Comparison of Multiple Linear Regression and Artificial Intelligence Models in Estimating Global Solar Radiation

Document Type : Full length article


1 Professor in Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran

2 MA in Agricultural Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran

3 Assistant Professor in Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran


Solar radiation is the main source of all energies on the Earth and is an important parameter in hydrology studies, water resource management, water balance equations, and plant growth simulation models. In the areas where ground measurements are not available, the Global Solar Radiation (GSR) can be estimated by empirical and semi-empirical models, satellite techniques, artificial intelligence models and other geostatistical approaches. In artificial intelligence models such as neural networks, various meteorological parameters like air temperature, relative humidity, sunshine hours, etc. are easily integrated to estimate global solar radiation.
In most commonly used radiation models (e.g. Angstrom-based models) for estimating daily GSR, the sunshine hours and cloud cover are two important input parameters. Unfortunately, those parameters are not measured very accurately in weather sites. Moreover, for time scales less than daily (e.g., hourly) using sunshine hour as an input, is not possible for predicting the sub-scale temporal GSR.
The main purpose of this study is to compare Multiple Linear Regression model and three types of artificial intelligence models (MLP, GRNN, and ANFIS) against each other to estimate GSR in cold semi-arid climate of Hamedan, Iran. This is to present the most accurate model by including the soil data and ignoring the sunshine hours.
Materials and methods 
According to the Extended De-Martonne climate classification model, Hamedan is located in a semi-arid-very cold area and has a mean altitude of 1851 meters above sea level. In this study, GSR and meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall) are recorded at Bu-Ali Sina University weather site, located at latitude 34°48″ and longitude 48° 28″. These data were recorded every 10 minute during 31 Dec. 2016, to 10 Mar. 2018 by using an automated Spanish GEONICA Logger.  
Multiple Linear Regressions (MR): This model is a simple and linear model that estimates the target variable by assigning a constant optimized coefficient for each input variable.
Adaptive Neuro-Fuzzy Inference System (ANFIS): A multi-layered network model that uses advanced neural network learning algorithms and fuzzy logic to describe the relationships between inputs and outputs. This model uses the neural network’s Learning ability and fuzzy rules to define the relationships between input-output variables.
Generalized Regression Neural Network (GRNN): This is a three-layered neural network, which the number of neurons in the first and last layers like other neural networks, is respectively equal to the input and output vectors. But, unlike other networks, the number of hidden layers of neurons in GRNN model is equal to the number of observational data.
Evaluation criteria: To evaluate the model performances against actual field measurements, we have used the Root Mean Square Error (RMSE) and Coefficient of Determination (R2).
Results and discussion
The correlations of models input variables (eight independent variables) versus GSR (dependent variable) were evaluated. The results revealed that maximum air temperature; average air temperature, relative humidity and soil temperature are the most influencing inputs for modeling GSR, using minimum numbers of meteorological parameters. Among them, maximum air temperature, minimum air temperature, atmospheric relative humidity and soil temperature, were selected as the best inputs for modeling least parameters. The percentages of train and test data were 75% and 25%, respectively. In this research, the models were run using two different samples. The results of the evaluations showed that random samples had higher accuracy in GSR estimates. In MR model, the 4-variables input, and in three artificial intelligence models (GRNN, ANFIS, MLP), 3-variables input showed the superior performances.
Finally, the models were evaluated by using all the eight inputs. At this stage, MLP with RMSE=3.04 and R2=86.33%, ANFIS with RMSE=3.26 and R2=84.43%, GRNN with RMSE=3.41 and R2=82.86%, and MR with RMSE=4.11 and R2=75.20%, provided the best GSR estimates, respectively.
The results showed that in all input variables, random and non-random samples, artificial intelligence models have better performance than linear regression. By availability of the whole eight meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall), MLP model can present the best GSR estimates. If all input parameters are not available, employing Generalized Regression Neural Network (GRNN) model and 3-variable inputs of mean air temperature, relative air humidity, and soil temperature is suggested for estimating the Global Solar Radiation (GSR) in cold semi-arid climate of Hamedan.
It is noteworthy that in estimating GSR, two important parameters of sunshine hours and cloud cover were not used in our research. Testing the models performances in other climate types is suggested as future works.  


Main Subjects

امامی‏فر، س. و علیزاده، ا. (1393). برآورد میزان تابش خورشیدی با استفاده از محصولات دمای سطح زمین سنجندة MODIS مدل شبکة عصبی، آب و خاک (علوم و صنایع کشاورزی)، ۲۷(۳): 617-625.
بیات، ک. و میرلطیفی، س.م. (1388). تخمین تابش کل خورشیدی روزانه با استفاده از مدل‏های رگرسیونی و شبکه‏های عصبی‏ مصنوعی، علوم کشاورزی و منابع طبیعی، ۱۶(۳): 270-280.
پیری، ج.؛ انصاری، ح. و فرید حسینی، ع. (1392). مدل‏سازی‏ تابش خورشید رسیده به‏ زمین‏ با استفاده‏ از ANFIS و مدل‏های‏ تجربی (مطالعة موردی: ایستگاه‏های زاهدان و بجنورد)، انرژی ایران، ۱۶(۳): 37-58.
سبزی‏پرور، ع.ا. و علیایی، ا. (1390). ارزیابی عملکرد شبکة عصبی مصنوعی در پیش‏بینی تابش خورشیدی کل روزانه و مقایسة آن با نتایج مدل آنگستروم (مطالعة موردی: ایستگاه همدیدی تبریز)، ژئوفیزیک ایران، ۵(۳): 30-41.
سبزی‏پرور، ع.ا. و بیات ورکشی، م. (1389). ارزیابی دقت روش‏های شبکة عصبی مصنوعی و عصبی‏- فازی در شبیه‏سازی تابش کل خورشیدی، پژوهش فیزیک ایران، ۱۰(۴): 347-357.
سبزی‏پرور، ع.ا. و ختار، ب. (1394). ارزیابی شبکة‏ عصبی مصنوعی و مدل تجربی ایرماک در تخمین تابش خالص خورشیدی روزانه در اقلیم سرد و نیمه‏خشک (مطالعة موردی: همدان)، دانش آب و خاک، ۲۵(۲): 37-50.
سبزی‏پرور، ع.ا. و ختار، ب. (1395). اعتبارسنجی مدل‏های تجربی و نیمه‏تجربی برآورد تابش خالص روزانه با استفاده از مقادیر اندازه‏گیری‏شده در اقلیم سرد و نیمه‏خشک، آب و خاک (علوم و صنایع کشاورزی)، ۳۰(۶): 2087-2100.
سیّدیان، س.م.؛ فراستی، م.؛ روحانی، ح. و حشمت‏پور، ع. (1396). تخمین تابش خورشیدی با استفاده از پارامترهای هواشناسی، تحقیقات منابع آب ایران، ۱۳(۱): 88-100.
قبایی سوق، م.؛ مساعدی، ا. و دهقانی، ا.ا. (1390). مدل‏سازی هوشمند تابش خورشیدی با استفاده از آزمون گاما و مقایسه با معادلات تجربی واسنجی‏شده در کرمانشاه، پژوهش‏های حفاظت آب و خاک، ۱۰(۴): 185-208.
کهخا مقدم، پ. و چاری، م.م. (1395). مقایسة‏ مدل‏های تجربی، رگرسیونی، و شبکة عصبی مصنوعی در برآورد تابش خالص دریافتی (Rs) در ایستگاه سینوپتیک زاهدان، جغرافیای طبیعی، ۹(۳۴): 137-150.
واثقیان، ی. (1395). تخمین تابش کلی خورشید در استان کرمانشاه با استفاده از شبکه‏های عصبی مصنوعی، انرژِی ایران، ۱۹(۱): 15-44.
هوشنگی، ن. و آل‏شیخ، ع.ا. (1393). ارزیابی روش‏های فازی، عصبی، و فازی- عصبی در تخمین تابش خورشیدی کشور، علوم و فنون نقشه‏برداری، ۴(۳): 187-200.
Abdallah, Y.A.G. (1994). New correlation of global solar radiation with meteorological parameters for Bahrain, Solar Energy, 16: 111-120.
Akinoglu, B.G. and Ecevit, A.A. (1990). Further comparison and discussion of sunshine based models to estimate global solar radiation, Energy, 15: 865-72.
Araghinejad, S. (2014). Data-Deriven Modeling: Using MATLAB in Water Resources and Environmental Engineering, NewYork, Springer.
Bayat, K.; Mirlatifi, S.M. (2009). Estimating global solar radiation using regression and artificial neural network models, Agricultural and Natural Resources Science, 16(3): 270-280.
Behrang, M.A.; Assareh, E.; Ghanbarzadeh, A. and Noghrehabadi, A.R. (2010). The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data, Solar Energy, 84(8): 1468-1480.
Benkaciali, S.; Haddadi, M.; Khellaf, A.; Gairra, K. and Guermoui, A. (2016). Evaluation of the global solar irradiation from the artificial neural network technique, Revue des Energies Renouvelables, 19(4): 617-631.
Bosch, J.L.; Lopez, G. and Batlles, F.J. (2008). Daily solar irradiation estimation over a mountainous area using artificial neural networks, Renewable Energy, 33: 1622-1628.
Bristow, K.L., Campbell, G.S., (1984).On the relationship between incoming solar radiation and daily maximum and minimum temperature, Agric. Forest Meteorol, Vol. 31, PP. 159-166.
Chen, R.S.; Ersi, K.; Yang, J.P.; Lu, S.H. and Zhao, W.Z. (2004). Validation of five global radiation models with measured daily data in China, Energy Convers. Manage, 45: 1759-1769.
Demirkaya, S. and Balcilar, M. (2012). The contribution of soft computing techniques for the interpretation of dam deformation, In FIG Working Week 2012 - Knowing to manage the territory, protect the environment, evaluate the cultural heritage, 6-10 May, Rome, Italy.
Elagib, N. and Mansell, M.G. (2000). New approaches for estimating global solar radiation across Sudan, Energy Convers Manage, 41: 419-34.
Emamifar, S. and Alizadeh, A. (2014). Estimation of Solar Radiation Using Land Surface Temperature MODIS Sensor Data and Neural Network Model, Journal of Water and Soil, 28(3): 617-625.
Fan, J.; Wang, X.; Wu, L.; Zhou, H.; Zhang, F.; Yu, X.; Lu, X. and Xiang, Y. (2018). Comparison of Support Vector Machine and Extreme Gradient Boosting for predicting daily global solar radiation using temperature and precipitation in humid subtropical climates: A case study in China, Energy conversion and management,  164: 102-111.
Ghabaei-Sough, M.; Mosaedi, A. and Dehghani, A.A. (2011). Solar radiation data and their intelligent modeling based on gamma test with evaluation of calibrated empirical equations, Journal of Water and Soil Conservation, 18(4): 185-208.
Guermoui, M.; Rahebi, A.; Benkaciali, S. and Dejelloul, D. (2016). Daily global solar radiation modelling using multi-layer perceptron neural networks in semi-arid region, Leonardo Electronic Journal of Practices and Technologies, 15(28): 35-46.
Guermoui, M.; Rabehi, A.; Gairaa, K. and Benkaciali, S. (2018). Support vector regression methodology for estimating global solar radiation in Algeria, The European Physical Journal Plus,  133(1): 22.
Halabi, L.M.; Mekhilef, S. and Hossain, M. (2018). Performance evaluation of hybrid adaptive neuro-fuzzy inference system models for predicting monthly global solar radiation, Applied energy,  213: 247-261.
Haykin, S. (1999). Neural Networks: a comprehensive foundation, MacMillan, New York.
Hooshangi, N. and Alesheikh, A.A. (2015). Evaluation of ANN, ANFIS and fuzzy systems in estimation of solar radiation in Iran, Journal of Geomatics Science and Technology, 4(3): 187-200.
Houichi, L.; Dechemi, N.; Heddam, S. and Achour, B. (2013). An evaluation of ANN methods for estimating the lengths of hydraulic jumps in U-shaped channel, Journal of Hydroinformatics, 15(1): 147-154.
Kahkha-Moghaddam, P. and Chari, M.M. (2017). Comparing empirical, regression and artificial neural network models, in estimating received net radiation of Zahedan synoptic station, Natural Geography, 9(34): 137-150.
Kassem, A.S.; Aboukarima, A.M.; El Ashmawy, N.M. and Zayed, M.F. (2016). Comparison of Empirical Models and an Adaptive Neuro Fuzzy Inference System for Estimating Hourly Total Solar Radiation on Horizontal Surface at Alexandria City, Egypt, Advances in Research, 7(5): 1-17.
Keshavarzi, A.; Sarmadian, F.; Shiri, J.; Iqbal, M.; Tirado-Corbala, R. and Evis Omran, E.S. (2017). Application of ANFIS-Based Subtractive Clustering Algorithm in Soil Cation Exchange Capacity Estimation Using Soil and Remotely Sensed Data, Measurement, 95: 173-180.
Khosravi, A.; Nunes, R.O.; Assad, M.E.H. and Machado, L. (2018). Comparison of artificial intelligence methods in estimation of daily global solar radiation, Journal of cleaner production,  194: 342-358.
Lopez, G.; Rubio, M.A.; Martinez, M. and Batlles, F.J. (2001). Estimation of hourly global photosynthetically active radiation using artificial neural network models, Agri Forest Meteorol, 107: 279-291.
Lotfinejad, M.M.; Hafezi, R.; Khanali, M.; Hosseini, S.S.; Mehrpooya, M. and Shamshirband, S. (2018). A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study, Energies, 11(5): 1-15.
Meenal, R. and Immanue Selvakumar, A. (2018). Assessment of SVM, empirical and ANN based solar radiation prediction models with most influencing input parameters, Renewable Energy, 121: 324-343.
Mohammadi, K.; Shamshirband, S.; Tong, C.V.; Amjad Alam, K. and Petkovic´, D. (2015). Potential of adaptive neuro-fuzzy system for prediction of daily global solar radiation by day of the year, Energy Conversion and Management, 93: 406-413.
Mohandes, M.; Rehman, S. and Halawani, T.O. (1998). Estimation of global solar radiationusing artificial neural networks, RenewEnergy, 14: 179-184.
Morshed Varzandeh, M.H.; Rahbari, O.; Vafaeipour, M.; Raahemifar, K. and Heidarzadeh, F. (2014). Performance of Wavelet Neural Network and ANFIS Algorithms for Short-Term Prediction of Solar Radiation and Wind Velocities, The 4thWorld Sustainability Forum, 1-30 Nov. 2014.
Mosavi, M.R. (2007). GPS Receivers Timing Data Processing using Neural Networks: Optimal Estimation and Errors Modeling, International Journal of Neural Systems, 17(5): 383-393.
Olatomiwa, L.; Mekhilef, S.; Shamshirband, S. and Petkovic´, D. (2015). Adaptive Neuro-fuzzy approach for solar radiation prediction in Nigeria, Renewable and Sustainable Energy Reviews, 51: 1784-1791.
Piri, J.; Ansari, H. and Farid-Hosseini, A. (2013). Modeling ground-reached solar radiation using ANFIS and empirical models (Case of study: Zahedan and Bojnourd stations), Iranian Journal of Energy, 16(3): 37-58.
Quej, V.H.; Almorox, J.; Arnaldo, J.A. and Saito, L. (2017). ANFIS, SVM and ANN soft-computing techniques to estimate daily global solar radiation in a warm sub-humid environment, Journal of Atmospheric and Solar–Terrestrial Physics, 155: 62-70.
Rahimi, J.; Ebrahimpour, M. and Khalili, A. (2013). Spatial changes of Extended De Martonne climatic zones affected by climate change in Iran, Theoretical ana Applied Climatology, 112(3-4): 409-418.
Sabziparvar, A.A. and Bayat-Varkeshi, M. (2011). Evaluation accuracy of artificial neural networks and neuro-fuzzy methods in simulating global solar radiation, Iranian Physics Research, 10(4): 347-357.
Sabziparvar, A.A. and Khataar, B. (2014). Evaluation of Artificial Neural Network (ANN) and Irmak Experimental Models to Predict Daily Solar Net Radiation (Rn) in Cold Semi-arid Climate (Case study: Hamedan), Water and Soil Science, 25(2): 37-50.
Sabziparvar, A.A. and Khataar, B. (2017). Validation of Empirical and Semi-empirical Net Radiation Models versus Observed Data for Cold Semi-arid Climate Condition, Journal of Water and Soil, 30(6): 2087-2100.
Sabziparvar, A.A. and Olyaie, E. (2012). Evaluation of the performance of artificial neural networks (ANN) in predicting the daily global solar radiation and comparison with results from the Angström model (case study: Tabriz synoptic station), Iranian Journal of Geophysics, 5(3): 30-41.
Seyedian, S.M.; Farasati, M.; Rouhani, H. and Heshmatpour, A. (2017). Solar Radiation Prediction Using Metrological Parameters, Iran-Water Resources Research, 13(1): 88-100.
Siva Krishna Rao K.D.V.; Premalatha, M. and Naveen, C. (2018). Analysis of different combinations of meteorological parameters in predicting the horizontal global solar radiation with ANN approach: A case study, Renewable and Sustainable Energy Reviews, 91: 248-258.
Sumithira, T.R. and Nirmal Kumar, A. (2012). Prediction of monthly global solar radiation using adaptive neuro fuzzy inference system (ANFIS) technique over the State of Tamilnadu (India): a comparative study, Applied Solar Energy, 48(2): 140-145.
Torabi, M.; Mosavi, A.; Ozturk, P.; Varkonyi-Koczy, A. and Istvan, V. (2018). September, A hybrid machine learning approach for daily prediction of solar radiation, In International Conference on Global Research and Education (PP. 266-274), Springer, Cham.
Tymvios, F.S.; Jacovides, C.P.; Michaelides, S.C. and Scouteli, C. (2005). Comparative study of Angstroms and artificial neural networks methodologies in estimating global solar radiation, Solar Energy, 78: 752-762.
Vakili, M.; Sabbagh-Yazdi, S.R.; Kalhor, K. and Khosrojerdi, S. (201). Using Artificial Neural Networks for Prediction of Global Solar Radiation in Tehran Considering Particulate Matter Air Pollution, Energy Procedia, 74: 1205-1212.
Vaseghian, Y. (2016). Estimating global solar radiation in Kermanshah province using artificial neural networks, Iranian Journal of Energy, 19(1): 15-44.
Yıldırım, H.B.; Çelik, Ö.; Teke, A. and Barutçu, B. (2018). Estimating daily Global solar radiation with graphical user interface in Eastern Mediterranean region of Turkey, Renewable and Sustainable Energy Reviews, 82: 1528-1537.