Effects of retro-reflective and angular-selective retro-reflective materials on solar energy in urban canyons

The study deals with the application of retro-reflective (RR) and angular-selective retro-reflective (AS-RR) coatings on surfaces (i.e. the street ground and the south-exposed façade) within the urban canyon. Solar analyses were conducted at different latitudes (Oslo, Milan, and Cairo) by varying the urban canyon height-to-width ratio (H/W) to determine the variation in solar irradiation absorbed by north and south façades. Both summer and winter conditions were considered, and up to five material patterns (one reference case and four enhanced scenarios) were investigated for each combination of latitude and height-to-width ratio values. A validated Monte Carlo-based numerical model was used to conduct full-ray tracing analyses and to simulate the behavior of these coatings. The outcomes allowed the development of guidelines for the adoptions of RR and AS-RR materials in different scenarios. It was demonstrated that RR and AS-RR materials applied to the street performed better in low-density urban environment (H/W ≤ 0.5) with a consequent increase of the solar energy gains on the north façade by up to 15%. Employing RR and AS-RR materials on the south-exposed façade showed greater effectiveness on high-density urban canyon (H/W ≥ 2.0) and reduced by up to − 8% the solar irradiation absorbed by the façade.


Introduction
Urban morphology and materials properties play a relevant role in assuring a healthy and comfortable living environment Zhou et al., 2016), especially because the recent growth of the population living in cities has caused an increase in the densification of the urban pattern (United Nations, 2014). Such a growth can lead to several climate-related issues amongst which the most documented is the so-called Urban Heat Island (UHI) effect (Rahman et al., 2017;Xu et al., 2018). The main causes of this phenomenon are found in the lack of permeable and vegetated surfaces, the materials used in the built environment, the anthropogenic heat, the worsened ventilation within urban canopies, and the higher pollutants concentration in the atmosphere (Oke, 1981;Piselli et al., 2018;Warren, 2014;Xie et al., 2005). Documented issues linked to the UHI effect are related to increase of energy use for cooling of buildings (Pantavou et al., 2013), worsening of human health, and pedestrian thermal stress (Pioppi et al., 2020). Such consequences are more evident within urban canyons (UC), which consist of street corridors defined by the height-to-width ratio (H/W) parameter (named "aspect ratio" from here on) where the height (H) is the average of the buildings' height and the width (W) refers to the street (i.e. the distance between the opposite façades facing the canyon).
Several studies focused on mitigation strategies through green infrastructures (e.g. urban park, tree lined street) and identified implementing evapotranspiration from plants (Grilo et al., 2020;Lobaccaro et al., 2019;Ziaul and Pal, 2020), creating blue infrastructure (i.e. bodies of water) (Battista et al., 2019), increasing energy storage potential (Kousis et al., 2020;Piselli et al., 2019), and applying cool materials (i.e. high-reflective coatings) on urban surfaces (i.e. terrain, façades and roofs) (Liu and Morawska, 2020;Manni et al., 2020b) as the most effective measures. Surface treatments and building coatings are demonstrated to impact on the urban microclimate, hence exploiting materials with a high solar reflectance in the visible range and high infra-red (IR) emissivity allows one reducing surface and air temperatures, lowering both energy use for cooling and electricity energy peaks, and improving indoor comfort conditions (Jandaghian and Berardi, 2020). Nonetheless, when applied to building façade, their effectiveness is negatively influenced by factors such as urban density and window-towall ratio (Nazarian et al., 2019).
High-reflective (HR) materials also presented some drawbacks in relation to solar energy gains through building envelope during winter, leading to the increase of the energy use for heating, and the progressive decrease of albedo value due to aging, pollution, and weathering effects (Tsoka et al., 2018). These effects occurred because cool materials generally reflect most of the solar irradiation in a diffuse way and this may contribute to exacerbate the UHI phenomenon by increasing the amount of multiple and mutual inter-buildings reflections (particularly when it comes to high dense built environments), while reducing the absorbed fraction. To overcome this issue, retro-reflective (RR) materials were proposed as innovative coatings capable of reflecting backward the solar irradiation. Such a behavior is more evident when sunrays hit the RR surface perpendicularly, while for higher and lower angles of incidence the RR properties progressively decrease, and specular and diffuse reflections are observed . Compared to HR materials, RR materials decrease the occurrence of multiple reflections within the urban canyon by directly reflecting solar irradiation towards the skydome.
Despite the advantages in the applications of RR materials, a pitfall of such a strategy is that they reduce the useful solar gains during the winter season Vallati et al., 2018). For this reason, the development of a selective behavior on RR materials represents a fundamental step to enable more effective cool materials capable of showing an optimized performance across the different seasons . The concept behind the angular-selective retro-reflective (AS-RR) materials is to have surface treatments capable of providing a selective response depending on the angle of incidence of the solar radiation. This behavior enables high solar gains during winter when the azimuth of sunrays is lower, and high reflection of the solar irradiation outside the urban canyon during summer when the azimuth of sunrays is higher. Some concepts of selective RR materials have recently been proposed (Sakai and Iyota, 2017) along with methodologies to define their angular range of activation Zinzi et al., 2015). However, the impact of AS-RR materials on urban microclimates and mutual solar reflections between buildings has only been investigated in preliminary studies (Manni et al., 2019). The aim of the present study is to investigate the potential applications of RR and AS-RR materials on the street ground and the southexposed façade, that is the most irradiated surface according to , and their influences on the solar gains considering all the façades of the UC. This study has the ambition to contribute to a better understanding of the effects of RR and AS-RR This work takes the move from the AS-RR materials conceptualized in , and later developed in (Manni et al., 2019), by defining guidelines about their exploitation as innovative urban coatings (i.e. building façade, street ground) through the Monte Carlo-based numerical model validated in (Manni et al., 2020a). The effectiveness of the angular ranges of activation of the RR properties identified in  is also addressed by the present study.

Nomenclature and acronyms
The paper is structured as follows. The Methods and materials section (Section 2) is articulated around three sub-sections describing the main steps of the workflow (Sections 2.1-2.3). The Result and Discussion section (Section 3) reports the simulation outcomes for the reference case (Section 3.1) and for the different enhanced scenarios (Section 3.2), and analyses them for each climate zone, before a cluster of guidelines is determined (Section 3.3) and limitations are highlighted (Section 3.4). Finally, the Conclusions and future developments section summarizes the knowlegde generated and the implications of this work (Section 4).

Methods and materials
The influences of RR and AS-RR materials on solar irradiation absorbed by building façades are assessed by using the numerical model developed in a previous study (Manni et al., 2020a). The workflow is arranged into three steps ( Fig. 1) from materials characterization (Step 1) to solar analyses (Step 2), and to data assessment (Step 3). These steps are described in the following sections.

Step 1: From material characterization to the virtual clones
In Step 1, the RR materials were characterized. The spatial distribution of the reflected irradiation was analyzed for various angles of incidence of the sunrays. Then, AS-RR coatings were modeled by applying the angular ranges of activation identified in a previous part of this research  to the RR materials previously characterized. The virtual clones of the materials were finally generated and utilized together with the aspect ratio and the orientation parameters to determine the investigated UC scenarios.
The RR materials consisted of barium titanate glass microspheres and they were characterized in (Castellani et al., 2017). The directional response of such materials was assessed through a dedicated experimental test rig, which is described in . It is composed by (i) an artificial solar radiation source, (ii) an inclined plane to test various exposures of the sample (i.e. various angles of incidence), (iii) 19 photodiodes arranged on a semi-cylinder every 10 • degrees (from − 90 • to 90 • , with the null value corresponding to the direction perpendicular to the plane of incidence), and (iv) a data acquisition system. The campaign for material characterization demonstrated that such microspheres not only implemented a RR behavior on treated surfaces, but they were also capable of enhancing the surface global reflectance up to around 0.4. The angular distribution of the reflected irradiation as assessed in (Castellani et al., 2017) is reported in the Appendix A of the paper (Table A.1). Data used to model the virtual clone of RR materials are presented in this manuscript, while a more complete description of the protocols applied for the characterization, and the characterization results themselves can be found in (Castellani et al., 2017).
These quantities were post-processed to determine the reflection coefficients for the Lambertian diffusively reflected, the specular reflected, and the retro-reflected components, for each incidence angle. The absorption coefficient was always considered equal or higher than 0.6 in accordance with (Castellani et al., 2017). These parameters, which describe the material optical behavior in the numerical model, are reported in Table 1.
It is worthwhile to mention that the investigated RR materials (barium titanate glass microspheres) do not show the highest possible solar reflectance. However, they currently provide the best performance as retroreflectors whithout a significant chromatic alteration of the treated surface . Higher solar reflectance values can be observed in other RR materials, but this happens at the cost of turning the color of the original surface into a metallic tone.
The AS-RR coatings conceptualized in  showed a selective behavior dependent on the angle of incidence of the solar radiation. Six angular ranges (Fig. 2) were taken into account for the RR layers on vertical and horizontal surfaces. Such surface treatments are expected to behave as retro-reflectors as long as the incident angle falls within the angular range of activation, while present a Lambertian (perfectly diffusive) behavior outside such angular range.

Step 2: Solar analyses
In Step 2, solar analyses were conducted. In addition to the input parameters which were outlined in Step 1 (i.e. virtual clones of the materials), the boundary conditions (i.e. location, TMY weather file) and the simulation system settings (i.e. number of ambient bounces (ab), number of finite elements (FE), number of events) were considered. The Table 1 Coefficients describing the material reflective properties depending on the angle of incidence of the solar irradiation.
Angle of incidence solar analyses were carried out for 15 scenarios, which were assessed for each latitude, and both summer and winter conditions were investigated. The values of the solar irradiation absorbed (Irr abs ) by the façades of the two buildings, facing north and south respectively, were estimated with an hourly time step throughout the selected days, which were considered to be representative of the summer and the winter season.

Numerical model and simulation variables
The numerical model to conduct solar analyses is based on a Monte Carlo approach implemented into an on-purpose developed script. The Monte Carlo method was used to estimate the solar irradiation collected by each FE of an urban canyon given the probability that sunrays impinge on a surfaceand are consequently absorbed or reflectedaccording to the input data. A specific energy amount is assigned to each sunray depending on the solar irradiation entering the urban canyon environment and on the number of simulated sunrays. A complete description of both the numerical model and its full-ray tracing routine can be found in a previous paper (Manni et al., 2020a) where the experimental validation of the approach was presented.
Input parameters required by the numerical model with the corresponding symbols and units of measurement are reported in Table 2.
Simulation variables were set to optimize the computational time while maintaining the uncertainty of the results below a 5% threshold. The amount of ambient bounces (i.e. sunrays reflections) considered in the ray-tracing analyses for each sunray before the cutoff was therefore set equal to six. The number of cells in which the UC surfaces are divided (number of FEs on a surface) is determined to guarantee an adequate discretization of the results, and the distance between two consecutive test points was thereofre set to around 1 m. Finally, the number of sunrays entering the UC through the top surface (named "number of events" in the numerical model environment) was set to 10 6 events. These settings allow conducting solar analyses with around 3% uncertainty (Manni et al., 2020a).

Investigated scenarios
Each urban canyon configuration was univocally defined by a combination of aspect ratio, orientation, and material properties. The values for height-to-width ratio adopted were 0.5, 1.0, and 2.0, so that different patterns of urban density such as low-, middle-, and high-density could be investigated. The study focused on assessing the west-east orientation which characterizes the UC with the greatest difference in solar accessibility between the two façades (Manni et al., 2019). The urban canyon geometry was simulated as two-dimensional, i.e. as observed in infinitely long street corridors by setting the the area of analysis in the middle of the UC, where the system is not affected by the boundary effects that take place at the extremes of the UC. The dimensions (reported as building's height by street's width) were 16 m by 8 m in case of a 2.0 H/W, 16 m by 16 m if H/W equaled 1.0, and 16 m by 32 m when H/ W was 0.5. The height of the buildings was kept constant throughout the study (Fig. 3).
When it comes to the surface materials, traditional diffuse materials from Radiance library were used for the "reference case". Such materials, whose reflection coefficients vary from 0.20 (asphalt) to 0.35 (brown painting), were applied to the urban canyon surfaces. In the "enhanced scenarios", either RR or AS-RR materials were alternatively applied to the most exposed façade (facing south) or to the street ground. In total, up to five cases were analyzed for each UC geometry (Table 3).   Each surface of the UC was considered to have a homogenous reflection coefficient. Through this approach, it was possible to avoid a more detailed level of modelling that includes the positioning of the transparent and opaque parts of the façade. This is coherent with the scope of the proposed approach that focuses on the energy perfromance at urban scale where the architectural and technological appearance of the façades is not detailed, but rather described (in terms of optical properties) with coefficients that regulate the overall behavior.
Three cities representative of different climate zones were chosen as locations to carry out the investigation: Oslo for the northern zone, Milan for the central zone, and Cairo for the southern zone. The 21 st of June and the 21 st of December were chosen as representative days for the summer and winter conditions, respectively. The duration of the day was determined by the daylight accessibility of an unobstructed horizontal surface, and it varies with the latitude and the season (Fig. 4).
Hence, the hours of the day showing an amount of direct solar irradiation (Irr dir,hor ) impinging on such a surface which differed from zero were selected. In Oslo, the solar irradiation was assessed from 5:00 a.m. to 7:00 p.m. in summer and from 10:00 a.m. to 1:00 p.m. in winter. Conversely, the number of hours with daylight in Milan and in Cairo were: from 5:00 a.m. to 6:00 p.m. (summer) and from 9:00 a.m. to 3:00 p.m. (winter) in Milan; and from 6:00 a.m. to 5:00 p.m. (summer) and from 8:00 a.m. to 4:00 p.m. (winter) in Cairo.

Step 3: Data assessment and definition of guidelines
The outcomes of the solar simulations were post-processed in Step 3 and analysed to identify guidelines for the potential applications of RR and AS-RR coatings to urban surfaces, for the different climate zones.
The weighted variation of absorbed solar irradiation (Δ %,wt ), as defined in Eq. (1) was adopted as main pefromance parameter to assess the perfomrnace in the different scenarios. This quantity represents the difference between the solar irradiation absorbed in the enhanced scenario (Irr abs,enh ) and the corresponding amount in the reference case (Irr abs,ref ), over the maximum difference in absorbed solar irradiation registered in the selected i urban canyon geometries for the reference case (max(Irr abs,ref,i ) -min(Irr abs,ref,i )). Furthermore, the variation of the absorbed solar irradiation from the reference case (Δ % ) was calculated as reported in Eq. (2) Both the Δ %,wt and the Δ % are here used as parameters to evaluate the influences of RR and AS-RR coatings in relation to solar energy gains through buildings' façades.

Solar accessibility of the façades in the reference case scenario
The outcomes of the solar analyses conducted on the reference cases highlighted that the most irradiated façade facing south was the one in Oslo (summer) and in Cairo (winter), for each aspect ratio. The same was observed for the north-exposed façade. This behavior is due to the variations in the geometry of the sun: in summer, the sunrays were almost parallel to the façade in the Southern zone (hence the Irr abs amount was minor), while in winter were lower above the horizon (worsening mutual shading phenomena in the Northern zone). The greatest Irr abs values for each latitude were observed on the façades overlooking wider UC (H/W = 0.5). The Irr abs on the north and south-exposed façades for each climate zone and aspect ratio, is shown in Fig. 5

Northern zone
Retro-reflective (case a) or angular-selective retro-reflective layers (case b) added to the street surface permitted to improve the solar accessibility of the façades ( Fig. 7 and Table 4). In summer, the Irr abs on the south-exposed façade is increased from 1% (H/W = 2.0) to 5% (H/ W = 0.5) for case a, and from 2% (H/W = 2.0) to 7% (H/W = 0.5) for case b. Similarly, the Irr abs on the opposite façade showed an increment from 2% (H/W = 2.0) to 7% (H/W = 0.5) for case a, and from 4% (H/W = 2.0) to 10% (H/W = 0.5) for case b. In winter, the influences of the cool street surface were negligible in the high-density configuration (H/ W = 2.0) for both case a and case b. However, in the UC characterized by H/W = 0.5, AS-RR materials (case b) were capable to increase the Irr abs on the north-exposed façade by up to 9%, while RR materials (case a) only achieved an increment of 6%.
The data reported in Fig. 8 highlighted that enhancements due to the variation in the material's pattern barely achieve the 20% (in summer, H/W = 0.5) of the maximum improvement of Irr abs achieved through the change of the urban density. Furthermore, the trend of Δ %,wt values was the same as the the Δ % amounts.
For case c and case d (RR and AS-RR materials applied to the southexposed façade), the solar accessibility of the buildings was worsened in summer, and unaltered in winter (Table 4). In summer, the Irr abs on the façade facing south is reduced by 8% from the reference case in all the assessed configurations (Fig. 9). In winter, this percentage varies from − 6% to − 8% in both case c and case d, with the higest changes in narrow UC (H/W = 2.0). The influences of RR materials (case c) on the north facing façade were more evident for H/W = 2.0 (high urban density): in summer, the Irr abs was lowered by 11%. On the contrary, AS-RR coating (case d) barely achieved a 2% reduction in summer. In winter, no variation was observed for case d geometries, while the middle-density urban canyon (H/W = 1.0) of case c showed a reduction of 6% of Irr abs . Percent changes weighted according to the highest variation in solar gains due to the geometrical pattern showed that RR and AS-RR materials caused up to 20% of reduction in the south-exposed façade when H/ W equal to 0.5 (low urban density), and up to 13% reduction with H/W equal to 2.0 (high urban density) (Fig. 10). The Δ %,wt values confirmed that Irr abs in winter by the façade facing north was unchanged from the reference case when AS-RR materials were exploited instead of the RR materials.

Central zone
The application of the optimized cool materials (case a and case b) on the street surface contributed to boosting the solar accessibility of the two façades ( Fig. 11 and Table 5). In summer, the Irr abs calculated for the south-exposed façade was increased by a percentage ranging from 3% (H/W = 2.0) to 6% (H/W = 0.5) for case a and from 5% (H/W = 2.0) to 12% (H/W = 0.5) for case b, respectively. In winter the increments were lower than 3% in all investigated scenarios, with minimum quantities observed with H/W equal to 2.0 (high urban density). In summer, the same trends were observed in the distribution of the percent variation values (even if slightly increased) concerning the opposite façade. In winter, the Irr abs quantities were increased from 1% to 5% for case a and from 3% to 5% for case b.
The results about Δ %,wt highlighted that enhancing the material pattern could cause an increment equal to 15% (case a) and to 30% (case b) of the greatest variation of Irr abs due to the geometry alteration, on both façades in summer (Fig. 12). In winter, such percent changes did not reach the 5% threshold on the south façade, while they were higher on the opposite façade with H/W equal to 0.5 and to 1.0.
Regarding the application on the south facing façade, RR and AS-RR materials reduced solar energy gains in summer and in winter (Fig. 13

Table 5
Calculated amounts of Irr abs by building façades and corresponding Δ % and Δ %,wt values for all the modelled scenarios in the Central zone.   and Table 5). The estimated Δ % values characterizing the south façade in case c and in case d were constant and equal to around − 8% in summer and in winter throughout the investigated UCs. In the north-exposed façade, RR surface treatments showed higher percent values in winter than in summer when the H/W is equal to 0.5 or 1.0 (low and medium urban density, respectively). Conversely, AS-RR treatments allowed reducing Irr abs by up to 6% (H/W = 2.0) in summer, while increasing by a maximum of 2% in winter (H/W = 1.0). Distribution of Δ %,wt values for the south façade showed some differences in the impact of RR and AS-RR materials between summer and winter (Fig. 14). The investigated surface treatments were responsible for the Irr abs reduction more in summer than in winter, and they resulted to be more effective in wider street corridors (H/W = 0.5). Regarding the north-exposed façade, Δ %,wt values were as high as the Δ % , except for the quantities referring to case c in winter whose distribution turned out to be flattened around the − 6% share.

Southern zone
The angular range of activation of RR properties which was defined in  for the horizontal surfaces (i.e. street application) in the Southern zone ranged from 0 • to 90 • for the case a and the case b. In both cases, the solar accessibility of the south-exposed façade was increased from 6% (H/W = 2.0) to 8% (H/W = 0.5) in summer, while in winter the values varied between 1% (H/W = 2.0) and 3% (H/W = 0.5) ( Fig. 15 and Table 6). The same shares were observed on the opposite façade (north oriented) in summer; while they turned out to be slightly increased in winter (around 2% higher than south façade).
The estimated Δ %,wt values highlighted that cool materials applied on the street played a significant role in increasing the solar irradiation absorbed by the façades when wider UC were considered by guaranteeing a percent variation up to 17% of the maximum increment due to geometry (Fig. 16).
Regarding the application of RR and AS-RR materials on the façade, solar energy gains on the south-exposed façade were reduced throughout the year, while the opposite façade was only mitigated in winter ( Fig. 17 and Table 6). The Δ % quantities calculated for the southexposed façade in case c and case d were distributed around the − 8% value. The north façade was characterized by a reduction in the Irr abs,win equal to 6% for both case c and case d. In summer, the solar accessibility of the façade was increased by up to 3% (H/W = 2.0) with the application of AS-RR materials.
The Fig. 18 showed how the Δ %,wt distribution of south façade ranges between − 20% and − 14% for case c, and between − 16% and − 8% for case d, in summer; while in winter, the distribution of the values from the two case studies coincided. In winter, the reduction on the opposite façade was mostly affected by the selected material pattern with H/W equal to 0.5, while in summer such reduction barely achieved the 3%.

Guidelines for the application of optimized cool materials
The outcomes of this study showed that RR and AS-RR materials always increased the solar irradiation absorbed by the two façades of the UC, when they were simulated as surface treatments for the street surface. The higher solar reflectance value characterizing the street (if compared to the asphalt from the reference case) played a significant role in this behaviour. The magnitude of the phenomenon was found to be inversely proportional to the aspect ratio, and the investigated cool coatings showed a greater impact in the Central zone, while being barely effective in the Southern zone.
The following guidelines can be carried out for the street application: • RR and AS-RR materials can be applied to the street in order to increase the solar irradiation absorbed by the two façades (greatest variations were observed in scenarios enhanced with AS-RR materials); • Effectiveness of both RR and AS-RR materials is higher in summer than in winter; • RR and AS-RR materials applied to the street surface achieve higher performance levels in low-density (H/W ≤ 0.5) urban environment.
Optimized cool materials on the south elevation reduced the solar irradiation absorbed by this façade throughout the year. The estimated variation from the reference case assumed values close to − 8% in every scenario. Conversely, on the opposite façade, the influences of the coating were mitigated by using AS-RR materials instead of RR ones. Furthermore, the absorbed irradiation was reduced more in summer than in winter in the Northern and Central zones, while the opposite tendency was observed in the Southern zone.
The following guidelines can be carried out for the façade application: • RR and AS-RR materials can always be applied to the south-exposed façade to reduce the irradiation absorbed by this surface; • Effectiveness of RR and AS-RR materials is higher in summer than in winter, when the Northern and Central zones are considered; • RR and AS-RR materials showed higher performance levels on highdensity (H/W ≥ 2.0) urban environment.

Limitations
The study reported in this paper presents two main limitations. Firstly, the research activities only focused on short-wave energy exchanges within the UC and between the UC and the surrounding environment, without linking solar gains within the possible overheating of the urban canyon. Therefore, the impacts of urban coatings on the energy balance is just partially assessed. However, using the variation in absorbed solar irradiation as the main output parameter (instead of variations in air temperature) to evaluate RR and AS-RR materials may also represented a strength of this study. The analysis of the Irr abs allowed more general conclusions to be taken on the effectiveness of these materials in different climate conditions without investigating the entire thermal domain of the canyon. Since the thermal domain of the UC depends on so many other variables (i.e. wind speed, humidity, air temperature), comprehensive investigation with such approach would be impossible in practical terms.
Secondly, the utilization of data about solar irradiation from statisticbased weather data files may result in incorrect computing of diffuse fractions as well as in systematic error within the evaluation of the potential benefits. Such type of weather data files is however the usual source of weather data at the preliminary phase of the design process, and are today the most used and accepted sources for input data in the design process based on building performance simulation.

Conclusions and future developments
Different effects were observed depending on the surfaces where RR and AS-RR materials were exploited. When applied to the street, such surface treatments were capable of increasing the solar irradiation absorbed by both the building façades (more in summer than in winter) with greater variations on the north-facing façade than on the southfacing façade. Implementing an angular-selective behavior led to increasing the estimated percent variations from the reference case. The exploitation of RR materials on the south façade caused a reduction of the absorbed solar irradiation: the magnitude of this phenomenon depends, in the north façade, on the geometry (i.e. H/W, orientation) of the UC . Angular ranges of activation of the RR properties demonstrated to be effective in reducing the mitigation potential of RR materials during the winter season in the Northern and Central zones while during summer in the Southern zone.
The findings of this study demonstrate that: • RR and AS-RR applied on the street surfaces affect the solar irradiation absorbed by the two façades at the same way, although with different magnitudes; • In their best street application (low-density UC in Milan, Central zone), optimized cool materials can increase the Irr abs by façades both in summer (around 13%) and in winter (around 4%) compared to a reference, conventional configuration; • RR and AS-RR materials applied to the south façade always reduce by around 8% the irradiation absorbed by the same façade; • In their best façade application (high-density UC in Milan, Central zone), optimized cool materials can reduce by 8% the Irr abs by south façade throughout the year, while lowering by 6% Irr abs by the other façade in summer with negligible effects in winter.
In conclusion, this investigation assessed cool materials to be effective technologies to enhance the solar accessibility of buildings' façades within street corridors while reducing the risk of the unwanted UHI. However, further analyses are needed in order to investigate the comprehensive effects of such materials by considering other parameters such as the amounts of solar irradiation that are reflected outside the canyon boundaries.
The future developments of this research may also concern: • The enhancement of the Monte Carlo-based numerical model by including other energy exchange phenomena in the calculation routines, such as long-wave radiative heat exhanges and convective heat exchanges. • The application of the current version of the numerical model to investigate visual comfort issues (e.g. glare) due to HR and RR materials. • The further optimization of the angular ranges of activation of the RR properties. • The assessment of the performance for the case of RR materials with enhanced solar reflectance.

Declaration of Competing Interest
The authors declared that there is no conflict of interest.

Table A1
Percentage angular distribution of the reflected radiation for eight angles of incidence of the sunray (Castellani et al., 2017).