# Thermal behaviour of a building in its environment:
Modelling, experimentation, and comparison

Auline Rodler, Sihem Guernouti, Marjorie Musy, Julien Bouyer

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Auline Rodler, Sihem Guernouti, Marjorie Musy, Julien Bouyer. Thermal behaviour of a building in its environment: Modelling, experimentation, and comparison. Energy and Buildings, 2018, 168, pp.19 - 34. 10.1016/j.enbuild.2018.03.008. hal-01745078

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# THERMAL BEHAVIOUR OF A BUILDING IN ITS ENVIRONMENT: MODELLING, EXPERIMENTATION, AND COMPARISON

Auline Rodler¹,², Sihem Guernouti¹,²,³, Marjorie Musy¹,²,³, Julien Bouyer⁴

¹Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement (Cerema), France, Nantes, France

²Institut de Recherche en Sciences et Techniques de la Ville (IRSTV), Nantes, France

³CNRS UMR 6183, GeM, Université de Nantes, F-44000 Nantes, France

⁴Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement, Nancy, France

Corresponding author: sihem.guernouti@cerema.fr

Present/permanent address: Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement (Cerema), France, Nantes, France

## Highlights:

- In this paper, we consider the thermal behaviour of the building in its environment. A building energy model is developed and coupled to an urban modelling tool.

- In-situ measurements are performed to enlarge the database of thermal values used to validate the presented building model and the urban scale model. The models show a close agreement with the in-situ measurements.

- A sensitivity analysis is undertaken to highlight the parameters of influence which affect the performance of the building model: the airflow rate, the opening of blinds and external convective heat exchanges have the greatest impact. The importance of considering the surfaces of the local urban scene surfaces around a building is demonstrated.
ABSTRACT

A building influences its surrounding external environment, and its indoor environment is usually sensitive to its surroundings. In order to obtain a more accurate prediction of the indoor thermal behaviour of a building or a building stock, it is necessary to consider the interactions between the indoor and outdoor thermal environments.

The modelling approach presented in this paper is based on a building energy model and the urban modelling tool SOLENE-Microclimat. A sensitivity analysis is undertaken to highlight the parameters which influence the performance of the building model. Then, the thermal indoor behaviour of a building is compared to in situ experimental measurements and the outdoor thermal environment is evaluated in terms of external surface temperatures. The model's accuracy and behaviour is evaluated and a crossover approach with the sensitivity analysis results is proposed. The model obtains a good level of performance for almost all variables, unless some external surface temperatures intervals.

**keywords:** sensitivity analysis, in situ thermal measures, urban simulation, micro climate, building energy simulation.

Nomenclature

Symbols :

Greek

α absorptivity coefficient

ρ density, kg/m³

ε emissivity

Φ heat flow, W

τ solar transmission coefficient

σ stefan-boltzmann constant, W.m⁻².K⁻⁴

λ thermal conductivity, W.m⁻¹.K⁻¹

Latin

air air

alb albedo

b beam

B1 building 1

B2 building 2

B3 building 3

B4 building 4

B5 building 5

B6 building 6

B7 building 7

B1 blind opening ratio

c ceiling

i cell (soil or wall)

cond conductive

conv convective

d diffuse

E east oriented

h exchange coefficient, W.m⁻².K⁻¹

f facet

floor floor

C heat capacity, J.kg⁻¹.K⁻¹

Q heating or cooling power, W

ins inside the building

G internal heat generation, W.m⁻³

I infiltration and air flow heat loss, W

LW longwave radiation

LWD longwave radiation descending

down lower sensor

m material

sc mesh element of the scene

N north oriented

NW number of walls

out outside the building

r radiative

s sky

S surfaces (facet or mesh), m²

S south oriented

T temperature, K

∂t time step, s

k thermal conductance of the layer, W.K⁻¹

tri triangular mesh element

up upper sensor

V volume, m³

F view factors

E wall radiation, W.m⁻²

W west oriented wall

v wind velocity, m/s
1. INTRODUCTION

As the requirements for building energy efficiency are increasing, building energy simulation (BES) tools have been improved and are able to accurately represent the behaviour of building envelopes and systems. However, most of these tools are designed for individual buildings and are not suited to perform district or urban scale simulations. The surrounding buildings in a BES models are often only assumed as shadows and the other thermal exchanges are not simulated. Most of the time the weather inputs data are normalized inputs, which are not detailed or adapted to the specific site when the building is affected by both the natural and the built environment. The induced uncertainties of the local weather data and/or the in-situ materials properties can lead to inaccurate simulations. Indeed, several studies have shown that the urban microclimate has a significant impact on the calculation of building energy performance [1]–[6]. For example some authors have demonstrated that in an urban context calculating the thermal interactions and solar inter-reflection are necessary to achieve an accurate energy performance assessment [3]. Depending on the configuration of the buildings in terms of, for example, density and glazing ratio, the infra-red exchanges calculation appears to be the second physical improvement that should be performed to increase the accuracy of a simulation.

Given this realisation some BES tools were coupled with a microclimate model as performed using EnergyPlus and ENVI-met<fnref n="1" /> to evaluate the effects of urban environments on building energy needs [5]. The TrnSys tool was also used to perform the simulation of a street ‘canyon’ considering both radiative and airflow induced effects[1].

Other tools have been specifically developed to model the interactions between urban structures, so that to express their impact on urban climatic conditions and a building’s energy behaviour. These tools propose thermo-radiative functions initially designed to simulate the heat and radiation exchanges of this urban district with the atmosphere [7], [8], [9] and include microclimate models to consider the local climate features [10]. Only a few of them were improved in order to evaluate building energy performance [6], [11].

These last tools are usually validated by comparing the results of simulations to other proven simulations tools. Only a few in-situ comparisons were done, but most of the time, they rely on integrated data like air temperature or fluxes over a district [12]. Validations combining both measures for the inside and outside of the building are uncommon. In the best cases, some outside surface temperature sensors are used but only on the studied building and not for a large number of surfaces of the surrounding urban environment. On the contrary, if the monitored data for the urban environment are consequent, they are not for the building’s internal environmental behaviour [8], [9], [13].

Several large international and national projects have been focused on the validity of models for predicting energy consumption in buildings [14], [15]. The performance predictions of full-scale buildings needs to be compared to measures in order to evaluate the reliability of the tools [16]. A model’s validation process is based on mainly three steps: the analytical verification, the comparison with other similar tools and with an experimental validation.

The different audit steps usually proposed for example by the IPMVP (International Performance Measurement and Verification Protocol) published by EVO [17] or by the above mentioned international projects [14], [15] generally show a lack of concern for the impact of the local climate environment surrounding the building (urban surface temperatures and external local air temperatures).

<footnote n="1">¹ http://www.envi-met.com</footnote>
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Hence, this paper fills this gap by providing in situ measures of a block of dwellings, with internal and external temperature measurements. These latter measurements will provide information regarding the consideration of the building in its environment and will enlarge the thermal database used to validate the simulated building and urban scale models as well as the climatic data.

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This paper is structured as follows: first, we present a model, which considers the interactions between urban structures, urban climatic conditions and building energy behaviour. Therefore, SOLENE-Microclimat tool is presented as well as the developed building energy model named hereafter DANA (DetAilled buildiNg simulAtion) and the iterative coupling method. Second, an in-situ experiment set up to determine the actual thermal behaviour of a building in its environment is introduced. Third, the adaptation of the modelling tool to the experimental site is presented. Fourth, a sensitivity analysis is introduced to study the uncertainties of the not well identified inputs of the building performance evaluation. Fifth, the comparison between simulations and measurements are discussed. Finally, the conclusion and outlooks closes the paper.

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## 2. MODELLING APPROACH

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The whole model used in this paper to carry out simulations is an integration between DANA and the existing radiative functions of SOLENE-Microclimat which represent the environment. SOLENE-Microclimat already contained a building simulation model [6], however, due to new requirements for greater accuracy, a new one has been developed.

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### 2.1 SOLENE-Microclimat

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SOLENE-microclimat [18] was first developed for urban amenity assessment with the possibility to take into account:

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1. radiative transfers, including long-wave radiation;

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2. conduction and storage in walls and soils;

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3. airflow and convective exchanges;

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4. evapotranspiration from natural surfaces like vegetation and water ponds or humidification systems.

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The SOLENE-microclimat thermo-radiative model, its validation and coupling with the Code-Saturne CFD model has previously been presented in [6], [18]. The thermo-radiative part of the model has been validated, as well as the green wall module [9], [13], [19]. To complete the validation, comparisons for ground, wall and roof models were realized. For this purpose, the measurement data acquired during FluxSap campaign have been used [19].

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In this paper, the radiative transfer (inter-reflections between all meshed elements of the urban scene), convective transfer for the urban structures, the conduction and storage of thermal energy in soils and buildings are considered as well as the shading of trees. The surfaces defined as buildings (brown line) are based on a thermal 1R2C model with a fixed inside air temperature of 20°C. The surfaces defined as soils (purple line) are based on a soil model [6]. Trees in the urban environment are included in the simulations. [20].

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### 2.2 Presentation of DANA model and the coupling with SOLENE-Microclimat

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Commercial tools such as TrnSys or EnergyPlus cannot be coupled easily to SOLENE-Microclimat so that in most applications, simulated urban climate data are used in BES, but the retro-actions are not taken into account in the iterations [21]. The BES coupling was presented in detail by Bouyer et al. [6]. This sub-function is based on a lumped parameter thermal modelling network, whose nodes correspond to a building floor. It is based on an 1R2C model and on the junction of internal cells in a single cell per floor. It is interesting for energy calculations of a building surrounded by a realistic
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environment [6]. However, this requires the monitoring of a building and this sub-function has not been validated yet. In addition, the impact of the orientations of walls on the inside surface temperatures is not considered and the wall are not discretized. Therefore, this thermal model is not adapted if the objective is to study in detail the envelope to assess the impact of structural defects or local changes in materials. Besides, the lack of refined spatial discretisation of the walls deprives us of one of the advantages of SOLENE-Microclimat regarding the accurate calculation of the solar radiation spatial distribution. That is why we have decided to develop a new thermal model: DANA.

In our work, the urban geometry is composed of facets, triangular mesh elements and cells. To illustrate these terms, some of the facets of the geometry are surrounded in brown on figure 3 and their temperature are named $T_{f,out}$. A facet includes several triangular mesh elements (surrounded in black in Figure 1) which have the same properties, and their temperature is named $T_{tri,out}$. Then, for each triangular mesh element a coupling with the cells, which temperature are named $T_i$, in the walls or soils is realized. These cells are finally connected to the inside surface elements, $T_{f,ins}$.

<figure><img src="image_2.png" /><figcaption>Figure 1: urban geometry elements: facets, triangular mesh elements and cells</figcaption></figure>

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DANA model can represent the dynamic thermal behaviour of a single building of any shape using a multizone approach, where each level is a zone. Internal gains and the air leakage through the external envelope are considered. Heating and cooling needs are calculated as well as the air and radiant temperatures for each floor. The external surfaces temperatures are calculated, with SOLENE-Microclimat, for each mesh element of the urban geometry, as we consider the discretised boundary conditions. The thermal conduction exchanges in the walls are still considered uni-dimensional but we have refined the spatial discretisation within the walls ($T_i, T_{i+1},...ect$.) and we have at least a single inside facet temperature $T_{f,ins}$ per identified wall at each level instead of a single inside facet. The wall model uses a finite difference method with a flexible spatial discretisation of the wall. As a result, with the DANA model more outputs can be obtained than before (Table 1).
<table><caption>Table 1: Outputs of the buildings models</caption><thead><tr><th colspan="2">Outputs of the first model [6]</th><th colspan="2">Outputs of DANA model</th></tr><tr><td colspan="2">For one level</td><td colspan="2">For one level</td></tr></thead><tbody><tr><td colspan="2">1 indoor air and radiant temperature<br>1 floor temperature<br>1 ceiling temperature<br>Heating or cooling load</td><td colspan="2"></td></tr><tr><td>1 inside surface temperature for all<br>the envelope walls</td><td colspan="3">Nw or more inside surface<br>temperatures, where Nw is the<br>number of walls</td></tr><tr><td colspan="4">N Outside surface temperatures, where N is the number of mesh<br>elements on the building envelope</td></tr></tbody></table>

The building model and SOLENE-Microclimat are linked with a dynamic coupling (Figure 2). For a time step, the short wave radiation after inter-reflection for each triangular mesh element is calculated, including the trees. Then, the thermo-radiative model of SOLENE is used to calculate all the temperatures of the urban scene considering the thermal exchanges in the soil and in the walls of the surrounding buildings. Thirdly, DANA model is run for a specific building where a higher level of modelling detail is required. In return, the outside surface temperatures calculated in the DANA model are used by SOLENE-Microclimat to correct all the long wave and heat exchanges between the buildings where the thermal model is used and the other facets of the urban scene (soil, surrounding buildings and trees). Finally, all the housing estates heat flows and temperatures are obtained for a time step (Figure 2).

Due to calculation time constraints, in this work, for each facet (ie. part of one elevation corresponding to a floor) we have matched the outside mesh element to a single facet. That is for example, for 5 external facets we will have 5 internal facet temperatures for the walls but a large number of meshed elements.

<figure><img src="image_3.png" /><figcaption>Figure 2: Calculation flow of DANA coupled to SOLENE-Microclimat</figcaption></figure>

The same is done for the roofs and windows. But for the floors, we do not apply a two dimensional discretisation.

For each mesh element, the heat equation is solved to get the temperatures, T [K] :
$$ \rho_m \cdot C_m V_m \frac{\partial T}{\partial t} = \vec{\nabla} \cdot \lambda \vec{\nabla} T + G \quad (1) $$

where $\rho_m$ is the density of the walls materials, $C_m$ the heat capacity of the walls materials, $V_m$ the volume of the material layer, $\lambda$ the thermal conductivity and $G$ a possible internal heat generation, in our case zero. The boundary conditions, for each facet of the walls in contact with the air, are expressed as a surface energy balance considering the convective, conductive and radiative exchanges (short wave and long wave exchanges).

The convective heat flow follows this equation:

$$ \Phi_{\text{conv}} = h_{\text{conv}} S(T_s - T_{\text{air}}) \quad (2) $$

$T_{\text{air}}$ is the outside or inside air temperature depending if the cell is in contact with the outside or inside environment, $T_s$ is the facet temperature $T_f$ or the mesh element temperature $T_{\text{tri}}$, $S_s$ is the surface of the facet or the surface of the mesh element. The convective exchange coefficient $h_{\text{conv}}$ is constant through the time for the inside of the building (6.1 W/m²K for the ceiling, 1.6 W/m²K for the floor and 4.1 W/m²K for the walls). For the outside, $h_{\text{conv}}$ changes in time, function of the wind velocity $v$ [m/s] according to :

$$ h_{\text{conv}} = 5.85 + 1.7 v \quad (3) $$

The conduction between two neighbour meshes i and i+1 in the wall is given by :

$$ \Phi_{\text{cond}} = k_{i,i+1}(T_i - T_{i+1}) \quad (4) $$

With

$$ k_{i,i+1} = \frac{S_{i,i+1}}{\frac{\delta_i}{2\lambda_i} + \frac{\delta_{i+1}}{2\lambda_{i+1}}} \quad (5) $$

Here, $T_i$ [K] is a cell temperature, $k$ the thermal conductance of the layer [W/K], $S$ [m²] the surface between two cells, $\lambda$ [W/mK] the conductivity and $\delta$ the thickness [m] between the two cells.

Here we will detail the short wave radiation $\Phi_{\text{SW,ins}}$ [W] for the inside of the building. The floor only will receive the primary radiation and therefore will receive the most of the incoming direct radiation but will absorb a part of it depending on its absorptivity coefficient $\alpha_{\text{floor}}$. The remaining incoming direct radiation is distributed on the other surfaces in the room in due ratio between the surface considered and the total surfaces $S_T$ (surfaces of the floor, walls and ceiling are considered). The diffuse radiation is considered to have an isotropic behaviour. Therefore, the incoming diffuse radiation is considered in all the surfaces balances and is distributed in due ratio between the surface considered and the total surfaces. $E_d$ and $E_b$ are calculated by SOLENE tool. The direct transmission coefficient $\tau_b$ depends on the incidence angle but the diffuse coefficient $\tau_d$ is fixed in time. The opening of the blind $Bl$ is also an input.

$$ \Phi_{\text{SW,ins,floor}} = \alpha_{\text{floor}} E_{\text{b,ins}} + \alpha_{\text{floor}} \frac{S_{\text{floor}}}{S_T} E_{\text{d,ins}} \quad (6.1) $$

$$ \Phi_{\text{SW,ins,w}} = \alpha_w \frac{S_w}{S_T} (\tau_d E_{\text{d,ins}} + (1 - \alpha_{\text{floor}}) E_{\text{b,ins}}) \quad (6.2) $$

$$ E_{\text{b,ins}} = \frac{S_{\text{windows}}}{S_{\text{floor}}} \tau_b Bl E_b \quad (6.3) $$
$$E_{d,ins} = S_{windows} / S_{floor} \tau_d blE_d \quad (6.4)$$

1. This radiation distribution is close to the intermediar model M1D,sp used in a past paper [22]. In the conclusions of the paper, this model was recommended to evaluate the air temperature but may not be accurate enough concerning the inside surface temperatures.

4. $\Phi_{LW}$ [W] is the long wave radiation flow. For a triangle exposed towards the outside environment, the long wave exchanges are given by:

$$\Phi_{LW,out,tri} = -S_{tri,out} \left( \varepsilon_{tri} F_{sky \to tri} (\Phi_{LWD} - \sigma T_{tri}^4) + (\sigma \sum F_{sc \to tri} (\varepsilon_{sc} T_{sc}^4 - \varepsilon_{tri} T_{tri}^4)) \right) \quad (7)$$

6. $S_{tri,out}$ is the surface of the mesh element on the outside surface [m²] and $\varepsilon_{tri}$ the emissivity of the mesh element. $T_{sc}$ [K] is the temperature of a mesh element of the scene, $T_{tri}$ [K] is the temperature of a mesh element of the building and $\Phi_{LWD}$ [W/m²] the long wave radiation descending from the sky. $F_{sky \to tri}$ and $F_{sc \to tri}$ are respectively the shape factors between the mesh element considered and the sky and the shape factor between a mesh element of the urban scene, a mesh element of the building and the sky vault. These shape factors are directly calculated by SOLENE using the line integral method implemented by Miguet [23]. Thus, this allows to have realistic long wave exchanges between the studied building and the surrounding. For the inside of the building, the long wave exchanges in the building for a facet is given by the linearized equation:

$$\Phi_{LW,Ins,f} = S_f h_r \sum_{j \neq f} \varepsilon_f F_{j \to f} (T_f - T_j) \quad (8)$$

14. Here $S_f$ [m²] is the surface of the facet, $h_r$ the radiative coefficient rounded to 5 W/m²K, $\varepsilon_f$ the emissivity, $F_{j \to f}$ the shape factor between facets, $T_f$ the temperature of the facet and $T_j$ the temperature of another facet. The finite difference equation for a cell in the wall is given by:

$$\rho_m \cdot C_m V_m \frac{T_i^{t+\Delta t} - T_i^t}{\Delta t} = k_{i,i+1} (T_i^{t+\Delta t} - T_{i+1}^{t+\Delta t}) + k_{i,i-1} (T_i^{t+\Delta t} - T_{i-1}^{t+\Delta t}) \quad (9)$$

17. If the mesh is located on a facet:

$$\rho_m \cdot C_m V_m \frac{T_S^{t+\Delta t} - T_S^t}{\Delta t} = k_{i,i+1} (T_S^{t+\Delta t} - T_{i+1}^{t+\Delta t}) + h (T_S^{t+\Delta t} - T_{air}^{t+\Delta t}) + \Phi_{SW}^{t+\Delta t} + \Phi_{LW}^{t+\Delta t} \quad (10)$$

18. Here, the air temperature can be the inside or outside air temperature, depending if the facet is located on the inside or outside of the envelope.

20. Finally, the air temperature for a level, inside, is given by:

$$\rho_{air} C_{air} V_{air} \frac{T_{air,ins}^{t+\Delta t} - T_{air,ins}^t}{\Delta t} = \sum_f h_{conv} S_f (T_{air,ins}^{t+\Delta t} - T_f^{t+\Delta t}) + Q^{t+\Delta t} + I^{t+\Delta t} \quad (11)$$

With $\rho_{air}$ [kg/m³] the air density, $C_{air}$ [J/kg K] the specific heat capacity of the air, $V_{air}$ [m³] the volume of the considered air zone, Q [W] the heating or cooling load, I [W] the heat exchange due to infiltration and ventilation and $T_{air,ins}$ [K] the inside air temperature for a level. The heating load can be either considered as a convective source in the air balance as it
1 is for equation 11, or if a heating floor is considered the heating load acts on the heat equation of the floor. Finally, the
2 entire problem is summarised as a matrix:

$$
\mathbf{M} \begin{pmatrix} \mathbf{T}_{\text{tri,out}}^{t+\Delta t} \\ \vdots \\ \mathbf{T}_{i}^{t+\Delta t} \\ \vdots \\ \mathbf{T}_{f,\text{ins}}^{t+\Delta t} \\ \mathbf{T}_{\text{air}}^{t+\Delta t} \end{pmatrix} = \begin{pmatrix} S_{\text{tri,out}} \\ \vdots \\ A_i \mathbf{T}_i^t \\ \vdots \\ S_{f,\text{ins}} \\ A_{\text{air}} \mathbf{T}_{\text{air}}^t \end{pmatrix} \qquad (12)
$$

3 Where $A_{air} = \frac{\rho_{air}C_{air}V_{air}}{\Delta t}$ and $S_{f,ins} = A_{f,ins}T_{f,ins}^t + \Phi_{LW,ins,f}$ with
$$ S_{\text{tri,out}} = A_{\text{tri,out}} \cdot T_{\text{tri,out}}^t + S_{\text{tri}}\varepsilon_{\text{tri}}h_r(F_{\text{sky}\to\text{tri}}T_{\text{sky}}^{t+\Delta t} + F_{\text{sc}\to\text{tri}}T_{\text{sc}}^{t+\Delta t}) + \Phi_{\text{SW,out}}^{t+\Delta t} \quad (13) $$

4 M represents the matrix coupling the entire calculated temperatures. The inversion of the matrix allows to calculate all
5 the temperatures at the time step t + Δt following an implicit numerical resolution method which is stable.

6 The developed model has followed a first validation process introduced in a past paper [23]. First, the thermal wall
7 response based on finite difference method was compared to analytical solution. Then, the thermal building model was
8 compared to the building simulation tool TrnSys<fnref n="2" />. This is an important evolution as until now, no thermal building model
9 coupled to SOLENE-Microclimat was validated or even compared to an analytical solution or validated tool. The wall
10 model showed a good agreement to the analytical solution and the envelope model agreed with the TRNSYS building
11 type. The lack of this last pre-validation is the comparison to in situ measurements. The presentation of the experimental
12 set up is introduced in the next section.

3. PRESENTATION OF THE EXPERIMENTAL SITE

14 In this part, we present an in situ experiment. The objective of this experiment is to determine the actual behaviour of a
15 building in its environment, to quantify the thermal needs and to assess the local climate.

16 It has been set up so that to have data for models validation and to experiment in future processes to check-up building
17 thermal properties. Measurements of the thermal behaviour of a building are presented, but also measurements of the
18 local climate as well as some outside surface temperatures in order to have information on the long-wave radiation
19 exchanges between buildings.

3.1 Site description

21 The monitored buildings are located in the north-east of Nantes (47.2184° N, 1.5536° W) (Figure 3). This housing estate
22 consists of 7 buildings (5 levels), with a total of 183 dwellings. The buildings are referenced in Figure 3, below.

23 All the buildings from number 2 to 7 have the same size: 21.5 m in length and 19.4 m in depth. Building 1 is 62 m in
24 length and 13 m in depth. All buildings have 5 floors and the total height of each building is 15 m.

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<footnote n="2">² TrnSys Mathematical reference. Solar Energy Laboratory Madison, United States, University of Wisconsin</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 3: Housing estate</figcaption></figure>

In this paper the real 3D geometry of the district is considered, which comes from the 3D vectorial description of the BD TOPO® of the French National Geographic Institute (IGN). This database contains information on the outlines of the buildings and their height, but nothing concerning the windows on the facades or about the roof shapes. This allows to get the buildings in LOD 2 only. The information related to the position of the windows and the exact sizes of building 3 are shown in Figure 4.

<figure><img src="image_5.png" /><figcaption>Figure 4: Building 3 dimensions (meter)</figcaption></figure>

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## 3.2 Building thermal characteristics

All walls of the external envelope are 30 cm thick and composed of an external 2 cm cladding, a small air layer the thickness of which is unknown, 3.5 cm external insulation, 19 cm concrete layer, 3 cm internal insulation layer and 1.13 cm plaster layer. The inside walls between flats are composed of 14 cm of concrete. The roof is 45 cm thick composed of a 20 cm internal insulation, 20 cm of concrete and 5 cm of gravel on the outside surface. Between each level, the flooring slab is 21 cm thick and composed of concrete. The thermal properties of each layer are given in Table 2. The local authority of the housing gave the information regarding the layers thickness and the materials. The U value of the roof and the external walls were identified on site by using the ISO-9869-1 protocol<fnref n="3" />. The average method of the norm was used and we obtained a U value of 0.52 W/m²K for the external wall and of 0.3 W/m²K for the roof. These values have been compared to the information given concerning the layers thickness and properties. The mean U value found was similar for both the external wall and the roof, which confirmed the information given by the social housing landlord.

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<table><caption>Table 2: Envelope thermal properties</caption><thead><tr><th></th><th>Coating</th><th>Insulation</th><th>Concrete</th><th>Plaster</th><th>Gravel</th></tr></thead><tbody><tr><td>Conductivity (W/mK)</td><td>0.13</td><td>0.035</td><td>0.8</td><td>0.42</td><td>0.1</td></tr><tr><td>Density (kg/m<fnref n="3" />)</td><td>1880</td><td>30</td><td>2300</td><td>1200</td><td>1000</td></tr><tr><td>Heat capacity (J/kgK)</td><td>1000</td><td>1000</td><td>880</td><td>850</td><td>100</td></tr></tbody></table>

For windows, standard properties of double glazing were considered for the simulations. The overall U value of the window is 2.1 W/m²K and the direct normal transmission $\tau_b$ is of 0.5 and the diffuse transmission $\tau_d$ equal to 0.35. These values were experimentally determined in a past work [25]. For all the buildings, double glazing windows are installed with manual blinds.

All apartments have mechanical exhaust-only ventilation. The dwellings are equipped with heated floors. The heating system is collective and connected to a gas boiler. The access to the supply and return pipes of the heating system at the level of the stairwell of each floor of each building makes it possible to measure the flow and temperatures of the supply and return water.

## 3.3 Experimental set-up for buildings 1, 2, 4, 5, 6 and 7

For the six buildings surrounding the studied building (3), continuous measurements are acquired with a time interval of 10 minutes. In the modelling approach, these buildings are modelled as single zone building with an indoor air temperature set at a constant value with only a few temperatures per external facet. They represent calculated boundary conditions influencing Building 3 thermal behaviour, which is modelled in more detail. Therefore, the measurements undertaken on these buildings concern only the outside surfaces temperatures. For these buildings, we measure (Figure 5):

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* One outdoor surface temperature at the centre of the roof of each building;

<footnote n="3">³ ISO 9869-1 Thermal insulation -- Building elements -- In-situ measurement of thermal resistance and thermal transmittance -- Part 1: Heat flow meter method</footnote>
1

2

* Outside surface temperature on each façade: two sensors for the façades, which are exposed to Building 3, and only one measure per façade for the others.

<figure><img src="image_6.png" /><figcaption>Figure 5: sensors location on the façades of buildings 1, 2, 4, 5, 6 and 7</figcaption></figure>

3

4

The energy provided by the gas boiler to the entire heating system is measured. A non-intrusive flow meter is used
associated to temperature probes placed at the supply and return pipes of the heating network.

5

**3.4 Experimental set-up for Building 3**

6

7

8

Continuous measurements are acquired with a time interval of 10 minutes on Building 3 as well. This central building is modelled in greater detail. Therefore, its instrumentation is more important and reinforced on each of the three apartments of the top floor (Figure 6). It contains:

9

10

11

12

13

14

15

16

17

18

19

20

21

22

- Ambient air temperature and brightness sensors placed in the three apartments of the top floor.

- An ambient air temperature sensor in the crawl space.

- Measurement of the air temperature on an intermediate level: an air sensor in a flat of the third floor.

- A sensor on each opening window to record its state: opened or closed. This is done for all the windows of the three flats of the top floor (numbered 20, 22 and 24 on Figure 6).

- Heating power meters to measure the total consumption of the building and also a consumption of the last floor: we measured the mass flow rate, the specific heat capacity of the water was known and the temperature difference of the heat transfer was measured too (inlet and outlet fluid temperature).

- One outdoor surface temperature of the building roof.

- Measurements of outside surface temperatures at each façade - two sensors per façade are fixed.

- Measurements of inside surface temperatures at each façade (at least one sensor per façade orientation). As a matter of priority, sensors are placed at the level of the dwelling for which indoor air temperature and inside wall surface temperature are measured. The sensors are placed at the same height as the inside surface temperature sensors.
<figure><img src="image_7.png" /><figcaption>Figure 6: Instrumentation of Building 3</figcaption></figure>

Sensors numbers used and their specifications in the experiment are presented in the table below (Table 3). All temperature sensors have been calibrated in January 2017.

The data measurements are transmitted by a wireless system in order to be less intrusive for the occupants.

<table><caption>Table 3: Metrology and sensors specifications</caption><thead><tr><td>Type of measurement</td><td>Quantity</td><td>Sensor Reference</td><td>Accuracy</td><td>Working range</td></tr></thead><tbody><tr><td>Air temperature</td><td>7</td><td>AMR wM-Bus ambient sensor (CTN external sensor)</td><td>±0.1 °C to ±0.5 °C</td><td>-30° to +85°C</td></tr><tr><td>Inside surface temperature and luminosity</td><td>5</td><td>GIVE-Ecotropy sensor 17.2.1</td><td>±0.5 °C</td><td>0 to 40 °C</td></tr><tr><td>Outside surface temperature and roof temperature</td><td>42</td><td>GIVE-Ecotropy sensor 17.1.1 TT</td><td>±0.1 °C to ±0.5 °C</td><td>-25°C to 60°C</td></tr><tr><td>Window opening sensor</td><td>13</td><td>AMR wM-Bus 0-10V, 4-20 mA On/Off, ARF8041AA</td><td>-</td><td>-</td></tr></tbody></table>
<table><tr><td>Flowmeter</td><td>3</td><td>Ultraflow 1000</td><td>± 1 to 3 % for a flowrate> 0,3 m/s</td><td>0.1 - 10 m/s</td></tr><tr><td>Water temperature</td><td>6</td><td>GIVE-Ecotropy 17.1.1 TT / ARF8041AA</td><td>±0.5 °C</td><td>0 - 85°C</td></tr></table>

## 3.5 Weather data and boundary conditions

A weather station has been installed to measure the local weather conditions. The weather data measurement consists of a global horizontal radiation pyranometer, a thermo hygrometer and an anemometer (Table 4). This mast is located on the roof of Building 3 and is 2 meters above the roof level.

<table><caption>Table 4: Technical specifications of the weather station sensors</caption><thead><tr><td>Type of measure</td><td>Technical specifications</td></tr></thead><tbody><tr><td>Anemometer (WSS420)</td><td>Accuracy : ± 4%<br>Working range: 0 - 50 m/s</td></tr><tr><td>Pyranometer (Vantage Pro2TM)</td><td>Accuracy : ±5% of full scale and drift of up to ±2% per year<br>Working range: 0 to 1800 W/m2</td></tr><tr><td>Temperature and humidity (Vaisala INTERCAP HMP60)</td><td>Accuracy : ±0.6 °C<br>Working range:<br>0 ... 100 %RH; -40 ... +60°C</td></tr></tbody></table>

The simulation period and measurement period started during winter conditions and ended for free-floating conditions (from the 27/04/17 to the 13/05/17).

The descending long wave sky radiation measured is represented by the pink dots on Figure 7. The global horizontal radiation measured on the roof of Building 3 is shown below (Figure 7) with red dots.

<figure><img src="image_8.png" /><figcaption>Figure 7: Radiation (27/04/17 – 13/05/17)</figcaption></figure>

The direct and diffuse components (Figure 7) are calculated from a model splitting the global irradiation into its two components. In several works, the evaluation of the diffuse component is studied using as input global irradiation on hourly basis. Several correlations between hourly values of diffuse and global irradiations are presented, validated and compared using solar data collected on Mediterranean sites [26]. The author compared ten correlations and concluded that there was not a model largely better than another to split the global irradiation into the diffuse and direct component. The RMSE found for the different correlations were of about 37% depending on the studied site. The inconvenience of all the existing correlations is that they are validated in a Mediterranean climate, and no model was validated on a temperate oceanic climate representative of Nantes. However we finally used the correlation published by De Miguel et al [27].

The relative humidity, wind speed and outside temperature are shown (Figure 8, Figure 9, Figure 10) as they were used as input for the building model and for the thermo-radiative model. The wind speed was measured 3 meters above the
1 roof. As no information on the construction of the crawl space was found, we measured the air temperature in the crawl space and used it directly as a boundary condition for the building envelope model (Figure 11).

<figure><img src="image_9.png" /><figcaption>Figure 8: relative humidity</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 9: local wind speed</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10: local outside temperature</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11: crawl space air temperature</figcaption></figure>

3 The weather data is saved at a 15 minute time interval, whereas the sensors measuring the air temperature in the crawl space or the sensors measuring the heating power acquire the data at a 10 minute interval. That is why all the data was extrapolated at a 15 minute interval and simulations were run with this interval.

6 The airflow rate through the air supply system was measured once in March in the 3 apartments 20, 22 and 24 and the total airflow rate measured of the level was of 85 m³/h. This value is coherent with the airflow rate according to the French Regulation<fnref n="4" /> which fixes a minimum value of 70 m³/h for these kind of apartments.

9 Figure 12 shows the 3D geometry and the site's albedos distribution. The albedo and emissivity values of the different surfaces of the building have not been measured but reference values for each surface type are used. They are given in Table 5.

<table><caption>Table 5: Albedo[28] and emissivity<fnref n="5" /> of the urban surfaces</caption><thead><tr><td>Type of surface</td><td>Albedo</td><td>Emissivity</td></tr></thead><tbody><tr><td>Grass and trees</td><td>0.25</td><td>0.8</td></tr><tr><td>Path</td><td>0.1</td><td>0.95</td></tr><tr><td>Playground</td><td>0.45</td><td>0.94</td></tr><tr><td>Window</td><td>0.3</td><td>0.04</td></tr><tr><td>Walls buildings</td><td>0.7</td><td>0.95</td></tr></tbody></table>

<footnote n="4">⁴ https://www.legifrance.gouv.fr/affichTexte.do?cidTexte=JORFTEXT000000862344</footnote>

<footnote n="5">⁵ http://www.thethermograpiclibrary.org/index.php?title=Tableau_%C3%A9missivit%C3%A9s_en_thermographie</footnote>
<table><tr><td>Roof</td><td>0.25</td><td>0.9</td></tr></table>

<figure><img src="image_13.png" /><figcaption>Figure 12: Albedo values of the urban scene</figcaption></figure>

## 4. RESULTS AND DISCUSSIONS: COMPARISON BETWEEN IN SITU MEASUREMENTS AND SIMULATION

In this section, the simulation results of the described modelling DANA tool coupled with SOLENE-Microclimat are compared to the measurements and the errors for each output of the model are estimated. Then a sensitivity analysis is introduced. This enables us to consider which of many input factors have the greater impact and this will help in reducing the list of critical factors on the thermal behaviour of Building 3. The ranking of these factors will help to explain the discrepancies between the model and the in situ measurements and to identify if additional sensors should be used for a better analysis. Finally, the urban scene's thermal behaviour is presented and the impact of the surrounding environment on Building 3 is shown.

### 4.1 Thermal behaviour of Building 3 with DANA

The simulations presented here, correspond to the application of the DANA model to the 3D geometry of Building 3, with the thermal properties of the envelope given in Table 2, and the albedo as well as the emissivity of surfaces given in Table 5. The blind opening is fixed to the value of 0.5, which is the best compromise regarding to the state of blinds of all apartments. The airflow rate for these simulations is fixed in time and corresponds to the measures undertaken. Climatic conditions are those measured in situ.

#### 4.1.1 Thermal inside behaviour of Building 3

Figure 13 presents the air temperature of the top floor of Building 3, measured and simulated between the 27/04/2017 and the 13/05/2017.

<figure><img src="image_14.png" /></figure>
<caption>Figure 13: Air temperature of the top floor of building 3</caption>

For each time interval, we show the minimum value, the maximum value, and the mean air temperature measured by the 1
2
3 sensors. An important difference between the minimum and maximum measures is observed, which can reach nearly
4
5 2.5 °C. These air temperature measurements were carried out in the different flats of floor 4 (Figure 6). The model
6
7 reproduces well the air temperature, as the simulated temperature is often located between the minimum and maximum
8
9 measured air temperature. The RMSE between the mean air temperature measured (the mean value between the three air
10 measurements) and simulated (T4th) is of 0.86°C (Table 6). For the first two days, the difference is higher than for the
11 other days, due to the initialization period. Between the 2nd and 5th of May, the number of opened windows has increased
12
13 (Figure 14) and the heating floor power has decreased (Figure 15), and therefore the air temperature decreases. The
modelling approach neglects the windows openings, which explains that during this period we have differences between
the simulation and the measure reaching 1.5 °C.

<figure><img src="image_15.png" /><figcaption>Figure 14: Number of windows opened (red) on the top floor correlated with the air temperature difference (blue) between the mean air measured and the model simulation</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 15: Heating for the top floor (red) and air temperature difference between the mean air measured and the model simulation (blue)</figcaption></figure>

In the hypothesis of the model, we consider a constant opening of the blinds during the simulated period, which is of
course a too simplistic approach and may explain the discrepancies.

<figure><img src="image_17.png" /><figcaption>Figure 16: Diffuse and global horizontal radiation, Air temperature difference between the mean air measured and the model</figcaption></figure>

The global and diffuse radiation is shown on Figure 16. During the last three days and for the 1st May and the 8th May, we can observe that the global radiation is low and mainly provided by the diffuse component. For these days, the simulation of the air temperature is better evaluated than for the other days. If the model used to split the radiation provides an error, the solar gains can be wrongly evaluated and the air temperature too. As presented before, the correlation used
to split the global irradiation into a diffuse and direct components presents a high level of errors, the consequences of which are important on the internal gains calculations through the envelope.

The inside surface temperatures measured and simulated are very close to the air temperature evolution and their root mean square error is relatively low. The RMSE for the inside surface temperatures (Table 6) are of 1.4°C for the western wall (T<sub>ins,w</sub>), of 1.48°C for the northern wall (T<sub>ins,N</sub>) and of 0.7 °C for the ceiling (T<sub>ins,c</sub>). The other sensors for the inside surface temperatures were defective during this period, and could not be used in the evaluation.

The air temperature of the third floor has been measured only in one apartment. Even if this sensor cannot be considered as representative of the entire floor we compared its measure to the simulation result for this floor. The model reproduces it well, with a RMSE of 1.2°C (T3rd).

## 4.1.2 Thermal outside behaviour of Building 3

For each comparison on the external envelope, in the 3D model, we have selected the mesh element, which is closest to the sensor's location. We can observe on Figure 17 to Figure 25 that the outside surface temperatures are well reproduced by the model.

<table><caption>Table 6: RMSE between sensors and simulation for building 3</caption><thead><tr><th></th><th>T<sub>Roof</sub></th><th>T<sub>3rd</sub></th><th>T<sub>4th</sub></th><th>T<sub>Eup</sub></th><th>T<sub>Edown</sub></th></tr></thead><tbody><tr><th>RMSE (°C)</th><td>1.1</td><td>1.2</td><td>0.86</td><td>2</td><td>2</td></tr><tr><th></th><th>T<sub>Sup</sub></th><th>T<sub>Sdown</sub></th><th>T<sub>Nup</sub></th><th>T<sub>Ndown</sub></th><th>T<sub>Wup</sub></th></tr><tr><th>RMSE (°C)</th><td>2.5</td><td>2.5</td><td>1.6</td><td>1.4</td><td>1.8</td></tr><tr><th></th><th>T<sub>Wdown</sub></th><th>T<sub>ins,W</sub></th><th>T<sub>ins,N</sub></th><th>T<sub>ins,c</sub></th><th></th></tr><tr><th>RMSE (°C)</th><td>1.8</td><td>1.4</td><td>1.48</td><td>0.7</td><td></td></tr></tbody></table>

Figure 17 shows the comparison between the calculated and measured roof surface temperature (T<sub>Roof</sub>) for Building 3. We can see a very good match of the model, with a RMSE of 1.1°C (Table 6).

<figure><img src="image_18.png" /><figcaption>Figure 17: Roof surface temperature</figcaption></figure>

The eastern outside upper wall surface temperature (T<sub>Eup</sub>) of Building 3 is represented in Figure 18. A RMSE of 2°C is obtained. The difference between the simulation and measured result is more important when solar radiation is important: for the first and third day. Concerning the simulated temperature compared to the lower sensor (T<sub>Edown</sub>) (Figure 19), we have again a RMSE of 2°C (Table 6).
<figure><img src="image_19.png" /><figcaption>Figure 18: Eastern upper surface temperature</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Figure 19: Eastern bottom surface temperature</figcaption></figure>

1. The general trend of the simulated upper ($T_{Wup}$) and lower western surface temperature ($T_{Wdown}$) is well reproduced despite some discrepancies observed for the last day, when the direct radiation is high. The model showed a RMSE of 1.8 °C for both surface temperatures on this wall (Table 6).

<figure><img src="image_21.png" /><figcaption>Figure 20: Western upper surface temperature</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Figure 21: Western lower surface temperature</figcaption></figure>

4. The northern outside surface temperature simulated compared to the values given by the sensors are shown on Figure 22 and Figure 23. These simulations show a good agreement. Here, the RMSE is 1.6°C when comparing the simulation of the corresponding mesh element to the upper sensor ($T_{Nup}$) and 1.4°C when comparing the corresponding mesh element to the lower sensor ($T_{Ndown}$).

<figure><img src="image_23.png" /><figcaption>Figure 22: Northern upper surface temperature</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Figure 23: Northern lower surface temperature</figcaption></figure>

8. Finally, the southern outside temperatures are shown (Figure 24 and Figure 25). The highest RMSE is observed for this wall. The RMSE between the simulation and the upper sensor ($T_{Sup}$) or the lower sensor ($T_{Sdown}$) is of 2.5 °C.
<figure><img src="image_25.png" /><figcaption>Figure 24: Southern upper surface temperature</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Figure 25: Southern lower surface temperature</figcaption></figure>

To sum up, we notice that the outside surface temperatures for the northern wall seem to better match the measures than for the other walls, which are exposed to more radiation and in particular, when the direct component is strong. During the night, the northern wall simulations also represents better the measures than the other walls.

### 4.1.2.1 Impact of the radiation and the dominant wind direction

For days with strong radiation and important fluctuations, the model tends to be less accurate than for days where the thermal stresses are less important and fluctuating. The incident diffuse and direct radiation for each wall orientation is shown in Figure 26 to Figure 29. For example, for the eastern wall, the fluctuations are important for the first and third days, especially for the direct radiation (Figure 26). These variations are reproduced by the simulated outside surface temperatures but less by the sensors (Figure 18 - Figure 19). The same is observed for the first, second and last days for the western wall (Figure 27) and for the first and third days for the southern wall (Figure 28), when the simulated temperature fluctuations are overestimated. At last, the northern wall's outside surface temperature fluctuations are very similar between the simulation and the measurement and the main irradiation is provided by the diffuse component (Figure 29). It seems that the model used to split the radiation over estimates the variations of the direct irradiation.

<figure><img src="image_27.png" /><figcaption>Figure 26: diffuse and direct irradiation for the wall east oriented</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Figure 27: diffuse and direct irradiation for the wall facing west</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Figure 28: diffuse and direct irradiation for the wall facing South</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Figure 29: diffuse and direct irradiation for the wall facing North</figcaption></figure>

In addition, the roof temperature is better represented than the other surface temperatures. It is worth mentioning that the weather data is measured on top of the roof: the wind speed for example, is representative for the roof and the wall exposed to the wind direction but less for the other walls exposed to a different wind speed. This weather station does not measure the wind direction. In order to assess the impact of wind, we checked the wind direction frequency measured at the airport close to Nantes city. For these days, the wind direction was North - North West (Figure 30) which may explain also why the model reproduces better the surface temperature for these wall orientation which are upwind (such an hypothesis could be verified using CHTC differing for upwind and downwind surfaces [29]).

<figure><img src="image_31.png" /><figcaption>Figure 30: Wind direction (airport of Nantes)</figcaption></figure>

#### 4.1.2.2 Infra-red measurements: homogeneity of the surfaces temperatures

In a second test we checked the homogeneity of the surfaces temperatures on each façade of Building 3 (wall facing south, east, west and north) on the 28th April 2017 at 7.30 am. We can see on Figure 31 and Figure 32 that the temperatures for each façade are relatively homogenous due to the external insulation. The infrared images of the camera (FLIR Thermacam B4) were corrected for the emissivity of the walls (0.95). To correct the images, a preliminary measure was carried out for each perspective point by placing an aluminium sheet on the walls (represented by the black dot on the infra-red images) so that we could calibrate the camera with an ambient temperature as required by Dactu et al. [30].
<figure><img src="image_32.png" /><figcaption>Figure 31: Infra-red measure of the eastern façade</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>Figure 32: Infra-red measure of the northern façade</figcaption></figure>

1. The temperature homogeneity of the walls is well reproduced by the model (Table 7). We have selected a temperature scale representative of the walls' temperatures and not the windows'. The measurements temperatures were:

3. between 5.9°C and 7.5°C for the southern façade;

4. between 5.9°C and 7.7 °C for the eastern façade;

5. between 4°C and 5.2 °C for the western façade;

6. and between 5.7°C and 7.1 °C for the northern.

7. Local values of these infrared measurements have been compared to values given by the sensors measuring the surface temperatures (Table 7). These sensors measured a temperature very close to the infrared measure. Note that the simulation was often closer to the infra-red measure.

<table><caption>Table 7: infra-red measure, sensor's measure and simulation for the 28/04/17 at 7.30 am</caption><thead><tr><td>Location</td><td>Infra-red [°C]</td><td>Sensor [°C]</td><td>Simulation [°C]</td></tr></thead><tbody><tr><td>Eastern upper</td><td>7.3</td><td>5.9</td><td>6.3</td></tr><tr><td>Eastern lower</td><td>7.4</td><td>6.2</td><td>6.6</td></tr><tr><td>Northern upper</td><td>6</td><td>5.3</td><td>5.9</td></tr><tr><td>Northern lower</td><td>4.9</td><td>3.2</td><td>4.7</td></tr><tr><td>Southern upper</td><td>5.7</td><td>4.4</td><td>5.9</td></tr><tr><td>Southern lower</td><td>5.8</td><td>4.8</td><td>5.8</td></tr><tr><td>Western upper</td><td>5.5</td><td>4.6</td><td>5.6</td></tr><tr><td>Western lower</td><td>5.7</td><td>5.3</td><td>5.2</td></tr></tbody></table>

## 4.2 Morris analysis method

First, we introduce the analysis method to identify the parameters which have an influence on the outputs of the thermal model adapted to Building 3. Ten parameters were selected for which we could estimate minimal and maximal limits and for which we had no measure or a measure with high uncertainty.

### 4.2.1 Presentation of Morris method

Morris analysis [31] is a global sensitivity analysis where the whole range of variation is covered. It evaluates global sensitivity of each parameter on the considered output. The main purpose of screening methods is to understand which of several factors are most important to reduce the list of important factors. The sampling plan is a One-At-a-Time (OAT) plan: for N parameters, minimal and maximal limits are defined (i.e. uncertainty of the input). These limits create the variation space of the parameter.
1 Each axis of the space is then divided in Q levels. The method consists to repeat r times the sampling plan OAT (One At a Time) randomly through by dividing each parameter into a number levels Q [0, 1/ (Q-1), 2/(Q-2),...,1].

3 The mathematical space of the inputs is a node grid of size K (number of uncertain factors). For each repetition R (R = 4 1...r), a departure point is taken randomly and then a move forward to another node using a step γ proportional to 1/(Q-1) is done. The methods requires r(K+1) evaluations of the model. At each repetition R, the procedure evaluates the 6 elementary effect E (variation of the model F) for the factor j defined by:

$$E_j^i = \mp \frac{F(x_1^i, \dots, x_j^i, \dots, x_K^i) - F(x_1^i, \dots, x_j^i, \dots, x_K^i)}{\gamma} \quad (14)$$

7 Once the simulations are done, the following sensitivity indices are calculated:

8 - mean effect: $\mu_j = \frac{1}{r} \sum_{1}^{r} E_j^i$ (7)

9 - absolute mean effect : $\mu_j^* = \frac{1}{r} \sum_{1}^{r} |E_j^i|$ (8)

10 - standard deviation :

$$SD_j = \sqrt{\frac{1}{r-1} \sum_{1}^{r} (E_j^i - \mu_j)^2} \quad (145)$$

11 The absolute mean effect and the standard deviation are then used to identify the important factors. Indeed, a high mean 12 means that the factor has a significant influence on the output and a high standard deviation that the factor has either 13 interaction or non-linear effects.

14 In this study, the Euclidean distance $d_j^*$ between the origin and the point $(\mu_j^*, SD_j)$ is calculated for each factor j and then 15 normalized using equation 16:

$$D_{j,k}^* = \frac{d_{j,k}^* - \min_j(d_{j,k}^*)}{\max_j(d_{j,k}^*) - \min_j(d_{j,k}^*)} \quad (156)$$

16 The maximum $D_{j,k}^*$ is used to rank the influence of each parameter on the studied outputs [31].

17 The influence of ten parameters are studied on the behaviour of building 3 (Table 8). They are related to the thermal 18 properties of the main materials of the building envelope (insulation and concrete), the albedo of the roof and façades, 19 the airflow rate, the blinds opening rate, the inside and outside convective exchanges.

20

21

<table><caption>Table 8: Parameters and their bounds</caption><thead><tr><th>Factor</th><th>Minimal bound</th><th>Maximal bound</th></tr></thead><tbody><tr><td>λ<sub>concrete</sub> [W/mK]</td><td>0.8</td><td>1.3</td></tr><tr><td>λ<sub>insulation</sub> [W/mK]</td><td>0.03</td><td>0.045</td></tr><tr><td>ρCp<sub>concrete</sub> [J/kg K]</td><td>1416800</td><td>2631200</td></tr><tr><td>ρCp<sub>insulation</sub> [J/kg K]</td><td>21000</td><td>39000</td></tr><tr><td>Store opening rate</td><td>0.2</td><td>0.8</td></tr><tr><td>Air flow rate [m<sup>3</sup>/h]</td><td>30</td><td>250</td></tr><tr><td>Δh<sub>out</sub> [W/m<sup>2</sup>K]</td><td>1</td><td>30</td></tr><tr><td>Δh<sub>ins</sub> [W/m<sup>2</sup>K]</td><td>1</td><td>10</td></tr><tr><td>alb<sub>w</sub></td><td>0.5</td><td>0.8</td></tr><tr><td>alb<sub>roof</sub></td><td>0.1</td><td>0.3</td></tr></tbody></table>
The bounds of the concrete characteristics are chosen according to the standard material ranges. Concerning the density and heat capacity of both materials, we have chosen the mean value ±30 %.

The store opening represents the mean opening ratio of all the blinds of a floor. For all floors, the same opening ratio was considered in the model. During the experimental campaign, the luminosity was measured in two locations: one in the northern bedroom of apartment 24 and one in the living room of apartment 20. These two measures are not representative of the entire floor. Therefore, the influence of this parameter is studied in this analysis. As presented before, the airflow rate was measured some days before the simulation period and only in three apartments. An important uncertainty remains on this input. We have set a lower minimum value during the analysis in order to enlarge the screening. Finally, the bounds considered are between 30 and 250 m³/h. The outside convective heat exchange coefficient was fixed between 1 and 30 W/m²K. In past works, authors showed the heterogeneity of convective heat exchanges in a small district varying between 5 and 23 W/ m²K [32][30] and reaching 31 W/ m²K [3]. For the inside, this coefficient was taken between 1 and 10 W/m²K. The higher bound corresponds to forced convection regarding the presence of a ventilation system. The albedo of the windows was considered certain while for the walls and roofs an uncertainty was considered. The albedo of the white façades was changed between 0.5 and 0.8. For the roof, composed of a gravel surface, the albedo was changed between 0.1 and 0.3.

The outputs of the thermal model are 15 minutes temperature time series. For each output, the RMSE (root mean square error) is calculated :

$$RMSE = \sqrt{\frac{1}{N} \sum_{i=0}^{N} (T_{mes} - T_{sim})^2} \qquad (167)$$

N is the length of the time series, Tmes is the measured temperature time series and Tsim is the simulated temperature time series. The analysis concerns only building 3. We focus on the last floor air temperature, the inside western surface temperature, the outside upper western surface temperature and the roof outside surface temperature.

To perform the Morris analysis, we choose a number of levels of 10, a grid jump of 2 and a number of samples of 1000. We have therefore used the Sensitivity Analysis Library (SALib) of Python.

### 4.2.2 Sensitivity analysis results

Apart from the variations described above, the simulations are carried out within the same conditions given previously. The sensitivity analysis was carried out for all the air temperatures or surface temperatures where measurements were provided. The calculations were launched for simulations between the 26/04/17 and the 05/05/17. The Euclidean distance for all time series was calculated using the mean effect and standard deviation. Only the main results are presented here.

The sensitivity analysis on the air temperature of the top floor is reported on Figure 33 and Figure 34. We observe a lot of non linear effects on these results. The Euclidean distance shown is normalized. The factor that has most influence on the inside air temperature time series is the airflow rate. The store opening is the second most important factor. Indeed, it has a high impact on the solar gains and thus on indoor air temperature. As the walls are insulated not only on the outside but also the inside, we can observe that the third most important factor is the insulation capacity and density. Finally, the properties of the concrete, the heat transfer coefficients and the albedo values are the last parameters.
<figure><img src="image_34.png" /><figcaption>Figure 33: standard deviation versus mean effect for the air temperature (left) and the inside surface temperature (right)</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>Figure 34: Normalized Euclidean distance with regard to the inside air and inside surface temperature (4th floor)</figcaption></figure>

The sensitivity analysis on the inside surface temperature located on the western wall showed very similar results to the air temperature analysis (Figure 34). The factors with the greatest effect follow the same order but the inside heat transfer coefficient seems to be more important. The same ranking is obtained for the other inside surface temperatures.

The sensitivity analysis for the outside surface temperature and roof temperature show again that a lot of non linear effects occur (Figure 35). The surface temperature located on the western wall shows that the most important factor is the outside convective heat transfer coefficient (Figure 36). The capacity and density of the insulation are the second most influential factor, which seems logical because it is the first layer in contact with the outside and the thermal stresses. The third factor is the density and capacity of the concrete. Contrary to what could be expected, the airflow rate has also an impact on the outside surface temperature. When the flow rate is very high, losses are important and affect the walls temperatures. The same ranking of the parameters is obtained for the other outside surfaces temperatures.

Finally, for the roof, the albedo of the roof has more influence regarding the roof surface temperature than for the wall outside temperature (Figure 36). This is not a surprise as for this case study, all buildings are at the same height and only the albedo of the roof can affect the total incident radiation absorbed by the roof (Figure 36).
<figure><img src="image_36.png" /><figcaption>Figure 35: standard deviation versus mean effect for the outside temperature (left) and the roof temperature (right)</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>Figure 36: Normalized Euclidean distance with regard to the outside western surface temperature and to the roof surface temperature</figcaption></figure>

In a similar work where the ranking was based on heating demand, Spitz *et al.* [33] obtained [31] the results were very similar to those we obtained for the air temperature. The authors showed that the main parameters affecting the air temperature were the airflow rate exchanges, the materials properties and the solar gains.

In several studies, the authors identified the errors observed between simulations and measurements. For example, during the empirical validation study on full size buildings [14], 21 simulation programs were run and compared to measures. This work reported the errors of the different tools. During this study only measures for the inside of the building were used and compared to simulations. Different tests were undertaken in this work. During a test undertaken - the Randomly Ordered Logarithmic Binary Sequence (ROLBS) study - the authors considered heat inputs into the living room. This ROLBS study is close to the hypothesis used in our work, that is, the heating floor power is injected and is an input to the model. For this blind validation, the maximum errors were of 10°C. Most of the programs, considered as reliable ones, showed a range of error between 0 and 2°C. On this base, we can conclude that the range of error we obtain for the simulations of building 3 with our DANA model are acceptable and close to those obtained by Strachan *et al* [14] and Spitz *et al.* [33] who showed that an uncertainty of ± 1°C (due to input uncertainties) around the air measure should be considered. From there, we have verified that our model reproduces correctly the measures in the uncertainty range defined by Spitz *et al* [33].
In view of the accuracy inherent in the sensors used in this experiment, the uncertainties of important inputs of the model and the range of errors obtained on other simulation tools [14], we can conclude that the modelling performances for building 3 are good.

## 4.3 Urban scene surface temperatures

The thermal behaviour of the urban scene obtained with SOLENE tool is presented here. 42 sensors have been placed on the outside surfaces of several buildings, but we will show only a part of the measurement to illustrate the comparison. We can see that for the northern wall of building 1, the outside surface temperature is well reproduced by the model (Figure 37). For the western wall of Building 4, the global behaviour is well reproduced (Figure 38) though some discrepancies are observed during moments of the days when the solar fluctuation is important. This last measure is located close to a tree, which has not been represented. We have tried to generate a geometry close to the reality mainly for the area seen by building 3. Therefore, the urban surfaces not seen by building 3 are less well represented in the 3D geometry, implying errors.

Globally, we have discrepancies between the thermo-radiative model and the measures during days when the solar radiation varies a lot. The important discrepancies occur at the same times as ones observed for the building thermal model simulation DANA. For example, for the outside western wall they are important for the last hours of the last day and for moments during the day when solar radiation varies a lot (Figure 38). This is due to an uncertain input used for both models, the irradiation measure.

<figure><img src="image_38.png" /><figcaption>Figure 37: Northern surface temperature of building 1</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>Figure 38: Western surface temperature of building 4</figcaption></figure>

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<table><caption>Table 9: RMSE of the surfaces temperatures for the surrounding buildings</caption><thead><tr><th>Building 1</th><th>T<sub>Eup</sub></th><th>T<sub>Wup</sub></th><th>T<sub>Wdown</sub></th><th>T<sub>Sup</sub></th><th>T<sub>Ndown</sub></th><th>T<sub>Nup</sub></th></tr></thead><tbody><tr><td>RMSE (°C)</td><td>3</td><td>2</td><td>2</td><td>2.7</td><td>1.73</td><td>1.7</td></tr><tr><td>Building 4</td><td>T<sub>Wup</sub></td><td>T<sub>Eup</sub></td><td>T<sub>Edown</sub></td><td>T<sub>Sdown</sub></td><td>T<sub>Sup</sub></td><td>T<sub>Nup</sub></td></tr><tr><td>RMSE (°C)</td><td>2.6</td><td>2.6</td><td>2.6</td><td>2.9</td><td>2.9</td><td>2</td></tr><tr><td>Building 5</td><td>T<sub>Wup</sub></td><td>T<sub>Eup</sub></td><td>T<sub>Edown</sub></td><td>T<sub>Sdown</sub></td><td>T<sub>Sup</sub></td><td>T<sub>Nup</sub></td></tr><tr><td>RMSE (°C)</td><td>-</td><td>-</td><td>-</td><td>3</td><td>3</td><td>-</td></tr><tr><td>Building 7</td><td>T<sub>Wup</sub></td><td>T<sub>Eup</sub></td><td>T<sub>Wdown</sub></td><td>T<sub>Sdown</sub></td><td>T<sub>Sup</sub></td><td>T<sub>Nup</sub></td></tr><tr><td>RMSE (°C)</td><td>2</td><td>2.8</td><td>2</td><td>2.8</td><td>2.7</td><td>2</td></tr></tbody></table>

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We have summarised in Table 9 the RMSE for each building, except building 2 and 6 as sensors on these buildings were not operating. Depending on the orientation of the wall, we have one or two sensors per building orientation. Some simulated temperatures could not be compared to measurements, as some sensors did not work. For the remaining surfaces, we see again that the simulated temperatures which follow the best the measurements are those of the northern
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walls. For the northern and eastern walls, the RMSE is between 1.7°C and 2°C. For the western and southern walls, we notice the highest RMSE, reaching sometimes 3°C.

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The thermo-radiative approach to model the urban scene has the advantage to represent a realistic environment but the inconvenient to use a simplistic wall model (1R2C). For calculations with important time steps (1 hour), this wall model can be kept. For shorter thermal stresses, it would be better to use at least a 3R4C model for better accuracy [34]. Furthermore, this urban scene model, considers that the internal air temperature of each building is constant in time. This approach should be improved too to improve the model accuracy.

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Finally, to demonstrate the importance of considering the urban scene surfaces around the studied building 3, we illustrate the surface temperatures seen by building 3. We have placed sensors only on the buildings and not at ground level (paths, grass or below trees), thus the temperatures shown are not representative of the entire urban scene surrounding building 3. However, we can see on Figure 39 that during the days the temperature differences can differ a lot from one sensor to another. When the thermal stress (solar irradiation) fluctuates and is significant, that is for the first and third day, we have differences which can reach 20°C. These discrepancies are relatively high, knowing that all the surfaces have the same radiative and thermal properties. This assessment of the urban surfaces temperature shows that it is too simplistic to neglect the temperature distribution for the surrounding environment of a building. When not evaluated, the long wave exchanges could explain discrepancies between simulation of a building thermal behaviour and measurements.

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<figure><img src="image_40.png" /></figure>

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<caption>Figure 39: outside temperature surfaces sensors on the urban scene (27/04/17 – 30/04/17)</caption>

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## 5. CONCLUSION AND FUTURE WORK

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This paper presents a building thermal model DANA integrating the urban environment by using the SOLENE-Microclimate tool. This work aims at comparing the modelled thermal behaviour of a building in its environment to in-situ measurements. It highlights uncertainties related to the assumptions for the inputs to the building energy model, and the impact of urban environment on the building thermal behaviour. The thermal model DANA as well as the thermo-radiative model of SOLENE-Microclimat showed acceptable errors and are coherent. Discrepancies are higher for the
urban scenes model, which is not a surprise, as this modelling approach is more simplistic regarding the thermal exchanges through the envelope.

Through the sensitivity studies, we identified additional measurements needed to ensure that experimental uncertainty is smaller and that all significant parameters are available to be used as model inputs. The airflow rate, the material's properties, the blinds' opening ratio and the external outside convective heat transfer coefficient were the parameters that had the most important impact on the thermal envelope performance. Therefore, in Building 3 the airflow rate needs to be more accurately measured during the experimental period. The opening ratio of the blinds could be measured by placing luminosity sensors in front of each window. The local wind direction is an additional measure which could be used to improve the accuracy of the outside simulated surface temperature. During the sensitivity study, we noticed that it is important to measure also the diffuse irradiation in order to avoid the use of correlations to split the global irradiation.

To conclude precisely on the impact of the exchanges with the urban scene on the thermal performance of buildings, simulations with and without the long wave exchanges will be done in future work.

## ACKNOWLEDGEMENT

This research work is carried out within the EU funded Built2Spec project (Grant Agreement No. 637221 – H2020-EeB-2014-2015). In-situ measurements are performed by means of sensors funded by ONEVU ('Observatoire Nantais des Environnements Urbains'). I would also like to thank M. Jay Stuart for his review and contributions.

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