Prediction of the Diffuse Solar Energy on Horizontal at Different Selected Locations

The main objective of this paper is to predict the diffuse solar energy on a horizontal surface by using data of global solar energy (H) and diffuse solar energy (H d ) at different selected geographical locations in Saudi Arabia during the period time from 1980 to 2019. The low values of the root mean square error RMSE for all correlations indicated a good agreement between the measured and calculated values of H d . The negative values of mean percentage error MPE % for all models show that for all locations, the proposed correlations slightly overestimate H d , and the absolute values of MPE never reach 1.35%. The first, second and third order correlations between the diffuse solar fraction H d /H and the clearness index K t and between the diffuse transmittance H d /H 0 and the sunshine hours have been proposed for the selected locations using the method of regression analysis. The differences be-tween the measured and calculated values of H d show that a first order correlation between H d /H and K t can be used for estimating H d at the present locations with good accuracy. However, second order correlations between H d /H or H d /H 0 and S/S o are recommended for estimating H d at these locations. The average annual differences between measured and calculated values of diffuse solar energy H d on horizontal at selected sites in the present research are discussed.


Introduction
Solar energy is considered one of the most important sources of renewable energy. Accurate knowledge of available solar energy with its direct and diffuse components in a particular place is of great importance in designing and sizing of solar energy conversion systems. A crucial input required in the simulation of buildings' energy performance is the availability of detailed information on the magnitudes of diffuse and direct irradiance data. Moreover, configuration and sizing of solar energy systems (e.g. photovoltaic cells, solar-thermal collectors) necessitates reliable solar radiation measurements. However, concurrent measured data of global and diffuse irradiance on horizontal surface or direct normal solar irradiance are available only for a limited number of locations [1] [2] [3]. The measurement of global horizontal irradiance is rather simple and cost-effective. It can be, conceivably, an integral part of the sensory equipment of every building. Given global solar irradiation measurements on a horizontal surface (as the most widely available data), direct and diffuse solar radiation components can be obtained through various correlations [4]. The models are usually expressed in terms of first to fourth degree polynomial functions relating the diffuse fraction k d (ratio of the diffuse-to-global solar radiation) with the clearness index k t (ratio of the global-to-extraterrestrial solar radiation on horizontal surface), as well as to other variables such as solar altitude, air temperature, relative humidity. Although these models are typically derived following sound approaches, their performance appears to lessen once they are applied to regions other than those, which provided the initial data for model development [5].
Solar radiation data is the basic input for solar applications, such as photovoltaic, solar thermal systems and passive solar design. The data should be reliable and can be used at any time to design, optimize and evaluate the performance of solar technology at any site. However, it is not economically feasible to install solar radiation measuring instruments wherever possible. Therefore, the use of mathematical models to forecast the solar radiation in a given area has proved to be a viable option based on the measurement results of limited locations [6] [7] [8]. Unfortunately, in many developing countries, solar radiation measurement is not yet available because they cannot afford the equipment and measurement technology. Hence, it is vital to create methods for evaluating solar radiation based on more promptly accessible meteorological data. Within the design and execution examination of solar energy projects, particularly within the design and measure assurance of solar PV as a future alternative energy source, exact forecast of diffuse solar radiation (DSR) is essential. Careful thought of DSR can much better assess the productivity of the solar system [9] [10] [11] [12]. In addition, in several regions of the world, there is no or very little measurement of diffuse solar radiation. Because of their wide application in other places, they can measure total horizontal irradiance and other standard meteorological variables, such as sunshine duration, temperature and relative humidity. In the field of meteorology and agriculture, given global solar radiation data and some meteo-

Data and Methodology
In the present research, the monthly average of daily global solar radiation H, diffuse solar radiation and the number of bright sunshine hours S available for three selected sites in Saudi Arabia (Al-Aqiq, Hail and Dammam) for the years from 1980 and 2019 are used. The geographical information of the selected locations are summarize in Table 1.
In the present research, the regression analysis is used for the proposed models, where the estimate and is the diffuse fraction (K d ) or diffuse coefficient (K D ) and the predictors are sunshine ratio (S/S o ) and clearness index (K t where H sc is the solar constant, n is the Julian day of the year, φ is the location latitude, and δ is declination angle, ω s is the sunset hour angle. δ and ω s are mathematically defined as: We can obtained the maximum possible sunshine duration (S o ) from In the present research, the results mentioned in the above section are used with the following correlations to express the dependence of diffuse radiation on various parameters in models of Equations (6)- (14) as follow [41] [42]:

Results and Discussion
The performance and evaluation of the statistical indicators mean bias error     The empirical models correlations in the form of Equations (15), (19) and (22) for all Saudi Arabia are developed. They may then be used for estimating H d for     sets of values). Figure 4 and Figure 5 provide the variations of H d /H with K t and S/S o , respectively. Figure 6 shows the variations of H d /H 0 and S/S o using the data collected for the three selected locations in the present research. A linear correlation between H d /H and K t found to fit the measured data see in Figure 4. Furthermore, second order correlations between H d /H and S/S o see in Figure 5, and H d /H 0 and S/S o are remarkable in Figure 6.
The following correlations have been obtained for all Saudi Arabia: Model A: The models from (27) to (29)     measured and calculated data of H d . The best estimate is obtained for Hail site see in Figure 8 and Hail site see in Figure 9, where the maximum percentage error is found to be ±9%. The maximum percentage errors are ±12% for Al-Aqiq site see in Figure 7. Therefore, comparisons between the measured and calcu-  Figure 10, the results obtained are a good Figure 10. The average annual differences between measured and calculated values of diffuse solar energy on horizontal at selected sites in the present research.
agreement is clear.

Conclusion
The as well as at any Saudi Arabia site with a reasonable accuracy. Therefore, the proposed modeling correlations can be used to accurately for estimating the annual averages of horizontal diffuse solar energy, which helps in predicted of the long-term performance of the various solar energy devices.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.