area. The deployment of large networks with up to 70 stations at this
height would thus not have to rely on new infrastructures as if the targeted
sampling height were significantly higher (which would be a critical barrier
for the practical implementation of the network). Local sources and
transport that are poorly represented with a 2 km resolution model may have
a large impact on the concentration measurements at such a height. However,
all real data assimilated by B15 were sampled at peri-urban stations at less
than 25 m a.g.l. By selecting the data during the afternoon only and for high
wind speeds, B15 limited such a local impact. Furthermore, their diagnostic
of the model error, which is used to setup the OSSEs in this study (see
Sect. 2.5.2), implicitly accounted for this impact. Still, assimilating
25 m a.g.l. measurement in the core of the urban area (which corresponds to a
significant number of the hypothetical sites investigated in this study) is
likely challenging due to the high density of strong sources and to the
complexity of the urban canopy, and this had not been attempted by B15 even
though they derived typical estimates of the model error for urban
measurements (see Sect. 2.5.2). This will be further discussed in Sect. 4.
The CO2 gradient computation demands selecting pairs of upwind and
downwind stations. For each observation at a given time, the station at
which that observation is made is first considered to be a downwind station.
We then select, for that observation, a matching observation at an upwind
station, based on the wind direction at the downwind station (given by the
ECMWF meteorological data, also used to drive the CHIMERE model). We
assume
that the angle between the direction from the upwind to the downwind
stations and the wind direction at the downwind station is between
±11.25∘. The choice of such a range of angles for the
gradient selection is a trade-off between the need to select enough data to
constrain the inversion and the need to ensure that we do not depart too
much from the objective of assimilating “downwind–upwind” gradients. It is
derived from the study of Staufer et al. (2016) who analyzed the impact of
such a choice on the results of the inversion when using real data. Figure 4
illustrates the principle of the gradient selection by showing the wind
direction for a downwind observation and the area that covers its
corresponding upwind stations.
We further assume that the distance between the upwind and downwind stations
should be larger than 5 km (to avoid assimilating gradients that are mostly
representative of local sources) and as close as possible to 10 km. This 10 km distance would correspond to the advection of an air parcel during 1 h
with a wind speed of 3 m s-1 (i.e., our threshold on the wind speed for
the assimilation of gradients). Here, the gradient computation in the
reference inversion ignores the time lag needed to advect an air parcel from
upwind to downwind stations and it is based on the difference between
simultaneous hourly mean observations. This explains why the 10 km distance
is seen as a good trade-off between the need for being representative of
large-scale emissions and the need to limit the impact of ignoring the time
required for transporting air masses from an upwind to a downwind site. We
discard the downwind observations for which no upwind station can be found
based on our selection rules. About 7–16 % of total observations are
retained for gradient computation with this data selection procedure,
depending on the size and type of the networks.
Results of selections of upwind stations for gradient computations
for EVE26 (see Fig. 4; R-type network of 10 stations) for the month of
January 2011: (a) the afternoon wind conditions at EVE26 during the given
month; (b) the afternoon wind conditions for the observations selected for
gradient calculation at EVE26; (c) the number of times a site is selected as
upwind for gradient computations at EVE26. The leftmost red cross indicates
a site that is never selected for gradient computation for EVE26.
Figure 6a shows statistics on the afternoon hourly wind conditions at an
example station EVE26 during January 2011, and Fig. 6b shows restriction of
this statistics to the wind conditions at EVE26 when EVE26 is selected as a
downwind site for gradient computation. Winds at station EVE26 blow
prevailingly along the southwest–northeast direction for this period (Fig. 6a). Since EVE26 is located to the northeast of the urban center (Fig. 6c),
the corresponding upwind stations for gradient computation are mostly
selected in the southwest direction (Fig. 6b–c).
As the observation operator is linear, one can evaluate the contribution of
a flux component to the CO2 mixing ratio at the measurement stations by
applying the observation operator to that specific flux component,
canceling all other flux components. We thus perform eight CHIMERE
simulations with, in input, respectively, the simulation of the NEE in
northern France and the inventories for the seven sectors of the fossil fuel
emissions in IDF described in Sect. 2.4.1 to evaluate the contribution of
these different types of flux to the CO2 variations during January 2011
at the hypothetical station locations considered in this study. This
corresponds to applying H to control vectors with scaling factors
corresponding to the NEE or to a specific sector of emission set to 1 and
others to 0 and ignoring CO2 boundary conditions. Figure 7 plots the time
series of CO2 mole fractions corresponding to the different types of
flux at 10 stations of an R network (which are indicated by red triangles in
Fig. 4), including 2 urban stations (EVE07 and EVE11 in Fig. 6c) and 8 rural
stations.
(a–d) CO2 mixing ratio series of sectoral CHIMERE simulations at
four selected stations of the R network (see Figs. 4 and 6c). EVE07 and
EVE11 are urban sites and EVE26 and EVE43 are rural sites but close to large
point emissions. The shadow marks out the nighttime. (e–h) The time series
of the difference in model simulations sampled at several site pairs among
the four sites. (i) The histogram of afternoon concentration gradients
following the data selection procedure detailed in Sect. 2.4.3 for all the
10 stations of the R network. These histograms are grouped according to the
type of downwind and upwind stations.
The correlation structures in (a) the error of prior scaling factor
estimates, (b) the posterior error obtained by inversion using a U network
with 10 stations, (c) the posterior error obtained by inversion using an E
network with 70 stations, and (d) the posterior error obtained by inversion
using a U network with 70 stations. Each row or column of the pixels
corresponds to the correlation between 1 scaling factor and all the 834
scaling factors (see Sect. 2.2). For clarity, we group these scaling factors
into eight sectors and organize them for each sector according to temporal
indices and spatial areas. The tickers show the name of these eight sectors.
Budget of uncertainties in total and sectoral emission estimates by
inversions using three types of networks of different sizes. Each sector has
a distinct color. In (a–d), we show the uncertainty budgets in percentage to
the corresponding emission budgets computed using the IER inventory. The
points indicate the percentage of prior uncertainty budgets before
inversion, and the bars demonstrate the percentage of posterior uncertainty
budgets after inversion. The error bars show the variations of the
uncertainty budget using 10 different networks of same size (10, 30, 50, or
70) constructed as detailed in Sect. 2.3. (a–c) Reduction of uncertainties
by inversions using three different types of networks of increasing sizes.
For each sector, the numbers of stations corresponding to the four bars from
left to right are 10, 30, 50, and 70, respectively. (d) Reduction of
uncertainties by inversions using three different types of networks of 70
stations. The types of network corresponding to the three bars from left to
right are E, R, and U, respectively. (e) Comparison between the inventory
budgets and uncertainty budgets (both in TgC) using the uniform network of
increasing sizes. For each sector, the leftmost bar shows the inventory
budget, and the four remaining bars to the right show the budget of
uncertainties in posterior emission estimates by inversions using 10, 30, 50,
and 70 stations, respectively.
For three types of networks of different sizes, we compute (a) the
average DFS, which is total DFS divided by the total number of observations
assimilated, and (b) the relative reduction of uncertainties in scaling
factor estimates computed by (1TB1-1TA1)/1TB1, where
1 is an all-one vector. The error bars show variations
due to inversions using 10 different networks of same size constructed as
detailed in Sect. 2.3.
CO2 series from northern France NEE in January have small daily
variations compared to that of CO2 from the fossil fuel emissions in
IDF and show very similar patterns at all the 10 stations. During
nighttime, CO2 emitted by the ecosystem respiration or by the
anthropogenic activities is trapped within the usually stratified nocturnal
planetary boundary layer, which generates peaks in the CO2 time series.
However, as explained in Sect. 2.3, the representation of the nighttime
variations (in particular of their amplitude) by the transport model is not
reliable. The diurnal variations of CO2 are driven by the diurnal
variations of the NEE (with a sink of CO2 due to photosynthesis during
daytime), the CO2 emissions from major sectors (building, road, and
energy), and the meteorology within the planetary boundary layer.
There are strong positive CO2 concentration gradients between the
urban–urban and urban–rural pairs of stations when analyzing the signature
of the major sectors of anthropogenic emissions (Fig. 7). Figure 7i shows
histograms of simulations of the concentration gradients corresponding to
the observation vector when using this 10-station R network for inversion.
These simulations are obtained by forcing CHIMERE with the estimates of the
total NEE and anthropogenic emissions described in Sect. 2.4.1 (i.e., by
applying H to control vectors with all scaling factors set to 1 and
accounting for the CO2 boundary conditions described in Sect. 2.4.2).
The three different histograms contain the gradients between two rural, two
urban, or one rural and one urban station, respectively. All the concentration
gradients between downwind urban and upwind rural stations are positive,
carrying a mean CO2 gradient of ∼ 14 ppm with a standard
derivation of ∼ 4 ppm. In contrast, the concentration
gradients between downwind rural and upwind urban stations have 20 %
negative values, with a mean of ∼ 3 ppm and a standard
deviation of ∼ 7 ppm. The gradients between rural downwind and
rural upwind stations have a mean of ∼ 5 ppm, a standard
derivation of ∼ 7 ppm, and ∼ 13 % negative
values. Most of these rural–rural negative gradients were found at station
pairs where the upwind rural station is much closer to the city center than
the downwind rural station (e.g., EVE34 and EVE85 whose distance is
∼ 23 km). Ignoring the time lag that is required for an air
parcel to be transported from the upwind to the downwind stations when
computing the CO2 gradients explains a large portion of these negative
gradients. The emissions vary in time, and, at a given time, the upwind
rural station can bear a signature of a peak dominated by the emissions from
the upwind nearby city center while this signature has not reached the
distant downwind rural station yet. Occasional changes in the wind
directions between the upwind to the downwind stations may also explain
that, sometimes, air masses reaching the downwind stations have not
necessarily been transported over the areas with high fossil fuel emissions.
Accounting for uncertainties
Prior uncertainties
Formal statistical methods, such as Monte Carlo approaches, can be used to
estimate errors due to uncertain activity data and emission factors and thus
the overall uncertainties in inventories at the global/national scale
(Fauser et al., 2011; Wang et al., 2013). However, to our knowledge, there
are currently no studies evaluating uncertainty in existing inventories at
the city scale. B15 used the AIRPARIF 2008 inventory as a prior emission
estimate for their inversions and assigned a 20 % 1σ uncertainty in
the monthly estimate of the total emissions from IDF. Following B15, we set
a prior 1σ uncertainty of about 20 % in monthly total emissions from
the Paris metropolitan area. In practice, few cities benefit from such high-resolution local inventories (Appendix A), and the setup of the prior
uncertainties for other cities may have to be higher since the quality of
the prior knowledge from their available inventories is not as good.
We assume that there is no correlation between the prior uncertainties in
the emission budgets (and thus in their scaling factors) for different
sectors of emissions (see Fig. 8a). For a given sector, the correlations of
the uncertainties in scaling factors for different areas and time windows
are given by the Kronecker product between spatial correlations (if there
are different control areas for this sector) and temporal correlations. We
set a value of 0.6 for the spatial correlations between prior uncertainties
in scaling factors for building or road emissions that correspond to two
different geographical areas (Fig. 2). The temporal correlation of the prior
uncertainties in scaling factors is modeled using an exponentially decaying
function with a characteristic correlation length of 7 days for each sector
(Fig. 8a). Uncertainties in individual scaling factors for a given control
tile are derived based on this configuration of the correlations and on the
two following assumptions: (1) the aggregation of uncertainties in all the
individual scaling factors leads to an overall 20 % 1σ uncertainty in
total emissions for January 2011 and (2) the 1σ uncertainties for the
budget for January 2011 of the seven sectors of emissions are approximately
equal to one another. The latter assumption is supported by a recent census,
which was conducted by National Physical Laboratory (NPL) based on a group
of 26 city inventories reported to the carbon Climate Registry (cCR)
suggesting that the data collected for different sectors can actually have a
similar level of quality (report available from www.carbonn.org). The sensitivity of the inversion results to the
configuration of B and thus the robustness of the inversion is
discussed in Sect. 4. By construction, the resulting 1σ uncertainties
in the budgets for the seven sectors of emissions are larger than that in
the total emission estimate. They are approximately equal to 36 % (Fig. 9). As B15, we set a prior uncertainty in the NEE scaling factors of about
70 %.
Controlling large control tiles with a single scaling factor does not mean
that the uncertainties in the emissions at higher resolution are assumed to
be entirely correlated within a control tile. The uncertainties in the
distribution of the emissions at higher resolution given by the observation
operator must actually be accounted for in the computation of the
observation error as indicated in the following section. This part of
observation error is generally called the aggregation error.
Observation uncertainties
Observation uncertainties arise from both the measurement errors and the
model errors associated with the observation operator (including the
transport model errors). The precision of the instruments presently used
(typically cavity ring down spectrometers) for the climate studies can have
a high precision that is better than 0.1 ppm (1σ) on hourly mean data.
When properly calibrated, typically every 2 weeks to 2 months, these high
precision instruments do not bear any significant drifts or biases, and the
systematic errors borne by their hourly measurements are smaller than
0.13 ppm. This level of measurement error is negligible compared to the
current transport model errors that are detailed later in this section. Even
though the deployment of dense networks with up to 70 sites would rely on
LCMP sensors and on a different calibration strategy, we conduct the main
inversion experiments assuming that they would measure CO2 with a
precision and accuracy still negligible compared to the model error.
However, some sensitivity tests will be performed to assess the impact of
much larger measurement errors (Sect. 3.2).
The model error, which applies to “downwind–upwind” CO2 gradients in
this study, is mainly a combination of the aggregation error due to
uncertainties in the spatial and temporal distribution of the fluxes within
a control tile that is not resolved by the inversion, of the
representativeness error (the difference in terms of spatial
representativeness between the measurements and the CO2 simulated with
a 2 to 10 km horizontal resolution model), of the atmospheric transport
modeling error, and of the errors in the model CO2 initial and boundary
conditions.
Following B15, we assume that the observation error covariance matrix
R is diagonal, which means that the model errors for the CO2 gradients
are not correlated in time or in space. This implies that there is no
correlation of the model errors in the direction orthogonal to the wind (see
later in this paragraph for a discussion about the direction parallel to the
wind). Based on statistics on the model–measurement misfits, B15 diagnosed
the total model error when simulating CO2 hourly concentrations at
individual urban and rural sites and for hourly city downwind–upwind
gradients between rural stations. They found that this error is of the order
of 5 and 10 ppm for hourly CO2 data at rural and urban stations,
respectively, and of 3 ppm for hourly gradients between rural stations. The
high model error at individual stations characterizes the difficulties of
atmospheric models to represent the CO2 transport within and in the
vicinity of urban areas, even when selecting data during the afternoon and
for high wind speed only. B15 explain the smaller model errors for gradients
than for individual CO2 data by the high spatial correlations between
model errors at upwind and downwind sites. These spatial correlations are
due to the large spatial coherence of the errors from the model boundary
conditions along the wind direction, whose canceling is the main aim of the
gradient computation. In principle, this is not incompatible with the
assumption mentioned above that there is no correlation of model errors in
the direction orthogonal to the wind since it bases on the idea that the
correlation follows the advection of air parcels and of the atmospheric
signature of remote sources and sinks. Still, the diffusion of the signature
of remote sources and sinks through their atmospheric transport could
correlate the model error between different gradients corresponding to close
locations. Characterizing such spatial correlations is very challenging and
falls beyond the scope of this paper.
The diagnostics of model error by B15 account for the transport and
representativeness errors and of errors in the CO2 initial and boundary
conditions of the same transport configuration as that used in our study. It
also accounts for aggregation errors since their inverse modeling framework
solves for emissions at a coarser resolution than in this study (they apply
scaling factors for the 6 h mean budget of the emissions in IDF). Smaller
aggregation errors should apply in our configuration but we conservatively
use their diagnostic to assign the model errors in our OSSEs. This setup of
the model errors in our study is also based on a simple derivation of the
spatial correlations of the model error for individual measurements between
upwind and downwind stations based on their results. This leads us to assign
a standard deviation of 3.5, 5.6, and 7 ppm, respectively, for the observation
error on gradients between rural stations, between rural, and urban stations
and between urban stations.
Results
Results with the reference inversion configuration
We conduct a series of inversions of sectoral and total emissions during the
month of January 2011 using E-, R-, and U-type networks with 10, 30, 50, and
70 stations. The inversion results are analyzed in terms of posterior
uncertainties in the inverted fluxes and in terms of uncertainty reduction
by the inversion (Fig. 9). The uncertainties discussed here are relative
uncertainties, which are defined as the uncertainty budgets in percentage of
the budgets of the corresponding emissions obtained from the IER inventory
(and included in the observation operator).
With small E, R, or U networks of 10 stations (i.e., the size of some of the
existing networks), inversions are effective in reducing uncertainties in
total emissions as well as in the emissions from the three major sectors
(building, road, and energy). The inversion on average reduces the 1σ
uncertainty in the total emissions estimates from ∼ 19 % a
priori down to ∼ 11 % a posteriori (a 42 % uncertainty
reduction). The 1σ uncertainties in building, road, and energy emission
estimates are reduced on average from ∼ 36 % (prior
uncertainty) down to about 23, 27, and 24 %, respectively (about
35, 23, and 31 % uncertainty reduction, respectively, over the prior
uncertainty). In contrast, the uncertainty reduction is very limited for
emissions from agriculture, airline, production, and remainder sectors.
However, the contribution of these four sectors of emissions to the total
budget is rather small and represents only ∼ 16 % of the
total emissions in IDF according to the IER inventory (Fig. 9e).
In order to limit the influence of specific station locations and to weight
the sensitivity to the network design (and thus the need for network design
studies), we performed inversions with 10 random networks of the same type
and size. These random networks differ from one another in their station
locations but still follow their respective network type (see Sect. 2.3 on
how we generate these random networks). The variation (error bars in Fig. 9)
of the inversion performance due to changes in the station locations is in
general small, compared to the variations due to the changes of the network
type and size (see Fig. 9). The influence of the station location is large
for the agriculture sector, but the emission budget for this sector is small.
Reduction of uncertainties by inversions using three different types
of networks of 70 stations with inflated observation error standard
derivation (50 % larger).
The uncertainty reduction increases with larger networks. However, this
increase generally slows down and is rather weak once the networks have more
than 30 stations (Fig. 9a–c). While there is not much difference between the
uncertainty reduction for energy emission estimates when using 30-station or
70-station E networks (Fig. 9a), the increase in uncertainty reduction for
building emissions when using 70-station compared to 30-station U networks
is still significant. To further illustrate this slowdown effect, we assess
the number of degrees of freedom for signal (DFSs; Rodgers, 2000) for
inversions using different networks (Fig. 10a). The DFS characterizes the
number of independent pieces of information brought by the observations and
therefore the relative weight of the signal from the observations against
the noise from the observations in the analysis. If the uncertainty in the
measurement is very high or if the measurements bring redundant information,
the measurements will provide a small DFS. In practice, the overall DFS is
the trace of matrix (B-A)B-1 and
has a value between zero and the number of observations d (Wu et al.,
2011). For our Paris case study, we find that the DFS per concentration
gradient observation (i.e., the ratio DFS/d) is less than 10 %;
that is, only a small percentage of observations are effectively assimilated
and correspond to the signal but not the noise. Such small DFS results from
the diffuse nature of atmospheric transport (which weakens the atmospheric
signature of the emissions from specific sources and spreads it throughout
the different concentration gradients) and from the uncertainty in
atmospheric modeling (which weakens the constraint given to observations
during the inversion analysis). When using denser networks, the DFS per
observation decreases, and the information brought by the different gradient
observations on the budgets of sectoral or total emissions over the full IDF
area has more redundancy. This is due to the decrease of the distances
between the upwind and downwind stations and between the different upwind
(or downwind) stations that are selected for gradient computations. Despite
such a densification of the network, many isolated and local sources, which
dominate some sectors of emissions, are still difficult to catch, in
particular with our 5 km threshold on downwind–upwind site distance (see
Sect. 2.4.3). Additionally, the selection of daytime observations for high
wind speed dramatically reduces the observational constraint on the
emissions at other periods of time (see Sect. 2.2 for the temporal
discretization of the control vector), which altogether have a large weight
on the total emission budget. Therefore, the slowdown of the uncertainty
reduction when using larger networks is also explained by their convergence
to a value which reflects this lack of constraint.
The 1σ posterior uncertainties obtained with 70-station networks of
type either E, R, or U are on average 32, 33, 18, and 31 %
smaller than those obtained with 10 stations for building, road, energy, and
total emission estimates, respectively (Fig. 9a–c). Compared to the prior
uncertainties, inversions with 70-station networks achieve an uncertainty
reduction of 60 % on average for the total emissions, which leads to an
8 % 1σ posterior uncertainty. In contrast, the 1σ posterior
uncertainties in building, road, and energy emissions are 16, 18, and
20 %, respectively, with uncertainty reductions by 56, 48, and
43 %, respectively, compared to the corresponding sectoral prior
uncertainties. Large networks are more promising for the estimation of
dispersed surface emissions such as those from the building sector.
Different types of networks show distinct ability for monitoring emissions,
which is usually sector specific. For instance, using a U- instead of a
E-type 70-station network leads to 18 % vs. 22 %, 18 % vs. 19 %,
15 % vs. 18 %, and 6 % vs. 9 % differences in the posterior
uncertainty in the estimates of the energy, road, building, and total
emissions (Fig. 9d). Compared to the U networks, the E networks result in
larger DFS values (Fig. 10a) but worse performances in uncertainty reduction
for total emission estimates (Fig. 10b). The stations in the E network are
around the area of high emissions (in particular central Paris), and therefore
their concentration gradients would be overall more sensitive to the nearby
emissions (hence with larger DFS values). However, focusing only on central
Paris makes the E network less efficient for controlling the emissions in
the rural area (see the spatial distribution of the energy, building, and
road emissions in Fig. 5a–c). This is because there are large point sources
(e.g., the EDF Porcheville power plant and the TOTAL Grandpuits refinery from
the energy sector; Fig. 2) and considerable building emissions located
outside of the largest ring of the E networks (Figs. 3 and 5).
In all experiments, the prior and posterior relative uncertainties in
sectoral budgets are higher than that in the total emissions due to the fact
that the sectoral budgets from inventories or atmospheric inversions are
based on a mix of independent information and the split of the
information on the total emissions (which is characterized by null or
negative correlations between the uncertainties in the different sectors).
The analysis of the negative correlations between posterior uncertainties in
different emission budgets is indicative of the capability of the inversion
system to well spread the attribution of an overall concentration increase
between them (Fig. 8). Large negative correlations associated with high
posterior uncertainties indicate that the posterior uncertainties in the
individual budget for the different corresponding emission components arise
from improper attributions of budget among these emission components, while
the sum of the emissions budget of all components may be well constrained by
the inversion. The skill of the larger U networks for separating the
sectoral emissions budgets is higher than that of the smaller U networks and
than that of the equal-sized E networks (see Fig. 8b–d for cross
correlations between building, road, and energy sectors).
However, the E networks perform better than the U networks for estimating
emissions from the airline sector. This is due to the fact that airport
emissions (see Figs. 2 and 5f) are located between the two outer rings
of the E networks. Moreover, the E networks perform well to reduce
uncertainty in road emission estimates, although a significant portion of
the road emissions occur in rural areas that are not covered by the E
networks. This is probably because (1) the smallest inner ring coincides
with the heavy-loaded Paris peripheral boulevard (25 % of the traffic in
Paris); (2) the Paris road network (Fig. 5b) sprawls mainly in the urban and
suburban area, which are comprised within the largest outer ring; and (3) the configuration of the E networks (as well as that of the R networks; Fig. 3)
is better adapted than that of the U networks to distinguish between the
signature of the road emissions and that of the other emission sectors.
Sensitivity to the measurement and model errors and to the
amplitude of the uncertainty in NEE
The results analyzed above are based on the reference inversion
configuration detailed in Sect. 2. However, as introduced in Sect. 2.5.2,
observation errors could be in practice larger than assumed, either because
we would need to use LCMP sensors with smaller accuracy than the present
high precision instruments in order to deploy dense networks or because our
assumptions regarding the model errors (derived from the diagnostics of B15
over a small number of sites) would not be adapted to dense measurement
locations.
We have thus repeated the inversion tests with values for the observation
error standard deviations inflated by 50 % compared to those described in
Sect. 2.5.2 for the reference configuration (which would corresponds to a
dramatic increase of the measurement error or decrease of the modeling
skills; see the discussion in Sect. 4). The 1σ posterior uncertainties
resulting from inversions with inflated (Fig. 11) and reference (Fig. 9d)
observation errors when using 70 sites and the type of network providing the
best performances (depending on the sector) are (1) 7 and 6 %,
respectively, for total emission estimates with U networks; (2) 16 and
15 %, respectively, for building emissions with U networks; (3) 19 and
18 %, respectively, for road emissions with R networks; and (4) 20 and
18 %, respectively, for energy emissions with U networks. The increase of
the posterior uncertainty in total emission estimates resulting from this
inflation of observation error standard deviation is significant (typically
1 % of the budget of prior total emissions). However, these increases are
relatively modest compared to the typical variations of posterior
uncertainties, depending on the different networks that are tested. This is
likely due to the fact that, at the monthly scale, the projection of the
uncertainty in the prior emissions into the concentration space is very high
compared to the observation errors and the fact that the observation
limitation is primarily related to their spatiotemporal coverage rather
than to the precision of the hourly measurements and of their simulation by
the observation operator.
Our reference experiments apply to a month in winter when the CO2
signal from the NEE is low and the heating emissions are high, which
decreases the difficulty to separate it from that of the anthropogenic
emissions in the concentration gradients. This could favor the monitoring of
the anthropogenic emissions during this season. In order to assess whether
the results obtained in this study can be indicative of the performance of
the inversion during summer, when the NEE is higher (we ignore here the
impact of the decrease in the heating emissions), we run inversions where
the prior error standard derivation for the NEE fluxes is inflated/shrunk by
100 % or where the NEE fluxes within the observation operator H1 (see Sect. 2.4.1) are multiplied by 3 or 5 (which typically
corresponds to the ratio between the NEE in July vs. January according to
the C-TESSEL simulations). The differences between the uncertainty
reductions for the total emission estimates obtained with the reference
configuration and when applying these changes are found to be less than
1 %. Actually, the correlation between the posterior uncertainties in the
NEE fluxes and in the total and sectoral fossil fuel CO2 emissions
(except the building emissions) are nearly zero (Fig. 8b–d), which implies
that the different networks are sufficiently dense to provide a clear
separation between natural and anthropogenic fluxes within our inversion
framework. This explains the weak influence of the prior uncertainty in the
NEE for the estimate of the fossil fuel CO2 emissions.
These sensitivity analyses strengthen the confidence in the robustness of
our inversion results that are based on the experiments with real data of
B15 and Staufer et al. (2016).
Discussions and conclusions
Summary with complementary analysis
We have developed an atmospheric inversion method to quantify city total and
sectoral CO2 emissions using networks of measurement sites within and
around a city. This method combines a prior emission estimate from an
inventory with the information from concentration gradient measurements
(independent of the inventory) to provide updated emission estimates with
reduced uncertainty. Such an inventory can be obtained, for instance, directly
from local agencies or interpolated from regional inventories developed by
public research establishments (see Appendix A). We examine the ability of
this inversion system to reduce uncertainty in emission estimates for
diverse emitting sectors of the Paris metropolitan area (∼ 12 % of France CO2 fossil fuel emissions) as a function of the size
and design (i.e., location of the stations) of the observation networks.
We perform inversions over a 1-month winter period (January 2011) under a
framework of OSSEs, in which we test
several types of theoretical networks of stations sampling CO2
atmospheric concentrations at 25 m a.g.l. When using 10 stations, which is the typical size of the few current networks, the
inversion considerably reduces the uncertainties in total emission estimates
for January 2011 (by ∼ 42 %) from a ∼ 20 %
1σ prior uncertainty down to ∼ 11 % 1σ posterior
uncertainty. The uncertainty reduction for sectoral budgets is also high but
the 1σ posterior uncertainties for these budgets is ∼ 25 %, i.e., more than twice as high as for total emissions. In the prior
inventories as in our inversion experiments, the total emissions are better
constrained (in relative terms) than the sectoral budgets. The inversion is
more efficient in decreasing uncertainties in the budget of dispersed
emissions from residential and commercial heating than those in other
sectoral budgets. We observe significantly larger uncertainty reduction in
sectoral emission budget estimates when using more stations. The decrease of
the uncertainties in the inverted emissions when using 70 stations vs. 10
stations is of 32 % for commercial and residential buildings, 33 %
for road transport, 18 % for the production of energy by power
plants, and 31 % for the total emissions. The three major
sectors (building, road, and energy) cover most of the emission budget
according to the IER inventory used in this study. Therefore, while the
extension of the networks does not seem to be critical for the verification
of the city emission total budgets, it likely provides advantages for
the monitoring of sectoral emissions. When using 70 sites, the 1σ
monthly posterior uncertainty in the building emission estimates can be
brought down to 15 % while that for transport and energy emissions
estimates is reduced to 18 %.
Discussion on the levels of posterior uncertainties and on the
relevance of the corresponding estimates
We can hardly determine whether the levels of precision in emission
accounting obtained by atmospheric inversions would be enough for a MRV
framework since the MRV experiences for citywide CO2 emissions are
still very limited (Appendix A). We still attempt at evaluating the
usefulness of estimates with these different levels of uncertainties. In MRV
practice, mitigation actions and climate plans are usually based on targets
for the reduction of annual budgets of the emissions and should thus be
evaluated based on the monitoring of annual budgets and/or their trends.
In this study, the accuracy of the inversion is analyzed for a single winter
month; inversion experiments over longer time periods are out of the
scope of the paper (for reasons of computational cost). However, results
from Sect. 3.2 indicated that its accuracy in spring, summer, and fall should
be similar. In order to get an indication on the accuracy of the inversion
at the annual scale, we thus assume that the scores obtained here apply to
all months during the year and use two opposed and extreme hypotheses
regarding the correlations between posterior uncertainties from month to
month. The first one is that these uncertainties are fully independent,
which can be supported by the independence of the measurements used to
constrain the estimates from month to month. The second one is that these
uncertainties are fully correlated, which can be supported by the fact that
part of the posterior uncertainty is related to residual prior uncertainties
that have not been decreased by the inversion and that the prior
uncertainties can be highly correlated from month to month. Actual
correlations should lie between these two extreme cases. By doing so, we
obtain a simple, conservative, and indicative assessment of a typical range
of 2σ annual uncertainties in the total and sectoral emission estimates
from the inversion. With such a conversion, the prior uncertainty in total
emissions would range between 12 and 40 %, while that in the sectoral
budgets of the emissions would range between 21 and 72 % depending on
the sectors. The 2σ annual posterior uncertainty in total emissions
would range between 4 and 23 % when using 10 to 70 sites. The 2σ
annual uncertainty in the budgets for the three main emitting sectors
(building, road, energy) would range between 13 and 59 % when using 10
sites and between 9 and 44 % when using 70 sites, while it would
systematically exceed 14 % for the production sector even when using 70
sites. Such annual uncertainty ranges vary a lot for the secondary sectors
of emissions (airline, agriculture, remainder), e.g., between 7 and
41 % for agriculture to systematically higher than 20 % for the
remainder emissions when using 70 sites.
We compare these numbers to the diagnostic (based on expert judgments as
well as error propagation calculations with the IPCC Tier 1 method) of the
typical uncertainty in the national inventories in developed countries,
which could apply to theoretical city-scale inventories under MRV
frameworks. The uncertainty in national inventories is country specific but,
for the seven Annex I countries surveyed by Pacala et al. (2010), the
uncertainty in CO2 fossil fuel emissions is consistently lower than
10 % (2σ). For France, the uncertainty of the CITEPA national
inventory (annually reported to UNFCCC) is estimated to be 5 %
(2σ) for year 2012 according to CITEPA (2014). The uncertainty levels
for estimates of emissions from different sectors can vary significantly at
the national scale (Pacala et al., 2010; CITEPA, 2014). For instance,
uncertainties for some activities such as mineral, metal, and chemical
productions are considerably larger than the 5 % value for total
emissions, but the share of these emissions in the total fossil fuel
emissions is usually small. Uncertainties for other sectors are closer to
5 % according to CITEPA (2014).
Furthermore, succeeding in delivering a 5 or 10 % 2σ annual
uncertainty for the total emissions of a city would translate into an
ability to assess a 25 % reduction of total emissions on a 15-year horizon
at a 95 % confidence level (detection interval [18, 32 %] or
[11, 39 %], respectively, p=0.05 for linear trends of emissions; see
Appendix C for numerical details). The Paris climate plan, for example, aims
at reducing the GHG emissions by 25 % by 2020 and by 75 % by 2050
relative to the 2004 baseline (Mairie de Paris, 2012). This means that a
10 % annual uncertainty would be enough to monitor the trend of Paris
emissions over time.
Comparing our indicative estimate of the typical range of posterior
uncertainties in annual total and sectoral emissions to these 5 and
10 % 2σ uncertainties confirms the need for dense observation
networks if willing to build a valuable MRV framework. A significant part of
the range of posterior uncertainties derived for the annual total emissions
when using 10 sites is below the 10 % 2σ uncertainty. However, it
does not reach the 5 % 2σ uncertainty and most of this range is lying
above the 10 % 2σ uncertainty. When using more than 30 sites and U
networks, the 5 % 2σ uncertainty can be reached by the most
optimistic estimates of posterior uncertainties in annual total emissions
and most of their range lies below the 10 % 2σ uncertainty.
Furthermore, as far as the most optimistic derivation of annual results is
concerned, inversions with more than 30 sites would be required to expect
that the posterior uncertainties in annual emissions for the three major
sectors can be close to 10 % 2σ uncertainty. This level can be
reached with U or R networks of more than 50 stations for building
emissions, but it cannot be reached for the road and energy sectors. Seventy
sites are required to expect posterior uncertainties of less than 10 %
2σ uncertainty for all these three sectors at the annual scale. For the
other types of sectors, the inversion with U, E, or R networks is likely not
adapted to reach the 10 % 2σ uncertainty level at the annual scale.
With 70 sites, a significant part of the ranges of 2σ posterior
uncertainties in annual emissions for the three major sectors is below
∼ 15 % (for any type of networks). Such a 2σ
uncertainty at the annual scale still corresponds to an ability to detect
the 25 % reduction of emissions on a 15-year horizon at a 95 %
confidence (detection interval [3, 46 %], p= 0.05 for linear trends
of emissions; see Appendix C). The 5 and 10 % 2σ uncertainties
can thus be viewed as stringent for the monitoring of sectoral emissions but
the comparisons to these levels of uncertainty indicate that dense networks
would be necessary to ensure that the inversion has a high potential to
verify sector-wide mitigation policies/actions or to check whether sectoral
mitigation targets are fulfilled.
Robustness of the inversion configuration and requirements on the
model, methods, and instruments supporting such a configuration
The results obtained in this study should not be over-interpreted since (1) we worked under synthetic settings for large city networks and (2) the
configuration of our inversion system may fail to be fully faithful to
reality (e.g., the idealized parameterization of the prior uncertainties in
scaling factors defined for different sectors and spatial zones and the
assumed independent errors in concentration gradient observations).
Nevertheless, our inversions were based on the experience from B15 and
Staufer et al. (2016) in which real data from a few number of stations
around Paris were used. In addition, we performed sensitivity analyses by
significantly inflating the observation error to account for a potential
increase of the measurement and modeling errors when deploying dense
networks with many sites in the core of the urban area, and this analysis
gave confidence in the robustness of the results obtained with our reference
inversion configuration.
Our tests ignored potential temporal correlations in the model and
measurement errors. Increasing the standard deviation of the observation
error for hourly data should have a similar impact on results at the monthly
scale as accounting for short temporal autocorrelations (over timescales
typically smaller than few days). Increasing the standard deviation of the
observation errors instead of modeling their autocorrelations is a common
technique in atmospheric inversion (Chevallier, 2007).
The results from B15 and Staufer et al. (2016) support the idea that the
model has no major biases or errors with large temporal correlations.
However, even though B15 diagnosed model errors for measurements in the core
of the urban area, they and Staufer et al. (2016) did not attempt at
assimilating such measurements. We thus implicitly make the assumption that
there is no major model errors with long temporal correlations associated
with high local sources for 25 m a.g.l. locations in the urban environment. This
assumption is supported by the idea that relevant investigations (mobile
measurement campaigns, high-resolution transport modeling) can be led to
avoid setting up sites close to such sources. In our study, the hypothetical
stations are all located without a precise definition of their specific
position within the 2 km × 2 km grid cells of CHIMERE, which are
sufficiently large to assume that they encompass areas less prone to local
sources. High-resolution transport modeling can also be used to develop
techniques for filtering the signal from the large-scale emissions against
that of local sources in the measurements.
The theoretical use of LCMP sensors to allow the deployment of networks of
up to 70 sites could be viewed as a source of systematic measurement errors
with long temporal scales of autocorrelation. Our results from Sect. 3.2
suggest that if the measurement errors are significant and increase the
observation errors by 50 %, they can have a significant impact on the
accuracy of the inversion. Such an inflation of the observation error would
result from 1 ppm systematic errors with 7-day temporal correlations in the
hourly measurements (since it would result in ∼ 1.5 ppm
systematic error in weekly mean gradients or, if converting the temporal
correlations into an inflation of the hourly standard deviations, in an
8 ppm measurement error for hourly gradients). Therefore, our sensitivity
tests indicate that the LCMP accuracy and calibration strategy should ensure
that the systematic errors do not exceed 1 ppm and, if they are close to
this value, that they are not auto-correlated over more than 1 week. This
recommendation adds to the recommendation that the cost of LCMP sensors
should not exceed EUR 1–5 k (see the discussion in Appendix B).
The choice to rescale the budgets of emissions over large areas and sectors
rather than at high resolution could make our results quite optimistic.
However, the aggregation errors associated with such a coarse scale
rescaling are accounted for in the inversion. Furthermore, the configuration
of the networks tested in this study is adapted to that of the “control
tiles” which helps avoiding aggregation artifacts. With such
configurations, the results show that having as many sites as possible
around the most prominent sources of a tile will give a better control on
the average budget of that tile. As would have been expected with a high-resolution inverse modeling system, our coarse inversion system identifies
the networks that can provide a strong constraint on most of the largest
sources within the tiles, and it demonstrates some sensitivity to the
network types and station locations.
The assumptions underlying our setup of the sectoral uncertainties (in
particular for the prior error covariance matrix B) can definitely
impact the results of the uncertainty reduction. It could raise some
concerns regarding the analysis of the absolute values of uncertainty
reduction for a given network. However, the comparative analysis of the
uncertainty reductions when using different networks but the same inversion
setup (i.e., the network design analysis) should bring more robust
conclusions.
Perspectives
While the deployment of dense city networks of more than 30 sites seems
presently excessively expensive, the present development and testing of LCMP
sensors whose cost would not exceed EUR 1–5 k give first hopes that it
could become realistic in the near future (see Appendix B).
The potential for monitoring sectoral budgets could be further increased by
the use of isotopic measurements such as 13C and 14C (Pataki et al., 2003; Lopez et
al., 2013; Vogel et al., 2013) and of co-emitted pollutants such as NOx and
CO (Ammoura et al., 2014), whose ratios to CO2 depend on the sectors of
activity.
Our inversions are shown to be highly sensitive to the types of networks
that we have defined and sometimes (e.g., for the agriculture sector) to the
specific station location for given type of network. While the results could
be improved if the stations location would follow some empirical rules (e.g.,
redistributing more stations along road networks or around power plants to
better distinguish emissions from road transport and energy production),
this motivates optimal network design studies, based on atmospheric
inversion OSSEs such as in this study, potentially coupled to optimization
algorithms (Wu and Bocquet, 2011).
One may consider further improving the current city-scale inventories as a
natural choice for emission accounting in the context of MRV, in a way
similar to what is experienced by the applications of national inventories
under UNFCCC and the Kyoto Protocol. However, such refinement requires
tedious efforts in order to continuously collect detailed and high-quality
local data. In this paper we highlight the potential of the alternative
approach of atmospheric inversion to provide accurate estimates of the total
and sectorial budgets of the emissions.
Atmospheric inversion distinguishes itself in a number of ways for the
quantification of city CO2 emissions. It would provide an estimate
method other than inventories based on IPCC guidelines. Estimating the same
source of emissions with two different approaches remains the best way to
detect biases, even when the approaches may not be fully independent. In
addition to the verification of inventories, atmospheric inversion can also
incorporate, whenever available, inventories into its modeling framework to
improve their emission estimates. The inverse modeling system assimilating a
cohort of measurements can provide a unique platform to investigate the
urban carbon cycle (e.g., the anthropogenic/biogenic land–atmosphere carbon
exchange of the urban ecosystem and the carbon flows into and out of the
urban area) and its implications for policy-making. Finally, atmospheric
inversion would bring a continuous monitoring of emissions changes (e.g.,
larger heating emissions during cold spells and larger than usual traffic
emissions during specific events), which offers important possibilities for
infrastructure operators to take appropriate measures with a fast response
time. This is in particular helpful to verify city climate mitigation
actions, when their impacts could be seen objectively in measured
atmospheric signals. With these features, atmospheric inversion appears to
be a promising MRV tool to mitigate city CO2 emissions.