Bertrand Bessagnet
email: bertrand.bessagnet@futuris-environment.com

Florian Couvidat

Vincent Lemaire

A statistical physics approach to perform fast highly-resolved air quality simulations -A new step towards the meta-modelling of chemistry transport models

Keywords: Air quality modelling, linear regression, statistics, metamodel, resolution, increment

A statistical physics approach to perform fast highly-resolved air quality simulations. A new step towards the meta-modelling of chemistry transport models

Bertrand Bessagnet, Florian Couvidat, Vincent

Introduction

Air pollution is the fourth leading fatal risk for human health globally, and in the latest estimates, more than 5 million pre-mature deaths are linked with air pollution (Forouzanfar et al., 2016).

Air pollution does not just cause danger to human health but also to the environment, the economy and food security (e.g. crop yield losses). Chemistry transport models (CTMs) are useful tools to assess, predict and analyse environmental policies to improve air quality. Since a large fraction of the population live in urban areas, models must run up to the urban scale.

The model outputs can feed integrated models to assess emission reduction strategies up to the local scale [START_REF] Amann | Managing future air quality in megacities: a case study for Delhi[END_REF][START_REF] Anil | Managing future air quality in megacities: Co-benefit assessment for Delhi[END_REF].

In atmospheric sciences the race on high resolution simulations over large domains started few years ago for short term forecast or climate studies perspectives [START_REF] Skamarock | Atmospheric Kinetic Energy Spectra from Global High-Resolution Nonhydrostatic Simulations[END_REF][START_REF] Fuhrer | Near-global climate simulation at 1 km 25/26[END_REF]. In a near future, meteorological 3D-fields will be commonly available over large domains at a few kilometers resolution. For air quality modelling, increasing the resolution is expected to provide better results. Even for remote background sites, increasing the resolution should improve the quality of simulations because the system is not fully linear mainly due to the use of non-linear chemistry schemes. The use of air quality models at high resolution is very computing time consuming mainly because of Courant-Friedrichs-Lewy (CFL) conditions. The CFL condition is a necessary condition for convergence while solving certain partial differential equations numerically by the method of finite differences. This condition imposes to adapt the time step. For the advection, it is proportional to the grid size for the horizontal transport involving a dramatic increase of simulation durations. Although a 20 km to 50 km resolution is sufficient to be representative of rural background concentrations, the use of resolution between 1 and 10 km is essential to estimate urban background concentrations of pollutants for small to large cities.

The notion of urban increment (or decrement for ozone due to the titration effect) has been introduced to estimate the impact of a city emissions to the urban background concentrations (Aman et al., 2007, Ortiz and[START_REF] Ortiz | A modelling approach for estimating background pollutant concentrations in urban areas[END_REF]. The calculation of this increment is expected to be influenced by local primary emission sources and meteorological parameters. The use of highly resolved bottom-up emission inventory usually provides better results [START_REF] Timmermans | Quantification of the urban air pollution increment and its dependency on the use of down-scaled and bottom-up city emission inventories[END_REF] compared to top-town downscaled emission datasets. Air quality models benefit from a downscaling of emissions dataset as mentioned by [START_REF] Schaap | Performance of European chemistry transport models as function of horizontal resolution[END_REF], [START_REF] Terrenoire | High resolution air quality simulation over Europe with the chemistry transport model CHIMERE[END_REF] and [START_REF] Colette | Frontiers in air quality modelling[END_REF] by mainly reducing the bias over urbanized areas with sometimes lower correlations. However, for ozone an optimal resolution could be found as explained by [START_REF] Valari | Does an increase in air quality models resolution bring surface ozone concentrations closer to reality?[END_REF] based on an analysis of the root mean square error. In a scenario perspective the concept of urban and even street increment was used in [START_REF] Kiesewetter | Modelling NO2 concentrations at the street level in the GAINS integrated assessment model: projections under current legislation[END_REF][START_REF] Kiesewetter | Modelling street level PM10 concentrations across Europe: source apportionment and possible futures[END_REF] to estimate the impact of emission reductions strategies at a given site, up to traffic-influenced stations.

In previous studies, the use of past observational air quality data crossed with predicted meteorological variables, traffic emission prediction was implemented in neural networks to propose statistical models able to perform air quality model predictions (Catalano and Galtioto, 2017 and references therein). Usually, these models can only be used at a given site, but they offer robust performances. Recently, [START_REF] Mallet | Meta-modeling of ADMS-Urban by dimension reduction and emulation[END_REF] proposed a first metamodel of a local air quality model to simulate NO2 and PM10 concentrations.

In our study, the concept of "urban increment" is extended to "grid cell increment" to perform highly-resolved air quality simulations rested on model-based "machine learning" using low resolution CTM simulations. This method avoids running the CTM at high resolution and therefore allows an impressive gain of computing time. This technique is applied for the main criteria pollutants PM10, PM25, NO2, and O3 concentrations. The method is evaluated for daily or maximum concentrations (for ozone only). This paper will answer four main questions: Does this technique provide satisfactory results by-passing the costly high resolution air quality simulation? What is the expected gain on computing time? For which type of application this technique can be used? How this technique could be improved?

Material and Methods

Model set-up

In this study, the CHIMERE model [START_REF] Menut | CHIMERE 2013: a model for regional atmospheric composition modelling[END_REF][START_REF] Bessagnet | An Evaluation of the CHIMERE Chemistry Transport Model to Simulate Dust Outbreaks across the Northern Hemisphere in March 2014[END_REF] as improved in [START_REF] Couvidat | Development of an inorganic and organic aerosol model (CHIMERE 2017β v1.0): seasonal and spatial evaluation over Europe[END_REF] is used over two domains: (i) a domain (EU) encompassing Europe at 0.5° x 0.25° regular resolution (LRE) over the 17°E -40°W and 32°N -70N window, and (ii) a nested domain (FR) centered over France at 0.09375° x 0.046875° regular resolution (HRE) over 5°E -10°W and 41°N -51.014625°N fed by the EU simulation (one-way nesting). The model configuration is summarized hereafter, but the reader can refer to the recent CHIMERE publications [START_REF] Couvidat | Development of an inorganic and organic aerosol model (CHIMERE 2017β v1.0): seasonal and spatial evaluation over Europe[END_REF][START_REF] Bessagnet | An Evaluation of the CHIMERE Chemistry Transport Model to Simulate Dust Outbreaks across the Northern Hemisphere in March 2014[END_REF][START_REF] Bessagnet | An Evaluation of the CHIMERE Chemistry Transport Model to Simulate Dust Outbreaks across the Northern Hemisphere in March 2014[END_REF] for details on the corresponding model components and references as well as non-user-specific model characteristics. The particle size ranges from 10nm to 10µm over 9 bins according to these ranges from bin n°1 to bin n°9 which are respectively [10.00 nm -22.01 nm], [2.20 nm -48.43 5/26 nm], [48.43 nm -106.7 nm], [106.7 nm -234.7nm], [234.7 nm -516.2 nm], [516.2 nm -1.14µm], [1.14 µm -2.50 µm], [2.5 mm -5.0 µm], [5.0 µm -10.0 µm]. In this study, the major PM species are considered: secondary inorganic aerosol (nitrate, sulfate and ammonium), secondary organic aerosols (anthropogenic and biogenic in origins), natural mineral dust, sea salt and Primary Particle Matter.

Horizontal transport is solved with the second-order Van Leer scheme (van Leer, 1979).

Subgrid scale convective fluxes are considered. Once the depth of the boundary layer is computed, vertical turbulent mixing can be applied following the k-diffusion framework after the parameterisation (without counter-gradient term) of [START_REF] Troen | A simple model of the atmospheric boundary layer: Sensitivity to surface evaporation[END_REF] detailed in [START_REF] Menut | CHIMERE 2013: a model for regional atmospheric composition modelling[END_REF]. A minimal vertical eddy diffusion k is assumed with values of 0.01 m 2 s -1 in the dry boundary layer and 1 m 2 s -1 in the cloudy boundary layer. k is capped to a maximal value of 500 m 2 s -1 to avoid unrealistic mixing. Above the boundary layer, a fixed value of 0.1 m 2 s -1 is used. The present setup also benefits from an improved representation of turbulent mixing in urban areas that yields lower horizontal wind and vertical mixing in order to better capture the difference between the urban canopy (where the first CHIMERE model level lies) and the top of the urban sublayer of which the lowermost meteorological model level is representative [START_REF] Terrenoire | High resolution air quality simulation over Europe with the chemistry transport model CHIMERE[END_REF]. As an offline chemistry transport model, CHIMERE requires prescribed meteorological fields which were provided here by ECMWF with the Integrated Forecasting System (IFS) model at 0.125° resolution with data assimilation. Although the study is performed in a forecasting perspective, meteorological data are issued from reanalyzes.

Emissions of the main pollutants are issued from EMEP (Cooperative programme for monitoring and evaluation of long range transmission of air pollutants in Europe) programme available at http://www.emep.int. Over France the spatialization of emissions is performed with a 1 km proxy based on the national bottom-up emission inventory (accessible at http://emissions-air.developpement-durable.gouv.fr/ ) that feeds the emission pre-processor of CHIMERE described in [START_REF] Bessagnet | An Evaluation of the CHIMERE Chemistry Transport Model to Simulate Dust Outbreaks across the Northern Hemisphere in March 2014[END_REF].

Air quality simulations

A complete CHIMERE simulation for the EU and FR domains is performed from 1 st July 2010 to 30 June 2011 (1 year) with a 10-day spin-up period in June 2010 for the initialization. As explained in [START_REF] Bessagnet | An Evaluation of the CHIMERE Chemistry Transport Model to Simulate Dust Outbreaks across the Northern Hemisphere in March 2014[END_REF], the CHIMERE simulation is divided in two main steps:

-Step (1): A pre-processing to prepare intermediary files from raw data for meteorology, emissions, boundary conditions. This step consists in performing horizontal, vertical and time interpolations and calculation of diagnostic variables (e.g. the vertical mixing coefficient). So far, this step is computed in a sequential way using only one processor.

-Step (2): The core CHIMERE simulation, which uses the previous intermediary files, provides the main model outputs on an hourly frequency. This computing step is parallelized, but this step is the costliest and it can roughly represent 80 to 90% of the total computing time depending on the number of processors and the size and grid resolution of the domain.

The increment methodology described hereafter is a two steps method with (i) a training part for a given version of the CHIMERE model on a given period (here 6 months in 2010) and (ii) an application part on another period of interest (here 6 months in 2011). All the programs are written in shell language using the NCO package [START_REF] Zender | Analysis of self-describing gridded geoscience data with netCDF Operators (NCO)[END_REF] to efficiently handle output NETCDF files. The method is depicted in Figure 1 and fully explained in the next subsections. In this study, the two distinct periods are defined:

-The "training period" from 1 st July 2010 to 31 December 2010 where the "increment methodology" called FR_INC (applied over the FR domain) is trained to cover a large range of meteorological conditions: summer, winter and intermediate seasons. This "learning" process uses the CHIMERE simulation outputs and intermediary variables over the EU and FR domains (EU_LRE and FR_HRE simulations).

-An "evaluation period" from 1 st January 2011 to 30 June 2011, where the "increment technique" is evaluated against observations and compared with the high resolution CHIMERE simulation (FR_HRE). This period covers the full spring period with usual high PM concentrations in the western part of Europe. 7/26

Principle of the increment methodology

Based on atmospheric diffusion theory, potential determinants of urban increments and functional forms of their relationships have been hypothesized. Under neutral atmospheric conditions, the vertical diffusion of a non-reactive pollutant from a continuous point source can be described in general form through the following relationship (Amann et al., 2007, Seinfeld and[START_REF] Seinfeld | Atmospheric Chemistry and Physics -From Air Pollution to Climate Change[END_REF]:

= 2
Eq. 1 with (m 2 ) indicating the variance of the vertical diffusion after a distance x from the source, k (m 2 s -1 ) as the eddy diffusivity and u (m s -1 ) the wind speed. Considering this assumption, in [START_REF] Amann | Cost-effective control of air quality and greenhouse gases in Europe: modeling and policy applications[END_REF] the delta between urban and background concentrations ΔC of primary PM is given as:

∆ = √ √8 Eq. 2 d is the characteristic length of the city, Q (µg m 2 s -1
) is the low level emissions of the city. This increment must be corrected to avoid emission double counting as explained in Amann et al.

(2011). Based on Amann et al. ( 2011) and [START_REF] Amann | Estimating Concentrations of Fine Particulate Matter in Urban Background air of European Cities[END_REF], we consider in this study that a given fine cell can behave as a "city". Then, the concentration delta (∆ ) between a fine grid and a coarse grid simulation of a species concentration influenced by low level sources of primary pollutants can be extended with a revised predictor variable as:

∆ = -= 1 √ √ -√ + d ∝ D ∝ √ ! "
Eq. 3

c and C (µg m -3 ) are respectively the concentrations at the fine grid point and interpolated from the coarse grid to the fine mesh, k is the vertical mixing coefficient (m 2 s -1 ) at the fine grid, u is the 10m horizontal wind speed (m s -1 ) at the fine grid, δX, δY, δx, δy are respectively the coarse longitude, latitude and the fine longitude, latitude increments of the grids (°). In our study they are constant, but they can vary and for each fine grid cell an average value of the surrounding coarse grids can be used.

d and D are characteristic lengths respectively for the fine and coarse meshes, they correspond here to an average of the grid cells size e and E (µg m -2 s -1 ) are respectively the low-level emission fluxes at the fine grid point and interpolated from the coarse grid. For the PM2.5 and PM10 concentrations, the sum of primary emissions is considered, for NO and NO2 the NOx emissions are considered. In our methodology, the emissions of the two first level (sum of emissions approximatively below 30 m) of CHIMERE are taken into account.

α and β are coefficients integrating geographical, physical and chemical processes that are lost in the simplification process, they also account for unit changes. Note that β here has not the same meaning than in [START_REF] Amann | Estimating Concentrations of Fine Particulate Matter in Urban Background air of European Cities[END_REF][START_REF] Amann | Cost-effective control of air quality and greenhouse gases in Europe: modeling and policy applications[END_REF], it is here residual value of the regression and would be expected to be close to 0.

Differently to [START_REF] Amann | Estimating Concentrations of Fine Particulate Matter in Urban Background air of European Cities[END_REF] the vertical eddy diffusion k is not integrated in the α coefficient but included in the predictor

# √$%
√ -√ , because this variable is calculated and stored during the CHIMERE preprocessing. Moreover, in our methodology E includes all low level emission sources in the coarse grid and can be eventually higher than e if the grid cell is in a remote areas surrounded by high emissions area. This change is to break the implicit assumption assumed in [START_REF] Amann | Estimating Concentrations of Fine Particulate Matter in Urban Background air of European Cities[END_REF][START_REF] Amann | Cost-effective control of air quality and greenhouse gases in Europe: modeling and policy applications[END_REF] that background concentrations could be only influenced by the city emissions (here the high resolution grid cell). It is then noteworthy that in the case of a fine grid cell with low emissions compared to higher background concentrations the predictor could turn negative which makes intuitively sense while in Amann et al. (2007,2011) the delta is always positive at it refers to a city implicitly influenced by lower background concentrations.

The principle of our methodology is to calculate on a daily basis these two coefficients α and β for each fine grid cell on the "training" period where all the other variables are known. The previous formula (Eq. 3) is used for primary PM, NO and NO2 concentrations, the main assumption is to neglect chemistry processes that are partially included in α and β and also included in the low resolution CHIMERE outputs.

Application of the methodology

Treatment of PM2.5, PM10, NO2 and NO

This "increment methodology" is then applied for PM2.5, PM10, NO2 and NO hourly ground concentrations over the "evaluation period" from 1 st January to the 30 June 2011 with the α and β coefficients computed over the "training period" (Figure 1

Special treatment for Ozone

For a secondary pollutant like ozone involved in a non linear chemistry scheme, the previous formulas (Eq. 3 and Eq. 4) based on delta of concentrations are not suited. During et al. (2011) proposed a simplified stationary model to estimate ozone and NO2 concentrations influenced by low level sources like traffic emissions. The main two equations of the ozone chemistry involving NOx and Ozone are:

/0 + 0 1 $ 2 3445 /0 + 0 /0 6 345 /0 + 0 1 with J (s -1
) the photolytic frequency of NO2, kr (ppb -1 s -1 ) the kinetic rate. The differential equations describing the reactions of NO2, NO, and O3 with a diffusion term due to transport and mixing gives:

[0 1 ] 9 = -: [/0] • [0 1 ] + < • [/0 ] + [0 1 ] = -[0 1 ] > Eq. 5
The first two terms on the right side describe the chemical transformation by thermal and photochemical reactions. The last term describes the mixing as a function of concentration differences between a background concentration (index B) and the point at which the concentration should be calculated (here on the fine mesh). In a stationary regime assumption with [0 1 ] 9 ⁄ = 0 the equation gives for ozone concentration the approximation ̃ :

̃[B C ] = D> [EB F ] + [B C ] G 1 + > : [EB]
> = H 8 D = 1.47 × 10 LM NOP -4.84 × 10 LQ NOP : = 3.9 × 10 LT UUV L# N L# Eq. 6

[B C ] G is the interpolated concentration over the fine grid of the low resolution concentrations (EU_LRE), [EB F ] and [EB] are the concentrations over the fine mesh (FR). > is defined in [START_REF] Amann | Estimating Concentrations of Fine Particulate Matter in Urban Background air of European Cities[END_REF] as a simplification of diffusion for a box model as previously discussed, is an average characteristic length of the grid cell. We considered here j as a polynomial function of the short wave radiation swrd (W m -2 ) as reported in [START_REF] Trebs | Relationship between the NO2 photolysis frequency and the solar global irradiance[END_REF] for low altitude sites considering an albedo equal to zero. Here we assumed the kinetic rate kr to be constant. A statistical method similarly to primary pollutants is implemented, two coefficients α and β are computed over the training period:

[W C ] = × ̃[B C ] + Eq. 7
Over the training period [W C ] is known and ̃[B C ] can be calculated each hour then α and β are calculated using a simple linear regression for each grid points on a daily basis. This technique suppresses systematic biases and accounts for missing processes due to the simplifications.

Afterwards, over the evaluation period α and β are applied over hourly concentrations for each grid cell (i,j), then the final ozone concentration c* is simply computed as:

[B C ] X,Y * = &,( × ̃[B C ] X,Y + &,(
Eq. 8

Regression coefficients

To avoid any overshoots when applying the methodology on hourly values, concentrations and delta of concentrations are capped according values reported in Table 1.

ΔC Limit inf ΔC Limit sup c* limit inf Unit

Table 1: Limits of concentrations to avoid overshoots when applying the increment technique on hourly values

In the supplementary material Figure S1, the α (slope), β (intercept) coefficients and the Pearson correlation of the linear regression calculated over the "training" period are reported for all pollutants. For each grid cell the coefficients are calculated using 184 daily values (6 months). The median correlations over the FR domain are 0.31, 0.33, 0.35 and 0.98 respectively for PM2.5, PM10, NO2 and O3 with generally higher values over urban areas. The low correlations result from the averaging process over the whole domain where low absolute values in remote areas deteriorate the statistic errors. The correlation is the highest for ozone since the linear regression is based on the absolute concentrations mainly driven by the background values and not a delta of concentrations as for primary pollutants. The α coefficient is generally below 1 confirming the tendency that the high resolution simulation produces lower concentrations compared to the low resolution run.

Results and discussion

Evaluation of the increment methodology

For the European domain (EU), background PM2.5, PM10, NO2 and O3 observational data are retrieved thanks to the EMEP-EBAS database (Tørset et al., 2012). The increment methodology can be evaluated against the raw CHIMERE simulation and observations over the FR domain for the 1 st January -30 June 2011. The French GEOD'AIR database provides hourly concentrations for all stations over France (available online at https://www.geodair.fr/).

All background observations are used on a daily basis for the main pollutants: Ozone, NO2, PM2.5 and PM10. Urban, periurban and rural stations are considered, daily maximum concentrations are only considered for Ozone. In this paper, periurban and rural are lumped into the category "rural" to better isolate the "urban" signal. Only the French data are considered for the evaluation over the FR domain as we benefit from the most accurate emission data only in France since a bottom-up emission proxy is used over this country. and "plus" symbols are plotted respectively for rural and urban sites when the increment methodology provides a better Root Mean Square Error compared to the CHIMERE high resolution, bold "triangle down" and "minus" symbols are plotted respectively for rural and urban sites when the increment methodology provides a worse Root Mean Square Error compared to the CHIMERE high resolution.

13/26

Figure 3 and Figure 4 show the added value on air quality simulations when using a higher horizontal resolution. Clearly, the regional patterns computed at low resolution are important drivers of the fine resolution outputs for PM and Ozone, however a urban signal is clearly identified for the major cities and in some Alpine valleys mainly due to the effect of stagnant conditions.

Table 2 reports global error statistics of pollutant concentrations for the three models at urban and rural sites over the 1 st January -30 June 2011, (i) the increment methodology applied over the FR domain (FR_INC), (ii) the CHIMERE high resolution simulation (FR_HRE) and (iii)

the CHIMERE low resolution simulation (EU_LRE). The Pearson correlations are rather good for the raw CHIMERE simulations generally in the range 0.7 to 0.8 for most of pollutants.

However, the highest PM concentrations in winter and early spring are underestimated (Figure 5). For NO2, differences are clearly identified over the cities and along the major road lines, the root mean square error is systematically improved for this species using a higher resolution (Table 2) mainly due to a reduction of the bias. Ozone concentrations are on average lower using a higher resolution, this is a usual behavior due to the non-linearities in chemistry processes (2 nd order kinetic reactions involving ozone).

For all pollutants the increment methodology provides very similar results compared to the high resolution simulation, the patterns of mean values over the evaluation period are very close and the average timeseries for all stations in France (Figure 5) confirm this statement all along the period particularly for PM. For NO2 concentrations, the increment methodology provides higher NO2 concentrations over urban areas particularly in winter with coherent lower ozone concentrations due to the titration effect with NO2. For all pollutants, the bias is improved by the increment methodology with a slight improvement of the Root Mean Square Error while the correlation is sometimes slightly impaired or improved. These results are very satisfactory and could be surprising taking into consideration the simplicity and rough assumptions of this methodology. For PM, the method produces better root mean square errors over the Paris region. The number of data used (e.g. up to 39 520 daily values for NO2) for the evaluation and the diversity of site locations in France is large enough to consider these results statistically representative, a deficiency of the method should have appeared in the error statistics. In the supplementary material, the Quantile-Quantile plots show these good performances particularly for the highest values (Figure S2 in supplementary material). The main discrepancies of this technique occur for maximum ozone concentrations which become slightly underestimated however this behavior can be explained by the technique that is based on daily values and applied over hourly values with certainly a tendency to smooth the extreme values. However, this smoothing effect is not as large as expected and could be suppressed in the future by some improvements of the methodology. Moreover, for the extreme values, 14/26 the increment technique provides better performances with values closer to the observations at rural and urban stations compared to the FR_HRE CHIMERE simulation (Figure S3 in supplementary material). This smoothing effect certainly helps the model to avoid some overshoots due to the extreme sensitivity of this type of air quality model like CHIMERE to the parameterization of the vertical diffusion coefficient which can be set to an arbitrary minimum value inducing unrealistic stagnant conditions.

Possible improvement of the methodology

This first version of the methodology already provides very good results. Such a technique based on first order linear regressions with some selected main physics and chemistry equations is sufficient to provide results as accurate as a usual simulation embedding much more detailed processes. Some improvements will be considered in the next version by investigating the following considerations:

-The use of a 2 nd order (or higher) linear regression could be tested for the incremental formula defined in section 2.4 such as:

∆ &,( = &,( + &,( × ∆ +,, -+ Z &,( × ∆ +,, -
Eq. 9

with α, β and γ the regression coefficients for grid cell (i,j).

-For ozone, an improvement of the technique in section 2.4.2 could be performed by the use of a multi variable methodology involving at least two predictors (the terms between brackets in Eq. 10):

[B C ] X,Y * = &,( + &,( × [ D> [EB F ] 1 + > : [EB] \ + Z &,( × [ [B C ] G 1 + > : [EB] \ Eq. 10
with α, β and γ the regression coefficients for grid cell (i,j).

-The regression techniques could also be defined per quantile of concentrations to improve the results on extreme concentrations.

-More meteorological variables could be implemented in the regression formulas to improve the robustness of the methodology.

-Ozone and nitrogen oxides could be treated by a single methodology to better accounts for their chemical interactions.

The methodology deserves to be tested on finer meshes up to 1 km resolution with an adequate bottom-up emission inventory to confirm these encouraging results and evaluate the linearity of scale dependency. One must keep in mind that the technique must remain simple to make it fast, robust, and the current results are already totally satisfactory for various uses.

So far, as it is currently designed, the technique can be applied for short term forecasts, analysis of episodes, long term simulation of past years for mapping. For emission reduction analyses the method is expected to work only for primary PM because primary emissions of PM are taken into account in the methodology. For ozone and more generally secondary pollutants, it could be less straightforward since the change of chemical regime and the VOC (Volatile Organic Compound) chemistry will be not sufficiently considered in the increment technique even through the statistical corrections. However, the sensitivity to emissions and meteorological changes is partially contained in the regression coefficients through the diversity of situations encountered over the "training" period.

Conclusions

A surrogate model of the CTM CHIMERE has been designed to downscale a low horizontal resolution simulation to a finer resolution. This first version of this methodology is based on a training process over a 6-months period and applied over the subsequent 6 months with an evaluation against the performances of the raw CHIMERE simulation at high resolution.

Definitively, our methodology is able to capture the main patterns and evolution of daily concentrations for the main pollutants, and the gain in computing time is very important since the costliest step of the simulation process is by-passed. Performances based on an evaluation against observations are similar to those obtained by the raw model simulations with CHIMERE at high resolution. Performances are even sometimes better certainly due to smoothing effects that suppress some overshoots due to the sensitivity of the model to the parameterizations of the eddy diffusion. Indeed, the vertical diffusion is a very sensitive parameter in CTMs, this coefficient is so sensitive that it is caped in all models and this bounding already results from a kind of 'learning' process as it derives from the experience of the model developer during the calibration phase.

In its current state, the methodology can work for short-term air quality forecasts, case studies and air quality concentration mapping. To extend its use to emission reduction assessment, the model could be improved (particularly for Ozone) by (i) implementing new variables available in the CHIMERE pre-processing, (ii) increasing the order of the linear regression or (ii) the use of multivariable regressions. However, this type of methodology mixing statistics, physics and chemistry is promising and could be run on mono-processor devices and gain a

Figure 1 :

 1 Figure 1: Synoptic scheme of the increment technique compared to the normal CHIMERE simulation over the EU and FR domains. All variables are explained in sections 2.3 and 2.4.

  c* the concentration on the fine mesh determined by the increment technique, C the interpolated coarse grid concentration on the fine mesh, i and j referring to the coordinates indexes of a given fine mesh grid cell. ∆ . is the predictor variable and ∆ the increment value 9/26 applied to the background concentration value C as discussed in the previous section. The other variables were previously defined, e, E, k and u are computed during the first step of the CHIMERE preprocessing as depicted in Figure1.

Figure 2 :

 2 Figure 2 : Maps of mean PM10, PM2.5, NO2 and O3 concentrations over the 1 st January -30 June 2011 period for the CHIMERE low resolution simulation at the European scale (EU_LRE). Filled circles represent the rural background observation sites issued from the EBAS database. At the European scale (Figure 2), CHIMERE is able to retrieve the main patterns of air pollution with the highest concentrations of PM over the Benelux, south of Poland and the north of Italy.The agreement with observations is rather good for PM2.5 concentrations over Spain and UK with a clear underestimation over Benelux. The underestimation of PM is commonly observed

Figure 3 :

 3 Figure3: Maps of mean PM10 and PM2.5 concentrations over the 1 st January -30 June 2011 period for the increment methodology FR_INC (right column) and the CHIMERE high resolution simulation FR_HRE (left column). On the left side: circles and squares filled symbol refer to observations respectively for urban and rural sites. On the right side: bold "triangle up" and "plus" symbols are plotted respectively for rural and urban sites when the increment methodology provides a better Root Mean Square Error compared to the CHIMERE high resolution, bold "triangle down" and "minus" symbols are plotted respectively for rural and urban sites when the increment methodology provides a worse Root Mean Square Error compared to the CHIMERE high resolution.

Figure 4 :

 4 Figure4: Maps of mean NO2 and O3 concentrations over the 1 st January -30 June 2011 period for the increment methodology FR_INC (right column) and the CHIMERE high resolution simulation FR_HRE (left column). On the left side: circles and squares filled symbol refer to observations respectively for urban and rural sites. On the right side: bold "triangle up" and "plus" symbols are plotted when the increment methodology provides a better Root Mean Square Error compared to the CHIMERE high resolution, bold "triangle down" and "minus" symbols are plotted when the increment methodology provides a worse Root Mean Square Error compared to the CHIMERE high resolution.In FigureS4of the supplementary material additional information regarding a comparison of the delta of concentration between the increment methodology and the reference high

Figure 5 :

 5 Figure 5: Timeseries of daily mean PM10, PM2.5, NO2 and O3 concentrations for the increment methodology FR_INC, the CHIMERE high resolution simulation FR_HRE and the CHIMERE low resolution simulation EU_LRE mediated at all urban and rural sites over the 1 st January -30 June 2011 period.

  lot of computing time. While the core CHIMERE simulation (step 2) can last several days depending on the number of cores and resolution, only few minutes is sufficient to perform a high resolution simulation with the increment technique, therefore a minimum of 100 to 1000 less computing times is expected for this step. The training process with NCO procedures lasts about 3 hours in our case to fit the regression parameters and this could be optimized with other programming languages. This could open rooms to new fields of research and operational uses in air quality modelling that was so far limited by computing time. These findings will also encourage the CHIMERE development team to parallelize the CHIMERE preprocessing (step 1) to fully take advantage of this technique.

Table 2 :

 2 Global error statistics for pollutants concentrations (O3 max is the daily maximum) for

				Obs.*	Pred.* Bias* RMSE* Cor.	Numb.
	Species	Method	Typology
		FR_INC			15.87	-9.85	13.78 0.77
		FR_HRE	rur	25.73	15.16 -10.56	14.23 0.78	10 233
	PM10	EU_LRE FR_INC			15.64 -10.09 16.84 -11.01	13.69 0.80 15.06 0.75
		FR_HRE	urb.	27.85	15.93 -11.92	15.69 0.75	29 987
		EU_LRE			15.44 -12.41	15.76 0.78
		FR_INC			12.55	-5.13	8.99	0.83
		FR_HRE	rur.	17.69	12.51	-5.18	9.18	0.82	1 565
	PM25	EU_LRE FR_INC			13.86 16.52	-3.82 -4.08	8.19 10.30 0.76 0.83
		FR_HRE	urb.	20.60	15.64	-4.95	10.54 0.77	10 987
		EU_LRE			15.09	-5.50	9.98	0.82
		FR_INC			8.96	-0.69	5.57	0.68
		FR_HRE	rur.	9.65	7.92	-1.74	5.26	0.71	13 572
	NO2	EU_LRE FR_INC			6.21 11.70	-3.45 -1.33	6.47 7.47	0.61 0.63
		FR_HRE	urb.	13.04	10.13	-2.91	7.28	0.64	39 520
		EU_LRE			6.41	-6.62	8.86	0.64
		FR_INC			29.67	-0.24	7.30	0.81
		FR_HRE	rur.	29.92	30.39	0.47	7.24	0.80	28 193
	O3	EU_LRE FR_INC			31.56 27.95	1.65 1.02	7.54 7.59	0.79 0.77
		FR_HRE	urb.	26.93	28.64	1.70	7.61	0.78	34 977
		EU_LRE			31.11	4.18	8.07	0.81
		FR_INC			40.52	-3.75	8.82	0.86
		FR_HRE	rur.	44.27	42.89	-1.38	8.07	0.85	28 618
	O3 max	EU_LRE FR_INC			43.60 39.54	-0.67 -2.38	7.59 8.50	0.86 0.85
		FR_HRE	urb.	41.92	42.25	0.33	7.96	0.85	35 412
		EU_LRE			43.33	1.42	7.94	0.85
	* µg m -3 for PM and ppb for gases
	the increment methodology (FR_INC), the CHIMERE high resolution simulation (FR_HRE) and
	the CHIMERE low resolution simulation (EU_LRE) at urban (urb.) and rural (rur.) sites over the
	1 st January -30 June 2011 period. Obs. and Pred. are the mean values. Biases, Root Mean
	Square Error (RMSE) and space and time correlation (Cor.) are based on daily mean values.
	Bold values are identified to highlight when FR_INC performs as good as or better than the
	CHIMERE simulation FR_HRE. Refer to Appendix 1 for the definition of error statistics
	indicators.

Acknowledgements

This work is partly funded by the French Ministry in charge of Ecology (MTES). The EBAS database has largely been funded by the UN-ECE CLRTAP (EMEP), AMAP and through NILU internal resources. Specific developments have been possible due to projects like EUSAAR (EU-FP5) (EBAS web interface), EBAS-Online (Norwegian Research Council INFRA) (upgrading of database platform) and HTAP (European Commission DG-ENV) (import and export routines to build a secondary repository in support of www.htap.org).

Appendix 1

Error statistics used to evaluate model performance (M and O refer respectively with Model and Observations data, and N is the number of observations)


Emmanuel Riviere

Julien Bernard

Agnès Hulin

Jonathan Virga

Fabrice Dugay

Marie-Aline Charles

Marie Cheminat

Jérôme Cortinovis

François Ducroz

Anne Laborie

Marie- Aline Charles

Laure Malherbe

Damien Piga

Elsa Real

Pierre-Yves Robic

Cecile Zaros

Emie Seyve

Johanna Lepeule
email: johanna.lepeule@univ-grenoble-alpes.fr

Air pollution modeling and exposure assessment during pregnancy in the French Longitudinal Study of Children (ELFE)

Keywords: Cohort, air pollution, dispersion modeling, exposure assessment, pregnancy

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

A large body of literature has been published in the last 20 years about the relationship between maternal exposure to air pollutants and pregnancy outcomes, including pre-eclampsia, fetal growth, and gestational duration [START_REF] Pedersen | Ambient air pollution and low birthweight: a European cohort study (ESCAPE)[END_REF]2014;Shah et al., 2011). The contribution of maternal exposure to air pollutants to child's respiratory health [START_REF] Korten | Air pollution during pregnancy and lung development in the child[END_REF], metabolic diseases [START_REF] Lavigne | Air Pollution Exposure During Pregnancy and Fetal Markers of Metabolic function: The MIREC Study[END_REF], or neurodevelopmental disorders [START_REF] Clifford | Exposure to air pollution and cognitive functioning across the life course -A systematic literature review[END_REF][START_REF] Xu | A Review of Epidemiological Research on Adverse Neurological Effects of Exposure to Ambient Air Pollution[END_REF] is an area of growing interest. Yet, little is known about the lasting influences of in utero exposure to air pollutants on child health.

Air quality monitoring stations provide a high temporal resolution, usually hourly or daily measures, but their spatial resolution is poor due to the low density of monitors for a usually large area of study. Thus using air quality monitors for exposure assessment is subject to measurement error. The last 10 years have seen a rapid development of air quality modeling [START_REF] Conti | A review of AirQ Models and their applications for forecasting the air pollution health outcomes[END_REF]. Models with fine spatial resolution have been implemented including dispersion models or land-use regressions, the most used in epidemiological studies, sometimes combined with geostatistical techniques. Most often, these models are developed for a few cities and focus on the most urbanized areas [START_REF] Eeftens | Development of Land Use Regression models for PM(2.5), PM(2.5) absorbance, PM(10) and PM(coarse) in 20 European study areas; results of the ESCAPE project[END_REF][START_REF] Sellier | Health effects of ambient air pollution: do different methods for estimating exposure lead to different results?[END_REF]. Annual estimates are usually provided [START_REF] Eeftens | Development of Land Use Regression models for PM(2.5), PM(2.5) absorbance, PM(10) and PM(coarse) in 20 European study areas; results of the ESCAPE project[END_REF], although some models may produce sub-annual predictions [START_REF] Sellier | Health effects of ambient air pollution: do different methods for estimating exposure lead to different results?[END_REF].

As part of a study on the effects of early exposure to air pollutants on pregnancy outcomes and child's health (the PATer project "Pollution Atmosphérique sur le territoire français: modélisation et effets sanitaires") in the ELFE cohort (The French Longitudinal Study of Children) [START_REF] Vandentorren | Rationales, design and recruitment for the Elfe longitudinal study[END_REF], we aimed to develop a nation-wide exposure model to NO 2 , PM 10 and PM 2.5 , with daily estimates in 2010 and 2011 (the time period covering the pregnancies of the ELFE cohort women) and a fine spatial resolution for France. We describe the development of air quality models at the national, regional and local scale, and the development of a confidence index based on the target plot [START_REF] Thunis | Model quality objectives based on measurement uncertainty. Part I: Ozone[END_REF], which was used to identify the best model for a given address, year and pollutant. The exposure of the women participating in the ELFE cohort are described for each modeling scale and for the best model as estimated by the confidence index. A specific challenge of the project was to bring together about 25 organizations able to produce air quality data from numerical simulations on a large number of urban areas of metropolitan France, but also at regional and national scale.

Methods

Population studied

The French Longitudinal Study of Children (ELFE, https://www.elfe-france.fr/en/) is a prospective birth cohort recruited in 2011 and designed to collect data on the health and development of children, their family, socio-cultural, nutritional and environmental factors from conception to 20 years of age. Women giving birth in one of the 344 randomly selected maternity wards (out of 540) in metropolitan France during the 4 enrollment periods (April 1st -4th; June 27th-July 4th; September 27th-October 4th; November 28th-December 5 th ) were invited to participate. Multiple births of three children or more, very preterm births (before 33 weeks of gestation), mothers under age 18, mothers who did not read French, Arabic, Turkish or English, mothers unable to give informed consent, or who planned to move abroad within three years were not eligible. Finally, 18 329 children and their mothers were included. Home addresses of the women during pregnancy and of the children after birth were collected and geocoded, but for 902 women, geocoded address was not available. Therefore our analysis included 17 427 women for whom at least one geocoded address during pregnancy was available (Figure 1). All participating women gave informed consent to participate in the study. The ELFE study was approved by the relevant ethical committees (CNIL, Commission nationale de l'informatique et des libertés; CCTIRS, Comité Consultatif sur le traitement de l'Information en matière de Recherche dans le domaine de la Santé; CNIS, Conseil National de l'Information Statistique).

Study area

We studied the metropolitan area of France (excluding Corsica island), which represents about 551,695 km 2 with a population of 65,058,000.

Modeling strategy

The characterization of exposure to air pollution is based on three simulation models at the national, regional and local scale (Figure 1). The national CHIMERE chemistry-transport model [START_REF] Mailler | CHIMERE-2017: from urban to hemispheric chemistry-transport modeling[END_REF][START_REF] Menut | CHIMERE 2013: a model for regional atmospheric composition modelling[END_REF][START_REF] Valari | Using a chemistry transport model to account for the spatial variability of exposure concentrations in epidemiologic air pollution studies[END_REF] is used to estimate air pollution levels for the metropolitan France, with a resolution of 4 km x 4 km. This model has long been run and evaluated in France as the main component of the national air quality forecasting and monitoring system PREV'AIR [START_REF] Honoré | Predictability of European air quality: Assessment of 3 years of operational forecasts and analyses by the PREV'AIR system[END_REF]. It is also implemented across several regional areas with resolution of 3 km x 3 km or 4 km x 4 km, depending on the regional area. In urban areas, air pollution levels are estimated by urban-scale models which are currently implemented on most agglomerations >250,000 inhabitants (20 out of 24), but also in smaller agglomerations (23 out of 31 agglomerations with more than 100,000 inhabitants), with a very high spatial resolution from ten to two hundred meters. The quasi-Gaussian Atmospheric Dispersion Modeling System (ADMS) Urban (Cambridge Environmental Research Consultants, Cambridge, United Kingdom (Carruthers et al., 2000a)) or the SIRANE model [START_REF] Soulhac | The model SIRANE for atmospheric urban pollutant dispersion. PART III: Validation against NO 2 yearly concentration measurements in a large urban agglomeration[END_REF]2011;2012b) are widely used in France as part of or to supplement the regulatory monitoring of air quality. The use of ADMS-urban and SIRANE is supported by validation studies ( (Carruthers et al., 2000b;[START_REF] Stocker | ADMS-Urban: developments in modelling dispersion from the city scale to the local scale[END_REF], for ADMS-Urban, https://www.cerc.co.uk/environmental-software/model-validation.html, Soulhac et al., 2017 for SIRANE) and comparison studies (inter-model and inter-laboratory comparisons) organized by the national reference laboratory [START_REF] Wroblewski | Evaluation de modèles pour la simulation de la pollution à proximité des axes routiers[END_REF][START_REF] Malherbe | Evaluation of numerical models used to simulate atmospheric pollution near roadways. hal-ineris[END_REF][START_REF] Tognet | Etude comparative des modèles ADMS Urban et SIRANE sur un cas test[END_REF].

Input data

Computations

Simulation runs were performed on the national, regional and urban scales to predict concentrations of nitrogen dioxyde (NO 2 ), particulate matter (PM 10 and PM 2.5 ), ozone (O 3 ), sulfur dioxide (SO 2 ) and benzene (C 6 H 6 ) for years 2010 and 2011.

On national and regional scales, hourly simulations were performed on regular grids of 3 to 4 km resolution. In a second stage, statistical or geostatistical approaches were applied to refine the modeling results and produce the most realistic concentration fields. On the national scale, model outputs and measurements from the permanent monitoring network were thus combined by external drift kriging [START_REF] Malherbe | Travaux relatifs à la plate-forme nationale de modélisation PREV'AIR : Réalisation de cartes analysées d'ozone (2/2)[END_REF][START_REF] Benmerad | Chronic effects of air pollution on lung function after lung transplantation in the Systems prediction of Chronic Lung Allograft Dysfunction (SysCLAD) study[END_REF]. In addition for NO 2 , NOx emission data from the national emission inventory were introduced as an auxiliary variable into the kriging to better account for concentration gradients in the vicinity of emission sources. An estimation grid mesh of 1 km was used for NO 2 and PM 10 pollutants (and by homogeneity PM 2,5 )

considering the resolution of NOx emission data and the spatial density of measurements in some urban areas whereas the initial grid resolution of 4 km was kept for ozone due to its more regional nature. Kriging-based or optimal interpolation methods were also applied on the regional scale to combine model outputs and observation data. In some regions, a mesh refinement technique was implemented to improve the accuracy of the modeling results and increase the resolution of the calculation efficiently. It interpolates the result of a pollutant concentration calculation on a finer mesh based on physical and physiographic principles governing the spatial differentiation of concentrations. This method makes it possible to highlight the concentration gradients near the sources of emissions. In concrete terms, the technique is based on the interpolation of a 3D field of a coarse mesh grid on a fine mesh grid, based on topology data and emissions (at a 1 x 1 km resolution).

On the urban scale, because of the high volume of data and the high computation time that is needed for generating hourly predictions, two types of outputs were considered: the first one consisted in hourly predictions of pollutant concentrations at each of the 17,427 addresses of the ELFE cohort for the specific needs of the project; the second one consisted in annual average predictions of pollutants concentrations on a grid, allowing reuse of data for other epidemiological studies. Depending on the characteristics and configuration of the modeling tools, different simulation grids were defined: usually a regular grid for SIRANE and an irregular one, sparse in background areas and denser close to roads and emission sources for ADMS Urban. In that second case annual modeling results were interpolated on a fine regular grid using interpolation techniques (Beauchamp et al., 2014).

The final spatial resolution of the concentration maps after post-processing is 1 to 4 km for the national scale model, 1 km for regional models and 10 to 200 meters for urban-scale models for annual concentrations.

Validation and indicators of quality of the models

Validation of the models was performed by comparing the predicted concentrations to the concentrations measured by the network of permanent air quality monitors using the Delta Tool methodology [START_REF] Pernigotti | Model quality objectives based on measurement uncertainty. Part II: NO2 and PM10[END_REF][START_REF] Thunis | Model quality objectives based on measurement uncertainty. Part I: Ozone[END_REF][START_REF] Thunis | DELTA Version 5.2. Concepts / User's Guide / Diagrams[END_REF][START_REF] Thunis | Performance criteria to evaluate air quality modeling applications[END_REF]. This method has been developed by the European Joint Research Center (JRC) within FAIRMODE (http://fairmode.jrc.ec.europa.eu) to perform diagnostics of air quality and meteorological model performances. Model performance assessment includes in particular the socalled Target Plot (Figure 3). This diagram is a representation of the Modeling Quality Indicator (MQI), a statistical indicator which describes the discrepancy between modeling results and measurements, taking the measurement uncertainty into account. The MQI combines different statistical scores: CRMSE -Centered Root Mean Square Error, R -Correlation coefficient, SD -Standard Deviation, NMB -Normalised Mean Bias (Figure 3). The modeling quality objective (MQO) is the quality criterion associated to the MQI. It is considered as fulfilled if the MQI is less than or equal to unity (points inside the circle of the Target Plot, Figure 3).

In the present project, the target plots were calculated for each of the three modeling scales using daily averaged concentrations. Predicted concentrations of each model have been compared to all the measurements of permanent monitors included in the modeled area. For the national and regional models, which combine CHIMERE outputs with measurements from rural and urban background monitors (see previous section), the target plots for background stations were calculated using a leave-one-out cross validation approach so that the resulting estimates and the measurements were independent and could be compared. For traffic stations (which are not used in the kriging), the target plots were calculated by interpolating the model results at the monitoring points. Higher MQI was logically obtained at those sites since the national and regional models are not intended to finely reproduce traffic-related concentration levels. As for the urban models, the performance of the modeling could not be as precisely characterized than for the national and regional models since there is a lack of measurement stations in some urban areas, with only one or two monitors for each pollutant. It can be observed that the points representing the model performance at each station tend to be located on the left part of the diagram (i.e. CRMSE error dominated by correlation, figure 3), which could be explained by a very high dynamic of pollution levels not precisely taken into account by the emission inventory at the point of the station.

Pregnancy exposures

We estimated air pollutants exposure of pregnant women according to each of the three models (national, regional and urban scale) for short-and long-term time windows during pregnancy including: whole pregnancy, each trimester of pregnancy, each month, each week and the 30 last days of pregnancy. Therefore, for each woman and each time-window, up to three different concentrations were available from the national, regional and urban-scale models. Exposure for time windows with more than 25% of missing values was not estimated.

Confidence index

In order to help the epidemiologists to choose the most relevant exposure model, we calculated a confidence index (C) based on the Model Quality Index (MQI). The MQI provides insight into the quality of the model average performances [START_REF] Thunis | DELTA Version 5.2. Concepts / User's Guide / Diagrams[END_REF]. The MQI varies on a scale from 0 to infinite, between the origin of the Target Plot (0, 0) and the position of the measuring station for which concentrations have been calculated with the model (Figure 3). The closer the station's position is to the origin, the lower the MQI and the better the modeling are (Figure 4). For proper comparisons of the quality of the estimates from the three models, the statistics compared across models should be on the same scale. Therefore, we calculated a Confidence index (C), which converts the result of the MQI (from 0 to infinite) to a value between 0 and 10 using the following equation: C = -6 x MQI + 10 (1)

with 10 being the best C (reached when the MQI is 0) indicating a perfect modeling result. On the contrary, for a MQI of 1 the C will be 4. A C with a value of 0 (bad confidence) will be reached for a MQI of about 1.67.

For the urban scale models, model performance was assumed to be homogeneous according to the type of location (i.e. background or traffic). The MQI was calculated for each measurement station and was then averaged separately for background and traffic stations, leading to two types of confidence index (C) depending on distance to traffic. A woman located close to traffic (i.e. in a 200 m buffer around motorway type roads, or in a 150 m buffer around a main link road, or in a 100 m buffer around a regional link road) was assigned the average confidence index calculated for near traffic monitors, whereas in other locations she was assigned the average confidence index calculated for background monitors. For the national and regional scale models, model performance was assumed to be more variable across the modeling domain. The MQI was calculated for each monitor as described in section 2.3.3. The MQI and the corresponding confidence index at each background (resp. near-traffic) address of the ELFE cohort women were then calculated by interpolating the MQI of all the available background (resp. traffic) measurement monitors using the inverse-distance weighting method between the address of the woman and the location of the monitors.

Since the spatial coverage of monitors is limited (497 monitors for NO 2 (297 background, 200 traffic), 390 for PM 10 (223 background, 167 traffic) and 106 for PM 2.5 (64 background, 42 traffic)), the Target Plot, MQI and C calculated do not account for the high spatial variability of air pollutants concentrations (especially for NO 2 ) and therefore for the potential variability of model performances. This high spatial variability in concentrations captured by urban-scale models (Figure 5) is a major asset of these models when one is interested in the local variations of exposure. This is illustrated in Supplemental Figure S1, which shows that smoothing concentrations on a kilometer grid obviously leads to a decrease in the accuracy of the concentrations near the main roads, better represented on a metric grid. Indeed, in the urban modeling tools, road emissions are precisely entered into the model while they are diluted on meshes of several square kilometers in the national and regional models. In our study, among the 17,427 addresses, 33% were located close to traffic. The urban models allow to account for the variability of concentrations near traffic. They are implemented with final spatial resolutions ranging from 10 (near sources) to 200 meters and are more adapted to the complexity of air pollutants sources in the cities than the regional or national models. Therefore, if an urban model exists, this one will be favored compared to the other scales, irrespectively of the confidence index, to provide the value of exposure of the ELFE women during pregnancy.

Statistical analyses

Coverage of the study area was heterogeneous for O 3 , SO 2 and C 6 H 6 . We therefore focused our analyses on NO 2 , PM 2.5 and PM 10 . We described pregnant women's exposures and their confidence index using each of the three models (national, regional and urban-scale) for the following time windows: pregnancy, each trimester of pregnancy, fifth month of pregnancy, third week before birth and day before birth. Then, for the sub-sample of women covered by the 3 models, we compared their exposures and confidence indexes as estimated by the 3 models and the final exposures as estimated by the most suitable model (i.e. the urban model if there is one, the model which has the highest confidence index among the regional and national model). For simplicity, this final exposure is hereinafter called the PATer (from the name of the project) estimate. Spearman correlation coefficients between the 3 models and the PATer estimates were calculated.

Results

Pregnancy exposures as estimated by each of the 3 models

NO 2 exposures during pregnancy as estimated by the national, regional and urban models are represented in figure 6. Depending on the exposure model used, women in the ELFE cohort were exposed on average during pregnancy between 20 and 26 µg/m 3 for NO 2 , 16 and 17 for µg/m 3 for PM 2.5 and 24 and 25 µg/m 3 for PM 10 (Table 1). These average values were quite similar for exposure during the other time windows studied. where a national, regional or urban model existed. .0 T1 15744 18.9 5.6 10.9 14.6 18.1 22.4 29.2 12869 17.4 6.3 7.8 13.0 16.7 21.1 28.9 8298 18.0 5.9 9.5 13.9 17.6 21.7 28.3 T2 16173 16.5 6.5 8.9 11.4 14.5 20.8 29.2 13183 15.0 7.0 5.9 9.3 14.1 19.0 28.0 8526 15.7 6.8 7.2 10.2 14.1 20.4 27.9 T3 16805 16.1 5.8 9.5 12.0 14.5 19.2 28.0 13687 14.8 6.4 6.7 9.7 13.9 18.5 26.8 9017 15.3 6.2 7.3 10.6 14.2 18.9 27.

Confidence index of estimated exposures and comparison across the 3 models

The confidence indexes were calculated for each address of the cohort, each pollutant and each year. The figure 7 presents the results of these calculations for NO 2 in 2010 in the Strasbourg metropolitan area. We compared the confidence indexes for women covered by the 3 models (Table 2). With the exception of PM 2.5 and NO 2 estimated by the regional models, the averaged confidence indexes were about 7.5 depending on the pollutant, year and exposure model considered (Table 2). For NO 2 and PM 2.5 , the lowest C was observed for the regional modeling (0 for both pollutants) and the highest C was observed for the national modeling for NO 2 (9.3) and for the urban modeling for PM 2.5 (9.3). For PM 10 , the urban modeling showed the lowest (1.5) and highest C (10).

Estimated confidence indexes were quite stable between 2010 and 2011. For NO 2 confidence indexes, 10% of women had differences greater than 1 across the 3 models. For both PM 2.5 and PM 10 confidence indexes, 10% of women had differences greater than 1 for the national modeling compared to the regional modeling. As for the urban modeling, 30% of women for PM 2.5 (20% for PM 10 ) had differences in confidence indexes greater than 1 compared to the regional modeling. The PATer final exposure of the women was mostly estimated from the urban model for NO 2 and PM 10 and from the national model for PM 2.5 (Figure 8). PM 2.5 estimates from the regional model showed in average the lowest confidence indexes (Table 2) and the regional model was almost never chosen to represent the PATer final PM 2.5 exposure estimate (Figure 8).

Comparison of pregnancy exposure estimates across the 3 models and with the final

PATer estimates

Depending on the exposure window, between 6,406 and 7,515 women were covered by the three exposure models and the final PATer estimates (Supplemental Table S1). Except PM 2.5 correlation during the whole pregnancy between the national and regional models, the three models were highly correlated (correlation coefficients from 0.71 to 0.96, Supplemental Table S2) for all pollutants and exposure windows. For the three pollutants, the exposure distributions of the urban model and the PATer estimates were very similar as shown by statistics in Supplemental Table S1 and by the very high correlation coefficients between exposures estimates from these 2 models (i.e. between 0.95 and 0.99, Supplemental Table S2); this result was expected because these statistics and correlation coefficients were calculated for women covered by the 3 models, which restricts the sample mainly to women living in urban areas, and the final PATer estimates gives priority to the urban model, which is therefore highly represented in this sub-sample.

NO 2 exposures (µg/m 3 ) as estimated by the national and regional models were very close (p 5 th , 50 th , 95 th during pregnancy 13, 26, 40 and 13, 27, 40, respectively), while the urban and PATer estimates showed a higher variability (larger standard deviation) and a wider distribution (p 5 th , 50 th , 95 th during pregnancy 11, 25, 50 for both models) compared to the national and regional models (Figure 5 and Supplemental Table S1).

As for PM 2.5 (µg/m 3 ), generally for the different time windows, the averages and standard deviations of exposures were slightly higher and the distributions were shifted to the right for the national model as compared to the regional, urban and PATer estimates. These results indicate that exposures from the national model were slightly higher (p 5 th , 50 th , 95 th for pregnancy 14, 18, 23) than those from the regional, urban and PATer estimates (p 5 th , 50 th , 95 th for pregnancy 10,17, 22 for the regional and 12, 17, 22 for the urban and PATer estimates).

For PM 10 (µg/m 3 ), the exposure distribution of the women as estimated from the national and regional models were very close (p 5 th , 50 th , 95 th for pregnancy 21, 26, 31, and 22, 26, 31 respectively). As compared to the national and regional models, the urban model and PATer estimates showed slightly higher standard deviations and medians as well as slightly wider distributions for the different time windows investigated (p 5 th , 50 th , 95 th for pregnancy 20, 26, 35 for both models).

Altogether, the urban and PATer estimates were finer and better captured the spatial variability compared to the national and regional models, especially for NO 2 and PM 10 . As expected, for the 3 pollutants and the 4 models, larger distribution of exposure was observed for shorter exposure Exposures of the women as estimated by the urban model when there is one available or by the 398 model with the highest confidence index from the regional and national models are described in 399 table 3. In average during pregnancy, women were exposed to 21 µg/m 3 for NO 2 , 16 µg/m 3 for 400 PM 2.5 and 24 µg/m 3 for PM 10 . As shown in table 3, 90% of the estimated exposures had a 401 confidence index comprised between 5.2 and 8.7 for NO 2 , 6.8 and 9.0 for PM 2.5 , and 6.

Discussion

To our knowledge, this is the first study combining three modeling tools available at different scales to estimate NO 2 , PM 10 and PM 2.5 concentrations at a fine spatial (down to 10 meters) and temporal (hourly) resolution over a large geographical area (the French metropolitan area). We further estimated a confidence index based on the target plot and Model Quality Indicator in order to provide guidance in the choice of the exposure model, when several models are available. Our results showed that the three models provided relatively similar exposure estimates for the women of the ELFE cohort, allowing a combination of the three models. The urban-scale model provides a finer spatial resolution compared to the national and regional models, which is relevant in urban and peri-urban areas that are more densely populated and where local emissions mainly originate from traffic and heating processes. We therefore chose to favor the urban-scale model first, and to then use the confidence index to choose between the regional-and nationalscale models for women who were not covered by the urban-scale model. We finally used the predicted concentrations of these models to evaluate the exposure during multiple time-windows of 17,427 pregnant women participating to the ELFE cohort.

Two main modeling tools were used for the urban-scale model: ADMS Urban (Carruthers et al., 2000a) and SIRANE [START_REF] Soulhac | The model SIRANE for atmospheric urban pollutant dispersion. PART III: Validation against NO 2 yearly concentration measurements in a large urban agglomeration[END_REF]2011;2012a). ADMS Urban accounts for linear sources such as traffic, but also for many stationary sources like industrial or residential sources.

It also includes an intelligent gridding option, which provides high spatial resolution in the vicinity of air pollution sources such as roads. SIRANE cannot include as many stationary sources as ADMS-urban and its spatial resolution is identical throughout the simulated geographical area. However, SIRANE works on a very high spatial resolution throughout the Rhône-Alpes region, which therefore benefits from a very fine assessment of concentrations, including in the interurban environment. At the regional scale, a special feature of the modeling is the harmonized procedure used by all regional platforms. This common approach included accounting for sharp specificities within regions by using regional emission inventories (i.e. integration of spatialized and temporalized local data) that are more precise compared to the national emission inventories; the use of models in their configuration used in routine daily forecasting (CHIMERE, SIRANE, WRF or MM5) at 4

x 4 km or 3 x 3 km resolution and then refined at 1 x 1 km resolution; the application of a daily or hourly kriging of the measurements over the whole 2010 and 2011 (rather than a yearly kriging). These improvements led to better representation of local processes that influence ambient pollutants concentrations. Comparing the confidence indexes between the national model and the regional models requires some considerations: the national model integrates unified input data as weather or emissions and operates a single configuration of model throughout the national territory. Similarly, geostatic post-treatments are applied according to the same methodology overall of this same territory. The regional model consists in an agglomeration of results from several regional platforms. Each of these platforms delivers representative and coherent results within its regional coverage, by managing its own modeling based on its knowledge and experience on the models used, emissions and meteorological datasets used for modeling, regional modeling calibration, local specificities, etc. The heterogeneity of the platforms used to fuel the regional scale modeling can explain, at least partly, the overall poor performances and lower confidence indexes of the regional model compared to the national (and urban) model, with some regional models performing better than others.

The three models, national, regional and urban showed consistent distributions of exposure estimates. The national and regional models were very close in terms of exposure estimates. The urban models have a higher spatial resolution and showed a higher variability with a wider range of exposure estimates, which is consistent with the stronger exposure contrasts observed in urban and peri-urban areas compared to more rural areas. Further, the implementation of dedicated validation methods such as the Delta tool, the target plot, the model quality indicator and the confidence index substantiates the use of several exposure models. We showed that for the ELFE cohort, the exposure estimates from the three models were close enough to be combined in order to estimate air pollution exposure in this nation-wide population. The distributions of exposure to the different air pollutants were very close across the three models and highly correlated. The variability of the exposures was increased for predictions of the urban models compared to those of the national and regional models; however, this is relevant as it reflects a real situation where exposures are more contrasted in urban and peri-urban areas that are more densely populated and where emissions due to traffic and heating are higher than in other areas. Since the ELFE cohort is a representative sample of the French pregnant women, there is a priori no reason for the combination of the three models to not be relevant for any other study. However, this would need some validation by comparing the distribution of exposure estimate from the three models. In ELFE, with the exception of NO 2 , pregnancy exposure estimates were higher than air quality values recommended by the WHO, respectively 40, 10 and 20 µg/m 3 in annual average for NO 2 , PM 2.5 and PM 10 . In France, the limit values (according to the environmental code Article R221-1

Modified by the decree n°2010-1250 of October 21st, 2010-art.1) are 40, 25 and 40 µg/m 3 respectively for NO 2 , PM 2.5 and PM 10 (PM 2.5 only from 2015) in annual averages.

A previous national model for France developed for the GAZEL cohort, used the European Monitoring and Evaluation Program (EMEP) emissions at a 50 x 50 km resolution and focused on a 10 x 10 km CHIMERE grid with further improvements from specific recalculated data for traffic and main industrial sources. After simulation, the exposure data were then refined to a 2 x 2 km resolution [START_REF] Bentayeb | Association between long-term exposure to air pollution and mortality in France: A 25-year follow-up study[END_REF]. The "Pater model" represents a major improvement compared to this previous approach. However, we acknowledge some limits of our approach.

One relates to the heterogeneity in the quality of predicted concentrations of the regional platforms (see above), which decreases the overall performances of the regional scale model.

There was a restricted number (106) of PM 2.5 monitors, which limited our ability to evaluate the performances of the three models using the target plot and corresponding MQI and C. The "Pater model" focus on years 2010 and 2011 in order to fit with the pregnancies of the women included in the ELFE cohort; this work needs to be expanded in order to estimate exposure of the ELFE children or to be used in other epidemiological studies that would have been conducted after 2011. The air pollutants exposure estimated for the women do not take into account the time spent by pregnant women inside the buildings (housing, workplace) or during commuting. A previous study performed in Grenoble, France, compared the exposure levels calculated from a dispersion model with those accounting for indoor and commuting sources [START_REF] Ouidir | Estimation of exposure to atmospheric pollutants during pregnancy integrating space-time activity and indoor air levels: Does it make a difference?[END_REF].

For NO 2 and PM 2.5 , exposure assessed from a personal air sampler was poorly correlated with exposure estimated from a model based on outdoor concentrations, suggesting that outdoor levels do not reflect personal exposure. However, this result was based on a very small population (n=9) and did not investigate the impact of measurement error on the association with the health outcome.

Conclusion

This work is an important step towards the harmonization and combination of the different air quality modeling tools used at different scales in France in order to promote a consistent approach throughout the national territory. In the ELFE cohort, prenatal exposures to air pollutants will be used to investigate their potential effects on the pregnant woman health, on the fetal health, and on the child's neurodevelopment and respiratory health. In a broader perspective, data from the PATer database can be used for other epidemiological studies as well as for health impact studies. The next step of this project is to maintain and update the database for year 2012 and following years in order to estimate postnatal exposures to air pollutants for children of the ELFE cohort and to allow more epidemiological studies conducted in 2010 and after to use these exposure data.

Figure 1 :

 1 Figure 1: Home addresses of ELFE pregnant women at delivery and models covering the metropolitan France at different scales

Figure 2 :

 2 Figure 2: Diagram of the modeling strategy

Figure 3 :

 3 Figure 3: Example of target plots for urban models for different cities, years, and pollutants

Figure 4 :

 4 Figure 4: Comparison between measurements from a station and predictions from a model for a high and low Model Quality Index (MQI).

P

  : Pregnancy, T1: trimester 1, T2: trimester 2, T3: trimester 3, M5: month 5, WBB3: 3 rd week before birth , DBB: day before birth, N: National model, R: Regional model, U: Urban model, P:PATer estimate (i.e. the most suitable model: the urban model if there is one, the model which has the highest confidence index among the regional and national model).

Figure 5 :

 5 Figure 5: Distribution of exposures during pregnancy as estimated by each of the 3 models and by the final PATer most suitable estimate, for all women covered by the 3 models

Figure 6 :

 6 Figure 6: Annual averaged NO 2 concentrations in 2010 for the addresses of the ELFE population

Figure 7 :

 7 Figure 7: NO 2 estimated confidence indexes for women of the ELFE cohort living in the Strasbourg agglomeration area in 2010

Figure 8 :

 8 Figure 8: Sources of the PATer final exposure estimate by pollutant and year.

  exposures as estimated by the final PATer most suitable estimate 397

  Three types of input data were used. National and local emission inventories came from the

	European	Monitoring	and	Evaluation	Program	emission	cadaster
	national coordination pole guidebook to ensure methodological consistency across local
	inventories (Pôle national de coordination des inventaires territoriaux, 2012). Meteorological data
	were provided by the Integrated Forecast System (IFS) data re-analyzed for the national model,
	coupling with the MM5 model for the great north-west zone. For regional modeling tools, NCEP
	FNL Operational Global Analysis data were used with the WRF or MM5 model. For urban tools,
	observed data were provided by Meteo-France. Boundary conditions were collected from a
	European dataset provided by CHIMERE France -European scale for the national model and
	from the measurement network observations (background monitors) for urban-scale models.

(http://www.emep.int/index.html) (Figure

2

). The local inventories are mainly based on the

Table 1 :

 1 Averaged exposures during pregnancy as estimated for each of the 3 models

	1

  the number of observations is lower for PM 2.5 compared to PM 10 and NO 2 because there were fewer monitoring stations measuring PM 2.5

	Pollutant Year n		National modeling		Regional modeling	Urban modeling
			mean sd	min max mean sd	min max mean sd	min max
	NO 2	2010 7817	7.2	1.9 3.0 9.2	6.9	2 .0 0	9.2	7.2	0.9 4.2 8.8
		2011 7725	7.3	1.9 3.1 9.3	7.0	1.9 0	9.1	7.3	1.0 3.7 8.6
	PM 2.5	2010 2330 1	7.5	0.5 6.9 8.9	5.9	2.1 0	8.3	8.0	0.3 7.1 9.2
		2011 2503 1	7.2	0.6 6.5 8.4	5.6	2.3 0	8.2	7.9	0.6 6.5 9.3
	PM 10	2010 7402	7.7	1.1 5.1 9.1	7.4	1.0 5.1 9.1	7.6	1.1 3.9 10
		2011 7616	7.7	0.9 5.0 9.1	7.4	1.0 4.1 8.8	7.8	0.9 1.5 10

1

Table 2 :

 2 Averaged confidence index by pollutant, year and type of modeling for all women covered by the 3 models

N: National model, R: Regional model, U: Urban model

Table 3 :

 3 Averaged exposures and confidence indexes during pregnancy as estimated by the most suitable model for pregnant women of the ELFE cohort

	1 and 8.6

Acknowledgment

We thank the members of the PATer (Pollution Atmosphérique sur le territoire français) project steering committee: Alina Holcroft (ATMO France); Emmanuel Rivière, Julien Bernard (ATMO Grand Est); Johanna Lepeule, Emie Seyve, Rémy Slama (INSERM); Jérôme Cortinovis, Véronique Delmas (ATMO Normandie); Pierre-Yves Robic, Dominique Tilak (ATMO Occitanie); Fabrice Dugay, Olivier Sanchez (AIRPARIF); François Ducroz, Arnaud Rebours (AIR Pays-de-la-Loire); Agnès Hulin, Alain Gazeau (ATMO Nouvelle Aquitaine); Laure Malherbe, Elsa Real, Augustin Colette, Anthony Ung (INERIS); Xavier Villetard, Jonathan Virga (AIR PACA); Mathilde Pascal, Malek Bentayeb (Santé Publique France).

We also express our gratitude to all the other metropolitan AASQAs who gave their time and expertise for the realization of this project: ATMO Hauts-de-France, AIR Breitzh, ATMO Auvergne-Rhône-Alpes, ATMO Bourgogne-Franche-Comté, Lig'Air, Qualit'Air Corse.

We thank the volunteers participating in the ELFE cohort. ELFE is a study conducted jointly by the National Institute of Demographic Studies (Ined), the French National Institute for Health and

Funding

This work was supported by ANSES (the French Agency for Food, Environmental and Occupational Health & Safety; Grant No EST 2013-1-216) in the context of the PATer (Pollution Atmosphérique sur le territoire français) project. Références Beauchamp, M., 2014. Estimation des populations exposées aux dépassements de seuils

Highlights

-NO 2 , PM 10 and PM 2.5 exposure during pregnancy for the ELFE mother-child cohort -Fine spatial (10-200 meters at the urban scale) and temporal resolution for France -Combination of three dispersion models at the national, regional, and local scale -Confidence index to choose the best exposure model -Mean pregnancy exposure was 21 µg/m 3 for NO 2 , 16 µg/m 3 for PM 2.5 , 24 µg/m 3 for PM 10