# A multi-criteria review of mean radiant temperature evaluation models for urban thermal comfort

A Merville, A Rodler, M Musy, Simon Rouchier, E Dufrasnes

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A Merville, A Rodler, M Musy, Simon Rouchier, E Dufrasnes. A multi-criteria review of mean radiant temperature evaluation models for urban thermal comfort. CISBAT 2023, Sep 2023, Lausanne, Switzerland. pp.092020, 10.1088/1742-6596/2600/9/092020. http://hal-05018374

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# A multi-criteria review of mean radiant temperature evaluation models for urban thermal comfort

A Merville¹,², A Rodler¹,², M Musy¹,², S Rouchier², E Dufrasnes³

¹Equipe de Recherche BPE, Cerema, Nantes, France

²LOCIE CNRS UMR 5271, Université Savoie Mont Blanc, Chambéry, France

³Laboratoire AMUP, Ecole d'Architecture de Strasbourg, France

E-mail: alexandre.merville@cerema.fr

**Abstract.** This article reviews the main tools used to simulate the mean radiant temperature ($T_{mrt}$) under outdoor conditions. Urban environment complexity and the multiplicity of the radiative fluxes force models' developers to simplify the problem. To summarize the common assumptions of these models, a graphical tool is proposed. In addition to the physical description, effective coherence of models as a tool for urban decision-making is analyzed. Based on this double vision, this article achieves a multi-criteria analysis of $T_{mrt}$ calculation. Nine tools (ENVI-met, Solene-microclimat, SOLWEIG, RayMan, CitySim, Ladybug-Grasshopper, VTUF, DART and LASER/F) are evaluated against five criteria. Three criteria relate to physics implementation: completeness of the considered radiative phenomena, representation of the environment and surface temperature modeling. Two criteria deal with the operational capabilities: consistency with the needs of city-planners and practical accessibility. These criteria highlight various issues, and in particular the conflict between user-friendly practicality and an accurate description of physical phenomena.

## Introduction

A wide variety of tools have been developed in recent years to overcome the mean radiant temperature ($T_{mrt}$) calculation. The diversity of the implementations testifies the difficulty of modeling $T_{mrt}$ due to the diversity of radiative sources and the complexity of the urban environment. This article focuses on the $T_{mrt}$ simulation and attempts to build a multi-criteria analysis of the current tools. It aims to physically describe the main models but also raises the question of the users' needs, and thus assesses the accuracy due to simplification choices.

## 1. An overview of existing simulation tools

Some assumptions need to be taken into account when modeling the radiative environment. To summarize them, a graphic representation is proposed in figure 1 for its general form and in figure 2 to show its application to SOLWEIG. Based on the reading of about a hundred papers, it summarizes main processes involved in the calculation of $T_{mrt}$. Its organization is built to meet the implementations of the various existing tools. In other words, it attempts to represent on a single graph the significant links, assumptions, sub-models, etc, that authors have chosen over the years. This representation is divided into three parts corresponding to interconnected sub-models: the **radiative model** which is directly linked to the $T_{mrt}$ and describes sources and transmission, the **thermal model** which is crucial for determining surface temperatures

<figure><img src="image_2.png" /></figure>
(and hence material thermal inertia) and the **airflow model** which contributes to the surface energy balance.

Vegetation receives a special treatment and is described in each of the three sections.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** The modeling of the $T_{mrt}$</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Application on SOLWEIG</figcaption></figure>

The proposed representation assumes finally some limitations, as it is based on commonly used modeling choices. For instance, the water model is only linked to the evaporation. So, in the case of the infrared flux emitted by leaves, we limit ourselves to the evocation of a 'detailed' modeling (which may therefore include a water model). Furthermore, for the convenience of the reader, we do not distinguish the different treatments usually used for the facades and for the ground. Nevertheless, this makes it possible to adapt to any model with a shading set, such as the representation proposed by Naboni [1].

## 2. Beyond physics considerations, taking into account the needs of city planners

Studies on urban climate have been carried out since at least the 80s and Oke's work. However, not all urban projects take thermal comfort into account. In this context, it seems essential to develop tools which are accessible to a wide range of actors, therefore adapted to non-specialist users [2] and which meet their needs [3].

### 2.1. A spatial scale adapted to the phenomenon under study

It is essential to target the right spatial scale of study depending on the problem being addressed. The physical review of $T_{mrt}$ proves the need to use a micro-scale approach in order to consider phenomena with a high resolution: transition from a shade to a sunny zone, consideration of materials and their storage capacity, ... [4]. For instance, LCZs which are very often cited as an accurate microclimate tool and are also implemented in a decision-support logic via several programs, don't address the issue of comfort. While a link between morphological indicators such as those used in the LCZ classification and climatic indicators has been demonstrated, thermal comfort requires more detailed consideration of the urban environment.
## 2.2. Ability of tools to represent mitigation solutions

One of the roles of city planners is to propose mitigation solutions. But the assumptions and simplifications that models take, limit the range of solutions that can be modeled. In order to meet city-planners' needs and rather than being a consequence of models implementation, the ability of tools to represent mitigation solutions needs to be studied by developers. Several aspects have to be considered based on the existing solutions [5]:

(i) Representation of vegetation: vegetation has multiple cooling roles through its ability to create shade and to evaporate. There are therefore many mitigation solutions based on vegetation (green roofs or walls, planting trees, desealing soils...). Parameters that play a role in the effectiveness of these solutions must be taken into account, such as foliage transparency, (that impacts shading) or water stress (which plays a role in the vegetation's capacity to evaporate).

(ii) Building representation: this can be divided into two categories, surface thermo-radiative properties (for instance cool paints) and geometric description. This second one deals with the capacity to represent structures that create shade (solar protection, porches,...).

## 2.3. Data adapted to city-planners’ knowledge

To obtain a more accurate model or to integrate mitigation solutions, the models are improved and integrate more parameters that must be documented by the user. However, the urban environment is complex and heterogeneous, which makes access to data difficult [6]. While cities' land registry are fairly accessible data, information concerning specific materials, precise geometries (such as slope), type of vegetation, etc, can be difficult to find for an urban planner. As a bad documentation of input (due to a lack of data) can lead to unrealistic results, a minimum number of inputs is more adapted to city planners use.

## 2.4. Additional factors for an overview of simulation tools

As thermal comfort is not just a function of $T_{mrt}$, it seems relevant to consider comfort indices through a bioclimatic approach by crossing radiative effect, wind and air temperature. For that purpose, compatibility with a GIS proves to be relevant because GIS are commonly used to cross data from different fields. More than limiting technical problems, the generation of a thermal comfort map on a GIS can enable actors of the city to confront several aspects and thus remove some of the above-mentioned problems. CAD tools are also well established in design offices but are used by a less diverse range of actors.

# 3. Simplifications and their impacts

The various models assumptions were described in the first part using figure 1 but were limited to a theoretical vision. This third part studies the comparisons carried out for several models or the comparisons carried out for one model but using different assumptions (or sub-models), in order to understand the impact of a simplification and the accuracy of each tool.

## 3.1. Models comparisons

The comparison of tools has two interests: determining which one has the best results and highlighting the impact of implementation differences on the results. The articles studied here were selected because they were involving the comparison of at least two tools, or focused on the simulation of the $T_{mrt}$ (or the different radiative components) or comparing simulations with observation [7]. Comparing the tools highlights the importance of certain simplifications:

* The transition from shadow to light leads to very significant differences, up to a simulated-observed $T_{mrt}$ difference of 10 to 20 degrees. The importance of a high resolution mesh is therefore essential.
* The ability to restore the energy stored in materials is crucial at night or in the case of long time shading.

* For trees, the shading effect (and thus the transmissivity associated with vegetation) is predominant over the evapotranspiration effect.

Concerning the comparison of tools results with experimental data, the disparity of experimental protocols makes it impossible to draw any general conclusions about the accuracy of the tools [8]. The diversity of the conclusions found when carrying out our bibliographic study should motivate us to take a critical look at the question of the validity of a tool. Finally, it should be noted that none of the articles studied emphasizes the calculation times.

## 3.2. Simplifications' impacts comparison

Although comparing models provides some insights, it does not allow us to fully understand a particular simplification, as it depends on many other factors. However, some studies focus on the weight of a single simplification, or the impact of switching from one assumption to another. This type of reasoning leads to several observations on the results:

* The choice of the diffusive model (isotropic or anisotropic sky) can lead to deviations of 3°C on the $T_{mrt}$ [9].

* Taking into account the inter-reflections is a decisive factor in the energy balance. The weight of the first one is largely preponderant on the following ones.

* Air absorption has a reduced impact compared to other phenomena in the general case.

The calculation time is occasionally investigated. The airflow model is particularly highlighted because, in the case of CFD resolution, this part can account for 90% of the calculation time, without being the key point of the calculation of the $T_{mrt}$ [10]. The method of ray-tracing for taking into account the inter-reflections is also very time-consuming compared with the radiosity method, or even to a simplified approach.

# 4. Multi-criteria analysis

## 4.1. Methodology

According to the considerations described so far, criteria have to be developed in order to describe the level of simplification of $T_{mrt}$ simulation tool and to understand their consequences. Five criteria are thus emphasized.

(i) Completeness of radiative phenomena: this expresses the ability of a tool to consider all radiatives fluxes;

(ii) Representation of the environment: this expresses the ability of a tool to correctly transpose the reality of the environment (diversity of urban forms, materials, vegetation);

(iii) Surface temperature modeling: this expresses the ability of a tool to simulate accurate surface temperature;

(iv) Consistency with the needs of city-planners: this expresses the ability of a tool to take into account users needs and levers;

(v) Practical accessibility: this expresses the ability of a tool to take into account the technical constraints of urban-planners.

The used scale to rate these criteria is detailed in figure 3.

No criteria based on tool performance were proposed, as comparisons in the literature were not deemed sufficiently consistent. Nevertheless the weight given to each sub-criterion of the first three criteria testifies to the review made in part 3. The change from 0 to 1 indicates that a phenomenon has been taken into account. The addition of half a point indicates greater
<table><thead><tr><th rowspan="2"></th><th rowspan="2">Source</th><th>Short-wave</th><th>Opt iso sky</th><th>Opt not included</th><th>Opt included</th></tr><tr><th>Surface long-wave</th><th colspan="3">2pt T<sub>50</sub>-T<sub>70</sub></th></tr></thead><tbody><tr><td rowspan="3">1</td><td rowspan="3">Transmission</td><td>Tree long-wave</td><td>Opt not included</td><td>2pt T<sub>50</sub>-T<sub>70</sub></td><td>2pt T<sub>50</sub> modeling</td></tr><tr><td>Inter-reflections</td><td>Opt not included</td><td>2pt T<sub>50</sub> globalized reflection</td><td>2pt one prior reflection</td><td>2pt more than one reflection</td></tr><tr><td>Air absorption</td><td>Opt not included</td><td colspan="3">0,5pt included</td></tr><tr><td rowspan="5">2</td><td rowspan="2">Overall geometry</td><td>Domain</td><td colspan="3">Opt reduce domain (canyon street)</td></tr><tr><td>Dimension</td><td colspan="3">Opt 2,50 or cube cell</td></tr><tr><td rowspan="2">Environment</td><td>Thermo-radiative properties (albedo emissivity, ...)</td><td>Opt single properties</td><td>2pt by group</td><td>2pt by mesh</td></tr><tr><td>Trees geometry</td><td colspan="3">Opt not included</td></tr><tr><td rowspan="3">3</td><td rowspan="3">Modeling</td><td>Trees type</td><td>Opt single tree</td><td colspan="2">2pt otherwise</td></tr><tr><td>Group</td><td colspan="3">Opt single T<sub>50</sub></td></tr><tr><td>Type of model</td><td>Opt not modelled</td><td>2pt by group</td><td>2pt T<sub>50</sub> by mesh</td></tr><tr><td></td><td></td><td>Convection</td><td>Opt not included</td><td>2pt simplified</td><td>2pt detailed (CFD or simuholder)</td></tr><tr><td></td><td></td><td>Evapotranspiration</td><td>Opt not included</td><td>2pt simplified</td><td>1,5 detailed</td></tr></tbody></table>

<table><caption>Figure 3. Scale of sub-criteria</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Output</th><th rowspan="2">Comfort indicator</th><th colspan="2">Opt without</th><th colspan="1">1pt with</th></tr><tr><th>Opt single properties</th><th>2pt by group</th><th>2pt by mesh</th></tr></thead><tbody><tr><td rowspan="5">4</td><td rowspan="5">Mitigation solution</td><td>Building</td><td colspan="2">Facade modification</td><td colspan="2"></td></tr><tr><td>Vegetation</td><td colspan="2">Mitigation solution (sun screen)</td><td colspan="2">Opt 2,50</td><td>1pt 3D</td></tr><tr><td>Water</td><td colspan="2">Green mitigation solution</td><td colspan="2">Opt not included</td><td>1pt included</td></tr><tr><td></td><td colspan="2">Tree type</td><td colspan="2">Opt single tree</td><td>1pt otherwise</td></tr><tr><td></td><td colspan="2">Blue mitigation solution</td><td colspan="2">Opt not included</td><td>0,5pt otherwise</td></tr><tr><td rowspan="5">5</td><td rowspan="5">Time cost</td><td>Technical limits</td><td colspan="2">Opt not compatible</td><td colspan="2">Opt not included</td><td>0,5pt included</td></tr><tr><td>Accessibility</td><td colspan="2">Open source</td><td colspan="2">Opt no</td><td>1pt yes</td></tr><tr><td></td><td colspan="2">Free</td><td colspan="2">Opt no</td><td>1pt yes</td></tr><tr><td></td><td colspan="2">Technical limits</td><td colspan="2">Opt strong</td><td>1pt medium</td><td>2pt good</td></tr><tr><td></td><td colspan="2">Compatibility</td><td colspan="2">Opt not compatible</td><td>1pt CAD compatible</td><td>2pt CAD compatible</td></tr></tbody></table>

<table><caption>Figure 4. Multi-criteria analysis</caption><thead><tr><th colspan="2">Criteria</th><th colspan="2">Sub-criteria</th><th>ENVI-Met</th><th>Solene-microclimat</th><th>SOLWEIG</th><th>RayMan</th><th>CitySim</th><th>Ladybug-Grasshopper</th><th>VTUF</th><th>DART</th><th>LASER/F</th></tr></thead><tbody><tr><td rowspan="5">1</td><td rowspan="5">Completeness of radiate phenomena</td><td rowspan="4">Source</td><td>Short-wave</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td></tr><tr><td>Surface long-wave</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Tree long-wave</td><td>1,5</td><td>1,5</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1,5</td><td>1,5</td><td>0</td></tr><tr><td>Inter-reflections</td><td>1</td><td>2</td><td>1</td><td>1</td><td>1</td><td>1</td><td>2,5</td><td>2</td><td>2</td></tr><tr><td>Transmission</td><td colspan="2">Air absorption</td><td>0,5</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0,5</td><td>0</td></tr><tr><td colspan="2"></td><td colspan="2">TOTAL</td><td>5</td><td>5,5</td><td>3</td><td>4</td><td>3</td><td>3</td><td>5</td><td>6</td><td>4</td></tr><tr><td rowspan="5">2</td><td rowspan="5">Representation of the environment</td><td rowspan="4">Overall geometry</td><td>Domain</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Dimension</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td></tr><tr><td rowspan="2">Environment</td><td>Thermo-radiative properties (albedo emissivity, ...)</td><td>2</td><td>2</td><td>1</td><td>0</td><td>2</td><td>2</td><td>2</td><td>2</td><td>2</td></tr><tr><td>Trees geometry</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td colspan="2"></td><td>Trees type</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td colspan="2"></td><td colspan="2">TOTAL</td><td>5</td><td>6</td><td>4</td><td>2</td><td>5</td><td>6</td><td>5</td><td>6</td><td>6</td></tr><tr><td rowspan="5">3</td><td rowspan="5">Surface temperature modeling</td><td rowspan="4">Domain</td><td>Group</td><td>2</td><td>2</td><td>1</td><td>0</td><td>2</td><td>2</td><td>2</td><td>2</td><td>2</td></tr><tr><td>Type of model</td><td>1</td><td>2</td><td>1</td><td>0</td><td>2</td><td>2</td><td>2</td><td>1</td><td>2</td></tr><tr><td>Convection</td><td>1,5</td><td>1,5</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1,5</td><td>0</td><td>1,5</td></tr><tr><td>Evapotranspiration</td><td>1,5</td><td>1,5</td><td>1</td><td>0</td><td>1,5</td><td>0</td><td>1,5</td><td>0</td><td>1,5</td></tr><tr><td colspan="2"></td><td colspan="2">TOTAL</td><td>6</td><td>7</td><td>3</td><td>0</td><td>6,5</td><td>4</td><td>7</td><td>3</td><td>7</td></tr><tr><td rowspan="5">4</td><td rowspan="5">Consistency with the needs of city-planners</td><td rowspan="4">Output</td><td>Comfort indicator</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td>Building</td><td>2</td><td>2</td><td>1</td><td>0</td><td>2</td><td>2</td><td>1</td><td>0</td><td>2</td></tr><tr><td>Mitigation solution (sun screen)</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td></tr><tr><td>Vegetation</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td rowspan="2">Water</td><td>Tree type</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td colspan="2"></td><td>Blue mitigation solution</td><td>0,5</td><td>0,5</td><td>0,5</td><td>0</td><td>0</td><td>0,5</td><td>0,5</td><td>0,5</td></tr><tr><td colspan="2"></td><td colspan="2">water stress</td><td>0,5</td><td>0,5</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0,5</td><td>0</td><td>0,5</td></tr><tr><td colspan="2"></td><td colspan="2">TOTAL</td><td>6</td><td>7</td><td>4,5</td><td>3</td><td>4</td><td>6,5</td><td>5</td><td>0</td><td>7</td></tr><tr><td rowspan="5">5</td><td rowspan="5">Practical accessibility</td><td rowspan="4">Time cost</td><td>Time cost</td><td>0</td><td>0</td><td>2</td><td>2</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Technical limits</td><td>0</td><td>1</td><td>2</td><td>2</td><td>1</td><td>2</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Compatibility</td><td>0</td><td>0</td><td>2</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Opensource</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td colspan="2"></td><td colspan="2">Free</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td colspan="2"></td><td colspan="2">TOTAL</td><td>0</td><td>1</td><td>8</td><td>5</td><td>3</td><td>5</td><td>4</td><td>1</td><td>2</td></tr></tbody></table>

precision, without it having been demonstrated that this was particularly decisive (switch to a CFD, consideration of more than one reflection, air absorption). In the case of a decisive precision, an increase of one point is preferred (taking into account of a new phenomenon, anisotropic sky, precision on the domain).

Criteria 4 and 5 follow continuous progressions (only blue solutions differ, as they are less well described in the literature). In addition to the elements described above, points are awarded for free and opensource models, contributing to their accessibility but also to their understanding and development.

It should be noticed that criteria depend on each other : the surface temperature will only be well modeled if all the radiative phenomena and the environment are themselves correctly modeled, the time cost will be considered as good if a reduced number of phenomena are accurately studied (in particular the airflow model), ...

## 4.2. Results

Nine models have been selected for the multi-criteria study: Solene-microclimat, ENVI-met, SOLWEIG, RayMan, CitySim, Ladybug, VTUF, DART, and LASER/F. All have been widely studied and validated (in spite of the limitations previously mentioned), and enable the simulation of the $T_{mrt}$ on the local scale. Figure 4 presents in a table all the scores received for each criteria and sub-criteria according to the proposed methodology.
**5. Discussion and conclusions**

It is possible to identify which models validate or fail to validate each criterion, and thus to highlight two groups. Firstly, a combined group of ENVI-met, Solene-microclimat, VTUF, LASER/F, DART and CitySim, which provides a detailed description of $T_{mrt}$, but performs poorly in terms of practicality. However, CitySim focuses more on the building scale and therefore limits the detail of radiative phenomena. DART, on the other hand, targets radiation scattering very precisely, and is therefore light on building detail (and therefore surface temperature). The other group includes SOLWEIG, RayMan and Ladybug. They greatly validate the 5th criterion, but show modeling limitations. SOLWEIG stands out for its accessibility. Ladybug shows the greatest balance.

The models addressed the problem from different approaches: seeking very precise results, concentrating on the $T_{mrt}$ or a wider spectrum, seeking an accessible tool... The trade-off between fine-tuned problem description and accessibility is particularly highlighted here.

It is interesting to note the different perspectives offered by each of these tools: most of the tools are subject to regular improvements that tend to remove technical obstacles. However, some of these obstacles are implementation-related and can't be unlocked without a deep rethinking of the model (for instance, the meshing used in ENVI-met complexifies the possibility to model inter-reflections). There are two possible strategies to reach the objective of an accurate but fast calculation of $T_{mrt}$: the simplification of a complex model, by accepting the drop in accuracy that this may entail or an improvement of physical phenomena representation in simplified model. In this 2^nd^ case, surface temperature often represents a limit to the relevance of the results, and is therefore an interesting way of development. Finally, the 4^th^ criterion, globally correlated with the precise description of phenomena, can also help to frame future developments.

**Acknowledgments**

This research project is financed by ADEME and Oteis. The funding from DESIVILLE project is also acknowledged.

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