Taei Fatemeh
email: fatemeh.taei@univ-ubs.fr

Mohammed Adel

Julien Nathalie
email: nathalie.julien@univ-ubs.fr

CODIT 2023 Modeling of smart batteries for the realization of a digital twin prototype

Keywords: Digital Twins, Battery, State Estimation, SoC and SoH Estimation, Digital Transformation

Digital Twin (DT) is one of the major technology trends that has attracted many industries lately. The safety and reliability of lithium-ion batteries is a critical issue for both their design and operation to qualify their degradation due to aging. The digital twin offers new paradigms that can provide an effective solution to evaluate the degradation of the lithium-ion battery as it provides an efficient solution to physical and digital systems integration. It reflects the behavior of the equipment by building a virtual representation of the latter, providing supports for real time control, reliability, and stability. In this paper, the steps towards battery digitization are studied through a real case study, aiming at providing a generic solution for battery digital twins development and integration.

I. INTRODUCTION

Since the beginning of the 21st century and the advent of Industry 4.0, the world is experiencing a fundamental change in the design and use of products and means of production. This paradigm shifting does not only concern the industrial sector, but also many other fields, such as energy, logistics, construction, health, and this within the framework of what is commonly called the digital revolution.

The key technologies that are driving this revolution are those that allow to capture data, process it, extract information from it, establish models, as well as provide services adapted to needs and uses such as: Internet of Things, Data mining, Artificial Intelligence, and especially the Digital Twin.

In addition to the industrial sector, which is certainly experiencing the most rapid digitalization, thanks in particular to Smart Manufacturing, the energy sector is not left behind, mainly due to the development of Smart Grids. These smart grids allow the collection and management of data between suppliers and consumers in order to adjust the flow of electricity in real time [START_REF] Zheng | Smart Meters in Smart Grid: An Overview[END_REF]. These new smart systems now allow for better management of a power grid powered by intermittent energy sources (wind, solar, tidal). However, even if this technology can overcome the constraints related to the control and management of this type of energy in the network, the need to have storage resources for this energy within the network remains paramount. This is one of the reasons why manufacturers are developing increasingly sophisticated batteries, both in terms of storage capacity and functionality [START_REF] Li | An electrochemically neutralized energy-assisted low-cost acid-alkaline electrolyzer for energy-saving electrolysis hydrogen generation[END_REF] [3] [4] [START_REF] Geng | Electrolyte additive engineering for aqueous Zn ion batteries[END_REF]. In order to be integrated into smart structures, batteries must therefore also have smart modules, or at least be able to interface with such systems.

If there were to be a technology that is essential for the integration of any physical object (in this case the battery) into a global digitalization process, it would be the "Digital Twin". This technology allows not only to keep a digital flow throughout the process of design and validation of the product (or physical object) upstream of its production, but also during the operation phase. Having a digital twin for the design, development, and use of a new generation of batteries can only provide a considerable competitive advantage. This offers the possibility to validate and improve the different versions of the product before it is manufactured and put on the market, but also to improve its performance and optimize its running in operation, in addition to providing feedback and having a digital continuity allowing the improvement of the product for future versions. It is also with the objective of investigating the feasibility of such an approach that we conducted the study that is the subject of this paper.

II. STATE OF THE ART A. The Digital Twin:

The digital twin has become a popular research topic in recent years due to its potential to improve decision making in many sectors, such as industrial production, construction, maintenance, and urban planning. The digital twin is used in industry to simulate production processes and improve efficiency, including real-time monitoring; production control; part performance prediction; human-robot collaboration and interaction; process evaluation and optimization; asset management; production planning [START_REF] Liu | Review of digital twin about concepts, technologies, and industrial applications[END_REF]. It is also found in the field of smart city construction and development [START_REF] Kaewunruen | A Digital-Twin Evaluation of Net Zero Energy Building for Existing Buildings[END_REF] [8] [9] [START_REF] Shahat | City Digital Twin Potentials: A Review and Research Agenda[END_REF]. Moreover, applications related to logistics and transportation [START_REF] Wang | Research on the Construction of Highway Traffic Digital Twin System Based on 3D GIS Technology[END_REF], energy [START_REF] Saad | IoT-Based Digital Twin for Energy Cyber-Physical Systems: Design and Implementation[END_REF], and even healthcare [START_REF] Erol | The Digital Twin Revolution in Healthcare[END_REF] are increasingly seeing the emergence of tools based on digital twin technologies.

Other works have focused on issues related to the definition of concepts and the proposal of formalism that allow this technology to be better understood given its growing use and the diversity of application domains. [START_REF] Tao | Digital twin driven smart manufacturing[END_REF] proposed one of the most robust models in the literature, allowing to define a digital twin as an entity composed of 5 distinct dimensions (Physical Element, Virtual Element, Data, Services, Connections). [START_REF] Julien | Typology of Manufacturing Digital Twins: A First Step Towards A Deployment Methodology[END_REF] proposed a typology composed of 11 elements, allowing to draw up the profile of the digital twin to be developed in the first stages of this process, this was validated thereafter by [START_REF] Blanchet | Typology as a Deployment Tool for Digital Twins: Application to Maintenance in Industry[END_REF] on maintenance applications. As for the interactions that this technology could have with its environment, [START_REF] Julien | Integrating Lean Data and Digital Sobriety in Digital Twins through Dynamic Accuracy Management[END_REF] looked at the different surroundings with which the DT would come to interact, as well as the effects that this could have on its evolution in operation. While [START_REF] Kamoise | Using Cognitive Work Analysis to deploy collaborative digital twin[END_REF] focused on the human aspects of this interaction.

For their part, [START_REF] Hamzaoui | Social Cyber-Physical Systems and Digital Twins Networks: A perspective about the future digital twin ecosystems[END_REF] were more interested in the modes of use of this technology from the point of view of the precision and complexity of the models as well as the rate of synchronization, according to the needs and uses. Although the digital twin is seen as a powerful tool for improving decision making, there are still challenges to overcome in order to get the most out of it. A key challenge is reconciling the accuracy of the data used to create the digital twin with the amount of data available [START_REF] Yu | Data reconciliation-based simulation of thermal power plants for performance estimation and digital twin development[END_REF]. In addition, there is a need to develop methods to manage the data in real time and ensure its quality. Finally, it is important to develop solutions to integrate the digital twins into existing systems seamlessly and efficiently [START_REF] Qian | Digital Twin-Cyber Replica of Physical Things: Architecture, Applications and Future Research Directions[END_REF].

B. Lithium Battery:

The state of the art in the design and development of new lithium batteries has been the subject of a large amount of research in recent years, due to the rapid growth of the portable and electric technology industry. Lithium batteries are considered the most promising for mobile and electric vehicle applications due to their high energy density and low cost.

The first step in designing new lithium batteries is to optimize the anode material. Conventional anode materials used for lithium batteries include graphite and graphite composites, but these materials have limitations in terms of energy density and stability [START_REF] Wang | Toward Practical High-Energy and High-Power Lithium Battery Anodes: Present and Future[END_REF]. New anode materials under development include metals such as lithium metal, silicon, and silicon alloys [START_REF] Sun | Intermetallic Interphases in Lithium Metal and Lithium Ion Batteries[END_REF].

The second step in the design of new lithium batteries is to optimize the cathode material. Conventional cathode materials used for lithium batteries include lithium oxides, such as LiCoO2 and LiMn2O4, but these materials also have limitations in terms of energy density and durability [START_REF] Shen | Advanced Electrode Materials in Lithium Batteries: Retrospect and Prospect[END_REF]. New cathode materials in development include lithium sulfides and lithium phosphates [START_REF] Vernardou | Recent Report on the Hydrothermal Growth of LiFePO4 as a Cathode Material[END_REF]. Finally, it is important to develop new electrolytes to improve the stability and durability of lithium batteries. Conventional electrolytes used for lithium batteries include organic solvents such as acetonitrile and propylene carbonate, but these solvents have safety and stability limitations [START_REF] Niu | Recent Advances in Application of Ionic Liquids in Electrolyte of Lithium Ion Batteries[END_REF]. New electrolytes in development include solid electrolytes and protective membranes [START_REF] Xu | Water-Stable Sulfide Solid Electrolyte Membranes Directly Applicable in All-Solid-State Batteries Enabled by Superhydrophobic Li+-Conducting Protection Layer[END_REF].

However, our partner in this study (the Otonohm company), aims to develop a new generation battery, which is innovative not from the point of view of the materials used, but rather from the internal architecture itself. Therefore, the possession of a Prototype Digital Twin would allow to have models offering the possibility of apprehending the conduct of the physical object, to simulate its behavior, as well as to evaluate its future performances according to various scenarios and modes of operation. Moreover, this prototype twin can be made to evolve into an Instance Digital Twin, which can be used during the operation of the battery at the customer's site in order to provide even more advanced services.

In this paper we present the main part of the conducted work in this perspective. In what follows, we will present the battery under development by our partner, the various tests carried out on it, as well as the various models developed to support the digital twin.

III. CASE STUDY:

A. Otonohm's technology

Othonohm is an engineering company that develops innovative solutions for lithium batteries. It has a breakthrough technology, the switched BMS, which aims to minimize losses in the power supply chain. Traditional batteries use a serial/parallel architecture where all the cells of the battery are already connected in the circuit, whereas in the switched BMS technology, the cells are not connected in a serial/parallel configuration, but are individually isolated and are put in series/parallel by means of switches according to the control commands provided by the micro-controllers. Currently, this technology allows batteries to deliver any type of signals and voltages by adding or removing cells in series without using a converter or inverter. In this study we chose one of Otonohm's prototypes to deploy the digital twin.

B. Battery pack 48V

A 48V battery pack was developed with a slave board divided into 4 slave blocks each consisting of 4 Sony VTC6 cells (Figure 1). There is also a power supply block and a master block. The pack is capable of charging and discharging at 48V. The cell voltage varies between 4.1V and 2.8V. To have the possibility of intelligent management of the battery and to optimize its functionality, we studied the deployment of a digital twin of the pack.

C. Battery modeling

One of the main steps for a digital twin is to have a model that matches its physical object well. The strategy adopted here is to first model the cell and then build a model of the pack using MATLAB/Simulink. There are a wide variety of cell models, which have been developed with different complexities that can be used in various application areas. An important factor in modeling a cell is parameter estimation. Different modeling strategies for extracting battery parameters are electrochemical, mathematical, circuit-oriented, and datadriven. In real-world applications, battery models are used to predict operating voltage, power and energy capacity to ensure reliable performance and safety. Battery models are critical to the development of accurate algorithms for estimating battery condition, such as state of health (SOH) and state of charge (SOC). Considering the research objective and application, the Equivalent Circuit Model (ECM) was chosen.

1) The ECM model: Currently, the equivalent circuit model (ECM) is widely used due to its simplicity. When modeling the dynamic behavior of a cell, accuracy and complexity are two important factors. The ECM effectively satisfies both of these factors. ECM uses different combinations of electrical components such as resistance, capacitance, voltage source to simulate the charging and discharging characteristics of lithium-ion cells. The model is simple but represents the non linearity of the cell very accurately. The model is composed of a resistor R0 and resistors Rn each in parallel with a capacitor Cn. The accuracy of the n-RC model increases with the number of resistors and capacitors in parallel [START_REF] Lai | A comparative study of different equivalent circuit models for estimating state-of-charge of lithiumion batteries[END_REF] [START_REF] He | Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach[END_REF]. However, the accuracy of the model with 2 resistors-capacitors in parallel is sufficient considering the accuracy and complexity of the model which increases very greatly when the number of resistors-capacitors in parallel increases [START_REF] Lai | A comparative study of different equivalent circuit models for estimating state-of-charge of lithiumion batteries[END_REF] (Figure 2). In this paper, the 2-RC model is finally chosen as the equivalent battery circuit model.

In the circuit model, Uoc represents the open circuit voltage; RQ is the internal resistance of the cell; circuits R1 and C1 are used to simulate the rapid voltage rise process of the cell; circuits R2 and C2 are used to simulate the slow voltage stabilization process; R1 and R2 are the internal biased resistances of the cell, and C1 and C2 are the biased capacitances of the cell. In this model, the steady state and transient Characteristics of the cell can be best simulated by the two RC circuits [START_REF] Johnson | Battery performance models in ADVISOR[END_REF].

D. Experimental protocol

In order to capture the dynamic characteristics of the cell accurately, a test was performed (Figure 3). The test is divided into three steps: (1) Capacitance test, (2) SOC-OCV test and (3) Hybrid Pulse Power Characterization (HPPC) test (Figure 4). This test measures the cell capacity in ampere-hours using a constant current equal to 1C. The discharge ends at a discharge voltage limit specified by the manufacturer. The one-hour rate (1C) is used as a reference for the static capacitance measurement and as a "standard" for the subsequent stages of the test. The capacitance measurement is performed to confirm the rated capacity of the cell and to ensure that the 1C current is accurate. To perform these tests, the cells were placed in an environmental chamber at 25°C for 2h, and then they were charged with constant current (CC) at 1C up to 4.2V and then the voltage is kept constant (CV) until a current equal to C/10. Then they were discharged in CC at 1C to 2.5V. Between each step a 30 minute pause was performed (Figure 5).

2) The OCV-SOC Test:

The characterization of the open circuit voltage (OCV) is to determine experimentally its correlation with the state of charge. To measure the OCV, one method consists in discharging the cell initially charged with a very low current compared to its capacity until 0%. Since the cell can be considered in a quasi-steady state during the solicitation at a low current, its voltage during the solicitation can therefore be considered as the OCV. In this study the test was performed at 25°C. For this purpose a discharge was made in DC at C/25 up to 2.5V and after a charge was made in DC at C/25 up to 4.2V then CV up to a current equal to C/250. Between each step a 30 minutes break was performed (Figure 6) 3) The HPPC Test:

The HPPC test protocol has been proposed in international standards. It consists of applying a train of current pulses in charge and discharge and then measuring the voltage response to each pulse. From the analysis of this voltage response, the model parameters can be extracted. In order to establish the parameters of the equivalent electrical circuit, the entire range of the SOC must be scanned. Pulses should be applied in charge and discharge to study the effect of the current direction on the evolution of the parameters. And finally, the whole test is to be repeated at different temperatures in order to integrate its effect on the battery behavior. In this study we have done the test at 25°C (Figure 7).

E. The cell model

The tests performed allow us to find the parameters of the cell as well as to model the cell. Figure 8 shows the cell model on Simulink. In this equivalent circuit model, the voltage is the output, and the current is the input, while OCV, R0, R1, C1, R2 and C2 are the parameters of the model and are a function of the SOC of the cell. Thanks to the cell model, the block composed of 4 cells has been built (Figure 9). Once the block model is complete, the pack model with the 4 connected blocks is built.

IV. RESULTS

In an attempt to validate the models, two comparisons were made. First, the cell model was compared to the validation test results. Second, the pack model was compared to the 48V pack cycling result.

A. Cell model validation experiments

In order to validate the models, fully charged cells were discharged to 1C for 5 minutes and then allowed to rest for 30 minutes. This step was repeated 3 times. Then they were discharged with a current equal to 1C up to 2.5V. The experimental current data was used as the input for the cell model, and the model voltage was then calculated as the output using MATLAB/Simulink. The predicted voltage from model was then compared to the experimental voltage to evaluate the model performance (Figure 10).

It is possible to say that the cell model performed relatively well in predicting the voltage, given that the root mean square error (RMSE) is relatively small, at 0.0252V. However, it is important to note that even a small error can have a significant impact on system performance. This cell model was used to build the 48V pack model.

B. Pack model validation experiments

Concerning the architecture of the battery pack, the model of the pack has been developed on Simulink. To verify the pack model a validation test was performed using the 48V pack (Figure 11). The test consisted of a cycling of the pack. The cells were switched every 30 ms. This means that Fig. 10. Validation test of the cell model every 30 ms, the software sorts the cells by voltage. If the pack is charged, the software disconnects the three cells with the highest voltage, if the pack is discharging, the software disconnects the three cells with the lowest voltage. Thus, at any given time, only 13 cells are connected, and 3 cells are set aside. The test was performed in a test chamber with a controlled ambient temperature of 25°C. To charge the pack, a constant current of 3A (equivalent to a 1C load) was applied and to discharge the pack, a constant current of 10A was applied. To compare with the model made on MATLAB, only the first three cycles were used because the model does not take into account cell aging. The result shows that there is a difference between the voltage output of the real pack and the voltage output of the model. There are reasons that can explain this difference.

• Our model does not take into account the internal temperature of the cells which can vary due to their internal resistance and cause changes in the cell voltage. • The components used in the real pack such as MOSFET (metal-oxide-semiconductor field-effect transistor) or operational amplifiers have not been modeled in Simulink due to the complexity required to simulate these components.

• The voltage of the modeled cell is not a perfect representation and the cumulative error of the 16 cells in the model make the error more pronounced in the pack model.

V. CONCLUSION In this paper, we have dealt with a topical issue, which is the development of new generation lithium-ion batteries, an important technology of the ecological transition. This, by using a technology just as topical, which is the Digital Twin (DT). By means of a digital twin of the "prototype" type, we were able to model our physical object of interest (the battery), in order to carry out various simulations, allowing us to better understand the behavior of this technology before moving on to its physical manufacture. Moreover, although this model is relatively accurate, it does not fully represent the operation of the real pack, it is therefore necessary to continue to improve its accuracy and reliability. To do so, we aim to act jointly on the models and on the data, on the one hand by using more accurate models or other modeling approaches (as physical-chemical models), and on the other hand by feeding the digital twin with new tests, and new data sets. These new data will also allow the development of new types of models, such as data-driven models (as machine learning models for example). Finally, once the first physical versions of the battery have been manufactured, it will be a question of evolving this "prototype" digital twin into an "instance" digital twin, by setting up bidirectional communication mechanisms between the digital twin and its physical counterpart (the battery) in order to ensure a certain level of synchronisation. This will allow the DT to offer various services depending on the use that will be made of the battery in operation.

Fig. 1 .

 1 Fig. 1. The 48V pack with 16 cells.

Fig. 2 .

 2 Fig. 2. Equivalent circuit model 2-RC

Fig. 3 .Fig. 4 .

 34 Fig. 3. The tests on the 4 cells of Sony VTC6

Fig. 5 .

 5 Fig. 5. The Capacity Test

Fig. 7 .

 7 Fig. 7. The HPPC Test

Fig. 8 .

 8 Fig. 8. The Cell Model

Fig. 9 .

 9 Fig. 9. The block model

Fig. 11 .

 11 Fig. 11. Validation test of the pack model


Thibaud Sarica
email: thibaud.sarica@enpc.fr

Alice Maison

Yelva Roustan

Matthias Ketzel

Steen Solvang Jensen

Youngseob Kim

Christophe Chaillou

Karine Sartelet
email: karine.sartelet@enpc.fr

Modelling concentration heterogeneities in streets using the street-network model MUNICH

Populations in urban areas are exposed to high local concentrations of pollutants, such as nitrogen dioxide and particulate matter, because of unfavourable dispersion conditions and the proximity to traffic. To simulate these concentrations over cities, models like the street-network model MUNICH (Model of Urban Network of Intersecting Canyons and Highways) rely on parameterizations to represent the air flow and the concentrations of pollutants in streets. In the current version, MUNICH v2.0, concentrations are assumed to be homogeneous in each street segment. A new version of MUNICH, where the street volume is discretized, is developed to represent the street gradients and to better estimate peoples' exposure. Three vertical levels are defined in each street segment. A horizontal discretization is also introduced under specific conditions by considering two zones with a parameterization taken from the Operational Street Pollution Model (OSPM). Simulations are performed over two districts of Copenhagen, Denmark, and one district of greater Paris, France. Results show an improvement in the comparison to observations, with higher concentrations at the bottom of the street, closer to traffic, of pollutants emitted by traffic (NO x , black carbon, organic matter). These increases reach up to 60 % for NO 2 and 30 % for PM 10 in comparison to MUNICH v2.0. The aspect ratio (ratio between building height and street width) influences the extent of the increase of the first-level concentrations compared to the average of the street. The increase is higher for wide streets (low aspect ratio and often higher traffic) by up to 53 % for NO x and 18 % for PM 10 . Finally, a sensitivity analysis with regard to the influence of the street network highlights the importance of using the model MUNICH with a network rather than with a single street.

Introduction

Pollution is estimated to have been responsible for approximately 9 million premature deaths in 2015 [START_REF] Landrigan | The Lancet Commission on pollution and health[END_REF]. This figure remains valid in 2019 despite an improvement in the types of pollution associated with extreme poverty (e.g. household air pollution and water pollution) [START_REF] Fuller | Pollution and health: a progress update[END_REF]. This is partly due to an increase in the number of premature deaths attributable to ambient air pollution. The consequences of air pollution are particularly substantial in urban areas, where individuals are exposed to local high concentrations of air pollutants due to unfavourable dispersion conditions and proximity to traffic. As more than half of the world's population already lives in urban areas, with this being expected to rise to 68 % by 2050 (United Nations, 2019), it is crucial to estimate as accurately as possible the exposure of the population to atmospheric pollutant concentrations in urban areas. For many years, various modelling approaches have been developed to contribute to the understanding of the phenomena that drive the concentrations of pollutants in the atmosphere and to provide decision support tools [START_REF] Collett | Air quality modelling: a technical review of mathematical approaches[END_REF][START_REF] Vardoulakis | Modelling air quality in street canyons: a review, Atmos[END_REF]El-Harbawi, 2013;Conti et al., 2017;Khan and Quamrul, 2021).

Published by Copernicus Publications on behalf of the European Geosciences Union.

T. Sarica et al.: Modelling concentration heterogeneities in streets using the street-network model MUNICH Regional-scale chemistry transport models, such as Po-lair3D (Mallet et al., 2007;[START_REF] Sartelet | Emission of intermediate, semi and low volatile organic compounds from traffic and their impact on secondary organic aerosol concen-trations over Greater Paris[END_REF], CHIMERE (Menut et al., 2021;[START_REF] Falasca | High-resolution air quality modeling: Sensitivity tests to horizontal resolution and urban canopy with WRF-CHIMERE[END_REF], and CMAQ (Wong et al., 2012;[START_REF] De La Paz | Implementation of road dust resuspension in air quality simulations of particulate matter in Madrid (Spain)[END_REF], represent the urban background concentrations by solving the chemistry transport equation for spatial resolutions down to 1 km 2 . However, they cannot represent street concentrations, which are often higher than background concentrations for pollutants such as NO 2 and particles (Lugon et al., 2020). To represent these concentrations, local-scale models are thus developed with different approaches of variable complexity and computational cost. Models based on computational fluid dynamics (CFD), such as code_saturne [START_REF] Archambeau | Code Saturne: A Finite Volume Code for the computation of turbulent incompressible flows -Industrial Applications[END_REF][START_REF] Gao | High resolution unsteady RANS simulation of wind, thermal effects and pollution dispersion for studying urban renewal scenarios in a neighborhood of Toulouse[END_REF], OpenFoam (Lin et al., 2023), and PALM (Wolf et al., 2020), are able to represent the dispersion of pollutants and the physicochemical processes taking place in urban districts and streets with a fine spatial resolution by solving the Navier-Stokes equations and mass conservation equations for pollutants. However, they suffer from high computational cost as they use fine meshes to describe the morphology of buildings and streets. Other models use approaches that are less accurate than CFD but that run faster. They are typically based on a Gaussian or an Eulerian approach [START_REF] Vardoulakis | Modelling air quality in street canyons: a review, Atmos[END_REF][START_REF] Liang | Vehicle Pollutant Dispersion in the Urban Atmospheric Environment: A Review of Mechanism, Modeling, and Application[END_REF]. Among these, the following can be mentioned: ADMS-Urban [START_REF] Mchugh | ADMS and ADMS-Urban[END_REF][START_REF] Hood | Comprehensive evaluation of an advanced street canyon air pollution model[END_REF], SIRANE [START_REF] Soulhac | The model SIRANE for atmospheric urban pollutant dispersion; part I, presentation of the model[END_REF][START_REF] Soulhac | Evaluation of Photostationary and Non-Photostationary Operational Models for NOX Pollution in a Street Canyon[END_REF], AERMOD [START_REF] Cimorelli | AERMOD: description of model formulation[END_REF][START_REF] Rood | Performance evaluation of AERMOD, CALPUFF, and legacy air dispersion models using the Winter Validation Tracer Study dataset[END_REF], EPISODE (Karl et al., 2019), and CALIOPE-Urban [START_REF] Amato | Vertical and horizontal fall-off of black carbon and NO 2 within urban blocks[END_REF]. Either they consider each street independently of the others with exchanges between the street and the background concentrations above the street (Berkowicz, 2000b), or they consider a street network with incoming and/or outcoming flows between streets at intersections [START_REF] Soulhac | Flow and dispersion in street intersections[END_REF][START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF]. The Operational Street Pollution Model (OSPM) couples a Gaussian plume model for traffic emissions and a box model for the recirculation in the street (Berkowicz, 2000b). It is thus able to represent concentration heterogeneities in the street but cannot include complex chemistry. The Model of Urban Network of Intersection Canyons and Highways (MUNICH) uses solely an Eulerian box model approach (Lugon et al., 2020). As MUNICH is coupled with the SSHaerosol model [START_REF] Sartelet | SSH-Aerosol v1.1: A Modular Box Model to Simulate the Evolution of Primary and Secondary Aerosols[END_REF], the formation and ageing of primary and secondary gas and particles in streets are represented. In the current version of MUNICH (v2.0) [START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF], concentrations are considered to be homogeneous in each street segment. However, as shown by several on-site and modelling studies, the concentrations are very heterogeneous in streets with traffic emissions [START_REF] Xie | Spatial distribution of traffic-related pollutant concentrations in street canyons, Atmos[END_REF][START_REF] Vardoulakis | Intra-urban and street scale variability of BTEX, NO 2 and O 3 in Birmingham, UK: Implications for exposure assessment[END_REF][START_REF] Lateb | On the use of numerical modelling for near-field pollutant dispersion in urban environments -A review[END_REF]Sanchez et al., 2016;[START_REF] Amato | Vertical and horizontal fall-off of black carbon and NO 2 within urban blocks[END_REF]Lin et al., 2023). They are higher near the ground than at the top of the street, especially for primary pollutants.

A heterogeneous version of MUNICH is developed in this study, with the aim of representing the concentration heterogeneities in the street while keeping the Eulerian approach of MUNICH to retain its ability to accurately model chemistry and aerosol dynamics. The street volume is discretized vertically in three subvolumes. Traffic emissions are not instantaneously diluted in the whole street volume, as in MUNICH v2.0, but only in the first subvolume, i.e. the one closest to the ground. With this discretization we do not aim to reproduce finely the vertical profile of concentrations. The main objective is to improve the representation of concentrations close to the ground by avoiding the excessive dilution associated with the homogeneity assumption. To represent the streets' horizontal heterogeneities, a recirculation zone in the shape of a trapeze is defined based on a parameterization of OSPM. It depends on the meteorological conditions and the street morphology, and it is applied under specific conditions in MUNICH that are described later.

A description of the differences between the homogeneous version of MUNICH (v2.0) and the new heterogeneous version is presented in Sect. 2. The applications to two street networks in Copenhagen, Denmark, with comparisons to observations of NO 2 and CO, and to concentrations simulated by OSPM are discussed in Sect. 3. MUNICH is applied in Sect. 4 to the street network near Paris, France, used to validate MUNICH v2.0 [START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF], and the impacts of the heterogeneous version on concentrations of NO 2 and particles are studied. To estimate the impact of the modelling hypothesis on the transport of pollutants between streets in the new version of MUNICH, a sensitivity analysis with regard to the presence of a street network is performed in Sect. 5.

Model description

The homogeneous version of MUNICH (v2.0) and the new heterogeneous version (see Fig. 1) are briefly described in this section, with a focus on the differences between the two versions. The heterogeneous version was developed from MUNICH v2.0. In the following, the homogeneous and heterogeneous versions of MUNICH are referred to as MUNICH-homo and MUNICH-hete, respectively. For a complete description of MUNICH, please refer to Kim et al. (2018[START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF] and Lugon et al. (2020Lugon et al. ( , 2021a)).

In order to solve the evolution equation of the street concentrations C str , a first-order operator splitting between transport and chemistry is performed:

dC str dt = dC str dt tr + dC str dt ch . (1)
The transport term includes advection from one street to another and vertical transport between the street and the background above it. The chemistry includes gas-phase chemistry, as well as aerosol dynamics (coagulation, condensation, and evaporation). As deposition and resuspension processes have minor effects compared to transport and chemistry (Lugon et al., 2021b;[START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF], they are omitted in the rest of this study.

Homogeneous approach

Using a box model approach, the concentrations are assumed to be homogeneous in the whole street volume, and the effects of the processes on the concentrations are represented by the following equation:

dC str dt tr = 1 V (Q em + Q inflow + Q outflow + Q vert ) , (2)
where V is the volume of the rectangular cuboid street, Q em is the traffic emission flux, Q inflow is the flux entering the street via the upwind intersection, Q outflow is the flux leaving the street via the downwind intersection, and Q vert is the vertical turbulent flux between the background and the street. The street volume is defined as V = H W L, with H being the average building height over the street segment, W being the mean street width, and L being its length. MUNICH considers it to be that buildings on each side of the street are continuous, thus not representing inflow and/or outflow that could be induced by gaps in the buildings. The inflow term Q inflow is obtained from the computation of the fluxes at the upwind intersection (Kim et al., 2018;[START_REF] Soulhac | Flow and dispersion in street intersections[END_REF] (see Sect. 5 for a brief description). The outflow term Q outflow is expressed as follows:

Q outflow = H W u str C str , (3)
with u str being the mean horizontal wind speed in the street.

The vertical turbulent flux Q vert between the street and the overlying atmosphere is

Q vert = q vert W L C str -C bkgd H , (4)
with q vert being the vertical transfer coefficient and C bkgd being the background concentration.

The vertical transfer coefficient and the horizontal wind speed are the key parameters representing the dispersion of concentrations. As their formulation differs between the homogeneous and the heterogeneous versions of MUNICH, they are now detailed.

Vertical transfer coefficient for turbulent flux

Three parameterizations are implemented in MUNICH to determine the vertical transfer coefficient q vert between the street and the overlying atmosphere [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF]. However, currently, only the parameterization adapted from Wang (2014) is designed to provide vertical profiles for both wind speed and mixing length within the street. We therefore limit our analysis to the latter.

In MUNICH-homo, the vertical transfer coefficient at the roof level is expressed as follows:

q vert = σ w l m (z = H ) with l m (z) = κz l c l c + κz , (5)
where σ w is the standard deviation of the vertical wind velocity at roof level, and l m is the mixing length defined as a harmonic mean between two length scales [START_REF] Coceal | A canopy model of mean winds through urban areas[END_REF], namely (i) κz, with the Von Kármán constant (κ = 0.42), and (ii) l c , which is a characteristic length of the street chosen to be equal to 0.5W [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF].

Mean horizontal wind speed in the street

As for the calculation of the vertical transfer coefficient, three parameterizations are proposed in MUNICH to determine the mean horizontal wind speed in the street [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF]. In the wind speed in the street u str is equal to

u str = 1 H -z 0s H z 0s u Y (z)dz = u H | cos(ϕ)| (H -z 0s ) H z 0s J 1 I 0 (g(z)) + J 2 K 0 (g(z)) dz, ( 6
)
with u H | cos(ϕ)| being the wind speed at roof level in the direction of the street and z 0s being the wall and ground roughness length in the street (fixed to 0.01 m). I 0 and K 0 are the first-and second-kind modified Bessel functions of order 0. J 1 and J 2 are integration coefficients equal to

J 1 = 1 I 0 (g(H )) -I 0 (g(z 0s ))K 0 (g(H ))/K 0 (g(z 0s ))
and

J 2 = - J 1 I 0 (g(z 0s )) K 0 (g(z 0s )) . ( 7
)
The function g(z) is calculated as follows:

g(z) = 2 C B a r z l m (H ) , (8)
with a r = H /W being the aspect ratio of the street and C B being a coefficient that is dependent on the wind angle with the street and the aspect ratio [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF].

Heterogeneous approach

In MUNICH-hete, the street is divided into three vertical levels to limit the artificial dilution of the traffic emissions and the concentrations in the whole street volume (see Figs. 1b and2). Levels are ordered from the ground to the top of the street. The first level (i = 1) contains the traffic emissions. The thickness h 1 is taken as 2 m, which corresponds to a zone where the traffic producing turbulence mixes and dilutes traffic emissions [START_REF] Solazzo | Modelling wind flow and vehicle-induced turbulence in urban streets[END_REF]. This trafficinduced turbulence is not explicitly considered in the model. The second-level (i = 2) thickness h 2 is also of 2 m. It acts as a buffer zone between the first level, where traffic emissions are, and the third level, where exchanges with the background take place. Starting at 4 m, the third level (i = 3) goes to the roof level (h 3 = (H -4) m). The minimum street height considered in the model is set at 6 m. The three levels of the heterogeneous version are referred to as MUNICHhete-l1, MUNICH-hete-l2, and MUNICH-hete-l3. Each level i is thus associated with a specific volume V i , and the evolution equations may be written as follows: where Q i em is the traffic emission flux (only in the first level (i = 1)), Q i inflow is the flux entering the level via the upwind intersection, Q i outflow is the flux leaving the level via the downwind intersection, Q i,i+1

dC i str dt tr = 1 V i Q i em + Q i inflow + Q i outflow + Q i,i+1 vert + Q i-1,i vert , (9)
vert is the vertical turbulent flux between the levels i and i + 1 (for i = 3, it is exchanged with the background), and Q i-1,i vert is the vertical turbulent flux between the levels i -1 and i (equal to zero if i = 1).

Note that more than three vertical levels could be defined in MUNICH-hete as the vertical variations within the streets of winds and mixing lengths are parameterized when discretizing the streets. However, the first vertical level at the bottom of the street should not be too thin because of mixing due to traffic turbulence. A minimum height for the first layer of 1.5 m seems reasonable.

In OSPM, the flow that develops into a vortex in the street between buildings is represented by a recirculation zone. It occupies the whole street volume for narrow streets, and it has the shape of a trapeze for wider streets [START_REF] Berkowicz | Modelling traffic pollution in streets[END_REF]Berkowicz, 2000b;Ottosen et al., 2015). When the recirculation zone does not occupy the whole street volume, there is a ventilation zone (see Fig. 2) where concentrations of pollutants emitted by traffic are usually lower than in the recirculation zone. In MUNICH-homo, the recirculation zone is not explicit, whatever the street ratio (H/W) is. In MUNICH-hete, the volume of the recirculation zone is computed as in OSPM, as detailed in Appendix A. For now, concentrations in the ventilation zone are considered to be homogeneous and equal to the background concentrations, i.e. concentrations above the street. The ventilation zone is thus taken into account when it is not affected by traffic emissions. In practice, this means that the width of the trapeze base can only be equal to or larger than the width W of the street (see Appendix A). The width W i of the level i can thus be inferior to the width W of the street, reducing the level volume (see Fig. 2). Appendix A presents the algorithm implemented in MUNICH-hete to consider the volume reduction of the ventilation zone. Further work is needed to differentiate the two zones for cases where the ventilation zone develops further into the street.

To quantify mass transfer through the intersections, the fluxes are assumed to be vertically homogeneous and remain determined as proposed by [START_REF] Soulhac | Flow and dispersion in street intersections[END_REF] as the shapes of the intersections may differ from one to another, and turbulence is not quantified. The flux Q inflow entering the street is assumed to be the same for each vertical level. The flux Q outflow leaving a street is a surface-weighted average of the fluxes leaving each vertical level of the street:

Q outflow = i=3 i=1 Q i outflow = i=3 i=1 S v i u i C i str , (10)
with S v i being the vertical surface of the level i, as presented in Appendix A, and u i being the mean horizontal wind speed of the level i (see Sect. 2.2.2).

Vertical turbulent fluxes

To compute the vertical turbulent transfer Q i,i+1

vert at the interface of the vertical levels i and i + 1, Eq. ( 4) is modified to represent the vertical exchanges between the levels i and i + 1:

Q i,i+1 vert = q i vert W i L (C i -C i+1 ) z m i , (11)
where C i and C i+1 are the concentrations in the levels i and i +1 respectively; W i is the width of the level i that is inferior or equal to the width W of the street; and z m i is the difference in altitude between the middles of the levels i + 1 and i, which are as noted z m 1 , z m 2 , and z m 3 (see Fig. 2). For i = 3, i.e. the highest level, z m i+1 is taken as the symmetrical of z m 3 to the roof level and is noted as z m bkgd . It gives an approximation of the volume that effectively exchanges with the third level.

Among the three parameterizations implemented in MU-NICH to determine the vertical transfer coefficient q vert , only the Wang parameterization is adapted to the discretization. It is thanks to its explicit vertical dependency and validity for a wide range of street canyon and wind characteristics [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF]. To compute the vertical turbulent transfer

Q i,i+1
vert , the vertical transfer coefficient is taken at the height of the interface between the two vertical levels considered, and Eq. ( 5) is now written as follows:

q i vert = σ w κz i l c l c + κz i , (12)
where z i is the height of the interface between levels i and i + 1. The influence of the atmospheric stability on vertical mixing is taken into account by modifying the standard deviation of the vertical wind velocity at roof level and thus the vertical transfer rate, depending on the length of Monin-Obukhov, as in MUNICH-homo.

By combining Eqs. ( 11) and ( 12), the vertical turbulent transfer Q i,i+1 can be written for each level as follows:

Q 1,2 vert = σ w κz 1 l c l c + κz 1 W i L C 1 -C 2 z m 2 -z m 1 , (13)
Q 2,3 vert = σ w κz 2 l c l c + κz 2 W i L C 2 -C 3 z m 3 -z m 2 , ( 14
) Q 3,bkgd vert = σ w κH l c l c + κH W i L C 3 -C bkgd z m bkgd -z m 3 , (15)
with C 1 , C 2 , C 3 , and C bkgd being the concentrations of the three levels and the background respectively.

Mean horizontal wind speed in the street

As for the vertical turbulent flux, the Wang parameterization is preferred among the three parameterizations available in MUNICH to compute the mean horizontal wind speeds in the street. This is thanks to its explicit vertical dependency and the no-slip condition at the ground that is always satisfied (u(z = 0) = 0) [START_REF] Maison | Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne[END_REF]. Therefore, the mean horizontal wind speed can be computed at each level in the street by modifying Eq. ( 6) to integrate vertically between the level heights:

u 1 = 1 z 1 -z 0s z 1 z 0s u Y (z)dz, (16)
u 2 = 1 z 2 -z 1 z 2 z 1 u Y (z)dz, (17)
u 3 = 1 H -z 2 H z 2 u Y (z)dz, (18)
with z 1 and z 2 being the limits of the first two levels, as presented in Fig. 2. simulations are performed only for the streets where there are observations. Thanks to its coupled approach of a Gaussian plume model and a box model, OSPM is able to calculate concentrations on the two sides of the street [START_REF] Berkowicz | Modelling traffic pollution in streets[END_REF]Berkowicz, 2000b;Ottosen et al., 2015). Two receptors are used to compare with the observed concentrations on each side of the street: OSPM-R1 and OSPM-R2. The height of the receptors is taken as 2 m to correspond roughly to the height at which observations were performed. They are compared to the concentrations simulated at the first two levels of MUNICH-hete, which are representative of the concentrations at 1 and 3 m. MUNICH and OSPM use the same input data to estimate the street concentrations. The meteorological parameters originate from simulations performed with the Weather Research and Forecasting model (WRF, [START_REF] Skamarock | A Description of the Advanced Research WRF Version 3[END_REF]. The background concentrations are simulated using the Urban Background Model (UBM, Berkowicz, 2000a), which is "a multiple source model that applies a Gaussian approach for horizontal dispersion and a linear approach for vertical dispersion up to the boundary layer" (Jensen et al., 2016). Traffic emissions are generated using the procedure implemented in the local-scale Gaussian air pollution model OML-Highway [START_REF] Olesen | User Guide to OML-Highway. A tool for air pollution assessments along highways[END_REF], allowing for precise information for each street segment. Traffic data (average daily traffic, travel speed, and share of heavy-duty vehicles) are used to generate emissions by use of the European emission model COPERT IV. Traffic emissions include exhaust emissions of gases and particles and non-exhaust emissions of particles. Non-exhaust emissions consist of brake, tyre, and road wear. The street parameters (building height and street width) used in MUNICH originate from the OSPM setups.

3
OSPM represents NO 2 and O 3 chemical transformations using a system of two reactions [START_REF] Berkowicz | Modelling traffic pollution in streets[END_REF]Berkowicz, 2000b). The first one describes the production of NO 2 due to the reaction of NO with O 3 , and the second one describes the photodissociation of NO 2 that leads to the reproduction of NO and O 3 . For a fair comparison, MU-NICH is configured to run with a simple chemistry scheme, the Leighton photostationary state for O 3 [START_REF] Leighton | Photochemistry of air pollution[END_REF]Kim et al., 2018):

NO 2 + hν → NO + O( 3 P), (R1) O( 3 P) + O 2 + M → O 3 + M, (R2) NO + O 3 → NO 2 + O 2 . (R3)
3.1 H. C. Andersens Boulevard H. C. Andersens Boulevard is a wide, densely trafficked boulevard, with an aspect ratio a r = H /W of about 0.2 (H = 9.9 m, W = 50 m). It is open on one side with trees instead of buildings. This configuration can be represented in OSPM. However, in MUNICH, a mean building height is defined for each street. Here, it is estimated by averaging the building and the tree heights. The simulated street network is com-posed of 86 street segments centred around the street where the observation station is located (see brown cross in Fig. 4). Figure 3 presents the monthly averaged concentrations of CO and NO 2 from the OSPM and MUNICH simulations compared to observations. Appendix C contains monthly averaged concentrations of NO x and O 3 and statistical indicators of the comparison for all four pollutants. OSPM-R1 is the receptor that is close to the measurement station and is thus better suited to be compared to observations. Differences in the concentrations between OSPM-R1 and OSPM-R2 highlight the importance of taking into account the horizontal heterogeneities in the street. Observations lie between the concentrations simulated at the two receptors, except in the case of CO, for which OSPM slightly underestimates concentrations in the first half of the year. This underestimation could be linked to underestimation of sources other than traffic, e.g. biomass burning, at the regional scale but could also be due to the absence of volatile organic compounds in the simulation. Overall, the concentrations are well estimated with OSPM, with errors between 26 % and 33 % for CO and between 34 % and 46 % for NO 2 .

For CO, NO 2 , and NO x , which are emitted by traffic in the bottom of the street, the concentrations are higher in the first level, MUNICH-hete-l1, near the bottom and are lower in the third level, MUNICH-hete-l3, near the roof level. For O 3 , the opposite behaviour is observed as it is mainly imported by the atmosphere above the street, and it is titrated by NO near the ground. The first two levels, MUNICH-hete-l1 and MUNICH-hete-l2, have higher concentrations of CO, NO 2 , and NO x than munich-homo, thus improving the comparison to observations and OSPM concentrations. For CO, the error is improved from 36 % in MUNICH-homo to 28 % in MUNICH-hete-l1, and for NO 2 , it is improved from 48 % in MUNICH-homo to 35 % in MUNICH-hete-l1. Although the concentrations of NO 2 and CO are underestimated in MUNICH-homo compared to observations, they are well modelled in the first level, MUNICH-hete-l1, with low errors and biases (see Appendix C). For CO, the concentrations simulated in the first level, MUNICH-hete-l1, lie between the two OSPM receptors for most of the year. This is the case for NO 2 as well, except between April and August, when NO 2 concentrations are underestimated in MUNICH-hete compared to observations and OSPM concentrations. The formation of NO 2 in the lower levels (see Reaction R3) could be limited with the current model setup because volatile organic compounds are not taken into account in the Danish cases. However, they may participate in O 3 and NO 2 formation through HO 2 and RO 2 radicals [START_REF] Atkinson | Atmospheric chemistry of VOCs and NO x , Atmos[END_REF][START_REF] Kwak | A CFD modeling study of the impacts of NO x and VOC emissions on reactive pollutant dispersion in and above a street canyon[END_REF]Zhong et al., 2017;[START_REF] Dai | Modelling chemistry and transport in urban street canyons: Comparing offline multi-box models with large-eddy simulation[END_REF]. Furthermore, the vertical discretization is coarse, limiting O 3 transport deep into the street.

Over the whole street network, as presented in Fig. 4, the differences between the concentrations simulated in the first vertical level of MUNICH-hete and those simulated in MUNICH-homo vary. For wide streets and avenues with dense traffic, the concentrations are higher in MUNICHhete-l1 than in MUNICH-homo, with an increase of up to 23 % for CO and 30 % for NO 2 . This increase is lower in more narrow and less frequented streets. Although the concentrations in MUNICH-hete-l1 are always higher than those in MUNICH-homo for CO, for NO 2 , in narrow streets, the concentrations are lower in MUNICH-hete-l1. These lower NO 2 concentrations are probably related to the limited transport of O 3 from the background to the bottom of the street, limiting the titration of NO.

Jagtvej

Jagtvej is a conventional street canyon with an aspect ratio of about 0.8 (H = 20.3 m, W = 26.2 m). The simulated street network is composed of 265 street segments centred around the street where the observation station is located (see brown cross in Fig. 6). The monthly averaged concentrations of CO and NO 2 from the OSPM and MUNICH simulations compared to observations for NO 2 only are presented in Fig. 5. Appendix D contains monthly averaged concentrations of NO x and O 3 and statistical indicators of the comparison for NO 2 and NO x . OSPM-R2 is the receptor that is close to the measurement station and is thus better suited to be compared to observations. The differences between the concentrations of the two OSPM receptors are lower in JGTV than in HCAB (see Fig. 3). JGTV is narrower, with higher buildings on both sides, thus limiting the ventilation zone and the penetration into the street of background concentrations that would reduce the concentrations at the downwind receptor. OSPM tends to slightly overestimate NO 2 and NO x concentrations (with errors between 41 % and 53 % and between 42 % and 63 % respectively).

Concentrations from the homogeneous version of MU-NICH are close to OSPM concentrations for CO. They are lower than OSPM concentrations for NO 2 , but they compare well to observations, with a bias of -3 % and an error of 46 %. These lower NO 2 concentrations are linked to lower NO x concentrations (with a bias of -19 % compared to observations and an error of 53 %). As for HCAB, the MUNICH-hete concentrations decrease from the bottom to the top of the street. For CO and NO x , only the first level has concentrations higher than MUNICH-homo, while for NO 2 , all three levels have concentrations lower than MUNICHhomo. O 3 concentrations are also higher for the three levels (see Fig. D1). The NO x concentrations of MUNICH-hete-l1 compare slightly better to observations than MUNICHhomo, while MUNICH-homo is slightly better for NO 2 . However, the statistics of the two models are quite close (Appendix D).

Conclusions are similar for the whole street network (see Fig. 6). The CO concentrations are slightly higher in the first level of MUNICH-hete than in MUNICH-homo. However, NO 2 concentrations at the bottom of the street in the first level of MUNICH-hete tend to be lower than in MUNICHhomo. In some specific street segments of the network, the differences in the concentrations for both CO and NO 2 are higher in MUNICH-hete-l1 than in MUNICH-homo. This is due to a mix of different traffic emissions and street morphologies which favour the transport of pollutants.

Application to a street network in greater Paris

The impacts of the discretization on gas and particle concentrations are evaluated over the street network near Paris, France, which was used to validate MUNICH v2.0 [START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF] and in several sensitivity studies (Lugon et al., 2021b;[START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF]Sarica et al., , 2023b)). The street network represents a district of Le Perreux-sur-Marne, a suburb 13 km east of Paris, France. It is composed of 577 street segments (see Fig. 8). The street parameters (building height and street width) were obtained from the BD TOPO database (https: //geoservices.ign.fr/bdtopo, last access: 12 September 2023). Simulations were performed from 22 March to 15 June 2014 to generate hourly concentrations with input data (emissions, including exhaust emissions and brake, tyre, and road wear; meteorological parameters; and background concentrations) from the reference simulation SCN0 of Sarica et al. (2023b). For this case, MUNICH is coupled to SSH-aerosol [START_REF] Sartelet | SSH-Aerosol v1.1: A Modular Box Model to Simulate the Evolution of Primary and Secondary Aerosols[END_REF] to represent gas-phase chemistry and aerosol dynamics. Observational data are available for the whole simulation period for NO 2 , NO x , PM 2.5 , PM 10 , and black carbon (BC) for a segment of Boulevard d'Alsace Lorraine (see brown cross in Fig. 8). The simulations were performed at a height of about 2 m, and they are thus to be compared to the concentrations of the first two levels (i = 1 and i = 2) of MUNICH-hete. The segment has an aspect ratio of about 0.3 (H = 8.6 m, W = 26 m).

The average daily profiles of NO x and PM 10 concentrations are shown in Fig. 7, and NO, NO 2 , and the statistical indicators are shown in Appendix E1. As in the Danish streets, for pollutants emitted by traffic, the concentrations are higher in MUNICH-hete at the bottom of the street, decreasing to the roof level. The concentrations of PM 10 , NO 2 , NO x , and BC are higher on average by 12 %, 21 %, 40 %, and 30 % respectively in MUNICH-hete-l1 than in MUNICHhomo. The lower concentration difference for PM 10 than for the other compounds reflects the fact that non-traffic sources are more important for PM 10 , and inversely, they are small for BC. Despite the higher concentrations in MUNICH-hete-l1, BC concentrations remain strongly underestimated compared to observations, in agreement with the CFD simulations of Lin et al. (2023). For PM 10 , NO 2 , and NO x , the concentrations compare well to observations; e.g. the error is 33 % for NO 2 and 37 % for PM 10 , with slightly better statistics using MUNICH-hete-l1 than MUNICH-homo. For all pollutants, the concentrations of the intermediate level (i = 2) are very close to the concentrations of MUNICH- homo. This is due to a mixture of different parameters such as street morphology and dispersion conditions over the simulated period.

In streets, both BC and organic matter (OM) exhibit higher concentrations than in the background (Lugon et al., 2021a). OM consists of primary and secondary aerosols that are formed from the oxidation of volatile organic compounds and/or the condensation of semi-volatile organic compounds. Concentrations of both BC and OM simulated in MUNICHhomo and in the first level of MUNICH-hete are compared in Fig 8 (see Fig. E2 for NO 2 and PM 10 ). The concentrations simulated in MUNICH-hete-l1 are always higher than in MUNICH-homo. In most streets of the network that are narrow and limited in terms of traffic, the increase in concentrations is limited. It is more important for more open and frequented streets, such as the Boulevard d'Alsace Lorraine.

With BC being a primary inert pollutant emitted by traffic, its concentrations are strongly influenced by the discretization as emissions are no longer artificially diluted in the whole street volume. They are now constraint at the bottom of the street, inducing an average increase of 30 % compared to the homogeneous version. For OM and PM 10 , the increase is lower (16 % and 12 % respectively) because of the stronger influence of non-traffic sources.

Sensitivity analysis

In this section, the influence of the aspect ratio a r on the concentrations in the heterogeneous version of MUNICH is studied. The sensitivity of the heterogeneous version of MU-NICH to the presence of a street network, which influences the concentrations entering the street via the upwind intersection, is also estimated.

Influence of the aspect ratio

The aspect ratio a r , defined as the ratio between building height H and street width W , is used to determine general behaviours of streets with similar geometries. When a r is small, i.e. when W is larger than H , the street is wide, such as in the case of a boulevard or an avenue. On the other hand, when a r is large, i.e. when H is larger than W , the street is narrow and closer to a typical street canyon. In the three cases presented in this study in greater Paris and Copenhagen, streets with small a r are associated with higher traffic emissions.

Table 1 and Appendix F present the influence of the aspect ratio on concentrations in the first vertical level of the heterogeneous version of MUNICH, MUNICH-hete-l1, compared to the homogeneous version. It is quantified using the normalized mean bias (NMB). The homogeneous version of MUNICH presents higher concentrations of pollutants in wide streets (interval [0, 0.5[) in greater Paris due to higher traffic emissions compared to in narrower streets. The increase in the concentration in the first level as a result of using the heterogeneous version of the model is more important for wide streets (up to 53 % for NO x ). Concerning particles, PM 10 concentrations are increased by up to 18 %, while the increase is about 42 % and 23 % for BC and OM respectively. In streets with larger a r (interval [1, 1.5[), NO x concentrations are only 12 % higher than in the homogeneous version, and the PM 10 concentrations are only 2.5 % higher.

Concerning the two cases in Copenhagen, CO and NO x concentrations present similar behaviour in comparison to the greater Paris case. For the JGTV street network, the increase is limited compared to the HCAB network -3 % against 11.5 % respectively for CO. Wide streets (interval [0, 0.5[) have higher concentrations of NO 2 compared to the homogenous version of MUNICH, whereas for the other intervals of a r , they are lower. Thus, O 3 concentrations are lower for wide streets and larger for the other intervals. This could be linked to the lack of volatile organic compounds in these two Copenhagen cases.

Sensitivity to the street network

The computation of inflow and outflow fluxes at intersections is performed by estimating the balance of fluxes entering and leaving the intersection from the different street segments attached to it. If this balance is not perfect, there are exchanges with the atmosphere above the intersection. When the total flux entering the intersection is higher than the one leaving it, the flow overload is directed to the atmosphere. When the total flux leaving the intersection is higher, a flux from the atmosphere to the intersection is considered. A further explanation is available in Kim et al. (2018[START_REF] Sarica | Modelling Pollutant Concentrations in Streets: A Sensitivity Analysis to Asphalt and Traffic Related Emissions[END_REF].

Without a street network around the street segment of interest, the pollutant mass fluxes entering the street are determined from the background concentration. The contribution of the neighbouring streets is thus not taken into account, and concentrations of pollutants emitted in streets are expected to be lower than when there is a street network.

Table 2 and Appendix G present the influence of the neighbouring streets for the three cases of the study. It is quantified using the normalized mean error (NME) and NMB between the simulations without and with the neighbouring streets. As expected, without the street network, the concentrations are lower. The bias is between 12 % and 21 % for NO 2 , between 18 % and 27 % for NO x , and 14 % for BC. Biases are lower for OM and PM (2 %) because of the stronger influence of background concentrations for those compounds.

Conclusions

The street-network model MUNICH v2.0 has been modified to introduce concentration heterogeneities in the street and to better represent population exposure. To model the vertical gradients frequently observed, the streets were discretized with three levels, thus limiting the artificial dilution of emissions and concentrations. Based on a parameterization from OSPM, a ventilation zone is considered under specific conditions to represent horizontal heterogeneities. In order to test these developments, the heterogeneous version of MUNICH (MUNICH-hete) has been applied to two cases in Copenhagen, Denmark, with comparisons to OSPM, and to one case near Paris, France. Overall, MUNICH-hete improves the comparison to observations compared to the homogeneous version. The errors compared to observations are reduced by up to 20 % for NO x and up to 15 % for BC.

As expected, in MUNICH-hete, concentrations of compounds emitted by traffic (CO, NO 2 , NO x , PM 10 , BC, and OM) are higher at the bottom of the street than at the top. These increases can reach up to 60 % and 30 % for NO 2 and PM 10 respectively. The intermediate level, serving as a buffer, presents concentrations higher than or similar to the homogeneous version (MUNICH-homo). Finally, concentrations in the highest level, in direct contact with the atmosphere above the street, are the lowest of the street. For the A sensitivity study of the influence of the street network on concentrations in the streets shows the importance of considering neighbouring streets in MUNICH. When no network is considered, concentrations in the street are lower due to the overestimated impact of the atmosphere above. At the bottom of the street, concentrations of NO 2 and BC are reduced by up to 28 % and 14 % respectively without a network. PM and OM are less impacted, with a reduction of about 2 % due to a strong influence of non-traffic sources.

For the next step, the ventilation zone will be fully discretized vertically to facilitate the penetration of background concentrations into the bottom of the street. The horizontal exchange fluxes between the two zones will also be modelled. Deposition and resuspension processes that were not considered in this development will be added. The fluxes that are currently assumed to be vertically homogeneous will be discretized. Finally, chemistry of volatile organic compounds could be added in the Danish cases if the background concentrations and emissions are available. -Mean fractional bias (MFB):

MFB = 2 × s -o s + o .
-Factor of 2 (FAC2): fraction of data that satisfy 0.5

≤ s o ≤ 2.0.
For comparison of the simulations, the normalized mean bias (NMB) and normalized mean error (NME) are used. X represents concentrations, with X 0 being the reference simulation and X i being the compared simulation. The overbar represents the average.

-Normalized mean bias:

NMB = (X i -X 0 ) X 0 .
-Normalized mean error:

NME = |X i -X 0 | X 0 .
Appendix C: Additional information for HCAB

Figure 1 .

 1 Figure 1. Representation of the processes in the homogeneous version (a) and the heterogeneous version (b) of MUNICH. The dotted red lines represent the street volume. In (a), the street canopy is represented by a single volume, whereas in (b), it is divided into three subvolumes delimited by the dotted blue lines. The rose arrows represent the traffic emissions (including brake, tyre, and road wear), the light-green arrows represent the fluxes entering the street via the upwind intersection, and the dark-green arrows represent the fluxes leaving the street via the downwind intersection. The yellow arrows symbolize the vertical turbulent exchanges with the background, and in (b), the orange arrows symbolize the vertical exchanges among the subvolumes.

Figure 2 .

 2 Figure 2. Schematic of the discretization in MUNICH-hete. The red triangle represents the ventilation zone that is present under specific conditions, and the white trapeze represents the recirculation zone. z m i is the middle height of level i.

Figure 3 .

 3 Figure 3. Monthly averaged concentrations (in µg m -3 ) of CO (a) and NO 2 (b) at HCAB monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represents the three levels of the heterogeneous version of MUNICH -the lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) is shown with diamond markers. The solid red line represents the OSPM receptor that is close to the measurement station, and the solid orange line represents the second OSPM receptor located on the other side of the street. The observations are in solid black, and the background concentrations are in solid grey.

Figure 4 .

 4 Figure 4. CO and NO 2 time-averaged concentrations (in µg m -3 ) for MUNICH-homo are shown in the upper-and lower-left panels (a, c) respectively for the HCAB street network. Relative differences (in %) between the first level of MUNICH-hete and MUNICH-homo for CO and NO 2 are shown in the upper-and lower-right panels (b, d) respectively for the HCAB street network. A positive relative difference indicates higher concentrations for MUNICH-hete. The brown cross in panels (a) and (c) represents the position of the measurement station.

Figure 5 .

 5 Figure 5. Monthly averaged concentrations (in µg m -3 ) of CO (a) and NO 2 (b) at JGTV monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represent the three levels of the heterogeneous version of MUNICHthe lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) is shown with diamond markers. The solid orange line represents the OSPM receptor that is close to the measurement station, and the solid red line represents the second OSPM receptor located on the other side of the street. The observations (only available for NO 2 ) are in solid black, and the background concentrations are in solid grey.

Figure 6 .

 6 Figure 6. CO and NO 2 time-averaged concentrations (in µg m -3 ) for MUNICH-homo are shown in the upper-and lower-left panels (a, c) respectively for the JGTV street network. Relative differences (in %) between the first level of MUNICH-hete and MUNICH-homo for CO and NO 2 are shown in the upper-and lower-right panels (b, d) respectively for JGTV. A positive relative difference indicates higher concentrations for MUNICH-hete. The brown cross in panels (a) and (c) represents the position of the measurement station.

Figure 7 .

 7 Figure 7. Average daily profile of the concentrations of NO x (a) and PM 10 (b) over the simulation period at the Boulevard d'Alsace Lorraine monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represent the three levels of the heterogeneous version of MUNICH -the lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) is shown with diamond markers. The observations are in solid black, and the background concentrations are in solid grey.

Figure 8 .

 8 Figure 8. OM and BC time-averaged concentrations (in µg m -3 ) for MUNICH-homo are shown in the upper-and lower-left panels (a, c) respectively for the district of Le Perreux-sur-Marne. Relative differences (in %) between the first level of MUNICH-hete and MUNICHhomo for OM and BC are shown in the upper-and lower-right panels (b, d) respectively for the district of Le Perreux-sur-Marne. A positive relative difference indicates higher concentrations for MUNICH-hete. The brown cross in panels (a) and (c) represents the position of the measurement station.

Figure A1 .

 A1 Figure A1. Representation of the recirculation zone in the heterogeneous version of MUNICH.

Figure C1 .

 C1 Figure C1. Monthly averaged concentrations (in µg m -3 ) of NO x (a) and O 3 (b) at HCAB monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represent the three levels of the heterogeneous version of MUNICH -the lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) is shown with diamond markers. The solid red line represents the OSPM receptor that is close to the measurement station, and the solid orange line represents the second OSPM receptor located on the other side of the street. The observations are in solid black, and the background concentrations are in solid grey.

  Figure D1. Monthly averaged concentrations (in µg m -3 ) of NO x (a) and O 3 (b) at JGTV monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represent the three levels of the heterogeneous version of MUNICH -the lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) s shown with diamond markers. The solid orange line represents the OSPM receptor that is close to the measurement station, and the solid red line represents the second OSPM receptor located on the other side of the street. The observations are in solid black, and the background concentrations are in solid grey.

  Figure E1. Average daily profile of the concentrations of NO (a) and NO 2 (b) over the simulation period at the Boulevard d'Alsace Lorraine monitoring station. The solid blue line represents the homogeneous version of MUNICH. The three dashed green lines represent the three levels of the heterogeneous version of MUNICH -the lowest level (l1) is shown with square markers, the intermediate level (l2) is shown with crossed markers, and the top level (l3) is shown with diamond markers. The observations are in solid black, and the background concentrations are in solid grey.

Figure E2 .

 E2 Figure E2. NO 2 and PM 10 time-averaged concentrations (in µg m -3 ) for MUNICH-homo in the left panel (a, c) for the district of Le Perreux-sur-Marne. Relative differences (in %) between the first level of MUNICH-hete and MUNICH-homo for NO 2 and PM 10 in the right panel (b, d) for the district of Le Perreux-sur-Marne. A positive relative difference indicates higher concentrations for MUNICH-hete. The brown cross in panels (a) and (c) represents the position of the measurement station.

Table 1 .

 1 Statistical indicators of the influence of the aspect ratio on concentrations in MUNICH-hete-l1 for the street network in greater Paris. Indicators are presented in Appendix B.

			Mean concentration	NMB
			[µg m -3 ]	[%]
	Pollutant	a r	MUNICH-homo MUNICH-hete-l1
	NO 2	[0, 0.5[	54.92	33.99
		[0.5, 1[	41.13	11.95
		[1, 1.5[	34.26	6.27
		≥ 1.5	-	-
	NO x	[0, 0.5[	84.31	53.06
		[0.5, 1[	59.85	22.90
		[1, 1.5[	43.71	12.02
		≥ 1.5	-	-
	PM 10	[0, 0.5[	23.06	18.01
		[0.5, 1[	20.59	6.09
		[1, 1.5[	19.13	2.63
		≥ 1.5	-	-
	PM 2.5	[0, 0.5[	21.10	16.01
		[0.5, 1[	19.01	5.32
		[1, 1.5[	17.91	2.50
		≥ 1.5	-	-
	BC	[0, 0.5[	1.56	41.84
		[0.5, 1[	1.19	16.28
		[1, 1.5[	0.96	7.78
		≥ 1.5	-	-
	OM	[0, 0.5[	5.60	22.58
		[0.5, 1[	4.91	7.98
		[1, 1.5[	4.46	3.27
		≥ 1.5	-	-

Table 2 .

 2 Statistical indicators of the influence of the street network on concentrations simulated with MUNICH-hete for the street segment of the Boulevard d'Alsace Lorraine with the monitoring station. Indicators are presented in Appendix B.

	MUNICH-hete level

Table C1 .

 C1 Statistical indicators of the evaluation of the hourly simulated concentrations compared to observations at HCAB monitoring station. Indicators are presented in Appendix B.

			CO	NO 2	NO x	O 3
	Observations	Mean concentration [µg m -3 ] 285.35	34.64	72.30	44.33
	MUNICH-homo	Mean concentration [µg m -3 ] 210.88	25.34	43.77	50.44
		MFE	0.36	0.48	0.55	0.38
		MFB	-0.29 -0.29 -0.42	0.14
		FAC2	0.91	0.73	0.63	0.83
	MUNICH-hete-l1 Mean concentration [µg m -3 ] 249.29	32.37	74.95	47.34
		MFE	0.28	0.35	0.35	0.37
		MFB	-0.14 -0.06	0.05	0.07
		FAC2	0.96	0.87	0.86	0.84
	MUNICH-hete-l2 Mean concentration [µg m -3 ] 223.39	27.69	53.86	49.36
		MFE	0.32	0.42	0.43	0.37
		MFB	-0.24 -0.21 -0.24	0.12
		FAC2	0.93	0.80	0.78	0.83
	MUNICH-hete-l3 Mean concentration [µg m -3 ] 197.59	21.87	32.90	52.59
		MFE	0.39	0.57	0.73	0.39
		MFB	-0.34 -0.43 -0.65	0.20
		FAC2	0.88	0.61	0.42	0.82
	OSPM-R1	Mean concentration [µg m -3 ] 272.86	40.59	86.60	39.50
		MFE	0.26	0.34	0.40	0.35
		MFB	-0.05	0.19	0.21 -0.11
		FAC2	0.96	0.87	0.82	0.86
	OSPM-R2	Mean concentration [µg m -3 ] 227.84	30.53	55.43	45.77
		MFE	0.33	0.46	0.61	0.36
		MFB	-0.23 -0.16 -0.33	0.05
		FAC2	0.93	0.74	0.61	0.84

Table D1 .

 D1 Statistical indicators of the evaluation of the hourly simulated concentrations compared to observations at JGTV monitoring station. Indicators are presented in Appendix B.

			NO 2	NO x
	Observations	Mean concentration [µg m -3 ]	24.50	46.94
	MUNICH-homo	Mean concentration [µg m -3 ]	21.69	32.10
		MFE	0.46	0.53
		MFB	-0.03 -0.19
		FAC2	0.75	0.66
	MUNICH-hete-l1 Mean concentration [µg m -3 ]	19.77	35.99
		MFE	0.49	0.51
		MFB	-0.13 -0.11
		FAC2	0.75	0.68
	MUNICH-hete-l2 Mean concentration [µg m -3 ]	18.37	27.78
		MFE	0.52	0.58
		MFB	-0.20 -0.32
		FAC2	0.71	0.61
	MUNICH-hete-l3 Mean concentration [µg m -3 ]	16.81	20.10
		MFE	0.57	0.74
		MFB	-0.29 -0.58
		FAC2	0.68	0.46
	OSPM-R1	Mean concentration [µg m -3 ]	25.60	40.46
		MFE	0.53	0.63
		MFB	0.15	0.03
		FAC2	0.67	0.56
	OSPM-R2	Mean concentration [µg m -3 ]	28.41	47.21
		MFE	0.41	0.42
		MFB	0.25	0.18
		FAC2	0.80	0.79

Table E1 .

 E1 Statistical indicators of the evaluation of the hourly simulated concentrations to observations at the Boulevard d'Alsace Lorraine monitoring station. Indicators are presented in Appendix B.

			NO 2	NO x	PM 10 PM 2.5	BC
	Observations	Mean concentration [µg m -3 ]	52.16 147.19	23.42	12.72	6.10
	MUNICH-homo	Mean concentration [µg m -3 ]	48.49	74.62	21.89	20.06	1.41
		MFE	0.36	0.65	0.38	0.53	1.17
		MFB	-0.11	-0.60 -0.08	0.38 -1.16
		FAC2	0.87	0.52	0.84	0.67	0.09
	MUNICH-hete-l1 Mean concentration [µg m -3 ]	58.92 104.74	24.58	22.18	1.84
		MFE	0.33	0.41	0.37	0.57	1.01
		MFB	0.08	-0.30	0.03	0.47 -1.00
		FAC2	0.91	0.80	0.86	0.61	0.16
	MUNICH-hete-l2 Mean concentration [µg m -3 ]	47.81	75.36	21.94	20.08	1.42
		MFE	0.36	0.64	0.38	0.53	1.17
		MFB	-0.12	-0.59 -0.08	0.38 -1.16
		FAC2	0.86	0.53	0.84	0.67	0.08
	MUNICH-hete-l3 Mean concentration [µg m -3 ]	37.97	52.63	19.91	18.41	1.09
		MFE	0.49	0.90	0.42	0.50	1.30
		MFB	-0.35	-0.88 -0.18	0.30 -1.30
		FAC2	0.71	0.25	0.80	0.70	0.06

Table G1 .

 G1 Statistical indicators of the influence of the street network on concentrations simulated with MUNICH-hete for the street segment HCAB with the monitoring station. Indicators are presented in Appendix B.

	MUNICH-hete level			CO	NO 2	NO x	O 3
	l1	With network	Mean concentration [µg m -3 ]	249.29	32.37	74.95 47.34
		Without network Mean concentration [µg m -3 ]	214.27	23.28	46.69 52.98
			NME [%]	14.05	28.06	37.70 11.90
			NMB [%]	-14.05 -28.06 -37.70 11.90
	l2	With network	Mean concentration [µg m -3 ]	223.39	27.69	53.86 49.36
		Without network Mean concentration [µg m -3 ]	198.12	20.78	33.47 53.79
			NME [%]	11.32	24.95	37.86	8.99
			NMB [%]	-11.32 -24.95 -37.86	8.99
	l3	With network	Mean concentration [µg m -3 ]	197.59	21.87	32.90 52.59
		Without network Mean concentration [µg m -3 ]	186.96	18.65	24.33 54.78
			NME [%]	5.38	14.73	26.05	4.17
			NMB [%]	-5.38 -14.73 -26.05	4.17

Table G2 .

 G2 Statistical indicators of the influence of the street network on concentrations simulated with MUNICH-hete for the street segment JGTV with the monitoring station. Indicators are presented in Appendix B.

	MUNICH-hete level			CO	NO 2	NO x	O 3
	l1	With network	Mean concentration [µg m -3 ] 201.21	19.77	35.99 55.19
		Without network Mean concentration [µg m -3 ] 189.24	17.46	27.56 56.45
			NME [%]	6.09	12.38	23.63	3.13
			NMB [%]	-5.95 -11.70 -23.43	2.29
	l2	With network	Mean concentration [µg m -3 ] 189.49	18.37	27.78 55.54
		Without network Mean concentration [µg m -3 ] 181.01	16.52	21.80 56.64
			NME [%]	4.71	10.87	21.85	2.85
			NMB [%]	-4.47 -10.03 -21.53	1.99
	l3	With network	Mean concentration [µg m -3 ] 178.59	16.81	20.10 56.12
		Without network Mean concentration [µg m -3 ] 176.03	15.92	18.30 56.80
			NME [%]	1.84	6.16	9.57	1.83
			NMB [%]	-1.43	-5.30	-8.92	1.21

Geosci. Model Dev., 16, 5281-5303, 2023 https://doi.org/10.5194/gmd-16-5281-2023

https://doi.org/10.5194/gmd-16-5281-2023Geosci. Model Dev., 16, 5281-5303, 2023

Code and data availability. MUNICH-hete is available at https://doi.org/10.5281/zenodo.7778271 (Sarica et al., 2023a). The configuration files, the input data, and the scripts to generate the figures and statistics are available at Sarica et al. (2023a).

Appendix A: Volumes of the recirculation and ventilation zones

The algorithm used in the heterogeneous version of MU-NICH to compute the volumes of the recirculation and ventilation zones is based on the parameterization of OSPM [START_REF] Berkowicz | Modelling traffic pollution in streets[END_REF]Berkowicz, 2000b;Ottosen et al., 2015). This algorithm is applied at the beginning of each time step as the size of the recirculation zone is dependent on wind speed and direction. Figure A1 presents the shape of the recirculation zone and the associated parameters.

The first step is to compute the length of the vortex in the direction of the wind:

with H being the height of the street, and

with u roof being the wind speed at roof level.

The width of the trapeze base is the projection of L vortex in the street:

with θ being the angle between the wind direction and the street orientation. The width of the trapeze top is equal to half of the base:

Knowing these lengths and using algebraic considerations, the widths W 1 and W 2 can be calculated:

The horizontal surfaces for vertical exchanges between the levels and with the concentrations above the street are calculated as follows:

with L being the street length.

The vertical surfaces for advection via intersections are determined with the following:

Finally, the volumes associated with each level of the recirculation zone are

In the current version of MUNICH-hete, it is assumed that traffic emissions are all affected to the recirculation zone. Therefore, its base W base has to be superior or equal to the street width W . If this is not the case, the recirculation zone is considered to fill the whole street volume.

When considered, the other widths are also limited by the street width: