Introduction

The city serves as the focal point of public management methods and is at the center of economic, social, and environmental development. The approach of the "smart city" paradigm addresses the issues of sustainable development by implementing new spatial planning schemes and guidelines (Nesticò et al. 2018).

These schemes require the selection of projects based on multi-criteria methods, including both technical and financial factors, which adds complexity to the urban planning process and requires low-cost, fast, and reliable methods. In addition, the recent evolution of cities requires effective integrated management of urban services, infrastructure, and communication networks on a metropolitan scale.

Although reduced-scale physical models are often highly simplified representations of real cities (Kanda 2006), they provide an alternative and powerful tool to study urban climate, to systematically investigate the relationships between surface structures and physical processes (O'Loughlin and MacDonald 1964; Wedding et al. 1977; Oke 1981), to analyze flow, dispersion, and radiative cooling (Osaka and Mochizuki 1987; Theurer et al. 1992; Rafailidis 1997) and to provide the physical parameters needed to construct numerical models.

Studies on scale modeling of energy balance are quite rare, due to the difficulty of accurately reflecting real urban environments, as they require both dynamical and geometric similarity (Kanda et al. 2005). Dynamical requirements include similarity of radiation, flow and thermal inertia, and control of exposure conditions.

In landscape design, scale modeling can be used to study heat transfer processes for nightly cooling of urban parks (Spronken-Smith and Oke 1999) and the characteristic temporal and spatial variation of surface temperature of cool pavements (Kowalski 2019). Therefore, urban energy balance models should be developed for mesoscale simulation and a database (energy balance and surface temperatures) should be established for model validation and to study unknown parameters (e.g. turbulent transfer coefficients) (Kawai and Kanda 2010b).

Many studies have been carried out with scaled models and related to different approaches, such as the cooling requirements of buildings (Krüger and Pearlmutter 2008). To analyze the effect of densification on energy consumption for air conditioning in buildings (Krüger and Pearlmutter 2007) and to investigate the thermal environment variables inside street canyons (Hang and Chen 2022).

In addition, to study the turbulence and fluid mechanics parameters in urban environments (Inagaki and Kanda 2008). A parameterization of convection in building energy models and urban computational fluid dynamics models (Nottrott et al. 2011). Field experiments on airflow and pollutant dispersion in a street canyon (Sato et al. 2011) using particle image velocimetry (Takimoto et al. 2011), pressure differences between building walls, and wind (Hirose et al. 2019). Finally, the influence of solar heating on turbulent flow have also been studied (Chen et al. 2020b).

Greening systems and vegetation in street canyons have been analyzed in physical experimental facilities to provide high quality validation data for numerical simulations and theoretical models, such as: the influence of tree planting on pedestrian visual and thermal comfort in street canyons (Chen et al. 2021a); integrated effects of tree planting and street layout on the thermal environment (Chen et al. 2021b); the spatio-temporal variation of the urban wind and thermal environment caused by west-facing vertical greening systems (VGS) in street canyons (Zheng et al. 2023); and finally, to understand the mechanisms of different components of green spaces, such as grass areas, trees, or a combination of gray and green infrastructure, on heat load reduction at local and urban scales and under different weather conditions (Rahman et al. 2021).

The quantification of evapotranspiration, latent (Pearlmutter et al. 2009) and sensible heat flux (Kawai and Kanda 2010a) is also challenging in a complex urban environment, given the heterogeneity of the terrain and its different dry and wet elements, as well as the sum of sensible fluxes. In this context, scaled models have also been applied to cities, including at the mesoscale (Kawai, Ridwan and Kanda 2009).

Some long-term field measurements have also been conducted in outdoor physical models (Kawai and Kanda 2010a), considering the perspectives of water and energy balance of the surface (Nakayoshi et al. 2009), under different sky conditions and scaled arrays (Wang et al. 2021; Hang et al. 2022).

Urban geometry, including street aspect ratio and urban heat storage (Chen et al. 2020a), influenced by materials, combine to create complex spatial, temporal, and directional patterns of long-wave infrared radiation (Morrison et al. 2018; Matias and Lopes 2023). An infrared camera positioned in the outdoor experimental setup allowed for the investigation of these effects on the spatial/temporal characteristics of the urban thermal environment.

Although cities around the world are testing the use of solar reflective coatings on roads to reduce the urban heat island (UHI), and area within a city or metropolitan area that experiences significantly warmer temperatures compared to its surrounding rural areas (Reis et al. 2022) little research has been conducted to investigate the urban albedo of canyon surfaces. Solar reflective pavement has been touted as a simple, low-cost solution that has been shown to reduce surface temperature, which affects human thermal exposure and comfort (Middel et al. 2020).

The interplay between scales (large-reduced), considering different pavement and facade material properties (Kotopouleas et al. 2021) are quite rare. The associative use of simulation methods (numerical-physical) (Salvati et al. 2022), dialoging the external environment, using ENVI-met and indoor environment, through EnergyPlus, are novel.

One of the applications of using different methodologies and multi-scale model, is to get the output data of a physical model to calibrate numerical simulation, or even to use outputs of numerical simulations to analyze urban scale studies. But the numerical errors between these models, environments and scales are still unclear.

Research purpose

To fill the literature gap, this study aims to analyze the impact of scale analysis and pavements simulation model modification on ambient and surface temperature in a physical model of street canyons, named PAVement and Street CAnyon Model (PAVSCAM).

Materials and methods

The understanding that smart city projects involve multiple dimensions of study, the selection of most appropriate methodology to define some elements of urban landscape, as the pavement materials, becomes a complex task. This section describes the experimental sites as well and the materials used in the construction of the model, input data of the simulation scenarios, including calibration procedures and experimental design.

Environmental characterization

The experimental setup was located in Engenheiro Coelho, a small city with population of 21,712 (IBGE - Instituto Brasileiro de Geografia e Estatítica. 2023) in the state of São Paulo, Brazil, at 880 m above sea level, and at 22°17′00''S; 47°07′00''W. The two study areas are stated 1 km far from each other (Fig. 1c). The urban scale data collection was carried out on a street located in the University District (Fig. 1d) and the reduced scale data collection was carried out on the PAVSCAM physical model (Kowalski et al. 2024) is located in the university campus of the Centro Universitário Adventista de São Paulo (UNASP) in a rural site (Fig. 1e).

Fig. 1
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Experimental site location: a. Brazil; b. São Paulo State; c. Study area; d. Point of data collection in urban area; e. Point of data collection in the university campus

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According to Stewart and Oke (2012) urban climate purpose classification, this area is classified as LCZ 6 (Fig. 2). The main characteristics are: “Open arrangement of low-rise buildings (1–3 stories). Abundance of pervious land cover (low plants, scattered trees). Wood, brick, stone, tile, and concrete construction materials” (Fig. 3). Figure 4 shows the scale model facilities and dimensions, and Fig. 5 presents the albedo of the surfaces and sky-view factor inside of the scaled model.

Fig. 2
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LCZ classification: Urban area (Neighborhood)

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Fig. 3
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a Sky-View-Factor; b Surface albedo (Neighborhood)

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Fig. 4
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Scaled model (PAVSCAM) facilities

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Fig. 5
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a Sky-View-Factor; b Surface albedo (PAVSCAM)

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Experimental design

The sensors were installed in the Universitary neighborhood, Engenheiro Coelho, São Paulo, Brazil. The data collected by the equipment served as the calibration data for the numerical model, related to the neighborhood (NB) environment analysis. An anemometer, air temperature and air humidity sensors were positioned in place, and an infrared camera collected the surface temperature of the pavement during the experiment related to the scaled model environment (SM) analysis. The environments of the study case are presented in Fig. 6.

Fig. 6
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a Numerical model of urban area; b Urban area; c Numerical model of scaled model; e Physical model

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The PAVSCAM model was design to evaluate different types of pavement, with different albedos. Therefore, in this study only the highest albedo (the asphalt pavement) was analyzed, because that is the most common material used in the cities. Although the figures show four types of pavement, only the asphalt was monitored and analyzed.

The general characteristic of each scenario and experimental setup are presented in Table 1.

Table 1 General characteristic of each scenario and experimental setup
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Field experimental setup

The field thermal monitoring round aimed to assess the impact an urban area within the street canyon layer, covered with black asphalt pavement albedo against the reference case of an asphalt pavement inside a scaled model, named PAVSCAM (PAVement and Street CAnyon Model). The goal was to identify the correlation level between the outputs in different scales scenarios. The monitoring round, in all scenarios, was conducted during winter in south hemisphere (June 23th – June 30th, 2021). It was monitored the surface temperature (Ts) of a paved street and air temperature (Ta) at a standard reference height, termed ‘pedestrian height’. Figure 7 shows the sensors’ position.

Fig. 7
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Position of air temperature sensors during the monitoring: All units in cm

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Clear-sky days (atmospheric clearness index Kt ≥ 0.5 with low wind speed (ws ≤ 2 m/s) were considered valid for measurements. The atmospheric clearness index was calculated using the equations, purposed by Duffie et al. (2020) presented in Table 2.

Table 2 Equations to determine the atmospheric clearness index
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The current study investigates the variations between scales (1:1 and 1:15), types of modelling (physical and numerical) and environments (neighborhood and scaled model). Table 3 describes the sensors positioning and input parameters in the urban and scaled model monitoring round.

Table 3 Input parameters in the urban and scaled model – Winter Conditions and site experiment
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The main specifications of the sensors during the experimental monitoring in urban (neighborhood) and scaled model (PAVSCAM) environments and sensors are presented (Table 4).

Table 4 Main specifications of the sensors in the Neighborhood and PAVSCAM environments
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The ALTA II portable spectrometer consists of 11 lamps positioned in a circular manner, with each lamp representing a distinct wavelength. Upon activation, these lamps emit radiation of their respective wavelengths, which is then reflected by the object and captured by the sensor located at the center of the circle.

In this study, the spectral reflectance of the asphalt pavement (AP) was measured with a portable spectrometer. In order to reduce voltage variations, the procedure was repeated three times (Couto and Dornelles 2023). The average value was used in the solar reflectance calculation.

Air temperature and surface temperature data in PAVSCAM were recorded by a Esp32 microcontroller with a 1-min timestep. Low-cost solar shields were used in each case for temperature measurements (0.3 m open-ended PVC pipes parallel to the canyon longitudinal axis). Surface temperature sensors were fitted with a copper casing and covered on top by an insulation layer with reflective cover, to avoid convective and radiative heat exchanges.

Inside the urban area of neighborhood, the air temperature and relative humidity data were measured with a HOBO thermo-hygrometer with a 15-min timestep, for 7 days. To get the surface temperature data, an infrared camera was positioned 1 m height to capture the top vision of the pavement.

The anemometer was positioned at a distance of 3 m from PAVSCAM and 1.5 m height above ground, in order to identify the instantaneous, average and maximum wind speed and direction data above the top of the canyons. The pyranometer was positioned 9 m height and 150 m away from the experimental site. All sensors underwent a calibration step prior to deployment at PAVSCAM and comply with precision requirements of EPA (2008).

We have used different equipment for surface temperature to be more suitable for each scenario. As the PAVSCAM is located in a private and controlled area, it is a safe place to state the sensors (thermocouples). Furthermore, the shield of HOBO thermo-hygrometer could modify the wind pattern inside the canyon due its size.

Numerical model setup and calibration

Table 5 shows the input parameters in the numerical simulation, under winter conditions, in a scaled model environment, named PAVSCAM, and in the neighborhood environment.

Table 5 Input parameters in the numerical simulation – Winter Conditions, scale model (SM) environment. Scenario “NumSca-SM” and NumUrb-NB”
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To determine quantitatively which forecasting model is optimal, three performance metrics were used to evaluate the accuracy of point forecasting, which are mean absolute error (MAE), mean absolute percentage error (MAPE) and goodness of fit (R2) regarding the air and surface temperatures for each comparative analysis.

Results and discussions

This section describes the environmental meteorological data during the onsite experiment, presents the air and surface temperature time-spatial variation of numerical simulation and finally, the correlation models and error analysis between scenarios, to discuss the most appropriate simulation modelling, considering scale and environment aspects.

Environmental meteorological data

Figure 8 shows the global irradiance measured onsite, during the experiment period, and the selected typical day (June 24th), that presented the highest atmospheric clearness index (Kt = 0.69).

Fig. 8
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a Global irradiance (I), all units in W/m2; b Atmospheric clearness index (kt) of the period

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Figure 9 shows the hourly average air temperature (Ta) and relative humidity (RH) of the hole period, measured at 3 m height on site, in the neighborhood (NB) environment.

Fig. 9
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Air temperature (Ta) and Relative humidity (RH) of the period at 3 m height, on site

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The wind speed measured at 3 m height nearby the experimental setup is presented in the Fig. 10.

Fig. 10
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Wind speed (m/s) and direction (°) of the time series at 3 m height, on site

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Due to technical problems, some wind data are missing, specially from midnight until the and beginning of the day. Data from the nearest meteorological station (CETESB database) are presented to understand the wind pattern and data discussion (Figs. 11 and 12).

Fig. 11
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Air temperature (Ta) and Relative humidity (RH) of the time series at the nearest meteorological station (CETESB database)

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Fig. 12
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Wind speed (m/s) and direction (°) of the time series at the nearest meteorological station (CETESB database)

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Overall conditions (average air temperature, relative humidity, atmospheric pressure, wind speed, wind direction and maximum global radiance) at the nearest meteorological stations are given in Table 6. The station is located in São Paulo State, Limeira Station (CETESB database), stated 13 km apart from the experimental site. No precipitation occurred during that monitoring series.

Table 6 Overall conditions at the meteorological at the nearest meteorological stations – Limeira
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Figure 13 shows the wind rose of both sites, PASCAM setup and at the nearest meteorological station.

Fig. 13
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Wind direction (°) of the time series, on site (PAVSCAM) and at the nearest meteorological station (CETESB database)

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Air and surface temperature spatial variation

The spatial variation of air and surface temperature at 12 am, 6 am, 12 pm and 6 pm, at an altitude of 655 m are presented. The Table 7 is related to a scenario “NumSca-SM” (modelling: numerical, scale: scaled 1:15 and environment: scaled model – SM).

Table 7 Surface Temperature (Ts) and Air Temperature (Ta). Scenario “NumSca-SM”
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It is shown in Table 8 the scenario “NumUrb-SM” (modelling: numerical, scale: urban 1:1 and environment: scaled model—SM).

Table 8 Surface Temperature (Ts) and Air Temperature (Ta). Scenario “NumUrb-SM”
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Compared with the reduced scale model (1:15), the urban scale (1:1) simulation, named full scale, had the same thermal properties and climatic characteristics. The maximum surface temperature (Ts) can be identified at 12 pm for the asphalt pavement, in the configuration with aspect ratio H/W = 0.33. These results suggest that the difference between the pavements were due to the combined effects of solar radiation exposition, as well as the higher albedo.

In addition, the air temperature (Ta) at the pedestrian level changes, during the daytime mainly due to the shading effect, solar geometry and longwave emission during the nighttime.

It is shown in Table 9 the scenario “NumUrb-NB” (modelling: numerical, scale: urban 1:1 and environment: neighborhood—NB).

Table 9 Surface Temperature (Ts) and Air Temperature (Ta). Scenario “NumUrb-NB”
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The highest surface temperature (Ts) can be seen over the paved area, during the daytime. These results suggest that the 6 K difference were due to the combined effect of albedo and materials’ thermal properties. Related to the air temperature (Ta), at the end of the daytime (6 pm), the street canyons NE-SW presented slightly higher values compared to the NW–SE orientations.

Finally, mapping the spatial and temporal variability of urban microenvironment is crucial for an accurate estimation of the ever-increasing vulnerability of urbanized humanity to global warming (Wang et al. 2017).

The distinctions between the three methodologies for characterizing urban temperature variability could have varied uses in sectors including urban planning, climate change mitigation, and epidemiological research (Zhou et al. 2020).

Correlation between scenarios

This section aims to analyze the correlation between different scenarios, related to: scales, environments and modelling changes. The structure is to identify which are the effects in site A, considering changes in site B conditions.

The matching of surface albedo with the input of downward solar radiation is required for shortwave radiation similarity. The matching of surface emissivity, as well as the inputs of downward atmospheric radiation and observed surface temperature, is required for longwave radiation similarity (Kanda 2006).

The correlation between the measurements of air and surface temperature in PAVSCAM (Scaled-Model) and in the Neighborhood (Urban-Model) are presented in Fig. 14; simulation CFD in urban environment (CFD_urb) and data collected on site (URB) in Fig. 15; and between data simulated in urban scale (CFD_urb) and physical modelling (PHY), in Fig. 16. The other scenarios correlation charts are shown in appendix.

Fig. 14
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Analysis A1—Correlation between different scales: physical (PHY) and urban (URB). a. onsite pavement surface temperature (Ts); b. onsite air temperature (Ta)

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Fig. 15
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Analysis A3—Correlation between simulation CFD in urban environment (CFD_urb) and data collected on site (URB): a pavement surface temperature (Ts); b air temperature (Ta)

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Fig. 16
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Analysis A5—Correlation between data simulated in urban scale (CFD_urb) and physical modelling (PHY): a. pavement surface temperature (Ts); b. air temperature (Ta)

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There are six prediction models for surface and air temperature. The range of temperatures to apply the equations are presented in Table 10.

Table 10 Surface and air temperature range of each prediction model
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After being calibrated the model was used to estimate the air and surface temperature in winter period for the same urban area, and the charts are presented below.

Time variation of air and surface temperature

The observed and predicted models of hourly air and surface temperature are presented in appendix However, the most important results for air temperture are shown in Fig. 17 and Fig. 18, scenario A1 and A3.

Fig. 17
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Observed and predicted models: a A1 hourly air temperature (Ta); b A3 hourly air temperature (Ta)

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Fig. 18
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Observed and predicted models: a A3 hourly air temperature (Ta); b A5 hourly air temperature (Ta)

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The predicted values have a great adjutement to the observed data, during all the day and nighttime. The Figure Y, show the most relevant results for surface temperature, scenarios A3 and A5.

Finally, the pavement surface temperature tends to be overestimated in CFD model, compared with measured data in field. The physical model during all the period present overestimated values for air temperature in relation to measured urban data (A1). Furthermore, the same behavior can be observed for numerical simulation and urban environment (A3). Other scientific works have found the same trend (Lee et al. 2016; Qaid et al. 2016; Qaid and Ossen 2015; Salata et al. 2016). On the other hand, numerous previous studies tend to underestimate the air temperature during the simulation period (Acero et al. 2018; Morakinyo et al. 2016, 2017; Sosa et al. 2018; Wang and Akbari 2016).

For numerical simulations the radiation comes from weather data format and they are less accurate compared to other variables measured in field. As the boundary conditions and materials’ thermal properties are very similar, the main factor to contribute to overestimation is the radiations exposure of the model as mentioned by Salvati et al. 2022.

Table 11 shows the comparative analysis of air temperature in the winter, between Site A and B. Also, the equation of the predictive model, the determination coefficient (R2), the mean absolute error (MAE) and mean absolute percentage error (MAPE) of the predicted and observed data (site A).

Table 11 Comparative Analysis – prediction models for air temperature (Ta) and surface temperature (Ts) in the winter
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Incoming radiation varies depending on location, and recorded surface temperatures are not always comparable due to the complex’s interactions of various physical processes such as turbulence transfer and air heat conduction into obstructions (Kanda 2006). Given the complexity of a neighborhood and the simplicity of a scaled model composed of concrete blocks with no surrounding objects, the interaction between the elements is different.

Both for studies on surface temperature of pavements and air temperature, within the range of 17 °C to 32 °C, the A3 combination is the most common way to validate simulation models using ENVI-met. This combination exhibits a very similar error between the physical model and the urban environment (A1) within the temperature range of 13 °C to 37 °C.

Figure 19 shows that the PAVSCAM is an extremely simple model to represent the complexity of real scale neighborhood. However even, with all limitations of materials, inertia and vegetation, it has presented an error of ± 0.66 in air temperature estimation.

Fig. 19
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Scheme of level of details in a scaled physical model (a) and real scale neighborhood (b)

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To overcome the mismatch between model thermal inertia and the real world, physical scale modeling must be supplemented with numerical models and field measurements (Kanda 2006). The investigation found that the model can be considered a useful tool for urban climate analysis, given that the user accounts for its limitations and characteristics while interpreting the simulation outputs (Tsoka et al. 2018).

The use of simulated models in ENVI-met for validating a physical model (A5) resulted in the lowest mean absolute percentage error (MAPE) among all analyzed combinations, with a value of 4.9% for a temperature range of 17 °C to 32 °C. Thus, it represents the best method for validating simulations that assess the surface temperature of pavements.

The ENVI-met model for microclimatic analysis during summer, under hot summer conditions reported MAE of air temperature 1.34 °C (Tsoka et al. 2018). Due to de fact that only a few studies have been carried out for winter and intermediate seasons similar conditions, the input data obtained through ENVI-met simulations or from urban scale and physical model showed the lowest mean absolute errors (MAE), namely ± 0.59 and ± 0.66, respectively.

Under the same exposure conditions, the effect of the thermal inertia difference of façades between an urban-scale model and a reduced-scale model, as analyzed in this study, explains the 4% error in the predictive model for air temperature at pedestrian level and approximately 6% for surface temperature.

Lower thermal inertia materials experiences smaller daily temperature range, an a less changing rate of wall temperature, because they storage and absorbs more heat in the daytime and releases more at night (Chen et al. 2020a). Increasing 13 times the thermal inertia experiences in average 4.0 °C the air temperature inside the models in warm and temperate climate.

Conclusions

Several numerical simulations were carried out to explore the impact of scale analysis and pavements simulation model modification on ambient and surface temperature in a physical model of street canyon. The mains conclusions are as follows:

For studies on the surface temperature of pavements, within the temperature range of 12 ºC to 37 ºC, it is recommended to calibrate physical models using data derived from numerical simulation models as input, yielding a mean absolute percentage error (MAPE) of 4.9%. Moreover, for estimating data in real-world urban scale, within the air temperature range of 15 ºC to 37 ºC, it is proposed to use output data from simulated models in ENVI-met, that presented a mean absolute error (MAE) of ± 0.59 or physical models (MAE =  ± 0.66).

The current study was carried out in the winter season of the south hemisphere, and the experimental setup was located in a tropical city. So, it its recommended to apply this method in different seasons and climatic contexts to identify the accuracy of the predicted models. Furthermore, the results cannot be extrapolated to different urban forms and different sky coverage, because we do not have measured or simulated data, and consequently the estimated errors for these scenarios. This study presented the errors considering a simplified model (made of concrete blocks) and field measurements (made with different walls color, materials and elements) with average values of sky clarity. For different urban forms and non-clear sky days we suggest a new paper to analyze these hypotheses.

Overall, this study provides a significant improvement to understanding the interaction between numerical simulations, reduced physical models and real-world urban scale data. Evaluating errors associated with methodologies, scales of analysis, environments, and the interplay between them. Finally, providing physical parameters needed to construct better calibration models.