Anthropogenic CO2 fluxes within the IdF region are imposed using the AIRPARIF inventory for the year 2010 at spatiotemporal resolutions of 1 km and 1 h (AIRPARIF, 2013). This inventory is based on various anthropogenic activity data, emission factors and spatial distribution proxies, which are described in detail in Bréon et al. (2015). It provides maps and diurnal variations for 5 typical months (January, April, July, August, and October) and 3 typical days (a weekday, Saturday, and Sunday) to account for the seasonal, weekly and diurnal cycles of the emissions (see Fig. 3 in Bréon et al., 2015). CO2 emissions from fossil fuel CO2 sources outside the IdF region are taken from the inventory of the European greenhouse gas emissions, together with country-specific temporal profiles (monthly, daily, and hourly) at a spatial resolution of 5 km (updated in October 2005). This inventory was developed by the Institute of Economics and the Rational Use of Energy (IER), University of Stuttgart, under the CarboEurope-IP project (http://www.carboeurope.org/, last access: 12 November 2019).

Both inventories are adapted to the WRF-Chem model for the period of simulation (September 2015–November 2016). Moreover, we scale these two data sets to account for annual changes in emission between the base years and simulation timeframe. This is accomplished by rescaling the maps with the ratio of the annual budgets of national CO2 emissions for the countries within the domain between the base year 2005 for IER and 2010 for AIRPARIF and the year of simulation (2015/2016), taken from Le Quéré et al. (2018) (https://www.icos-cp.eu/GCP/2018, last access: 12 November 2019). See also Table S1 in the Supplement for details about original data sources). Finally, we interpolate the emissions onto the WRF-Chem grids, making sure to conserve the total budget of emission in the process, as done in previous studies (e.g., Ahmadov et al., 2007). Note that for the point sources such as stacks, industries, and mines, CO2 emissions are distributed over a single grid cell corresponding to their locations. Figure 2 shows the spatial distribution of the total CO2 emissions for a weekday in March over the IdF region at the resolution of 1 km × 1 km. It can be seen that there is a large spatial variability of CO2 emissions ranging from 0 to more than 600 g CO2 m-2 d-1 in this area and the largest emissions are concentrated over the Greater Paris area, accounting for about 50 % of the emitted CO2.

Based on the analysis of sectorally specific fossil fuel CO2 emissions over the IdF region by Wu et al. (2016), we group the detailed sectoral AIRPARIF emissions into five main sectors, namely building (43 %), energy (14 %), surface traffic (29 %), aviation-related surface emissions (4 %), and all other sectors (10 %), where the percentages in parenthesis express the relative contribution of each sector to the yearly total. All emissions are injected in the first model layer. Distinct CO2 tracers are used for each of the five main sectors in the transport model to record their distinct CO2 atmospheric signature. Figure 3 shows averages at the monthly scale of emissions below the GreenLITE^™ chords for those different sectors. It illustrates that CO2 emissions have a large seasonal cycle, mostly due to the residential heating (the “building” sector) which is strongly driven by variations in the atmospheric temperature. Figure 3 also reveals lower emissions for those chords (TX and R01-03) in the west of Paris than those in the other quadrants.

Biogenic CO2 fluxes are simulated with the VPRM model forced by meteorological fields simulated by WRF and online-coupled to the atmospheric transport. VPRM uses the simulated downward shortwave radiation and surface temperatures, along with the vegetation indices (enhanced vegetation index and land surface water index) derived from the 8 d MODIS Surface Reflectance Product (MOD09A1) and four parameters for each vegetation category (PAR0, λ, α, β) that are optimized against eddy covariance flux measurements over Europe collected during the Integrated EU project “CarboEurope-IP” (http://www.carboeurope.org/, last access: 12 November 2019). The land cover data used by VPRM (see Fig. S5) are derived from the 1 km global Synergetic Land Cover Product (SYNMAP; Jung et al., 2006) reclassified into eight different vegetation classes (Ahmadov et al., 2007, 2009).

Figure 4a shows the spatial distribution of daytime-averaged (06:00–18:00 UTC) CO2 biogenic flux (the net ecosystem CO2 exchange, hereafter NEE, with a negative sign indicating net CO2 uptake by the vegetation surface) in June 2016. The model simulates negative values of NEE (uptake of more than 5 gCO2 m-2 d-1) over most of the region with the exception in urban areas where the values are assigned to 0. Figure 4b shows the mean diurnal cycles of NEE for 12 calendar months and for eight vegetation classes used in VPRM over Domain 03. The magnitude of NEE is highly dependent on the vegetation types, although the diurnal cycles are similar across these vegetation types. From November to January, the VPRM estimates within the IdF region show a small diurnal cycle and a positive NEE explained by ecosystem respiration exceeding gross primary productivity. One exception to positive wintertime NEE is for evergreen trees which, according to the VPRM model, sustain enough gross primary productivity to keep a negative daytime NEE throughout the year. The model shows large CO2 uptake between late spring and early summer. Note that the seasonal cycle of crops, which dominates over the IdF region, is somewhat different from that of forests, with an NEE that decreases after the harvest in June/July; this crop phenology signal is being driven by the MOD09A1 data. Grasses also have a shorter uptake period than the other vegetation types, with a positive NEE as early as August.

Initial and lateral boundary conditions for CO2 concentration fields used in the WRF-Chem model are taken from the 3-hourly fields of the CAMS global CO2 atmospheric inversion product (Chevallier, 2017a, b) with a horizontal resolution of 3.75∘ × 1.90∘ (longitude × latitude) and 39 vertical levels between the surface and the tropopause.

We analyze the horizontal differences between pairs of in situ stations as a function of wind speed and direction, expecting a larger concentration at the downwind station with respect to the upwind station, in this region of high emission. For wind fields, we use the ECMWF high-resolution operational forecasts (HRES) linearly interpolated at the hourly resolution and extracted at a height of around 25 m a.g.l. (https://www.ecmwf.int/en/forecasts/datasets/set-i, last access: 12 November 2019) as a proxy for all stations located within the IdF region. The HRES wind product is used here for two reasons: firstly, our previous study has shown that the wind speeds provided by HRES are, in general, closer to the observations than those provided by WRF (Lian et al., 2018). Secondly, the WRF-Chem model was run with two configurations (UCM and BEP urban canopy schemes) in this study. If we make use of the modeled winds, the UCM and BEP modeled CO2 spatial differences should be analyzed using their corresponding modeled wind fields, and the observed winds are then needed for the analysis of the observed CO2 spatial differences. However, given the small-scale wind variations reproduced by the model, it is hard to determine from which station the wind data used in the analysis should come. For the purpose of a fair and uniform comparison, we thus use an independent wind product. Furthermore, the hourly afternoon CO2 data are classified into the wind classes with a bin width of 1 m s-1 for wind speed and 11.25∘ for wind direction. Figure 5 shows the patterns of the observed and modeled CO2 concentration differences between pairs of in situ stations, averaged accounting for the wind classes. The standard deviations of CO2 concentration differences for each wind class are shown in Fig. S8.

Figure 5a shows the observed and modeled CO2 horizontal differences between AND and COU, two suburban stations located to the north of the city of Paris. One expects that stations downwind of sources of emissions would have a higher CO2 concentration than those upwind so that the sign of the difference should vary with the wind direction. For this pair of sites (AND and COU), both the model and observations show the expected pattern with a similar amplitude. The values of RMSE and MBE are 4.53 and -0.14 ppm, respectively, for the BEP scheme, implying a slightly better performance than the UCM scheme (6.34 and -0.47 ppm, respectively).

Figure 5b and c show similar figures but for the CO2 differences between (COU–SAC) and (CDS–SAC). The city of Paris is located between both pairs of stations when the wind is roughly from the northeast or from the southwest directions. Both COU and SAC are located outside of the city and show a pattern with fairly symmetric positive and negative values. Conversely, CDS is in the city of Paris, within an urban environment, and is strongly affected by significant urban emissions from its surroundings. As a consequence, the CDS–SAC differences in concentration are mostly positive for all wind sectors, with the exception of very specific wind conditions (low winds in the 45∘ northeast sector). The wind speed also has a strong influence on the differences. The CO2 difference signal and its variability are generally larger for smaller wind speeds. The model plots (second and third rows) illustrate that the models reproduce the expected cross-city upwind–downwind differences in CO2 concentrations well. In term of signal amplitude, the BEP scheme is also in better agreement with the observations than the UCM scheme, which is particularly true for the standard deviations shown in Fig. S8.

Conversely, both urban canopy schemes fail to reproduce the wind-related pattern of the observed CDS–JUS difference (Fig. 5d). These observed differences do not show any upwind–downwind patterns and are mostly negative, which can be expected since JUS is close to the city center where strong emissions impact the concentration, whereas CDS is in the middle of a park and is therefore less affected by emissions from its surroundings. The model pattern is dominated by the simple upwind–downwind structure, and it is very much different from the observed values, especially when the winds are from the west to southwest, where the model values are positive and the observed differences are strongly negative. This model–measurement discrepancy is likely the result of a poor description of the emissions in the city center that are not well reproduced by the 1 km resolution inventory with periodic temporal profiles. It may also indicate that the complex urban structure and morphology, such as buildings and street canyons, affect the energy budget and atmospheric transport, all of which lead to fine-scale (sub-kilometer) CO2 concentration features that cannot be captured by the WRF-Chem model at a 1 km horizontal resolution. The in situ point measurement may then not be representative of the average within the larger area (1 km2) that is simulated by the model.

The analysis of the in situ point measurement differences within and around Paris, together with the simulations, indicates that the model reproduces both the general structure and the amplitude of the cross-city differences in CO2 concentrations and the CO2 difference in the Paris surroundings but that it fails to simulate CO2 differences between the two stations located in the inner city.

One expects that the GreenLITE^™ principle, that provides averaged CO2 concentrations along the chord lines, is less affected by the local unresolved sources of CO2 emissions than the in situ point measurements. Meanwhile, the wide spatial coverage of the GreenLITE^™ system is expected to provide additional information about CO2 spatial variations within the city of Paris. In this section, we focus on the spatial variation in CO2 concentration measured with the GreenLITE^™ system. As a first step, we analyze the distribution of the absolute values of the observed hourly afternoon CO2 difference between all pairs of chords for each month together with their simulated counterparts shown in Fig. 6.

We first focus on the winter period (December to February). During that period, the median value of the measured T1 inter-chord range is mostly on the order of 2 ppm. That of T2 is somewhat larger, on the order of 3–4 ppm with some excursions up to 9 ppm. The two simulations with UCM and BEP show very large differences. Whereas BEP simulates spatial variations that are of the right order of magnitude compared to the GreenLITE^™ data, those of UCM are much larger. Thus, the GreenLITE^™ measurements provide clear information that favors the BEP over the UCM. During the winter period, there is little vertical mixing, which leads to large vertical gradients in CO2 concentrations close to the surface. The two simulations differ in their representations of this mixing, which leads to large differences in the modeled CO2 concentrations. Figure S9 shows that the UCM scheme reproduces a much larger vertical gradient in CO2 concentrations close to the surface, a few tens of meters above the emissions than the BEP scheme does during the afternoon (11:00–16:00 UTC). The differences are not as large higher up; neither are they further downwind of the emissions as the vertical gradient is then smoother as a result of mixing.

During the summer period, solar insulation generates more instability and the convection generates vertical mixing that limits the horizontal gradients. Both simulations indicate an inter-chord range of less than a few parts per million. Conversely, the GreenLITE^™ data indicate much larger values, of 3–4 ppm (the median) for T1 and even larger for T2. Further analysis indicates that this spatial variation is mostly systematic, i.e., that some chords are consistently lower or higher than the in situ values. At this point, there are three hypotheses.

H1: the spatial differences of T1 and T2 are true features linked to fine-scale spatial variations in the emissions between the west and east part of Paris that are under-represented or not included in the emission inventory.

Another potential source of measurement–model discrepancy is the atmospheric transport modeling as proposed in H2. According to previous studies (e.g., Hu et al., 2010), the turbulent eddies and thermals are unlikely to be reproduced properly by the local closure MYJ PBL scheme, which results in insufficient vertical mixing under convective (unstable) conditions, i.e., during summer. It may also indicate that the WRF-Chem model at a 1 km horizontal resolution cannot reproduce the fine-scale (sub-kilometer) CO2 concentration features over a complex urban environment in Paris, as the analysis of JUS and CDS in situ measurements has shown in Sect. 4.2.1.

Atmospheric transport simulations make it possible to assess the respective contributions of various areas/sectors to the measurements. Our preliminary sensitivity experiments (see Figs. S10 and S11 for details) have shown that the anthropogenic emission from the Greater Paris area is the dominant contribution (∼80 %) to the anthropogenic CO2 signal at the urban measurement stations. In order to get further insights into the characteristics of CO2 spatial variations within the city of Paris, it is therefore necessary to analyze the CO2 differences with the consideration of the anthropogenic CO2 emissions shown in Figs. 2 and 3. We thus group the 15 chords from T1 into three bins according to both their geographic locations and the amounts of anthropogenic CO2 emissions averaged along the chords: the western, middle, and eastern parts consist of reflectors R01–R03, reflectors R06–R08, and reflectors R13–R15, respectively, overlying three different regions within Paris. Figure 7 shows the covariations in the GreenLITE^™ observed and modeled CO2 spatial difference with winds. The standard deviations of CO2 concentration differences for each wind class are shown in Fig. S12.

In Fig. 7b and c, we show the east–west and the middle–west differences, where the CO2 anthropogenic emissions in the western part are systematically lower than the other two regions and the observed CO2 concentrations in the middle and east are on average higher than in the west. The patterns of observed CO2 difference are characterized by positive values no matter where the wind blows. The CO2 differences reproduced by the model are positive in the southwest direction; however, it shows a nearly opposite pattern with those from observations when the wind is from the northeast. A plausible explanation for this is that the influence of kilometer-scale anthropogenic emissions over different parts of Paris on the observed CO2 concentration has a greater effect than the atmospheric transport and dispersion of the fluxes over the period of study.

Figure 7a shows similar figures but for the east–middle difference. There is a better measurement–model agreement than for Fig. 7b and c. Indeed, as expected, the spatial variations in CO2 concentrations show negative values over upwind directions and positive values over downwind directions both for the observation and the model. According to the inventory, the two Paris areas that are covered by the set of chords used here have similar anthropogenic emissions. As a consequence, the overall CO2 concentration difference, as shown in Fig. 7a, is then better linked to the impact of atmospheric transport.

We therefore conclude that the pattern of CO2 concentration differences is consistent with winds only over the areas with similar anthropogenic emissions. In other words, if we compare the CO2 concentrations of the chords overlaying different level of emissions, the model may be insufficient in accurately modulating the dispersion of CO2 emissions, the ventilation, and dilution effects at such a high urban microscale resolution.