Abstract
Considering the three intrinsic components (of autoregressive, seasonality, and error) of streamflow time series, the overall performance of the streamflow modeling tool is associated with the correct estimation of these components. In this study, a new hybrid method based on the wavelet transform (WT) as a multiresolution forecasting tool and exponential smoothing (ES) method, with two presented scenarios (WES1 and WES2), was introduced. To this end, the performance of the proposed method was investigated versus four conventional methods of the autoregressive integrated moving average (ARIMA), ES ad-hoc, artificial neural network (ANN), and wavelet-ANN (WANN) for daily and monthly streamflow modeling of West Nishnabotna and Trinity River watersheds with different hydro-geomorphological conditions. In the presented WES technique, firstly, WT is employed for decomposing the observed signal to one approximation (deterministic trend) and more diverse components of subseries (each at a specific frequency). Then, for the first scenario (WES1), only two subseries are introduced to the model as input parameters; however, for the second scenario (WES2), decomposed subseries are separately used as the inputs of ES models. The obtained results indicated that combining WT with the ES method and ANN led to more accurate modeling. The proposed methodology (WES2) that used all decomposed subseries separately improved the efficiency of models up to 30% and 10% for the daily dataset and up to 88% and 57% for the monthly dataset, respectively, for the West Nishnabotna and Trinity Rivers.
Highlights
Forecasting streamflow has been investigated by several researchers [1,2,3,4,5] as it is a fundamental subject in hydrological modeling
The exponential smoothing (ES), autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and WANN as benchmark models were developed beside the WES method to one-time step ahead modeling of daily and monthly streamflow time series
In this study, the initial point of view to select of the decomposition level was taken from L but since many seasonal characteristics may be embedded in hydrological signals, 2–8 resolution levels (L ± x) for the daily and 2–5 resolution levels (L ± x) for the monthly modeling were examined via the proposed WANN and WES models which, respectively, denote to the 22-day mode and 23-day mode, 24-day mode, 25-day mode, 26-day mode, 27-day mode, and 28-day mode in the daily scale and 22-month mode, 23-month, 24month, and 25-month mode in the monthly scale
Summary
Forecasting streamflow has been investigated by several researchers [1,2,3,4,5] as it is a fundamental subject in hydrological modeling. The black-box models can be more efficient than the physical base models due to the complexity of streamflow time series [8,9,10,11,12]. Linear and stationary time series can be properly modeled by the classic black-box methods by using seasonal auto-regressive integrated moving average (SARIMA) [13, 14]. Such models (e.g., SARIMA) may not be a suitable model for hydrological time series that are highly nonlinear and complex. Nonlinear AI-based methods, especially the artificial neural network (ANN), have achieved real success in modeling hydrological time series because of its significant advantages that are as follows [15]:
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