Investigation of the Interaction of Water and Energy in Multipurpose Bio-Solar Green Roofs in Mediterranean Climatic Conditions

Abstract

The advantages of green roofs and solar panels are numerous, but in dry periods, green roofs can place urban water resources under pressure, and the efficiency of solar panels can be affected negatively by high temperatures. In this context, our analysis investigated the advantages of bio-solar green roofs and evaluated the impact of green roofs on solar panel electricity production and solar panels on green roof water consumption. The assessment was conducted through simulation in a selected case study located in Cosenza, a city with a Mediterranean climate, with solar panels covering 10% to 60% of the green roof. Analyses were performed on the power outputs of four kinds of photovoltaic panels: polycrystalline, monocrystalline, bifacial, and Passivated Emitter and Rear Contact (PERC). The energy production and shade frequencies were simulated using PVGIS 5.3 and PVSOL 2024 R3. The impact of photovoltaic (PV) shade on the water consumption of green roofs was evaluated by image processing of a developed code in MATLAB R2024b. Moreover, water–energy interconnections in bio-solar green roof systems were assessed using the developed dynamic model in Vensim PLE 10.2.1. The results revealed that the water consumption by the green roof was reduced by 30.8% with a bio-solar coverage area of 60%. However, the electricity production by the PV panel was enhanced by about 4% with bio-solar green roofs and was at its maximum at a coverage rate of 50%. This investigation demonstrates the benefits of bio-solar green roofs, which can generate more electricity and require less irrigation.

1. Introduction

Numerous researchers have highlighted the benefits of green roofs (GRs) in various climates, including Mediterranean climates. The benefits are greater during the hot season than during the cold season [1,2,3], and they can be impacted by various components, including the plant type and irrigation technique [4]. In addition, the dry season can have a detrimental effect on available urban water resources for the green roofs [5]; aside from the direct relationship between the water content and thermal impact, plant life during specific months depends on irrigation [6]. The water demands of green roofs can be evaluated by evapotranspiration (ET). ET is the loss of water from both the soil surface and plant leaves by evaporation and plant transpiration due to sunlight, temperature, wind, and humidity [7]. Climate, vegetation, and precipitation (both amount and distribution) affect how much water is needed to irrigate green roofs [4,8]. A green roof usually includes a root barrier, drainage layer, vegetation layer, growth substrate layer, and waterproof membrane [9].

One type of green roof is a bio-solar green roof (BS-GR), a combination of green roofs and solar panels [10]. It has been suggested that bio-solar roofs produce more energy than traditional solar panels and may decrease the water footprint of energy [11]. This is so that the vegetation on these roofs can improve the effectiveness of the solar panels by lowering their temperature through evapotranspiration, which creates a cooler microclimate. Additionally, by displaying higher solar reflectivity and releasing more latent heat than conventional concrete roofs, bio-solar roofs contribute to the regulation of rooftop temperatures [12]. Water shortages are becoming a serious worldwide problem, which could worsen over time due to climate change and population increase [13]. Green roof efficiency and performance can be increased by integrating solar PV systems with green roofs. The overall effectiveness of a green roof can be improved by solar panels’ shading and cooling effects [14]. A viable synergistic relationship between PV panels and green roofs maximizes the roof area for stormwater management and energy production. PV panels can lower solar radiation and wind flow on green roofs, which lowers evapotranspiration rates and water usage. Furthermore, the panels’ shading function contributes to a reduction in the outside temperature [15].

1.1. Water Consumption in Conventional and Bio-Solar Green Roofs

Different researchers have evaluated water consumption by green roofs in different climates. Pirouz et al. evaluated the water consumption by green roofs in different climates [16,17], and to decrease the water consumption, they proposed sub-atmospheric water harvesting and subsurface irrigation [17]. The differences in water consumed in shaded areas and the reduction in evapotranspiration (ET) by PV shade in different climatic conditions are tabulated in

Table 1. ET reduction in shaded areas for different climatic conditions.

Case Study	Shade Analysis Condition	ET Reduction in Shade	Climate	Ref.
Montpellier (France)	Agrivoltaic	33% the ET0 level	Mediterranean climate	[20]
		14–29% decrease in actual evapotranspiration (AET)		[21]
Oregon (US)		Water efficiency increased by 328%	Warm summer Mediterranean climate	[22]
Toronto (Canada)	Bio-solar	81% in summer and 38% in fall	Continental	[23]
Fuyang (China)	Concentrated-lighting Agrivoltaic System (CAS)	Reduced water evaporation in soil surface: 21%	Temperate semi-humid	[24]
	Even-lighting Agrivoltaic System (EAS)	Reduced water evaporation in soil surface: 33%
California (US)	Shading greenhouses	25%	Mediterranean, Arid, Semi-arid	[25]
Berlin (Germany)	Tree (Tilia cordata)	50%	Humid continental	[26]

. The analysis showed that the ET reduction in shaded areas in Toronto (Canada) was up to 81% in summer. Meanwhile, the table shows that in the Mediterranean climatic conditions, the maximum and minimum ET reduction due to shade were 33% and 14%, respectively. Likewise, the analysis of Schweitzer and Erell [18] in a Mediterranean climate showed water demands by green roofs of between 2.6 and 9.0 L/m²/day. In another investigation, the values for the same climates were calculated by Brunetti et al. [19] to be roughly 7.0 L/m²/day. Alternatively, places with shade will use less water.

1.2. Efficiency of Solar Panels in Conventional and Bio-Solar Systems

Henri Becquerel discovered the photovoltaic (PV) phenomenon in 1839, which converts solar energy into electricity. PV systems are the best option for producing electricity since they are long-lasting, silent, and effectively convert sunlight into electrical energy. The PV panels are made up of various systems and parts, each of which is essential and has unique characteristics [27]. The effectiveness of solar panels fluctuates with temperature and declines when the temperature goes above 25 °C, depending on the temperature coefficient. Heat causes the resistance in solar panel cells to rise, affecting the flow of electrons within the cell and reducing solar panel efficiency [28,29]. There are several active and passive cooling techniques to maintain the efficiency of solar panels, ranging from passive to active methods, as presented in

Table 2. Classification of PV cooling techniques.

Cooling Technique	Method	PV Temperature Reduction [°C]	Efficiency Enhancement [%]	Study Type	Refs.
Active air cooling	An inlet/outlet manifold is attached to a parallel array of ducts on the panel’s rear	30.0	4.0	Experimental	[30]
	Geothermal air cooling	9.8	23.0		[31]
	Cooling with a channel under the PV	5.0	2.6		[32]
	Forced air cooling	15.0	5.7		[33]
Active water cooling	Back-surface water cooling	11.0	9.0		[34]
	Water flowing on the anterior surface of the panel	30.0	12.0	Theoretical and experimental	[35]
	Converging channel heat exchanger	19.0	36.0		[36]
	Heat exchanger cooling	29.1	22.8	Experimental	[37]
	The pipe for water cooling is linked to the PV’s back surface	12.0	2.4		[38]
	Pulsed-spray water cooling	26.9	28.9		[39]
	Back-surface spray cooling	28.2	7.8		[40]
Active cooling by nanofluids	Heat exchanger on the rear of the panel (Zn-H2O nanofluid)	18.0	7.8		[41]
Active thermoelectric cooling	Heat sink with thermoelectric module	35.0	18.0	Theoretical	[42]
	Heat sink with thermoelectric module	10.0	10.5	Experimental	[43]
Passive water cooling	Solar-driven rainwater cooling system	19.0	8.3	Theoretical	[44]
	Underwater cooling	34.0	11.8	Experimental	[45]
	Heat spreaders and cotton wicks together	6.1	14.0		[46]
	Atmospheric water sorption–desorption cycle	10.0	16.0		[47]
	Solar-driven PV cooling	47.0	8.0	Theoretical and experimental	[48]
	Evaporative cooling (Burlap cloth and water)	20.0	14.8	Experimental	[49]
Passive air cooling	Heat sink (Al and Cu fins) and wick structure on the rear of the panel	5.2	3.1		[50]
	Heat sink	10.0	6.3	Theoretical	[51]
	Natural cooling with a channel under the PV	10.0	4.0	Theoretical and experimental	[52]
	Fin-attached heat sink	9.5	1.1	Experimental	[53]
	Air duct (fins, flat and curved) placed on the rear of the panel	18.1	18.9	Theoretical	[54]
Passive phase-change material	PCM (RT35HC paraffin wax)	24.9	11.0		[55]
	PCM (paraffin wax)	4.2	1.5	Experimental	[56]
	PCM-integrated natural cooling	5.4	12.4	Experimental	[57]
Passive radiative cooling	Radiative cooling	17.2	1.6	Experimental	[58]
	Night radiative cooling	5.0	6.2	Theoretical	[59]
Hybrid cooling	Thermoelectric cooling with PCM (RT25) integrated	27.7	3.0	Theoretical	[60]
	Radiative cooling with nano- and microstructuring	5.1	3.0	Theoretical	[61]

.

Different cooling methods when compared exhibit the following:

• Active cooling techniques, including active air, water, nanofluids, and thermoelectric cooling, can enhance efficiency by around 3.0–36.0%;
• Passive cooling techniques such as passive air, water, phase-change material, radiative, and hybrid cooling can enhance efficiency by 1.6–19.0%.

Several types of photovoltaic (PV) panels are available.

Table 3. Efficiency and specifications of different solar panels.

Type of PV		Efficiency (%)	Temperature Coefficient of Pmax (%)	Refs.
Monocrystalline		15.0–24.7	−0.3 to −0.4	[62,63,64,65]
Polycrystalline		13.0–20.4	−0.3 to −1.0
PERC	Mono PERC	17.0–25.0	−0.4	[65,66,67,68,69]
	Poly PERC	16.0–17.0	−0.4
Thin-film panels	CIGS	13.0–19.2	−0.4	[17,67,70,71,72,73]
	GaAs	20.0–25.1	−0.1
	CdTe	9.0–19.5	−0.2
	Amorphous silicon (a-Si)	6.0–12.3	−0.1 to −0.2
Bifacial	Mono or poly	18.9–23.0	−0.3 to −0.4	[74,75,76]

tabulates the efficiencies and specifications of different solar panels. From the table, it can be seen that the efficiencies of monocrystalline solar panels range between 15.0 and 24.7%, polycrystalline solar panels range between 13.0 and 20.4%, Mono PERC (Passivated Emitter and Rear Contact) solar panels range between 17.0 and 25.0%, and bifacial solar panels range between 18.9 and 23.0%. Based on the minimum and maximum efficiencies of solar panels, the annual electricity production of each panel varied.

Additionally, previous studies show that the power generation by PV modules decreases each year due to the degradation of PV modules, from 0.5 [77,78] to about 5.0% [79,80]. The main factors causing the degradation of PV modules include hail, humidity, wind and snow, high temperature, and ultraviolet radiation (UV) [79]. The effectiveness of solar panels declines when the temperature goes above 25 °C. In addition to conventional cooling techniques, recent research showed that green roofs could reduce the ambient temperature depending on the climatic conditions and vegetation types. As a result, it could enhance the efficiency of the solar panels [81]. The details of some case studies about bio-solar systems are tabulated in

Table 4. Case studies of PV-GR and increase in PV efficiency.

Case Study	Type of Analysis	Increase in PV Efficiency	Type of System	Climate	Ref.
Kansas (US)	Experiment	1.4% annually, 2.4% in summer	PV-GR	Humid subtropical	[82]
Berlin (Germany)		6.0%		Moderate continental	[83]
Hong Kong (China)	Experiment (in summer)	4.3%		Subtropical	[14]
	Simulation	8.3%
Toronto (Canada)	-	2.0%		Continental	[84]
New York (US)	Experiment	2.4%		Humid subtropical	[85]
Singapore	Experiment and simulation	2%		Tropical	[86]
Pittsburgh (Russia)	Experiment	0.8–1.5%		Humid continental	[87]
Malaysia		1.6%		Tropical climate	[88]
Sydney (Australia)		4.5%		Humid subtropical	[10]
Bucaramanga (Colombia)		1–1.3%		Warm tropical	[89]
Nagpur (India)	Model	18.0%	Agrophotovoltaics	Tropical wet and dry	[90]
Portland (US)	Experiment (summer)	0.7–1.2%	Dianthus PV-GR	Mediterranean climate	[9]
Lleida (Spain)	Experiment (a sunny, five-day time period)	3.3%	Sedum PV-GR	Subtropical (Mediterranean)	[91]
		1.3%	Gazania PV-GR

. The table illustrates how PV efficiency might be boosted through the impact of green roofs, by about 1.0% to 8.3% (or 0.7 to 3.3% in the Mediterranean). The efficiency values might increase when other passive cooling techniques are combined with the bio-solar system.

PV systems are regarded as a mature technology and have been widely implemented across various sectors, including the building industry. Still, there is room for improvement, especially when combining PV systems with other “green” technologies like green roofs. Green roofs and PV panels are a growing trend with many advantages. Green roofs act as insulators for buildings, which leads to energy savings. Beyond only being energy-efficient, green roofs have many other benefits. They enhance the air quality, control temperature, preserve energy, safeguard building envelopes, prolong the life of roofing membranes, and offer advantages for the environment and the economy. The PV–green roof combination also makes urban food production possible, which maximizes the available area and lowers CO₂ emissions related to moving food from suppliers to homes. Therefore, integrating PV systems with green roofs is an interesting choice for building roofing solutions. This article investigates possible synergies between plants and PVs, and combines the benefits of a soil/plant layer for building with in situ energy generation from PV panels. Very few research studies have been published on PV–green roofs in the literature, despite their apparent benefits, such as higher PV output via the impact of plants. The main focus of this article is to investigate the advantages of multipurpose bio-solar green roofs and to evaluate the impact of green roofs on different types of solar panel electricity production and solar panels on green roof water consumption. In addition, the assessment of the water usage of bio-solar green roofs in the Mediterranean city of Cosenza, with PV panels covering between 10% and 60% of the roof, is contributed for the investigation. Therefore, the annual power outputs of four distinct types of solar panels, including polycrystalline, monocrystalline, PERC, and bifacial, are analyzed in conventional roof and bio-solar systems. Furthermore, using PVSOL 2024 R3, PVGIS 5.3, and MATLAB R2024b image processing, the shade frequencies of the solar panels on the green roof area are identified, and a dynamic model developed in Vensim PLE 10.2.1 evaluates the corresponding water reductions in the bio-solar green roofs. In this way, the results are generalized and can be expanded to other types or sizes of green roofs, as well as various types of solar panels with various percentages of coverage area on green roofs.

2. Materials and Methods

This investigation focuses on establishing the interconnection between the water requirement and the performance of PV panels on green roofs. To these ends, initially, we identify the water consumption of conventional green roofs and determine the reduction in water requirement in the shade. This is based on an extensive database of the water consumption of green roofs in sunlight and shadow according to literature reviews, integration of shadow frequency simulation in PVSOL 2024 R3 [92], image processing in MATLAB R2024b [93], and dynamic simulation in Vensim PLE 10.2.1 [94]. For this purpose, the different configurations of bio-solar green roofs were defined, 48 simulations were carried out, and a code for image processing in MATLAB R2024b was developed. Following this, a database for the efficiency of different PV solar panels and the enhancement due to the decrease in the temperature on the panels installed on green roofs was compiled. In the next step, the database was used to develop a dynamic decision support system in Vensim PLE 10.2.1. Accordingly, using the dynamic model, the influence of PV panels on the green roof water requirements (due to shaded areas by PV panels) and the effect of green roofs on the PV panel annual production (due to temperature modification) was evaluated. The analysis of the shadow frequency of PV panels on the roof is a geographic parameter that depends on the location, weather conditions, and installation inclination of PV panels. Consequently, as applied in this study, a long-term simulation (as in this research, the MeteoNorm 8.2 database of 2001 to 2020) can be the most effective analytical technique, and additional experiment validation will not affect the results. A schematic of the methodology is shown in Figure 1, and a schematic of the PV–green roof concept is shown in Figure 2.

The methodological steps are as follows:

• Step 1 (case study parameters’ definition): Determine bio-solar green roof configurations, such as the coverage of the solar panels on the roof area, which in the current study, included 10%, 20%, 30%, 40%, 50%, and 60%. In addition, select the types of PV panels, which in our study, were the following four: polycrystalline, monocrystalline, PERC, and bifacial. Finally, select the roof type, as the reflection of solar radiation from roofs (albedo) toward solar panels depends on it; in the current study, we considered two types of roofs, and the corresponding albedos were 20% for conventional roofs and 60% for green roofs;
• Step 2 (PV power computation): Perform power output calculation for the selected (in step 1) types and percentages of solar panels on the conventional and green roofs in PVSOL 2024 R3/PVGIS 5.3 software. For this purpose, PVGIS can be applied to have the optimum inclination (tilt) of the PV panels in the case study location, which in this study, for the city of Cosenza, is equal to 33°. Moreover, since the radiation depends not only on the location of the case study but also on weather conditions (i.e., cloudy and rainy conditions), and to have an accurate calculation, MeteoNorm 8.2 software can be applied to provide the hourly climate data. In the last stage, PVSOL 2024 R3 software can be used (with the optimum inclination by PVGIS 5.3 and climate data by MeteoNorm 8.2) for separate calculation of the power output for four types of PV panels, six types of percentages, and two types of albedos, meaning 48 simulations. At the end of this stage, the power production by PV modules for all conditions can be determined;
• Step 3 (shade frequency pattern of PV panels on the roof surface): Analyze the shadow frequency of PV panels on the roof, which is a geographic parameter and depends on the location (Cosenza in our case study), weather conditions (calculated in step 2 using MeteoNorm 8.2), the installation inclination of PV panels (determined in step 2 using PVGIS 5.3; in our case study, equal to 33°), and configuration of PV modules on the roof surface (10% to 60% in our study), which can be simulated by PVSOL 2024 R3. For this purpose, PVSOL 2024 R3 estimates the shape of the PV module shadow on the roof for all solar hours in a year and provides shade frequency images. The produced images can show the shade condition in four colors: white (meaning area with % shade), green (meaning near zero % shade), yellow (meaning 33% of the time is shade), and red (meaning 100% of the time is shade);
• Step 4 (percentages of shade by PV on the roof): Determine the amount (percentage) of zero shade area or full shade area, for which image processing of the provided images by PVSOL 2024 R3 is required. For this purpose, we developed a code in MATLAB R2024b (Appendix A), which can determine the percentages of four colors (white, green, yellow, and red) in an image by applying different color masks. In that regard, in this stage, the images of step 3 are analyzed using image processing, and the results provide the numerical quantity of the full shadow, 33%, as well as those for the near 0% shadow and 0% shadow due to the PV modules on a roof;
• Step 5: Prepare the database for the Vensim PLE 10.2.1 model:

  (a)

  Providing the PV power production amounts for different configurations: for four types, six patterns, and two types of roofs, as calculated in step 2 by PVSOL 2024 R3;

  (b)

  Providing the increase in the efficiency with a decrease in surface temperature due to the installation of PVs on green roofs based on data presented in Table 2;

  (c)

  Providing the maximum and minimum efficiency of each type of solar panel based on the data in Table 3. In this way, the PV power production will not be limited to the selected modules in PVSOL 2024 R3 (in our cases, four types of panels with specific efficiency);

  (d)

  Arranging the data about water consumption of conventional green roofs in different climates, which are available in Table 4, and in cases where data are not available, applying Equation (3);

  (e)

  Providing the data about the water consumption decline of green roofs due to shadow, which are available in Table 1;

  (f)

  Providing the amount (percentage) of shade on the roof in each pattern of PV modules, according to the results of step 4.

• Step 6 (generalizing the results by developing a dynamic model): In this stage, the databanks in step 5 can be used to provide a dynamic analysis model in Vensim PLE 10.2.1 software. The input of the Vensim PLE 10.2.1 can be single data, tables, or graphs. For example, it can be the minimum or maximum efficiency of polycrystalline modules or green roofs’ water consumption in different climates. Therefore, in this stage and for our case study, according to the results of PV production (by 48 simulations in PVSOL 2024 R3), the data can be added based on the type of module, type of roof, percentage of the PV on the roof, etc. The same can be performed for water consumption by green roofs in the Mediterranean climate, for the decline in water demand (ET reduction for each color of shadow provided by PVSOL 2024 R3, and amounts based on percentages of the roof area in MATLAB R2024b) with a full shadow and 33% shadow;
• Step 7: Analyze water and energy interactions in bio-solar green roofs with the developed dynamic model in Vensim PLE 10.2.1. In this step, instead of calculating each state separately (new simulations based on the type of PV, percentage of PV, size of roof, type of roof, etc.), different scenarios can be easily evaluated with a single run in Vensim PLE 10.2.1 software. For this purpose, just the boundary conditions (roof area, PV type, PV efficiency, and percentage of PV to the roof area) need to be selected, and the model can provide the impact of a conventional roof or green roof on the power production of a type of PV module with specific efficiency dynamically. The same goes for water demands and by choosing the roof area—the percentage of PV panels on the roof to the roof area—the shadow impact will be considered, and the model will provide the water consumption levels of conventional (0% PV module) and bio-solar green roofs.

2.1. Bio-Solar Green Roof Configurations and Analysis Procedures

To understand the influence of solar panels on the green roof and vice versa, a bio-solar green roof with the size of 100 m² (10 m × 10 m) and various cover percentages of PV panels are defined. Figure 3 illustrates the various configurations of PV panels on green roofs with different coverage degrees of roof area. The coverage of the solar panels on the roof area varied from 10% to 60%. For a 10% coverage of the roof area, it uses 8 panels in two rows, whereas for 60%, it uses about 48 panels in six rows. The analysis for PV panels, such as shade frequency, irradiation, and electricity production with polycrystalline, monocrystalline, PERC (Mono), and bifacial solar panels, is carried out in a selected Mediterranean climate location, Cosenza (South Italy). The annual sum of global irradiation in Cosenza is 1635.0 kWh/m², and the annual average temperature is about 17.7 °C. The annual electricity production by different types and patterns of solar panels and the efficiency increase due to green roofs will be determined using PVGIS 5.3 and PVSOL 2024 R3, considering the local location, radiation, and long-term weather data.

Table 5. Simulation details in PVGIS 5.3 and PVSOL 2024 R3.

Item	Description
Solar panel coverage percentage	Six patterns: 10, 20, 30, 40, 50, and 60%
Weather data	MeteoNorm 8.2 (2001–2020)
Albedo	20% conventional roof [96], 60% green roof [97]
Model for irradiation on the inclined plane	Hay and Davies (software method)
Types of PV panels	Polycrystalline, monocrystalline, PERC, and bifacial
Inclination (Tilt)	33°
Polycrystalline module specification	Width: 1 m × 1.6 m, Efficiency: 14.7%, Nominal power: 240.0 W, MPP voltage: 29.9 V, MPP current: 8.0 A
Monocrystalline module specification	Width: 1 m × 1.6 m, Efficiency: 15.6%, Nominal power: 255.0 W, MPP voltage: 30.9 V, MPP current: 8.3 A
PERC module specification	Width: 1 m × 1.6 m, Efficiency: 20.3%, Nominal power: 335.0 W, MPP voltage: 35.66 V, MPP current: 9.4 A
Bifacial module specification	Width: 1 m × 1.6 m, Efficiency: 18.9%, Nominal power: 310.0 W, MPP voltage: 31.1 V, MPP current: 10.0 A
Dimensions of solar panels	Length: 1.5 m, Width: 1 m, Installation height: 0.4 m

presents the simulation details in PVGIS 5.3 [95] and PVSOL 2024 R3 [92]. Moreover, the reduction in the water requirement of green roofs due to the shade created by solar PV will be calculated using the developed image-processing code in MATLAB R2024b (Appendix A).

The power output of a PV module in PVSOL 2024 R3 is calculated based on irradiation, temperature, and module electrical characteristics, as follows [98]:

• The determination of irradiance on the module surface is based on the tilt and orientation of the PV array, diffuse and direct radiation from weather data, shading effects from obstacles from 3D analysis, and reflection losses due to the module surface.
• Calculating the temperature effect on the PV module efficiency in PVSOL 2024 R3 is based on Equation (1).

$${\mathsf{\eta }}_{\mathrm{PV},\mathrm{MPP}}={\mathsf{\eta }}_{\mathrm{PV},\mathrm{MPP}}\left(\mathrm{G},{\mathrm{T}}_{\mathrm{Module}}=25°\mathrm{C}\right).\left[1+\Delta \mathrm{T}.{\displaystyle \frac{\mathrm{d}\mathsf{\eta }}{\mathrm{dT}}}\right]$$

(1)

where η_PV,MPP (G, T_Module = 25 °C): module efficiency under standard conditions, ∆T: temperature difference from 25 °C, and dη/dT: temperature coefficient of efficiency.

• Calculate the power output at the maximum power point (MPP) operating condition, which is the highest possible power output of PV panels under given conditions. The MPP power output is calculated based on the solar irradiance and module’s efficiency using Equation (2).

$${\mathrm{P}}_{\mathrm{MPP}}={\mathsf{\eta }}_{\mathrm{PV},\mathrm{MPP}}.\mathrm{G}.\mathrm{A}$$

(2)

where η_PV,MPP: efficiency of PV module at MPP, G: solar irradiance on the module (W/m²), and A: solar module area.

• Deduct the losses from the efficiency of the modules due to the deviation from the standard spectrum AM_1.5 (standard test conditions: 1000 W/m² vertical radiation, 25 °C module temperature, and radiation spectrum), mismatch or reduced yield as a result of deviation from manufacturer information, and losses in diodes. The mentioned losses are deducted percentages from the module output in PVSOL 2024 R3.

For the calculation of the shade frequency of the solar panels on the mounting surface (green roof in our case) and on the surfaces of other panels, PVSOL 2024 R3 considers the solar path and the solar position (azimuth and altitude) for the entire year and at different times of the day. Then, the software casts shadows of solar panels for each time step to determine which parts of the roof or the surfaces of the other panels are shaded. The annual shade frequency is calculated based on the annual average of the shade time to the total time of one year for different roof areas and other panels’ surfaces.

The value of potential ET (PET) can be calculated according to the Thornthwaite equation [99,100] as follows:

$$\mathrm{PET}={\mathrm{PET}}^{*}\left({\displaystyle \frac{\mathrm{N}}{12}}\right)\left({\displaystyle \frac{{\mathrm{d}}_{\mathrm{m}}}{30}}\right)$$

(3)

$${\mathrm{PET}}^{*}=16\times {\left({\displaystyle \frac{10\mathrm{T}}{\mathrm{I}}}\right)}^{\mathrm{a}}$$

(4)

$$\mathrm{I}={\displaystyle \sum }_{\mathrm{j}=1}^{12}{\left({\displaystyle \frac{\mathrm{T}}{5}}\right)}^{1.514}$$

(5)

$$\mathrm{a}=675\times {10}^{-9}{\mathrm{I}}^3-771\times {10}^{-7}{\mathrm{I}}^2+1792\times {10}^{-5}\mathrm{I}+0.49239$$

(6)

where PET: potential evapotranspiration values (mm/month), PET*: normative potential evapotranspiration, T: mean monthly temperatures (°C), I: annual heat index, a: constant.

However, our previous studies [101] showed that the temperature-based formula of the Hargreaves equation, 1985 [102] for PET, and monthly correction factors, k [103], can effectively estimate the actual ET (AET) of green roofs in the Mediterranean climate, as provided in Equations (7) to (9).

PET = 0.0135 (T + 17.78) R_s

(7)

$$\mathrm{AET}=\mathrm{PET}\times \mathrm{k}$$

(8)

$$\mathrm{k}={\displaystyle \frac{\mathsf{\beta }+\frac{1}{2}{\sum }_1^{\mathrm{x}}\mathrm{n}\left(1+\mathsf{\alpha }\right)}{\mathrm{D}}}$$

(9)

where PET = potential daily evapotranspiration (mm/day); T = mean temperature (°C); R_s = incident solar radiation converted to depth of water (mm/day), x = number of continuous dry periods in the month; α = actual ET rate at the end of the dry period, which is a proportion of PET; β = wet days in the month; n = duration of the dry period; D = total days in the month.

2.2. Study Limitations and Potential Weaknesses

The current study was conducted based on long-term simulations, image processing, and systematic literature review analyses. While the additional experimental validation did not affect the correlated analysis of the shadow frequency of PV panels on the roof and on other panel surfaces as geographic parameters, it still confronted some limits:

• The impact of the green roof type and irrigation technique is not taken into account;
• This study does not consider the type of plant and age of the green roof;
• The hodological performance of BS-GRs is not investigated in this study.

3. Results and Discussion

3.1. Shade Frequency of PV Panels on Panel Surfaces and the Impact on Annual Electricity Production

The PV panels’ shade frequencies on other panel surfaces were identified through 48 simulations in PVSOL 2024 R3 software. Figure 4 depicts the annual shade frequency of PV panels on other panel surfaces. The figure indicates that the shade frequency for the 10% coverage area is about 0%. Meanwhile, the shade frequency on other panels increases with the coverage area. The maximum shade frequency is observed in the 60% coverage area, at about 12.1%.

The annual electricity production by four types of solar panels with specified efficiency levels and various configurations (type and percentage of PVs) on the conventional and bio-solar green roofs in the selected Mediterranean climate location (Cosenza, South Italy) is calculated using PVSOL 2024 R3 software. The variations in the annual production of electricity with polycrystalline (14.8% efficiency), monocrystalline (15.7% efficiency), PERC (Mono, 20.3% efficiency), and bifacial (18.9% efficiency) solar panels for different configurations are shown in Figure 5 and Figure 6. The annual electricity production is enhanced with the coverage area until a certain percentage, 50%, and then decreases due to the dominant impact of solar panels’ shadow on each other. The highest electricity production from the PV panel is observed in PERC (Mono) and bifacial solar panels with a 50% coverage area configuration. For the 10% coverage area, the annual electricity production levels are 2896.4, 3139.2, 4175.1, and 4105.7 kWh/Year by polycrystalline, monocrystalline, PERC (Mono), and bifacial PV panels, respectively. Meanwhile, the generation of power is enhanced to 11,234.0, 12,210.6, 16,164.3, and 16,116.4 kWh/Year in polycrystalline, monocrystalline, PERC (Mono), and bifacial PV panels with the 50% coverage area. Figure 6 shows that the PV production in bio-solar green roofs increased by about 4% compared to conventional roofs.

3.2. Shade Frequency of PV Panels on Green Roof Surfaces and the Impact on ET

The shade frequency of PV panels on the green roof was simulated by PVSOL 2024 R3 software, as shown in Figure 7. In the figures, white, green, yellow, and red represent 0%, near 0%, 33%, and 100% shade frequencies, respectively. From the figure, it is clear that shade frequency increased with the coverage area. For the 10% coverage area, the shade frequency is mostly in the 0% and near 0% zones. However, it is mostly in the zone of 100% for the 60% coverage area.

To determine the amount of the area in each zone, the annual shade frequencies of PV panels on the green roof surface were analyzed using the image-processing technique in MATLAB R2024b. The developed code is provided in Appendix A. Figure 8 shows the contribution of each shade frequency in various configurations of PV panels on the green roof. The figure shows that the white mask (0% shade frequency) is only present in the 10% PV coverage area configuration, as can also be detected in Figure 7a. The green mask (near 0% shade frequency) was reduced with the PV coverage area increase. The green mask is at 48% and 0% for the 10% and 60% coverage areas, respectively. The yellow mask (33% shade frequency) increased up to 51% at a 20% PV coverage area and decreased to 10% at a 60% PV coverage area. Meanwhile, the red mask (100% shade frequency) increased constantly from 12% to 90% as the coverage area of solar panels increased.

The water reduction in bio-solar green roofs in the Mediterranean climatic conditions can be estimated based on the boundaries of green roofs’ ET reduction in shade, which was between a minimum of 14% and a maximum of 33%. Therefore, according to the shade frequency analysis of PV panels on the roof, the water reduction (ET reduction) for each shading zone of Figure 7 can be estimated according to

Table 6. Reduction amount of ET in each shade frequency zone.

ET (Water Consumed by Plants) Reduction Rate in Different Sections of Bio-Solar GR		White	Green	Yellow	Red
		0% Shade	Near 0% Shade	33% Shade	100% Shade
Min	14%	1.0	1.0	1.0	0.9
Max	33%	1.0	1.0	0.9	0.7

. The table illustrates that the water consumed in the white zone (absolute 0% shade frequency) and that in the green zone (near 0% shade frequency) are not impacted by PV. Therefore, water consumption in these two zones will be similar to that of conventional GRs. However, in the red zone with a 100% shade frequency, the water consumed by GRs will be less than that for conventional GRs, which can be between 0.9 (1−0.14% ET reduction) and 0.7 (1−0.33% ET reduction). In the yellow zones, the impact of the shadow is 33% (which means 33% of the time, it is under shadow) of the minimum and maximum values.

3.3. Evaluation of Bio-Solar Green Roof Water–Energy Performance

In this section of our work, a dynamic decision support system was developed in Vensim PLE 10.2.1to evaluate the interconnections between water and energy in bio-solar green roofs, as presented in Figure 9. For this purpose, the simulation results of shade frequency in MATLAB R2024b and PVSOL 2024 R3 were applied as databases, and other variables, such as the maximum and minimum values of different PV efficiencies, water consumption levels in different types of green roofs based on the literature review analysis achievement (Table 1, Table 3, and Table 4), as the boundary conditions in Vensim PLE 10.2.1. In this way, the analysis can be carried out for different types of solar panels with various efficiency and coverage percentages in the case of conventional and bio-solar systems. The boundaries and limits of the variables are shown in Figure 10.

Figure 11 shows the simulation results for two different operational conditions. Figure 11a shows the maximum and minimum annual power production, and Figure 11b exhibits the daily water consumption in a conventional (0% PV) and a bio-solar green roof (60% PV). The evaluations show that using PV panels on the green roof can reduce water consumption in Mediterranean climatic conditions. When a 10% to 60% area of green roofs is covered with PV panels, the reduction in the water demand ranges between 2.9% and 30.8%. The reduction in water consumption is due to decreased water losses caused by irradiation, resulting from PV shade to the green roofs.

The comparison of minimum and maximum capacities to produce electricity per year in the conventional roof configurations and of different solar panels with various bio-solar green roof configurations showed better annual electricity production in bio-solar systems. The results show that the production of electricity for a roof with an area of 100 m² in the first operation year in polycrystalline solar panels increases by 512 kWh; in monocrystalline panels, by 635 kWh; in PERC, by 656 kWh; and in bifacial, by 647 kWh in a 50% bio-solar green roof configuration in comparison with conventional PV systems.

3.4. Scope for Future Works

Suggested directions for further study are listed below:

• Analysis of other inclinations (tilts) of solar panels in bio-solar green roofs and comparison with the optimized tilt angle in conventional roofs. In bio-solar green roofs, other angles might further decline the temperature of PV (effect of the power production) and also affect shade frequency (impact on the ET value). Therefore, optimization of PV inclination is suggested for future works;
• Further studies can be conducted for other roofs with higher values of albedos (such as white roofs) to investigate the impact of green roofs in comparison;
• Analyses of a windy climate and the impacts of PV on wind reduction and wind on PV panel temperature can improve the knowledge in this field and are suggested for future investigations;
• Analysis of different types of plants and green roofs is suggested for future studies;
• Finally, the thermal impact of bio-solar green roofs on building envelopes and the energy efficiency of buildings in the Mediterranean climate can be analyzed in future studies.

4. Conclusions

This investigation mainly focused on establishing the interconnection between the water requirement and the performance of PV panels on green roofs. For this purpose, the evaluation was conducted on conventional and bio-solar roofs for the selected case study of 100 m² size in Cosenza city (Mediterranean climate) with 10% to 60% coverage percentages by four types of PV panels: polycrystalline, monocrystalline, PERC, and bifacial. The results show that the water consumption by the green roof is reduced with the increase in PV coverage area due to the increase in shade frequency. According to the dynamic analysis of different conditions, the highest percentage reduction in water demand is obtained at a 60% green roof coverage with PV panels, as 30.77%. However, the electricity generation is enhanced with the coverage area until a certain percentage of 50%, and then it decreases by about 13% due to the dominant impact of solar panels’ shadow on other panel surfaces. The highest electricity production from the PV panels is observed in PERC (Mono) and bifacial solar panels, with a 50% coverage area configuration. In conclusion, this investigation shows the advantages of bio-solar green roofs for buildings, as they make lower water demands and can produce more electricity. Moreover, it exhibits the optimum coverage rate of PV panels on bio-solar green roofs, which is around 50%.