# Optimizing computation time in 3D air quality models by using aerosol superbins within a sectional size distribution approach: Application to the CHIMERE model

Florian Couvidat, Lya Lugon, Palmira Messina, Karine Sartelet, Augustin Colette

► To cite this version:

Florian Couvidat, Lya Lugon, Palmira Messina, Karine Sartelet, Augustin Colette. Optimizing computation time in 3D air quality models by using aerosol superbins within a sectional size distribution approach: Application to the CHIMERE model. Journal of Aerosol Science, 2025, 187, pp.106572. 10.1016/j.jaerosci.2025.106572. ineris-05065083

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Submitted on 13 May 2025

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# Optimizing computation time in 3D air quality models by using aerosol superbins within a sectional size distribution approach: Application to the CHIMERE model

Florian Couvidat<sup>a, b, *</sup>, Lya Lugon<sup>b</sup>, Palmira Messina<sup>a</sup>, Karine Sartelet<sup>b</sup>, Augustin Colette<sup>a</sup>

## ARTICLE INFO

Editor: Chris Hogan

**Keywords:**

Air quality

Modeling

CPU time Optimization

Numerical resolution

Superbin approach

Aerosol size distribution

## ABSTRACT

One limitation of the operational application of air-quality models at high resolution for forecasting or for the evaluation of emission mitigation scenario is the computational cost. It may also be an important limitation to the use of more complex (but more realistic) secondary organic aerosol (SOA) schemes. While the size distribution may be accurately described with a sectional approach to resolve processes involved in aerosol dynamics, it also leads to large CPU time due to the number of size bins that need to be used.

In this study, we developed a “superbin” approach consisting in lumping for a given species several size bins into a single size superbin and to use a specified size distribution to distribute the superbin concentration into the different bins of CHIMERE when needed.

Together with the revision of the numerical resolution algorithm, the "superbin" approach was implemented into a new version of CHIMERE (based on v2020r1) in order to optimize the CPU time performance. The computation time was reduced by 60% with induced errors on PM10 concentrations around 3% to 7% over most of Europe. The use of the "superbin" approach proved to be much more efficient in terms of computational time and errors compared to simply reducing the number of bins.

## 1. Introduction

Three dimensional Chemical Transport Models (CTM) are widely used to simulate air quality, especially in order to perform forecasts or to estimate the efficiency of emission mitigation strategies. One common issue limiting the application of CTM is the significant amount of computational resources necessary to perform high-resolution simulations over long period and/or for several scenarios.

Due to these constraints, the computational cost of CTM generally receives a lot of attention from model developers. The general structure of the model, the Input/Output strategies, the computer environment and the CPU time of each subroutine is generally optimized to reduce CPU time without affecting the model results. However, the computational time is always limited by the complexity of the system of equations. Therefore, CPU time optimization can be achieved via two main strategies: numerical

<footnote><sup>a</sup> INERIS, Institut National de l'Environnement Industriel et des Risques, Parc Technologique ALATA, Verneuil-en-Halatte, 60550, France</footnote>

<footnote><sup>b</sup> CEREA, Centre d'Enseignement et de Recherche en Environnement Atmosphérique, 6-8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455, Marne-la-Vallée, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: florian.couvidat@ineris.fr (F. Couvidat).</footnote>
integration optimization and model simplification. While the first can be achieved by the implementation of an efficient numerical solver, the latter can be achieved in different ways.

A common strategy consists in reducing the dimensionality of the model by reducing the number of model species or particle size bins for sectional approaches. For example, Matsui (2017) reduced in the Community Atmosphere Model the number of species and size bins from 50 to 26 and from 136 to 20, respectively. The reduction of the number of species is especially important for the representation of secondary organic aerosols (SOA). Currently, mechanisms used in 3D models are generally reduced mechanisms aiming at representing SOA formation with a limited number of species. While explicit mechanisms representing the formation of the most important species have been used in 3D air quality models (Li et al., 2015), the huge number of species involved in these mechanisms (several thousand in the case of the Master Chemical Mechanism) greatly limits their application. Some reduced mechanisms like the two-dimensional volatility basis set (2D-VBS, volatility basis set approach described in terms of saturation mass concentrations and oxygen contents) (Donahue, Epstein, Pandis, & Robinson, 2011), the Hydrophilic/Hydrophobic Organics (H₂O) (Chrit et al., 2017; Couvidat, Debry, Sartelet, & Seigneur, 2012) or VBS-Gecko (Lannuque et al., 2018; Lannuque, Couvidat, Camredon, Aumont, & Bessagnet, 2020) still contains several dozens of species (and almost reach 150 SOA species in the case of VBS-Gecko). Li et al. (2015) even used the Master Chemical Mechanism containing 5727 species to simulate SOA formation in the Community Air Quality Model (CMAQ). However, reducing the size of mechanisms by reducing or removing species is not straightforward and may induce large errors. To deal with this issue, Wang, Couvidat, and Sartelet (2022) developed the GENerator of Reduced Organic Aerosol Mechanisms (GENOA) in order to reduce SOA mechanisms based on a list of reduction strategies (such as removing reactions or lumping species together) and a series of 0D simulations. The authors managed to reduce the number of species of quasi-explicit mechanisms by 97% for sesquiterpene SOA (Wang et al., 2022) and by 93% for monoterpene SOA with an induced error lower than 3% (Wang, Couvidat, & Sartelet, 2023).

In parallel to the number of aerosol species, the representation of the size distribution also greatly affects the dimensionality of the model. For example, in the sectional approach, each aerosol species is separated into a specified number of size bins, each bin covering a specified range of aerosol diameters. The dimensionality of the model is, therefore, directly proportional to the number of size bins.

Alternatively, the tracer-compression methods (and referred to as a "superspecies" approach by Sturm et al. (2023)) are used in several studies in order to optimize CPU time used to solve the advection operator. In this type of method, model species are aggregated into superspecies before transport and are decompressed into SOA species after the transport operation. This method was inspired by Liao, Henze, Seinfeld, Wu, and Mickley (2007) who lumped species prior to transport and redistributed them by using the concentrations of individual compounds in the previous time step in the GEOS-Chem model. Recently, Sturm et al. (2023) used a "superspecies" approach to reduce the dimensionality of the LOTOS-EUROS model by matrix factorization to find correspondences between SOA species and a smaller set of superspecies. The authors managed to accelerate the advection operator by a factor of 1.5-1.8. Such a method is possible if the numerical approach is based on a "splitting" strategy where each process is solved one after another and not if all processes (chemistry, transport, deposition, aerosol formation) are solved together.

In this study, we investigated ways to reduce the computational cost of CHIMERE v2020r1 (Menut et al., 2021), without degrading the model results. CHIMERE is one of the 11 models used within the Copernicus Atmosphere Monitoring Service (CAMS) regional services to provide air quality forecasts over Europe. The model is also used within the PREV'AIR operational platform (Rouil et al., 2009), for the forecasting over France. The size distribution used in CHIMERE is more detailed than the other CAMS regional models, leading to long CPU times. While most models use a simple description of particle size distributions (with a modal section or a few diameter bins), CHIMERE is used within CAMS with 10 diameter bins (covering particle diameters from 0.01 µm to 40 µm) for every species (Collin, 2020) (configuration often used with CHIMERE).

The objective of this study is to optimize, for time-critical operational purposes, the CPU time of chemistry transport models employing a sectional size distribution of particles. The reduction of the CPU computation time also allows exploring new scientific questions with more complex models, as well as offering obvious financial and environmental gains related to the high-performance computing burden. One possible solution would be to reduce the number of diameter bins, but this simplification could result in a deterioration of simulation results. In order to perform this optimization while maintaining the quality of the simulations, a "superbin" approach was constructed by analogy with the superspecies approach of Sturm et al. (2023), but applied instead to particle size bins. This approach consists of, for a given species, lumping several bins into a single superbin and using a size distribution given by a climatology to distribute the superbin concentration into the different bins of CHIMERE. The climatology is a monthly average of the size distribution, determined for each cell of the simulation domain. It was constructed from a CHIMERE simulation with 10 bins (without superbins) over a full year for the selected simulation domain. In parallel, CPU time was also reduced by revising the numerical solver. The errors and gain in CPU time generated by the modifications of the model are analyzed.

## 2. Method

A superbin approach based on a climatology of particle-size distributions has been implemented in a modified version of CHIMERE v2020r1 (Menut et al., 2021) as detailed in Section 2.2. Moreover, in order to further decrease computation time, the numerical integration has been revised by developing a hybrid method between the twostep (Verwer, Blom, & Hundsdorfer, 1996) and splitting approaches as detailed in Section 2.3.

The quantity of model outputs has also been reduced, as an extensive amount of data is written by default in CHIMERE v2020r1. While users have the ability to limit the amount of data by choosing whether to write the size distribution of each aerosol species or not, the user does not have the possibility to reduce the number of vertical levels or to decide whether some diagnostic variables
(such as biogenic emissions, dust emissions, sea salt emissions) should be written. Modifications have been made to choose the
vertical levels that can be written in the output and to enable or disable the writing of diagnostic variables.

All simulations are performed over Europe for the year 2018 with a horizontal resolution of 0.2° × 0.2° in order to test the new version of CHIMERE. Boundary conditions were taken from CAMS CIFS global model simulations (Flentje, Mattis, Kipling, Rémy, & Thomas, 2021). Meteorology was obtained from the operational analysis of the Integrated Forecasting System (IFS) model of the European Centre for Medium-Range Weather Forecasts (ECMWF) (Flentje et al., 2021). The anthropogenic emissions of gas and particles were taken from the CAMS-REG-AP inventory (version v5.1_REF2.1) (Kuenen et al., 2022).

## 2.1. SOA mechanisms

One of the motivations to focus on run-time optimization is to be able to port into 3D air quality models more sophisticated representations of the formation of secondary organic aerosols. Several SOA mechanisms of different complexities are available in CHIMERE. We chose to study three SOA mechanisms representative of the complexity range. The first two mechanisms are embedded in the standard aerosol module of CHIMERE (Couvidat et al., 2018), while the third can be used through the coupling of CHIMERE with the aerosol module SSH-aerosol (Sartelet, Couvidat, Wang, Flageul, & Kim, 2020).

* The first aerosol mechanism used in this study is the one developed by Bessagnet et al. (2008), called “medium complexity” (MED) in the CHIMERE model documentation. It is based on Pun, Seigneur, and Lohman (2006) and is one of the first SOA mechanisms implemented in CHIMERE along a simplified version (referred to as SPL) and a complex version (referred to as CPX) of the same mechanism. MED has only 5 semi-volatile organic compound (SVOC) species, and it is the SOA mechanism used within CAMS and the PREV’AIR platform due to its low CPU time. With this mechanism, primary organic aerosols (POA) are assumed to be non-volatile and do not produce SOA by aging. The mechanism assumes that each SVOC species is either hydrophobic (condense into the organic phase of aerosols) or hydrophilic (condense into the aqueous phase of aerosols). The gas/particle partitioning of hydrophilic compounds is computed with a tabulated version of the thermodynamic algorithm used by Pun et al. (2006), while the partitioning of hydrophobic compounds is computed with Raoult’s law by assuming ideality.

* The “Hydrophilic/Hydrophobic Organics” (H<sup>2</sup>O) mechanism (Couvidat et al., 2012) is an evolution of the mechanism of Pun et al. (2006). As MED, the mechanism assumes that SVOC species are either hydrophilic or hydrophobic, but the gas/particle partitioning is explicitly simulated with the thermodynamic model SOAP (Couvidat & Sartelet, 2015), which accounts for interactions between organic and inorganic compounds based on the molecular structure of the molecules. Following Couvidat and Bessagnet (2021), POA are assumed to be semivolatile and are separated into 6 different species (BOAIP, BOAmP and BOAhP for primary SVOC from biomass burning and having a low, medium and high volatility, respectively; POAIP, POAmP and POAhP for primary SVOC from other sources and having a low, medium and high volatility, respectively) that can be oxidized and form 6 other SOA species to account for aging. In total, the mechanism accounts for 27 SVOC species.

* The GENOA-based mechanism (GBM) (Wang, Couvidat, & Sartelet, 2024) is a SOA formation mechanism from the oxidation of monoterpenes and sesquiterpenes developed by the reduction of the near-explicit mechanisms MCM and Peroxy Radical Autoxidation Mechanism (PRAM) for the formation of extremely low-volatility organic compounds from monoterpenes (Roldin et al., 2019). The reduction was done using GENOA v2.0, as described in Wang et al. (2023). To simulate SOA formation from precursors other than monoterpenes, the mechanism is coupled to an extended version of H<sup>2</sup>O (Lanzafame et al., 2022; Majdi et al., 2019; Sartelet et al., 2020) accounting for specific SOA precursors from wood burning. To be able to use the GBM mechanism, CHIMERE is coupled with the aerosol module SSH-aerosol (Wang et al., 2024). In this case, SSH-aerosol replaces the standard aerosol module of CHIMERE, simulating the evolution of concentrations due to aerosol dynamic processes (nucleation, condensation/evaporation and coagulation). Similarly to the H<sup>2</sup>O mechanism, the thermodynamic module SOAP (Couvidat & Sartelet, 2015) is used for gas/particle partitioning of SVOC species, accounting for the non-ideality of aerosols. All SVOC species are both hydrophilic and hydrophobic (can condense on both the organic and aqueous phases), and, unlike the MED and H<sup>2</sup>O mechanisms, no specific assumption on hydrophilicity is needed. In total, the mechanism accounts for 72 SVOC species.

The CPU time reduction due to optimization was determined for these 3 different mechanisms. The errors generated by the optimization were determined using the MED mechanism as a reference.

## 2.2. Superbin approach

### 2.2.1. Description of the approach

A sectional approach is used in CHIMERE to represent the particle size distributions of particles. Each particle compound is divided into N<sub>bins</sub> size bins. The geometric mean diameter of each bin is needed to compute different variables such as the deposition rate, coagulation rate and the kinetic rate of heterogeneous reactions. The size distribution calculated by the model is the result of the different processes taken into account in the model (such as particle emissions and their size distribution, deposition, coagulation, condensation/evaporation that leads to the growth or the shrinking of the particle, etc.). While this approach provides a faithful representation of processes involving aerosol, it is computationally time-consuming, as each particle is represented by N<sub>bins</sub> model species.

The standard particle size discretization of CHIMERE is used: particles are separated into 10 logarithmically spaced diameter bins (covering particle diameters from 0.01 µm to 40 µm) for every species (Collin, 2020). The calculated distribution is modified
to fix 2.5 µm and 10 µm as bin bounds. The obtained bin bounds with 10 bins are (in µm): 0.01, 0.022, 0.048, 0.107, 0.235, 0.516, 1.14, 2.5, 5.0, 10.0, 40.0.

In order to limit the total number of model species, a superbin approach was implemented in CHIMERE: for each type of particle, the bins are gathered into a lower number of superbins. The model concentrations are then calculated for a low number of superbins for each species.

### 2.2.2. Determination of the size distribution climatology

In a sectional approach, the evolution of concentrations is represented for each species and each bin with the following equation:

$$ \frac{\partial C_{i,b}}{\partial t} = - \nabla \cdot \mathbf{V}C_{i,b} + \frac{\partial}{\partial z} \left( K_z \frac{\partial C_{i,b}}{\partial z} \right) + R_{i,b}^{\text{Condensation/evaporation}} + R_{i,b}^{\text{Coagulation}} - R_{i,b}^{\text{Deposition}} \quad (1) $$

with $C_{i,b}$ the concentrations of species i in bin b, V the wind speed vector, $K_z$ the vertical diffusion coefficient; $R_{i,b}^{\text{Condensation/evaporation}}$, $R_{i,b}^{\text{Coagulation}}$, $R_{i,b}^{\text{Deposition}}$ are the rate of condensation/coagulation, coagulation and deposition, respectively. The calculation of these rates is described in Couvidat et al. (2018).

In the superbin approach, several bins are lumped into a single superbin. Assuming that the aggregation of superbins remain spatially and temporally constant, the superbin approach requires defining a size distribution to distribute the concentration of a specific superbin between the different bins making up the superbin such as:

$$ C_{b,i,j} = C_{i,j}^{\text{superbin}} \times f_{b,i,j}^{\text{superbin}} \quad (2) $$

with b defined as the bin number, i the species index and j the cell index of the domain, $C_{b,i,j}$ the concentration of species i inside the bin b for cell j, $C_{i,j}^{\text{superbin}}$ the concentration of the superbin corresponding to bin b and $f_{b,i,j}^{\text{superbin}}$ a factor giving the fraction of the superbin inside bin b. $f_{b,i,j}^{\text{superbin}}$ values are determined for each species i. The values used in this study vary only spatially and monthly.

In order to simulate the concentrations of superbins, Eq. (1) was rewritten:

$$ \frac{\partial C_i^{\text{superbin}}}{\partial t} = - \nabla \cdot \mathbf{V}C_i^{\text{superbin}} + \frac{\partial}{\partial z} \left( K_z \frac{\partial C_{i,b}^{\text{superbin}}}{\partial z} \right) + \sum_{b=1}^{b2} \left( R_{i,b}^{\text{Condensation/evaporation}} + R_{i,b}^{\text{Coagulation}} - R_{i,b}^{\text{Deposition}} \right) \quad (3) $$

with $b1$ and $b2$, the first and last bins constituting the superbin. Superbin method is used to solve horizontal and vertical transport, therefore reducing remarkably the CPU time, while superbin concentrations are disaggregated into bin concentrations with Eq. (2) when computing the rate of condensation/evaporation, coagulation and deposition. These rates are then aggregated to reconstitute the rates for superbins.

$f_{b,i,j}^{\text{superbin}}$ values are based on averaged (referred to hereafter as climatology) size distributions determined for each cell of the simulation domain built from a “complete” CHIMERE simulation (without using the superbin approach) for year 2018. In this study, three size distribution methods were tested (in each case the distribution for each particle type):

* DIST1: an average 3D climatology of the size distribution is calculated for each cell of the domain and each month of the year in order to conserve the spatial and seasonal evolution of the distribution.

* DIST2: An average 3D climatology of the size distribution calculated for a specific month for each cell of the domain. This method conserves the spatial evolution of the distribution but assumes that there is no significant seasonal evolution and that the distribution can be calculated from a simulation over a limited period. April was selected as it may offer a good compromise between different situations that may be encountered by the model: the period is characterized by high ammonia emissions over Europe leading to inorganic aerosol formation, the start of spring may lead to some formation of organic aerosols and primary emissions due to residential wood burning may still be present.

* DIST3: The spatial and seasonal evolution of size distributions is not taken into account. The distribution is calculated by averaging the distribution over the whole domain and over a one-year simulation period.

The climatology only needs to be created once and can be used to run simulations with a configuration similar to that used to determine the climatology. However, it must be recreated for configuration changes affecting particle size distributions (e.g. changes in deposition velocity settings or changes in size distribution of emissions).

Due to the overwhelming CPU time consumption with GBM, the climatology for this mechanism was calculated only with the “DIST2” approach to limit the duration of the reference simulation.

### 2.2.3. Aggregation of bins into superbins

To use the superbin approach, the user must determine how to gather the bins into superbins. We propose two methods:

* A “monobin” approach where the size distribution is represented by a single superbin for each particle type
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Relative errors on dry and wet deposition fluxes generated by the superbin approach for different compounds as a function of the number of superbins. For each number of superbins, only the best selection was kept.</figcaption></figure>

* An “optimized” superbin approach for which a subset of bins was chosen to offer a good compromise between the CPU time and the effect on simulation results.

In the “optimized” approach, the subset of bins was chosen in order to reproduce deposition with an error close to 10%. To determine the error, daily dry and wet deposits are recalculated by post-processing deposition velocities by bins in the simulation results of the reference simulation of CHIMERE. The errors are computed by “replacing” the local size distribution calculated by CHIMERE by the climatology of the size distribution.

In order to determine the optimal superbin selection, all 512 possibilities of superbin selection from 10 bins are tested, and the best choice for a given number of superbins is kept. The best choices are determined by minimizing the maximum between dry and wet deposition errors (this metric was selected as deposition should be the size-dependent process influencing particle concentrations the most). Fig. 1 shows the errors on daily deposition fluxes over the simulation domain generated by the superbin approach for different number of superbins for different aerosol types: nitrate aerosol (named HNO₃ in CHIMERE), sulfate (named H₂SO₄), BiA1D one specific SOA compound formed by the oxidation of monoterpenes (Bessagnet et al., 2008) (similar figures were obtained for other SOA species of the mechanism), sodium and other cations in sea salts (named NA), chloride (named Cl), and non-carbonaceous primary aerosols (PPM). Errors on deposition fluxes are generally high with the “monobin” configuration (a single superbin) and range from 10 to 50% (except for NA for which errors below 10% were found). The errors can be efficiently reduced by increasing the number of superbins. For example, the errors for PPM are reduced from nearly 20% with one superbin to less than 1% with 4 superbins.

In order to obtain a good compromise between the errors on deposition fluxes and the CPU time, several criteria were applied to select the optimal numbers of superbins for each aerosol type:

* Errors should be less than 2% for mineral dusts, NA and Cl. This criterion was used in order to reproduce almost exactly deposition fluxes as the size distribution during episodes related to these aerosol types (especially during the outburst of dusts towards Europe) may differ from the size distribution in the climatology. Using a low error ensures that the concentration errors are minimal. Moreover, an important part of these compounds is present in the coarse fraction making them more sensitive to deposition fluxes than other species.

* Errors should be under 10% for other species, except for SOA for which an error of 15% was used. A slightly higher error was used for SOA in order to limit more efficiently CPU time. With 15% as a criterion for SOA, 2 superbins are selected for the mechanism of Bessagnet et al. (2008) with a generated error around 12%–13%. With 10% as a criterion, the number of superbins for SOA would increase to 4 to respect the criterion.

Table 1 shows how the bins are aggregated into superbins and the errors generated for dry and wet deposition. The aggregation of SOA into superbins was calculated for MED. The same aggregation was found to be optimal for every SOA species of the mechanism. The same aggregation was also found for most species of the H²O mechanism (a different decomposition in superbins was found for only 4 species; 3 superbins were necessary for those species to respect the 15% criterion). For GBM, either 2 or 3 superbins are selected (the selection of superbins for GBM is illustrated in Table A.1). For most aerosol types, the first 3 bins (corresponding to particles with an aerodynamic diameter lower than 0.1 µm) are often aggregated in a specific superbin. This is due to differences in the deposition behavior of smaller particles between dry and wet deposition. While dry deposition velocities increase strongly for very low diameters (Wesely, 1989), CHIMERE assumes that in-cloud scavenging for particles under 0.1 µm is not as efficient as for bigger particles (Couvidat et al., 2018) forcing the superbin selection process to separate particles under 0.1 µm from larger particles. In total, the number of model aerosol species advected in the model was reduced by 73%, 74% and 76% for the MED, H²O and GBM mechanisms, respectively.
<caption>**Table 1**</caption>

Aggregation of bins into superbins determined for MED and the errors generated on deposition fluxes for the different aerosol types.

<table><thead><tr><th rowspan="2">Aerosol type</th><th rowspan="2">Description</th><th colspan="10">Aggregation of bins into superbins</th><th colspan="2">Error on deposition (in %)</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>dry</th><th>wet</th></tr></thead><tbody><tr><td>BCAR</td><td>Elemental carbon from boundary conditions</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>2</td><td></td><td></td><td></td><td>8.3</td><td>3.4</td></tr><tr><td>ECres</td><td>Elemental carbon from residential sector</td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>2</td><td></td><td></td><td>7.4</td><td>8.9</td></tr><tr><td>ECtotmres</td><td>Elemental carbon from other sectors</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>3</td><td></td><td>3.5</td><td>6.9</td></tr><tr><td>DUST</td><td>Mineral Dust</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3</td><td>4</td><td>5</td><td>0.5</td><td>1.6</td></tr><tr><td>NA</td><td>Sodium and other cations from sea salt</td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>2</td><td></td><td>3</td><td>0.3</td><td>1.2</td></tr><tr><td>Cl</td><td>Chloride from sea salts</td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>2</td><td>3</td><td>0.1</td><td>0.5</td></tr><tr><td>OCAR</td><td>Primary organic aerosols</td><td>1</td><td></td><td></td><td>2</td><td></td><td></td><td></td><td>3</td><td></td><td></td><td>8.1</td><td>5.9</td></tr><tr><td>SOA</td><td>SOA compounds</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>2</td><td></td><td>13</td><td>12</td></tr><tr><td>PPM</td><td>Other primary particles</td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>2</td><td>3.5</td><td>7.9</td></tr><tr><td>SO<sub>4</sub></td><td>Sulfate (including contribution from sea salt)</td><td>1</td><td></td><td></td><td>2</td><td></td><td></td><td>3</td><td></td><td></td><td>4</td><td>6.8</td><td>5.6</td></tr><tr><td>NO<sub>3</sub></td><td>Nitrate</td><td>1</td><td></td><td>2</td><td></td><td>3</td><td></td><td></td><td></td><td></td><td>4</td><td>3.7</td><td>7.0</td></tr><tr><td>NH<sub>3</sub></td><td>Ammonium</td><td>1</td><td></td><td>2</td><td></td><td></td><td></td><td></td><td></td><td>3</td><td></td><td>3.5</td><td>9.1</td></tr><tr><td>Water</td><td>Water content</td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>2</td><td>3</td><td>5.7</td><td>9.0</td></tr></tbody></table>

## 2.3. Numerical integration

Two types of numerical methods can be used within CHIMERE to calculate the evolution of concentrations, depending on whether the transport and the chemistry are resolved sequentially or not: the two approaches (splitting and twostep approaches) are illustrated in Fig. 2.

For the two numerical methods, the evolution of the concentrations are computed using two time steps defined by the user: the physical time step $\Delta t_{phys}$ and the chemical time step $\Delta t_{chem}$ (with $\Delta t_{chem} \le \Delta t_{phys}$). $\Delta t_{phys}$ determines how often the meteorological data are updated. In the offline mode, meteorological fields are pre-calculated by a meteorological model and the hourly meteorological fields provided as input data are linearly interpolated between 2 consecutive hours. In the online mode, the meteorological fields for the current time step are directly calculated with WRF. $\Delta t_{chem}$ is the maximal time step specified by the user for the numerical integration. $\Delta t_{CFL}$ is the chemical time step used for the numerical integration and is constrained in order to respect the Courant–Friedrichs–Lewy (CFL) condition ($\Delta t_{chem}$ is used as the maximal value of $\Delta t_{CFL}$).

If the standard aerosol module of CHIMERE is used rather than the SSH-aerosol module, the particle-phase concentration is considered at equilibrium with the gas-phase concentration, and a default first-order kinetic rate constant of condensation/evaporation is set to numerically solve condensation/evaporation simultaneously with the other processes considered. This kinetic rate constant was chosen equal to $3/(4 \times \Delta t_{aero})$ with $\Delta t_{aero}$ being the time-step used for the numerical integration of aerosols (equal to $\Delta t_{CFL}$ for twostep and $\Delta t_{chem}/3$ for the splitting approach). This kinetic rate constant was chosen to guarantee the numerical stability of the model and to ensure that the gas/particle partitioning is close to equilibrium in the model. With this approach, the dynamics of the condensation/evaporation cannot be solved explicitly. This method would therefore not be suitable for calculating concentrations of smaller particles (less than 10 nm), for which the representation of the competition between condensation/evaporation, nucleation and coagulation can be critical.

If the SSH-aerosol module is used, which is only possible with the splitting approach, the time step for aerosol dynamics is adaptive and estimated in SSH-aerosol, allowing for dynamic partitioning between gas and particles.

In the twostep approach, all processes are solved together using the algorithm of Verwer et al. (1996). The process is iterative (by default two iterations are performed) and concentrations are calculated with this formula:

$$C^i(t + \Delta t_{CFL}) = \frac{\frac{4}{3}C^n(t) - \frac{1}{3}C^n(t - \Delta t_{CFL}) + \frac{2}{3}\Delta t_{CFL} \text{Prod}(C^{i-1}(t + \Delta t_{CFL}))}{1 + \frac{2}{3}\Delta t_{CFL} \text{Loss}(C^{i-1}(t + \Delta t_{CFL}))} \quad (4)$$

With $C^i$ the vector of concentrations of each species at the end of the time step for iteration i, $C^n$ the vector of concentrations at the final iteration obtained for the previous time steps, Prod the production rate of each species (due to emissions, transport and chemical production) and Loss the loss rate of each species (due to deposition, transport and chemical destruction).

In the splitting approach, the temporal evolution of concentrations due to the processes is solved sequentially, and different solvers are used. The splitting approach is divided into three parts. First, the temporal evolution of concentrations due to transport (advection and vertical mixing), emissions and deposition is estimated using the trapezoidal method (Li et al., 2023). Then, the evolution of concentrations due to gas-phase and aqueous-phase chemistry is solved with the Verwer (1994) algorithm. As ordinary differential equations for chemistry are stiff, the adaptive time-step method of Verwer (1994) is used in order to optimize the time step without inducing large errors. The time-step used to solve chemistry varies according to conditions with a minimum value of 10 s. Transport (including deposition and emissions) and chemistry are solved over $\Delta t_{chem}$. The operation is repeated until concentrations have been integrated over the physical time step. Third, processes involving aerosols (nucleation, condensation/evaporation and nucleation) are solved. In order to limit the computation time, the aerosol modules were chosen to be launched once per chemical time-step while the transport and chemical solvers are launched once over $\Delta t_{CFL}$. In the standard aerosol module, $\Delta t_{chem}/3$ is used as
<figure><img src="image_5.png" /><figcaption>Fig. 2. Illustration of the twostep, splitting and hybrid approaches. CFL stands for Courant–Friedrichs–Lewy.</figcaption></figure>

a time-step (the routine to solve aerosols is launched three times sequentially). In the SSH-aerosol module, the time step is adaptive with a minimum time step specified by the user.

Each method has its own strengths and weaknesses. The twostep approach avoids errors associated to process splitting, but is associated with numerical errors linked to the dependence of the Verwer et al. (1996) algorithm on the order of the species. Furthermore, while the algorithm of Verwer et al. (1996) is very efficient to solve transport and most chemical mechanisms, it was found to not be stable for very fast reversible processes (equilibrium reactions with a characteristic time much shorter than the time-step of integration), which is the case for the condensation/evaporation of semivolatile compounds. Kinetic rates need to be limited in those cases. On the other hand, with the splitting approach, a large part of the CPU time is taken by the numerical solver for chemistry due to the adaptive time-step approach. Indeed, the splitting approach that can lead to sudden changes in
<caption>**Table 2**</caption>

CPU time and data storage for a 5-day simulation with different configuration of CHIMERE. CPU time is given in core hours. CPU time reduction is calculated by comparison to a simulation with the same SOA mechanism and the same level of outputs but with the twostep solver, $\Delta t_{phys} = 10$ min and without the superbin approach.

<table><thead><tr><th rowspan="2">SOA mechanism</th><th rowspan="2">Solver</th><th rowspan="2">Δt<sub>phys</sub> (min)</th><th rowspan="2">N<sub>binz</sub></th><th rowspan="2">Superbin approach</th><th colspan="3">Full list of outputs</th><th colspan="3">Short list of outputs</th></tr><tr><th>CPU time (ch)</th><th>Storage (GB)</th><th>CPU time reduction</th><th>CPU time (ch)</th><th>Storage (GB)</th><th>CPU time reduction</th></tr></thead><tbody><tr><td rowspan="7">MED (Bessagnet et al., 2008)</td><td>Twostep</td><td>10</td><td>10</td><td>none</td><td>248</td><td>103</td><td>0</td><td>176</td><td>4</td><td>0</td></tr><tr><td>Splitting</td><td>10</td><td>10</td><td>None</td><td>232</td><td>103</td><td>6%</td><td>173</td><td>4</td><td>2%</td></tr><tr><td>Twostep</td><td>60</td><td>10</td><td>None</td><td>188</td><td>103</td><td>24%</td><td>122</td><td>4</td><td>31%</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>None</td><td>162</td><td>103</td><td>35%</td><td>94</td><td>4</td><td>46%</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>Monobin</td><td>85</td><td>55</td><td>66%</td><td>58</td><td>4</td><td>67%</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>Optimized</td><td>99</td><td>64</td><td>60%</td><td>66</td><td>4</td><td>63%</td></tr><tr><td>Hybrid</td><td>60</td><td>5</td><td>None</td><td>118</td><td>67</td><td>52%</td><td>69</td><td>3.7</td><td>61%</td></tr><tr><td rowspan="3">H<sup>2</sup>O (Couvidat et al., 2012)</td><td>Twostep</td><td>10</td><td>10</td><td>None</td><td>426</td><td>175</td><td>0</td><td>296</td><td>4.7</td><td>0</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>None</td><td>265</td><td>175</td><td>33%</td><td>154</td><td>4.7</td><td>44%</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>Optimized</td><td>142</td><td>88</td><td>67%</td><td>95</td><td>4.7</td><td>68%</td></tr><tr><td rowspan="3">GBM (Wang et al., 2022, 2023)</td><td>Splitting</td><td>10</td><td>10</td><td>None</td><td>884</td><td>295</td><td>0</td><td>683</td><td>5.8</td><td>0</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>None</td><td>566</td><td>295</td><td>36%</td><td>345</td><td>5.8</td><td>50%</td></tr><tr><td>Hybrid</td><td>60</td><td>10</td><td>Optimized</td><td>315</td><td>140</td><td>64%</td><td>228</td><td>5.8</td><td>67%</td></tr></tbody></table>

concentrations after transport is solved (together with emissions and deposition) force the model to use small time-step in order to solve fast chemical evolution of concentrations.

However, depending on the CFL, the splitting approach may be more efficient than the twostep approach for the numerical integration of aerosol processes as the subroutines used to calculate condensation/evaporation, nucleation and coagulation are called at each iteration with a time-step equal to $\Delta t_{CFL}$ with twostep and thrice at each chemical time step with a time-step equal to $\Delta t_{chem}/3$ with the splitting approach. To improve computation CPU time, we propose to use a hybrid approach (illustrated by Fig. 2) similar to the twostep approach but where aerosol related processes are split from other processes in order to limit the CPU time. Eq. (4) is reformulated into:

$$C^i(t + \Delta t_{CFL}) = \frac{C^n(t) + \frac{1}{3}\Delta C + \frac{2}{3}\Delta t_{CFL} \text{Prod}(C^{i-1}(t + \Delta t_{CFL}))}{1 + \frac{2}{3}\Delta t_{CFL} \text{Loss}(C^{i-1}(t + \Delta t_{CFL}))} \quad (5)$$

with $\Delta C$ the last difference of concentrations calculated with the twostep algorithm for transport coupled to chemistry, deposition and emissions. Aerosol-oriented processes are then solved similarly to the splitting approach. Note that with the standard aerosol module, the gas/particle partitioning is then recalculated in order to ensure that concentrations have reached thermodynamic equilibrium. This is not necessary with SSH-aerosol as the adaptive time-step algorithm embedded in the model ensures the possibility to simulate dynamic partitioning between gas and aerosols.

## 2.4. Configuration of simulations and evaluation

Several simulations (with the different numerical solvers, with different values of $\Delta t_{phys}$, with the monobin or optimized superbin approaches) are performed for the year 2018 with MED to determine whether the optimizations introduced in this study lead to significant deviation through a model-to-model comparison. The performed simulations are summarized in Table 2. Additionally, the CPU time reduction is also diagnosed for the H<sup>2</sup>O and GBM mechanisms by performing 5-day simulations. Simulations are also performed with MED to assess the effect of the size distribution method on simulation results using DIST1, DIST2 or DIST3 with $\Delta t_{phys} = 60$ min and the hybrid solver. Simulations with 5 and 40 bins (instead of 10 bins) are also performed in order to diagnose the interest of the superbin approach compared to a reduction of the number of bins (the bins are selected with the standard method of CHIMERE described in Section 2.2.1) and to show the uncertainty of simulation results due to the precision of the size distribution.

Finally, as the superbin approach assumes that the size distributions of superbins are not affected by emission mitigation, simulations were performed to evaluate whether the superbin approach can be used for the evaluation of emission mitigation strategies and reasonably reproduce the decrease of concentrations simulated by the standard CHIMERE due to decrease of anthropogenic emissions. In theory, lower anthropogenic emissions of primary particles could affect the size distribution of all other compounds as primary particles do affect condensation/evaporation and nucleation. The simulations are performed with $\Delta t_{phys} = 60$ min and the hybrid solver using the optimized superbin approach or no superbin with several factors of anthropogenic emission reduction (reduction by 1%, 15%, 30%, 50%, 75% and 100%) for all compounds.

The differences between two simulations are evaluated by estimating the Mean Fractional Error (MFE) of daily concentrations such as:

$$MFE = \sum \frac{|Sim - Ref|}{0.5 \times (Sim + Ref)} \quad (6)$$

where Sim and Ref are the daily concentrations of a sensitivity simulation and the reference simulation, respectively. The errors are computed over the land areas (cells of the domain with more than 1% of lands). To avoid computing a relative error with very low concentrations, a cutoff value of 0.25 µg/m<sup>3</sup> is used.
<figure><img src="image_6.png" /><figcaption>Fig. 3. Box plot of MFE (in %) on daily concentrations of PM10 and PM2.5 over year 2018. Errors generated by the various simplifications are calculated over the land areas of the simulation domain.</figcaption></figure>

Similarly, to MFE, the Mean Fractional Bias (MFB) is computed with:

$$MFB = \sum \frac{Sim - Ref}{0.5 \times (Sim + Ref)} \qquad (7)$$

The root-mean-square error (RMSE) is also computed on daily concentrations. In order to provide general indications on errors and bias of the different optimizations, Global MFE, MFB and RMSE are computed with daily concentrations over all land areas of the simulation domain.

These metrics are calculated for PM concentrations, main gases (O₃ and NO₂) and the Aerosol Optical Depth (AOD). AODs are calculated within CHIMERE with the fastJX model at 200 nm, 300 nm, 400 nm, 600 nm and 999 nm (Mailler et al., 2016; Wild, Zhu, & Prather, 2000).

The performance of the different simulations is assessed by comparison to in-situ measurements of surface concentrations from the European air quality observation network AQ e-Reporting (EEA, 2023). This database gathers observations provided by the different member countries of the European Environment Agency (EEA). Only the background rural stations are selected because of the resolution, which is not sufficient to represent appropriately urban areas.

Simulations are performed on the supercomputer Topaze at CCRT using AMD EPYC Milan 7763 processors running at 2.45 GHz.

# 3. Results

## 3.1. Impact of optimizations on CPU time and error analysis

Table 2 shows the CPU time and storage needed for a 5-day simulation performed over 200 processors while Fig. 3 shows the errors for PM10 and PM2.5 due to various simplifications (change of numerical methods, change of Δt<sub>phys</sub>, use of the superbin approach, etc.). The errors for O₃ and NO₂ are also shown in Appendix B. As the errors for PM2.5 and PM10 are almost identical, only the errors for PM10 will be discussed. The daily MFE for O₃ and NO₂ are generally quite low (below 1%) and are generally
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Maps of mean fractional errors (in %) generated by the different optimization strategies. *: the effect of activating superbins, monobins or changing the number of bins is calculated using the hybrid approach ($\Delta t_{phys}$ = 60 min) and are compared to the simulation with hybrid approach ($\Delta t_{phys}$ = 60 min), 10 bins and no superbin approach.</figcaption></figure>

much lower than the MFE for PM. For these two species, the highest MFE are obtained when comparing concentrations simulated with the splitting and twostep numerical methods that lead to errors of a few percents (average error around 1% for O$_{3}$ and 3% for NO$_{2}$) due to differences in the numerical methods. The spatial distribution of MFE is illustrated in Fig. 4. The spatial distributions of RMSE and MFB are also illustrated in Figs. C.1 and C.2, respectively.

With a timestep ($\Delta t_{phys}$) of 10 min, the two numerical methods of CHIMERE (splitting and twostep approaches) lead to very similar CPU time (difference within a few percent). The daily MFE between these two methods is generally between 2 to 5% but can locally exceed 10% for PM10 concentrations. The global (calculated for the daily concentrations over the land areas of the
domain) MFE, MFB and RMSE are equal to 3.4%, 2.8% and 0.35 µg/m³ respectively. These results indicate that the errors are largely due to slightly higher concentrations with the splitting approach.

Changing the timestep (from $\Delta t_{phys}$ = 10 min to $\Delta t_{phys}$ = 60 min) with the twostep approach significantly reduces the CPU time for the MED mechanism (by 24% with all outputs and by 31% with the short list of outputs) while the error generated by increasing the timestep is fairly low (average MFE below 1%, can locally reach MFE around 5%), especially when compared to the differences in concentrations between the splitting and twostep approaches.

Switching the numerical method from the splitting approach to the hybrid numerical method with $\Delta t_{phys}$ equal to 60 min leads to an additional CPU time decrease of 30% with the full list of outputs (and by 45% with the short list of outputs). In total, compared with the reference simulation (twostep, with $\Delta t_{phys}$ = 10 min), the CPU time is reduced by 35% with all outputs (and by 46% with the short list of outputs). The simulated concentration differences are quite low when changing from the twostep to the hybrid method (global MFE, MFB and RMSE equal to 0.87%, 0.04% and 0.06 µg/m³ respectively) with $\Delta t_{phys}$ equal to 10 min. However, when changing the numerical method with $\Delta t_{phys}$ equal to 60 min, higher errors are obtained (global MFE and RMSE of 3.5% and 0.28 µg/m³) due to a decrease of concentrations (MFB equal to -3%). However, the MFE are within the range of MFE between the splitting and twostep simulations with $\Delta t_{phys}$ equal to 10 min and can therefore be considered reasonable. The MFE reaches 10% over part of Northern Europe as shown in Fig. 4. However, this is not significant because the simulated PM10 concentrations in this region are below 1 µg/m³.

The final optimization corresponds to using the superbin approach with DIST1, DIST2 or DIST3. Using the superbin approach (with hybrid numerical method and $\Delta t_{phys}$ = 60 min) reduces the CPU time by 39% (by comparison to the simulation with hybrid numerical method and $\Delta t_{phys}$ = 60 min but without the superbin approach) with all outputs (and by 30% with the short list of outputs) and is therefore the most efficient method to reduce the CPU time while the global MFE and RMSE (2.8% and 0.21 µg/m³) are below the errors introduced by the use of the hybrid method with $\Delta t_{phys}$ = 60 min. The global MFB is equal to 2.6% indicating that most of the errors are due to a slight increase in concentrations. Using DIST1, DIST2 or DIST3 produces very similar results with slightly higher MFE with the DIST3 method (no spatiotemporal evolution of the size distribution), especially over Germany, Poland and the United Kingdom. These results indicate that accounting for the spatial distribution of the size distribution should be preferred but that it may not be necessary to account for a seasonal evolution. Therefore, the DIST2 method is sufficient, and performing simulation over a single month to obtain a spatial evolution of the size distribution can be considered as a reasonable approach.

In total, the CPU time is reduced by 60% with all outputs (and by 63% with the short list of outputs) compared to the reference simulation (twostep, $\Delta t_{phys}$ = 10 min, no superbin approach). Altogether, the induced error by the combination of the superbin approach, the increase of the time step and the use of the hybrid approach is around 3% to 7% over most of Europe. The global MFE, MFB and RMSE are equal to 3.7%, -0.8% and 0.29 µg/m³, respectively.

The MFE for the different PM components are illustrated in Fig. D.1. Generally, MFE are below 1% for primary PM components. The strongest errors for primary PM are obtained for dusts with a global MFE of 1.5% (90th percentile of 3.2%, strongest MFE over Turkey). Although the RMSE exceeds 4 µg/m³ over the Sahara desert due to high dust concentrations (above 250 µg/m³), MFE over this region are rather low (below 2%). The errors on dust concentrations are mostly due to the superbin approach that leads to a global MFE of 1.3% due to a slight overestimation of concentrations (global MFB of 1.3%).

Most of the errors on PM10 concentrations are due to the errors on NO₃ concentrations with a global MFE of 5.8% (MFE between 2 and 8% over most of Europe, the RMSE for PM10 over the domain is 0.29 µg/m³ against 0.18 µg/m³ with NO₃). This is due to a decrease of NO₃ concentrations (MFB of -4.7%) mainly due to an increase of total nitrate dry deposition (deposition of gas phase HNO₃ + deposition of particle phase NO₃) by 4%. With the hybrid approach, gas/particle partitioning is calculated one per physical timestep whereas the condensation onto particles can limit deposition as vapors are generally deposited faster than particles (Couvidat & Bessagnet, 2021).

A Large increase in RMSE due to the use of the superbin approach (over 0.5 µg/m³ and up to 1.0 µg/m³ but associated to moderate MFE below 3%) is also obtained for concentrations over seas along marine fleet trajectories (especially in the Strait of Gibraltar and the English Channel). This increase in errors is due to large RMSE values along these trajectories exceeding 0.5 µg/m³ for NO₃ concentrations (MFE between 10 and 20%). These errors are due to large NOₓ emissions leading to high HNO₃ formation combined with high sea salt concentrations. The condensation rate of HNO₃ onto sea salts represented in CHIMERE is indeed highly dependent on the size distribution. Using a climatology of the size distribution may therefore not be precise enough to describe precisely this specific process.

MFEs for AOD at the different wavelengths are illustrated in Appendix E. The MFEs generated by the superbin approach and the numerical optimizations for AOD are below 1% for wavelengths greater than or equal to 400 nm with a low global MFE (0.065% at 400 nm). Reducing the number of bins from 10 to 5 generates a much higher MFE than using the superbin approach (0.42% vs 0.05% at 400 nm). Higher global MFEs are generated by the superbin approach and the numerical optimizations for wavelengths lower than or equal to 300 nm (0.93% at 200 nm and 0.21% at 300 nm) but remain below the global MFE for PM10 (3.7%).

The effect of using the superbin approach should be compared with the effect of using a monobin approach or reducing the number of bins (from 10 to 5). In these two cases, the induced errors are very high, generally exceed 10% and range from about 15 to 30% over a large part of Europe. The results indicate that simply reducing the number of bins is not a satisfactory method. Moreover, the superbin approach leads to a more efficient reduction of CPU time (total reduction by 60% instead of 52% with a reduction of the number of bins from 10 to 5). The monobin approach would be more efficient in the reduction of the CPU time but this reduction (by 66% instead of 60% with the superbin approach) is quite low compared to the error induced by this method.
<caption>**Table 3**</caption>

Bias, RMSE and correlation of the reference simulation compared to measurements of PM10 and PM2.5 and changes in these metrics (Δ|Bias|, ΔRMSE and ΔR) due to the various optimizations. Improvement and deterioration of the metrics by more than 1% are shown in blue and red (respectively).

<table><thead><tr><th rowspan="2">Reference simulation performance</th><th colspan="4">PM10</th><th colspan="4">PM2.5</th></tr><tr><th>Bias µg/m³</th><th>RMSE µg/m³</th><th>MFE</th><th>R</th><th>Bias µg/m³</th><th>RMSE µg/m³</th><th>MFE</th><th>R</th></tr></thead><tbody><tr><td>Induced changes</td><td>Δ|Bias| µg/m³</td><td>ΔRMSE µg/m³</td><td>ΔMFE</td><td>ΔR</td><td>Δ|Bias| µg/m³</td><td>ΔRMSE µg/m³</td><td>ΔMFE</td><td>ΔR</td></tr><tr><td>Twostep (60 min vs. 10 min)</td><td>0.04</td><td>0.01</td><td>0.00</td><td>0.00</td><td>0.04</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Splitting vs. Twostep</td><td>-0.46</td><td>-0.15</td><td>-0.02</td><td>0.00</td><td>-0.47</td><td>0.05</td><td>-0.01</td><td>0.00</td></tr><tr><td>Hybrid vs. Twostep (10 min)</td><td>-0.01</td><td>0.00</td><td>0.00</td><td>0.00</td><td>-0.01</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Hybrid (60 min vs. 10 min)</td><td>0.51</td><td>0.12</td><td>0.02</td><td>0.01</td><td>0.52</td><td>-0.06</td><td>0.01</td><td>0.00</td></tr><tr><td>Use of superbins (DIST1)<sup>a</sup></td><td>-0.21</td><td>-0.12</td><td>-0.02</td><td>0.01</td><td>-0.22</td><td>-0.07</td><td>-0.01</td><td>0.01</td></tr><tr><td>Overall effect (Hybrid 60 min with superbins vs. reference)</td><td>0.30</td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.30</td><td>-0.13</td><td>0.00</td><td>0.01</td></tr><tr><td>Effect of using DIST2<sup>a</sup></td><td>-0.22</td><td>-0.13</td><td>-0.02</td><td>0.01</td><td>-0.22</td><td>-0.09</td><td>-0.01</td><td>0.01</td></tr><tr><td>Effect of using DIST3<sup>a</sup></td><td>-0.24</td><td>-0.14</td><td>-0.02</td><td>0.01</td><td>-0.28</td><td>-0.09</td><td>-0.02</td><td>0.01</td></tr><tr><td>Effect of using Monobins<sup>a</sup></td><td>0.42</td><td>0.39</td><td>0.08</td><td>-0.02</td><td>0.41</td><td>0.35</td><td>0.07</td><td>-0.03</td></tr><tr><td>Effect of using 5 bins<sup>a</sup></td><td>0.83</td><td>0.57</td><td>0.11</td><td>-0.01</td><td>0.59</td><td>0.35</td><td>0.07</td><td>-0.03</td></tr><tr><td>Effect of using 40 bins<sup>a</sup></td><td>0.58</td><td>0.39</td><td>0.08</td><td>-0.01</td><td>0.56</td><td>0.26</td><td>0.06</td><td>-0.02</td></tr></tbody></table>

## 3.2. Comparison to measurements

A comparison to the measurements of the AQ e-Reporting database is performed in order to determine if optimizations significantly affect the quality of the results. Table 3 shows the bias, root mean square error (RMSE), MFE and correlation (R) of the reference simulation compared to measurements as the variations of absolute bias (Δ|Bias|), of the RMSE (ΔRMSE), of the MFE (ΔMFE) and of the correlation (ΔR). The reference simulation (using twostep, Δt<sub>phys</sub> = 10 min and no superbin approach) is characterized by a bias of -6.4 µg/m³, a RMSE of 10.59 µg/m³, a MFE of 62% and a correlation of 0.59 for PM10. These results are consistent with the evaluation performed by Guion, Couvidat, Colette, Guevara, and Petiot (2022) (with all the models participating in CAMS) who reported RMSE generally between 8 and 14 µg/m³. Better performance is obtained for PM2.5 with a bias of -2.4 µg/m³, a RMSE of 7.65 µg/m³, a MFE of 50%, and a correlation of 0.63.

Generally, all modifications have a low impact on the metrics. Most optimizations marginally modify the metrics (by less than 5%, which can be considered insignificant when considering the uncertainty of measurements and of the model inputs). The largest deterioration of results is obtained when using the monobin approach, when reducing the number of bins from 10 to 5 or when increasing the number of bins from 10 to 40. In the three cases, the absolute bias for PM10 is increased by more than 0.42 µg/m³ (increase by 6.5%), the MFE by more than 0.08 and the RMSE by more than 0.39 µg/m³ and the correlation is reduced by 0.01. The decrease in performance when increasing the number of bins above 10 can be attributed to a decrease of error compensation or the fact that some parameters (like the size distribution of emissions of primary particles, wet deposition scavenging coefficient of particles) may have been chosen to optimize the results of simulations performed with 10 bins (which is the standard configuration of CHIMERE). Indeed, increasing the number of bins to 40 mostly affect secondary inorganic aerosols (global MFE between 10 and 40 bin simulations of 9.5% for NO<sub>3</sub> and SO<sub>4</sub>) indicating that the issues could be related to the formation of secondary inorganic aerosols. The use of the hybrid method with Δt<sub>phys</sub> = 60 min also leads to an increase in the absolute bias by 0.51 µg/m³ (increase by 7.9%), in the MFE of 0.02 and in the RMSE by 0.12 µg/m³ (increase of 1.1%). However, this slight decrease is compensated by better performance when using the superbin approach. In total, using all optimizations leads to a negligible effect on RMSE, a slight improvement in correlation, and a slight increase in the bias by 5%.

## 3.3. Validity of the superbin approach for emission mitigation scenarios

Using the superbin approach for emission mitigation scenarios can induce a bias in the results as the size distribution of superbins would be assumed constant. In order to assess the validity of this assumption, the effect of reducing all anthropogenic emissions on PM10 concentrations was tested for different levels of reduction (1%, 15%, 30%, 50%, 75% and 100%). Decreases in concentrations due to reduced emissions are hereafter referred to as “prevented concentrations”. The concentrations simulated without the superbin approach, the prevented concentrations due to a 100% reduction of anthropogenic emissions, and the errors due to the use of the superbin approach in prevented concentrations are shown in Fig. 5. As expected, the strongest reductions in concentrations are obtained for areas associated with large anthropogenic emissions (cities, central Europe, Northern Italy).

Fig. 6 shows the yearly averaged prevented PM concentrations over the land areas of the domain due to the different levels of emission reduction as well as the normalized mean error (NME) and the normalized mean bias (NMB) on simulated prevented daily concentrations due to the use of the superbin approach. NME and NMB were preferred to MFE and MFE to avoid giving high weights when prevented daily concentrations are close to zero. NME and NMB were calculated by normalizing the error and the

<footnote><sup>a</sup> The effect of activating superbins, monobins or changing the number of bins is calculated using the hybrid approach (Δt<sub>phys</sub> = 60 min) and are compared to the simulation with hybrid approach (Δt<sub>phys</sub> = 60 min), 10 bins and no superbin approach.</footnote>
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Maps of PM10 annual concentrations (in µg/m³, top left), of the decrease of PM10 concentrations (prevented concentrations) due to a 100% reduction of anthropogenic emissions (in µg/m³, top right) and of the NME on prevented daily concentrations due to the use of the superbin approach (in %, bottom left). Simulations are performed with the hybrid method with $\Delta t_{phys} = 60$ min and without superbin.</figcaption></figure>

bias by the annual prevented concentrations calculated without the superbin approach. For a reduction of anthropogenic emissions by 100%, the superbin approach leads to a slight overestimation of the prevented concentrations between 1.5% (10th percentile of the NMB) and 6.4% (90th percentile of the NMB) with a median around 2.6%. The NMB is close to the NME and ranges between 1.8% (10th percentile) and 7.8% (90th percentile) with a median around 3.0%.

For primary PM, NMB and NME are close to zero (median NMB and NME over the land areas are around -0.5% and 0.7% respectively) indicating that the superbin approach leads to almost no significant error. The strongest errors are obtained for sulfate (median NMB and NME over the land areas are around 4.7% and 5.0%, respectively) and nitrate (median NMB and NME over the land areas are around 4.4% and 6.9%, respectively). These errors are consistent with the errors due to the use of the superbin approach with no emission reduction (median NME over lands of 3.7% and 6.0% for sulfate and nitrate, respectively; median NMB over lands of 3.3% and 3.2% for sulfate and nitrate, respectively).

However, higher NME and NMB for PM10 are obtained in sea areas and can exceed 15% where the prevented annual concentrations are under 0.5 µg/m³ (which correspond to a relative decrease of PM10 concentrations below 3%). This is due to high relative error over sea areas for nitrate that can be explained by the issues related with the condensation of $HNO_3$ onto sea salts identified in Section 3.1.

## 4. Discussions and conclusions

The version developed in this study manages to simulate air quality with a reduction of CPU time by 60 to 67% depending on the SOA mechanism with an induced MFE on PM concentrations between 3 and 6% over most of Europe (which is significantly lower than the MFE due to a reduction of the number of bins or the MFE obtained by the comparison to observations). A large part of the reduction in CPU time (43%) is obtained by revising the model numerical integration (implementation of an hybrid solver and increase of the timestep). The most efficient method to reduce the CPU time was the implementation of the superbin approach which consists of lumping for a given species several size bins into a single size superbin and to use a size distribution to distribute the superbin concentration into the different bins of CHIMERE when needed. This method manages to reduce CPU time by around 45% with an induced MFE of a few percent. Currently, the size distribution is based on a climatology determined by calculating an average distribution for each cell of the domain. This distribution should at least be based on a one-month period simulation. This approach could be improved by using an artificial intelligence algorithm in order to predict the most appropriate distribution at each time step of the simulation according to local conditions (like precipitation and other meteorological parameters). The error and the number of superspecies (and therefore the CPU time) could therefore be reduced significantly.

Moreover, the superbin approach was found to provide better results, both in terms of errors and CPU time, than simply reducing the number of bins, indicating that the superbin approach can provide an accurate description of the size distribution. Although the superbin approach was primarily developed to decrease the CPU time for operational purposes, it could also be used as a mean to investigate microphysical processes and provide a sub-discretization of bins. For example, whereas deposition
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Decrease of the domain-averaged PM10 concentrations due to different level anthropogenic emission reduction concentrations with the reference simulation (black) and the superbin approach (red). The blue and the green curves indicate the median NME and NMB on the decrease of PM annual concentrations respectively. The shaded area correspond to the area between the 10th and 90th percentiles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

velocities of particles increase sharply after 1 µm, only one single bin represents particles between 1.14 and 2.5 µm when 10 bins are used with CHIMERE. Using the superbin method could therefore be used to improve the calculation of deposition, coagulation or condensation/evaporation rates.

One interest in decreasing the CPU time is the possibility to use operationally more complex SOA mechanism. Compared to the MED mechanism, using the H₂O and GBM mechanisms would increase the CPU time by a factor 1.7 and 3.6, respectively. This significant increase in the CPU time makes difficult to use such mechanisms. However, their use may become operationally possible with the optimizations developed in this study. With GBM, using the hybrid solver with a time step of 60 min and the superbin approach would reduce the CPU time by 64% and largely offset the increase in CPU time by a factor 3.6. However, the optimizations presented in this study may lead to errors around a few percent on some PM components (especially on secondary inorganic aerosols). Although these errors remain small compared to the uncertainties of the processes represented in the model and of observations, it may be recommended to use CHIMERE with a lower timestep or without using the superbin approach to study the influence of PM concentrations of specific processes.

### CRediT authorship contribution statement

**Florian Couvidat:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Conceptualization.
**Lya Lugon:** Writing – original draft, Software, Conceptualization.
**Palmira Messina:** Writing – original draft, Methodology, Conceptualization.
**Karine Sartelet:** Writing – review & editing, Methodology, Conceptualization.
**Augustin Colette:** Writing – review & editing, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work has been carried out thanks to the support of the ACRA/Primequal project funded by ADEME and Support from French Ministry in charge of ecology, France.
<table><caption>**Table A.1**
Number of superbins (N<sub>s</sub>) and errors on daily dry and wet deposition fluxes obtained for SSH-aerosol and the GBM mechanism.</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">N<sub>s</sub></th><th colspan="2">Error (in %)</th><th rowspan="2">Species</th><th rowspan="2">N<sub>s</sub></th><th colspan="2">Error (in %)</th><th rowspan="2">Species</th><th rowspan="2">N<sub>s</sub></th><th colspan="2">Error (in %)</th></tr><tr><th>Dry</th><th>Wet</th><th>Dry</th><th>Wet</th><th>Dry</th><th>Wet</th></tr></thead><tbody><tr><td>BCAR</td><td>2</td><td>2.7%</td><td>2.5%</td><td>BiNIT3</td><td>2</td><td>8.7%</td><td>6.0%</td><td>H3C25C6PAN</td><td>3</td><td>5.2%</td><td>5.9%</td></tr><tr><td>DUST</td><td>5</td><td>0.3%</td><td>1.1%</td><td>BiPER</td><td>2</td><td>12.8%</td><td>10.1%</td><td>LIMALNO3</td><td>2</td><td>14.4%</td><td>6.3%</td></tr><tr><td>E Cres</td><td>3</td><td>0.3%</td><td>0.9%</td><td>C106OOH</td><td>3</td><td>4.4%</td><td>4.7%</td><td>LIMALOOH</td><td>2</td><td>10.7%</td><td>6.8%</td></tr><tr><td>E Ctotmres</td><td>2</td><td>3.0%</td><td>6.8%</td><td>C10H14O11</td><td>2</td><td>10.5%</td><td>8.6%</td><td>NAPINAOOH</td><td>3</td><td>4.2%</td><td>4.7%</td></tr><tr><td>NA</td><td>1</td><td>6.8%</td><td>7.4%</td><td>C10H14O9</td><td>2</td><td>10.7%</td><td>8.3%</td><td>NBPINAOOH</td><td>3</td><td>4.4%</td><td>4.6%</td></tr><tr><td>OCAR</td><td>3</td><td>1.8%</td><td>2.5%</td><td>C131CO2H</td><td>2</td><td>9.9%</td><td>8.1%</td><td>NC102OOH</td><td>2</td><td>10.5%</td><td>5.6%</td></tr><tr><td>PPM</td><td>1</td><td>6.2%</td><td>8.1%</td><td>C132OOH</td><td>2</td><td>9.2%</td><td>8.0%</td><td>NORLIMOOH</td><td>2</td><td>9.7%</td><td>6.5%</td></tr><tr><td>ACIDMAL</td><td>2</td><td>13.5%</td><td>6.7%</td><td>C133CO</td><td>2</td><td>9.2%</td><td>8.2%</td><td>PAHhN</td><td>3</td><td>6.1%</td><td>5.8%</td></tr><tr><td>AnBlP</td><td>2</td><td>10.3%</td><td>8.2%</td><td>C133NO3</td><td>2</td><td>9.0%</td><td>8.2%</td><td>PAHIN</td><td>2</td><td>8.6%</td><td>8.3%</td></tr><tr><td>AnBmP</td><td>2</td><td>11.2%</td><td>6.4%</td><td>C141CO2H</td><td>2</td><td>11.8%</td><td>7.3%</td><td>PINIC</td><td>2</td><td>10.8%</td><td>5.3%</td></tr><tr><td>AnClP</td><td>2</td><td>8.4%</td><td>9.0%</td><td>C20H30O13</td><td>2</td><td>11.2%</td><td>8.7%</td><td>POAhP</td><td>3</td><td>5.1%</td><td>5.8%</td></tr><tr><td>BCKSOZ</td><td>3</td><td>4.3%</td><td>5.1%</td><td>C516OOH</td><td>2</td><td>8.6%</td><td>7.6%</td><td>POAIP</td><td>2</td><td>6.1%</td><td>5.9%</td></tr><tr><td>BOAhP</td><td>3</td><td>5.1%</td><td>5.2%</td><td>C621OOH</td><td>2</td><td>9.4%</td><td>7.7%</td><td>POAmP</td><td>2</td><td>14.2%</td><td>3.7%</td></tr><tr><td>BOAIP</td><td>2</td><td>7.4%</td><td>7.9%</td><td>C719OOH</td><td>2</td><td>11.3%</td><td>6.6%</td><td>PSYR</td><td>3</td><td>5.4%</td><td>5.6%</td></tr><tr><td>BOAmP</td><td>3</td><td>4.9%</td><td>5.6%</td><td>C812OOH</td><td>2</td><td>8.4%</td><td>7.1%</td><td>SOAhP</td><td>2</td><td>10.4%</td><td>6.3%</td></tr><tr><td>BPINAOOH</td><td>3</td><td>4.5%</td><td>4.8%</td><td>C813NO3</td><td>2</td><td>9.5%</td><td>8.3%</td><td>SOAIP</td><td>2</td><td>9.7%</td><td>10.1%</td></tr><tr><td>BSOAhP</td><td>2</td><td>10.9%</td><td>5.7%</td><td>C813OOH</td><td>2</td><td>8.4%</td><td>7.6%</td><td>SOAmP</td><td>2</td><td>9.6%</td><td>8.6%</td></tr><tr><td>BSOAlP</td><td>2</td><td>9.8%</td><td>9.3%</td><td>C920PAN</td><td>3</td><td>4.8%</td><td>4.9%</td><td>H<sub>2</sub>SO<sub>4</sub></td><td>4</td><td>4.6%</td><td>5.6%</td></tr><tr><td>BSOAmP</td><td>2</td><td>9.4%</td><td>8.8%</td><td>C97OOH</td><td>2</td><td>13.4%</td><td>5.1%</td><td>Cl</td><td>4</td><td>0.1%</td><td>0.3%</td></tr><tr><td>BiDER</td><td>2</td><td>13.9%</td><td>7.7%</td><td>C98NO3</td><td>3</td><td>4.2%</td><td>5.4%</td><td>HNO<sub>3</sub></td><td>4</td><td>6.2%</td><td>4.1%</td></tr><tr><td>BiMGA</td><td>2</td><td>14.7%</td><td>6.9%</td><td>C98OOH</td><td>2</td><td>13.6%</td><td>6.6%</td><td>NH3</td><td>4</td><td>6.0%</td><td>8.9%</td></tr><tr><td>BiMT</td><td>2</td><td>14.0%</td><td>9.4%</td><td>DHMB</td><td>3</td><td>5.1%</td><td>5.7%</td><td>WATER</td><td>3</td><td>8.7%</td><td>9.1%</td></tr><tr><td>BiNGA</td><td>2</td><td>9.9%</td><td>6.6%</td><td>GHDPerox</td><td>3</td><td>5.2%</td><td>5.7%</td><td></td><td></td><td></td><td></td></tr></tbody></table>

**Appendix A. Number of superbins for the GBM mechanism**

See Table A.1.

**Appendix B. MFE for O<sub>3</sub> and NO<sub>2</sub>**

See Fig. B.1.

**Appendix C. Maps of RMSE and MFB generated by the different optimization strategies**

See Figs. C.1 and C.2

**Appendix D. MFE for PM components**

See Fig. D.1.

**Appendix E. MFE for AOD**

See Fig. E.1.

**Data availability**

Data will be made available on request.
<figure><img src="image_11.png" /><figcaption>**Fig. B.1.** Box plot of MFE (in %) on daily concentrations of O₃ and NO₂ over year 2018. Errors generated by the various simplifications are calculated over the land areas of the simulation domain.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. C.1.** Maps of RMSE (in %) generated by the different optimization strategies. *: the effect of activating superbins, monobins or changing the number of bins is calculated using the hybrid approach ($\Delta t_{phys}$ = 60 min) and are compared to the simulation with hybrid approach ($\Delta t_{phys}$ = 60 min), 10 bins and no superbin approach.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. C.2.** Maps of MFB (in %) generated by the different optimization strategies. *: the effect of activating superbins, monobins or changing the number of bins is calculated using the hybrid approach ($\Delta t_{phys}$ = 60 min) and are compared to the simulation with hybrid approach ($\Delta t_{phys}$ = 60 min), 10 bins and no superbin approach.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. D.1. Box plot of MFE (in %) on daily concentrations of PM components over year 2018. Errors generated by the various simplifications are calculated over the land areas of the simulation domain.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. E.1.** Box plot of MFE (in %) on daily AOD over year 2018. Errors generated by the various simplifications are calculated over the land areas of the simulation domain.</figcaption></figure>

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