7
Estimating Global Solar Radiation Using Sunshine Hours
M. Chegaar, A. Lamri and A. Chibani 1
Physics Institut, Ferhat Abbas University, Setif 1 Physics Institut, University of Annaba, Annaba
Abstract - In the present paper, we describe how an empirical model, originally formulated by Sivkov to compute the monthly global irradiation, has been modified to make it fit some Algerian and Spanish sites.
Appropriate parameters have been introduced. The monthly average daily values of global irradiation incident on a horizontal surface at some Algerian and Spanish meteorological stations are computed by this method using sunshine hours and minimum air-mass. The obtained values, for Algeria, are then compared to those calculated by M. Capderou. Measurements of global solar irradiation on horizontal surface at some Spanish meteorological stations, published by J Canada, are compared to predictions made by this model.
The agreement between the measured and computed values and those estimated by this model is remarkable.
Résumé - Dans le présent article, nous décrivons comment un modèle empirique originairement formulé par Sivkov, pour calculer l’irradiation globale mensuelle, a été modifié pour être appliquer à quelques sites algériens et espagnols. Des paramètres appropriés ont été introduit. Les valeurs de l’irradiation globale moyenne mensuelle journalière, incidente sur une surface horizontale sur quelques stations météorologiques algériennes et espagnoles, ont été calculées par cette méthode en utilisant la durée d’ensoleillement et l’air- mass minimum. Les valeurs obtenues sont ensuite comparées à celles calculées par M. Capderou pour le cas de l’Algérie. Les valeurs mesurées de l’irradiation solaire globale, incidente sur une surface horizontale, par quelques stations météorologiques espagnoles et publiées par J. Canada, ont été comparées aux prédictions obtenues par ce modèle. L’accord entre les valeurs mesurées, calculées et celles obtenues par ce modèle est remarquable.
Keywords: Solar radiation - Global radiation - Algeria - Spain - Sunshine duration - Horizontal surface - Monthly average – Measured values.
1. INTRODUCTION
The development of many solar energy devices and for estimates of their performances require an accurate knowledge of solar radiation distribution at a particular geographical location. Unfortunately, solar radiation measurements are not easily available for many developing countries for not being able to afford the measurement equipment and techniques involved. Therefore, it is rather important to elaborate methods to estimate the solar radiation on the basis of more readily meteorological data.
Several empirical formulae have been developed to calculate the solar radiation using various parameters.
Some works used the sunshine duration [1-8] others used the sunshine duration, relative humidity and temperature [9, 10], while others used the number of rainy days, sunshine hours and a factor that depends on latitude and altitude [11].
Algeria is a high insolation country, The number of sunshine hours amounts almost 3300h./year. The weather is most favourable for the utilisation of solar energy, but the distribution of the solar radiation is not well known.
The importance of this work lies on the fundamental need of knowledge of the global solar radiation data in the country.
In the present work, an empirical method originally formulated by Sivkov [1] has been modified to make it fit some Algerian and Spanish meteorological stations. The model only requires the duration of sunshine and minimum air-mass. Sivkov has proposed the following relation :
1 . n 2 31
. m 1
m 4.9(s ) 10500(sinh )
G = + (1)
Where Gm is the monthly global radiation (cal.cm-2), Sm is the monthly average daily number of bright sunshine (hours), and hn is the noon height of the sun on the 15th of the month.
2. CALCULATION PROCEDURE
In the present work, data of monthly mean of daily global solar radiation and sunshine duration from four Algerian meteorological stations (Algiers, Oran, Béchar and Tamanrasset) and five Spanish stations (Alicante, Castellon, Cofrentes, Murcia and Valencia) are used. The geographical location of stations and the sources of data are presented in Table 1. Measurements of global solar radiation were performed with Robitzsh and Kipp &
Zonen pyranometers. For the recording of sunshine duration there are used Campbell-Stokes heliographs.
Table 1: Geographical location of stations and sources of data Country Station Latitude
(deg)(N) Altitude
(m) Longitude
(degree) Duration of records
sunshine radiation Source of data
Algiers 36.43 25 3.15 E 25 10 [4]
Oran 35.38 99 0.37 W 25 10 [4]
Béchar 31.38 806 2.15 W 25 10 [4]
Algeria
Tam. 22.47 1378 5.31 E 25 10 [4]
Alicante 38.36 81 0.5 W 22 6 [1]
Castellon 39.95 27 0.68 W 30 5 [1]
Cofrentes 39.20 387 1.05 W 9 9 [1]
Murcia 37.98 72 1.11 W 16 8 [1]
Spain
Valencia 39.46 15 0.36 W 23 11 [1]
The monthly average of daily global irradiation on a horizontal surface is obtained by changing sm to the daily value s and dividing the constant by 30 days of the month and introducing an appropriate parameter (K).
The modified formula is :
+
= −2 1.11 (sinh)2.08
30 10500 )
s ( K 10 18 . 4
G (2)
Where G is the computed daily global irradiation (MJ.m-2.day-1), s is the monthly average daily bright sunshine hours (hours) and h is the noon solar altitude on file 15th of the month (degrees). K is a zone parameter that depends on the climate. The values obtained using eq. (1), for the Algerian meteorological stations, are then compared with calculations made by Capderou [4]. He used the regression equation of Angstrom’s type :
+
=
0
0 s
b s H a
H (3)
Where H is the monthly average daily global irradiation on a horizontal surface (MJ.m-2.day-1), H0 is the monthly average daily extraterrestrial irradiation on a horizontal surface ( MJ.m-2.d-1), s is the monthly average daily number of hours of bright sunshine, s0 is the monthly average daily maximum number of hours f possible sunshine and a and b are regression constants. Capderou found : a = 0.41 and b = 0.58. For the Spanish stations the monthly average daily global irradiation values obtained using the proposed formula are compared to those estimated by Canada [1]. He proposed the following formula :
24
) h sin ( 10 )
h sin ( 30 / 10550 )
180 / h ( ) s ( H K
3 1
. 2 19
. 0 24
. 1
e π + +
= − (4)
Where He is the daily global irradiation (MJ.m-2.day-1). The used zone parameter is K = 14.
3. RESULTS AND DISCUSSION
The Algerian meteorological stations are divided into three zones according to the characteristics of their climate, Mediterranean climate for Algiers and Oran, Sahara climate for Béchar and Tamanrasset which is influenced by the African tropical climate.
Fig. 1: Monthly average of daily global
in irradiance in Algiers Fig. 2: Monthly average of daily global irradiance in Oran
The monthly average daily global irradiation values are calculated using eq. (2). Appropriate zone parameters have been determined, K = 19.4 (Algiers and Oran), K = 21.3 (Béchar) and K = 23.3 (Tamanrasset).
The results are presented in Table 2.
Where a comparison with measurements and with calculation made by Capderou is also given. The variation of the daily global irradiation measured and computed are represented in Figs (1-4). The best estimates of global irradiation were calculated for Béchar and Tamanrasset. The maximum errors are -10.65 per cent for Algiers, 10.64 per cent for Oran, 5.94 per cent for Béchar and 8.12 per cent for Tamanrasset, whether the maximum errors using Capderou model are respectively -11.04 %, 10.45 %, 13.42 % and -13.56 %.
The peak solar insolation occurs in the cases of Algiers, Oran and Béchar in June, July and for Tamanrasset in May, July. The solar radiation fluctuates from 25.38 MJ.m-2.day-1 to 28.26 MJ.m-2.day-1 for all the stations.
Table 2 Comparison between G1 and Gm, and Gm and G2 for Algerian stations
Station Var. Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
Algiers S H G1
Gm
G2
E1
E2
4.70 32.02
8.43 7.88 7.91 -6.91 -0.27
5.98 40.32 11.82 10.69 11.69 -10.5 -9.29
7.08 50.82 15.73 14.87 15.95 -7.83 -7.26
7.91 62.76 19.51 17.68 19.63 -10.7 -11.0
9.91 71.96 23.52 21.64 23.75 -8.69 -9.78
10.27 76.56 24.57 22.21 24.47 -10.6 -10.1
11.12 74.95 25.36 25.38 24.97 0.08 1.62
10.73 67.60 23.72 22.90 23.01 -3.62 -0.50
9.11 56.63 19.48 18.43 18.51 -5.67 -0.43
6.91 45.06 14.06 12.71 12.99 10.65 -2.21
5.15 35.00
9.60 9.79 8.68 1.91 11.32
4.68 30.06
7.97 7.42 7.09 -7.47
4.37
Oran S H G1
Gm
G2
E1
E2
5.24 33.10
9.26 9.36 8.75 1.11 6.54
5.68 41.40 11.77 12.53 11.75 6.08 6.21
7.55 51.90 16.54 18.50 16.91 10.64 8.60
8.14 63.84 20.00 20.28 21.24 5.85 4.54
9.57 73.04 23.29 23.08 23.55 -0.91 -2.06
9.91 77.64 24.28 27.00 24.18 10.09 10.45
11.33 76.03 25.74 26.60 25.52 3.23 4.06
10.56 68.68 23.72 24.16 23.12 1.80 4.29
8.85 57.71 19.44 20.56 18.58 5.44 9.63
7.37 46.14 14.86 14.00 13.90 -6.08 0.77
5.39 36.08 10.12 9.94 9.25 -1.89
6.88 5.11 31.14
8.67 8.03 7.82 -7.99
2.60
Béchar S H G1
Gm G2
E1 E2
7.91 37.10 14.00 14.47 13.38 3.23 7.56
8.72 45.40 17.07 17.14 17.39 0.385 -1.47
9.94 55.90 21.28 22.00 22.29 3.28 -1.34
10.75 67.83 24.90 24.59 24.25 -1.27 1.38
11.16 77.04 26.82 26.03 27.77 -3.05 -6.53
11.64 81.64 27.88 28.26 28.45 1.33 -0.69
11.63 80.03 27.74 26.78 27.88 -3.56 -4.09
10.93 72.68 25.94 24.52 25.62 -5.82 -4.49
10.05 61.71 22.76 22.07 22.41 -3.15 -1.57
9.03 50.14 18.68 18.47 18.06 -1.16 2.18
8.04 40.08 14.86 14.58 13.93 -1.90 4.44
7.58 35.14 13.07 13.90 12.03 5.94 13.42
Tam.
S H G1
Gm G2
E1 E2
8.40 45.95 17.70 18.25 17.86 3.02 2.17
9.12 54.25 20.80 22.10 21.69 5.881 1.86
9.98 64.75 24.39 22.57 25.63 -8.06 -13.6
9.66 76.68 25.90 28.19 26.78 8.12 4.98
9.95 85.89 27.03 27.52 25.92 -4.28 -6.17
9.23 89.51 26.11 26.00 26.14 0.11 0.52
9.94 88.88 27.09 26.87 26.35 -2.79 -1.97
9.85 81.53 26.64 26.28 25.96 -2.63 -1.25
8.89 70.56 23.96 23.99 24.01 0.22 0.09
8.87 58.99 21.60 21.41 22.07 2.13 3.00
8.86 48.93 19.10 18.84 18.68 -2.22 -0.81
8.40 43.99 17.19 16.93 16.13 -6.60 -4.96 For the Spanish stations, solar radiation data are computed for all the stations using the proposed formula with a single zone parameter, K = 19.9. The results are in very good agreement with the measured values. They are given in Table 3. Where a comparison with the predicted values obtained by Canada's model. The errors ranged between the following minima and maxima values : (-4.30 %, 7.77%) for Alicante, (-5.74%, 0.93%) for Castellon, (-5.19%, 4.63%) for Cofrentes, (-2.361%, 5.71%) for Murcia and (-7.86% , 4.11%) for Valencia.
Using Canada's model the errors minima and maxima are respectively (-3.67%, 9.18%), (-4.16%, 4.44%), (- 2.94%, 6.74%), (-2.31%, 7.38%) and (-5.32%, 6.26%). It is observed that for all the stations, the obtained results fit the experimental data within 8 % using the proposed model and within 10 % using Canada's model.
Fig. 3: Monthly average of daily global
irradiance in Béchar (Algeria) Fig. 4: Monthly average of daily global irradiance in Tamanrasset (Algeria)
4. CONCLUSION
The monthly average daily global irradiation incident on a horizontal surface has been estimated by the formula originally formulated by Sivkov and modified by the authors to make it fit some Algerian and Spanish meteorological stations. The formula requires only the sunshine duration and the noon solar altitude of the sun.
Appropriate zone parameters have been determined K=19.4, 21.3 and 23.3 for the Algerian stations and a single parameter (K=19.9) for all the Spanish stations. The accuracy is better than 10.7 per cent for Algiers and Oran, 6 per cent for Bechar and 8.2 per cent for Tamanrasset and within 8 % for all the Spanish stations. The proposed formula gives better estimates of global irradiation when compared to Capderou and Canada formulas. It is possible to determine other zone parameters by extending this model to more Algerian meteorological stations and stations in the Mediterranean coast and then to predict the global solar irradiation in these different locations.
NOMENCLATURE s : Monthly average daily sunshine hours
Gm : Measured monthly average of daily global irradiance (MJ.m-2) h : Noon solar altitude on the 15th of the month (degrees)
G1 : Computed monthly average of daily global irradiance using the proposed model (MJ.m-2) G2 : Computed monthly average of daily global irradiance using Capderou's model (MJ.m-2) El : Per cent deviation between G1 and G2
E2 : Per cent deviation between G2 and Gm
Table 3: Comparison between G1 and Gm, and Gm and G2 for Spanish stations
Station Var. Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
Alicante S H G1
Gm
G2
E1
E2
5.57 30.37
9.14 9.04 9.10 -1.09 -0.66
6.47 38.67 12.11 12.14 11.96 0.25 1.48
8.11 49.17 16.68 18.09 16.43 7.77 9.18
9.11 61.11 20.76 20.94 20.32 0.87 2.96
10.13 70.31 23.78 23.75 23.19 0.11 2.36
11.43 74.91 26.03 26.57 25.36 2.03 4.55
11.83 73.30 26.29 26.28 25.66 -0.04 2.36
10.50 65.95 23.42 22.79 22.96 -2.78 -0.75
9.00 57.98 19.19 19.48 18.79 1.49 3.54
7.33 43.41 14.30 14.45 14.03 1.06 2.91
6.27 33.35 10.60 10.90 10.52 2.78 3.49
5.14 28.41
8.24 7.90 8.19 -4.30 -3.67
Castellon S H G1
Gm G2
E1
E2
4.92 28.78
8.08 8.06 8.01 -0.19
0.62 5.48 37.08 10.60 10.05 10.42 -5.51 -3.68
6.92 47.58 14.90 15.30 14.62 2.59 4.44
7.98 59.51 19.08 19.23 18.63 0.79 3.12
9.09 68.72 22.27 22.48 21.68 0.93 3.56
10.22 73.32 24.36 24.56 23.70 0.83 3.50
11.22 71.71 25.31 24.60 24.70 -2.89 -0.41
9.26 64.36 21.63 20.44 21.09 -5.83 -3.18
7.66 53.39 17.23 16.97 16.80 -1.55 1.00
6.63 41.82 13.09 12.92 12.81 -1.30 0.85
5.31 31.76
9.16 8.66 9.02 -5.74 -4.16
4.68 26.82
7.41 7.38 7.36 -037 0.27
Cofrentes S H G1
Gm G2
E1 E2
4.06 29.53
7.30 7.21 7.14 -1.24
0.97 4.75 37.83
9.98 9.84 9.75 -1.45 0.91
6.46 48.33 14.57 15.28 14.25 4.63 6.74
7.31 60.26 18.47 18.29 18.01 -1.01 1.53
7.78 69.47 20.87 20.39 20.28 -2.37 0.54
9.43 74.07 25.53 23.05 22.85 -2.07 0.87
10.15 72.46 24.15 23.73 23.49 -1.75 1.01
8.69 65.11 21.11 20.39 20.54 -3.55 -0.74
7.53 54.14 17.27 16.69 16.81 -3.47 -0.72
5.98 42.57 12.55 11.97 12.21 -4.81 -2.01
5.24 32.51
9.25 8.83 9.09 -4.76 -2.94
3.70 27.57
6.50 6.18 6.24 -5.19 -0.97
Murcia S H G1
Gm
G2
E1 E2
4.85 29.27
8.10 8.12 8.02 -2.30 -1.59
5.07 37.57 10.27 10.71 10.04 -3.71 -2.31
6.69 48.07 14.77 14.62 14.46 5.71 7.38
7.18 60.01 18.27 18.17 17.81 0.92 3.23
7.65 69.21 20.68 20.86 20.09 0.95 3.34
9.00 73.81 22.98 22.29 22.32 1.50 4.05
9.73 72.20 23.61 22.96 22.95 4.81 7.18
8.84 64.85 21.24 19.95 20.66 0.01 2.31
7.78 53.88 17.49 16.70 17.05 -0.21 2.01
6.42 42.31 12.98 12.03 12.67 -2.36 -0.15
5.43 32.25
9.40 9.01 9.27 -1.86 -0.60
4.71 27.31
7.54 7.31 7.47 -1.43 -0.38
Valencia S H G1
Gm
G2
E1 E2
4.85 29.27
8.10 8.12 8.02 0.21 1.23
5.07 37.57 10.27 10.71 10.04 4.11 6.26
6.69 48.07 14.77 14.62 14.46 -1.01 1.09
7.18 60.01 18.27 18.17 17.81 -0.53 1.98
7.65 69.21 20.68 20.86 20.09 0.88 3.69
9.00 73.81 22.98 22.29 22.32 -3.11 -0.13
9.73 72.20 23.61 22.96 22.95 -2.82 0.04
8.84 64.85 21.24 19.95 20.66 -6.45 -3.56
7.78 53.88 17.49 16.70 17.05 -4.76 -2.10
6.42 42.31 12.98 12.03 12.67 -7.86 -5.32
5.43 32.25
9.40 9.01 9.27 -4.35 -2.89
4.71 27.31
7.54 7.31 7.47 -3.14 -2.19
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