University of TehranPhysical Geography Research Quarterly2008-630X51220190622Comparison of Multiple Linear Regression and Artificial Intelligence Models in Estimating Global Solar RadiationComparison of Multiple Linear Regression and Artificial Intelligence Models in Estimating Global Solar Radiation3533727337210.22059/jphgr.2019.264084.1007263FAAli AakbarSabziparvarProfessor in Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, IranPouyaAghelpourMA in Agricultural Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran0000-0002-5640-865XVahidVarshavianAssistant Professor in Meteorology, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, IranJournal Article20180819Introduction
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.
<em>Multiple Linear Regressions (MR):</em> This model is a simple and linear model that estimates the target variable by assigning a constant optimized coefficient for each input variable.
<em>Adaptive Neuro-Fuzzy Inference System (ANFIS):</em> 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.
<em>Generalized Regression Neural Network (GRNN):</em> 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 (R<sup>2</sup>).
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 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=86.33%, ANFIS with RMSE=3.26 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=84.43%, GRNN with RMSE=3.41 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=82.86%, and MR with RMSE=4.11 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=75.20%, provided the best GSR estimates, respectively.
Conclusion
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. Introduction
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.
<em>Multiple Linear Regressions (MR):</em> This model is a simple and linear model that estimates the target variable by assigning a constant optimized coefficient for each input variable.
<em>Adaptive Neuro-Fuzzy Inference System (ANFIS):</em> 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.
<em>Generalized Regression Neural Network (GRNN):</em> 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 (R<sup>2</sup>).
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 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=86.33%, ANFIS with RMSE=3.26 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=84.43%, GRNN with RMSE=3.41 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=82.86%, and MR with RMSE=4.11 Mj.m<sup>-2</sup>.day<sup>-1</sup> and R<sup>2</sup>=75.20%, provided the best GSR estimates, respectively.
Conclusion
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. https://jphgr.ut.ac.ir/article_73372_5405f1bd3f45cc5a3ace6ee4e561efa2.pdf