Elsevier

Applied Energy

Volume 64, Issues 1–4, 1 September 1999, Pages 369-378
Applied Energy

Empirical model development and comparison with existing correlations

https://doi.org/10.1016/S0306-2619(99)00108-7Get rights and content

Abstract

This study utilized monthly mean daily values of global solar-radiation and sunshine duration at 41 locations in Saudi Arabia and developed an empirical correlation for the estimation of global solar radiation at locations where it is not measured. The paper also presents the comparison between the present correlation and other models developed under different geographical and varied meteorological conditions. The comparisons are made using standard statistical tests, namely mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE) tests. The errors are calculated using monthly mean daily measured and estimated values of global solar radiation at all 41 locations. The study found that the present correlation produced the best estimates of global solar radiation.

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:H/H0=0.3465+0.352S/S0where 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:H/H0=a1+b1(S/S0)where a1=−0.14+1.2S/S0−0.82S/S02andb1=1.32−2.89S/S0+2.24S/S02

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:MBE=Σi=1nHic−HimnRMSE=Σi=1nHic−Him2nMPE=Σi=1nHic−HimHim×100nMABE=Σi=1nHic−Himn

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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