Optimum ARX model prediction for monthly air temperature in delta. Egypt

كوكب الجغرافيا سبتمبر 25, 2019 سبتمبر 25, 2019
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Optimum ARX model prediction 

for monthly air temperature in delta. Egypt 

 Mosbeh R. Kaloop, 
Department of Public Works Engineering, Faculty of Engineering, Mansoura University, 35516, Egypt

 Mohamed M. Abdelaal
Department of Geography, Faculty of Education, Mansoura University, 35516, Egypt

H.T. El Shambaky
Department of Civil Engineering, Misr Higher Institute for Engineering and Technology, Mansoura, Egypt

research journal of environmental sciences - 2015


  This study aims to study the ability application of nonlinear Auto-Regression model with exogeneous inputs (ARX) in forecasting time series monthly temperatures changes in Delta, Egypt for 49 years (1960 to 2009) monitoring data. Three methods are used to estimate the optimal parameters of ARX model identification which are the normalized Least Mean Square (LMS), artificial Neural Network (NN) and Wavenet Neural network (WN). The time series temperature changes from 18 weather stations in Delta are used to compare and estimate the best method for the temperature change models. The models results indicate that the worst case solution for ARX model is LMS while the WN is found to be better than NN in the training period. The NN is found an acceptable performance for training and testing periods. The 95% auto-correlation function for the residuals models shows that there is no loss of information is observed for the applied ARXNN model; however, the ARXNN technique can be successfully used to predict the monthly temperatures of any site at the Delta area in Egypt. 

Key words: Temperature, ARX, least mean square, neural network, wavenet, delta, Egypt


   This study aims to apply the least mean square, arti cial Neural Network (NN) and Wavenet Neural network (WN) techniques for modeling long-term air temperature values by using time series observation data. In this study, the abilities of nonlinear auto-regression model with eXogeneous inputs (ARX), ARXNN and ARXWN models were investigated to predict air temperature and precipitation values using time series air temperature input-output observation data.

  The data from 18 weather stations in the Nile Delta region in Egypt were used for training and testing of the introduced models. The ARX [99] least mean square, neural network and wavelet neural network models were compared with each other with respect to root-mean-squared error, determination coefficient statistics and 95% of the confidence interval for ACF. The pre-analysis observation data concluded that the maximum variance is occurred in the summer time for the monitoring stations, while low variance occurs during winter time. However, the summer time temperature change is higher than winter time. Moreover, it can be seen that the Delta main temperature changes occur for the coastal points monitoring.

  The ARX model is shown lower quality in the training and testing periods. ARXWN model was found to be better than the ARXNN in the training period. In the test period, however, the ARXNN model performed better than the ARXWN model in five of nine stations. For the ARXNN and ARXWN models, the maximum determination coefficient values were found to be 0.989 and 0.996 in Rossetta and Khatatba stations, respectively. The minimum determination coefficient values were respectively found as 0.978 and 0.938 for the ARXNN and ARXWN models in Belbess and Zagazig stations. Moreover, the 95% ACF for the residuals models shown that no loss of information was observed since the residuals of the ARXNN model stayed within the confidence interval of the auto-correlation function. It can be concluded that the ARXNN technique can be used successfully to predict the long-term monthly temperatures of any site at Nile Delta region based on previously time series temperature measurements.

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