Comparison of Classical and Machine Learning Methods in Estimation of Missing Streamflow Data

Recovering missing data and access to a complete and accurate streamflow data is of great importance in water resources management. This article aims to comparatively investigate the application of different classical and machine learning-based methods in recovering missing streamflow data in three mountainous basins in northern Iran using 26 years of data duration extending from 1991 to 2017. These include Taleghan, Karaj, and Latyan basins that provide municipal water for the capital Tehran. Two periods of artificial gaps of data were considered to avoid possible duration-based impacts that may affect the results. For this purpose, several methods are investigated including simple and multiple linear regressions (LR & MLR), artificial neural network (ANN) with five different structures, support vector regression (SVR), M5 tree and two Adaptive Neuro-Fuzzy Inference System (ANFIS) comprising Subtractive (Sub-ANFIS) and fuzzy C-means (FCM-ANFIS) classification. Although these methods have been used in different problems in the past, but the comparison of all these methods and the application of ANFIS using two clustering methods in missing data is new. Overall, it was noticed that machine learning-based methods yield better outputs. For instance, in the Taleghan basin and in the gap during 2014–2017 period it shows that the evaluation criteria of Root Mean Square Error (RMSE), Nash–Sutcliffe Index (NSE) and Coefficient of Determination $${({\text{R}}}^{2})$$ ( R 2 ) for the Sub-ANFIS method are 1.67 $${{\text{m}}}^{3}/s$$ m 3 / s , 0.96 and 0.97, respectively, while these values for the LR are 3.46 $${{\text{m}}}^{3}/s$$ m 3 / s , 0.83 and 0.87 respectively. Also, in Latyan basin during the gap of 1991–1994, FCM-ANFIS was found to be the best method to recover the missing monthly flow data with RMSE, NSE and $${{\text{R}}}^{2}$$ R 2 criteria as 3.17 $${{\text{m}}}^{3}/s$$ m 3 / s , 0.88 and 0.92, respectively. In addition, results indicated that using the seasonal index in the artificial neural network model improves the estimations. Finally, a Social Choice (SC) method using the Borda count was employed to evaluate the overall performance of all methods.