Affordable and clean energy is the 7th goal in the Sustainable Development Goals (SDGs), which not only satisfies the sustainability but also saves the climate and environment. The most sustainable source of energy with unlimited and infinity reserves is the solar energy, which is the main source of all types of energy on earth. Accurate knowledge of solar radiation is considered to be the primary step in solar energy availability assessment and serves as the first input for various applications of solar energy [(Janjai et al., 2009); (Wong & Chow, 2001); (Hassan et al., 2017)]. The unavailability of the solar radiation measurements for several sites around the world, because of the high cost and equipment calibration and maintenance requirements [(El-Sebaii et al., 2010); (Hassan et al., 2017)], leads to proposing different models for predicting the global solar radiation. (Angström, 1924) introduced the primary sunshine-based model, which was modified by (Prescott, 1940) and has become the most widely used model around the world for evaluating solar radiation [(Unknown Author, 2013); (Almorox et al., 2005)]. The study of investigating the performance of 31 non-sunshine-based models for predicting the monthly average of daily global solar radiation on a horizontal surface was carried out by (Youssef et al., 2016). The models that have the most accurate estimations are recognized, and the best model among all models is also identified. Similarly, (Hassan et al., 2016) presented a new temperature-based model for estimating global solar radiation. The results showed that the new suggested models have accurate and excellent predictions for global solar radiation at different locations, especially at coastal sites. Furthermore, the new presented formulas of the best temperature-based model also provide better results compared with those for the most accurate sunshine-based models from the literature. In addition, the issue of assessing the performance of different day-of-the-year-based models to estimate global solar radiation - Case study: Egypt was carried out by (Hassan et al., 2016). The obtained results illustrated that the hybrid sine and cosine wave model and the 4th order polynomial degree model have the best estimations for global solar radiation on a horizontal surface. (Jiang, 2009) proposes study of computation of the monthly average daily global solar radiation using artificial neural networks and comparison with other empirical models in China. The developed ANN model used feed-forward back propagation algorithm in the analysis. (Şenkal & Kuleli, 2009) evaluated solar radiation in Turkey using artificial neural networks and satellite data. The ANN model used Scale Conjugate Gradient (SCG) and Resilient Propagation (RP) learning algorithms and logistic sigmoid transfer function.

This study aims to investigate the performance of artificial neural network models for estimating the monthly average daily global solar radiation on a horizontal surface, (G), at study location as a case study. For achieving this purpose, the measured global solar radiation data at New Borg El-Arab, Egypt (Lat. 30° 51 N and long. 29°3 4 E) are utilized for establishing and validating the proposed models. Moreover, the most commonly statistical indicators, such as Root Mean Square Error (RMSE) and coefficient of determination (R²), are calculated to evaluate the performance of these models [(Unknown Author, 2013); (Unknown Author, 2010)].

The performance of the models is evaluated using the most commonly statistical indicators, namely: Mean Percentage Error (MPE), Mean Bias Error (MBE), Root Mean Square Error (RMSE) and Coefficient of Determination (R²) (Hassan et al., 2016). The value of MPE between ±10% is considered an acceptable value, and it is clarified by (Eq. 1). The values of mean bias error (MBE) (Eq. 2) give information about the long-term performance of the developed model, where the positive MBE value refers to overestimation in the calculated value, and the negative MBE value refers to under-estimation in the calculated value. The smaller MBE value refers to the better model performance, and the small value is desired. The values of RMSE (Eq. 3) give information about the short-term performance of the model and are always positive values. A smaller value refers to a better performance of the model, and zero represents the ideal case. The values of (R²) (Eq. 4) illustrate information about the goodness of fit; R² values are between zero and one (0 ≤ R² ≤1), and the largest value is the desired value. The accepted range of RMSE, MPE, MBE is between ±10% MJ/m² day⁻¹[22]. The values of these statistical indicators are calculated using equations:

(1)

(2)

(3)

(4)

where Gi,c is the i h calculated value, and Gi,m is the i the measured value is the average value of the measured and calculated values; and n is the number of observations.

The measured data of daily global solar radiation and air temperature are divided into two data sets and averaged to acquire the monthly average daily values. The first data set from 1st July 1983 to 31st December 2002, is used to establish models. The second data set, from 1st January 2003 to 30th June 2005, is employed for evaluating and validating the developed models using statistical indicators. The predictions of three ANN models are compared with the measured data of global solar radiation. The values of statistical indicators for three ANN models (2-3- 1, 2-4-1, 2-5-1) are computed using equations Eqs. (1-4). The obtained values of different statistical indicators (RMSE, MPE, MBE and R²) are summarized in Table 1. The acceptable models are recognized, and the most accurate model is identified by comparing the statistical indicators associated with three models. The best ANN model is recognized in bold, as illustrated in Table 1.

According to the obtained results, the three ANN models have excellent estimations for the monthly average of daily global solar radiation, with good statistical indicators values in the acceptable range. The predictions of the three developed ANN models are compared with the measured data as illustrated in (a). Similarly, (b) demonstrates the prediction of the best ANN model (Model 1; 2-3-1) compared with the measured data. The statistical indicators graphs for the estimated values of monthly average of daily global solar radiation using three ANN models at New Borg El-Arab are clarified in Figure 3.

For MPE, all the models have values within the acceptable range and less than 1 %, with the lowest value of 0.18 for Model 3. All the three models give negative small values for MBE, which indicates a good long-term performance for the models with slight under-estimation in the calculated value. As shown in (a), all the three models accurately predict the global solar radiation for the period from January to April and from September to October. For November and December, the global solar radiation is slightly predicted. During the months from May to August, both Model 1 and Model 3 under predict the global solar radiation while Model 2 over predicts the global solar radiation during May.

These results are consistent with the values of MBE, which have small negative values with the lowest value of 0.0575 for Model 2, as shown in Figure 3. For RMSE, all the three models give small values, which indicate good short-term performance for the models with the smallest RMSE value of 0.657 and the best short-term performance for Model 1.

The R² values for three models are higher than 0.989 %, which indicate good fitting. In addition, all ANN models show a slight variation in their performance with excellent R² values, higher than 0.989 %. On the other hand, Model 1, which has three neurons in the hidden layer, provides the best performance with the highest R² value (Ajayi et al., 2014), followed by Model 3 that has five neurons in the hidden layer. For Model 1, the statistical indicators RMSE and R² are 0.66 MJ/m² and 0.9916%, respectively.

From the above discussion, it can be concluded that the developed models in this study can be employed for estimating global solar radiation with high accuracy. Consequently, the presented models are adequate for estimating monthly average daily global solar radiation on a horizontal surface. In addition, the proposed models indicate that the artificial neural network models demonstrate promising predictions of monthly mean daily global solar radiation by using commonly available data of extra-terrestrial solar radiation and temperature.

This work aims to investigate the performance of artificial neural network models for estimating the monthly average daily global solar radiation on a horizontal surface. To achieve this goal, the measured data of extra-terrestrial solar radiation, temperature and global solar radiation at study location are utilized for establishing and validating the proposed ANN models. According to the obtained results, the presented ANN models are applicable and significant for the quick and accurate prediction of the monthly average daily global solar radiation on a horizontal surface.

This work is supported by the Egyptian Science and Technology Development Fund (STDF) . The project number is " 10495 " and is entitled " Solar-Greenhouse-Desalination System Self productive of Energy and Irrigating Water Demand ".