The exterior surfaces of the roofing systems are exposed to several environmental factors specific to the local climate such as dirt, wind, sunlight, snow, rain, outdoor temperature, relative humidity, and cloud index. All these environmental factors and roofing specifications (materials, dimensions, etc.) contribute to the variations in the thermal and moisture performance of the roofs. Figure 1 shows that when the incident solar radiation hits a roof surface, part of the solar radiation is reflected to the environment and the other part is absorbed by the roofing system. The absorbed part of solar radiation results in increasing the surface temperature of the roof, thereby increasing the cooling energy load in summer and decreasing the heating energy load in winter. As indicated earlier, white roofing systems use bright surfaces with high short-wave solar reflectivity to reflect a significant part of the solar radiation, thus lowering the rooftop temperature and the cooling energy load compared to conventional roof systems.

With the new advanced technology of radiative cooling materials that can be used as reflective materials in white/cool/radiative roofing systems (Kubota, 2017; Knoss, 2019; SurfaPaint ThermoDry Elastomeric Roof Paint., 2019), their short-wave solar absorption coefficients are very small and close to zero, and long-wave thermal emissivities are very high and close to 1.0 (i.e., behaves approximately as blackbody in emitting thermal energy from the reflective material to the environment). For example, Kubota and his team from Stanford University (Kubota, 2017) have recently used a multilayer optical film that reflected about 97% (i.e., the short-wave solar absorption coefficient, α_s = 0.03) of the sunlight. Due to the high long-wave thermal emissivity, their material was simultaneously being able to emit the surface's thermal energy through the atmosphere. As well, Knoss and his team from University of Colorado Boulder (Knoss, 2019) developed a new material that can reflect most of the incoming solar rays back into the atmosphere (i.e., α_s ≈ 0.03); while it still providing a means of emitting its surface thermal energy to the environment.

Fernandez and his team from Pacific Northwest National Laboratory (PNNL) (Fernandez et al., 2015) have used the radiative cooling material that was developed by Stanford University team (Kubota, 2017) to investigate the potential energy savings as results of using this material against using the best cool roof surfaces on the market. Their simulation results using EnergyPlus model showed that using this radiative cooling material has resulted in electricity saving of 10 MWh in Miami, 13 MWh in Las Vegas, 8 MWh in Los Angeles, 3 MWh in San Francisco and 6 MWh in Chicago, per year, which represented 9, 16, 23, 22, and 14% of cooling electricity savings, respectively, in the above five cities (Fernandez et al., 2015). As provided in ASHRAE (2005), most of construction materials have a surface emissivity of 0.9. In this study, the value of the long-wave emissivity of the rooftop was taken equal 0.9. This value is same as that taken in many previous studies related to assessing the energy and moisture performance of black and white roofing systems [e.g., (Bludau et al., 2009, 2010; Saber et al., 2011b, 2012c, 2019b)].

The dust and/or dirt accumulations on the rooftops can reduce their short-wave solar reflectivity, leading to an increase in solar heat gain. Various studies and field test measurements investigated the effect of aging factors and dust and/or dirt accumulations on the changes in the rooftop properties (Akbari et al., 2005; Levinson et al., 2005; Berdahl et al., 2008; Suehrcke et al., 2008; Algarni and Nutter, 2015). With regard to the accumulation of dirt, various cleaning methods are available to bring the short-wave solar reflectivity of the roof surfaces to their original values. In the experimental study by Levinson et al. (2005), different cleaning processes were applied on light-colored roofing membrane samples (collected from roofs across the US) in order to study the effect of these cleaning processes on their short-wave solar reflectivity. The results of that study showed that inorganic carbon and black carbon were found on the sample surfaces, which led to reductions in their short-wave solar reflectivity. The cleaning processes applied to the surfaces of the samples included wiping process to mimic the wind action, rinsing to mimic the operation of the rain, washing with a dishwashing detergent to mimic homemade cleaning, and finally treating the surfaces of the samples with a mixture of sodium hydroxide and sodium hypochlorite to mimic professional cleaning. By applying the rinsing process and washing process, the dirt on the surfaces was removed, with the exception of a thin layer of contaminants. With the bleaching process, however, the layer of contaminants was removed, whereby the original short-wave solar reflectivity of these surfaces were restored (Levinson et al., 2005).

In another study (Akbari et al., 2005), the same cleaning processes that were developed by Levinson et al. (2005) were applied on 41 samples of unweathered (i.e., new materials) and weathered white membranes. These membranes were collected from different locations across the US and Canada where 16 samples were analyzed at Lawrence Berkeley National Laboratory, and 25 samples were analyzed at the National Research Council of Canada. The results showed that ~90% of the short-wave solar reflectivity of these samples were recovered (Akbari et al., 2005). Currently, an experimental study is being conducted on a number of coatings and reflective roofing materials when they are subjected to the natural dusty and highly polluted climate of Jubail Industrial City in Saudi Arabia. The main goals of that study are to: (a) investigate the changes in the short-wave solar reflectivity of these materials (b) develop cleaning technical guide for these materials, and (c) quantify the impact of dirt/dust accumulations on the overall thermal and moisture performance of the roofing systems. The results of that study will be published at a later date.

Automatic indoor air temperature control with an Optic-Variable Wall (OVW) was recently proposed by Wang et al. (2018) to reduce the HVAC (Heating, Ventilation & Air-Conditioning) energy consumption in containers. The external surface of the OVW is coated by a layer called “responsive coating.” Within the wavelength region of visible light, the characteristic of this responsive coating on the absorption and the reflection of solar radiation is sensible to its temperature. The surface characteristic of the responsive coating is quite attractive in building applications. This is because at high temperature, the responsive coating shows strong reflection (i.e., low short-wave solar absorption coefficient) to the solar radiation exposing on the OVW; while the solar reflection becomes weak (i.e., high short-wave solar absorption coefficient) at low temperature.

Wang et al. (2018) verified experimentally under natural winter conditions (i.e., low ambient temperature) the feasibility of the OVW performance on air temperature control inside a container. The test results showed that the color of OVW varies from dark at low temperature to light at high temperature, where the solar reflectivity of OVW was small at low temperature and high at high temperature. In addition, with the adoption of the OVW, their theoretical investigation on the air temperature inside a container showed that it was possible to simultaneously keep air cool in summer and warm in winter.

In another study, Wang et al. (2019a) theoretically investigated the effect of responsive coating properties on the potential of energy saving with OVW for stable air temperature control in buildings. The results of that study showed that with the adoption of the OVW, the heating load and cooling load could be simultaneously reduced. Furthermore, the results showed that the cooling load was reduced compared to optic-fixed wall having a constant low solar reflectivity, and as well the heating load was reduced compared to optic-fixed wall having a constant high solar reflectivity.

Wang et al. (2019b) conducted dynamic simulation to investigate the effect of the OVW having responsive coating on the façades of high-rise residential buildings when these buildings were subjected to the climatic conditions of Shanghai and Paris. The results showed that the potential use of the responsive coating on the south walls (or facing equator) resulted in more contribution to the energy saving than walls of other orientations. Also, the results showed that the contribution of the responsive coating to energy savings for the climatic conditions of Shanghai was (17%) about twice of that for a colder climatic conditions of Paris (8%).

By allowing more absorption of the solar radiation in winter while maintaining high solar reflection in summer, the concept of the responsive coating when it is applied on the rooftops would simultaneously result in reducing the cooling load during the summer season and as well reducing the heating load during the winter season. For a wide range of the short-wave solar absorption coefficient of the rooftop (0–0.88) and a wide range of insulation thickness [0–8″ (203 mm)], this study focused on the energy performance of a roofing system, that is commonly used in the buildings of the Gulf Cooperation Council countries, when it was subjected to Saudi hot and humid climates. Each value of the short-wave solar absorption coefficient was taken constant through the whole year. This represents the case of installing optic-fixed roof. Under different climatic conditions, a future study is recommended to compare the overall energy savings as a result of installing responsive coating on the rooftop (i.e., optic-variable roof) against the overall energy savings for the case of using optic-fixed roof (i.e., similar to this study).

In short, a logical step toward achieving energy-efficient buildings is to design roofing systems that offer potential energy savings at low risk of condensation and mold growth. The main parameters that affect the hygrothermal performance of the roofing systems are roof type, climate conditions (wind, sunlight, snow, rain, etc.), amount of insulation and the value of α_s for the rooftop. With regard to the accumulation of dust and dirt on the rooftops, some cleaning processes are currently available that can be used to bring their short-wave solar reflectivity to approximately their initial values.

As an example of a roofing system with δ_ins = 6″ (152 mm), Figure 3A shows comparisons of the hourly rooftop temperatures for white roofing systems with α_s = 0.05 and black roofing system (α_s = 0.88). During the daytime, this figure shows that the high value of α_s (i.e., large amount of the absorbed incident solar radiation) for the black roofing system has resulted in its rooftop temperature was greatly higher than that of the white roof with α_s = 0.05. Throughout the whole year, the highest rooftop temperature for the black roof (occurred in August) was 91.5°C compared to 50.8°C for the white roofing system of α_s = 0.05. However, during the night, the rooftop temperatures of the black roof and white roof were roughly the same. For a wide range with α_s (0.88–0.05), Figure 4 shows the monthly average rooftop temperature of roofing systems with δ_ins = 6″ (152 mm). As shown in this figure, the monthly average rooftop temperature increases with increasing α_s. The highest values of these temperatures occurred in July followed by August. In July, the highest average rooftop temperature for the white roofing system with α_s = 0.05 (39.1°C) was 11.3°C lower than that of black roofing system (50.4°C).

On the indoor surface of the black roofing system (α_s = 0.88) and white roofing system (α_s = 0.05), Figure 3B shows comparisons of the hourly heat fluxes. In this figure, when the heat flux is positive, this is called “heat gain” (i.e., heat enters the building where the system contributes to the cooling energy load). However, when the heat flux is negative, this is called “heat loss” (i.e., the heat leaves the building where the system contributes to the heating energy load). Throughout this paper, unless otherwise specified, the terms of cooling energy load, heating energy load and total energy load represent the contributions to the energy loads from the roofing system only. As can be seen in Figure 3B, because of the high rooftop temperature of the black roofing system (see Figure 3A), its heat gain is considerably higher than that of the white roofing system. Throughout the whole year, the highest hourly heat gain for black roofing system was 5.90 W/m², which was 1.86 times that for white roofing system with α_s = 0.05 (3.17 W/m²). However, the highest hourly heat loss throughout the year for the black roof was 2.11 W/m², 0.74 times that for the white roofing system (2.84 W/m²). Accordingly, a black roof requires a higher cooling load than that with white roof. Conversely, a black roof requires lower heating load than that with white roof. In Saudi Arabia, the high heat gain takes place during peak electrical demand periods that occur in summer. Thus, installing white roofing systems can help reduce the peak electricity demand. It is important to point out that decreasing the energy consumption during the period of peak electricity demand can also reduce demand fees that some utilities charge.

The hourly heat fluxes on the indoor surface [e.g., see Figure 3B) for the case of roofing systems with δ_ins = 6″ (152 mm)] were used to determine the monthly cooling and heating loads for wide ranges of δ_ins, [0–8″ (203 mm)] and α_s (0.88–0.05). As examples of roofing systems with different values of α_s and having δ_ins of 2″ (51 mm), 4″ (102 mm), 6″ (152 mm), and 8″ (203 mm), Figures 5A–D, respectively, show the monthly cooling loads (+ve values) and the monthly heating loads (–ve values). In cold climates, the energy sources needed for heating the residential buildings are frequently fossil fuels; while those needed for the cooling loads are electrical energy. Because of the difference in prices per thermal unit due to using fossil fuels and the electrical energy, the heating load and the cooling load must be specified individually (Bludau et al., 2009; Saber et al., 2011b, 2012c). In hot climates such as that in Saudi Arabia, however, the energy sources for both heating and cooling loads are mainly electrical energy. So, the total load can be obtained as the sum of the heating load and cooling load (see Figures 6A–D) for roofs having different values of δ_ins.

For a given value of δ_ins, Figures 5A–D show that the monthly cooling load decreases with decreasing α_s. Conversely, the monthly heating load increases with decreasing α_s. For a given value of α_s, because the highest rooftop temperatures occurred in July (see Figure 4), Figures 5A–D show that the highest cooling load occurred in July, followed by August. In July, the cooling loads for the black roofing systems (α_s = 0.88) having δ_ins of 2″ (51 mm), 4″ (102 mm), 6″ (152 mm), and 8″ (203 mm), were 364, 214, 152, and 117 Wd/m², respectively. For white roofing systems with α_s of 0.2, the corresponding cooling loads were 237, 139, 98, and 76 Wd/m², respectively. Additionally, for white roofing systems with α_s of 0.05, the corresponding cooling loads were 208, 122, 86, and 67 Wd/m², respectively. For different values of δ_ins, these represent energy savings in the monthly energy loads by 35 and 43%, respectively, as results of using white roofing systems with α_s of 0.2 and 0.05 instead of black roofing systems (α_s = 0.88).

Note that the largest share of electricity consumption in buildings is used for cooling in Saudi Arabia (e.g., see Figure 5). This may cause significant strain on the country's electricity grid during the summer. The Saudi Electricity and Cogeneration Regulatory Authority has announced that the Council of Ministers has approved gradual revision of energy prices including changes to electricity tariffs that has taken effect on January 1, 2018, where lower energy consumption (1–6,000 kWh/month) are charged at a lower rate of 18 halala/kWh, whereas higher energy consumptions (>6,000 kWh/month) are charged at a higher rate of 30 halala/kWh. Consequently, the Saudi buildings should be designed/retrofitted with the intent of minimizing the cooling energy loads so as to help not only reduce the annual electrical peak demand especially during the summer but also reduce the cost for operating the buildings.

As examples of roofing systems with different values of α_s and having δ_ins of 2″ (51 mm), 4″ (102 mm), 6″ (152 mm) and 8″ (203 mm), the results for the yearly cooling and total loads are provided in Figures 7A–D, respectively. For a given δ_ins, these figures show that decreasing α_s has resulted in reductions in the yearly cooling and total loads. In addition, for a given α_s, increasing δ_ins resulted in reductions in the yearly cooling loads and yearly total loads. For examples, with α_s = 0.88 (black roof), 0.2 and 0.05, the yearly cooling and total loads for the roofing system having: (a) δ_ins of 2″ (51 mm) were 2242, 1238, and 1043 Wd/m², and 2303, 1502, and 1386 Wd/m², respectively (Figure 7A), (b) for δ_ins of 4″ (102 mm) were 1314, 728, and 614 Wd/m², and 1350, 883, and 814 Wd/m², respectively (Figure 7B), (c) for δ_ins of 6″ (152 mm) were 931, 515, and 435 Wd/m², and 955, 625, and 577 Wd/m², respectively (Figure 7C), and (d) for δ_ins of 8″ (203 mm) were 720, 399, and 337 Wd/m², and 738, 484, and 447 Wd/m², respectively (Figure 7D). For different values of δ_ins, Figures 7A–D show that decreasing α_s from 0.88 (black roof) to 0.2 and 0.05 resulted in savings in the yearly cooling loads by 45 and 53%, respectively. As well, the corresponding savings in the yearly total loads were 35 and 40%, respectively.

This study mainly focuses on the energy performance of only one part of the building envelope, which is the roofing system. As indicated above, using reflective roofing materials/coatings with low α_s in Saudi climates has resulted in significant reductions in the yearly energy loads in relation to black roofing systems of the same δ_ins. However, to explore the effect of these reductions on the overall energy requirements for the whole building, another study is currently being conducted to assess the energy performance of the whole building instead of the roofing system only in which the effect of the following factors are accounted for:

For black roofing systems (α_s = 0.88) of different values of δ_ins, the results of the yearly cooling and total loads are provided in Figure 8. Because the yearly heading load for the case of a black roofing system is much lower than the yearly cooling load, the yearly total load (i.e., heating load + cooling load) is a little higher than the yearly cooling energy load (see Figures 8A,B). For small values of δ_ins [δ_ins ≤ 2″ (51 mm)], Figure 8 shows that the yearly energy loads and the associated reduction rates in these energy loads (i.e., the derivative of the energy load w.r.t. δ_ins, |dYCL_B/d δ_ins| and |dYTL_B/d δ_ins|, plotted on the right y-axis of Figure 8) significantly decrease with increasing δ_ins. For example, the reduction rates in the yearly energy loads |dYCL_B/d δ_ins| and |dYTL_B/d δ_ins| were, respectively, 151, 72, and 30 (Wd/m²)/mm for δ_ins of 0.5″ (13 mm), 1″ (25 mm), and 2″ (51 mm). However, for large values of δ_ins (δ_ins ≥ 4), the yearly energy loads and the associated reduction rates in these energy loads slightly decrease with increasing δ_ins. For example, for δ_ins of 4″ (102 mm), 6″ (152 mm), and 8″ (203 mm), the values of |dYCL_B/d δ_ins| and |dYTL_B/d δ_ins| were, respectively, only 11, 6, and 4 (Wd/m²)/mm.

For black roofing systems (α_s = 0.88) of different values of δ_ins, the yearly cooling energy loads (YCL_B) and the yearly total loads (YTL_B) that are provided in Figures 8A,B, respectively, can be given as functions of δ_in as:

The coefficients a₀ through a₅ in Equations (1) and (2) are listed in Table 1. Also, for specified YCL_B and YTL_B, the associated value of δ_ins that is needed can be determined from the following correlations:

Where the coefficients a₀ through a₅ in Equations (3) and (4) are listed in Table 1. Note that in Equations (1) through (4), the units of YCL_B and YTL_B are in Wd/m² and the unit of δ_in is in inch.

As example, Figure 11A shows that the yearly cooling energy load for a black roofing system (α_s = 0.88) having δ_ins = 8″ (203 mm) is 720 Wd/m². This load can be achieved with the pairs of δ_ins and α_s that are given as:

The value of δ_ins in Equation (5) should be in inch. For this yearly cooling load (YCL) of 720 Wd/m², Figure 11A shows that a 0, 25, 50, and 59% savings in insulation thickness [i.e., δ_ins = 8″ (203 mm), 6″ (152 mm), 4″ (102 mm), and 3.26″ (83 mm)] would require that the value of α_s must be, respectively, 0.88 (i.e., black), 0.55, 0.19, and 0.05.

As an example, a yearly total energy load of YTL = 738 Wd/m² that relates to a black roofing system with δ_ins = 8″ (203 mm) and α_s = 0.88 (Figure 11B) can be obtained with the pairs of δ_ins and α_s that are given as:

The value of δ_ins in Equation (6) should be in inch. From Figure 11B or Equation (6) for YTL = 738 Wd/m², a 0, 12.5, 25, and 44% savings in insulation thickness [i.e., δ_ins = 8″ (203 mm), 7″ (178 mm), 6″ (152 mm), and 4.48″ (114 mm)] would require that the value of α_s must be, respectively, 0.88 (i.e., black), 0.70, 0.48, and 0.05. Next, a practical design tool was developed for the roofing system shown in Figure 2 that can be used to determine all δ_ins and α_s pairs for different yearly energy loads.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.