Estimation of the Global Solar Radiation with the Artificial Neural Networks for the City of Sivas

In this study, global solar radiation in the city of Sivas was estimated by artificial neural networks (ANNs) using meteorological and geographical data obtained from four different measurement stations. Mean bias error (MBE), root mean square error (RMSE) and R2 ranged from -1.264 MJ/m2 to 0.938 MJ/m2, 0.710 MJ/ m2 to 1.598 MJ/m2 and 0.984 to 0.994, respectively. It is believed that ANN models could be used to predict global solar radiation for locations where only the temperature and sunshine duration data are available in the city of Sivas.


INTRODUCTION
Solar radiation is the most important meteorological parameter for many engineering applications, such as heating, cooling, energy production and storage, agricultural production, transport and building design.However, it is not widely available because of the cost of measuring equipment and its difficult maintenance and calibration [1].Therefore, other more readily available meteorological data such as sunshine hours, air temperature, cloudiness, relative humidity, precipitation, etc. have been widely used to estimate solar radiation by means of several prediction models [2][3][4][5][6][7][8][9][10][11][12][13].
In this study, the ANN method was used for estimating the monthly mean daily global solar radiation of Sivas City using meteorological data of four different measurement stations, namely Divriği, Gemerek, Kangal and Sivas City Center.Sivas is situated in the central part of Turkey, geographically located between east longitudes 35 0 50′ to 38 0 14′ and north latitudes 38 0 32′ to 40 0 16′.It has a continental climate with cold and snowy winters and hot and dry summers.Its long term annual mean temperature, mean minimum and maximum temperatures and mean sunshine duration for the years 1926-2016 are 8.9 0 C, 2.8 0 C, 15.3 0 C and 80.5 h, respectively [26].

MATERIAL AND METHOD
Artificial neural networks (ANNs) are information processing structures that are inspired by biological nervous systems, such as the human brain.Typically, an ANN consists of three main layers, each of which has a number of interconnected parallel processing units, called neurons (shortly nodes).These are the input layer, the output layer, and between them the hidden layers that can consist of one or more layers.ANNs learn the relation between input and output variables by examining (training) the previously recorded data.Basically, a neuron takes input from incoming connections, combines the input, performs usually a non-linear operation and outputs the final results [27,28].
In this study, a feed-forward backpropagation (FFBP) ANN model was used for estimating the solar radiation of Sivas City.The ANN architecture used in this study is schematically presented in Figure 1.It had three layers: the input layer, the hidden layer with 6 neurons and the output layer.The meteorological data obtained from the Turkish State Meteorological Service for the years 1986-2000 (2010-2016 for Divriği) were used to perform ANN modeling.A total of six geographical and meteorological variables, month, latitude, longitude, altitude, average temperature and sunshine duration were used in the input layer of the network.The output parameter was the solar radiation.Hyperbolic tangent and sigmoid transfer functions were used in the hidden and output layers, respectively.The Levenberg-Marquardt al-gorithm was chosen as the learning algorithm.The performance of the ANN model for each measurement station was validated by mean bias error (MBE), root mean square error (RMSE) and R-squared statistical test methods given by the formulas below.Low values of MBE are desired.Ideally, a zero value should be obtained.A positive and a negative value of MBE indicate overestimation and underestimation, respectively.RMSE is a measure of the deviation between the predicted and measured values.It is always positive and the ideal value is zero.The smaller the RMSE value, the better the model performance.The R-squared coefficient is the measure of goodness-of-fit between the measured and predicted data.As the value approaches 1, the accuracy of the model increases.

RESULTS AND DISCUSSION
In this study, 70% of the data was used for training and the remaining 30% for testing.Training and testing of the network continued until there was no improvement in the output.For each measurement station, the measured global solar radiation data in the year 2000 (2016 for Divriği) was used to compare with the predicted results.Figure 2 compares the measured and predicted monthly mean daily global solar radiation values for four stations.It can be seen that the predicted values are in good agreement with the measured data.
Monthly distribution of measured and predicted solar radiation values are given in Figure 3.In general, again, the predicted values obtained from the ANN model are in good agreement with the measurement data for all measurement stations.However, starting from March, the model showed overestimation of solar radiation for Kangal, while it tended to underestimate the values of the Sivas City Center.

CONCLUSION
In this study, global solar radiation values of the four measurement stations in the Sivas City were estimated using artificial neural network (ANN) method.The predicted results are in good agreement with the measurement data for all stations.It is concluded that ANN models could be used to estimate global solar radiation for the regions where only measured temperature and sunshine duration data are available in Sivas City.

Figure 2 .Figure 3 .
Figure 2. Comparison of measured and predicted global solar radiation

Table 1
presents the mean bias error (MBE), root mean square error (RMSE) and R-squared statistical test results for the measurement stations.The MBE values ranged from -1,264 MJ/m 2 to 0.938 MJ/m 2 .The lowest MBE value was 0.055 obtained for the measurement station Gemerek.The RMSE values varied from 0.710 MJ/m 2 to 1.598 MJ/m 2 obtained from the Divriği and Sivas City Center, respectively.The R-square values varied from the highest of 0.994 for Divriği to the lowest of 0.984 for Kangal.

Table 1 .
Statistical test results