# Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun

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## Abstract

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^{−2}year

^{−1}. Finally, a correction factor, introduced in a recent publication, is used; it is confirmed that the linear relationship between the correction factor and the ground-albedo ratio is general enough to be graphically representable as a nomogram. A discussion regarding the differences among solar systems on horizontal, fixed-tilt, 1-axis, and 2-axis systems is presented.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

_{b,0}(direct horizontal solar irradiance in Wm

^{−2}) and H

_{d,0}(diffuse horizontal solar irradiance in Wm

^{−2}) were downloaded from the PV—Geographical Information System (PV-GIS) tool [21] using the latest Surface Solar Radiation Data Set—Heliostat (SARAH) 2005–2016 database (12 years) [22,23]. This platform provides solar radiation data through a user-friendly tool for any location in Europe, Africa, the Middle East including Saudi Arabia, Central and Southeast Asia, and most parts of the Americas. Nevertheless, the platform provides solar maps for Europe, Africa, Turkey, and Central Asia only. The methodologies used for estimation of solar radiation from satellites by the PV-GIS tool are described in various works [24,25,26].

#### 2.2. Data Processing and Analysis

_{g}, values were estimated at all sites as the sum H

_{g}= H

_{b}+ H

_{d}.

^{−2}and corresponding to γ ≥ 5° (to avoid the cosine effect) were retained for further analysis. Moreover, the criterion of H

_{d,0}≤ H

_{g,0}was required to be met at the hourly level.

_{g,t}(in Wm

^{−2}), the isotropic model of Liu-Jordan [30] was adopted (the subscript t stands for “tracking”). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, H

_{r,t}(in Wm

^{−2}), received on the inclined plane. This model was adopted in the present study because of its simplicity and effectiveness in comparison to other anisotropic models in providing the tilted total solar radiation in many parts of the world; the good performance of the isotropic model has been verified by various studies (e.g., [31,32,33,34,35]).

_{z}; the incidence angle, θ (the angle between the normal to the surface and the direction toward the sun); the solar azimuth, ψ; and the azimuth of the tilted plane, ψ’. In this graph, the sun lies in the N-S plane that is normal to the local horizon (therefore, ψ = 180°). In the case of a surface tracking of the sun, it is easy to conclude that θ = 0° (the solar rays are normal to the tilted surface), β = 90° − γ, and ψ = ψ’.

_{g,t}= H

_{b,t}+ H

_{d,t}+ H

_{r,t},

_{d,t}= H

_{d,0}·R

_{di},

_{r,t}= H

_{g,0}·R

_{r}·ρ

_{g0}, (or H

_{g,0}·R

_{r}·ρ

_{g})

_{di}= (1 + cosβ)/2 = (1 + sinγ)/2,

_{r}= (1 − cosβ)/2 = (1 − sinγ)/2,

_{b,t}= H

_{b,0}· cosθ/sinγ = H

_{b,0}· cos0/sinβ = H

_{b,0}/cosγ

_{di}and R

_{r}are the isotropic sky-configuration and ground-inclined plane-configuration factors, respectively. In the L-J model, the ground albedo usually takes the value of ρ

_{g0}= 0.2 (Equation (3)). This value was used in the present study. Apart from using ρ

_{g0}in the calculations, values of ρ

_{g}close to reality were also adopted in this study as in [1,2]. To retrieve such values for the 82 sites, we made use of the Giovanni portal [36]; pixels of 0.5° × 0.625° spatial resolution were centered over each of the 82 sites for which monthly mean values of the ground albedo were downloaded in the period 2005–2016. Annual mean ρ

_{g}values were then computed and were used to re-calculate H

_{g,t}.

_{g,t}were estimated twice from Equation (1); the first time by using computations with ρ

_{g0}= 0.2 in Equation (3), being considered as reference value in solar modelling, and a second time by using calculations with ρ

_{g}equal to the ground-albedo value retrieved from the Giovanni platform. From the hourly H

_{g,t}values, annual, seasonal, and monthly solar energy sums (in kWhm

^{−2}) under all-sky conditions were estimated for all sites and both ground-albedo values.

## 3. Results

#### 3.1. Annual Energy Sums

_{g0}and ρ

_{g}, in Equation (3). The annual solar energy sum (or yield) at each location was estimated by aggregating (summing up) all hourly solar radiation values within the period of 2005–2016. Table 2 shows these annual H

_{g,t}sums. It should be noted here that the reference value of ρ

_{g0}is used for grassland areas (and widely used in the L-J model), while surfaces with different vegetation or no vegetation (such as tundra, desert, and snow-covered area) may have different reflectance far from 0.2 [25]. Figure 3 shows the variation of the annual solar energy yields on horizontal as well as on inclined flat-plate surfaces for all three solar system types (static and dynamic) across all 82 sites. The difference in the mean values between the mode (iii) and (ii) systems is only 4.2%, and between the mode (i) and horizontal cases only 6.4%. At first glance, these small differences imply a preference to use mode (ii) solar systems with constant tracking-the-sun ability instead of the more sophisticated mode (iii) ones, or to use horizontal surfaces instead of mode (i) inclined ones with constant tilt towards the South. As shown in Figure 4, the above difference of 4.2% is equivalent to 11,883 kWhm

^{−2}year

^{−1}, and the second difference of 6.4% to 10,353 kWhm

^{−2}year

^{−1}. Indeed, the first difference is equal to 3.81 times the average annual solar energy sum for a mode (iii) solar system, i.e., 3.81 × 3120 kWhm

^{−2}year

^{−1}= 11,887 kWhm

^{−2}year

^{−1}, or 3.97 times the average annual solar energy sum for a mode (ii) solar system, i.e., 3.97 × 2994 kWhm

^{−2}year

^{−1}= 11,886 kWhm

^{−2}year

^{−1}. The second difference is equal to 4.27 times the average annual energy sum for a mode (i) solar system, i.e., 4.27 × 2422 kWhm

^{−2}year

^{−1}= 10,342 kWhm

^{−2}year

^{−1}, or 4.55 times the average annual solar energy sum for a horizontal surface, i.e., 4.55 × 2277 kWhm

^{−2}year

^{−1}= 10,360 kWhm

^{−2}year

^{−1}. Therefore, these solar energy differences cannot be ignored as they correspond to sites producing 3.81 (3.97) more energy than mode (iii) ((ii)) solar systems or corresponding to sites deriving 4.27 (4.55) more energy than mode (i) (horizontal) solar systems. On the other hand, it is clear about what type of solar system to use if one has to choose between the first group with modes (ii) and (iii) systems and between the second group with horizontal and mode (i) systems, as the gap between the two groups was found to be rather high (i.e., 707 kWhm

^{−2}year

^{−1}= (3120 kWhm

^{−2}year

^{−1}- 2994 kWhm

^{−2}year

^{−1})/2 − (2422 kWhm

^{−2}year

^{−1}− 2277 kWhm

^{−2}year

^{−1})/2, see Figure 3). Nevertheless, the choice of the solar system type depends upon the cost-benefit criterion. This criterion is discussed in Section 4.

#### 3.2. Monthly Energy Sums

_{g,t/ρg}for all sites is shown in Figure 5. It is seen that the variations of almost all sites are very close to each other, creating a bundle, a zone. There are, however, two sites that present exceptional monthly yields and, therefore, lay above the bundle (i.e., sites #28, and 52). Site #28 lies in the very southeastern part of Saudi Arabia and receives high solar insolation throughout the year. On the contrary, site #52 lies in the very northern part of the country, and lower solar insolation would be expected; this unevenness could probably be attributed to local climatology with very clear skies occurring most time of the year or miscalculation of the ground albedo at the Giovanni platform or inaccurate estimation of solar radiation by the PV-GIS tool or a combination of them. The exceptional performance of solar energy at these two sites is also depicted in Figure 3.

_{g,t}values within some limits (i.e., the band of mean ± 1σ), the upper limit (mean + 1σ) corresponds to the dispersion of the higher solar energy values and the lower limit (mean − 1σ) to the dispersion of the lower solar energy values. In other words, the red line in Figure 6 denotes the weighting of the higher values in the whole sample of the 82 H

_{g,t}values, while the blue line is weighted towards the lower values in the same sample. This implies that the upper limit is dominated by the high H

_{g,t}values in the south of the country (i.e., SEZ-A, Figure 3 in [2]), while the lower limit by the low H

_{g,t}values that occurred in the northern part of Saudi Arabia (i.e., SEZ-C, Figure 3 in [2]). Therefore, the upper limit is influenced by a solar energy pattern with maximum in the summer (August), and the lower limit by a solar energy pattern with a main peak in the summer (June, July) and minor peaks in April and September. These observations are justified by Figure 5 in [2]. Table 3 provides the expression for the monthly H

_{g,t}values over all Saudi Arabia as function of the month number, s (s = 1,…,12); the regression equation has a very high R

^{2}equal to 0.96, implying an almost perfect fit to the data.

#### 3.3. Seasonal Energy Sums

_{g,t/ρg}levels, Figure 7 presents the seasonal variation of the solar energy values; each individual data point in the graph is the average seasonal energy yield for the specific site over the period 2005–2016. To find an overall expression for the received seasonal energy sum in Saudi Arabia, as done for the monthly case, we averaged the energy values for each season from all sites over the period 2005–2016 under all-sky conditions; Figure 8 presents the results. Table 3 provides the regression equation for the curve that best fits the mean seasonal values. The fit is ideal (R

^{2}= 1).

#### 3.4. Maps of Annual Energy Sums

_{g,t,β/ρg}sums. A gradual increase in the annual solar potential in the direction NE–SW for the sun-tracking inclined flat planes is observed. Very similar patterns to that in the present study are given in the Solar Radiation Atlas for Saudi Arabia [37]. The interpretation for this gradient is attributed to two reasons. (i) Latitude: the higher the latitude, the lower the solar radiation levels received on the surface of the earth. (ii) Meteorology: more frequent precipitation is observed in the north-eastern part of the country, which is related to the precipitation occurring in southern Iraq and Iran [38].

#### 3.5. Evaluation of the PV-GIS Tool

_{g}values measured at the Actinometric Station of the National Observatory of Athens (ASNOA, 37.97° N, 23.72° E, 107 m above sea level) and corresponding values from the PV-GIS platform in the period 2005–2011. Figure 10 presents this comparison, which shows an excellent agreement (R

^{2}= 0.99). Although the PV-GIS-estimated values seemed to overestimate the measured H

_{g}ones by +10%, this figure is within the acceptable range (−14%, +11%). For this reason, the PV-GIS data were accepted for use in the present study.

#### 3.6. The Correction Factor

_{g,t/ρg}/H

_{g,t/ρg0}. CF is, therefore, the ratio of the annual H

_{g,t}sum at each site of the 82, calculated twice, once for ρ

_{g0}= 0.2 and a second time for ρ

_{g}= actual value. The practicality of using CF is that it corrects the solar energy incident on an inclined surface under the influence of a ground albedo equal to 0.2 to that which is under the influence of a near-real ground-albedo value. Despite the variation of CF as function of β for all 82 sites in [1,2], the present analysis of the H

_{g,t}values does not depend on this parameter at all because of the ever varying tilt angle of the receiving flat-plate surface during the operation of a mode (iii) system. Therefore, a different graph was prepared, i.e., a graph of CF as function of the ground-albedo ratio, ρ

_{r}= ρ

_{g0}/ρ

_{g}. Figure 11 shows this dependence, which is linear: CF = 0.0203$\xb7$ρr + 0.9797 with R

^{2}= 0.98 at the 95% confidence level; similar dependence was firstly found by Farahat et al. [1,2]. The two lines CF = 1 and ρ

_{r}= 1 in Figure 11 cross each other at the site #24, which has a ground albedo ρ

_{g}= ρ

_{g0}= 0.2, and, therefore, H

_{g,t/ρg}= H

_{g,t/ρg0}. The blue and red bands show the confidence and prediction intervals around the best-fit line, respectively. It is seen that many sites are within the blue zone, but most of them are accommodated in the red band. Only four sites lie outside the prediction interval. This observation means that some of the sites (i.e., their CF-ρ

_{r}data pairs) that lie within the confidence interval are significant at the 95% level, while others that are within the prediction zone will be significant at the 95% level in the future (i.e., they will tend to be significant), and those four sites that are outside the prediction zone will be non-significant at the 95% level anyway.

_{g}= (H

_{g,t/ρg}− H

_{g,β,S/ρg})/(H

_{g,t/ρg}− H

_{g,β,t/ρg}), we derived two more plots. Figure 12a shows the dependence of CF on RΔH

_{g}, and Figure 12b the dependence of ρ

_{r}on RΔH

_{g}. Both plots show the mean RΔH

_{g}(black lines) and the (mean RΔH

_{g}+ 1σ, mean RΔH

_{g}− 1σ) zone; this zone includes most of the 82 sites, a fact that is interpreted as meaning that most of the RΔH

_{g}values are statistically significant at the 95% level in relation to those of CF vs. ρ

_{r}(Figure 11). The other 24 sites outside the band (as #24 for which CF = ρ

_{r}= 1) can be characterised as reflecting a loose dependence of CF or ρ

_{r}on RΔH

_{g}; this may occur because of the following reasons: (i) inaccurate estimation of ρ

_{g}at the Giovanni platform, (ii) inaccurate estimation of H

_{g}by the PV-GIS tool, or (iii) both.

## 4. Comparison of the Three Configuration Modes

^{−1}, 0.82 $W

^{−1}, and 1.23 $W

^{−1}for fixed-tilt, 1-axis, and 2-axis systems, respectively. In the same way, their operation and maintenance costs were estimated at 25 $kW

^{−1}year

^{−1}, 32 $kW

^{−1}year

^{−1}, and 37.5 $kW

^{−1}year

^{−1}, respectively.

^{−1}and 0.10 $kWh

^{−1}.

## 5. Discussion

_{r}was derived for this case, as in [1,2]. (iii) Accommodation of most sites within the mean RΔH

_{g}± 1σ band was found in both relations CF vs. RΔH

_{g}and ρ

_{r}vs. RΔH

_{g}; the last two statements remain to be confirmed at other locations in the world to constitute universality.

- If a solar radiation station exists in the area, hourly or daily values of the solar global horizontal radiation are collected for a climatological period of 10 years at least.
- If no solar radiation exists, then data from relevant websites (e.g., BSRN, GEBA, PV-GIS, ARM) are obtained.
- In the extreme case that this option is not possible, use of a solar energy model can be made to derive the anticipated data from other available variables (e.g., from meteorological parameters as the Meteorological Radiation Model-MRM does [44]).
- Transposition of the selected data from horizontal to inclined planes that track the sun takes place by setting the tilt angle always equal to 90° − γ. The transposition is achieved by selecting the desired model (the L-J model is sufficient). It is recommended that a near-real ground-albedo value is used in these calculations; if knowledge of this value is not available for the site, use of the nomogram of Figure 11 is made to correct the solar energy values derived.
- Annual solar energy sums for the inclined planes are calculated.
- Monthly solar energy sums are estimated, and a regression line can be derived that serves as guideline for estimating the expected solar energy on flat planes.
- The last step is repeated for the seasonal solar energy sums and the derivation of best-fit curves.

## 6. Conclusions

^{−2}year

^{−1}within Saudi Arabia. Along with the annual energy sums, monthly solar energy values averaged over all locations and over the mentioned period were estimated under all-sky conditions. A regression equation was provided as best-fit curve to the monthly mean energy sums that estimates the solar energy potential at any location in Saudi Arabia with great accuracy (R

^{2}= 0.96). This expression may prove very useful to architects, civil engineers, solar energy engineers, and solar energy system investors in order to assess the solar energy availability in Saudi Arabia for sun-tracking flat-plate solar systems throughout the year.

^{2}= 1). Maximum sums were found in the summer (882 kWm

^{−2}), and minimum ones in the winter (667 kWm

^{−2}), as expected.

_{r}showed a linear dependence with increasing CF values as ρ

_{r}increased. Such a behaviour was claimed to be considered universal (i.e., representable as nomogram). Nevertheless, this universality remains to be confirmed at other locations in the world with different climate and terrain characteristics. Two more plots were also prepared: (i) a graph of CF vs. RΔH

_{g}, and (ii) a graph of ρ

_{r}as function of RΔH

_{g}. In both cases, 58 of the 82 sites were found to be accommodated within the ±1σ band around the mean RΔH

_{g}value of 5.57. The other 24 sites remained outside the band, thus indicating a loose dependence of CF (ρ

_{r}) on RΔH

_{g}. These two graphs may be used as criteria for a strong (weak) dependence of CF (ρ

_{r}) on the received solar energy, but this conclusion remains to be confirmed at other sites worldwide with different climate and terrain characteristics.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Inclined surface at a tilt angle β with arbitrary orientation. E, W, N, S denote East, West, North, and South, respectively. Moreover, the solar altitude, γ; the solar azimuth, ψ; the tilted surface’s azimuth, ψ’; and the incidence angle, θ, are shown.

**Figure 3.**Variation of the maximum annual solar energy yield across the 82 selected sites in Saudi Arabia on horizontal surface (green lines), on inclined flat-plate surfaces of mode (i) static (purple lines), of mode (ii) dynamic (red lines), and of mode (iii) dynamic (brown lines) systems. The solid lines represent the variation of the annual yield across all sites, while the dashed ones represent the means of the curves.

**Figure 4.**Annual solar energy aggregate (sum, yield) across all 82 sites in Saudi Arabia for each type of installation; 0: horizontal surface; 1: mode (i) static system; 2: mode (ii) dynamic system; 3: mode (iii) dynamic system.

**Figure 5.**Intra-annual variation of H

_{g,t/ρg}under all-sky conditions for all 82 sites. The monthly values are sums of the hourly solar radiation ones for each site and averaged over the period 2005–2016. The numbers in the legend correspond to the sites shown in column 1, Table 1.

**Figure 6.**Intra-annual variation of H

_{g,t/ρg}under all-sky conditions, averaged over all sites and over each month in the period 2005–2016. The black solid line represents the average monthly H

_{g,t/ρg}sums. The red line corresponds to the mean + 1σ curve, and the blue line to the mean − 1σ one. The green dotted line refers to the best-fit curve to the mean one.

**Figure 7.**Seasonal variation of H

_{g,t/ρg}under all-sky conditions for all 82 sites. The seasonal values are sums of the hourly solar radiation ones for each site and averaged over each season in the period 2005–2016. The numbers in the legend correspond to the sites shown in column 1, Table 1. The numbers 1–4 in the x-axis refer to the seasons in the sequence spring to winter.

**Figure 8.**Seasonal variation of H

_{g,t/ρg}in Saudi Arabia. The black line represents the seasonal mean. The red line refers to the mean + 1σ curve, and the blue one to the mean − 1σ curve, under all-sky conditions. All H

_{g,t/ρg}values were averaged over all 82 sites and over each season in the period 2005–2016. The green dotted line refers to the best-fit curve to the mean one. The numbers 1–4 in the x-axis refer to the seasons in the sequence spring to winter.

**Figure 9.**Distribution of the annual H

_{g,t/ρg}(kWhm

^{−2}year

^{−1}) sums across Saudi Arabia, averaged over the period 2005–2016, under all-sky conditions.

**Figure 10.**Comparison of monthly mean solar energy values from PV-GIS, H

_{g,PV-GIS}, to measured ones at ASNOA, H

_{g,ASNOA}, in the period 2005–2011. The red dashed line represents the best fit to the data points and is expressed by the regression equation: H

_{g,PV-GIS}= 1.06$\xb7$H

_{g,ASNOA}+ 14.96 (R

^{2}= 0.99). The solid black line is the 1:1 (or y = x) line. This figure is a reproduction of Figure 8 in [1] and Figure 9 in [2].

**Figure 11.**Variation of the correction factor, CF, as function of the ground-albedo ratio, ρ

_{r}, under all-sky conditions; both CF and ρ

_{r}data points are annual averages over each site and over the period 2005–2016. The straight dotted green line expresses the best fit to the data points. The blue and the red zones are the confidence and prediction intervals at the 95% level, respectively. The horizontal black dash-dotted line and the vertical black dashed line indicate the crossing point of CF = 1 and ρ

_{r}= 1.

**Figure 12.**The correction factor, CF, as function of the ratio of the annual solar energy sum differences, RΔH

_{g}(

**a**), and the ground-albedo ratio, ρ

_{r}, as function of RΔH

_{g}(

**b**) for the 82 sites in Saudi Arabia. The data points in the plots are averages over each site and over the period 2005–2016. The green dashed lines represent the values CF = ρ

_{r}= 1; the vertical black lines are the means of RΔH

_{g}; and the red and blue ones are the limits of the (mean + 1σ, mean − 1σ) band, respectively.

**Table 1.**The 82 sites arbitrarily selected over Saudi Arabia to cover the whole area of the country; φ is the geographical latitude, and λ the geographical longitude in the WGS84 geodetic system. The “unnamed” sites refer to those away from known locations. This table is a reproduction of Table 1 in [1,2]. N = North, E = East.

# | Site | φ (Degrees N) | λ (Degrees E) |
---|---|---|---|

1 | Dammam | 26.42 | 50.09 |

2 | Al Jubail | 26.96 | 49.57 |

3 | Ras Tanura | 26.77 | 50.00 |

4 | Abqaiq | 25.92 | 49.67 |

5 | Al Hofuf | 25.38 | 49.59 |

6 | Arar | 30.96 | 41.06 |

7 | Sakaka | 29.88 | 40.10 |

8 | Tabuk | 28.38 | 36.57 |

9 | Al Jawf | 29.89 | 39.32 |

10 | Riyadh | 24.71 | 46.68 |

11 | Al Qassim | 26.21 | 43.48 |

12 | Hafar Al Batin | 28.38 | 45.96 |

13 | Buraydah | 26.36 | 43.98 |

14 | Al Majma’ah | 25.88 | 45.37 |

15 | Hail | 27.51 | 41.72 |

16 | Jeddah | 21.49 | 39.19 |

17 | Jazan | 16.89 | 42.57 |

18 | Mecca | 21.39 | 39.86 |

19 | Medina | 24.52 | 39.57 |

20 | Taif | 21.28 | 40.42 |

21 | Yanbu | 24.02 | 38.19 |

22 | King Abdullah Economic City | 22.45 | 39.13 |

23 | Najran | 17.57 | 44.23 |

24 | Abha | 18.25 | 42.51 |

25 | Bisha | 19.98 | 42.59 |

26 | Al Sahmah | 20.10 | 54.94 |

27 | Thabhloten | 19.83 | 53.90 |

28 | Ardah | 21.22 | 55.24 |

29 | Shaybah | 22.52 | 54.00 |

30 | Al Kharkhir | 18.87 | 51.13 |

31 | Umm Al Melh | 19.11 | 50.11 |

32 | Ash Shalfa | 21.87 | 49.71 |

33 | Oroug Bani Maradh Wildlife | 19.41 | 45.88 |

34 | Wadi ad Dawasir | 20.49 | 44.86 |

35 | Al Badie Al Shamali | 21.99 | 46.58 |

36 | Howtat Bani Tamim | 23.52 | 46.84 |

37 | Al Duwadimi | 24.50 | 44.39 |

38 | Shaqra | 25.23 | 45.24 |

39 | Afif | 24.02 | 42.95 |

40 | New Muwayh | 22.43 | 41.74 |

41 | Mahd Al Thahab | 23.49 | 40.85 |

42 | Ar Rass | 25.84 | 43.54 |

43 | Uglat Asugour | 25.85 | 42.15 |

44 | Al Henakiyah | 24.93 | 40.54 |

45 | Ar Rawdah | 26.81 | 41.68 |

46 | Asbtar | 26.96 | 40.28 |

47 | Tayma | 27.62 | 38.48 |

48 | Al Khanafah Wildlife Sanctuary | 28.81 | 38.92 |

49 | Madain Saleh | 26.92 | 38.04 |

50 | Altubaiq Natural Reserve | 29.51 | 37.23 |

51 | Hazem Aljalamid | 31.28 | 40.07 |

52 | Turaif | 31.68 | 38.69 |

53 | Al Qurayyat | 31.34 | 37.37 |

54 | Harrat al Harrah Conservation | 30.61 | 39.48 |

55 | Al Uwayqilah | 30.33 | 42.25 |

56 | Rafha | 29.63 | 43.49 |

57 | Khafji | 28.41 | 48.50 |

58 | Unnamed 1 | 21.92 | 51.99 |

59 | Unnamed 2 | 21.03 | 51.16 |

60 | Unnamed 3 | 22.33 | 52.53 |

61 | Unnamed 4 | 23.42 | 50.73 |

62 | Unnamed 5 | 21.28 | 48.03 |

63 | Unnamed 6 | 31.70 | 39.26 |

64 | Unnamed 7 | 32.02 | 39.65 |

65 | Unnmaed 8 | 31.02 | 42.00 |

66 | Unnamed 9 | 30.63 | 41.31 |

67 | Unnamed 10 | 29.78 | 42.68 |

68 | Unnamed 11 | 28.68 | 47.49 |

69 | Unnamed 12 | 28.41 | 47.97 |

70 | Unnamed 13 | 28.05 | 47.53 |

71 | Unnamed 14 | 27.97 | 47.88 |

72 | Unnamed 15 | 27.15 | 48.98 |

73 | Unnamed 16 | 27.21 | 48.56 |

74 | Unnamed 19 | 27.15 | 48.02 |

75 | Unnamed 18 | 27.66 | 48.52 |

76 | Unnamed 19 | 24.74 | 48.95 |

77 | Unnamed 20 | 28.34 | 35.17 |

78 | Unnamed 21 | 26.27 | 36.67 |

79 | Unnamed 22 | 21.89 | 43.06 |

80 | Unnamed 23 | 18.76 | 47.54 |

81 | Unnamed 24 | 21.38 | 53.28 |

82 | Unnamed 25 | 19.24 | 52.79 |

**Table 2.**Maximum annual solar energy sums for the 82 sites in Saudi Arabia for flat-plate solar collectors that are: horizontal (H

_{g,0}), mode (i) static (H

_{g,β,S/ρg}), mode (ii) dynamic (H

_{g,β,t/ρg}), and mode (iii) dynamic (H

_{g,t/ρg}) derived by using a ground albedo of ρ

_{g}, under all-sky conditions in the period 2005–2016. The H

_{g}values are rounded integers in kWhm

^{−2}year

^{−1}.

Site # | H_{g,0} | H_{g,β,S/ρg} | H_{g,β,t/ρg} | H_{g,t/ρg} |
---|---|---|---|---|

1 | 2237 | 2359 | 2846 | 2938 |

2 | 2239 | 2374 | 2873 | 2932 |

3 | 2206 | 2320 | 2782 | 2893 |

4 | 2275 | 2409 | 2925 | 2972 |

5 | 2286 | 2409 | 2925 | 2985 |

6 | 2214 | 2409 | 2993 | 3033 |

7 | 2279 | 2470 | 3081 | 3136 |

8 | 2359 | 2544 | 3173 | 3283 |

9 | 2256 | 2443 | 3022 | 3076 |

10 | 2318 | 2452 | 2991 | 3058 |

11 | 2271 | 2415 | 2955 | 3034 |

12 | 2220 | 2298 | 2804 | 2857 |

13 | 2260 | 2406 | 2944 | 3015 |

14 | 2284 | 2423 | 2953 | 3016 |

15 | 2300 | 2462 | 3035 | 3113 |

16 | 2344 | 2436 | 2917 | 3029 |

17 | 2301 | 2192 | 2767 | 2903 |

18 | 2339 | 2432 | 2909 | 3020 |

19 | 2374 | 3503 | 3021 | 3161 |

20 | 2316 | 2420 | 2931 | 3053 |

21 | 2392 | 2517 | 3053 | 3186 |

22 | 2349 | 2453 | 2940 | 3066 |

23 | 2480 | 2568 | 3128 | 3250 |

24 | 2267 | 2342 | 2803 | 2920 |

25 | 2446 | 2549 | 3086 | 3212 |

26 | 2422 | 2543 | 3109 | 3169 |

27 | 2407 | 2528 | 3103 | 3171 |

28 | 2699 | 2980 | 4078 | 4245 |

29 | 2349 | 2478 | 3043 | 3101 |

30 | 2434 | 2603 | 3314 | 3471 |

31 | 2460 | 2567 | 3132 | 3200 |

32 | 2400 | 2522 | 3069 | 3126 |

33 | 2455 | 2559 | 3131 | 3193 |

34 | 2405 | 2512 | 3062 | 3146 |

35 | 2381 | 2501 | 3050 | 3128 |

36 | 2363 | 2491 | 3046 | 3110 |

37 | 2346 | 2480 | 3028 | 3101 |

38 | 2277 | 2414 | 2956 | 3019 |

39 | 2365 | 2492 | 3025 | 3127 |

40 | 2418 | 2539 | 3091 | 3197 |

41 | 2383 | 2503 | 3037 | 3173 |

42 | 2279 | 2423 | 2967 | 3036 |

43 | 2335 | 2479 | 3033 | 3131 |

44 | 2382 | 2519 | 3076 | 3211 |

45 | 2286 | 2443 | 3008 | 3111 |

46 | 2348 | 2513 | 3111 | 3202 |

47 | 2369 | 2566 | 3228 | 3287 |

48 | 2290 | 2472 | 3058 | 3123 |

49 | 2378 | 2556 | 3181 | 3248 |

50 | 2261 | 2450 | 3056 | 3153 |

51 | 2188 | 2393 | 3004 | 3042 |

52 | 2179 | 2381 | 3692 | 3972 |

53 | 1560 | 1763 | 2365 | 2445 |

54 | 2228 | 2411 | 2980 | 3048 |

55 | 2219 | 2401 | 2964 | 2998 |

56 | 1520 | 1724 | 2324 | 2387 |

57 | 2163 | 2275 | 2696 | 2821 |

58 | 2401 | 2530 | 3100 | 3144 |

59 | 2418 | 2538 | 3097 | 3156 |

60 | 2391 | 2523 | 3091 | 3137 |

61 | 2356 | 2487 | 3042 | 3081 |

62 | 2413 | 2527 | 3069 | 3142 |

63 | 2138 | 2350 | 2892 | 3033 |

64 | 2157 | 2308 | 2926 | 2988 |

65 | 2130 | 2354 | 2913 | 2966 |

66 | 2170 | 2396 | 2922 | 2961 |

67 | 2221 | 2396 | 2978 | 3021 |

68 | 1529 | 1721 | 2553 | 2737 |

69 | 2168 | 2333 | 2827 | 2864 |

70 | 2201 | 2321 | 2833 | 2865 |

71 | 2187 | 2351 | 2821 | 2868 |

72 | 2212 | 2374 | 2859 | 2881 |

73 | 2233 | 2421 | 2863 | 2921 |

74 | 2229 | 2397 | 3067 | 3149 |

75 | 2235 | 2397 | 2945 | 3005 |

76 | 1464 | 1613 | 2159 | 2226 |

77 | 2316 | 2521 | 3002 | 3030 |

78 | 2353 | 2517 | 3125 | 3279 |

79 | 2377 | 2533 | 3086 | 3248 |

80 | 2416 | 2578 | 3078 | 3170 |

81 | 2474 | 2511 | 3170 | 3216 |

82 | 2383 | 2537 | 3051 | 3141 |

**Table 3.**Regression equations for the best-fit curves to the monthly (seasonal) mean H

_{g,t,β/ρg}sums averaged over all 82 sites in the period 2005–2016, together with their R

^{2}values; s is month in the range 1–12; 1 = January,…,12 = December (season in the range 1–4; 1 = spring, 2 = summer, 3 = autumn, 4 = winter).

Time Scale | Regression Equation | R^{2} |
---|---|---|

Months | H_{g,t/ρg} = 0.005$\xb7$s^{6} − 0.186$\xb7$s^{5} + 2.712$\xb7$s^{4} − 19.668$\xb7$s^{3} + 71.696$\xb7$s^{2} − 100.840$\xb7$s +264.580 | 0.96 |

Seasons | H_{g,t/ρg} = 37.983$\xb7$s^{3} − 325.370$\xb7$s^{2} + 780.750$\xb7$s + 318.820 | 1 |

**Table 4.**Increase (in %) in the annual solar energy sums from all 82 sites in Saudi Arabia when using horizontal, mode (i) static, and modes (ii) and (iii) dynamic configurations.

Definition of Ratio | Increase (%) |
---|---|

H_{g,t/ρg}/H_{g,β,t/ρg} (mode (iii)/mode (ii)) ∙ 100 | 4.22 |

H_{g,t/ρg}/H_{g,β,S/ρg} (mode (iii)/mode (i)) ∙ 100 | 28.81 |

H_{g,t/ρg}/H_{g,0} (mode (iii)/horizontal) ∙ 100 | 37.00 |

H_{g,β,t/ρg}/H_{g,β,S/ρg} (mode (ii)/mode (i)) ∙ 100 | 23.60 |

H_{g,β,t/ρg}/H_{g,0} (mode (ii)/horizontal) ∙ 100 | 31.47 |

H_{g,β,S/ρg}/H_{g,0} (mode (i)/horizontal)∙100 | 6.36 |

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**MDPI and ACS Style**

Kambezidis, H.D.; Farahat, A.; Almazroui, M.; Ramadan, E.
Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun. *Appl. Sci.* **2021**, *11*, 11564.
https://doi.org/10.3390/app112311564

**AMA Style**

Kambezidis HD, Farahat A, Almazroui M, Ramadan E.
Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun. *Applied Sciences*. 2021; 11(23):11564.
https://doi.org/10.3390/app112311564

**Chicago/Turabian Style**

Kambezidis, Harry D., Ashraf Farahat, Mansour Almazroui, and Emad Ramadan.
2021. "Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun" *Applied Sciences* 11, no. 23: 11564.
https://doi.org/10.3390/app112311564