# Qualification of microclimate models and simulation tools: An academic benchmark

Teddy Gresse, Julie Soriano, Auline Rodler, Jean-Claude Krapez, Jean Pierro, Félix Schmitt, Mathieu Galtier, Frédéric André, Frédéric Kuznik, Lionel Soulhac, et al.

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Teddy Gresse, Julie Soriano, Auline Rodler, Jean-Claude Krapez, Jean Pierro, et al. Qualification of microclimate models and simulation tools: An academic benchmark. Building and Environment, 2025, 278, pp.112913. 10.1016/j.buildenv.2025.112913. hal-05073994

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# Qualification of microclimate models and simulation tools: an academic benchmark

Teddy Gresse<sup>a,*</sup>, Julie Soriano<sup>a</sup>, Auline Rodler<sup>b</sup>, Jean-Claude Krapez<sup>c</sup>, Jean Pierro<sup>c</sup>, Félix Schmitt<sup>d</sup>, Mathieu Galtier<sup>d</sup>, Frédéric André<sup>e</sup>, Frédéric Kuznik<sup>d</sup>, Lionel Soulhac<sup>f</sup>, Damien David<sup>a</sup>, Jérôme Jacob<sup>g</sup>, Marjorie Musy<sup>b</sup>, Lucie Merlier<sup>a</sup>

<sup>a</sup>Univ Lyon, UCBL, INSA Lyon, CNRS, CETHIL, UMR 5008, Villeurbanne, F-69621, France

<sup>b</sup>Cerema BPE/IRSTV, Nantes, F-44262, France

<sup>c</sup>ONERA, The French Aerospace Lab, DOTA, Salon cedex Air, F-13661, France

<sup>d</sup>Univ Lyon, INSA Lyon, CNRS, CETHIL, UMR5008, Villeurbanne, F-69621, France

<sup>e</sup>Univ Lyon, CNRS, UCBL, INSA Lyon, CETHIL, UMR5008, Villeurbanne, F-69621, France

<sup>f</sup>Laboratoire de Mecanique des Fluides et d'Acoustique, University of Lyon, CNRS UMR 5509

Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, Ecully, F-69134, France

<sup>g</sup>Aix Marseille Univ, CNRS, Centrale Med, M2P2, UMR 7340, Marseille, F-13451, France

## Abstract

In recent decades, numerous urban microclimate models have been developed to address various applications, such as diagnosing urban overheating and evaluating heat mitigation strategies using green or grey solutions. These models account for complex physical interactions; however, their qualification and validation remain significant challenges due to their complexity and the lack of a standardized framework and comprehensive reference datasets.

This paper presents the first step of a comprehensive qualification and validation methodology through the definition of an academic benchmark and its application to four urban microclimate models. The proposed methodology follows an incremental

*Postal adress: Bâtiment Sadi-Carnot, 9, rue de la Physique, Campus LyonTech La Doua, 69621 Villeurbanne cedex France

Email address: teddy.gresse@insa-lyon.fr (Teddy Gresse)
phenomenological approach, systematically analyzing heat transfer processes within an idealized street canyon with well-defined conditions across four cases: shortwave radiation, longwave radiation, aeraulics, and their coupling with heat conduction and storage in walls and ground. The benchmark aims to analyze the behavior of different microclimate models, quantify deviations between simulation results, and identify their underlying sources within the physical models. This is achieved through the intercomparison of simulation results, incorporating reference data with a known standard deviation where available.

The results show good agreement between models for solar radiation, infrared ra-
diation, and heat conduction but reveal significant deviations in surface convection,
stressing the need for further research into convection modelling and its influence
on coupled processes. Additionally, the results confirm the suitability of the pro-
posed methodology in identifying the sources of deviations between models. This
benchmark provides a robust framework for model qualification and is expected to
be widely adopted in future studies.

*Keywords:* Academic benchmark, Urban microclimate modelling, Model qualification, Street canyon, Conduction-convection-radiation coupling
1. Introduction

In the current context of global warming and urban development, it becomes
critical to be able to characterize relevantly urban overheating in relation to the
local site specificities and to have an in-depth understanding of the phenomena that
influence it. Such a knowledge is especially useful to stress particularly vulnerable
areas and design suitable urban policies. In this context, numerical modelling and
simulation can provide diagnosis for urban overheating and decision support for
developing urban heat adaptation strategies [1].

In recent decades, numerous urban climate modellings have been developed and
applied across various contexts [2]. These modelling approches are tailored to dif-
ferent spatial scales, determined by the representation of land surface features and
the resolution at which the governing equations are formulated. City-scale models
are designed to simulate entire cities and their surrounding areas, including subur-
ban and rural regions, over zones spanning several kilometers. Due to their coarse
spatial resolution, these models rely on parameterization to represent local urban
characteristics. Examples of meso-scale models include the MESO-NH model [3] and
the Weather Research and Forecasting (WRF) model [4]. In contrast, neighborhood-
scale models focus on smaller urban areas with dimensions ranging from a few hun-
dred meters to several kilometers. These models allow for the detailed representa-
tion of microclimatic phenomena within the urban canopy layer (UCL). Depending
on their approach, neighborhood-scale models can either use parameterized repre-
sentations—based on aggregated properties like roughness and albedo—or explicit
representations that incorporate detailed building geometries and material proper-
ties. Parametric neighborhood-scale models include examples such as the Urban Weather Generator (UWG) [5], the Canyon Air Temperature (CAT) model [6], and the Canopy Interface Model (CIM) [7]. Explicit models, which handle realistic geometries and offer higher spatial and physical details, include RayMan [8] and SOLWEIG [9], which focus solely on radiative phenomena, as well as ENVI-met [10] and SOLENE-Microclimat [11], which can simulate the different heat transfers determining urban microclimates, including aeraulics through CFD coupling. Intermediate models, such as EnviBatE [12], CityFFD+CityBEM [13], and LASER/F [14], are also able to simulate urban microclimates but use simpler aeraulics models, such as zonal approaches or urban canopy schemes, to reduce computational costs. Figure A.18 provides a classification of urban climate models based on the spatial scale of the represented areas and the horizontal resolution of their grid cells.

This study specifically focuses on neighborhood-scale urban climate models with explicit geometries, commonly referred to as urban microclimate models. These models can simulate a range of complex processes, including turbulent and buoyant airflows, heat and moisture transport in the air domain around and above buildings, solar and longwave radiative exchanges between the sun, the sky and the built environment, and heat and moisture transport processes in urban materials. They allow the diagnostic of urban overheating or the evaluation of different heat mitigation strategies, e.g. based on green or grey solutions, properly considering all physical interactions. However, a critical and challenging step in the modelling process is the qualification or validation of the numerical modelling approaches to avoid misinterpretation of simulation results and ensure their reliability. The complexity arises
from several factors. First, the models are inherently multiphysics, meaning that errors in one sub-model can propagate to others, or even be masked by compensatory errors, ultimately influencing the overall simulation results. Second, urban environments are open systems, which makes it challenging to define precise boundary and initial conditions. Additionally, the knowledge of key input data, such as material properties like thermal conductivity and heat capacity, is often incomplete, introducing uncertainties. Furthermore, the models require scene geometries to be simplified to meet spatial resolution constraints, which may deviate from real-world configurations. Finally, the objectives of the qualification and validation process determine the nature of the assessment, which may target variables such as air temperature, surface temperature, or surface heat flux. The required accuracy may range from mean values to more detailed profiles or spatially mapped data across air volumes or surfaces, which can be challenging to obtain from experimental measurements.

Numerous validation studies have been conducted on the most commonly used urban microclimate models, including ENVI-met [15, 16, 17, 18], SOLWEIG [9, 19], RayMan [20, 21], SOLENE-Microclimat [22, 23, 24], FLUENT CFD model [25, 26, 27, 28]. Some validation studies perform inter-comparisons of models involving ENVI-met, SOLWEIG, and RayMan [29, 30, 31, 32, 33, 34]. Several review articles have analysed these studies, providing detailed discussions of their validation processes [35, 36, 37, 38]. The validation of model outputs typically involves statistical comparisons between field data and simulation results. Field data are primarily derived from weather station networks or fixed sensors installed at specific locations. These validation studies mainly focus on key microclimatic variables, including air
temperature, surface temperature, mean radiant temperature, and, less frequently, 70 wind speed. The simulation domains for these validation studies usually cover urban 71 areas smaller than 1 km². Most validation efforts rely on statistical metrics such as 72 Root Mean Square Error (RMSE) and Mean Bias Error (MBE) to assess the agree- 73 ment between simulated and measured data. Despite progress in validation studies, 74 significant gaps remain. Jänicke et al. [35] identified a lack of inter-model compar- 75 isons, highlighting the need for further research, while Zezzo et al. [36] emphasized the 76 absence of a standardized methodological framework for validating microscale model 77 data. Indeed, although reference validation frameworks exist for building energy 78 modelling (BESTEST [39]) and urban land surface modelling (Urban-PLUMBER 79 [40]), no established validation methodology currently exists for urban microclimate 80 models. Developing such a framework would not only support researchers new to 81 urban climatology but also facilitates the development of existing or new simulation 82 tools by ensuring consistent qualification and validation standards. 83

Hence, as a first step toward a comprehensive reference methodology to qualify 84 and validate urban microclimate models at the neighborhood scale [41], this paper 85 introduces an academic benchmark and presents its application with four microcli- 86 mate models. The proposed methodology follows an incremental phenomenological 87 approach, structured around the key physical processes occurring in an idealized 88 street canyon with well-defined conditions. The benchmark aims to analyse the be- 89 havior of different microclimate models, quantify deviations between microclimate 90 simulation results, and identify their underlying sources within the physical models. 91 This is achieved through the intercomparison of simulation results, incorporating 92
reference data with known a standard deviation where available. For that purpose,

section 2 details the general framework and configuration of the benchmark. Section

3 presents then the four microclimate models used for the models intercomparisons

(MATHIS [42], SOLENE-Microclimat [11], SOLENE-SUSHI [43] and TRABOULE-

ProLB [44]) and simulation settings. Finally, section 4 gives and analyses simulation

results and section 5 provides the discussion and conclusions.
## 2. General framework and configuration of the benchmark

100

### 2.1. Methodology

101

The methodology follows an incremental phenomenological approach, structured around the key physical processes occurring in urban areas. Specifically, it is based on four cases that allow for the independent analysis of each heat transfer process and their coupling:

102

103

104

105

* Case A focuses on shortwave radiation at a specific time in the afternoon when the incident solar heat flux is high and the sun is not at its zenith, resulting in the formation of shadows in urban areas.

106

107

108

* Case B focuses on longwave radiation also at a specific time around noon when the incident heat flux from the sky is high.

109

110

* Case C focuses on aeraulics aspects considering a steady state and isothermal condition for airflow.

111

112

* Case D combines the different above-mentioned phenomena with heat conduction and storage in walls and ground. The coupling is simulated dynamically over a period of six days. Only the last day of the period is studied to ensure that the initialization of the models does not affect the results. Two subcases, namely a base case and a variant case ($D_1$ and $D_2$ respectively), are suggested to stress the impact of the convective heat transfer model.

113

114

115

116

117
## 2.2. The ideal street canyon

To implement the methodology, an ideal street canyon is designed as this geometry is usually considered as the basic urban archetype.

**Geometry.** As shown on Figure 1a, the buildings and street are 70 m long and 10 m high with an aspect ratio of 1. They are centered on an 90×130 m open ground and oriented West-East. The coordinate system is centered at the center of the soil in the street canyon, with the y-axis corresponding to the main direction of the street.

The benchmark focuses on four faces represented in Figures 1b and 1c: the roof of Building A (RoofA), the wall of Building A inside the street canyon (WallA), the soil delimited by the street canyon (Soil), and the wall of Building B inside the street canyon (WallB), as well as the air volume around the street canyon (Air).

**Surface, material and air properties.** Table 1 gives the optical properties of the surfaces, including albedo and emissivity, as well as their roughness and corresponding cases. Table 2 gives the thermal properties and dimensions of the materials used in the two wall layers and three ground layers in the case D. The properties were defined based on literature [45, 46, 47], except for the roughness, which was set to zero to simplify the airflow boundary conditions. Note that although these values were chosen to be realistic, they do not correspond to a real configuration. For the air properties, the density is set to $ρ = 1.2 \text{ kg m}^{-3}$ and the kinematic viscosity to $ν = 1.56 × 10^{-5} \text{ m}^2 \text{ s}^{-1}$, corresponding to air at 20°C and at standard atmospheric pressure.
<figure><img src="image_2.png" /><figcaption>Figure 1: Geometry of the ideal street canyon.</figcaption></figure>

## 2.3. Boundary conditions

*Meteorological conditions.* Hourly weather data from the meteorological station located in Dijon (France) for the period from July 13 to 19, 2022 are used to define the variables in the different cases. For case A, the data correspond to the direct and diffuse shortwave flux densities on an horizontal surface at 5:30 pm on July 18,
<table><caption>Table 1: Surface properties for the different cases.</caption><thead><tr><th>Properties</th><th>Soil</th><th>Wall</th><th>Roof</th><th>Cases</th></tr></thead><tbody><tr><td>Albedo [-]</td><td>0.15</td><td>0.4</td><td>0.2</td><td>A, D<sub>1</sub>, D<sub>2</sub></td></tr><tr><td>Emissivity [-]</td><td>0.9</td><td>0.9</td><td>0.9</td><td>B, D<sub>1</sub>, D<sub>2</sub></td></tr><tr><td>Roughness [m]</td><td>0</td><td>0</td><td>0</td><td>C, D<sub>2</sub></td></tr></tbody></table>

2022 ($K^{\downarrow, dif}$ = 115.3 W m⁻², $K^{\downarrow, dir}$ = 112.5 W m⁻²). For case B, the data correspond to the longwave flux density on a horizontal surface at 12:30 pm on July 18, 2022 ($L^{\downarrow}$ = 394.4 W m⁻²). For case C, a southerly wind aligned with the positive x-direction is considered. This wind direction, perpendicular to the street canyon, is selected as it represents a classical airflow configuration. The velocity at the building height at 12:30 pm on July 18, 2022 ($U_{10}$= 3.6 m s⁻¹) is used to compute the inlet velocity and Turbulent Kinetic Energy (TKE) inlet profiles as follows:

$$U_{in}(z) = \frac{u_{*}}{\kappa} \ln \left( \frac{z}{z_{0}} \right) \qquad (1)$$

$$k_t(z) = 0.03 U_{in}^2(z) \qquad (2)$$

with $U_{in}(z)$ [m/s] the inlet velocity, $u_{*}$ [m/s] the friction velocity, $\kappa$ ≈ 0.4 the Von Karman constant, and $z_0$ [m] the aerodynamic roughness length. The aerodynamic roughness length is taken equal to 10⁻⁵ m, i.e. very small, to remain consistent with the assumption of zero roughness.

For case D, all previously defined variables are used together with the air temperature
<table><caption>Table 2: Thermal properties and dimensions ($e$: thickness, $\lambda$: conductivity, $\rho$: density, $c_p$: specific heat capacity) of the materials used for the walls and ground in case D.</caption><thead><tr><th colspan="2">Parameters</th><th>Ground</th><th>Wall/Roof</th></tr></thead><tbody><tr><td rowspan="4">Layer 1<br>(exterior)</td><td>Material</td><td>Asphalt</td><td>Concrete</td></tr><tr><td>e [cm]</td><td>5</td><td>30</td></tr><tr><td>λ [W m<sup>-1</sup> K<sup>-1</sup>]</td><td>0.7</td><td>1.7</td></tr><tr><td>ρ [kg m<sup>-3</sup>]</td><td>2400</td><td>2100</td></tr><tr><td colspan="2">c<sub>p</sub> [J kg<sup>-1</sup> K<sup>-1</sup>]</td><td>880</td><td>1000</td></tr><tr><td rowspan="4">Layer 2</td><td>Material</td><td>Gravel</td><td>Insulation</td></tr><tr><td>e [cm]</td><td>35</td><td>5</td></tr><tr><td>λ [W m<sup>-1</sup> K<sup>-1</sup>]</td><td>1.8</td><td>0.03</td></tr><tr><td>ρ [kg m<sup>-3</sup>]</td><td>1660</td><td>50</td></tr><tr><td colspan="2">c<sub>p</sub> [J kg<sup>-1</sup> K<sup>-1</sup>]</td><td>960</td><td>1200</td></tr><tr><td rowspan="4">Layer 3</td><td>Material</td><td>Soil</td><td>-</td></tr><tr><td>e [cm]</td><td>160</td><td>-</td></tr><tr><td>λ [W m<sup>-1</sup> K<sup>-1</sup>]</td><td>0.5</td><td>-</td></tr><tr><td>ρ [kg m<sup>-3</sup>]</td><td>1900</td><td>-</td></tr><tr><td colspan="2">c<sub>p</sub> [J kg<sup>-1</sup> K<sup>-1</sup>]</td><td>800</td><td>-</td></tr></tbody></table>

at 2 m ($T_{a,2}$) over six days from July 13 to 19, 2022 (see Figure A.19) imposed at the inlet as a uniform temperature condition.

*Forced variables.* For case B, the exterior surface temperature is fixed at 25 °C for the buildings' walls and roof and the soil surface temperature is fixed at 17 °C. For case
D, the indoor surfaces temperature is fixed at 25°C, and, for finite-depth models, the ground temperature at a depth of 2 m is fixed at 20°C. These temperatures are representative of the temperatures observed in buildings and in the ground in July at the considered location. When required, the surfaces and walls are initialized with a temperature of 20°C. In the base case $D_1$, a fixed convective heat transfer coefficient (CHTC) is set to 30 W m⁻² K⁻¹, corresponding to an incident wind speed of about 20 km h⁻¹. For the variant case $D_2$, the convective heat flux at exterior surfaces is directly estimated by the models.

## 2.4. Framework for result analysis

### 2.4.1. Variables of interest

Two types of output variables are distinguished: surface-related variables, including heat fluxes and temperatures, and air-related variables, including mean velocity fields and streamlines. These variables were selected because they are of paramount importance in the context of pedestrian comfort studies. In addition, to allow a wide variety of models with different spatial and temporal resolutions to be analysed and compared, three levels of results are suggested: surface averages, 1D profiles centered on the faces of interest (PS1 and PS2 - see Figure 2a), and 2D fields on the faces of interest and within the air volume (FA1 and FA2, corresponding to the median plane at $y = -17.5$ m and the horizontal plane at $z = 5$ m - see Figure 2b).

Note that analyzing results at these locations generally involves interpolating simulation outputs as they do generally not correspond to computational points. Typically, for 2D fields, interpolation on a structured grid is performed in this study before using a contour plot function.
<figure><img src="image_3.png" /><figcaption>Figure 2: Definition of the 1D profiles and 2D fields locations for the results comparison.</figcaption></figure>

2.4.2. Reference data

For cases A and B, additional data were produced using a radiative Monte-Carlo-based model [48] assuming an isotropic sky, diffuse reflections and emissions on surfaces, an infinite ground that reflects isotropically the incoming longwave flux and emit an isotropic longwave flux, and transparent air. Used with a regular mesh with a spatial resolution of 0.5 m, the model is able to get results with a standard deviation below 0.2%. Therefore, these data are considered as reference data for model comparisons on these two cases.

Experimental validation data from urban measurement campaigns were not in-
cluded in the benchmark due to their frequent incompleteness, which limits their
suitability for systematic model evaluation. Instead, the benchmark focuses on the
analysis and intercomparison of simulation results, allowing for the models’ qualifi-
cation under well-defined conditions.
## 3. Urban microclimate models

Four urban microclimate models were selected for application in this benchmark and subsequent analysis: MATHIS [42], SOLENE-Microclimat [11], SOLENE-SUSHI [43], and TRABOULE-ProLB [44]. All of these models, developed by the authors, operate at different spatial and temporal scales and involve different levels of physical modelling and development. Their spatial domain scales and resolutions are presented in Figure A.18, alongside those of other urban climate models commonly used in the literature. The selected models share comparable spatial scales and resolutions with existing microclimate models, but address distinct simulation objectives. The following subsections describe the selected models and give details on their underlying physical modelling. Additional information on the resolution schemes of these models can be found in Appendix B.

### 3.1. General presentation of the models

MATHIS [42] is a simplified microclimate model whose purpose is to compute the spatial distribution of the air urban heat island (UHI) in a district on a typical domain size of a square kilometer and over a few weeks period. MATHIS is based on a street-network approach and represents the urban surface as a network of ideal street canyons connected by intersections. Each street is treated similarly as a Single Layer Urban Canopy Model - as defined in [49]. The spatial resolution therefore corresponds to a street, and the temporal resolution is fixed to one hour.

SOLENE-Microclimat [11] aims to model the urban microclimate and the thermal behavior of buildings on a neighbourhood scale and over a typical period of one week.
The geometry of the neighbourhood is discretised using unstructured surface and volume meshes with cells typical length of 10 cm to 1 m, providing a simulation close to a realistic 3D urban form. Its temporal resolution is fixed to one hour. It is the most developed of the four models, having benefited from numerous contributions since the first version of the shortwave radiation model SOLENE in 2002 [50, 51, 52, 53].

SUSHI [43] aims to describe the surface temperature field and longwave radiance in an urban scene on a city block scale and for a few days. It includes therefore a longwave radiation model and a rigorous multilayer conduction model leveraging transfer functions in the Fourier domain. It can be coupled to the model SOLENE [50] in order to access shortwave radiation fluxes. In the SOLENE-SUSHI coupled model, no aeraulic modelling is implemented, implying to consider a uniform air temperature and velocity over the domain. The temporal and spatial resolution of SOLENE-SUSHI are the same as SOLENE-Microclimat, with cells between 10 cm and 1 m and timesteps of one hour or less.

TRABOULE [44, 54] is a detailed radiative model, designed to be able to take account of a participating medium, i.e. non transparent air. It also includes a model of conduction in the walls and ground. It can be coupled with the ProLB software [55], a state of the art CFD model. TRABOULE-ProLB discretises the urban scene with a structured surface mesh and a structured volume mesh, with cells typical length of 10 cm to 1 m. The timesteps for ProLB are of the order of magnitude of one second, while timesteps of a few minutes are sufficient for TRABOULE. Due to its high resolution and detailed physics, TRABOULE-ProLB is aiming to model a
district on over period of the order of magnitude of a day. Nevertheless, simulating
a period of a few days is possible with a degraded resolution for CFD simulations.

## 3.2. Modelling of physical phenomena

Table 3 summarizes the physical models used to simulate radiation, thermo-aeraulics, convective exchange, and conduction in the four microclimate models analysed in this study. To better position these models with respect to the other existing models, in terms of their approaches for physical modelling and their scaling, Table 3 also summarizes the models underlying ENVI-met, EnviBatE, CityFFD+CityBEM, and LASER/F. Note that the scope of this analysis is limited to these specific processes, excluding considerations for building, vegetation, and humidity models. Table 3 highlights that the four models included in the study cover diverse approaches for physical modelling. Some of these are well-established in microclimate modelling, such as the radiosity method for radiation modelling. Others, however, are more innovative techniques, such as the Lattice Boltzmann Method combined with Large Eddy Simulation (LBM-LES) for thermo-aeraulic modelling.
<table><caption>Table 3: Specifications of the physical models in the four microclimate models compared in this study, as well as in other widely used models from the literature.</caption><thead><tr><th></th><th>MATHIS</th><th>SOLENE-Microclimat</th><th>SOLENE-SUSHI</th><th>TRABOULE-ProLB</th><th>ENVI-met</th><th>EnviBatE</th><th>CityFFD+<br>CityBEM</th><th>Laser/F</th></tr></thead><tbody><tr><td rowspan="4">Radiation</td><td>Isotropic sky</td><td colspan="2">Solene<br>Perez' sky model [56]</td><td>Isotropic sky</td><td></td><td>Perez' sky<br>model [56]</td><td></td><td>Perez' sky<br>model [56]</td></tr><tr><td>Radiosity<br>method<br>view factors:<br>analytical</td><td colspan="2">Radiosity method<br>view factors: contour<br>integration</td><td>Radiative<br>transfer<br>equation<br>resolution</td><td>Indexed View<br>Sphere (IVS)<br>radiation<br>scheme [57]</td><td>Radiosity<br>method<br>view factors:<br>contour<br>integration</td><td>-</td><td>Radiosity<br>method<br>view factors:<br>Monte Carlo<br>integration</td></tr><tr><td>Multiple<br>reflections</td><td>3 reflections<br>(0 for LW<br>from walls)</td><td>LW: multiple<br>reflections</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>One node for<br>each face<br>(wall, ground,<br>roof)</td><td>Unstructured surface mesh<br>(triangle)</td><td>Structured<br>surface and<br>volume meshes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Detail level</td><td>●</td><td>● ●</td><td>● ●</td><td>● ● ●</td><td>● ●</td><td>● ●</td><td>-</td><td>● ●</td></tr><tr><td rowspan="2">Thermo-<br>aeraulics</td><td>Parametric<br>model</td><td>Code_Saturne<br>CFD RANS<br>k - ε</td><td>-</td><td>ProLB<br>CFD<br>LBM-LES</td><td>CFD RANS<br>k - ε</td><td>QUIC urban<br>airflow model<br>[58]</td><td>Semi-<br>Lagrangian-<br>based FFD<br>solver [59]</td><td>Simplified<br>urban canopy<br>scheme</td></tr><tr><td>Zonal mesh</td><td>Unstructured<br>volume mesh</td><td></td><td>Structured<br>volume mesh</td><td></td><td></td><td></td><td></td></tr><tr><td>Detail level</td><td>●</td><td>● ●</td><td>-</td><td>● ● ●</td><td>● ●</td><td>●</td><td>● ●</td><td>●</td></tr><tr><td>Convective<br>exchange</td><td>Empirical<br>correlations<br>[60]</td><td>Empirical<br>correlations<br>[61]</td><td>Empirical<br>correlations<br>[62]</td><td>CFD fluxes<br>computation</td><td>CFD fluxes<br>computation</td><td>Constant</td><td>Empirical<br>correlations<br>[63]</td><td>Empirical<br>correlations<br>[64]</td></tr><tr><td>Detail level</td><td>● ●</td><td>● ●</td><td>● ●</td><td>● ● ●</td><td>● ● ●</td><td>●</td><td>● ●</td><td>● ●</td></tr><tr><td rowspan="3">Conduction</td><td>Finite volume</td><td>Electrical<br>analogy (RC)</td><td>Transfer<br>functions<br>(Fourier<br>domain)</td><td>Finite volume</td><td>Finite<br>differences</td><td>Response<br>factor</td><td>Electrical<br>analogy (RC)</td><td>Finite<br>differences</td></tr><tr><td>Multi-layers<br>1D<br>3 layers</td><td>Multi-layers<br>1D<br>Soil: 3 layers<br>Walls: 1 layer</td><td>Multi-layers<br>1D<br>No mesh</td><td>Multi-layers<br>1D<br>Refined</td><td>Multi-layers<br>1D</td><td>1D</td><td>1D</td><td>1D</td></tr><tr><td>Detail level</td><td>● ●</td><td>● ●</td><td>● ● ●</td><td>● ●</td><td>● ●</td><td>● ●</td><td>● ●</td></tr></tbody></table>
### 3.2.1. Radiation

Some modelling fundamentals are common to the four considered models. In particular, all the radiative models distinguish longwave and shortwave bands, and attribute specific properties (albedo or emissivity) to each band. All models also consider both a diffuse and a direct component for shortwave primary fluxes. Additionally, they all account for diffuse reflections and Lambertian emissions.

Nonetheless, MATHIS's radiation model is based on an infinite street canyon hypothesis, which allows to compute the view factors with analytical formulas [65]. It is a surface-to-surface model, computing the reflections with the radiosity method [65], which considers transparent air. Multiple reflections are taken into account, with a stopping criteria of $10^{-6}$ W m$^{-2}$ on the fluxes between two iterations. The sky is supposed isotropic, allowing to use sky view factors to compute the diffuse shortwave primary fluxes.

SOLENE-Microclimat is based on the radiation model SOLENE [50], which discretises the urban surfaces with an unstructured mesh with triangular facets. A contour integration method [50, 66] is employed to compute the view factors between the facets of the urban scene. SOLENE relies on a surface-to-surface radiative model, computing the reflections with the radiosity method. For this study, the number of reflections was limited to three. In the case of longwave radiation, multiple reflections are calculated only for atmospheric radiation to reduce the number of iterations required for the radiosity method and thus limit the computational cost. SOLENE uses the Perez sky model [56], which models a stronger diffuse shortwave flux coming from the sky vault near the sun position.
SOLENE-SUSHI uses SOLENE model for the calculation of shortwave radiation fluxes. It also imports the mesh and view factors of SOLENE in order to compute the longwave fluxes with a progressive refinement radiosity method. It considers multiple reflections, with a stopping criteria corresponding to a relative error inferior to $10^{-4}$ on the longwave fluxes between two iterations.

TRABOULE solves the radiative transfer equation in the air volume with a finite volume method [67, 68]. This method supposes to consider a volume mesh as well as a surface mesh, which are both chosen Cartesian. Convergence is assumed to be reached when the relative error on irradiance is below a fixed threshold (typically $10^{-6} - 10^{-7}$) everywhere in the domain. In addition, TRABOULE uses an isotropic sky model and, as for Monte-Carlo model, an infinite ground surrounding the simulation domain is considered in lateral boundary conditions, reflecting isotropically the incoming longwave flux, and emitting an isotropic longwave flux. Despite its ability to consider non transparent atmosphere, a simple case with transparent air is considered in this study.

### 3.2.2. Thermo-aeraulics and convective exchanges

MATHIS aeraulic model is derived from the pollutant dispersion model SIRANE [69]. Two distinct layers are considered in the simulated domain: the urban boundary layer, where the Monin-Obukhov similarity theory [70] is used (see [42]), and the urban canopy layer, where a coarse zonal mesh is designed based on the street canyon volumes. Within each street canyon, characteristic velocities i.e. vertical exchange velocity, longitudinal mean velocity, and near-wall velocities, are computed with parametric models, taking as input the vertical velocity profile in the urban boundary
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layer. Notably, near-wall velocities are computed as a fraction of the velocity above the street, based on wind tunnel experiment [71] and CFD simulations [42]. For walls and grounds, the convective heat fluxes are computed based on coefficients estimated using the correlation of Loveday and Taki [60], and the near-wall velocities. For roofs, the correlation of Kobayashi and Morikawa [72], developed specially for roofs, is used.

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In SOLENE-Microclimat, the CFD tool Code-Saturne [73] is used with a steady Reynolds Average Navier Stokes (RANS) $k-\epsilon$ turbulence model, and a unstructured volume mesh. The buoyancy is not taken into account. A non-slip condition is set for the solid walls constituted by the soil of the domain and the urban physical surfaces. The convective heat fluxes are calculated using convective heat transfer coefficients based on the McAdams [61] correlation, using the local air temperature and velocity values calculated by Code-Saturne.

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In SOLENE-SUSHI, no aeraulic model is included. Temperature and air velocity fields are therefore assumed to be uniform, and meteorological data values are used directly. The convective heat fluxes are calculated using convective heat transfer coefficients based on a correlation corresponding to the average of the correlations collected in the literature review by Palyvos [62].

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In TRABOULE-ProLB, CFD is performed with the ProLB software which is based on the Lattice Boltzmann Method (LBM) and a Large Eddy Simulation (LES) technique - therefore able to simulate transient phenomena [74, 75]. Thermal calculations are addressed through a hybrid approach [76]: the velocity field is solved using the LBM, while the energy equation is solved with a classical finite volume method. The buoyancy is taken into account with the Boussinesq approximation. Concerning
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the boundary conditions, no-slip conditions are set for solid surfaces, with wall func-
tions for velocity [77] and temperature [78]. At the inlet, the vertical velocity profile
is fixed and the turbulence is constructed with a Synthetic Eddy Method [79].

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3.2.3. Conduction

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The four models are based on the assumption of a 1D transfer within solid walls
and do not take into account the effects of thermal bridges.

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In MATHIS, the heat equation is discretised and solved using a finite volume
method. The walls and floor are discretised with one cell per wall layer. The limited
number of layers was chosen to keep the model simple. For the walls, the internal
boundary condition is a fixed surface temperature. For the floor, a zero flux condition
is imposed at 2 m depth.

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In the default version of SOLENE-Microclimat, the heat equation is discretised
and solved with an electric analogy [80]. On the ground, a model with three resis-
tances and three thermal capacitors is used, with the first resistance covering the
layers defined by the user, which is here the first two ground layers. Moreover, the
ground’s depth is fixed at 2 m where a temperature boundary condition is imposed.
For the building walls, a simplified model with only one resistance and two thermal
capacitors is used.

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In contrast to the other models, SUSHI uses a detailed semi-analytical method
based on the computation of 1D (optionally 2D) periodical transfer functions in the
Fourier space involving thermal admittances for semi-infinite soil and quadrupoles
for layers of finite thickness, without requiring any space discretisation. The model
assumes periodic conditions with a period corresponding to the number of days of
the meteorological data, thereby avoiding the need for an initial condition.

In TRABOULE, the heat equation is discretised and solved using a finite volume method as for MATHIS. The model enables the use of a fine wall discretisation, comprising multiple cells per wall layer, along with an expansion factor to set smaller cells close to the outdoor surface down to 2 cm. For the walls and the ground, the internal boundary condition is a fixed surface temperature.

### 3.2.4. Synthesis

The four urban microclimate models selected for this study incorporate a diverse range of physical modelling approaches, reflecting the variety of methods used across different urban microclimate models. Applying these models to the benchmark enables the evaluation of the methodology's effectiveness in analyzing model behavior, quantifying deviations between simulation results, and identifying their underlying sources within the physical models. Potential sources of deviations include view factor calculations and multireflections in the radiosity method, differences in sky models used in radiation simulations, the impact of turbulence modelling on aeraulic simulations, and variations in heat equation resolution, whether through discretisation methods or transfer functions in conduction models.

## 3.3. Street canyon modelling

### 3.3.1. Radiation and conduction modelling

The wall properties as well as the boundary conditions were set in accordance with the values given in sections 2.2 and 2.3, respectively. Furthermore, the spatial discretisation of the surfaces was adapted for each model.
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In MATHIS, the surface discretisation consists of a single node per surface in the street canyon.

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In SOLENE-Microclimat and SOLENE-SUSHI, the unstructured surface mesh represented in Figure 3a is used. It is composed of 8190 facets in total, with 1800 facets on each street canyon surface (WallA, WallB and Soil) with an average area of 0.39 m² (0.2 m² minimum and 0.65 m² maximum). On the rest of the domain, the facet area increases up to 16.5 m² far from the street canyon.

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In TRABOULE, the structured surface mesh shown in Figure 3b is used. It is composed of 59600 facets in total, with 2600 facets on each street canyon surface (WallA, WallB and Soil) with an area of 0.25 m² everywhere. It should be noted that a coarser surface mesh, with a facet area of 1 m², is used in case $D_2$ to limit the computational demand of the coupling between ProLB and TRABOULE.

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The surface meshes presented here result from a grid sensitivity study and prove to be good compromises between accuracy and computational cost. Typically, the computational cost of the dynamic simulations for case $D_1$ was of the order of one second for MATHIS, of the order of one minute for SOLENE-Microclimat and SOLENE-SUSHI, and of the order of one hour for TRABOULE.

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### 3.3.2. CFD modelling

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The numerical problem requires the specification of four types of boundary conditions for CFD: air inlet conditions, air outlet conditions, wall boundary conditions, and lateral at top conditions. At inlet, the velocity and turbulent kinetic energy are imposed according to the profiles defined Equations 1 and 2 in section 2.3. At outlet, the standard atmospheric pressure is imposed. At ground and street canyon

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walls, classical no-slip boundary conditions for velocity are enforced. To avoid the
need to use an excessively fine mesh at walls to fully resolve the boundary layer, wall
functions are used to calculate the temperature and velocity values at the first fluid
nodes. Finally, lateral and top boundaries are modelled as frictionless walls.

Specificities arise from SOLENE-Microclimat and ProLB concerning the compu-
tational domain and the volume discretisation to limit the influence of the computa-
tional conditions on CFD prediction results. In particular, CFD simulations require
an extended computational domain, which differ from the one presented in subsec-
tion 2.2.

In SOLENE-Microclimat, the computational domain was set to 200 × 200 × 100m³.
The lateral, top, inlet, and outlet boundaries were positioned at distances of 6.5H,
8.5H, 9H, and 8.5H from the street canyon buildings, respectively, which extends the
domain presented in subsection 2.2. An unstructured mesh consisting of 1.54 × 10⁶
fluid volumes is used for cases C and D₂ (see Figure 3c). The characteristic length
in the most refined region near the street canyon walls is approximately 1 m, which
corresponds to the standard grid refinement used in SOLENE-Microclimat. This
refinement was chosen to ensure feasibility within limited computational resources
rather than being the result of a grid sensitivity study. The computations were
performed on 4 processors (11th Gen Intel Core i5-1135G7 @ 2.40GHz) for a com-
putational cost of 30 CPU hours.

In ProLB, the computational domain was set to 250 × 150 × 80m³. The lateral, top,
inlet, and outlet boundaries were positioned at distances of 4H, 7H, 7H, and 15H
from the street canyon buildings, respectively, which also extends the domain pre-
sented in subsection 2.2 in accordance with the AIJ guidelines [81]. The domain is discretised into a series of nested volumes of uniform Cartesian grid cells. For case C, the mesh, resulting from a grid sensitivity study, is refined within the street canyon, using a resolution of $\Delta x = H/48 = 0.21$ m. Five refinement zones are introduced, leading to a maximum mesh size of $\Delta x = H/3 = 3.33$ m in the far-field region (see Figure 3d). The total mesh consists of $18.24 \times 10^6$ grid points, with a computational time step of $2.41 \times 10^{-3}$ s, chosen to maintain a maximum Mach number of 0.075 and ensure compliance with the low Mach condition of the LBM. Parallel computations were performed on 288 processors (Intel Skylake @ 2.7GHz, 2x24 cores (AVX 512)), with a total computational cost of approximately $3.1 \times 10^4$ CPU hours. For case $D_2$, using the same mesh as in case C was computationally prohibitive for simulating the full study period due to the coupling procedure between ProLB and TRABOULE. Therefore, a coarser mesh was selected, with a minimum resolution in the street canyon of $\Delta x = H/10 = 1$ m, resulting in $6.97 \times 10^5$ grid points and a computational time step of $1.65 \times 10^{-2}$ s.
<figure><img src="image_4.png" /><figcaption>Figure 3: Representation of the surfacic and volumic meshes used to discretise the street canyon.</figcaption></figure>
4. Results

4.1. *Shortwave radiation (A)*

*Surface averaged values.* Figure 4 shows the average net shortwave radiation *K*\* on RoofA, WallA, Soil, and WallB. The four models show good agreement with the reference Monte-Carlo results. The largest deviations are observed on the Soil for MATHIS and SOLENE, with 14.8 W m⁻² representing a relative deviation of 13.5%, and 7.7 W m⁻² representing a relative deviation of 7.1%, respectively. Among the models studied, TRABOULE is the closest, with relative deviations below 2% for all faces. The analysis of 1D profiles and 2D fields will help to explain the deviations.

<figure><img src="image_5.png" /><figcaption>Figure 4: Average net shortwave radiation *K*\* on RoofA, WallA, Soil, and WallB at 5:30 pm on July 18, 2022 (case *A*).</figcaption></figure>

1D profiles. Figure 5 shows the PS1 and PS2 profiles of net shortwave radiation *K*\*
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the average values computed by MATHIS for comparison. The results show similar trends for the different models. However, the fluxes simulated by SOLENE show deviations of the order of 10 W m⁻² in average on the different profiles compared with Monte-Carlo or TRABOULE results, representing a relative deviation up to 40% on WallB. This can be explained by the use of the Perez sky model by SOLENE, and, to a lesser extent, the treatment of multireflection with a contour integration method for the view factor calculation and a limitation to three reflections.

*2D fields.* The order of magnitude of the 2D fields of net shortwave radiation K* shown on Figure 6a indicates that WallA is in sunlight, WallB is in shade, and Soil is partially in sunlight and partially in shade, with a sharp transition. The inhomogeneous fields observed on WallA and WallB, can be attributed to the inhomogeneous diffuse primary flux distribution due to the higher sky view factors near the top and the edges of the street. Furthermore, the results show that sunlight penetrates into the street canyon from its west side due to the sun position in the sky, resulting in an asymmetric flux distribution on the Soil that cannot be modelled with MATHIS.

The 2D fields of net shortwave radiation difference ΔK* with Monte-Carlo for SOLENE (Figure 6b) and TRABOULE (Figure 6c) on WallA, Soil, and WallB highlight a correct prediction of the shaded zone. Nevertheless, deviations are observed at the sun/shade transition due to the different meshes used in the models. Elsewhere, deviations with Monte-Carlo results are globally higher for SOLENE than for TRABOULE. The highest deviations are located on the west edge of WallA (around 10 W m⁻², 14%) and Soil (around 25 W m⁻², 14%), where the portion of the sky vault visible from the faces is the closest to the sun position. This discrepancy may
<figure><img src="image_6.png" /><figcaption>Figure 5: 1D profiles of net shortwave radiation $K^*$ on WallA, Soil, and WallB at 5:30 pm on July 18, 2022 (case A).</figcaption></figure>

be again attributed to differences in the sky model used. Furthermore, deviations of approximately 5 W m⁻² are also observed on WallA and WallB near the Soil, especially in the central area of the street, where the sky view factor is minimal. This discrepancy may therefore be related to the treatment of multireflections.

In conclusion, while the models generally show good agreement with the Monte-Carlo results, deviations are observed, particularly for the SOLENE model. These
<figure><img src="image_7.png" /><figcaption>(a) Monte-Carlo reference calculation</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) Difference between SOLENE and Monte-Carlo</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(c) Difference between TRABOULE and Monte-Carlo</figcaption></figure>

Figure 6: 2D fields of net shortwave radiation $K^*$ on WallA, Soil, and WallB at 5:30 pm on July 18, 2022 (case A). The contour lines are drawn with a value step of 20 W m$^{-2}$ for graph (a) and 5 W m$^{-2}$ for graphs (b) and (c). On the last two graphs, only the contour line at 0 W m$^{-2}$ deviation is labeled to enhance the clarity of the graphs. 31
can be attributed to its use of the Perez sky model as compared to the isotropic sky model used by the other models, limitations in the treatment of multireflections and mesh resolution. TRABOULE shows the best alignment across all analysis given.

## 4.2. Longwave radiation (B)

*Surface averaged values.* Figure 7 shows the average net longwave radiation $L^*$ on RoofA, WallA, Soil, and WallB. All results but those on the Soil, have negative net longwave fluxes, corresponding to a net loss of energy from those surfaces. The Soil shows an opposite balance, with a lower temperature (set to 17°C) than the one of WallA and WallB (both at 25°C), resulting in a lower emitted flux. As for shortwave radiation, the TRABOULE results are in accordance with those of Monte-Carlo, with relative deviations below 2% for all faces. For MATHIS, the deviations are also small, below $2 \text{ W m}^{-2}$, which corresponds to a maximum relative deviation of 8% on the Soil. However, in this case, the infinite street hypothesis results in an underestimation of the longwave flux from the sky, which is compensated by an overestimation of the longwave flux emitted by urban surfaces. However, in a case of higher surface temperatures, this discrepancy would be higher. The deviation of SOLENE results with Monte-Carlo of approximately $8 \text{ W m}^{-2}$ (30%) on Wall A and Wall B will be explained by a detailed analysis of the 1D profiles and 2D fields.

*1D profiles.* The PS1 and PS2 profiles from SOLENE, TRABOULE, and Monte-Carlo plotted on Figure 8 show a decrease in net longwave flux values at the edges and the top of the wall faces because of the higher view factors with the sky and the surrounding area. The profiles from SOLENE show that the deviations on the
<figure><img src="image_10.png" /><figcaption>Figure 7: Average net longwave radiation $L^*$ on RoofA, WallA, Soil, and WallB at 12:30 pm on July 18, 2022 (case B).</figcaption></figure>

different walls observed on the previous average values analysis are mostly uniform offsets compared to those of Monte-Carlo and TRABOULE, that may be related to the treatment of multireflections. Furthermore, the MATHIS averaged values are in reasonable agreement with the PS1 profiles from Monte-Carlo, as the side effect is low, with a maximum deviation of 4 W m⁻² (13%) near the edge of Wall A and Wall B. However, the MATHIS results diverge by up 13 W m⁻² (200%) from the Monte-Carlo-based PS2 profiles, near the edge of the Soil, which highlights the limitations of the infinite street canyon hypothesis.

*2D fields.* The 2D fields of net longwave radiation $L^*$ simulated by the Monte-Carlo reference model (Figure 9a) show lower net longwave fluxes near the top and the edges of the street and a logically symmetrical overall field. Nevertheless, the 2D
<figure><img src="image_11.png" /><figcaption>Figure 8: 1D profiles of net longwave radiation $L^*$ on WallA, Soil, and WallB at 12:30 pm on July 18, 2022 (case B).</figcaption></figure>

fields of net longwave radiation difference $\Delta L^*$ with the Monte-Carlo reference for
SOLENE (Figures 9b) and TRABOULE (9c) highlight low deviation of TRABOULE
but deviations up to 13.5 W m$^{-2}$ (36%) with SOLENE, especially near the edges of
the faces. This behavior may be attributed to the view factor calculation. Sim-
ilarly, the deviations at the lateral edges with SOLENE may be attributed to the
boundary conditions at the domain sides, which do not assume a ground surrounding
the simulation domain that reflects and emits the longwave flux as in Monte-Carlo and TRABOULE. However, except at these locations, the differences are smaller, around 5 W m⁻², which may be due to the number of reflections or the view factor calculation.

In conclusion, the longwave radiation results show that TRABOULE has good agreement with the Monte-Carlo results across all analysis. SOLENE shows larger deviations, particularly near the edges of surfaces, due to limitations in the view factor calculation and lateral boundary conditions that do not account for a surrounding ground. Additionally, MATHIS shows deviations linked to the infinite street canyon hypothesis.

### 4.3. Aeraulics (C)

Figure 10 shows the mean velocity field in the median plans FA1 and FA2 for ProLB and Code-Saturne, the CFD models included in TRABOULE-ProLB and SOLENE-Microclimat respectively. In both simulations, the airflow deflects around and over Building A, and flow separations occur at the top and side corners of the building. However, the separated recirculations are predicted significantly shorter by LES than by RANS. As a result, the airflow in the LES simulation skims above the two buildings and penetrates the street laterally, which does not occur in the RANS simulation. In addition, the near wake recirculation is predicted also much shorter by LES than RANS. The streamlines in Figure 11 show the two different recirculation patterns in and around the street. In the LES simulation, the recirculation within the street is distinct from the near wake recirculation and shows two lateral corner vortices that allow lateral flow penetration and leading to a clockwise
<figure><img src="image_12.png" /><figcaption>(a) Monte-Carlo reference calculation</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(b) Difference between SOLENE and Monte-Carlo</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(c) Difference between TRABOULE and Monte-Carlo</figcaption></figure>

Figure 9: 2D fields of net longwave radiation $L^*$ on WallA, Soil, and WallB at 5:30 pm on July 18, 2022 (case B). The contour lines are drawn with a value step of 5 W m⁻² for graph (a) and 2 W m⁻² for graphs (b) and (c). On the last two graphs, only the contour line at 0 W m⁻² deviation is labeled to enhance the clarity of the graphs.
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helicoidal vortex in the centre of the street. Conversely, in the RANS simulation, a counterclockwise vortex develops in the street.

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The configuration of wind perpendicular to a long street canyon has been widely studied in the literature. Hunter et al. [82] conducted RANS simulations of airflow in a street canyon with a length-to-width ratio of 7 and an inlet velocity of 5 m s⁻¹ at building height. More recently, Bazdidi-Tehrani et al. [83] investigated airflow and pollutant dispersion around a street canyon with a length-to-width ratio of 10, using LES simulations with an inlet velocity of 4.7 m s⁻¹ at building height. Both studies, consistent with the airflow patterns described by Oke [84], tend to corroborate the clockwise helicoidal vortex obtained in LES simulations. The opposite flow pattern observed in the RANS simulation may be attributed to an overestimation of recirculation lengths, a known limitation of RANS modeling [85, 86], which can modify the overall flow structure. Additionally, mesh resolution may have contributed to these deviations.

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### 4.4. Heat conduction and storage in walls and ground (D)

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This section presents and analyses the various output variables at the surface-averaged values level on July 18, 2022. For the sake of brevity, it focuses on WallB and Soil only. The analysis carried out for these two walls is still applicable to RoofA and WallA. Furthermore, the 1D profiles and 2D fields are discussed solely in relation to surface temperature and the base case ($D_1$) at 6:00 pm, which corresponds to a transitional period. This allows for the observation of dynamic effects, with WallA in direct sunlight and WallB in shade.
<figure><img src="image_15.png" /><figcaption>Figure 10: Mean velocity fields in the median plane FA1 and the horizontal plane FA2 (case C).</figcaption></figure>

4.4.1. Base case ($D_1$)

Surface averaged values. Regarding the average surface temperature on the Soil (Figure 12a), the results of the different models considered show consistent orders of magnitude and dynamics, with values within a range of variations of less than 1 °C, corresponding to a relative deviation of 5% with respect to the daily minimum and maximum temperature difference. Regarding the shortwave fluxes, no significant difference is observed (Figure 12b), but TRABOULE shows small variations in peak shape due to its mesh and a shorter timestep. Focusing on the conductive fluxes (Figure 12d), differences up to 40 W m⁻² can be observed for SOLENE-Microclimat during the night and on the afternoon compared to the other models results. This deviation in the conductive fluxes also induces a difference in the convective (Figure
<figure><img src="image_16.png" /><figcaption>Figure 11: Lateral and top views of the time-averaged velocity streamlines colored by the mean velocity (case C).</figcaption></figure>

12e) and longwave (Figure 12c) fluxes.

Also for WallB (Figure 13), the surface temperatures simulated by the four models are close, within a range of less than 1 °C, corresponding to a relative deviation of 5% with respect to the daily minimum and maximum temperature difference. A small lag of the simulated conductive fluxes is observed for SOLENE-Microclimat between 12 pm and 7 pm (Figure 13d), which causes the observed lower temperature during the day and consistently lower longwave emissions (Figure 13c). This induces a higher temperature difference between the air and WallB in the afternoon and consequently a higher convective flux (Figure 13e) for SOLENE-Microclimat. Finally, the small difference in the shortwave fluxes estimated by SOLENE-microclimat or -SUSHI (Figure 13b) involves lower fluxes than for MATHIS and TRABOULE-ProLB. This
<figure><img src="image_17.png" /><figcaption>Figure 12: Average surface temperature and heat fluxes density on Soil on July 18, 2022 (case $D_1$).</figcaption></figure>
deviation can be explained by the different shortwave radiative models used, but cannot explain the deviation observed in the other fluxes and the temperature, as it is not observed for SOLENE-SUSHI. Hence, these deviations are rather due to the solid wall model and the limitation to three longwave reflections for SOLENE-Microclimat.

1D profiles. The PS1 and PS2 profiles from SOLENE-Microclimat, SOLENE-SUSHI, and TRABOULE shown on Figure 14 highlight constant deviations between the different models, except on WallB where SOLENE-SUSHI and TRABOULE results are close. Regarding more specifically the PS1 profile on WallA, TRABOULE shows a sudden decrease in surface temperature from $z = 0$ m to $z = 2.5$ m, which may be attributed to the presence of a shadow cast by its surrounding. On the contrary, regarding the PS1 profile on WallB, all curves have a similar slope, showing a surface temperature decreasing with $z$. This expected behavior is due to stronger longwave emissions from the Soil reaching the walls close to the ground. Regarding the PS2 profiles, a slight difference in the shape of TRABOULE can be observed, with a decreasing temperature toward the side edges for wallA and wallB, while the other two models show an increasing temperature. These deviations can be explained by the differences in the sky models, the meshing, and the modelling of the surrounding ground. The different models predict the part of the Soil in the sun approximately between $y = 20$ m and $y = 35$ m, with a temperature increase of about $1°C$ at the transition. This temperature difference between the shaded and sunlit surface is small because the solar heat flux is low at this time, and the temperature of the rest of the surface in the shade is still high due to the inertia of the ground, which has
<figure><img src="image_18.png" /><figcaption>Figure 13: Average surface temperature and heat fluxes density on WallB for the four models under study (case $D_1$).</figcaption></figure>
been heated up by the sun during the afternoon. Similarly, a surface temperature variation between 1°C and 1.5°C is predicted by all models along the PS1 profile on the Soil because of the inertia of the ground, which was in the shade near WallA (negative x) and in the sunshine near WallB in the afternoon.

<figure><img src="image_19.png" /><figcaption>Figure 14: 1D profiles of surface temperature $T_s$ on WallA, Soil, and WallB at 6:00 pm on July 18, 2022 (case $D_1$).</figcaption></figure>

2D fields. The Soil temperature field from SOLENE-Microclimat shown on Figure 15a clearly highlights the sun patch formed on the surface between $y = 10$ m and $y =$
35 m. Similarly, a band of lower temperatures is observed for negative x near WallA due to thermal inertia. For both WallA and WallB, the higher surface temperatures near the western edge of the street (y = 35 m) can be explained by the shortwave reflections or longwave emission from the sunlit part of the Soil. This effect is also due to the non-isotropic sky model used in SOLENE.

Figure 15 shows the corresponding 2D fields of surface temperature difference $\Delta T_s$ with SOLENE-Microclimat for TRABOULE (15c) and SOLENE-SUSHI (15b). For both models, the higher deviation with SOLENE-Microclimat is observed on the Soil near WallA, corresponding to the part of the ground that was in shadow in the afternoon. This deviation of around 1°C highlights the effects of the different conduction models. In addition, for TRABOULE, temperature deviations up to 1.7°C with respect to SOLENE-Microclimat can be observed on the Soil around the transition zone between shaded and sunlit zones, due to the differences in the mesh. The deviations observed between TRABOULE and SOLENE-Microclimat on WallA and WallB near the edges of the street are due to differences in the view factor calculation and lateral boundary conditions treatment, already identified in the analysis of case B. Finally, the sudden decrease in surface temperature from $z = 0$ m to $z = 2$ m for negative y values can be attributed to the shadow cast by WallB. This is observed only for TRABOULE because of its smaller timesteps, which allows for a finer evolution of shadows.

In conclusion, the temperature fields on the Soil, particularly at the transition between sunlit and shaded areas, show the largest deviations between models, attributed to differences in conduction models and meshing. TRABOULE, with its
<figure><img src="image_20.png" /><figcaption>(a) SOLENE-Microclimat</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>(b) Difference between SOLENE-SUSHI and SOLENE-Microclimat</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>(c) Difference between TRABOULE and SOLENE-Microclimat</figcaption></figure>

Figure 15: 2D fields of surface temperature $T_s$ on WallA, Soil, and WallB at 6:00 pm on July 18, 2022 (case $D_1$). The contour lines are drawn with a value step of 0.5 °C for graph (a) and 0.2 °C for graphs (b) and (c). On the last two graphs, only the contour line at 0 °C deviation is labeled to enhance the clarity of the graphs.
finer timestep, captures more precise shadow dynamics, while the specific behav-
ior of SOLENE-Microclimat is linked to its non-isotropic sky model but simplified
conduction treatment.

4.4.2. Variant case (D₂)

Figure 16 shows the average surface temperature and heat fluxes density on Soil for MATHIS, SOLENE-Microclimat, SOLENE-SUSHI, and TRABOULE-ProLB. Note that two curves are plotted for TRABOULE-ProLB. The curve labelled TRABOULE-ProLB<sub>TWF</sub> refers to the model as presented in section 3, which uses a Temperature Wall Function (TWF), while the curve labelled TRABOULE-ProLB<sub>CRL</sub> replaces the TWF with a convective heat transfer coefficient calculated using the McAdams correlation [61] to separate the effects of the TWF from the other aspects of the aeraulic model. The surface temperatures simulated by the four models differ significantly, with a range of variations up to 15 °C. In particular, when using a TWF, TRABOULE-ProLB always predicts a higher surface temperature, around 8 °C, than other models. However, even when correlations are used, the surface temperatures predicted by the different models differ by up to 7 °C. According to Figure 16e, this is mainly due to the estimation of the convective heat flux, and in particular the choice of the correlation used to calculate the convective heat transfer coefficients. In addition, the conductive fluxes (Figure 16d) differ when estimated by SOLENE-Microclimat compared to the other models. These deviations in the convective and conductive fluxes are likely to cause the deviations observed in the longwave radiative fluxes (Figure 16c), which are consistent with the surface temperature deviations.

Regarding WallB (Figure 17), no difference compared to case D₁ is observed in the
<figure><img src="image_23.png" /><figcaption>Figure 16: Average surface temperature and heat fluxes density on Soil on July 18, 2022 (case $D_2$).</figcaption></figure>
shortwave fluxes, except for TRABOULE-ProLB, which shows slight deviations due to the use of a coarser surface mesh in this variant case. As for the Soil, the surface temperatures simulated by TRABOULE-ProLB with the TWF are always higher, about 4°C, than those predicted using a CHTC correlation (Figure 17a). When using CHTC correlations, the surface temperature remains in a range of variation around 3°C. These variations result from deviations in all fluxes. In particular, the convective fluxes show significant variations, with a range of 50 W m⁻², mainly due to the aeraulic model and the choice of correlations. Deviations up to 40 W m⁻² are also observed for the conductive fluxes, but the strong discrepancy found for SOLENE-Microclimat results on the Soil is not found for WallB. Smaller deviations of around 20 W m⁻² are observed for the longwave and shortwave fluxes. For longwave radiative fluxes, SOLENE-Microclimat simulates lower net emissions than the other models, certainly due to the limitation to three reflections in the model, as the deviation is not observed for SOLENE-SUSHI.

In conclusion, significant variations are observed between the models, particularly with TRABOULE-ProLB when using a TWF, which consistently predicts higher temperatures. These deviations are mainly due to the calculation of the convective heat fluxes, with the use of CHTC correlations or TWF, which significantly impacts the simulation results.

## 4.5. Synthesis

Case A: The main deviations on shortwave radiation results are observed on WallB, which is shaded. These deviations can be primarily explained by the difference in the sky models used: Perez or isotropic. Other deviations are observed on the
<figure><img src="image_24.png" /><figcaption>Figure 17: Average surface temperature and heat fluxes density on WallB on July 18, 2022 (case $D_2$).</figcaption></figure>
sunlit/shaded boundary on the Soil due to mesh differences. In addition, deviations are observed on WallA and WallB near the Soil, especially in the central area of the street, that may be related to the treatment of multireflections. Moreover, the asymmetric flux distribution observed on the Soil cannot be accounted by the infinite street canyon hypothesis.

Case B: In regard to longwave radiation, deviations are observed near the edges of the surfaces. These deviations can be attributed to the view factor calculation. On the lateral edges of WallA and WallB, deviations are observed due to lateral boundary condition differences, with some models accounting for an infinite ground surrounding the simulation domain, while others do not. Moreover, as for case A, the infinite street canyon hypothesis cannot model the non-homogeneous flux field, leading to deviations near the edges of the faces.

Case C: The two CFD models compared give results with similar average velocities within the canyon, but distinct flow structures. In particular, the direction of rotation of the vortex within the street was found to be opposite and the different recirculation lengths substantially deviate.

Case $D_1$: The most significant temperature deviations among models occur on the Soil, particularly at the sunlit/shaded boundary. These deviations can be explained by differences in conduction models and meshing. Notably, the finite volume method with coarse discretisation and the electric analogy model (using three resistances and three thermal capacitors) show significant deviations, whereas the detailed semi-analytical method and the finely discretised finite volume method produce similar results.
Case $D_2$: Finally, in fully coupled models, significant deviations were observed, particularly when using a Temperature Wall Function, which consistently resulted in higher temperature predictions. These deviations can be primarily attributed to differences in the calculation of convective heat fluxes, whether through correlations for the convective heat transfer coefficient or the use of a Temperature Wall Function.
706 **5. Conclusions and perspectives**

707 This paper presented an academic benchmark framework as a first step of a
708 comprehensive reference methodology for qualification and validation of urban mi-
709 croclimate models at the neighborhood scale. The proposed methodology follows
710 an incremental phenomenological approach, structured around the key physical pro-
711 cesses occurring in an idealized street canyon with well-defined conditions. The
712 methodology relies on the intercomparison of simulation results, incorporating refer-
713 ence data with a known standard deviation where available. Applied to four urban
714 microclimate models, MATHIS [42], SOLENE-Microclimat [11], SOLENE-SUSHI
715 [43], and TRABOULE-ProLB [44], the results highlighted that:

• The methodology enables the analysis of surface-related data (e.g., heat fluxes, temperatures) based on surface averages, 1D profiles and 2D fields and wind-related data based on 2D fields and streamlines.

• The deviations observed among the simulations results were attributed to dif-
ferences in view factor calculations, sky models, turbulence modelling, meshing,
conduction methods, and convective flux modelling.

• The suggested incremental framework allows to identify the potential sources
of deviations within the physical models, that usual measurement-based vali-
dation methods often fail to detect due to the coupling of physical phenomena.

* Convective flux modelling emerged as the main source of surface temperature deviation in the fully coupled case, and is stressed as a critical limitation of current microclimate models.
728

On the basis of the above conclusions, four main perspectives can be outlined:

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* Convective flux models, whether based on heat transfer coefficient correlations or Temperature Wall Functions in CFD, require further research to improve reliability.

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737

* In addition to analyzing surface- and wind-related data, evaluating the impact of different modelling assumptions, particularly convective flux modelling, on thermal comfort or building energy performances could provide valuable insights. While differences in thermal comfort estimation due to unsuitable convective models are likely smaller than surface temperature deviations, they could still be significant.

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* This framework is aimed to be applied to more urban microclimate models. Therefore, the complete dataset, including additional unexamined results, along with an analysis tool and a data paper, will be made publicly available via the ANR DIAMS project.

742

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747

* Future developments should integrate additional physical phenomena, such as vegetation and humidity transport, and expand to more realistic laboratory configurations and real urban environments with measurements to validate microclimate simulations and evaluate the performance of physical models. This will require the production and diffusion of comprehensive experimental datasets.
748 **CRediT authorship contribution statement**

749 **Teddy Gresse**: Software, Validation, Formal analysis, Investigation, Data cu-
ration, Visualization, Writing - Original Draft. **Julie Soriano**: Software, Investiga-
750 tion, Visualization, Writing - Original Draft. **Auline Rodler**: Conceptualization,
751 Methodology, Software, Investigation, Validation, Supervision, Writing - Review &
752 Editing. **Jean-Claude Krapez**: Software, Investigation, Writing - Review & Edit-
753 ing. **Jean Pierro**: Software, Investigation. **Félix Schmitt**: Software, Investi-
754 gation. **Mathieu Galtier**: Software, Investigation. **Frédéric André**: Software,
755 Methodology, Supervision. **Frédéric Kuznik**: Software. **Lionel Soulhac**: Soft-
756 ware. **Damien David**: Software. **Jérôme Jacob**: Software. **Marjorie Musy**:
757 Conceptualization, Methodology, Software, Writing - Review & Editing, Supervi-
758 sion, Funding acquisition. **Lucie Merlier**: Conceptualization, Methodology, Soft-
759 ware, Writing - Review & Editing, Supervision, Project administration.
760

761 **Declaration of Competing Interest**

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

765 **Acknowledgments**

766 This work was supported by the ANR DIAMS project, grant ANR-21-CE22-0010
767 of the French Agence Nationale de la Recherche.

768 The ProLB software used in this study is developed within a scientific collaboration
<footnote n="769">⁷⁶⁹ including CS GROUP, Renault, Airbus, Safran, Ecole Centrale de Lyon, CNRS and
⁷⁷⁰ Aix-Marseille University.</footnote>

<footnote n="771">⁷⁷¹ This work was granted access to the HPC resources of TGCC under the allocation
⁷⁷² 2022-A0132A13804 and 2023-A0152A14631 made by GENCI.</footnote>
<figure><img src="image_25.png" /><figcaption>Figure A.18: Classification of urban climate models in terms of their spatial scales and resolution. The four urban microclimate models selected for the study are also indicated in white boxes in the figure.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Figure A.19: Meteorological data for configuration *D* over the studied period.</figcaption></figure>
## Appendix B. Resolution schemes of the microclimate models

Figure B.20 shows the differences in the resolution schemes of the four microclimate models used in this study.

*Common features in the resolution schemes.* For each timestep, the shortwave radiative transfer is preprocessed in the different models using the direct and diffuse shortwave primary fluxes on an horizontal surface as input. Then, the models use an iterative method to perform surface energy balances, which take into account shortwave, longwave, convective and conductive fluxes, and to compute temperature in solids with a conduction model. As longwave exchanges are dependent on surface temperatures, the treatment of this phenomenon is coupled to the surface energy balance, and takes as input the longwave primary flux on an horizontal surface.

*Differences in timesteps integration.* For all models but SUSHI, the energy balance is solved iteratively time step after time step. SUSHI solves it in the Fourier domain while considering simultaneously all time steps of the period. The iterations made necessary by the non-linear couplings are performed afterwards, by switching alternately from the Fourier domain to the time domain and vice versa.

*Differences in the resolution of the thermo-aeraulic transfers.* The thermo-aeraulics model in MATHIS is separated in two modules. The velocities are first computed as a preprocessing at each timestep, taking as input a vertical velocity profile (equation 1). Then, air temperatures are computed within the iterative loop involving the surface energy balance, the conduction model and the longwave model. A boundary condition for air temperature is necessary, and taken as the temperature $T_{a,2}$ for this
<figure><img src="image_27.png" /><figcaption>(a) MATHIS</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>(b) SOLENE-Microclimat</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>(c) SOLENE-SUSHI</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>(d) TRABOULE-ProLB</figcaption></figure>

Figure B.20: Resolution scheme of the four studied microclimate models. Input data are in green and defined in section 2.3. Computed variables are in red: $T_s, T_a$ [K]: surface and air temperatures, $K^*, L^*, Q_H$ [W m$^{-2}$]: net shortwave, net longwave, and convective flux densities, $U$ [m s$^{-1}$]: air velocity. Model names are in blue.
796

benchmark. This resolution scheme suppose to neglect the impact of the computed
air temperatures on the velocity field.

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In SOLENE-Microclimat, the CFD model Code-Saturne is used first as a prepro-
cessing to compute a steady velocity field at each timestep. It takes as input vertical
profiles of velocity and turbulent kinetic energy, (equations 1 and 2). Then, Code-
Saturne computes the air temperature field coupled with the iterative loop involving
the surface energy balances, the conduction model and the longwave model. For that
purpose, a vertical air temperature profile is needed as input. In this study, a uni-
form vertical temperature profile is taken with the temperature $T_{a,2}$. This approach
prevent to model the buoyancy effects.

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No aeraulic model being included in SOLENE-SUSHI, a uniform field of velocity
and air temperature are taken, respectively equal to $U_{10}$ and $T_{a,2}$.

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Finally, in ProLB, a coupling between the velocity field and the air temperature
field is used, allowing to take buoyancy into account. ProLB is therefore able to
transmit directly the surface temperature to TRABOULE, the air temperature being
only used within the ProLB module. Concerning the input data, the same velocity,
turbulent kinetic energy and air temperature vertical profiles described for SOLENE-
Microclimat are necessary to estimate the inlet quantities.

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