Empirical model development and comparison with existing correlations
Introduction
For the appropriate and accurate design of solar-energy conversion and utilization devices, a proper knowledge of the long term behaviour of measured global solar-radiation, beside other components, is necessary. Long-term data on global solar radiation are scarce for developing countries, while available for most of the industrialized countries. The Kingdom of Saudi Arabia has 41 solar radiation stations spread over the country. These stations have been operational since 1970 and data on global solar-radiation and sunshine-duration, as mentioned in Saudi Arabian Solar Radiation Atlas abbreviated to SASRA hereafter [1], are being recorded. The mean values of global solar-radiation H (Whm−2), sunshine duration in hours, along with latitude, longitude, and altitude of all the 41 locations are summarized in Table 1.
The prime objective of this study is to establish that the correlation developed in this study is accurate and can be used for the prediction of global solar-radiation on horizontal surfaces in Saudi Arabia. To achieve this objective, the author compared the present correlation with other existing models developed by researchers in different parts of the world.
Section snippets
Present empirical correlation
Angström [2] proposed the earliest correlation for the estimation of monthly average daily global solar radiation on horizontal surfaces. This technique then was used by many researchers like Prescott [3], Leung [4], Flocas [5], and others to develop empirical correlations.
The following relation gives the present correlation, developed using monthly mean daily pairs of H/H0 and S/S0 at all 41 locations:where H0 is the monthly mean daily extraterrestrial solar-radiation and S
Description of existing models
Samuel [6] used monthly average daily values of H and S along with H0 and S0 for four locations; namely Alutharama, Batalagoda, Colombo, and Peradeniya in Sri Lanka and proposed the following quadratic type of correlation for the estimation of H, if S is known:
The quadratic correlation for the estimation of H proposed by Akinoglu and Ecevit [7] is also used for comparison purposes. This correlation was developed using
Method of model evaluation
In general, the models are evaluated in terms of MBE, RMSE, MPE, and MABE. These error terms are calculated using the following equations:
In the above equations, Hic and Him are ith calculated and measured values of monthly average daily global solar radiation respectively, and n is the number of observation (n=12 for one location and n=492 for all 41 locations). A positive value of MBE shows an over-estimate while a
Results and discussion
As mentioned earlier, the models of , , , , , , , , , are evaluated in terms of four statistical tests namely MBE, RMSE, MPE and MABE. These error terms are obtained using measured monthly mean daily values of H for 41 locations and estimated values of H from 10 models. The mean, maximum and minimum values of all the error terms are given in Table 2. In evaluating the performance of all the models, only mean values of error terms are used. The maximum and minimum values are included to show
Conclusions
The present correlation of Eq. (1) having MBE=−0.015, RMSE=0.595, MPE=10.02% and MABE=0.533 produced the best estimates of H. The second best estimates were obtained from the model of Khogali et el. [11] given by Eq. (7), with MBE=0.067, RMSE=0.593, MPE=10.20%, and MABE=0.533. The frequency distribution analysis also shows that almost all the present correlation gave higher frequencies in lower intervals and vice versa. Hence this correlation should be used for the estimation of global
Acknowledgments
The authors wish to acknowledge the support of the Research Institute of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
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