Performance evaluation of artificial neural network model in hybrids with various preprocessors for river streamflow forecasting

In different geographical areas, especially in arid and semi-arid regions due to climate change and excessive use of water resources, accurate forecasting of hydrological processes is required. Surface water resources in these areas play an essential role in meeting the needs of drinking, agriculture, and industry due to easy access and lower cost. Streamflow forecasting is a fundamental step in formulating strategies and sustainable management of water resources, and plays a valuable role for different reasons, including optimizing water resource systems and reducing flood risks. Very accurate streamflow forecasting is essential due to the nature of rainfall and fluctuations in river flows in the catchments of these areas. On the other hand, in watersheds, it is very difficult and costly to measure and record all the observed quantities and variables required for flow modeling and analysis. Therefore, a simple model that requires little data and area information can be a good choice.

Usually, three main approaches are used to model streamflow, including empirical, physical, and conceptual approaches (Beck 1991; Ahooghalandari et al. 2016). Numerous studies have compared these approaches and found that most experimental (data-driven) models are less structured, run more simply, and are more efficient in their predictions than physical and conceptual models (e.g., Carcano et al. 2008; Kim & Pachepsky 2010; Panda et al. 2010; Ahooghalandari et al. 2016; Young et al. 2017; Ahmadi et al. 2019; Wagena et al. 2020). When field data is not sufficiently available, and accurate estimation is more consequential than understanding the process and recognizing system mechanisms, the data-driven model (black box) can be efficient (Jha & Sahoo 2015; Ebrahimi & Rajaee 2017). Data-driven models do not have a complete interpretation and understanding of the physics and processes of the watershed, but these models are capable of relatively accurate streamflow forecasts. The data-driven model with linear approaches, including autoregressive integrated moving average (ARIMA) and multiple linear regression (MLR) models, are traditionally used for river flow forecasting. These models do not perform satisfactorily when modeling nonlinear hydrological processes due to their inherent linear structure (Nourani et al. 2014a). In later years, the nonlinear and artificial intelligence (AI) models, such as artificial neural networks (ANNs), were the streamflow forecasting applications utilized. Using comparisons between the ANN and linear models, the researchers found that ANN performed better for forecasting streamflow (Hsu et al. 1995). ANN models extract the relationship between input and output observational data by developing algorithms and generalizing them to neural networks. Gradually, AI models were increasingly used to find inherent relationships and pattern recognition between streamflow fluctuations and various hydrological variables without the need to construct a conceptual model and understand the physical mechanism and complex relationships. Things like climate change and precipitation pattern change, land use change, increase in water consumption and withdrawal in the watershed, and other variables cause runoff to become unsteady and complicate the fluctuations of river flows. Rainfall-runoff modeling, optimization of several objectives of agricultural planning by considering the climate change plan in the upstream watershed, optimal development of agricultural sectors in the basin based on economic efficiency, and social equality can improve the management of water resources in different regions (Shekhar et al. 2021; Omar et al. 2022). Although AI-based techniques are due to their ability to discover and recognize latent patterns in the structure of complex systems, if the inputs are more unstable, linear/nonlinear data-driven models, often such behavior of the data is not countered. Therefore, these models require preprocessed input data (Cannas et al. 2006).

To deal with noisy and complex data it must be preprocessed before being input into the model. One of the effective techniques to improve the training and performance of data-driven models is to use appropriate preprocessors (Wang et al. 2021). In the present study, different preprocessors, including discrete wavelet transform (DWT), empirical mode decomposition (EMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), successive variational mode decomposition (SVMD), and multi-filter of the smoothing (MFS) in hybrids with ANN model, have been utilized. By applying their unique approaches, preprocessors convert and decompose input signals (data) into several sub-signals by passing through various filters. These preprocessors can detect information and extract hidden features in the physical structure of data, such as trends, breakpoints, and discontinuities. Using an AI-based approach such as ANN coupled with data decomposition or noise cancelation techniques, it is possible to predict time series well and accurately. Data preprocessing has been widely used with time series decomposition and connection to various AI models to forecast hydrological phenomena (e.g., Kisi 2009; Adarsh et al. 2016; Meng et al. 2018; Hu et al. 2019; Zuo et al. 2020; Gaur et al. 2021; Moosavi et al. 2021; Nourani et al. 2021; Momeneh & Nourani 2022). The data preprocessing before using them as input to the ANN model can considerably improve the efficiency and performance of these models for forecasting streamflow hydrology. For example, Wu et al. (2009) applied a moving average (MA) as a preprocessor on inputs ANN model for predicting monthly streamflow. The results of their studies showed that the integrated MA-ANN model has better predictability compared to separate models. Adamowski & Sun (2010) examined the use of the ANN model with wavelet transform (DWT-ANN) to forecast 1 and 3 days for two rivers in Cyprus and compared them with the outcomes of single ANN models. The results illustrated that preprocessing with DWT could significantly increase the ANN accuracy in predicting daily flows. Zhang et al. (2015) used ANN and ARIMA models in hybrid with EMD and DWT preprocessors to forecast the monthly streamflow of two sites in the Yangtze River in China. The results showed that models with preprocessors had better forecasts provided. Seo et al. (2018) used the technique of combining EEMD and VMD preprocessors with the ANN model to study the flow behavior of the river in the Nanchang watershed in South Korea. Their findings showed that the VMD-ANN and EEMD-ANN models performed better than the ANN model. Rezaie-Balf et al. (2019) examined the ability of the CEEMDAN-ANN model to predict streamflow. The results showed that CEEMDAN-ANN models performed better than ANN models. Shukla et al. (2022) did discharge forecasting using ANN, ANFIS, and DWT-ANN models at a site in the Uttarakhand state of India. They evaluated the DWT-ANN model better than ANN and ANFIS models for discharge estimation.

In this study, there were three main approaches to forecast the streamflow used. The first approach is to predict the streamflow rate at the downstream station using the streamflow rate at the upstream stations. The second approach is to forecast the streamflow rate at the downstream station location using delayed data from the same station itself. The third approach is a combination of the first and second approaches. Data preprocessors to achieve more accurate prediction, including MFS, EMD, CEEMDAN, SVMD, and DWT preprocessors, were used in hybrid with ANN models. A comparison between the performance of the developed models and the models without preprocessing had performed to evaluate and prove the efficiency of the preprocessing technique for predicting daily flow in the Gamasiab River Basin located in the catchment area in western Iran.

In the present study, for the training and testing period of the ANN model, 31 years of daily river streamflow data (23 September 1986–22 September 2017) measured at hydrometric stations of the basin have been used. In most studies, the data have been divided into two parts and considered sufficient in the process of modeling and evaluations (Nourani et al. 2015). In this way, 70 and 30% of the input data sets were used in integrated models for training and testing, respectively. Also, 1 and 3 time-step-ahead was selected as the forecast time horizon. The data recorded and used were obtained in this study from the hydrometric stations under the supervision of the regional water company of Kermanshah province.

Several methods were used by applying different combinations to feed input data to the ANN model. As presented in Table 2, in Methods 1, 2, and 3, the data of two upstream hydrometric stations (i.e., Doab and Hyderabad stations) for estimating and forecasting streamflow at the downstream station (i.e., Polechehr station) are unchanged, and with one time-step-ahead was used, respectively. Also, in Methods 4, 5, and 6, the data of the same hydrometric station (i.e., Polechehr station) to forecast the 1 and 3 time-step-ahead was used. In Method 7, the upstream stations' data and the station's historical data were input into the ANN model combined. Then, these were used from different preprocessors in all methods to analyze and decompose the data to evaluate the effect of data preprocessing on the performance of the ANN model. The aim is to use preprocessors to help the ANN model better understand process behavior in the streamflow time series.

The use of preprocessors is to parse data and add information, and to improve interpretation and understanding of the components of the data. Their main feature is the removal or decomposition of noise from the data. Preprocessors convert signals (data) into several useful sub-signals using filters, including low-pass, high-pass, band-pass, and notch-pass. The time series of natural and hydrological phenomena often contain complex and hidden information, which needs to be discovered and extracted due to the intricacy of several factors and processes. Therefore, preprocessors can greatly assist in forecasting and modeling hydrological processes, especially data-driven approaches such as AI models, by feeding decomposed data to models (Nourani et al. 2014b). The data used in this study were analyzed using five different preprocessors in a hybrid model with ANN and used to forecast the streamflow rate, which is discussed below.

Wavelet transform (WT) is one of the relatively old preprocessors introduced by Mallat (1989) that has been used widely in data analysis in recent decades. The WT is a mathematical instrument derived from the Fourier transform, but unlike this it does not lose information in the transformation of signal from the frequency domain to the time domain (Daubechies 1990; Tiwari & Chatterjee 2011). DWT is one of the types of WTs, which performs well for various reasons, including simplicity and low and sufficient data generation, as well as the need for short computing time. The DWTs with concise and beneficial analysis provide a discrete spectral time-dependent analysis. Also, the DWTs produce a very sufficient and efficient output (Partal & Küçük 2006). Using different filters and various mother wavelets, DWT can decompose and reveal some of the hidden features and aspects of the original time series (Nalley et al. 2012). The original time series (observational data) is decomposed by DWT into approximate and detailed sub-series using two low-pass and high-pass filters at different scales. DWT has been used to analyze time series in many hydrological problems (Nourani et al. 2014b).

EMD was proposed by Huang et al. (1998). EMD decomposes nonlinear and nonstationary time series into several sub-time series called intrinsic mode functions (IMFs). It is in this way that this technique decomposes a time series into its inherent components. In the sifting process in the EMD mechanism, they separate and extract IMFs. In addition, each IMF has a lower frequency than the previous IMF. Through the IMF extraction method, two envelopes are calculated based on the local maximum and minimum of the sequence. Then, the initial sequences are determined by calculating the average of these envelopes and subtracting it from the original sequence average value. The IMF extraction process continues until the data become monotonic and the monotonous data are introduced as residuals. The IMF provides instantaneous frequencies as time functions by Hilbert transform (HT) to accurately identify structures embedded in time series.

Due to the mode mixing that EMD may occur during the decomposition of the original time series was introduced, a technique called EEMD (ensemble EMD) by Wu & Huang (2009) to solve this problem. EEMD solved this problem by adding residual noise in the computational process. But this technique requires more calculations as the number of sifting processes increases and may create modes with different numbers. But this technique requires more calculations as the number of sifting processes increases and may create modes with different numbers. CEEMDAN (complete EEMD with adaptive noise) is an upgraded version of EEMD to overcome these problems designed and proposed by Torres et al. (2011) and Colominas et al. (2014). CEEMDAN can extract more efficient and beneficial IMFs with fewer calculations and trials, also noise level control in each decomposition.

To overcome the limitations and problems that EMD in data decompositions posed, a new approach proposed by Dragomiretskiy & Zosso (2014) called variational mode decomposition (VMD) was used. This approach finds an ensemble of modes and respective central frequencies and is much more robust to sampling and noise. For this reason, simultaneous time series decompositions to their constituent intrinsic modes by VMD are usually more efficient than time series decomposed by EMD. There is a limit to the optimal VMD performance that a number of the modes in the time series must be precisely specified. The SVMD technique to overcome this limitation was developed by Nazari & Sakhaei (2020). SVMD detects and extracts modes through a sequential process. SVMD has advantages over VMD, including convergence without the need to know the number of modes, much less computational complexity, and greater robustness to the initial values of the central frequencies of the modes. Due to these advantages, this technique can be used to preprocess time series.

The moving average (MA), Savitzky-Golay (Sgolay) filters, locally weighted regression (Lowess), robust local regression (Rloess), and robust locally weighted regression (Rlowess) are data smoothing methods and are known as nonparametric regression. These smoothings for noisy (time series) signals are used with a high-frequency span.

The MA filtering mechanism is such that it considers each data as equal to the average number of adjacent data specified. This method uses averaging from each point of data and a specific range of before and after data points to prevent sudden jumps and thus smoothes the data (Harrell 2015).

The Sgolay smoothing filter was introduced by Savitzky & Golay (1964). The Sgolay filter is a generalized MA. Its mechanism is such that it obtains filter coefficients by performing a weightless linear least-squares fit using a polynomial of a certain degree. The Sgolay filter eliminates noise and preserves high-frequency components well. In addition, the higher the polynomial degree of this filter, the further smoothing it does.

The Lowess approach to estimate the regression surface is through a multivariate smoothing method that fits a function of independent variables locally and operates in a manner similar to how the MA method is calculated for a time series. A weighted process is such that the toolbox defines the regression weight function for the data points existing in the span. A robust addition to Rlowess and Rloess is a weight function that can withstand the process against resistant outliers and deflection points (Cleveland 1979; Cleveland & Devlin 1988; Cleveland et al. 1988).

In this study, we used the MA, Sgolay, Lowess, Rloess, and Rlowess smoothing filters for preprocessing, called MFS because each of these preprocessing methods can contain a different aspect of the original time series to get a better understanding of the process.

The preprocessors used in this study include MFS, EMD, CEEMDAN, SVMD, and DWT, which are among the most widely used data preprocessors, and those for forecasting were used in hybrid with the ANN model. The decomposed data by these preprocessors were entered into the ANN model as an alternative to the original data time series. It is necessary to mention forecast for the daily streamflow time series on two different horizons was performed (i.e., 1- and 3-day forecasts). Meanwhile the ANN model was coded for preprocessors from open-source code used in MATLAB software. ANN network architecture and parameter tuning were optimized using the trial-and-error method.

The present study applied seven different combinations of input variables with three main approaches to evaluate the performance of data preprocessing in hybrids with the ANN model for estimating and forecasting streamflow. The first approach is a hybrid of the ANN model with preprocessors and was employed for downstream flow forecasting using upstream flow, which includes Methods 1, 2, and 3. Also, in the second approach, the streamflow data of the same station itself is used to predict the streamflow of the downstream station, which includes Methods 4, 5, and 6. The third approach is a fusion of the first and second approaches, and the data used for this approach provided in Method 7. The effect of merging the volume values of two upstream stations' streamflow on the amount of streamflow volume in the downstream station can make the model more difficult to understand from the process in the first approach. Of course, evaporation and withdrawal of river water in the distance between the station, and the physical effects, local flow, and local rainfall on the amount of downstream stations are effective. In addition, the architecture of AI models with the same number of neurons in the hidden layer was considered constant in preprocessed models and models without preprocessing for better comparison. The purpose of using AI models such as ANN is to understand the time series behavior of streamflow and the hydrological and hydraulic complexity of surface water without understanding the process and complex calculations. Overall, the ANN hybrid and preprocessors forecast quiet flows and peaks of flow well. Table 2 presents seven different methods of using data. From the comparison of Methods 4, 5, and 6 with Methods 1, 2, and 3 it is concluded that the delay data of the station itself compared to the data of the upstream stations in the performance of the ANN model and especially in the performance of hybrid models with preprocessors is more appropriate. Besides, from the comparison of Method 4 and Method 7, it is found that the combination of data from upstream stations and historical data of the same station did not have a favorable effect on the efficiency of the models. Besides, the results obtained from the comparison of Methods 5 and 6 indicate that longer-term forecasts reduced the accuracy of the models. In general, the results show the superiority of Method 5 over other used methods. Comparing the preprocessors in the hybrid with the ANN model, the SVMD preprocessor performed better in long-term prediction (i.e., three time-steps), and the MFS preprocessor performed better in the short-term prediction (i.e., one time-step). MFS, SVMD, and DWT preprocessors performed better than CEEMDAN and EMD preprocessors. In general, results showed the superiority of SVMD-ANN and DWT-ANN models for different methods compared to other models. The results of hybrid models are evaluated and presented in the following.

This study has done daily streamflow forecasting using three main approaches. In the first approach, which is discussed in this section, using the flow rate at the location of the upstream stations, was forecasted the flow rate at the downstream station for Methods 1, 2, and 3. Table 2 presents how to apply the data of these stations as the input and output time series of the ANN model. Performance evaluation of the models was performed using Equations (1)–(3) in the calibration and verification steps. The hybrid model has the lowest RMSE value and the highest NSE and R values in both calibration and verification stages, selected as the superior model in this study. Table 3 presents the RMSE, NSE, and R criteria values for the ANN model and its hybrids with the preprocessor.

In Method 2, the DWT-ANN model and thus in Method 3, the MFS-ANN model performed better than the ANN model in forecasting daily streamflow in both calibration and verification stages. However, the amount of performance increase by these models was not significant. But other preprocessors used improved the results in the calibration phase and worsened in the verification phase (see Table 3). For example, the RMSE value in the verification step in Method 2 is 12.49 m³/s for the ANN model and 12.40 m³/s for the DWT-ANN model, and the R and NSE values in the verification stage are equal to 0.858 and 0.736 for the ANN model and 0.862 and 0.739 for the DWT-ANN model, respectively. The RMSE value in the verification stage in Method 3 is 13.17 m³/s for the ANN model and 12.62 m³/s for the MFS-ANN model, and the R and NSE values in the verification stage are equal to 842 and 0.706 for the ANN model and 0.857 and 0.730 for the MFS-ANN model, respectively.

The results indicate that Method 1 is better than Methods 2 and 3 for forecasting daily streamflow. In general, the results showed that preprocessors did not significantly improve the performance of the ANN model and sometimes caused the model to deviate during the verification period. This work occurred, especially in the case of the EMD and CEEMDAN preprocessors in the hybrid with the ANN model (see Table 3).

As mentioned in the previous section of this study, daily streamflow forecasting is done using three main approaches. In the second approach, which is discussed in this section, using the flow rate at the location of the downstream station, was forecasted the flow rate at the same station for Methods 4, 5, and 6. The values of the RMSE, NSE, and R criteria indicate that the ANN model understanding is suitable and the appropriate correlation of the data of this approach for streamflow forecasting (see Table 4). Table 2 presents how to apply the data of these stations as input and output time series of the ANN model. Combined models MFS-ANN, CEEMDAN-ANN, EMD-ANN, SVMD-ANN, and DWT-ANN were used to minimize daily streamflow forecasting errors. Performance evaluation of the models was performed using Equations (1)–(3) in the calibration and verification steps. The hybrid model has the lowest RMSE value and the highest NSE and R values in both calibration and verification stages, selected as the superior model in this study. Table 4 presents the RMSE, NSE, and R criteria values for the ANN model and its hybrids with the preprocessor.

In Methods 4 and 5, the performance of MFS-ANN models is better than the ANN model and other models coupled with preprocessors in forecasting daily streamflow at both calibration and verification stages. Figure 9 also shows that the highest correlation (i.e., R criterion) between observed and forecasted data belongs to the MFS-ANN model. As shown in Table 4, most ANN models hybridized with preprocessors, especially in Method 5, dramatically increased the performance of this model. The results of Method 5 are better than Method 4, which indicates the effect of time delays on the performance of the models. For example, the RMSE value in the verification stage in Methods 4 and 5 for the ANN model are equal to 6.10 and 5.37 m³/s, and for the MFS-ANN model they are 4.99 and 0.0005 m³/s, respectively.

In Method 6, the performance of SVMD-ANN models in predicting daily streamflow in both calibration and verification stages is better than the ANN model and other models coupled with preprocessors. Figure 9 also shows that the highest correlation (i.e., R criterion) between observed and forecasted data belongs to the SVMD-ANN model. As shown in Table 4, all ANN hybrid preprocessors much improved the performance of this model. The outcomes of the Method 6 are worse than Method 5, which shows the adverse effect of the long-term time-step-ahead on the efficiency and accuracy of the models. For instance, the RMSE value in Method 6 is 12.53 m³/s for the ANN model and 2.20 m³/s for the SVMD-ANN model in the verification stage.

The results illustrate that Method 5 is better than Methods 4 and 6 for forecasting daily streamflow. Overall, the results showed that in Methods 4, 5, and 6, unlike Methods 1, 2, and 3, the preprocessors significantly improved the performance of the ANN model. This work occurred, particularly in the case of SVMD, MFS, and DWT preprocessors in the hybrid with the ANN model (see Table 4).

This study aimed to investigate the performance of different preprocessors in hybrid with the ANN model to forecast the time-step-ahead streamflow. The present study focuses on modeling river streamflow forecasts using inputs with different approaches to the models and employing various preprocessors. Also, this study can help other researchers to select time series modeling approaches and methods. For this purpose, various preprocessors, including MFS, EMD, CEEMDAN, SVMD, and DWT, were used to parse the input data into the ANN model. To better evaluate the performance of data preprocessing seven methods were used. How to apply the input and output variables of the models in Methods 1–7 is presented in Table 2. The amount of error due to modeling the ANN model based on RMSE, R, and NSE criteria indicated the suitable performance of this model in estimating and forecasting streamflow. In this study, three main approaches to predict streamflow were used. The first approach is forecasting the streamflow data at the downstream station using the streamflow data at the upstream station. The second approach is to anticipate the streamflow at the downstream station location using data with delay from the same station. The third approach is a fusion of the first and second approaches, and the data used for this approach provided in Method 7. In this study, the results of seven methods and six models with different preprocessors (i.e., 42 different combinations) are presented.

The results of the first approach in Table 3 are presented and include three methods of applying input variables to the ANN model. The results of Method 1 in the verification period show that the preprocessors are either ineffective or have a detrimental effect on the model performance. Nevertheless, the data preprocessing improved the model performance in the calibration stage. As shown in Table 3, the results obtained from Methods 2 and 3 also indicated the preprocessing reduced the accuracy of the ANN model during the verification period. However, among the hybrid models with different preprocessors, the DWT-ANN and MFS-ANN models had the best performance in these methods for streamflow modeling. In general, the results of simple models without preprocessing the input data into the model are satisfactory in all methods used.

The results of the second approach in Table 4 were presented and included three methods of applying input variables to the ANN model. Examination of the results obtained in Method 4 indicates better performance of the ANN hybrid model, with MFS, SVMD, DWT, CEEMDAN, and EMD preprocessors, respectively. As shown in Table 4, results from Method 5 improved the performance of the ANN model by using 1–7 delayed time steps in the hybrid model with different preprocessing. The MFS, DWT, SVMD, CEEMDAN, and EMD preprocessors improved the performance of the ANN model in Method 5. We used Method 6 to evaluate the performance of the models in forecasting multi-time-step, and SVMD, CEEMDAN, and DWT preprocessors performed better than other preprocessors in forecasting three time-step-ahead, respectively. In this approach, a hybrid of various models and preprocessors predicted quiet flows and peaks of flow well.

By comparing Method 3 with Methods 1 and 2 it can be concluded that time delays in Method 3 have improved the model efficiency without preprocessing but have worsened the results of hybrid models. Unlike Method 3, inputs with delay much improve the results of the hybrid models in Method 5 (see Tables 3 and 4). Results are presented for Method 7 in Table 5. Method 7 obtained weaker results in comparison to Method 4.

In general, preprocessors did not perform well in Methods 1, 2, and 3. In Methods 4 and 5, the MFS-ANN hybrid model had the best performance. In Method 6, with a longer time step, the SVMD-ANN hybrid model performance was better than other hybrid models. In all methods used, SVMD, MFS, and DWT preprocessors outperformed EMD and CEEMDAN preprocessors in forecasting time series. The application of preprocessors to the input of the ANN model to use the discharge rate in the upstream stations (sub-watersheds) to forecast the downstream station discharge rate (watershed) in the study area was unsuccessful. But the preprocessors performed very well in the forecasting streamflow rate by using the recorded data of the same station as delayed inputs. However, due to the more significant correlation of the station data with the future data of the same station, it is evident that in Methods 4, 5, and 6, the performance of models is better than in Methods 1, 2, and 3. In Methods 4, 5, and 6, much more accurate streamflow predictions were obtained than in Methods 1, 2, and 3, which is evident in Figures 5–9. Therefore, it was expected that the preprocessors, like Methods 4, 5, and 6 in Methods 1, 2, and 3, would also improve the relative performance of the ANN model in prediction. But the results indicate that the preprocessors are inefficient in improving the performance of the ANN model in forecasting downstream station streamflow (i.e., Polechehr station). This event may be related to paying too much attention to the calibration data time series (over-training) and deviating from forecasting the verification data time series. The magnification of unknown and complex data in the test phase has affected the understanding of the model in methods 1, 2, and 3 and has made the results worse. Comparing Methods 1, 2, and 3, it concluded that the preprocessors do not help significantly in the forecasting of the ANN model because the data of the upstream stations contain some noise and uncertain values that may be due to physiographic and morphological factors and also water receiving and withdrawing in the basin in the distance between the stations. The comparison of the results of the methods showed that the longer the time steps for forecasting chosen the lower the accuracy of the model. The results also indicated that longer time delays cause improved learning of the ANN model. In addition, the comparison of the methods showed that using the data of separate upstream stations or coupled with the historical data of the same station reduced the model efficiency. In general, selecting and using input data with the right type, approach, delays, and preprocessor can improve the performance of data-driven models such as the ANN model. Preprocessors can enhance the efficiency of generalized neural networks on hydrological processes in the forecast by analyzing information and revealing different aspects of the data. Finally, this conclusion showed that the widely used method of time-delayed input data for forecasting time series time steps forward and selecting the appropriate preprocessor requires further investigation by relevant experts and researchers.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.