A New Methodology to Assess Building Integrated Roof Top Photovoltaic Installations at City Scales: The Tropical Coastal City Case

Due to concerns on environmental pollution on a global and societal level, there has been an urge to shift the fossil fuel and nuclear energy generation to reliable and sustainable energy sources installed at the location of the load. Among all the renewable energy sources, solar energy is one of the most abundant and the cleanest energy source [1]. To support the shift to sustainable generation, integrated urban and energy planning on every aspect of the energy demand and integration of different systems has to be considered [2]. In addition to integrated planning, a recent study highlights that the built environment of the future would transform buildings into resource assets-fully self-aware, adaptive and communicative with added market value [3]. Present and future buildings: residential, commercial, or industrial sectors can have additional value if utilized through generation at specific location and space. Direct solar energy conversion stemming from roof areas will play a significant role in the context of sustainable generation by a mix of renewable energies [4]. As an example, the relevance of the large availability of roof surface area for some northern cities of Spain was found to have relatively high potential for solar PV despite lower irradiance [5]. For other locations, it has been estimated that the application of solar PV technology can provide about two-thirds of the current electricity consumption in the city of Bardejov in eastern Slovakia [6] with a population of 33,000. As an additional example, the modern residential district of Scharnhauser Park near Stuttgart/Germany, with a population of 7000 people, was used to calculate the potential of photovoltaic (PV) energy and to evaluate the ratio of “own consumption” defined as the ratio of total electricity consumption by the energy produced. Ratio of own consumption of 17% was estimated with the total yearly electricity consumption of 10,700 MW h [7]. The electricity potential generated from the rooftop solar PV system in the Gangnam district in Seoul, South Korea, can be enough to supply 303,496 households (3724.5 kW h/year/household), almost 1.5 times more than the households in the district (202,906 households) [8].

To determine the PV potential of larger spaces, tools have also been developed to estimate the energy production and cost of energy of grid-connected photovoltaic applications around the world, e.g., PV Watts developed by the U.S. National Renewable Energy Laboratory (NREL²) as a good example. However, these tools are single building or site specific and do not consider urban effects for large city applications. It is therefore important to incorporate urban morphology to consider the urban heterogeneity that includes the radiation trapping and shadowing due to building heights. Also, the role of PV installation on meeting and mitigating energy demands, mitigating Urban Heat Islands (UHIs), and consequently air pollution on a city-scale are important considerations to take into account. We find that integration into the larger built environment and the larger utility system is just as important as other drivers such as solar resource and cost to the use of PV to achieve energy sustainability and resilience goals. In hot, humid climates, the coincidence of cooling load with solar resource provides a valuable opportunity for such integration of supply with demand.

Energy demand can be influenced by socioeconomic factors; however, air conditioning (AC) demand is amplified in very warm climates in the tropics or during extreme heat conditions in temperate climates and here we seek to mitigate this demand in order to reduce the stress on the electric grid and facilitate increasing amounts of PV generation. The U.S. Department of Energy (DOE) reports that energy consumption by heating ventilation and air conditioning (HVAC) accounts for 63% and 36.7% of the total electrical energy use for residential and commercial buildings, respectively [9]. For the entire world, the building energy consumption by HVAC in 2010 was 61% for residential and 40% for commercial buildings [10]. Further, the energy consumption by HVAC has been increasing due to economic growth and global climate change. It has been estimated that energy demand for cooling would increase by 15% over the 21st century [11], and summer loads would increase by 10% for most U.S. buildings [12]. AC demands peak during an extreme heat wave day and increases by 20% as compared with a normal day [13]. For the specific context of tropical coastal locations, the extreme heat events were studied for the Mesoamerican and Caribbean (MAC) region defined as three consecutive days with daily maximum heat index greater than the 97th percentile of the datasets [14,15]. In the same study, it was reported that 144 extreme heat wave events were recorded for entire Mesoamerican and Caribbean region out of which 11 events were recorded for the city San Juan, Puerto Rico for a period of 35 years (1980–2014) [14]. During an extreme heat event, a high-pressure atmospheric system induced southeasterly winds (as opposed to normal easterly winds) was responsible for the recorded high summer temperatures, leading to high rates of mortality related to heat stroke and cardiovascular diseases as reported for San Juan during the summer of 2012 [16]. Also, the projection of the number of heat wave events per year was estimated to be between 12 and 15 for the future climate period of 2026–2045 for Puerto Rico [15]. Heat waves in general would be occurring with a higher frequency and intensity in the future, resulting in risks to the population and without air conditioning systems maybe at higher health risks under these conditions. For the MAC region, a research agenda is proposed in order to better understand and inform on appropriate mitigation and adaptation efforts as a consequence of extreme events, to secure local infrastructure and health of community residents [17]. It thus becomes important to quantify energy demand requirements to maintain human comfort level during these very warm conditions in tropical coastal regions and to apply best mitigating strategies to reduce the overall and peak cooling demands. Here, we explore different active (building integrated PV systems) and passive (cool roof (CR)) technologies in order to mitigate peak demands with its added benefits of power production at a city scale.

At least 40 GW of PV systems were installed globally in 2014, up from 37 GW in 2013 setting a new record for the solar PV sector. China, Japan, and USA were the three top markets in 2014. The 540 GW mark at a global level could be reached in 5 years' time (by 2019) [18]. The large sector of PV installation is seen in utility-scale PV installation, accounting 57.0% and building-scale PV accounting for 42% of the total market share in China [19]. As building-scale PV is gaining popularity because of the availability of roof space and utility-cost savings, the importance of geo-spatial information and 3D information, which could be unique for each city, becomes necessary for the estimation of PV potential for sites within urban areas. A recent development in the estimation of PV potential in urban areas uses CityGML,³ which describes 3D city and landscape model including geometry, semantic, topology, and appearance. This model has been improved to include PV simulations including shading of buildings in urban settings [7]. However, the interaction between the urban climate and the buildings as well as determining the ratio of demand to production becomes essential for every urban environment and it is missing from current analysis tools. To account for the interaction between climate, buildings, and energy demand with PV mounted roof, the use of non-hydrostatic version of the Weather Research and Forecast (WRF). WRF [20] coupled to the multilayer building energy (BEP + BEM) system [21] has been recently conducted for the cities of Tucson and Phoenix in Arizona [22]. The results demonstrate that the deployment of cool roofs and rooftop solar photovoltaic panels reduce near-surface air temperature and cooling energy demand at the scale of the metropolitan area. The parameterization adopted here, to characterize solar photovoltaic arrays in the multilayer BEM [22], is based on the scheme proposed by Masson et al. [23] and assumes horizontal PV mounted roof with reparameterizing of BEM including the balancing of sensible heat flux through roof. However, the methodology proposed in the present work considers horizontal PV roof (HPV) as well as tilted rooftop PV and cool roof, modifying the roof surface temperature as a consequence of the energy balance on roof under different conditions. This study focuses on roof surface temperature for different roof applications reporting on 2 m air temperature, AC demands, and solar power production.

Different roofing properties and technologies influence roof surface temperatures, which in turn affects the surface heat flux to the built environment. As an example, the roof surface temperature in Miami, FL is reported to reach 60 °C, 30 °C greater than air temperature, for roof surface albedo of 0.3 [24]. Thus, the use of different roof surface applications for city-scale deployment are effective means of reducing air temperature and energy consumptions [22,24–28]. For tropical conditions or summer seasons, cool roofs, by virtue of increased roof albedo, absorb less incoming shortwave radiation than dark roofs, thereby promoting a lower roof temperature. As a result, cool roofs reduce heat transfer into the urban environment and into the buildings, simultaneously decreasing near-surface air temperature and cooling energy demands. It has been recently reported that the cool roofs (albedo 0.85) and green roofs reduce the roof surface temperature by almost 8–10 °C [29]. Short-term simulation shows that the urban area is more efficient in partitioning surface energy balance when green roofs are specified as opposed to including vegetation inside the urban core [30]. However, the net positive effect of green roofs still unknown as some recent reports indicate that large-scale use has adverse impacts on the air quality due to changes in the atmospheric stability [31]. On the other hand, large-scale PV installations (on ground) have been shown to increase UHI effects significantly, especially during nights for all four seasons [32]; however, the effect on rooftop PV has been shown to decrease the temperature and UHI effects [22,23]. However, for the South Coast Air Basin of California, it was reported that rooftop PV have a net positive effect on the thermal storage of the buildings, an effect enhancing the existing UHI by up to 0.2 °C [33]. On building level studies carried for the city of San Diego, CA, maximum roof temperature reached 60 °C for normal roof (NR) (albedo 0.25) and 40 °C for tilted rooftop PV with a cooling load reductions potential of 4.8 W/m² (clear days) to 1.6 W/m² (under cloudy days) [34]. The observations and the simulations showed that the air quality became worse after the wind strength weakened and its direction disturbed due to strong UHI; these are conditions that led a convergence zone persisting over an urbanized area caused very high concentrations of pollutants, thereby affecting hospital respiratory admissions counts [35,36] and higher risk of human morbidity [37,38] due to heat stroke. Documented examples of the relations between discomfort index based on poor air quality and UHIs were reported for several locations. In Dali district of Taiwan, it was found that high UHI worsens the air quality, thus significantly increasing hospital admissions [36]. In other studies, it was determined that compact cities amplify the overall human discomfort by amplified UHI placing the population at higher risk [39]. For the costal tropical city of San Juan, Puerto Rico, it was recently reported that at an increase in UHI by 1 °C increases the Human discomfort index by 5% [40]. In the context of the coastal tropical cities such as those in the Caribbean, relevant science questions are how do the regional warming climate and the local urbanization effects interact?; how do these interactions change with different building roofing technologies as mitigation options? and what may be the impacts of these two variables in social value variables such as energy and human comfort? The first question has been addressed by other researchers such as Comarazamy et al. [41] and Velazquez-Lozada et al. [42], reporting that urbanization has a larger effect in the maximum surface temperatures while a changing regional climate in the hydrological cycles. This study will focus on the second and third question and study the comprehensive effect on 2 m air temperature, UHI, energy demands, and PV power potential as mitigation option for urban settings of tropical coastal environments, an important consideration to capitalize on environmental and energy sustainability stemming from roof areas.

As a case study, this study considers the San Juan Metropolitan Area (SJMA) of the Island of Puerto Rico, as a representative of tropical coastal urban environments. SJMA has a population of over 1.25 million containing nearly one-third of the overall population of the Island of Puerto Rico. The total coverage area for the city is 575 km² and electrical energy per capita is 282 kW h/year. The case study of the city of San Juan, Puerto Rico is considered due to the potential of this city to undergo rapid changes as part of the transformation post Hurricane Maria.⁴ According to Puerto Rico Integrated Resource Plan 2018–2019 report, the renewable and alternative sources needs to increase by 20% by 2035 [43].

We thus investigate environmental and energy sustainability of urban coastal tropical city utilizing different roofing technologies. The changes in roof surface temperature for normal roof, horizontal PV roof, tilted PV roof, and cool roof are utilized to investigate 2-m air and roof temperatures along with energy demands. The radiation parameters are further utilized to study the potential of PV power output.

The structure of this contribution is as follows. Section 2 presents the methods used describing the proposed energy balance for normal flat roof, horizontal PV on the roof, and tilted rooftop PV. Section 3 elaborates the results and highlights different cooling load reduction potential for different roof applications, along with PV power potential. Section 4 summarizes the main conclusions and future works.

Energy balance is carried out for normal roof (Eq. (1)), horizontal PV roof (Eq. (10)), and tilted PV roof (Eq. (12)). These conditions are schematically represented in Figs. 1 and 2. For normal roof, the heat flux from the roof surface is balanced by the incoming solar radiation both shortwave and longwave and heat transfer by convection from the roof surface. The computed sol–air temperature (Eq. (5)) of the normal roof is a function of albedo (α), incoming solar radiation (I), the heat transfer coefficient (h_c and h_r), the ambient temperature (T_a), and the radiant temperature of sky (T_R). The roof surface temperature is computed from sol–air temperature by utilizing Eq. (17).

The surface energy balance of a horizontal PV roof is given by Eq. (10), where E_pv is the power produced by PV panel. The temperature of PV panel is assumed to be the surface temperature of the horizontal PV roof given by Eq. (11). The sol–air temperature in this case is dependent on ambient temperature and solar radiation, which is converted to surface temperature utilizing Eq. (17).

Finally, the surface energy balance of the tilted PV roof assumes that the radiation from the back of the PV panel is absorbed by the roof along with the incoming longwave radiation from the sky which is balanced by the outgoing radiation and convective heat flux from the surface of tilted PV roof. The sol–air temperature in this case is dependent on PV temperature, air temperature, the heat transfer coefficients, and surface albedo. Each of the parameters in the equations is defined in the nomenclature section. The following equations are per unit collector area (m²) and per unit time (s).

T_a, U_a, I are used from the WRF outputs.

To quantify the building energy demands on different roof applications, this study employs an urbanized version of WRF model [20], a numerical weather prediction system developed by the National Center for Atmospheric Research. The two urban schemes used in this work are the building effect parameterizations (BEPs) [47] and the building energy model (BEM) [48] that takes into account the shadowing and radiation trapping effects within urban canyons and computes heat fluxes between the indoor and outdoor sides of each buildings accounting the presence of air conditioning systems, windows equipment, and occupancy inside the building's room. It uses indoor heat fluxes based on an hourly schedule to quantify the combination of these components to the building energy budget. The surface temperature of roof in BEP-BEM was modified to incorporate the proposed changes as depicted by Eq. (5) (twice), (11), and (16) to represent normal roof (average albedo of roof 0.15), cool roof (roof albedo 0.7), horizontal PV roof, and tilted PV roof, respectively. Modification of roof surface temperature on BEM due to different roofing application with the energy balance on PV and roof is presented in Fig. 2. To resolve the interaction between the land surface and the atmosphere, the Noah land surface model [49] is used. The Noah land surface model makes use of land use classes to determine thermal, radiative, and hydrological properties of the land surface.

The modified urbanized WRF model is set up to run at a spatial resolution of 1 km by 1 km over the SJMA, where the highest urban density and variability in land cover and land use is found. Two nested domains of decreasing grid spacing (5 km and 1 km) are embedded in areas of interest with a 25 km resolution parent domain as depicted by Fig. 3(a). The model was configured to use the rapid radiative transfer modal for longwave radiation [50], the Dudhia scheme for shortwave radiation [51], the Mellor–Yamada–Janjic planetary boundary layer scheme [52], the Kain–Fritsch cumulus parameterization [53], and the WSM6 microphysics [54]. The urban morphology and topography for SJMA are represented by World Urban Database Access Portal Tool (WUDAPT), LCZs as shown in Fig. 3(b) previously developed by Pokhrel et al. [13]. Figure 3(b) also locates San Juan International Airport (SJIA) and indicates compact high rise (CHR) (1), compact low rise (CLR) (2), and open low rise (OLR) (3) LCZs in the region. It depicts that for SJMA, there is abundant compact low rises with scattered compact high rises, and sparsely built LCZs are dominant more at higher altitudes (altitude is represented by yellow contours). Building heights of Fig. 3(c) show a more homogeneous region with heights of 3–10 m with scattered buildings with more than 25 m heights. Initial and boundary conditions used include six-hourly re-analysis with 250 km horizontal resolution, National Center for Environmental Prediction (NCEP-FNL) model for a period of Sep. 29 to Oct. 8, 2014, which represents a high temperature event in between, previously studied by Pokhrel et al. [13,40].

The different urban parameters used in the WRF simulations are presented in Table 1.

The offline version of roof temperature (T_s) is presented for different roof applications, namely, NR, horizontal PV roof (HPV), tilted PV roof (TPV), and cool roof (CR) as shown in Fig. 4 with an input from urban WRF variables. The roof temperature is seen to be maximum for NR and HPV reaching as high as 50 °C, whereas for tilted PV roof and cool roof the maximum temperature reduces by 8–13 °C, respectively. The minimum temperature however is the same for normal roof and cool roof, whereas it is higher by 2–3 deg for HPV roof. The maximum roof temperature for NR, HPV roof, and TPV roof is also measured to be 60 °C, 58 °C, and 42 °C for a hot summer day in the city of San Diego, CA [34]. In another study, on the similar day in the city of Chicago, the maximum roof temperature for cool roof was measured to be 40 °C [55], consistent with our results. The results of modified version of BEP_BEM for 2 m air temperature for different roof application including the original version of BEP_BEM (without modification) is compared with the observation from SJIA in Fig. 4(b). To validate the simulated temperature (estimator) with the observation (SJIA), linear regression was applied both for modified BEP_BEM and original BEP_BEM including the residuals. Both models appear to fit the data well and the residuals appear to be randomly distributed around zero indicating that the models describe the data well. Therefore, the graphical evaluation of the fits (of Fig. 4) does not reveal any obvious differences between the two models. However, the fits and residuals fail to capture the slight overestimation of 2 m air temperatures for some days for modified roof surface temperature of BEP_BEM and are attributed to low wind speeds during these days. For the purpose of this study, that is to evaluate the response of PV applications of roof on 2 m air temperature and AC demand difference, this assumption (changes in roof surface temperature due to PV installation) is followed in all configurations in order to create a consistency in the formulations. In previous studies, temperature, humidity, wind speed, wind direction, and potential temperature have been validated for the same input data. In addition to the metrological variables, the air conditioning demand from urban WRF have also been compared with the utility records and validated with Energy Plus™ software [13]. The global horizontal irradiance of WRF for dense urban settings of New York has recently been validated with the observational records for clear, cloudy, and overcast conditions [56]. We use the similar approach to compute total radiation on horizontal and tilted surfaces.

The UHI for San Juan, Puerto Rico is studied to increase at a rate of 0.06 °C per year and estimated to reach as high as 8 °C by 2050 [42]. In order to understand the role of roof applications on UHI, a time series of 2-m air temperature for densely populated and sparsely populated region (as delineated in Fig. 2(b)) is presented in Fig. 5 along with spatial plots of maximum and minimum temperatures as represented in Fig. 6. For densely populated region, the maximum temperature is simulated to be higher than 30 °C for NR and HPV roof but less than 30 °C for sparsely populated region. The minimum temperature for densely populated region is higher by 2 °C compared with the sparsely populated region. Also, the minimum temperature for densely populated region for HPV roof is simulated to be 0.25 deg higher than NR during 8 a.m. LST. In other words, HPV slightly reduces the daytime UHI, whereas it increases the peak night time UHI. NR, HPV, TPV, and CR show maximum 2 m air temperature in the decreasing order, where TPV reduces it by 2 °C and CR reduces it by 4–5 °C at compact low rise LCZs compared with NR. The minimum temperature, however, for NR is 26 °C, whereas the difference of minimum temperature for HPV with NR indicates an increase in UHI by 0.5–0.75 °C. The increase in night time UHI for HPV is due to the absence of radiative cooling from HPV roof as compared with NR. There are, however, no significant changes in night time UHI for TPV and CR.

The average total air conditioning demand for each LCZ on a day for the entire SJMA is shown in Table 2, for different roof applications. The W/m² is per horizontal grids and includes both built and non-built surfaces. However, the sum of AC demand for each LCZs is multiplied by building area fraction in order to compute the total AC demand of Table 2, which has been previously used by Pokhrel et al. [13]. Compact high rise and compact low rise together represents more than 85% of the total air conditioning demand for the region. TPV and CR decreases the total demand by 4% and 12%, respectively; however, HPV roof increases the demand by 3%. The increase in AC demand for HPV roof is attributed to net increase in UHI during night and morning hours. The peak AC demand for normal roof follows the LCZs distribution, height of 20 W/m² at compact high rise, 10–12 W/m² at compact low rise, and 6–8 W/m² at open low rise as presented in Fig. 7. In previous studies [13], the total AC demand for the same time period is compared with the utility data and it was found to be very comparable with this study. We are collaborating with the Puerto Rico Power Authority to share hourly data of electrical energy demand, which will allow us to extract the AC hourly demand using well-known methods for baseline loads [57].

Peak AC demand savings of 0.5–1 W/m² is simulated for the TPV and 1.5–2 W/m² for CR, respectively, for compact low rise LCZ. The peak demand savings potential for tilted PV and CR for some location in the metropolitan area is equivalent to 8% and 16%, respectively. However, the peak demand reduction potential for HPV roof is very insignificant and is not presented in Fig. 7.

Radiation components are the important parameters in estimating the PV power potential. The output from urban WRF for shortwave direct normal (SWDDNI), shortwave direct diffuse (SWDDIF), downward shortwave (SWDOWN), and total radiation (as estimated utilizing Eqs. (17) and (18) on tilted surface of 20 deg (Total I) is presented in Fig. 8. For the entire simulation period, large cloud cover is simulated during late morning and midafternoon hours. However, for tilted surface, early morning and late afternoon hours are simulated to have more incoming radiation than the horizontal surface.

Daily solar total radiation on a titled surface of 20 deg is 8.7% more than the daily solar radiation on a horizontal surface for SJMA for a day on the month of October as shown in Fig. 9. The values of daily solar total radiation are comparable with those estimated by open source tools such as PV Watts,⁵ which estimates average daily solar radiation for SJMA for the month of October for horizontal and 20 deg tilted surface to be equal to 5.25–5.88 kW h/day, respectively. However, the modeled results are 5.75 and 6.25 kW h/day with an overestimation of 0.5 and 0.37 kW h/day for both horizontal and tilted surfaces, respectively.

Hourly average AC demand and PV power production for large office represented as CHR, multifamily low rise apartment represented as CLR, and single family detached unit represented as OLR for both HPV and TPV is shown in Fig. 10. The floor areas for large office (CHR), multifamily low rise apartment (CLR), and single family detached (OLR) unit are 41,549 ft² (3860 m²), 10,404 ft² (967 m²), and 3602 ft² (335 m²) taken from US DOE reference buildings.⁶ For large office (Fig. 10(a)), hourly demand peaks at 463 kW with daily AC demand reaches 6790 kW h/day whereas productions are 2670 and 3032 kW h/day for horizontal and tilted PV, respectively. For multifamily (Fig. 10(b)), the hourly demand peaks at 31 kW with the daily demand as 467 kW h/day, whereas production is 667 and 744 kW h for HPV and TPV, respectively. Demand and production for single family detached unit (Fig. 10(c)) are 190, 250, and 260 kW h, respectively, with a peak demand of 13 kW.

Figure 11 presents weekly AC demand for normal roof, HPV roof, and TPV roof and available roof area for each LCZs in the region of interest consisting entire SJMA. It is simulated that for high rise and midrise, the demand is close to power production given the small total roof area. However, for CLR and OLR, the AC demand is 20–22% of the power production potential, indicating that 22% of the suitable roof area is enough to meet the total AC demands for the CLR and OLR LCZs.

Our goal in this study is to investigate environmental and energy sustainability of an urban coastal tropical city utilizing different building integrated roofing technologies. Tropical coastal cities are experiencing rapid energy growth due to economic development and a rapid changing climate. This study utilizes the changes in roof surface for normal roof, horizontal PV roof, tilted PV roof, and cool roof to investigate 2-m air and roof temperatures along with AC energy demands. The radiation parameters are further utilized to study the PV power potential. A new methodology is presented that represents the integration of solar PV technologies in buildings and scale up to the whole city. The WUDAPT LCZs for the SJMA is represented mostly by compact low rises, sparsely built and open low rises with scattered areas of compact high rises. The case study of the city of San Juan, Puerto Rico is considered due to the potential of this city to undergo rapid changes as part of the energy transformation post Hurricane Maria. The peak roof temperature is seen to be maximum for NR and HPV reaching higher than 54 °C, whereas for tilted PV roof and cool roof the maximum temperature reduces to 46 and 41 °C, respectively. As a result, the reduction in peak AC demand is simulated to be 8% for tilted PV roof and 16% for cool roof for some locations in SJMA. Horizontal PV does not show significant changes in peak AC demand compared with normal roof; however, the daily demand for HPV is seen to increase by 3% and decrease by 4% and 10% for TPV and CR, respectively. For the month of October 2014, the daily total radiation on a tilted surface is 5.5–6.5 kWh/m² for SJMA, which is 6–10% higher than daily total radiation on a horizontal surface. Finally, the ratio of AC demand to PV power production for compact high rise and compact midrise LCZs is close to 1; however, for compact low rise and open low rise, it is 0.2. The proposed methodology of PV power potential and cooling load mitigation alternatives may have similar results in other tropical coastal cities, although the magnitude would be different depending on the size, form, and function of the urban coverage. Future studies will be focused on utilizing both active and passive building integrated technologies for mitigating heat during extreme conditions for different climate change scenarios.

I =

total solar radiation

a_r =

abrobtivity of roof

h_c =

convective heat transfer coefficient

h_r =

radiative heat transfer coefficient

E_pv =

PV power production

I_b =

beam or direct radiation

I_d =

diffuse radiation

T_a =

ambient temperature

T_room =

room temperature

T_ref =

reference temperature

T_s =

surface temperature

T_PV =

temperature of PV panel

T_R =

radiant temperature of horizontal surface

T_R1 =

radiant temperature of tilted surface

U_a =

wind speed

U_pv =

PV loss coefficient

U_r =

heat loss coefficient of roof

T_s′ =

sol–air temperature

β =

tilt

δ =

declination

Δx =

roof thickness

ɛ_s =

emissivity of surface

ɛ_sky =

emissivity of sky

ɛ_R =

reference module efficiency

μ =

temperature coefficient

σ =

Stefan Boltzmann constant

τα_PV =

transmitivity of glass and absorptivity of PV panel

ϕ =

latitude

ω =

hour angle

LCZs =

local climate zones

The authors would like to acknowledge the assistance and suggestions from the members of the Coastal Urban Environmental Research Group from City College New York and of the University of Puerto Rico Mayaguez. The analysis process was conducted at the high performance computing facilities at City College of New York (http://cuerg.ccny.cuny.edu/) and College of Staten Island CUNY, high performance computing center (https://cunyhpc.csi.cuny.edu/). Financial support for this research was provided by the US National Science Foundation (Grant No. CBET-1438324; Funder ID: 10.13039/100000001) and the US Agency for International Development (Grant No. AID-517-A-15-00002; Funder ID: 10.13039/100000200).