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Babak Mohammadi

Doctoral student

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Developing hybrid time series and artificial intelligence models for estimating air temperatures


  • Babak Mohammadi
  • Saeid Mehdizadeh
  • Farshad Ahmadi
  • Nguyen Thi Thuy Lien
  • Nguyen Thi Thuy Linh
  • Quoc Bao Pham

Summary, in English

Air temperature is a vital meteorological variable required in many applications, such as agricultural and soil sciences, meteorological and climatological studies, etc. Given the importance of this variable, this study seeks to estimate minimum (Tmin), maximum (Tmax), and mean (T) air temperatures by applying a linear autoregressive (AR) time series model and then developing a hybrid model by means of coupling the AR and a non-linear time series model, namely autoregressive conditional heteroscedasticity (ARCH). Hence, the hybrid AR-ARCH model was tested. To that end, the Tmin, Tmax, and T data from 1986 to 2015 at two weather stations located in Northwestern Iran were used for both daily and monthly time scales. The results showed that the hybrid time series model (i.e., AR-ARCH) performed better than the single AR for estimating the air temperature parameters at the study sites. Multi-layer perceptron (MLP) was then employed to estimate the air temperatures using lagged temperature data as input predictors. Next, the single AR and hybrid AR-ARCH time series models were utilized to implement the hybrid MLP-AR and MLP-AR-ARCH models. It is worth noting that developing the hybrid MLP-AR and MLP-AR-ARCH models, as well as AR-ARCH one is the novelty of this study. Three statistical metrics including root mean square error (RMSE), mean absolute error (MAE), and normalized RMSE (NRMSE) were used to investigate the performance of whole the developed models. The hybrid MLP-AR and MLP-AR-ARCH models were found to perform better than the single MLP when estimating the daily and monthly Tmin, Tmax, and T; however, the MLP-AR models outperformed the MLP-AR-ARCH ones. At the end of this study, the performance of MLP was evaluated under an external condition (i.e., estimating the temperature components at any particular site using the temperature data of an adjacent location). The results indicated that the temperature data of a nearby station can be used for estimating the temperatures of a desired station. Most accurate results during the test stage were obtained under a local assessment through the hybrid MLP-AR(1) at the Tabriz station when estimating the monthly Tmax (RMSE = 0.199 °C, MAE = 0.159 °C, NRMSE = 1.012%) and hybrid MLP-AR(12) at the Urmia station when estimating the daily Tmax (RMSE = 0.364 °C, MAE = 0.277 °C, NRMSE = 1.911%).

Publishing year







Stochastic Environmental Research and Risk Assessment



Document type

Journal article




  • Meteorology and Atmospheric Sciences
  • Oceanography, Hydrology, Water Resources


  • Air temperatures
  • Autoregressive
  • Autoregressive conditional heteroscedasticity
  • Estimation
  • Multi-layer perceptron




  • ISSN: 1436-3240