REVUE INTERNATIONALE D'HÉLIOTECHNIQUE    N° 40 (2009) 18-23

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Estimation of global solar radiation using meteorological parameters

M. Chegaar ¹, F. Guechi²

¹L.O.C., Ferhat Abbas University, Sétif, 19000, Algeria

²LAMA, Ferhat Abbas University, Sétif, 19000, Algeria

 Reçu  10-05-2009. Accepté le 27-05-2009. En ligne le 8-09-2009

ABSTRACT

Solar radiation is the most important parameter in the design and evaluation of solar energy devices. In this paper, ready models are developed to estimate the monthly global solar radiation in the Algerian territory. Measured global solar radiation on a horizontal surface and sunshine hours in different sites are analysed. Different expressions have been used to estimate global solar radiation from sunshine hours and maximum air temperature for the considered locations. For testing the models, statistical analysis of the results was performed. The root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE) are the fundamental measures of accuracy. The results show a remarkable agreement between the measured and the computed values using the different models.

 Keywords: Global solar radiation, sunshine duration, air temperature, Algeria

1.  INTRODUCTION

           An accurate knowledge of solar radiation distribution at a particular geographical location is of vital importance for surveys in agronomy, hydrology, ecology and sizing of the photovoltaic or thermal solar systems and estimates of their performances. Unfortunately for many developing countries solar radiation measurements are not easily available, therefore it is rather important to elaborate methods to estimate the solar radiation on the basis of more readily meteorological data. Over the years, many models have been proposed to predict the amount of solar radiation using various parameters [1-24]. Some works used the sunshine duration [1-8], others used mean daytime cloud cover or relative humidity and maximum and minimum temperature [9-11], while others used the number of rainy days, sunshine hours and a factor that depends on latitude and altitude.

Algeria is a high insolation country. It is situated in the region which is generally referred to as the solar belt. The number of sunshine hours amounts almost 3300h./year. The climate is most favourable for solar energy utilization, but the distribution of the solar radiation is not well known. The main objective of this work lies on the fundamental need of knowledge of the global solar radiation data in the country using relative sunshine duration, maximum air temperature and relative humidity.

Most analyses of the correlation between solar radiation in Algeria and climatological parameters involve the use of the percent possible sunshine in the Angstrom Prescott-Page equation and the noon height of the sun on the 15th of the month and an appropriate climatic parameter and is given by [12].

                                                    (1)

where G is the computed daily global radiation (MJ m⁻² day⁻¹), S is the monthly average daily bright sunshine hours and h is the noon solar altitude on the 15th of the month (degrees). K is a zone parameter that depends on the climate.

In this paper different correlations are applied to predict monthly average daily global solar irradiation on horizontal surface for several locations in Algeria. The obtained results are compared to measurements and good agreement is reported.

2. Calculation procedure

In the present work, data of the monthly mean of daily global solar radiation and sunshine duration from four Algerian meteorological stations (Algiers (36.43N, 3.15E), Oran (35.38N, 0.37W), Bechar (31.38N, 2.15W) and Tamanrasset (22047N, 5.31E)) are used [4].The duration of the records of sunshine duration is 25 years and of global solar radiation is approximately 10 years. Measurements of global solar radiation were performed with Robitzsh and Kip–Zonen pyranometers. For recording of sunshine duration, Campbell–Stokes heliographs are used. The duration of the records of the relative humidity and the maximum air temperature is 18 years.

The first model tested is a linear regression equation of Angstrom’s type [13]:

                                                                                    (2)

The second model is a  modified Swartman-Ogunlade equations [14] and is given as:

                                                  (3)

and finally a proposed equation involving the use of the maximum air temperature in the  Angstrom equation:

                                        (4)

where G is the monthly average daily global radiation on a horizontal surface (MJ m⁻² day⁻¹), G₀ is the monthly average daily extraterrestrial radiation on a horizontal surface (MJ m⁻² day⁻¹), S is the monthly average daily number of hours of bright sunshine, S₀ is the monthly average daily maximum number of hours of possible sunshine, R is the mean monthly relative humidity, T_m is the mean monthly maximum air temperature and a_i and b_i are correlations coefficients.

However, air temperature should also be considered as an important climatological variable for solar radiation prediction because it is a reflection of both the duration and intensity of the solar radiation incident on a given location. It may be recalled that the Campbell Stokes sunshine recorder, which is widely used to determine sunshine duration, does not give any indication of intensity as long as this exceeds the burning threshold value of about 140-280 W m^-2.

G₀ and S₀ can be obtained from

                                                  (6)

                                                           (7)

where I₀ is the solar constant equal to 1367 W m⁻², N is the day number starting from the first of January, δ is the declination, λ is the latitude and  is the hour angle. The coefficients a and b are determined by the method of least squares.

The four meteorological stations are divided into three zones according to the relative duration of sunshine [12] (Table 1).

Table 1. Relative duration of sunshine

The relative percentage error is defined as follows:

                                                                (8)

Gi,m and Gi,c are the ith measured and computed values of global radiation.

For testing the models, statistical analysis of the results was performed. The root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE) are the fundamental measures of accuracy. Thus, RMSE, MBE and MAE are given by:

       ,

       ,                                                                                                                      (9)

N is the number of measurements taken into account.

3. Results and discussion

Using Eq. (2)-(4), the monthly average daily global radiation values were calculated and appropriate correlations coefficients determined. These coefficients are presented in Table 2.

Table 2: Correlations coefficients for the different locations

Statistical indicators of accuracy, the root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE), for the different models are presented in Table 3. It is observed from the results that the maximum errors are obtained for the angstrom type model where the RMSE = 4.16% for Algiers, 4.64% for Oran, 4.83% for Bechar and 5.22% for Tamanrasset. However, the best results are obtained when combining relative duration of sunshine with maximum air temperature. In this case the RMSE = 3.48% for Algiers, 4.52% for Oran, 2.48% for Bechar and 4.18% for Tamanrasset. This shows that the relative duration of sunshine is not always the best single parameter to be used for predicting solar radiation. Introducing the maximum air temperature gives better results.

Table 3. Statistical indicators of accuracy for the different models

The variations of the daily global radiation measured and computed are represented in Fig.1, Fig.2, Fig.3 and Fig.4. The peak solar insolation occurs in the cases of Algiers, Oran and Bechar in June and July and for Tamanrasset in May to July, the solar radiation fluctuates from 22.21 to 29.37 MJ m⁻² day⁻¹ for all the stations.

4. Conclusion

The monthly average daily global radiation on a horizontal surface has been estimated using different empirical models. The first one is a linear regression equation of Angstrom’s type. The two last ones involve the use of the mean monthly relative humidity or the maximum air temperature in the Angstrom equation. The values of the coefficients a_i and b_i change from place to place according to the site climatic characteristics. The agreement between the measured and the estimated values is remarkable, and the models are recommended for use in any location in Algeria or station with similar climate especially the model considering the mean maximum air temperature.

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