Hydrological modeling is one of the important subjects in managing water resources and the processes of predicting stochastic behavior. Developing Data-Driven Models (DDMs) to apply to hydrological modeling is a very complex issue because of the stochastic nature of the observed data, like seasonality, periodicities, anomalies, and lack of data. As streamflow is one of the most important components in the hydrological cycle, modeling and estimating streamflow is a crucial aspect. In this study, two models, namely, Optimally Pruned Extreme Learning Machine (OPELM) and Chi-Square Automatic Interaction Detector (CHAID) methods were used to model the deterministic parts of monthly streamflow equations, while Autoregressive Conditional Heteroskedasticity (ARCH) was used in modeling the stochastic parts of monthly streamflow equations. The state of art and innovation of this study is the integration of these models in order to create new hybrid models, ARCH-OPELM and ARCH-CHAID, and increasing the accuracy of models. The study draws on the monthly streamflow data of two different river stations, located in north-western Iran, including Dizaj and Tapik, which are on Nazluchai and Baranduzchai, gathered over 31 years from 1986 to 2016. To ascertain the conclusive accuracy, five evaluation metrics including Correlation Coefficient (R), Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), the ratio of RMSE to the Standard Deviation (RSD), scatter plots, time-series plots, and Taylor diagrams were used. Standalone CHAID models have better results than OPELM methods considering sole models. In the case of hybrid models, ARCH-CHAID models in the validation stage performed better than ARCH-OPELM for Dizaj station (R = 0.96, RMSE = 1.289 m³/s, NSE = 0.92, MAE = 0.719 m³/s and RSD = 0.301) and for Tapik station (R = 0.94, RMSE = 2.662 m³/s, NSE = 0.86, MAE = 1.467 m³/s and RSD = 0.419). The results remarkably reveal that ARCH-CHAID models in both stations outperformed all other models. Finally, it is worth mentioning that the new hybrid “ARCH-DDM” models outperformed standalone models in predicting monthly streamflow.

A gradient boosting regression tree (GBT) approach is introduced for 1- and 3-month-ahead standardized precipitation–evapotranspiration index (SPEI) classification for Antalya and Ankara in Turkey. First, the numerical target series of SPEI-6 was converted into the categorical vectors of extreme wet, wet, near normal, dry, and extremely dry labels. Then, a GBT model was trained and validated using the lagged SPEI-6 series of four global grid points closest to each city. The model efficiency was surveyed in terms of kappa, overall accuracy, misclassification rate, class recall, class precision, and F1 score. The GBT was also compared with the traditional decision tree and state-of-the-art random forest models developed as the benchmarks. Despite facing the unbalanced label vectors, the GBT approach showed promising processing performance with an overall accuracy of 77% (83%) and 74% (72%) in Antalya (Ankara) at 1- and 3-month-ahead prediction scenarios, respectively.

Accurate streamflow prediction is essential in reservoir management, flood control, and operation of irrigation networks. In this study, the deterministic and stochastic components of modeling are considered simultaneously. Two nonlinear time series models are developed based on autoregressive conditional heteroscedasticity and self-exciting threshold autoregressive methods integrated with the gene expression programming. The data of four stations from four different rivers from 1971 to 2010 are investigated. For examining the reliability and accuracy of the proposed hybrid models, three evaluation criteria, namely the R², RMSE, and MAE, and several visual plots were used. Performance comparison of the hybrid models revealed that the accuracy of the SETAR-type models in terms of R² performed better than the ARCH-type models for Daryan (0.99), Germezigol (0.99), Ligvan (0.97), and Saeedabad (0.98) at the validation stage. Overall, prediction results showed that a combination of the SETAR with the GEP model performs better than ARCH-based GEP models for the prediction of the monthly streamflow. Abbreviations: ADF = Augmented Dickey-Fuller; AIC = Akaike Information Criterion; ANFIS = Adaptive Neuro-Fuzzy Inference System; ANNs = Artificial Neural Networks; AR = Autoregressive Models; ARIMA = Autoregressive Integrated Moving Average; ARCH = Autoregressive Conditional Heteroscedasticity; ATAR = Aggregation Operator Based TAR; BL = Bilinear Models; BNN = Bayesian Neural Network; CEEMD = Complete Ensemble Empirical Mode Decomposition; DDM =Data-Driven Model; GA = Genetic Algorithm; GARCH = Generalized Autoregressive Conditional Heteroscedasticity; GEP = Gene Expression Programming; KNN = K-Nearest Neighbors; KPSS = Kwiatkowski–Phillips–Schmidt–Shin; LMR = Linear and Multilinear Regressions; LR = Likelihood Ratio; LSTAR = Logistic STAR; MAE = Mean Absolute Error; PACF = Partial Autocorrelation Function; PARCH = Partial Autoregressive Conditional Heteroscedasticity; R² = Coefficient of Determination; RMSE = Root Mean Square Error; RNNs = Recurrent Neural Networks; SETARMA = Self-Exciting Threshold Autoregressive Moving Average; SETAR = Self-Exciting Threshold Autoregressive; STAR = Smooth Transition AR; SVR = Support Vector Regression; TAR = Threshold Autoregressive; TARMA = Threshold Autoregressive Moving Average; ULB = Urmia Lake Basin; VMD = Variational Mode Decomposition; WT = Wavelet Transforms