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The value of the global solar radiation GSR reaching the earth is very important because it is an essential variable for different applications. Unfortunately, solar radiation measurements are not available, most of the time, in developing countries because of the lack of measurement means. Moreover, these measurements are difficult to obtain under complicated weather conditions. Thus, solar radiation evaluation models are used. In this study, a new semiempirical model for the estimation and prediction of the global solar radiation of Souk Ahras area in Algeria is proposed. The model developed is based on meteorological data such as daily hourly temperatures and average relative humidity required from several stations and databases, over a period of four years. The values of the regression coefficients a, b and c calculated are 0.0142, 10.6206 and 57.8367 respectively. To set the modal valid, we have applied it to 10 Algerian cities and we calculated the H/H0 ratio for each site from our model. They have been then compared with the values from the (CDER). We can conclude that our new model gives a good estimate of the average daily global solar radiation (H) for the studied regions (error between 2.49% and 8.93%) and can also be used elsewhere in areas with the same climatic conditions.
solar energy, global solar irradiance, modeling, prediction
In Algeria, energy needs are totally dependent on fossil fuels. The entire economy of the country is based on the export of these products. Unfortunately, with the fall in oil prices in recent years and the tear sounded by scientists and world leaders (Paris agreement) for the protection of the environment and climate from the adverse effects of excessive use of energy conventional. Our country is forced to move towards other energy alternatives such as the use of renewable energies.
As a reaction and a contribution to the world policy for the preservation of the environment, the Algerian government has proposed several strategies for the reduction of the greenhouse effect. Hereby, we can clearly mention the Horizon 2030 project [1] that is all based on the partial substitution (total in the long term) of fossil energy by renewable energies, in particular solar energy given the enormous deposit that Algeria possesses. Several attractive projects have been set up and investors have been encouraged to invest in the technological promotion of renewable energies, for example the project SOLAR [2].
Therefore, information about local solar radiation is considered necessary and important for many applications, including architectural designs and solar energy systems. However, in many developing countries, data on solar energy, unfortunately, are not always available due to the lack of station measuring the parameters of incident solar radiation because of the cost of measuring equipment and their maintenance. Therefore, methods must be devised to estimate solar radiation. Based on meteorological data, many experimental models have been developed to calculate global solar radiation GSR using different climates (Figure 1). Parameters include extraterrestrial radiation, sunshine hours, average temperature, relative humidity, altitude, longitude, latitude, clouds and radiation, which are measured.
Figure 1. Global solar radiation by EUMETSAT 2019
Solar energy is one of the most important forms of renewable energy, which has become the center of interest of several countries in the world because of its enormous potential especially in the countries of the southern hemisphere as for the 'Algeria. In addition to being clean energy that does not pollute the environment, it is free and accessible to everyone. The aim of this research is to develop a modern method for calculating the amount of total radiation received every hour from sunrise to sunset based on a numerical calculation using mathematical relationships on a horizontal surface located in the Souk Ahras area, which is a city located in the extreme north east of the country, on the Tunisian border, its area is 812 km^{2}. Its location is as follows:
Geographical coordinates [3]:
 Latitude 36° 17′ 15″ north,
 Longitude 7° 57′ 15″ east,
 Altitude 653 m.
The climate of Souk Ahras is a Mediterranean hotsummer climate according to the KöppenGeiger (Csa) classification [4].
Figure 2. Solar of radiation components
The method used in our work, to calculate the global solar radiation, depends on a set of factors related to the geographical area of the place studied such as the angle of longitude, the width, the altitude, the relative humidity and the temperature.
The intensity of the external solar radiation decreases as it passes through the Earth’s atmosphere [5]. The reason for the decrease in the intensity of the external solar radiation in the sixth month is the fact that the Earth is located at the aphelion point relative to the Sun, which is the farthest point of the Earth from the Sun, or its height in the first and twelfth months, due to the fact that the Earth is located in Perigee, which is the closest point to the sun and reaches the Earth, three types of solar radiation represent 50% of solar radiation.
It is the rays that reach directly from the sun to the earth, and it represents a large percentage on sunny days, about 27% [6]. On cloudy days, the sun is almost nonexistent radiation, when the scattered solar radiation is the majority in this case [7].
This radiation comes from different parts of the sky due to the presence of clouds, water vapor, the ozone layer. The amount of this radiation is 10% in this case when the sky is clear and 100% when the sky is cloudy [7, 8].
The amount of radiation reflected from the ground and reaching the surface of the solar panels depends on the ground reflection, which is known as albedo. The Albedo (reflectivity) is the energy reflection factor of a surface subjected to solar radiation. This coefficient is dimensionless and represents the ability of a surface to reflect solar radiation. A= Reflected solar flux / incident solar flux, and its value ranges between 0.2 for the usual case and 0.7 when there is snow, and this amount constitutes 13% of the total incoming solar radiation [7, 8]. The Figure 2 shows the types of solar radiation connecting to a tilted solar panel roof.
In general, the amount and intensity of solar radiation are affected by all the previous types by several factors, including: the state of the sky in terms of its clarity and in the case of clouds, the four seasons, the height above sea level, the position of the sun in the sky, the angle of inclination of the sun and the thickness of the atmosphere in addition to the solar angles.
The Site and Data source SoukAhras city
Description of the site and data source Souk Ahras is a semicontinental and humid region located in eastern Algeria, about 640 km east of the capital (Figure 3). The measured data on solar radiation used in this study were collected over a period of 4 years (20172020) by a radiometric station of the Renewable Energy Development Center presented in (Figure 4) with high resolution, installed on the roof of the solar radiation laboratory, based on the weather conditions of the day which are described by several parameters, namely: pressure, temperature, humidity, wind direction and speed, precipitation, cloudy conditions and fog, etc., at the surface and at altitude of the given location in addition to measurements of global solar radiation (GSR) on horizontal surface, solar direct normal irradiance (DNI) and diffuse solar radiation (DSR) on the horizontal plane.
N° 
Name of Model 
Analytic Model 
N° 
Name of Model 
Analytic Model 
01 
Glover and McCulloch (1958) [9] 
$\frac{H}{H_{0}}=0.29 \cos \emptyset+0.52 \frac{S}{S_{0}}$ 
02 
Page (1961) [10] 
$\frac{H}{H_{0}}=0.23+0.48\left(\frac{S}{S_{0}}\right)$ 
03 
Swartman and Ogunlade (1967) [11] 
$\frac{H}{H_{0}}=a+b\left(\frac{S}{S_{0}}\right)+c(R H)$  04 
Iqbal (1979) [12] 
$\frac{H_{d}}{H}=0.7910.635\left(\frac{S}{S_{0}}\right)$ $\frac{H_{d}}{H}=0.1630.478\left(\frac{S}{S_{0}}\right)0.655\left(\frac{S}{S_{0}}\right)^{2}$ 
05 
Kholagi et al. (1983) [13] 
$\frac{H}{H_{0}}=0.191+0.571\left(\frac{S}{S_{0}}\right)$ $\frac{H}{H_{0}}=0.297+0.432\left(\frac{S}{S_{0}}\right)$ $\frac{H}{H_{0}}=0.262+0.454\left(\frac{S}{S_{0}}\right)$ 
06  Benson et al. (1984) [14]  $\frac{H}{H_{0}}=0.18+0.60\left(\frac{S}{S_{0}}\right)$ for Jan, Mar and Oct $\frac{H}{H_{0}}=0.24+0.53\left(\frac{S}{S_{0}}\right)$ for Apr and Sep 
07 
Ogelman et al. (1984) [15] 
$\frac{H}{H_{0}}=0.1950.676\left(\frac{S}{S_{0}}\right)0.142\left(\frac{S}{S_{0}}\right)^{2}$  08 
Bahel et al. (1986) [16] 
$\frac{H}{H_{0}}=0.175+0.552\left(\frac{S}{S_{0}}\right)$ 
09 
Bahel et al. (1987) [17] 
$\frac{H}{H_{0}}=0.160.87\left(\frac{S}{S_{0}}\right)0.61\left(\frac{S}{S_{0}}\right)^{2}$ $+0.34\left(\frac{S}{S_{0}}\right)^{3}$ 
10 
Gopinathan (1988) [18] 
$\frac{H}{H_{0}}=(0.309+0.539 \cos \emptyset0.0693 Z+$$\left.0.290\left(\frac{S}{S_{0}}\right)\right)+(1.5271.027 \cos \emptyset+$$\left.0.0926 Z0.359\left(\frac{S}{S_{0}}\right)\right)\left(\frac{S}{S_{0}}\right)$ 
11 
Newland (1989) [19] 
$\frac{H}{H_{0}}=0.34+0.40\left(\frac{S}{S_{0}}\right)+0.17 \log \left(\frac{S}{S_{0}}\right)$  12 
Alsaad (1990) [20] 
$\frac{H}{H_{0}}=0.174+0.615\left(\frac{S}{S_{0}}\right)$ 
13 
Akinoğlu and Ecevit (1990) [21] 
$\frac{H}{H_{0}}=0.1450.845\left(\frac{S}{S_{0}}\right)0.280\left(\frac{S}{S_{0}}\right)^{2}$  14 
Samuel (1991) [22] 
$\frac{H}{H_{0}}=0.14+2.52\left(\frac{S}{S_{0}}\right)3.71\left(\frac{S}{S_{0}}\right)^{2}$$+2.24\left(\frac{S}{S_{0}}\right)^{3}$ 
15 
Lewis (1992) [23] 
$\frac{H}{H_{0}}=0.14+0.57\left(\frac{S}{S_{0}}\right)$ $\frac{H}{H_{0}}=0.813.34\left(\frac{S}{S_{0}}\right)+7.38\left(\frac{S}{S_{0}}\right)^{2}$$4.51\left(\frac{S}{S_{0}}\right)^{3}$ 
16 
Aksoy (1997) [24] 
$\frac{H}{H_{0}}=0.148+0.668\left(\frac{S}{S_{0}}\right)0.079\left(\frac{S}{S_{0}}\right)^{2}$ 
17 
Ampratwum and Dorvlo (1999) [25] 
$\frac{H}{H_{0}}=0.6376+0.2490 \log \left(\frac{S}{S_{0}}\right)$  18 
Chegaar and Chibani (2001) [26] 
$\frac{H}{H_{0}}=0.309+0.368\left(\frac{S}{S_{0}}\right)$ For Algiers and Oran $\frac{H}{H_{0}}=0.367+0.367\left(\frac{S}{S_{0}}\right)$ For Beni Abbas $\frac{H}{H_{0}}=0.233+0.591\left(\frac{S}{S_{0}}\right)$ For Tamanrasset 
19 
Akpabio and Etuk (2003) [27] 
$\frac{H}{H_{0}}=0.23+0.38\left(\frac{S}{S_{0}}\right)^{2}$  20 
Ahmad and Ulfat (2004) [28] 
$\frac{H}{H_{0}}=0.324+0.405\left(\frac{S}{S_{0}}\right)$ $\frac{H}{H_{0}}=0.348+0.320\left(\frac{S}{S_{0}}\right)0.070\left(\frac{S}{S_{0}}\right)^{2}$ 
21 
Chen et al. (2004) [29] 
$\frac{H}{H_{0}}=a\left(T_{\max }T_{\min }\right)^{0.5}+b$  22 
Bakirci (2007) [30] 
$\begin{aligned} \frac{H}{H_{0}}=0.6307 &0.7251\left(\frac{S}{S_{0}}\right) \\ &+1.2089\left(\frac{S}{S_{0}}\right)^{2} \\ &0.4633\left(\frac{S}{S_{0}}\right)^{3} \end{aligned}$ 
23 
Bakirci (2009) [31] 
$\frac{H_{c}}{H_{0}}=0.6716+0.0760\left(\frac{S}{S_{0}}\right)$ $c \frac{H_{c}}{H_{0}}=0.5622+0.5444\left(\frac{S}{S_{0}}\right)$$0.4490\left(\frac{S}{S_{0}}\right)^{2}$ 
24 
Olayinka (2011) [32] 
$\frac{H}{H_{0}}=a_{1}+a_{2} T_{\max }+a_{3} \sigma$ 
25 
Adaramola (2012) [33] 
$\frac{H}{H_{0}}=a_{1}+a_{2} T_{m}$ $\frac{H}{H_{0}}=a_{1}+a_{2} \frac{T_{\min }}{T_{\max }}$ 
26 
Adhikari et al. (2013) [34] 
$\frac{H}{H_{0}}=a+b \frac{S}{S_{0}}+c \frac{T_{a v g}}{T_{\max }}+d \ln (R H)$ 
27 
Li et al. (2013) [35] 
$\frac{H}{H_{0}}=a_{1}\left(1+a_{2} R H\right) \Delta T$  28 
Hassan et al. (2016) [36] 
$\frac{H}{H_{0}}=a_{1}+a_{2} \Delta T^{0.5}$ 
29 
Jahani et al. (2017) [37] 
$\frac{H}{H_{0}}=a_{1}+a_{2} \Delta T+a_{3} \Delta T^{2}+a_{4} \Delta T^{3}$  30 
Fan et al. (2018) [38] 
$\frac{H}{H_{0}}=a_{1}+a_{2} \Delta T+a_{3} \Delta T^{0.25}+a_{4} \Delta T^{0.5}$ $\begin{aligned} \frac{H}{H_{0}}=a_{1}+a_{2} \Delta T &+a_{3} \Delta T^{0.25}+a_{4} \Delta T^{0.5} \\ &+a_{5} \frac{T_{m}}{H_{0}} \end{aligned}$ 
31 
Ekici and Teke (2018) [39] 
$\frac{H}{H_{0}}=a_{1}\left[a_{2}\left(1e^{(\tau / R H}\right)^{a_{3}}\right)+a_{4}(\tau / R H)^{a_{5}}$ $+a_{6} \cos \left(a_{7} \tau / R H\right)$ $+a_{8} \cos \left(a_{7} T_{\min } / \Delta T\right)$ $\left.+a_{9} \sin \left(a_{7} T_{\min } / \Delta T\right)\right]$ 
32 
Yildirim et al. (2018) [40] 
$\frac{H}{H_{0}}=a_{1}+a_{2} R H+a_{3} \sigma+a_{4} \sigma^{2}+a_{5} \sigma^{3}$ 
The station consists of two parts:
• The stator consists of EKO MS64 thermometers for measuring global solar radiation on a horizontal surface (shortwave sensitivity is 7.0 (mV / kW / m^{2})) and on an inclined surface at the latitude of the site.
• A moving part capable of tracking the path of the sun from sunrise to sunset.
The last one consists of an EKO MS101D thermometer with a short wave sensitivity of 6.71 (mV/kW/m^{2}), which is pointed at the sun disk to measure the DNI component. Another thermometer EKO MS64 with a shortwave sensitivity of 7.0 (mV / kW / m^{2}) used for measuring diffuse solar radiation on the horizontal plane. It is equipped with a shade bar to mask the radiation flux coming directly from the sun.
Figure 3. Souk Ahras site location
Figure 4. Radiometric station
Figure 5. H/H_{0} taken for CDER
All solar components are made with a fiveminute interval for each component. (Figure 5) shows the variation of H / H_{0 }changes in terms of months measured in the Souk Ahras region. With H is the monthly average daily global irradiation on a horizontal surface (W/m^{2} day) and H0 is the monthly average the daily extraterrestrial irradiation (W/m^{2}).
In the literature, several types of models exist for the evaluation and prediction of global solar radiation, the difference between them is the parameters that come into play. These parameters depend on the characteristics and climatic specificities of the region considered. In our case we used the regression equation which depends of temperature and relative humidity. They are the two main parameters that influence the climate of Souk Ahras, this semiempirical relationship is based on statistical methods applied to available data. Our objective is to find a, b and c that represent the determinants of the matrix for the first, second and third column, respectively, in the following form:
$\frac{H}{H_{0}}=a T^{2}+b R H+c$ (1)
$H_{0}$ can be computed from the following equation $[41]$ :
$H_{0}=\frac{24}{\pi} I_{s c}\left[\cos \emptyset \cos \delta \sin w_{s}+\frac{\pi}{180} w_{s} \sin \emptyset \sin \delta\right]$ (2)
${\left[1+0.033 \cos \frac{360 n}{365}\right] }$
where:
$I_{s c}$ represents the solar constant $\left(I_{s c}=1367 \mathrm{~W} / \mathrm{m}^{2}\right), \emptyset$ is the latitude of the site, $\delta$ presents the solar declination, $w_{s}$ is themean sunrise hour angle for the given month and $n$ is the number of days of the year starting from first January. The solar declination $\delta$ and the mean sunrise hour angle $w_{s}$ can be calculated by Eqns. (3) and (4), respectively [41]:
$\delta=23.45 \sin \left(\frac{360(284+n)}{365}\quad\right)$ (3)
$w_{s}=\cos ^{1}(\tan \emptyset \tan \delta)$ (4)
$S_{0}=\frac{2}{15} w_{s}$ (5)
We conducted a study for the year 2020, taking into consideration the average values of temperatures T and the percentages of the average values of relative humidity RH for each season (three months) of the year. These values are taken from Renewable Energy Development center (CDER) [42] and Global Surface Summary of Day (GSOD) [43].
We calculated the mean values for each day of the month of the Souk Ahras area, for example the month of October, by taking the mean of each day $T_{j}$ with: $T_{j}=\frac{T_{\max }T_{\min }}{2}$, for more precision. Then, we take the average of the temperaturevalues for the whole month $T_{m}$ with $T_{m}=\sum_{j=1}^{=31} \frac{T_{j}}{31}$. We reproduce the same work for the months of November and December. After that, we calculate the midpoint of temperature $T$ with $T=$ $\sum_{m=1}^{m=3} \frac{T_{m}}{3}$ for the three months we have chosen. Hourly temperature values and relative humidity values for each day of the month are taken from GSOD. As for the value of the average solar radiation of the area H is taken from the data of the CDER. For the solar radiation on the ground H0is calculated from Eq. (2) for the three months considered.
The same work is done for the other chosen quarters, namely January, February, March and July, August and September (we chose three quarters in the year because we have three unknown determinants in our proposed model). Our results are shown in Table 1.
Table 1. Results for T, T², RH, H, H_{0} and H/H_{0}
T [°C] 
T2 [°C] 
RH 
H)W/m^{2}) 
H_{0})W/m^{2}) 
H/H_{0} 
9.8 
96.04 
0.697 
8588 
165.8 
51.80 
27.5 
756.25 
0.583 
11081 
177.60 
62.4 
9.1 
82.81 
0.845 
8012 
160.10 
50.04 
To solve our system of equations of order 3, we used Cramer's rules for a system of order 3. This method, which is valid when the system has a unique solution, allows to define our determinants as follows:
$\left\{\begin{array}{l}\frac{2401}{25} a+\frac{697}{1000} b+c=\frac{259}{5} \\ \frac{3025}{4} a+\frac{583}{1000} b+c=\frac{312}{5} \\ \frac{8281}{100} a+\frac{169}{200} b+c=\frac{1251}{25}\end{array}\right.$ (6)
$a=0.0142$ (7a)
$b=10.6206$ (7b)
$c=57.8367$ (7c)
Using the results our model will have the following form:
$\frac{\boldsymbol{H}}{\boldsymbol{H}_{0}}=0.0142 \boldsymbol{T}^{2}10.6206 \boldsymbol{R} \boldsymbol{H}+57.8367$ (8)
Table 2. Calculated H of the area of Souk Ahras for 2017
Month 
T[°C] 
T²[°C]^{2} 
RH 
C 
H/H_{0} 
1.Jan 
5.62 
31.5844 
0.705 
57.8367 
50.79768 
2.Feb 
10.3 
106.09 
0.735 
57.8367 
51.53704 
3.Mar 
12.46 
155.2516 
0.661 
57.8367 
53.02106 
4.Apr 
14.54 
211.4116 
0.662 
57.8367 
53.80791 
5.May 
19.09 
364.4281 
0.491 
57.8367 
57.79686 
6.jun 
26.2 
686.44 
0.474 
57.8367 
62.54998 
7.Jul 
29.55 
873.2025 
0.341 
57.8367 
66.61455 
8.Aug 
29.06 
844.4836 
0.369 
57.8367 
65.90937 
9.Sep 
22.55 
508.5025 
0.492 
57.8367 
59.8321 
10.Oct 
17.24 
297.2176 
0.61 
57.8367 
55.57862 
11.Nov 
11.64 
135.4896 
0.636 
57.8367 
53.00595 
12.Dec 
7.84 
61.4656 
0.754 
57.8367 
50.70158 
Year 2017 
Table 3. Calculated H of the area of Souk Ahras for 2018
Month 
T[°C] 
T²[°C]^{2} 
RH 
C 
H/H_{0} 
1.Jan 
9.9 
98.01 
0.901 
57.8367 
49.65928 
2.Feb 
10.11 
102.2121 
0.77 
57.8367 
51.11025 
3.Mar 
10.98 
120.5604 
0.668 
57.8367 
52.4541 
4.Apr 
15.24 
232.2576 
0.679 
57.8367 
53.92337 
5.May 
19.09 
364.4281 
0.739 
57.8367 
55.16296 
6.jun 
22.52 
507.1504 
0.569 
57.8367 
58.99511 
7.Jul 
28.37 
804.8569 
0.373 
57.8367 
65.30418 
8.Aug 
31.54 
994.7716 
0.62 
57.8367 
65.37768 
9.Sep 
22.68 
514.3824 
0.605 
57.8367 
58.71547 
10.Oct 
16.88 
284.9344 
0.718 
57.8367 
54.25718 
11.Nov 
11.61 
134.7921 
0.731 
57.8367 
51.98709 
12.Dec 
7.28 
52.9984 
0.765 
57.8367 
50.46452 
Year 2018 
Table 4. Calculated H of the area of Souk Ahras for 2019
Month 
T[°C] 
T²[°C]^{2} 
RH 
C 
H/H_{0} 
1.Jan 
5.89 
34.6921 
0.81 
57.8367 
49.72664 
2.Feb 
7.96 
63.3616 
0.764 
57.8367 
50.6223 
3.Mar 
10.97 
120.3409 
0.722 
57.8367 
51.87747 
4.Apr 
12.91 
166.6681 
0.654 
57.8367 
53.25751 
5.May 
18.87 
356.0769 
0.673 
57.8367 
55.74533 
6.jun 
23.8 
566.44 
0.671 
57.8367 
58.75373 
7.Jul 
25.4 
645.16 
0.652 
57.8367 
60.07334 
8.Aug 
25.8 
665.64 
0.546 
57.8367 
61.48994 
9.Sep 
22.77 
518.4729 
0.712 
57.8367 
57.63715 
10.Oct 
18.77 
352.3129 
0.755 
57.8367 
54.82099 
11.Nov 
12.8 
163.84 
0.79 
57.8367 
51.77295 
12.Dec 
10.2 
104.04 
0.757 
57.8367 
51.27427 
Year 2019 
Table 5. Calculated H of the area of Souk Ahras for 2020
month 
T[°C] 
T²[°C]^{2} 
RH 
C 
H/H_{0} 
1.Jan 
7.62 
58.0644 
0.394 
57.8367 
54.4767 
2.Feb 
10.8 
116.64 
0.435 
57.8367 
54.78303 
3.Mar 
14.15 
200.2225 
0.422 
57.8367 
56.19797 
4.Apr 
16.3 
265.69 
0.425 
57.8367 
57.09574 
5.May 
20.4 
416.16 
0.475 
57.8367 
58.70139 
6.jun 
23.7 
561.69 
0.478 
57.8367 
60.73605 
7.Jul 
27.02 
730.0804 
0.437 
57.8367 
63.56264 
8.Aug 
28.05 
786.8025 
0.422 
57.8367 
64.5274 
9.Sep 
24.5 
600.25 
0.755 
57.8367 
58.3417 
10.Oct 
17.56 
308.3536 
0.592 
57.8367 
55.92793 
11.Nov 
15.75 
248.0625 
0.65 
57.8367 
54.4558 
12.Dec 
7.6 
57.76 
0.677 
57.8367 
51.46675 
Year 2020 
Now, we spread our calculations over a period of four years, 2017, 2018, 2019 and 2020. We used our proposed model (Eq. (8)) to find the values of H (monthly average daily global solar radiation on horizontal surface). The values of T and RH of Souk Ahras region, for each hour of each day of the month of the year, are taken from GSOD. The results are presented in Tables 2, 3, 4 and 5.
The following figures show us the evolution of the temperature T with H/H_{0 }ratio calculated by our new proposed model (Eq. (8)).
Figure 6. (a) the Variations of (H / H_{0}) and T temperature versus months of 2017, (b) The variation of H / H0 changes in terms of months of 2017
Figure 7. (a) the Variations of (H / H_{0}) and T temperature versus months of 2018, (b) The variation of H / H_{0} changes in terms of months of 2018
Figure 8. (a) The variations of (H / H0) and T temperature versus months of the year 2019, (b) The variation of H / H0 changes in terms of months of 2019
Figure 9. The variations of (H / H0) and T temperature versus months of 2020, (b) The variation of H / H0 changes in terms of months of 2020
As we can see in the Figures (6, 7, 8, 9), the range of H/H_{0 }calculated for each day of the month of the four years (20172020) follows that of the temperatures.
To validate our model, we conducted a study for different sites in Algeria with different climates. Daily data, concerning the values of the average temperature T and the relative humidity RH, were collected for the year 2020, for several cities in Algeria. These data are taken from GSOD and CDER. The geographical characteristics of each city (latitude, longitude and elevation above sea level) are taken from the center of renewable energy development. For our calculations, we chose a typical day for each season, the 20th of February for winter (n=51), the 20th of April for spring (n=110) the 20th of July for summer (n=201) and the 20th of November for the fall (n = 324).
We calculated the extraterrestrial solar irradiance on a horizontal surface $\mathrm{H}_{0}$ (W/m²) for each selected typical day. Then, we used our proposed new model for the calculation of the global solar radiation $\mathrm{H}_{\text {Calculated }}$ for each zone, as shown in Table 6.
Table 6. The data of longitude, the sun declination, height, temperature; the average humidity, the ratio of global radiation to daily radiation form CDER DATABASES compared with our results which are obtained by our proposed model
State 
Date 
Day Number in the year 
Ø[°] 
Δ[°] 
h(m) 
T[°C] 
RH 
$\mathrm{H}_{0}$ (W/m^{2}) 
$\frac{H_{\text {calculated }}}{H_{0}}$ 
$\frac{H_{C D E R}}{H_{0}}$ 
$H_{\text {calculated }}$ (W/m^{2}) 
$H_{C D E R}$ (W/m^{2}) 
$\Delta H / H_{\text {Calculated }}$ 
The average value of $\Delta H / H_{\text {Calculated }}(\%)$ 
20/02/2020 
51 
7.95 
11.22 
680 
10.8 
0.688 
181.36 
52.18 
56.29 
9463.36 
10209 
7.87 


Souk Ahras 
20/04/2020 
110 
7.95 
11.23 
680 
13,5 
0.66 
175.04 
64.83 
68.45 
11348.88 
11983 
5.58 

20/07/2020 
201 
7.95 
20.82 
680 
27.3 
0.472 
171.44 
68.42 
67.64 
10869.2 
11597 
6.69 
6.49 

20/11/2020 
324 
7.95 
19.52 
680 
9,9 
0.904 
160.64 
53.41 
50.29 
8580 
8079 
5.83 


20/02/2020 
51 
0.28 
11.22 
263 
18.4 
0.233 
181.9 
60.16 
56.15 
10943.1 
10215 
6.65 


Adrar 
20/04/2020 
110 
0.28 
11.23 
263 
23.8 
0.545 
175.95 
60.09 
64.23 
10572.83 
11303 
6.9 

20/07/2020 
201 
0.28 
20.82 
263 
39.2 
0.125 
138.47 
78.32 
76.65 
10845.15 
10615 
2.12 
4.71 

20/11/2020 
324 
0.28 
1952 
263 
17.1 
0.412 
158.65 
57.6 
55.75 
9138.24 
8846 
3.19 


20/02/2020 
51 
0.12 
11.22 
137 
16.9 
0.646 
177.91 
55.02 
53.4 
9788.6 
9501 
2.93 


20/04/2020 
110 
0.12 
11.23 
137 
21 
0.455 
186.17 
59.36 
60.14 
11051.05 
11197 
1.32 


Mostaganim 
20/07/2020 
201 
0.12 
20.82 
137 
31.9 
0.474 
164.87 
67.26 
65.32 
11087.5 
10770 
2.86 
2.49 
20/11/2020 
324 
0.12 
19.52 
137 
15.3 
0.832 
174.09 
52.32 
44.09 
7899.1 
7674 
2.85 

20/02/2020 
51 
0.6 
11.22 
90 
13.2 
0.761 
185.46 
52.22 
50.97 
9684.72 
9453 
2.39 


20/04/2020 
110 
0.6 
11.23 
90 
20.9 
0.677 
185.76 
56.83 
59.32 
10556.74 
11020 
4.38 


Oran/Senia 
20/07/2020 
201 
0.6 
20.82 
90 
26.5 
0.666 
163.58 
60.72 
65.29 
9933.67 
10681 
7.52 
5.72 
20/11/2020 
324 
0.6 
19.52 
90 
14.6 
0.725 
175.98 
53.16 
43.39 
8355.09 
7636 
8.6 


20/02/2020 
51 
8.13 
11.22 
813 
11.6 
0.527 
184.89 
58.7 
56.35 
10853.04 
10420 
4 


20/04/2020 
110 
8.13 
11.23 
813 
18.5 
0.456 
188.86 
58.14 
64.3 
10980.32 
12144 
10.59 


Tebessa 
20/07/2020 
201 
8.13 
20.82 
813 
26.5 
0.393 
170.91 
63.62 
68.63 
10873.29 
11730 
7.87 
6.82 
20/11/2020 
324 
8.13 
19.52 
813 
9.7 
0.844 
164.82 
50.2 
52.63 
8273.26 
8675 
4.84 


20/02/2020 
51 
7.82 
11.22 
4 
11.3 
0.764 
176.81 
51.52 
52.35 
9109.25 
9259 
1.64 


Annaba 
20/04/2020 
110 
7.82 
11.23 
4 
18.7 
0.922 
189.2 
53 
58.21 
10027.6 
11014 
9.83 


20/07/2020 
201 
7.82 
20.82 
4 
24.4 
0.739 
170.71 
58.44 
62.21 
9976.29 
10621 
6.46 
6.85 

20/11/2020 
324 
7.82 
19.52 
4 
16.3 
0.704 
165.32 
54.12 
43.49 
7947.11 
7191 
9.5 


20/02/2020 
51 
5,52 
11.22 
1378 
16,9 
0.446 
180.65 
57.17 
64.09 
10327.76 
11579 
12.11 


20/04/2020 
110 
5.52 
11.23 
1378 
26.6 
0.207 
178.69 
65.88 
69.86 
11736.35 
12484 
6.37 

Tamanrasset 
20/07/2020 
201 
5.52 
20.82 
1378 
32.5 
0.164 
169.56 
71.08 
68.6 
12052.32 
11632 
3.48 
7.19 

20/11/2020 
324 
5.52 
19.52 
1378 
16.8 
0.263 
168.66 
59.06 
63.09 
9961.05 
10641 
6.82 


20/02/2020 
51 
5.42 
11.22 
1038 
6 
0.505 
177.6 
52.79 
60.1 
9407.47 
10675 
13.47 


20/04/2020 
110 
5.42 
11.23 
1038 
17.2 
0.422 
188.61 
56.68 
66.08 
11690.41 
12464 
6.61 

Setif 
20/07/2020 
201 
5.42 
20.82 
1038 
25.8 
0.296 
169.46 
64.13 
71.32 
10867.46 
12097 
11.3 
8.93 

20/11/2020 
324 
5.42 
19.52 
1038 
7,6 
0.882 
180.44 
49.28 
47.13 
8892.08 
8505 
4.35 


20/02/2020 
51 
3.82 
11.22 
450 
13.6 
0.442 
179.01 
55.74 
57.05 
9978.01 
10213 
2.35 

Gherdaia 
20/04/2020 
110 
3.82 
11.23 
450 
22,8 
0.466 
187.94 
60.26 
62.05 
11325.26 
11662 
2.97 


20/07/2020 
201 
3.82 
20.82 
450 
32.7 
0.258 
167.27 
70.27 
66.09 
11754.06 
11055 
5.94 
5.36 

20/11/2020 
324 
3.82 
19.52 
450 
15.6 
0.486 
171.11 
56.12 
50.38 
9602.69 
8622 
10.21 


20/02/2020 
51 
5.4 
11.22 
141 
14.2 
0.481 
180.66 
55.58 
54.73 
10041.08 
9888 
1.52 


20/04/2020 
110 
5.4 
11.23 
141 
27.8 
0.465 
178.62 
61.72 
63.02 
11579.9 
11257 
2.78 

Ouergla 
20/07/2020 
201 
5.4 
20.82 
141 
30.1 
0.239 
169.43 
68.16 
62.86 
11548.34 
10651 
7.77 
6.04 
20/11/2020 
324 
5.4 
19.52 
141 
16.1 
0.541 
168.87 
56.12 
49 
9416.19 
8276 
12.1 
We compared our values of $\left(\mathrm{H}_{\text {Calculated }} / \mathrm{H}_{0}\right)$ computed using the proposed model for each typical day of each season for each chosen city, with the values of $\left(\mathrm{H}_{\mathrm{CDER}} / \mathrm{H}_{0}\right)$ taken from the CDER database. We note that the smaller the value of $\Delta \mathrm{H} / \mathrm{H}_{\text {Calculated }}$, the more precise the value of $\mathrm{H}$ calculated according to the proposed model.
If we take the case of Souk Ahras (extreme east of the country), the value of $\Delta H / H_{\text {Calculated }}$ is $6.49 \%$. The others are $4.71 \%$ for Adrar (south west of the Algeria), $2.49 \%$ for Mostaganem and $5.72 \%$ for Oran. For the cities of the Algerian Sahara, the value of $\Delta \mathrm{H} / \mathrm{H}_{\text {Calculated }}$ is between $5.36 \%7.19 \%$ and it is $8.93 \%$ for Setif city. Given these values, it can be confirmed that the proposed model gives very satisfactory results for the evaluation of global solar radiation across the country of Algeria.
This model shows the global solar radiation reaching the Earth’s surface affected by several factors. The most important of which are:
From the Table 6 we draw graphs (H/H0 Calculated), (H/H0 Taken for CDER) as the following (Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19).
Figure 10. The variation of Hcal / H0 and HCDER / H0 in terms of months in Souk Ahras
Figure 11. The variation of Hcal / H0 and HCDER / H0 in terms of months in Adrar
Figure 12. The variation of Hcal / H0 and HCDER / H0 in terms of months in Mostaganem
Figure 13. The variation of Hcal / H0 and HCDER / H0 in terms of months in Oran/Senia
Figure 14. The variation of Hcal / H0 and HCDER / H0 in terms of months in Tebessa
Figure 15. The variation of Hcal / H0 and HCDER / H0 in terms of months in Annaba
Figure 16. The variation of Hcal / H0 and HCDER / H0 in terms of months in Tamanrasset
Figure 17. The variation of Hcal / H0 and HCDER / H0 in terms of months in Setif
Figure 18. The variation of Hcal / H0 and HCDER / H0 in terms of months in Ghardaia
Figure 19. The variation of Hcal/ H0 and HCDER / H0 in terms of months in Ouergla
The future of the use of solar energy, which is a renewable and sustainable energy, requires accurate information about solar radiation and its components in any place on earth. That is why, the modeling of solar radiation for its evaluation or prediction is of great importance, especially in areas where there are no measured values. The main goal of this work is to propose a new model to estimate the global solar radiation for the region of Souk Ahras in Algeria especially that direct measurement data are difficult to obtain or even impossible to find because of the lack of means and stations for climatic and meteorological measurements in that area.
In this article, we presented a literature review on various existing models based on the regression equation and the duration of sunshine or on the temperature or even hybrid models based on several parameters for the calculation of global solar radiation for several regions in the world. We noticed that almost every model is proposed for a given area because of the diversity of climate, meteorological and geographical parameters.
The proposed model is made on data collection over four years (20172020). These data relate to the duration of sunshine, the daily temperature per hour of the air, the daily relative humidity and the geographical coordinates taken from the database (GOSD) and from (CDER). Based on the regression equation, we arrived at estimating the regression coefficients a, b and c specific to the Souk Ahras region. We made a comparison of the calculation result of the global solar radiation of several other sites in Algeria made from our model $\mathrm{H}_{\text {calculated }}$) and those experimental proposed by the center for the development of renewable energies ( $\mathrm{H}_{\text {CDER }}$ ). We found that there is a good agreement between the results and that the proposed model has a very acceptable precision for the majority of the cities considered.
The model proposed in this study can be used anywhere in the world where climatic conditions are the same.
H 
the monthly average daily global solar irradiation on horizontal surface )W/m^{2}) 
H_{0} 
the extraterrestrial solar radiance on a horizontal surface )W/m^{2}) 
H_{c} 
the monthly average clear sky daily global radiation )W/m^{2}) 
H_{d} 
the monthly mean daily diffuse solar irradiance on a horizontal surface )W/m^{2}) 
I_{sc} 
the solar constant (W/m^{2}) 
δ 
the solar declination (°) 
N 
the number of days of the year starting from first January 
S 
the monthly average daily bright sunshine duration (hours) 
S_{0} 
The day length (hours). 
w_{s} 
the sunset hour angle (°) 
$\varnothing$ 
the latitude of location (°) 
RH 
the mean relative humidity (%) 
T 
Average temperature(°C) 
∆T 
the temperature term difference (°C). 
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