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

^{1}

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## Abstract

**:**

^{−2}year

^{−1}and 4078 kWhm

^{−2}year

^{−1}. Finally, a correction factor, introduced in a recent publication, is used; it is confirmed that the relationship between the correction factor and either the tilt angle or the ground-albedo ratio has a general application and it may constitute a nomogram.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

_{b}(in Wm

^{−2}), and diffuse, H

_{d}(in Wm

^{−2}), horizontal solar radiation. These values were downloaded from the PV—Geographical Information System (PV-GIS) tool [10] using the latest Surface Solar Radiation Data Set—Heliostat (SARAH) 2005–2016 data base (12 years) [11,12]. The PV-GIS provides solar radiation data for any location in Europe, Africa, Middle East including Saudi Arabia, central and southeast Asia and most parts of the Americas. Solar radiation in the PV-GIS platform is calculated from satellite observations and modelling [13,14].

_{b}and H

_{d}were downloaded from PV-GIS for all 82 sites; Table 1 shows the names and provides the geographical coordinates of these sites, while Figure 1 is a map of Saudi Arabia showing their location. The criterion for selecting these sites is mentioned in [1].

#### 2.2. Data Processing and Analysis

_{g}(in Wm

^{−2}), values were estimated as the sum H

_{g}= H

_{b}+ H

_{d}.

^{−}

^{2}, (ii) corresponded to γ ≥ 5°, and (iii) H

_{d}≤ H

_{g}.

_{g,t,β}(in Wm

^{−2}), there was adopted the isotropic model of Liu-Jordan (L-J) [18] (the subscript t stands for ‘tracking’, and β is the tilt angle of the inclined plane with respect to the local horizon, in degrees). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, H

_{r,t,β}(in Wm

^{−2}), received on the inclined flat-plate surface. The L-J model has proved to be as efficient as other more sophisticated models in providing the tilted total solar radiation in many parts of the world [19]. For a Sun-tracking surface mounted on a vertical axis the received total solar radiation is given by a slight modification of Equation (1) in [1]

_{g,t,β}= H

_{b,t,β}+ H

_{d,t,β}+ H

_{r,t,β},

_{d,t,β}= H

_{d}·R

_{di},

_{r,t,β}= H

_{g}·R

_{r}·ρ

_{g0}, (or ρ

_{g})

_{di}= (1 + cosβ)/2,

_{r}= (1 − cosβ)/2,

_{b,tβ}= H

_{b}·cosθ/sinγ,

_{di}and R

_{r}are called 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)), which is considered as reference in solar radiation modelling, although it refers to grassland areas [19]. Also, close-to-reality ground-albedo values, ρ

_{g}, were used in this work. To retrieve such values for the 82 sites, use of the Giovanni portal [20] was made (details in [1]). Annual mean ρ

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

_{g,t,β}.

_{g,t,β}were estimated from Equation (1) for both ρ

_{g0}= 0.2 and ρ

_{g}. From the hourly H

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

^{−2}) under all-sky conditions were estimated for 82 sites, 11 tilt angles, and 2 ground-albedo values.

## 3. Results

#### 3.1. Annual Energy Sumss

_{g0}and ρ

_{g}in Equations (1)–(7). From the calculated annual energy sums, the maximum sum and its corresponding (optimum) tilt angle were then obtained. Table 2 shows these maximum annual H

_{g,t,opt. β}sums for all sites with the corresponding optimum tilts, opt. β (columns 2 and 3 for ρ

_{g0}and ρ

_{g}, respectively). From this table, it is seen that the average H

_{g,t,opt. β}/ρ

_{g0}(column 2) is 2745.5 kWhm

^{−2}, while the average H

_{g,t,opt. β}/ρ

_{g}(column 3) is 2769.7 kWhm

^{−2}, i.e., a 0.9% increase. Because of this small difference, the annual maximum solar energy sums from calculations with ρ

_{g}were only considered in this study, as done in [1]. The reason for using both ground-albedo values was to show the difference in the derived maximum annual energy sums (columns 2, and 3 in Table 2). Therefore, it is interesting to see how the annual energy sums for the opt. β-derived values under the ρ

_{g}calculations (H

_{g,t,opt. β/ρg}) are distributed across the 82 sites in Saudi Arabia. Figure 2 shows this spatial coverage of the country. Surprisingly no consistent pattern in terms of opt. β exists; to the contrary, there is a great mix of opt. β in the country, which does not seem to follow any particular logic. This may be attributed to intrinsic errors when deriving the solar horizontal radiation values in the PV-GIS tool. Therefore, such a distribution has no practical value to the solar energy industry as no clear application zones are formed as energy-application guidelines (as in the case of southward-oriented solar collectors in [1]) and may simply create confusion about the selection of the most appropriate tilt angle for the installation of a solar system at any particular location in Saudi Arabia. This unexpected outcome led to the idea of an ‘innocent manipulation’ of the opt. β values. This manipulation was based on the adoption of the three solar energy zones (SEZ) defined in [1]. This means that at a site for which the methodology has selected a ‘wrong’ opt. β, a manual selection of the ‘correct’ tilt (according to the SEZ where the site itself belongs to) was made. Then, the corresponding annual solar energy sum was obtained. This is shown in the fourth column of Table 2, which provides the correct distribution of the 82 sites along the 3 SEZs (SEZ-A with selected opt. β = 40°, SEZ-B with selected opt. β = 45° and SEZ-C with selected opt. β = 50°). The corrected distribution is shown in Figure 3, which coincides with that of Figure 4 in [1]. After this correction, one would like to see what the created solar energy-sum differences are; Figure 4 shows these differences across all 82 sites. These energy differences, ΔH

_{g,t,β/ρg}, are defined as: ΔH

_{g,t,β/ρg}= H

_{g,t,opt. β/ρg}− H

_{g,t,selected opt. β/ρg}. From Figure 4a, it is seen that most of the sites 1–43 do not produce large differences, while the sites 44–82 result in annual energy deficits as low as −55 kWhm

^{−}

^{2}year

^{−1}. The mean annual solar energy sums for all sites 1–43 and 44–82 are 3026.3 kWhm

^{−}

^{2}year

^{−1}and 2954.7 kWhm

^{−}

^{2}year

^{−1}, respectively, while their corresponding mean differences are −4.4 kWhm

^{−}

^{2}year

^{−1}and −5.7 kWhm

^{−}

^{2}year

^{−1}. This means that in the first group of sites, the absolute error derived from the manual selection of the optimum tilt angles is 0.15% (100 × 4.4/3026.3) while the error for the second group 0.19% (100 × 5.7/2954.7), both being quite insignificant. Therefore, the new distribution of the 82 sites in Figure 3 does not influence the solar energy yield across Saudi Arabia.

_{g,t,β/ρg}refers to the selected optimal β, i.e., to H

_{g,t,selected opt. β/ρg}.

#### 3.2. Monthly Energy Sums

_{g,t,β/ρg}in each specific SEZ region is shown in Figure 5. Figure 5a refers to all sites in SEZ-A with optimal β = 40°, Figure 5b to all sites in SEZ-B with optimal β = 45°, Figure 5c to the sites in SEZ-C with optimal β = 50°, and Figure 5d to all sites irrespective of SEZ and optimal β. The expressions for the lines that best fit the means and their coefficient of determination, R

^{2}, are given in Table 3. It is seen that the R

^{2}statistic obtains high values; this allows a solar energy user or investor in Saudi Arabia to estimate the monthly energy production in any of the three SEZs in an accurate way by applying the regression equations. The graphs also contain curves for the mean ± 1 standard deviation (σ). It is apparent in all graphs (and especially in those that refer to SEZ-A and SEZ-B) that two secondary H

_{g,t,β}maxima in March and October exist. These occur because of the variation of the solar elevation (or altitude, γ) throughout the year at a certain time during the day. To demonstrate this, Figure 6 shows the variation of H

_{g,t,40}during 2005–2016 at three sites in Saudi Arabia at high, mid and low latitudes, i.e., Arar (#6, 30.96 degN), Jeddah (#16, 21.49 degN), and Jazan (#17, 16.89 degN). Jazan has two energy maxima, one in April and another in October; Jeddah has two, one in March and another in October, while Arar shows a normal behaviour (maximum energy in July).

#### 3.3. Seasonal Energy Sums

^{2}= 1) in all cases.

#### 3.4. Maps of Annual Energy Sums

_{g}and H

_{g,t,β/ρg}sums. A gradual increase in the annual solar potential in the direction NE–SW for both horizontal and optimally-inclined flat planes is observed. Very similar patterns to those in the present study are given in the Solar Radiation Atlas for Saudi Arabia [23]. Farahat et al. [1] have come to similar conclusion as regards the maximum solar energy received by flat-plate collectors oriented to south with optimum inclination. They justified this observation by the latitude gradient of the sites and the variability in meteorology across the country from north to south [24].

#### 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 for the period 2005–2011. Figure 9 presents this comparison, which shows an excellent agreement (R

^{2}= 0.99). Nevertheless, the PV-GIS-estimated values seem to overestimate the measured H

_{g}ones by +10%, a figure that is within the range in the above-mentioned studies, i.e., from −14% to +11%. Therefore, the PV-GIS data were accepted for use in the present study.

#### 3.6. Correction Factor

_{g,t,β/ρg}/H

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

_{g,t,β}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 meaning of the CF is that it corrects the energy on an inclined surface under the influence of a ground albedo equal to 0.2 to that which is under the influence of the near-real ground-albedo value. Figure 10 presents the variation of CF as function of β for all 82 sites; the controlling parameter is the ratio ρ

_{r}= ρ

_{g}/ρ

_{g0}. Note that the higher the ρ

_{r}value is (i.e., for ρ

_{g}> ρ

_{0}), the more concave the best-fit curve is; in contrast, the lower the ρ

_{r}value is (i.e., for ρ

_{g}< ρ

_{0}), the more convex the best-fit curve becomes. In the exceptional case of ρ

_{g}= ρ

_{0}(as for site #24), CF = 1. All the data points at every β in Figure 10 correspond to the 82 sites. Figure 11 shows the distribution of the ρ

_{r}values across the 82 sites.

_{r}is shown in Figure 12, where a linear relationship exists along all sites at the same β. The controlling parameter in this case is β; as β increases, so does the slope of the linear fit to the data points. The data points along each line correspond to the 82 sites.

_{g,t,β/ρg}/H

_{g,t,β/ρg0}were calculated for all βs in the range 5°–55° and all sites belonging to the same SEZ, as well as all sites irrespective of SEZ. The results are shown in Figure 13. It is clearly seen that all mean CF values have an increasing trend with increasing β, because a flat-plate tilted surface receives more reflected radiation from its surroundings as its tilt angle increases. Moreover, the standard deviation, σ, of the mean CF increases with β, because H

_{g,t,β}increases with increasing β, a fact that produces larger dispersion of the annual solar energy across all sites. In contrast, σ becomes smaller in the transition from SEZ-A to SEZ-C sites, a result that comes from the combination of the multitude of sites in each SEZ and the dispersion of the individual H

_{g,t,β}values in the SEZ as shown by R

^{2}in Table 3 (decreasing dispersion by increasing R

^{2}from SEZ-A to SEZ-C). Note that the majority of the sites lies in SEZ-B (28 sites in SEZ-A, 40 in SEZ-B, and 14 in SEZ-C). Table 4 gives the regression equations for the curves that best fit the data points in each SEZ and all SEZs, too. These regression relationships have the same shape as those of the sites in Figure 10. This occurs because few sites have ρ

_{r}< 1, and, therefore, the average of the CF across all sites in the same SEZ, or all SEZs, gives a relationship resembling a site with ρ

_{r}> 1.

## 4. Conclusions and Discussion

^{−2}year

^{−1}(average 3044.9 kWhm

^{−2}year

^{−1}in SEZ-A), 2159–4078 kWhm

^{−2}year

^{−1}(average 2975.6 kWhm

^{−2}year

^{−1}in SEZ-B), 2324–3692 kWhm

^{−2}year

^{−1}(average 2932.5 kWhm

^{−2}year

^{−1}in SEZ-C), and 2159–4078 kWhm

^{−2}year

^{−1}(average 2991.9 kWhm

^{−2}year

^{−1}in all SEZs). In relation to fixed-tilt solar systems reported in [1], the one-vertical axis solar systems in Saudi Arabia show an average increase in the maximum annual solar energy yield of +21.8% for SEZ-A, +22.6% for SEZ-B, +31.2% for SEZ-C, and +23.5% for all SEZs. Beside the annual energy sums, monthly solar energy values averaged over all locations belonging to the same SEZ as well as to all SEZs were estimated under all-sky conditions. Regression equations were provided as best-fit curves to the monthly mean energy sums that estimate the solar energy potential per SEZ (and all SEZs) with great accuracy (R

^{2}≥ 0.82). These expressions 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 collectors throughout the year.

^{2}= 1). Maximum sums were found in the summer (836.6 kWm

^{−2}), and minimum ones in the winter (664.1 kWm

^{−2}), as expected. The corresponding figures for the maximum energy received on a flat-plate solar collector in Saudi Arabia having an optimum tilt angle towards south are 659.9 kWm

^{−2}and 532.3 kWm

^{−2}, respectively for summer and winter [1]. Therefore, the single-axis solar systems provide a high increase in the maximum seasonal energy yield in comparison to the static ones of +26.8% and +24.8%, respectively.

_{r}= ρ

_{g}/ρ

_{0}> 1, or exponential decay in the cases of ρ

_{r}< 1. Such curves are assumed to be universal (i.e., representable as nomograms), since similar graphs in [1] had the same shape. Nevertheless, this universality remains to be confirmed at other locations in the world with different climate and terrain characteristics. A graph of CF as a function of ρ

_{r}was prepared for different values of the tilt angle in the range 5°–55°. Best-fit curves to the data points were estimated and were found to be linear, with decreasing slopes in proportion to decreasing tilt angles. These curves are also assumed to be nomograms, since similar graphs in [1] had the same shape. Nevertheless, this kind of nomogram has to be confirmed at other sites worldwide with different climate and terrain characteristics.

_{r}were derived for this case, too.

^{−1}) for the two systems at five sites (two in Spain, one in Saudi Arabia, one in Brazil, and one in the USA) and found it varying according to site and type of the PV system. Overall, the LCOE for the single-axis PV system is a little bit higher than that for a fixed-tilt one. Nevertheless, the difference is not big and varies as +4.4%, 0%, 0%, +8.6%, and +1% for the five sites, respectively. Another study [27] concluded that the amount of electricity generation by a single-axis PV system in the USA is about 12–25% higher than that for a fixed-tilt one. A study for Jordan [28] showed that a dual-axis PV system generates 31.29% more annual electricity than a fixed-tilt one. For Europe, it has been found [29] that a single-axis PV system produces an annual energy yield of 30% higher in southern, and 25% in central Europe and up to 50% in northern Scandinavia.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Correction Statement

## References

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**Figure 2.**Distribution of the 82 selected sites in Saudi Arabia for maximum H

_{g,t,opt. β/ρg}. The numbers in the circles refer to those in column 1 of Table 1. The red circles correspond to sites with opt. β = 40°, the orange with opt. β = 45°, and the green ones with opt. β = 50°.

**Figure 3.**Corrected distribution of the 82 selected sites in Saudi Arabia for maximum H

_{g,t,opt. β/ρg}. The numbers in the circles refer to those in column 1 of Table 1. The red circles correspond to sites with selected opt. β = 40° (SEZ-A), the orange with selected opt. β = 45° (SEZ-B), and the green ones with selected opt. β = 50° (SEZ-C). This figure is a reproduction of Figure 4 in [1].

**Figure 4.**Differences of the annual maximum solar energy sums, ΔH

_{g,t,β/ρg}, on flat planes between optimally-derived and selected tilt angles for sites (

**a**) 1–43 and (

**b**) 44–82, under all-sky conditions and averaged over the period 2005–2016. ΔH

_{g,t,β/ρg}= H

_{g,t,opt. β/ρg}− H

_{g,t,selected opt. β/ρg}, where t refers to the tracking mode. The individual H

_{g,t,β/ρg}values in the differences are shown in Table 2 (columns 3 and 4, respectively) together with their optimal β.

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

**a**) H

_{g,t,40/ρg}in SEZ-A, (

**b**) H

_{g,t,45/ρg}in SEZ-B, (

**c**) H

_{g,t,50/ρg}in SEZ-C, and (

**d**) H

_{g,t,β/ρg}in all SEZs, under all-sky conditions and averaged over the period 2005–2016. The black solid lines represent the monthly H

_{g}sums averaged over all corresponding sites. The red lines correspond to the mean + 1σ curves, and the blue lines to the mean − 1σ curves. The green dotted lines refer to the best-fit curves to the mean ones.

**Figure 6.**Intra-annual variation of the solar energy sum on a 40°-tilted plane, H

_{g,t,40/ρg}, at the sites of Arar (#6 in Table 1), Jeddah (#16), and Jazan (#17). The values of H

_{g,t,40/ρg}are averages over each month in the period 2005–2016 at 13.00 LST. The name and the geographical latitude of each site are shown in the legend.

**Figure 7.**Seasonal variation of (

**a**) H

_{g,t,40/ρg}in SEZ-A, (

**b**) H

_{g,t,45/ρg}in SEZ-B, (

**c**) H

_{g,t,50/ρg}in SEZ-C, and (

**d**) H

_{g,t,β/ρg}in all SEZs. The black lines represent the seasonal mean. The red lines refer to the mean + 1σ curves, and the blue ones to the mean—1σ curves, under all-sky conditions and averaged over the period 2005–2016. The green dotted lines refer to the best-fit curves to the mean ones. The numbers 1–4 in the x-axis refer to the seasons in the sequence spring to winter.

**Figure 8.**Distribution of the annual (

**a**) H

_{g}(kWhm

^{−2}year

^{−1}) and (

**b**) H

_{g,t,β/ρg}(kWhm

^{−2}year

^{−1}) sums over Saudi Arabia, under all-sky conditions and averaged over the period 2005–2016. The different colouring in the H

_{g}levels is due to the different colour scales used. Figure 8a is reproduction of Figure 7a in [1].

**Figure 9.**Comparison of monthly mean H

_{g}values from PV-GIS to measured H

_{g}values at 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 H

_{g,ASNOA}+ 14.96 (R

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

**Figure 10.**Variation of the correction factor, CF, as function of the tilt angle of the inclined flat plane, β, under all-sky conditions and averaged over the period 2005–2016. The dotted lines are the best-fit curves to the data points for each site, expressed as 3rd-order polynomials. The blue horizontal line indicates CF = 1.

**Figure 11.**Annual mean ratios of ground albedo, ρ

_{r}, for the 82 sites in Saudi Arabia; (

**a**) sites 1–43, (

**b**) sites 44–82, averaged over the period 2005–2016. The site #24 has ρ

_{r}= 1, because its ρ

_{g}= ρ

_{g0}= 0.2.

**Figure 12.**Variation of the correction factor, CF, as function of the ground-albedo ratio, ρ

_{r}, for various tilt angles, β, for a flat plane tracking the Sun in Saudi Arabia, averaged over the period 2005–2016. The blue lines correspond to CF = ρ

_{r}= 1. Notice that the datum point (1,1) is the site of Arar (#24), as expected. The black dotted lines are the best fits to the CFs of all sites having the same tilt angle.

**Figure 13.**Variation of the correction factor, CF, as function of the tilt angle, β, for an inclined surface in (

**a**) SEZ-A, (

**b**) SEZ-B, (

**c**) SEZ-C, and (

**d**) all SEZs, averaged over the period 2005–2016. The black solid lines are the mean CF values, while the red and blue ones correspond to the mean + 1σ, and mean − 1σ, respectively. The green dotted lines are the best fits to the mean curves and can hardly be distinguished as they coincide with the mean curves.

**Table 1.**The 82 sites selected over Saudi Arabia to cover the whole territory of the country; φ is the geographical latitude, and λ the geographical longitude in the WGS84 geodetic system. This table is reproduction of Table 1 in [1].

# | 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 H

_{g,t,β}annual sums for the 82 sites in Saudi Arabia for optimal tilt angles, opt. β, with reference albedo ρ

_{g0}and a near-real albedo ρ

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

_{g}values are rounded integers.

Site # | H_{g,t,}_{β}_{/}_{ρ}_{g0} (kWhm^{−2}Year^{−1})/Optimum β (Degrees) | H_{g,t,β/ρg} (kWhm^{−2}Year^{−1})/Optimum β (Degrees) | H_{g,t,}_{β}_{/}_{ρ}_{g} (kWhm^{−2}Year^{−1})/Selected Optimum β (Degrees) |
---|---|---|---|

1 | 2826/45 | 2846/45 | 2846/45 |

2 | 2824/45 | 2873/45 | 2873/45 |

3 | 2785/45 | 2782/40 | 2782/45 |

4 | 2862/40 | 2925/45 | 2925/45 |

5 | 2872/40 | 2925/45 | 2925/45 |

6 | 2921/45 | 2993/50 | 2993/50 |

7 | 3015/45 | 3081/50 | 3081/50 |

8 | 3149/45 | 3173/45 | 3173/45 |

9 | 2963/45 | 3022/50 | 3022/50 |

10 | 2937/45 | 2991/45 | 2991/45 |

11 | 2915/45 | 2955/45 | 2955/45 |

12 | 2748/45 | 2804/45 | 2804/45 |

13 | 2897/45 | 2944/45 | 2944/45 |

14 | 2900/45 | 2953/45 | 2953/45 |

15 | 2991/45 | 3035/45 | 3035/45 |

16 | 2912/40 | 2918/40 | 2917/40 |

17 | 2794/40 | 2767/35 | 2767/40 |

18 | 2903/40 | 2909/40 | 2909/40 |

19 | 3035/45 | 3021/40 | 3021/40 |

20 | 2926/40 | 2931/45 | 2931/40 |

21 | 3058/45 | 3054/45 | 3053/40 |

22 | 2946/40 | 2940/40 | 2940/40 |

23 | 3111/40 | 3129/45 | 3128/40 |

24 | 2803/40 | 2803/40 | 2803/40 |

25 | 3078/40 | 3086/40 | 3086/40 |

26 | 3041/40 | 3123/45 | 3109/40 |

27 | 3039/40 | 3118/45 | 3103/40 |

28 | 4013/50 | 4115/55 | 4078/45 |

29 | 2974/45 | 3043/45 | 3043/45 |

30 | 3268/45 | 3360/50 | 3314/40 |

31 | 3069/40 | 3144/45 | 3132/40 |

32 | 3002/40 | 3083/45 | 3069/40 |

33 | 3062/40 | 3144/45 | 3131/40 |

34 | 3017/40 | 3070/45 | 3062/40 |

35 | 2999/40 | 3061/45 | 3050/40 |

36 | 2984/40 | 3046/45 | 3046/45 |

37 | 2976/45 | 3028/45 | 3028/45 |

38 | 2899/45 | 2956/45 | 2956/45 |

39 | 3001/45 | 3032/45 | 3025/40 |

40 | 3065/45 | 3097/45 | 3091/40 |

41 | 3041/45 | 3038/45 | 3037/40 |

42 | 2917/45 | 2967/45 | 2967/45 |

43 | 3005/45 | 3033/45 | 3033/45 |

44 | 3078/45 | 3082/45 | 3076/40 |

45 | 2984/45 | 3008/45 | 3008/45 |

46 | 3073/45 | 3111/45 | 3111/45 |

47 | 3149/45 | 3239/50 | 3228/45 |

48 | 3004/45 | 3060/50 | 3058/45 |

49 | 3118/45 | 3183/50 | 3181/45 |

50 | 3027/45 | 3058/50 | 3056/45 |

51 | 2926/45 | 3004/50 | 3004/50 |

52 | 3666/55 | 3731/55 | 3692/50 |

53 | 2332/50 | 2365/50 | 2365/50 |

54 | 2936/45 | 2980/50 | 2980/50 |

55 | 2891/45 | 2964/50 | 2964/50 |

56 | 2272/50 | 2325/55 | 2324/50 |

57 | 2721/45 | 2700/40 | 2696/45 |

58 | 3018/40 | 3100/45 | 3100/45 |

59 | 3029/40 | 3111/45 | 3097/40 |

60 | 3011/40 | 3091/45 | 3091/45 |

61 | 2961/40 | 3042/45 | 3042/45 |

62 | 3015/40 | 3079/45 | 3069/40 |

63 | 2841/45 | 2892/50 | 2892/50 |

64 | 2877/45 | 2926/50 | 2926/50 |

65 | 2845/45 | 2913/50 | 2913/50 |

66 | 2852/45 | 2922/50 | 2922/50 |

67 | 2908/45 | 2978/50 | 2978/50 |

68 | 2546/55 | 2608/55 | 2553/45 |

69 | 2760/45 | 2827/50 | 2827/45 |

70 | 2763/40 | 2833/45 | 2833/45 |

71 | 2764/45 | 2821/45 | 2821/45 |

72 | 2779/40 | 2859/50 | 2859/45 |

73 | 2817/45 | 2863/45 | 2863/45 |

74 | 2995/45 | 3082/50 | 3067/45 |

75 | 2883/45 | 2947/50 | 2945/45 |

76 | 2113/50 | 2171/50 | 2159/45 |

77 | 2914/40 | 3002/50 | 3002/45 |

78 | 3145/45 | 3138/45 | 3125/40 |

79 | 3114/45 | 3086/45 | 3086/40 |

80 | 3041/40 | 3085/45 | 3078/40 |

81 | 3084/40 | 3170/45 | 3170/45 |

82 | 2988/45 | 3076/50 | 3051/40 |

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

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

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

SEZ | Regression Equation | R^{2} |
---|---|---|

A (months) A (seasons) | H_{g,t,40/ρg} = 0.0054 s^{6} − 0.218 s^{5} + 3.4241 s^{4} − 25.977 s^{3} + 95.627 s^{2} − 142.65 s +296.38H _{g,t,40/ρg} = −2.0956 s^{3} − 0.5587 s^{2} + 10.341 s + 787.81 | 0.82 1 |

B (months) B (seasons) | H_{g,t,45/ρg} = 0.0049 s^{6} − 0.1809 s^{5} + 2.5754 s^{4} − 18.215 s^{3} + 65.134 s^{2} − 90.585 s +248.07H _{g,t,45/ρg} = 44.915 s^{3} − 367.88 s^{2} + 870.06 s + 216.23 | 0.94 1 |

C (months) C (seasons) | H_{g,t,50/ρg} = 0.0051 s^{6} − 0.1867 s^{5} + 2.6857 s^{4} − 19.7280 s^{3} + 74.6630 s^{2} − 106.5200 s +235.9800H _{g,t,50/ρg} = 74.807 s^{3} − 627.99 s^{2} + 1499.1 s − 174.91 | 0.98 1 |

A,B,C (months) A,B,C (seasons) | H_{g,t,β/ρg} = 0.0051 s^{6} − 0.1955 s^{5} + 2.9007 s^{4} − 21.259 s^{3} + 77.717 s^{2} − 112.08 s +263.4H _{g,t,β/ρg} = 33.967 s^{3} − 286.87 s^{2} + 683.91 s + 344.56 | 0.94 1 |

**Table 4.**Regression equations for the best-fit curves to the CF–β data points averaged over all respective sites in the period 2005–2016, together with their R

^{2}values, for SEZ-A, SEZ-B, SEZ-C, and all SEZs.

β (SEZ) | Regression Equation | R^{2} |
---|---|---|

40° (A) | CF = 8.0863 × 10^{−9} β^{3} + 4.1615 × 10^{−6} β^{2} + 3.9379 × 10^{−5} β + 0.9998 | 1 |

45° (B) | CF = 1.1413 × 10^{−8} β^{3} + 7.0911 × 10^{−6} β^{2} + 7.0532 × 10^{−5} β + 0.9997 | 1 |

50° (C) | CF = 2.0347 × 10^{−8} β^{3} + 6.4319 × 10^{−6} β^{2} + 9.3106 × 10^{−5} β + 0.9996 | 1 |

40°,45°,50° (A,B,C) | CF = 1.1802 × 10^{−8} β^{3} + 5.9782 × 10^{−6} β^{2} + 6.4260 × 10^{−5} β + 0.9997 | 1 |

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**MDPI and ACS Style**

Farahat, A.; Kambezidis, H.D.; Almazroui, M.; Al Otaibi, M.
Solar Potential in Saudi Arabia for Inclined Flat-Plate Surfaces of Constant Tilt Tracking the Sun. *Appl. Sci.* **2021**, *11*, 7105.
https://doi.org/10.3390/app11157105

**AMA Style**

Farahat A, Kambezidis HD, Almazroui M, Al Otaibi M.
Solar Potential in Saudi Arabia for Inclined Flat-Plate Surfaces of Constant Tilt Tracking the Sun. *Applied Sciences*. 2021; 11(15):7105.
https://doi.org/10.3390/app11157105

**Chicago/Turabian Style**

Farahat, Ashraf, Harry D. Kambezidis, Mansour Almazroui, and Mohammed Al Otaibi.
2021. "Solar Potential in Saudi Arabia for Inclined Flat-Plate Surfaces of Constant Tilt Tracking the Sun" *Applied Sciences* 11, no. 15: 7105.
https://doi.org/10.3390/app11157105