The aim of this study is the determination of a suitable solar radiation model for the twelve cities of Chad based on meteorological data. Three appropriate models are used to estimate the solar radiation of each site. The choice of these models is based on statistical tests such as the Root Mean Square Error (RMSE), the Mean Bias Error (MBE), the Mean Percentage Error (MPE), and the Nash-Sutcliffe Equation (NSE). The obtained results show that the Angstrom-Prescott model is the most suitable for the calculation of global solar radiation in the sites of Bongor, Pala, Am-timan and Mongo. For the sites of Moundou, Sarh and Bokoro the Allen model is the most adapted for the calculation of global solar radiation. On the other hand the Sabbagh model is the most appropriate for the sites of Faya-Largeau, Abeche, N ’ Djamena, Ati and Moussoro. It has been revealed that Abeche is the site with the highest solar radiation value equal to 6.354 kWh/m2 and Ati is the site where the solar radiation has the lowest value around 5.523 kWh/m2. Based on the obtained results, it is demonstrated that the three climatic zones of Chad have a good solar potential and consequently suitable for the exploitation of the solar energy systems.
The energy sector of Chad, which is still weakly developed, is characterized by high consumption of wood fuels (wood and charcoal), which accounts for more than 90% of the total energy consumption of the country. The use of conventional energies (petroleum products and electricity) occupies a marginal part of the national energy balance. These energies, although crucial in the development of a modern economy, account for only about 10% of total energy consumption in the country. There is no interconnected network in the country. Chad, however, has significant energy potential such as hydrocarbons, biomass and renewable energies, including solar and wind energy, whose exploitation could have contributed to the development of the sector. Solar energy applications require, above all, knowledge of the global solar radiation of a site. Thus, a reliable estimation of global solar radiation for a site is fundamental. Doing this will allow adequate knowledge of how to channel such application for either electricity generation, water heating, or irrigation, to mention a few [
This study was therefore focused to develop a mathematical model to estimate the solar radiation coming from extraterrestrial radiation, with meteorological and geographical data as governing parameters. The model was validated by comparing its results with experimentally measured data across the twelve sites of Chad. The impact of this is the fact that such model can now be used to analyse and make informed decisions on solar technology applications without recourse to several years of experimental measurements around the studied sites and across the region.
Solar data employed for the study were obtained from the General directorate of the National Meteorology of Chad, in June 2014 covering the period of 63 years (i.e. 1950-2013). They are monthly data of the relative humidity, maximum temperature, minimal temperature, and sunshine duration. The geographical coordinates of the twelve stations of the National office of Meteorology (ONM) are given in
To calculate the global solar radiation, one has recourse to the ideal models. These models are in the form of empirical relations which connect the components of the solar radiation to the principal weather parameters and the astronomical parameters. The weather parameters are the ambient temperature, the relative humidity, the sunshine duration. Amongst the astronomical parameters one has the maximum duration of the day, the variation of the sun, the variation of the ground-sun distance and the solar radiation in the extraterrestrial radiation [
The monthly mean of the daily extraterrestrial solar radiation on a horizontal surface is determined according the following relation [
H 0 = 24 π I s c [ 1 + 0.33 cos ( 360 D n 365 ) ] ∗ [ cos φ cos δ sin ω s + 2 π ω s 360 sin φ sin δ ] (1)
Zones | City | Latitude (˚N) | Longitude (˚E) | Elevation (m) |
---|---|---|---|---|
Saharan zone | Faya-Largeau | 17.55 | 19.7 | 233 |
Abeche | 13.51 | 20.51 | 545 | |
N’Djamena | 12.8 | 15.2 | 294 | |
Sahelian zone | Ati | 13.13 | 18.19 | 334 |
Bokoro | 12.23 | 17.3 | 300 | |
Mongo | 12.11 | 18.41 | 430 | |
Moussoro | 13.39 | 16.3 | 301 | |
Am-timan | 11.2 | 20.17 | 432 | |
Bongor | 10.17 | 16.22 | 328 | |
Sudanese zone | Moundou | 8.37 | 16.4 | 420 |
Pala | 9.22 | 14.55 | 420 | |
Sarh | 9.9 | 18.23 | 364 |
where δ and ω s are respectively the monthly mean of the daily solar declination and the sunshine hour angle defined by [
δ = 23.45 sin [ 360 ( 284 + D n ) 365 ] (2)
ω s = cos − 1 ( − tan L tan δ ) (3)
where I s c is the solar constant (Isc =1367 W/m2), L is the location latitude, Dn is the number of the day in the year.
Angstrom has been the first to propose an ideal model (linear model) to estimate the horizontal global solar radiation with in entry the data over the sunshine duration [
H H 0 = a + b ( S S 0 ) (4)
The parameters a, bare respectively defined by the Equations (5) and (6).
a = − 0.110 + 0.235 cos L + 0.323 ( S S 0 ) (5)
b = 1.449 − 0.553 cos L − 0.694 ( S S 0 ) (6)
The possible maximum monthly mean of the daily sunshine duration is [
S 0 = 2 15 cos − 1 ( − tan L tan δ ) (7)
Allen [
H H 0 = K r ( T M − T m ) 0.5 (8)
Where Kr is defined as:
K r = K r a ( P P 0 ) 0.5 (9)
In the relation (9), Kra = 0.17 and P/P0 may be defined as:
P P 0 = exp ( − 0.0001184 h ) (10)
where P and P0 are respectively the values of local and standard atmospheric pressure, and h is the altitude of the place in meters.
While being based on data relating to several countries of the Gulf, in particular, the sites of Saudi Arabia, Sabbagh et al. developed two empirical relations binding the various weather parameters which affect the attenuation of the solar radiation, namely: sunshine duration, relative humidity, the maximum temperature, the altitude, the geographical situation (longitude, latitude) and its situation compared to the sea and a lake of water characterized by the characteristic factor of the zone, which is given by the following relation [
H = 1.530 K ∗ exp L ( S S 0 − R H 1 / 3 100 − 1 T max ) , (11)
With:
K = 100 ( n T max + ψ i j cos ( L ) ) , (12)
n = 1 ( 1 + 0.1 L ) , (13)
RH and Tmax are respectively the monthly average per day of the sunshine duration, the relative humidity and the maximum average temperature of the considered month.
ψ i j , climatic factor
n, number of the month considered
S, monthly average daily bright sunshine duration (h)
In order to compare the data of the solar radiation provided by NASA (National Aeronautic and Space Administration) with those obtained from the various presented models, all the different models were implemented by creating a code using MATLAB and Excel. From each of these programs and for each studied site, on the one hand we drew up in the same graph, the values of whole-body radiation by NASA and those calculated, and in the other hand we drew up the relative error. The presented models in paragraph 3 permitted to evaluate the calculated global radiation Hi,c in order to be compared to the measured global radiation Hi,m.
Several statistical indicators used in the literature [
RMSE (Root Mean Square Errors) is a measure of the variation of calculated values; it gives information about the performance of the model and is always positive values. The model is best when its RMSE value is the smallest. It is defined by the relation:
R M S E = ∑ i = 1 n ( H i , c − H i , m ) 2 n (14)
n is the number of the month.
The mean bias error (MBE) is the mean inclination error giving information on the performance of the long-term model. To this end, a negative value refers to underestimation, while positive value refers to an overestimation. It is given by Equation (15):
M B E = ∑ i = 1 n ( H i , c − H i , m ) n (15)
The MPE (Mean Percentage Error) is defined by the relation:
M P E ( % ) = 1 n ∗ ∑ i = 1 n ( H i , c − H i , m ) H i m ∗ 100 (16)
For this indicator, for a given model, an error expressed as a percentage between −10% and +10% is acceptable.
The NSE (Nash-Sutcliffe Equation) represents a measure of the precision of the model results. The NSE is defined by the relation:
N S E = 1 − ∑ i = 1 n ( H i , m − H i , c ) 2 ∑ i = 1 n ( H i , m − H ¯ m ) 2 (17)
where: H ¯ m is the mean measured global radiation.
To estimate the overall solar radiation using the Angstrom-Prescott model, apart from the geographical coordinates of the site, the average daily insolation duration was considered.
Meteorological data such as relative humidity, maximum temperature and average daily sun exposure measured the overall solar radiation using the Sabbagh model. Maximum temperature and minimum temperature were considered in the Allen model.
Tables 2-5 present the total results obtained through the relations of Angstrom-Prescott, Allen, Sabbagh equation and Sabbagh model for the twelve sites of the three climatic zones of Chad.
In
Cities | a | b | H0 | S(h) | S0(h) | H/H0 | S/S0 | H (kWh/m2/day) | Err (%) |
---|---|---|---|---|---|---|---|---|---|
Faya-Largeau | 0.39 | 0.33 | 8.19 | 9.59 | 11.2 | 0.67 | 0.86 | 5.457 | −13.791 |
Abeche | 0.45 | 0.2 | 8.722 | 11.62 | 11.39 | 0.64 | 1.02 | 5.600 | −7.807 |
Am-timan | 0.37 | 0.36 | 9.069 | 8.97 | 11.52 | 0.65 | 0.78 | 5.917 | −0.887 |
N’Djamena | 0.37 | 0.38 | 8.936 | 8.74 | 11.47 | 0.65 | 0.76 | 5.791 | 1.265 |
Bongor | 0.35 | 0.41 | 9.158 | 8.3 | 11.55 | 0.64 | 0.72 | 5.839 | 1.590 |
Moundou | 0.34 | 0.43 | 9.351 | 7.97 | 11.62 | 0.63 | 0.68 | 5.88 | 1.482 |
Pala | 0.34 | 0.44 | 9.265 | 7.77 | 11.59 | 0.62 | 0.67 | 5.792 | 2.454 |
Sarh | 0.32 | 0.47 | 9.29 | 7.17 | 11.6 | 0.61 | 0.62 | 5.658 | −1.765 |
Ati | 0.46 | 0.18 | 8.802 | 12.09 | 11.42 | 0.65 | 1.06 | 5.681 | −6.446 |
Bokoro | 0.46 | 0.18 | 8.905 | 12.08 | 11.46 | 0.65 | 1.05 | 5.748 | −1.547 |
Mongo | 0.46 | 0.18 | 8.93 | 12.09 | 11.47 | 0.65 | 1.05 | 5.763 | −1.829 |
Moussoro | 0.46 | 0.17 | 8.748 | 12.1 | 11.4 | 0.65 | 1.06 | 5.646 | 3.400 |
Sites | TM | Tmin (˚C) | H0 | H/H0 | H (kWh/m2/day) | Err (%) |
---|---|---|---|---|---|---|
Faya-Largeau | 35.65 | 21.13 | 8.19 | 0.65 | 5.3 | −16.723 |
Abeche | 37.42 | 22.28 | 8.722 | 0.66 | 5.747 | −5.482 |
Am-timan | 34.78 | 20.54 | 9.069 | 0.64 | 5.771 | −3.958 |
N’Djaména | 36.38 | 22.02 | 8.936 | 0.64 | 5.724 | 0.078 |
Bongor | 36.42 | 20.74 | 9.158 | 0.665 | 6.085 | 5.154 |
Moundou | 34.525 | 21.066 | 9.351 | 0.616 | 5.76 | −3.074 |
Pala | 33.925 | 21.266 | 9.265 | 0.601 | 5.563 | −0.844 |
Sarh | 35.083 | 21.55 | 9.29 | 0.619 | 5.751 | −0.878 |
Ati | 36.22 | 21.41 | 8.802 | 0.651 | 5.726 | −5.825 |
Bokoro | 36.73 | 21.13 | 8.905 | 0.666 | 5.932 | 1.181 |
Mongo | 36.45 | 26.15 | 8.93 | 0.543 | 4.849 | −17.506 |
Moussoro | 35.56 | 22.13 | 8.748 | 0.621 | 5.429 | −7.523 |
The Angstrom-Prescott model is the most suitable for the calculation of global solar radiation based on the relative error with NASA data especially for the sites: Bongor (1.590%), Pala (1.482%), Am-timan (−0.887%) and Mongo (−1.829%).
Am-timan : H = 3.6080 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
---|
Mongo : H = 3.7637 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Sarh : H = 3.6497 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Pala : H = 3.5344 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
N ’ Djamena : H = 3.7575 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Faya-Largeau : H = 3.6463 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Abeche : H = 3.8466 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Ati : H = 3.7346 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Bongor : H = 3.7742 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Moundou : H = 3.5982 ∗ 10 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Moussoro : H = 3.6668 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Bokoro : H = 3.7893 ∗ 10 3 ∗ exp φ ( S S 0 − H R 1 / 3 100 − 1 T max ) |
Sites | S | S0 (h) | RH (%) | Tmax (˚C) | S/S0 | H (kWh/m2/day) | Err (%) |
---|---|---|---|---|---|---|---|
Faya-Largeau | 9.59 | 11.2 | 20.37 | 35.65 | 0.857 | 6.013 | −6.766 |
Abeche | 11.62 | 11.39 | 36 | 37.42 | 1.02 | 6.354 | 3.704 |
Am-timan | 8.74 | 11.47 | 44.85 | 36.38 | 0.76 | 5.742 | −8.837 |
N’Djamena | 8.74 | 11.47 | 44.85 | 36.38 | 0.76 | 5.742 | −0.348 |
Bongor | 8.3 | 11.55 | 56.83 | 36.42 | 0.72 | 5.656 | -2.162 |
Moundou | 7.97 | 11.62 | 59.09 | 34.52 | 0.68 | 5.377 | −7.879 |
Pala | 7.76 | 11.59 | 52.93 | 33.92 | 0.67 | 5.285 | −6.892 |
Sarh | 7.17 | 11.6 | 59.31 | 35.08 | 0.62 | 5.385 | −6.946 |
Ati | 12.09 | 11.42 | 39.52 | 36.22 | 1.06 | 6.151 | 0.356 |
Bokoro | 12.08 | 11.46 | 42.13 | 36.73 | 1.05 | 6.189 | 5.032 |
Mongo | 12.09 | 11.47 | 36.37 | 36.45 | 1.05 | 6.195 | 4.825 |
Moussoro | 12.1 | 11.4 | 33.18 | 35.56 | 1.06 | 6.126 | 3.4 |
The Sabbagh model is the most suitable for calculating global radiation based on the relative error with NASA data especially for the sites: Faya-Largeau (−6.766%), Abeche (3.704%), N’Djamena (−0.348%), Ati (0.356%) and Moussoro (3.400%).
It can also be noted that all three models can only be applied if weather data and geographic parameters are available for a given site. The reliability of these models is the correct estimate of global solar radiation without going through direct and diffuse radiation. Moreover, it is observed that the solar radiation is affected by the meteorological parameters because the decrease of the parameters such as the temperature and the relative humidity leads to the reduction of the solar radiation. For example, the month of August seems the most unfavorable because the more it rains, the more radiation decreases.
Angstrom-Prescott | ||||
---|---|---|---|---|
Sites | MPE(%) | RMSE (kWh/m2/day) | MBE (kWh/m2/day) | NSE (kWh/m2/day) |
Abeche | −7.8073 | 0.9141 | −0.0781 | −1.5902 |
Faya-Largeau | −13.791 | 1.289 | −0.1379 | −1.2293 |
Am-timan | −0.8875 | 0.4256 | −0.0089 | 0.291 |
N’Djamena | 1.2655 | 0.6038 | 0.0127 | 0.2408 |
Moundou | 2.4541 | 0.4353 | 0.0245 | 0.6596 |
Sarh | −1.7654 | 0.4417 | −0.0177 | 0.6453 |
Pala | 1.4822 | 0.3338 | 0.0148 | 0.7241 |
Bongor | 1.5902 | 0.3368 | 0.0159 | 0.6999 |
Ati | −6.4463 | 0.7823 | −0.0645 | −0.8224 |
Bokoro | −1.5466 | 0.5834 | −0.0155 | −0.0377 |
Mongo | −1.8291 | 0.5609 | −0.0183 | −0.0373 |
Moussoro | −4.1310 | 0.6887 | −0.0413 | −0.3560 |
Allen | ||||
---|---|---|---|---|
Sites | MPE (%) | RMSE (kWh/m2/day) | MBE (kWh/m2/day) | NSE (kWh/m2/day) |
Abeche | −5.4824 | 0.8835 | −0.0548 | −1.4197 |
Faya-Largeau | −16.724 | 1.297 | −0.1672 | −1.256 |
Am-timan | −3.9584 | 0.5638 | −0.0396 | −0.2442 |
N’Djamena | 0.0784 | 0.8275 | 0.0008 | −0.4261 |
Moundou | −0.8437 | 0.3962 | −0.0084 | 0.7181 |
Sarh | −0.8779 | 0.5114 | −0.0088 | 0.5245 |
Pala | −3.0737 | 0.4175 | −0.0307 | 0.5684 |
Bongor | 5.1543 | 0.7879 | 0.0515 | −0.6421 |
Ati | −5.8254 | 0.9031 | −0.0583 | −1.4289 |
Bokoro | 1.1811 | 0.799 | 0.0118 | −0.9464 |
Mongo | −17.506 | 1.2438 | −0.1751 | −4.1008 |
Moussoro | −7.523 | 1.0278 | −0.0752 | −2.0198 |
Sabbagh | ||||
---|---|---|---|---|
Sites | MPE (%) | RMSE (kWh/m2/day) | MBE (kWh/m2/day) | NSE (kWh/m2/day) |
Abeche | 3.7042 | 0.5418 | 0.037 | 0.0899 |
Faya-Largeau | −6.7662 | 0.513 | −0.0677 | 0.6468 |
Am-timan | −8.8376 | 0.5406 | −0.0884 | −0.1439 |
N’Djamena | −0.3477 | 0.3842 | −0.0035 | 0.6927 |
Moundou | −6.8922 | 0.475 | −0.0689 | 0.5949 |
Sarh | −6.9461 | 0.4677 | −0.0695 | 0.6023 |
Pala | −7.8795 | 0.4787 | −0.0788 | 0.4327 |
Bongor | −2.1625 | 0.3344 | −0.0216 | 0.7042 |
Ati | 0.3564 | 0.2314 | 0.0036 | 0.84056 |
Bokoro | 5.0317 | 0.3798 | 0.0503 | 0.5602 |
Mongo | 4.8254 | 0.3722 | 0.0483 | 0.5432 |
Moussoro | 3.4003 | 0.3879 | 0.034 | 0.5697 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 3.080 | 10.634 | 7.663 |
February | −13.117 | 1.203 | 4.810 |
March | −24.563 | −10.714 | 6.064 |
April | −28.133 | −15.446 | 7.581 |
May | −17.467 | −19.488 | 2.635 |
June | −12.379 | −22.939 | −7.667 |
July | −3.725 | −13.289 | −6.577 |
August | −0.478 | −17.065 | −11.451 |
September | −2.886 | −7.701 | −1.493 |
October | −5.668 | 0.541 | 12.200 |
November | 2.898 | 7.263 | 13.184 |
December | 8.750 | 21.212 | 17.500 |
Average | −7.807 | −5.482 | 3.704 |
Month | Angstrom-Presott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 4.981 | −4.696 | −14.049 |
February | −10.066 | −13.944 | −14.802 |
March | −16.757 | −17.934 | −11.84 |
April | −23.745 | −21.456 | −5.409 |
May | −25.766 | −24.973 | −5.040 |
June | −27.056 | −26.26 | −4.164 |
July | −23.684 | −22.859 | −7.781 |
August | −23.314 | −21.857 | −9.331 |
September | −18.124 | −21.876 | −1.256 |
October | −11.506 | −16.619 | 0.865 |
November | −1.523 | −9.839 | −3.638 |
December | 11.066 | 1.630 | −4.748 |
Average | −13.791 | −16.724 | −6.766 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | −1.433 | 7.941 | −10.148 |
February | −7.705 | 2.388 | −9.643 |
March | −13.606 | −7.328 | −9.358 |
April | −9.865 | −10.885 | −5.277 |
May | −5.056 | −12.162 | −7.138 |
June | 0.458 | −10.951 | −8.829 |
July | 7.021 | −9.677 | −10.911 |
August | 8.853 | −11.415 | −12.83 |
September | 6.033 | −10.906 | −12.736 |
October | 2.911 | −4.298 | −8.870 |
November | −0.807 | 7.331 | −5.371 |
December | 2.547 | 12.462 | −4.941 |
Average | −0.887 | −3.958 | −8.838 |
Month | Angstrom-Prescot Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 13.41 | 22.629 | 1.562 |
February | −0.372 | 4.730 | 0.186 |
March | −11.604 | −5.652 | −4.183 |
April | −13.001 | −11.828 | −0.208 |
May | −10.214 | −12.63 | −0.673 |
June | −7.577 | −12.649 | −4.943 |
July | 0.054 | −9.729 | −5.975 |
August | −0.414 | −15.951 | −12.373 |
September | 2.094 | −11.264 | −7.69 |
October | 6.993 | 3.877 | 5.543 |
November | 13.416 | 18.321 | 12.405 |
December | 22.402 | 31.088 | 12.177 |
Average | 1.265 | 0.078 | −0.348 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | −3.103 | 6.442 | −13.401 |
February | −9.452 | −3.185 | −10.681 |
March | −8.754 | −2.913 | −5.300 |
April | −4.235 | −3.925 | −1.482 |
May | 4.319 | −3.628 | −2.690 |
June | 9.065 | −7.576 | −5.019 |
July | 11.074 | −3.554 | −3.079 |
August | 13.418 | −9.262 | −4.873 |
September | 9.981 | −5.778 | −7.918 |
October | 7.635 | 0.776 | −7.708 |
November | −0.58 | 7.585 | −9.871 |
December | 0.081 | 14.894 | −10.683 |
Average | 2.454 | −0.844 | −6.892 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | −4.619 | 9.429 | −11.667 |
February | −12.012 | 0.148 | −9.068 |
March | −13.67 | −10.817 | −10.758 |
April | −9.747 | −14.028 | −7.899 |
May | −0.293 | −7.534 | −3.224 |
June | 1.015 | −6.222 | −6.241 |
July | 7.899 | 1.870 | −0.819 |
August | 9.040 | −0.939 | −3.173 |
September | 1.184 | −2.175 | −7.359 |
October | 2.645 | −2.844 | −8.134 |
November | −1.252 | 6.524 | −8.023 |
December | −1.375 | 16.056 | −6.989 |
Average | −1.765 | −0.878 | −6.946 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 2.205 | 7.542 | −10.337 |
February | −4.787 | −3.902 | −11.801 |
March | −9.800 | −5.223 | −5.330 |
April | −6.407 | −11.008 | −2.358 |
May | 0.000 | −10.572 | −3.085 |
June | 6.398 | −3.002 | −7.167 |
July | 7.265 | −7.126 | −9.541 |
August | 10.123 | −6.311 | −8.012 |
September | 2.662 | −7.319 | −11.73 |
October | 4.860 | −4.947 | −9.877 |
November | 0.542 | 5.895 | −6.880 |
December | 4.725 | 9.089 | −8.436 |
Average | 1.482 | −3.073 | −7.879 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 4.184 | 20.972 | −6.024 |
February | −5.381 | 4.397 | −4.397 |
March | −9.154 | 0.619 | −1.888 |
April | −5.276 | 7.283 | 5.703 |
May | −2.985 | 2.952 | 3.947 |
June | 6.093 | 28.100 | 9.677 |
July | 7.579 | −16.349 | −6.528 |
August | 2.731 | −6.715 | −8.501 |
September | 6.972 | −5.271 | −7.645 |
October | 4.542 | −9.119 | −6.753 |
November | 2.538 | 14.805 | 0.423 |
December | 7.239 | 20.177 | −3.965 |
Average | 1.590 | 5.154 | −2.162 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 4.478 | 14.712 | −1.007 |
February | −10.204 | −0.692 | −5.881 |
March | −16.710 | −7.263 | −0.582 |
April | −19.872 | −14.188 | 3.091 |
May | −19.276 | −18.22 | 1.563 |
June | −16.039 | −20.470 | −0.926 |
July | −6.829 | −17.148 | −1.074 |
August | −0.811 | −20.635 | −5.961 |
September | −4.613 | −13.249 | −2.054 |
October | −3.277 | −2.588 | 4.739 |
November | 4.090 | 9.261 | 6.360 |
December | 11.708 | 20.576 | 6.008 |
Average | −6.446 | −5.825 | 0.356 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbag hErr (%) |
---|---|---|---|
January | 7.217 | 22.675 | 3.303 |
February | −5.759 | 9.364 | 1.811 |
March | −14.027 | −1.516 | 1.322 |
April | −14.948 | −6.278 | 8.685 |
May | −13.775 | −13.623 | 6.088 |
June | −9.417 | −14.903 | 4.531 |
July | 3.333 | −10.421 | 4.963 |
August | 7.321 | −9.962 | -0.415 |
September | 1.058 | −9.171 | -0.847 |
October | 1.183 | 2.487 | 6.609 |
November | 6.978 | 18.791 | 14.158 |
December | 12.275 | 26.73 | 10.172 |
Average | −1.547 | 1.181 | 5.032 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 4.537 | −7.438 | 3.292 |
February | −7.030 | −12.777 | 4.462 |
March | −13.418 | −22.701 | 3.269 |
April | −15.481 | −29.689 | 3.481 |
May | −12.33 | −27.670 | 5.216 |
June | −9.011 | −26.694 | 2.707 |
July | 3.419 | −24.881 | 1.682 |
August | 6.998 | −21.351 | 0.150 |
September | 2.043 | −23.357 | −1.314 |
October | 0.743 | −11.710 | 8.325 |
November | 6.087 | −6.051 | 14.855 |
December | 11.496 | 4.242 | 11.780 |
Average | −1.829 | −17.506 | 4.825 |
Month | Angstrom-Prescott Err (%) | Allen Err (%) | Sabbagh Err (%) |
---|---|---|---|
January | 7.963 | 12.822 | −0.430 |
February | −7.087 | −0.491 | −4.157 |
March | −15.216 | −22.28 | −7.258 |
April | −15.537 | −24.469 | −1.283 |
May | −17.130 | −21.794 | −0.179 |
June | −13.249 | −24.216 | 2.076 |
July | −3.327 | −15.079 | 6.375 |
August | 2.194 | −9.744 | 5.229 |
September | −2.222 | −7.622 | 7.257 |
October | −3.993 | −5.872 | 9.899 |
November | 3.124 | 5.135 | 10.467 |
December | 16.909 | 23.333 | 12.808 |
Average | −4.131 | −7.523 | 3.400 |
RMSE = 0.4256; MBE = −0.0089; NSE = 0.291) and Mongo (MPE (%) = −1.8291; RMSE = 0.5609; MBE = −0.0183; NSE = −0.0373).
The Allen model is appropriate for Moundou (MPE (%) = −0.8437; RMSE = 0.3962; MBE = −0.0084; NSE = 0.7181), Sarh (MPE (%) = −0.8779; RMSE = 0.5114; MBE = −0.0088; NSE = 0.5245) and Bokoro (MPE (%) = 1.1811; RMSE = 0.799; MBE = 0.0118; NSE = −0.9464). For the cities of Faya−Largeau (MPE(%)= −6.7662; RMSE = 0.513; MBE = −0.0677; NSE = 0.6468), Abeche (MPE(%) = 3.7042; RMSE = 0.5418; MBE = 0.037; NSE = 0.0899), N’Djamena (MPE (%) = −0.3477; RMSE = 0.3842; MBE = −0.0035; NSE = 0.6927), Ati (MPE(%) = 0.3564; RMSE = 0.2314; MBE = 0.034; NSE = 0.5697) and Moussoro (MPE(%) = 3.4003; RMSE = 0.3879; MBE = −0.0677; NSE = 0.6468), it is the Sabbagh model which is adapted for the calculation of the global solar radiation.
We can justify that one model is more suitable than another if the statistical values tend towards zero.
The Comparison between the measureddataandthe estimated values of the monthly global solar radiation is presented in
In this work, the most adapted mathematical model of estimating the global solar radiation has been determined for twelve sites of Chad. The main results show that Abeche, a site in the Sahelian zone, has an radiation of 6.354 kWh/m2, while Ati has solar radiation of 5.523 kWh/m2. In the Saharan zone to the north, Faya-Largeau has the best solar radiation potential around 6.013 kWh/m2. In southern of Chad, the site with highest solar radiation is Bongor (with 5.839 kWh/m2), but Sarh is the site with the lowest solar radiation of 5.751 kWh/m2. Three models, including the Angstrom-Prescott, Sabbagh and Allen models have been used to estimate the global solar radiation of each city, and these methods have been compared to the various statistical tests used to choose the appropriate model.
In terms of theoretical contributions, three equations were chosen:
Angstrom-PrescottModel : H / H 0 = 0.3721 + 0.3659 ( S / S 0 )
AllenModel : H = 0.6160 ∗ H 0
SabbaghModel : H = 3.7575 ∗ 10 3 ∗ exp L ( S S 0 − R H 1 / 3 100 − 1 T max )
The authors would like to thank the persons in charge of the National Meteorology for Chad, that of Bongor as well as the personnel who deal with the collection and the processing weather data on these sites, to have placed at our disposal the data used in this work.
Soulouknga, M.H., Falama, R.Z., Ajayi, O.O., Doka, S.Y. and Kofane, T.C. (2017) Determination of a Suitable Solar Radiation Model for the Sites of Chad. Energy and Power Engineering, 9, 703-722. https://doi.org/10.4236/epe.2017.912045