2.2.1. Model Configuration
We implement the Weather Research and Forecasting (WRF) model [
47] with Chemistry [
48], following the setup used in the INFLUX project by [
49,
50]. This allows for independent simulation of each CO
2 component in a passive tracer mode, which can be useful for comparison against in situ observations. Simulations were run using WRF-Chem Version 3.7. For the land surface model (LSM), the default Noah LSM scheme was used [
51,
52], which accounts for vegetation categories and fractions and includes information such as plant roots, evapotranspiration, soil runoff, and snow/ice cover. With respect to the boundary layer physics, the MYNN 2.5-level TKE scheme was used along with the corresponding built-in urban canopy model, which is compatible with the Noah LSM scheme. For comparison, an additional set of simulations was run with this urban canopy model turned off. In our investigation, we used three nested domains at 9 km, 3 km, and 1 km, as shown in
Figure 1. The meteorological driver data were supplied by the European Centre for Medium-Range Weather Forecasts (ECMWF) (
https://www.ecmwf.int, accessed on 7 May 2024), from which we used the reanalysis product.
We configured the WRF system to run simulations spanning three one-month periods: July 2016, which we call “Summertime 2016”, 27 January–27 February 2017, which we call “Wintertime 2017”, and 22 April–22 May 2017, which we call “Springtime 2017”. This was to allow for seasonal comparisons, as typically more CO
2 uptake is expected in the summer after the plants have bloomed. Springtime 2017 was included because most of the CO
2 uptake in the region was found to occur during this period rather than during the summer. Following [
49], each month of simulations was created in segments of 5 d with an additional 12 h overlapping time window to allow the meteorology to spin up. In addition, an extra segment of 5.5 d was run before the period of interest to spin up the CO
2 mixing ratios in the region from the boundary conditions, i.e., to allow enough time for the domain to be filled with ambient background values.
The model was adapted to include multiple CO
2 components which could run simultaneously and be combined post-simulation for direct comparison against other models and in situ measurements taken at the sampling sites. For this study, the relevant components included the Open-source Data Inventory for Anthropogenic CO
2 (ODIAC2017) product for anthropogenic emissions [
53,
54], the European Centre for Medium-Range Weather Forecasts (ECMWF)-based C-TESSEL model estimates for biogenic emissions (gross primary production (GPP), net ecosystem emissions (NEE), respiration (including both autotrophic and heterotrophic) [
55,
56], Fire INventory from NCAR (FINN), consisting of the version 1.5 model estimates for fire emissions [
57], a manually-created ocean flux product, and Carbon Tracker Europe for boundary conditions [
58,
59]. Each of these components are explained in further detail in the following subsection.
2.2.2. Model CO2 Flux Components
For the anthropogenic component, ODIAC estimates from the 2017 version were used, hereinafter referred to as ODIAC2017. ODIAC is a satellite-based product that uses nighttime light data to estimate population, which is then used as a proxy for CO
2 emissions [
53,
54]. Although it lacks the sector-specific nature of more traditional bottom-up inventory assessment, it provides a global product, allowing for estimates in regions where trustworthy bottom-up products may not yet be available. In comparisons, it has been shown to match well with other inventory flux estimates [
50,
60]. For our study, the ODIAC2017 estimates were taken at 1 km resolution and then interpolated onto the 9 km, 3 km, and 1 km simulation domains, as shown in
Figure 1.
Figure 2 shows three example hourly flux maps for the innermost domain for 3 July 2016 at 14:00 UTC, 3 February 2017 at 14:00 UTC, and 3 May 2017 at 14:00 UTC. The emissions are plotted on a log-10 scale to allow the spatial variations to be seen, otherwise the very strong point sources would wash out the colorscale.
The ODIAC2017 files are provided as monthly totals for the years 2015 and 2016 [
61]. For this analysis, we used the files from 2016 for each of our July 2016, Wintertime 2017, and Springtime 2017 periods of interest, as 2017 files were not yet available at the time of this analysis. In order to convert these emissions files to the hourly resolution needed to match our WRF model, the emissions were first divided equally among all the hours of the month. We then imposed a diurnal cycle on the model based on the one used by corresponding emission files provided by AtmoSud (formerly AirPACA), the local Air Quality institute in the region. The diurnal cycle was extracted and imposed in an hourly fashion by calculating a scaling factor
where
J indicates the total number of pixels in the domain,
j specifies an individual pixel,
hr is the subscript denoting a particular hour,
is the AtmoSud estimated flux at a given pixel at this hour, and
is the mean AtmoSud estimated flux at this pixel for the whole day. The sum of emissions for all hours in a day is then preserved at the same value irrespective of whether or not this scaling factor is used. Pixels with emissions greater than
mol/km
2/h are assumed to contain a plant with emissions that are not expected to follow a normal diurnal cycle, and as such are excluded from this scaling factor treatment.
For the biogenic CO
2 flux estimates, we use the ECMWF land–surface model known as C-TESSEL [
55], which offers global coverage of natural land CO
2 fluxes that are especially useful in atmospheric-model-based CO
2 emissions analyses (e.g., [
18,
20,
62]). C-TESSEL provides estimates of GPP, NEE, and Respiration (including both autotrophic and heterotrophic) at a resolution of approximately 0.09° latitude and longitude. These are then interpolated onto our relevant WRF grid using linear triangulation, as was done with the other CO
2 component estimates.
Figure 2 includes example flux maps of NEE on the innermost 1 km domain for 3 July 2016 (middle row, left column), 3 February 2017 (middle row, middle column), and 3 May 2017 (middle row, right column), all at 14:00 UTC.
Fire estimates are obtained through the Fire Inventory from NCAR (FINN) version 1.5 [
57], which provides global fire emissions estimates at ∼1 km
2 resolution. There are multiple speciation options; for this study, we chose the product based on the MOZART-4 chemical mechanism [
63]. To create the flux maps for the WRF simulations, the emissions were assigned to the relevant WRF domain and scaled appropriately to suit the pixel size. For example, a fire burning in a space of approximately 1 km
2 would have its emissions scaled down by 1/9 when assigned to the domain with (3 km)
2 resolution.
We calculated the ocean fluxes manually using the sea surface temperature (SST), surface pressure, and 10 m u and v wind speed component values provided in the ECMWF model files used to drive WRF. With these values, we incorporated measured pCO
2 values from the Bay of Marseille along with background atmospheric CO
2 mixing ratios measured at the ICOS station at Cap Corse. These were combined to solve the following formula:
where
is the measured partial pressure of CO
2 in the water,
is the measured dry air mole fraction of CO
2,
K0 is the solubility,
F is the solubility function, and
k is the gas transfer velocity. For
, we used values measured in the Bay of Marseille during the same period [
64]. For
, we used the monthly mean observed CO
2 dry air mixing ratio values from ERSA, except for the Springtime 2017 period, when such measurements were not available. For this period, measurements from the SME site were used as a background instead (see
Figure 1), a change which is expected to have a minimal impact on the resulting flux values [
64], particularly considering how low these values are compared to the other CO
2 flux components. The calculation of the other parts of the oceanic flux equation is complex; here, we follow recommendations from [
65,
66] and the detailed explanation in [
67]. As with the other flux variables, a positive value here indicates that the oceanic reservoir is acting as a source, while a negative value indicates that it is acting as a sink.
By using the six-hourly ECMWF maps for the u and v wind components, surface pressure, and SST to solve Equation (
2), we obtained ocean flux maps for every 6 h. These were linearly interpolated to create hourly ocean flux maps and appropriately converted to units of mol/km
2/h for use in our WRF-Chem simulations.
Figure 2 includes example sea flux maps on the bottom row, where the left-hand map shows the fluxes for 3 July 2016 at 14:00 UTC, the middle map shows the fluxes for 3 February 2017 at 14:00 UTC, and the right-hand map shows the fluxes for 3 May 2017 at 14:00 UTC.
We also maintained a tracer strictly to set the boundary conditions. This was achieved by providing blank (i.e., zero-emission) flux maps for the three domains. The boundary conditions of the outer ((9-km)
2) domain were defined based on the output of a global CO
2 model. For this study, these boundary condition values were provided by the latest available output from CarbonTracker Europe [
58,
59] (specifically, CTE2017-FT), which was originally an offshoot of the CarbonTracker CO
2 data assimilation system developed at the National Oceanic and Atmospheric Administration (NOAA) [
68,
69]. This latest version of CarbonTracker Europe implements a gridded state vector for improved accuracy of ecosystem emission regional estimates [
59]. Newer versions of the CarbonTracker Europe results have been used in studies of various regions and fields of research, including Amazon carbon balance (e.g., [
70]), China/Asia CO
2 balance (e.g., [
71]), global methane inversions (e.g., [
72]), and more.
The provided CarbonTracker Europe files come with 1° latitude and longitude spatial resolution and three-hourly temporal resolution. They are 3D molefraction files, which were converted from the forward run’s molefraction files with the optimized fluxes from CTE2017-FT. As previously suggested by Díaz-Isaac et al. [
73], strong vertical gradients affecting near-surface mixing ratios in the first two vertical levels of CarbonTracker were smoothed by averaging over the first three levels weighted by thickness of each vertical level. This approach conserves the mass and removes excessive accumulation or depletion caused by incorrect representation of vertical mixing in the first levels above the surface. The CTE2017-FT three-hourly simulated mixing ratios were then interpolated onto our WRF boundaries and continuously advected into the domain. The interpolation of pressure levels and mass balance conservation was achieved using the algorithm described in Butler et al. [
74], which has been adapted from a script originally developed by Rainer Schmitz (University of Chile, Santiago, Chile) and Steven Peckham (NOAA/ESRL/GSD, Boulder, CO, USA), and has adaptations specifically suited to a WRF-Chem setup using multiple tracers.
The mean CO
2 fluxes emitted from each of the respective components are shown in
Figure 3 for the innermost 1 km WRF domain, showing both the spatial and temporal means. Spatially, the means are taken across every land pixel for the land-based fluxes and across every ocean pixel for the ocean flux. Temporally, the mean is taken across all hours in the three periods of interest: Summertime 2016, Wintertime 2017, and Springtime 2017. We chose to include all three biogenic components here, namely, GPP, NEE, and Respiration, for illustrative/comparative purposes. Fire emissions were left out because they are point sources, meaning that the spatial average over the whole domain is effectively zero even during emission events.
The summertime fluxes are the most dynamic, as was expected. The magnitudes of both the GPP and Respiration are significantly higher in summer than in winter. The dryness of the Marseille cityscape explains the respiration; however, the region around Marseille is well forested (in fact, forests represent almost half of the PACA territory [
75,
76]), which accounts for the increased GPP. Unlike many regions, NEE is positive in the summertime and negative in the winter. This is a known feature of this climate (e.g., [
77]) and is primarily driven the hot and dry the summers are, which lead to increased respiration, while the winters are relatively mild and wet. Because of how unusual this feature is, we include the Springtime 2017 period for comparison. During the spring, there is significantly more GPP with a moderate amount of respiration, leading to a significantly more negative NEE than during the winter, as would be expected.
2.2.3. Coupling a Dispersion Model
Lagrangian models simulate random pathways through the turbulent flows that fluid elements carve [
78], which makes them especially adept at simulating tracer paths through atmospheric turbulent flow. When used in the context of atmospheric dispersion models, trajectories are created for a large number (often tens of thousands) of particles over the course of hours, which can trace out the atmosphere’s mean flow and turbulence as well as account for subgrid-scale transport processes. By contrast, in Eulerian simulations a point source is instantly averaged out into its corresponding grid box, resulting in loss of resolution. In Lagrangian models, each air parcel can be assigned a mass and a loss process to match the limitations of the particular investigation. Although their stochastic differential equations may lead to some numerical errors [
79], in general Lagrangian models have less numerical diffusion than their Eulerian or semi-Lagrangian counterparts [
80,
81]. When factoring in that Lagrangian models can simulate backwards in time, allowing them to act as reliable tracers to source regions, they become especially useful in investigating emission regions and making comparisons against in situ measurements [
82].
Here, we couple the Lagrangian Particle Dispersion Model (LPDM) defined in [
83] as an adjoint to the WRF forward model to create influence functions from current CO
2 measurement sites in the Aix-Marseille region. The influence functions are used to understand the footprint of the airmass before its arrival at the observation site in order to understand the fluxes that influence atmospheric CO
2 concentrations at the location. The LPDM is provided with the u, v, and w wind components, the temperature, and the Turbulent Kinetic Energy (TKE) from the WRF output files for our innermost (1 km × 1 km) domain at hourly resolution. Then, at the desired receptor spots and altitudes corresponding to the aforementioned real or potential future measurement sites (see
Table 1), 35 particles are released backwards in time every 30 s, advecting through the WRF-generated wind fields. Files are saved every 2 min; these files are then used to create hourly influence function files by integrating along all particles within the lowest 400 m, following the procedure laid out in [
84]. This height was chosen to account for the difficulties LPDM has with sudden terrain height changes, which are present within our domain. Following the procedure set out in [
50], 12 hours of influence function files are used to create a single influence function (footprint) for a receptor site of interest at a given time of interest in order to allow enough time for all particles to sufficiently traverse the domain.
In our study, influence functions were generated from the three receptor positions outlined in
Table 1: Observatoire Haute-Provence (OHP), Marseille Longchamp (CAV), and Endoume (SME). These were the sites for which measurements were available during our period of interest. Their respective positions in the 1 km domain can be seen in
Figure 1. These influence functions are used in
Section 3.4 to showcase the differences in potential source regions during the different seasons as well as during particular distinct wind condition events, as demonstrated with a case study of 24 July 2016.