Evaluating the capability of hybrid data-driven approaches to forecast monthly streamflow using hydrometric and meteorological variables

Streamflow forecasting has attracted wide attention among hydrologists owing to the fact that this issue plays a key role in decision-making cases related to water resources management and planning. The first attempts made to forecast the streamflow in various climatic conditions were based on time-series methods such as auto-regressive (AR), autoregressive moving average (ARMA), autoregressive moving integrated average (ARIMA), and K-nearest neighborhood (KNN) (Abrahart & See 1998; Cigizoglu 2003; Huang et al. 2004; Wu and Chau 2010). In these mathematical techniques, time-dependent variables should have complete time series so that results of forecasting stand at the reliable level. Accordingly, the performance of time-series models has a low potential of streamflow forecasting when time-series information is incomplete (Huang et al. 2004). With the emergence of soft computing models, a broad range of artificial intelligence (AI) techniques was applied to predict the streamflow in rivers. AI methods have shown sufficient capacity to detect the hidden patterns in time series, and they have proven high reliability in comparison with traditional approaches (e.g., Solomatine & Ostfeld 2008; Yaseen et al. 2015; Karimi et al. 2017; Khairuddin et al. 2019; Najafzadeh & Saberi-Movahed 2019; Boucher et al. 2020; Hussain & Khan 2020). In the case of hydrological investigations, various meteorological variables (e.g., evapotranspiration, temperature, precipitation, and streamflow) are characterized by time series in which effects of many properties of time series (e.g., noise, sudden, and irrelevant patterns) on the performance of data-driven models (DDMs) may be inventible. There have been various investigations in which preprocessing of time series improved the efficiency level of DDMs. In the early 21st century, wavelet transform (WT) functions, as one of the most efficient preprocessors, have been widely applied to boost the intrinsic capabilities of DDMs in terms of precision level and generalization (e.g., Parasuraman & Elshorbagy 2005; Adamowski 2008; Jacquin & Shamseldin 2009; Yarar 2014; Shoaib et al. 2015; Fahimi et al. 2017; Shahabi et al. 2017; Nourani et al. 2019; Zakhrouf et al. 2020).

Additionally, some investigations indicated that the use of meteorological data increased the accuracy level of DDMs for the prediction of the peak flows (i.e., Abdollahi et al. 2017; Diop et al. 2018; Akcakoca & Apaydin 2020). Similarly, Hadi & Tombul (2018) used wavelet-multigene genetic programming (W-MGP) to take advantage of meteorological data to simulate rainfall–runoff. Furthermore, Kratzert et al. (2018) proposed a novel DDM utilizing the long short-term memory (LSTM) network to model the rainfall–runoff process of a large number of completely various catchments at the daily time scales. This study showed the LSTM capability as a regional hydrological model in which a model predicts the discharge for the different catchments. Adnan et al. (2019) selected streamflow, rainfall, and temperature via autocorrelation and partial autocorrelation. Through their research, this analysis not only forecasted monthly flow accurately but also showed rainfall and temperature alone was adequate inputs for 511 basins in the United States. Tyralis et al. (2019) and Chu et al. (2020) employed random forest and least absolute shrinkage and selection operator to optimally select climatic features for forecasting the streamflow.

Through the literature review, a broad range of investigations applied hydrological or meteorological data in order to forecast streamflow, while there are a few research in which both types of data were considered for modeling the streamflow. Simultaneous use of hydrological and meteorological variables increased the precision level of AI models in forecasting the streamflow for a long-time period (Hadi & Tombul 2018). Therefore, there is still an essential need for doing research in this respect in order to investigate the effects of both types of information on the accuracy level of AI techniques in the presence of wavelet models as preprocessors. In the present study, monthly streamflow is forecasted for two distinctive basins (Polroud and Khoshkroud) by using wavelet-M5 prime (WM5P) model tree and gene expression programming (GEP) techniques. Additionally, the efficiency of hydrological and meteorological data application as input variables for running the hybrid AI models and the performance of preprocessing process for both basins (with various length of time series or missing data) were investigated. These cases have not been frequently studied for the forecasting streamflow.

To the best of the authors' knowledge, WT is used to preprocess hydrometric and meteorological variables in forecasting monthly river flow. To be more specific, in order to identify the influential factors on the streamflow (discharge), hydrological (discharge) and meteorological (monthly maximum precipitation, average of monthly temperature, atmosphere pressure, and dew point) variables, accumulated from two Polroud and Khoshkroud basins, are considered to train and test M5P and GEP techniques. In addition, the performance of M5P and GEP models are statistically compared and then used to describe the beneficial impacts of various factors (i.e., geometry of basins, the number of recorded data, availability of meteorological data, and the preprocessing stage with various wavelet characteristics) on the proposed DDMs.

In the current study, Khoshkroud basin was utilized as the study area. The elevation of basin varies from 74 to 3,608 m altitude with an average slope of 15% whose the length of the main stream path and basin area is 20 km and 100 km², respectively. The time series of monthly streamflow was collected from Bajiguabar hydrometric station for a 32-year period beginning in 1985, provided by Guilan Regional Water Company (GRWC). Figure 1 displays the monthly discharge histogram of Bajiguabar station.

The question is: ‘whether the proposed hybrid AI models can accurately forecast the monthly streamflow in any situation or its performance is good only in some ranges of input and output time series?’ This is an important challenge of this research. To get rid of this challenge, the Polroud River basin whose characteristics are different from those of Khoshkroud is considered. The basin elevation varies between 52 and 3,931 m with an average slope of 5%. In the case of Polroud River, the length of the main stream path and basin area are 67 km and 1,700 km², respectively. Additionally, the monthly streamflow time series of this river was collected from Tollat hydrometric station for a 60-year period beginning in 1956. Figure 2 depicts the monthly discharge histogram of Tollat station.

Both rivers flow through the city of Roudsar located at the east of Guilan province in the north of Iran. They rise in Chakroud Mountain, passing through coastal plains, and finally reaching the Caspian Sea. The geographical location of the study area is shown in Figure 3. Furthermore, the monthly meteorological data were acquired from the Ramsar synoptic station in the north of Iran, which was in the near vicinity of both hydrometric stations. In this paper, discharge (Q), pressure (P), average of monthly temperature (T_m), average of monthly dew point (T_d), and average of monthly precipitation (P_r) were considered as attributes. The pieces of statistical information about both basins are delineated in Tables 1 and 2.

In order to train the AI models, the first 70% data of streamflow time series for both stations were utilized. In addition, the 30% of the remaining dataset was dedicated to test the AI models.

The characteristics of the original time series in frequency (a or j) and time-domain (b or k) at the same time are presented by or ⁠.

The DWT operates two sets of functions, e.g., high-pass and low-pass filters, as seen in Figure 2. The original time series are passed through these filters and then separated at different levels. The time series is decomposed into one comprising its trend (the approximation) and one comprising the high frequencies and the fast events (the detail) (Karimi et al. 2015). In the present research, integer time steps are utilized, and additionally, the detail (D) coefficients and approximation (A) sub-time series are extracted using Equation (5).

GEP was introduced by Ferreira (2001). The GEP is known as an evolutionary algorithm with the potential to produce explicit formulations of the relationship that describes the physical phenomena. It is one of the supremacies of the GEP model over other DDTs (Martí et al. 2013). In general, similar to other evolutionary algorithms, the GEP utilized population of individuals, chooses them according to fitness, and conducts genetic variations by exploiting one or more genetic operators (Ferreira 2006). The GEP procedure is as follows. The first step is defining the fitness function. Here, the root-mean-square error (RMSE) fitness function was utilized. The second step consists of choosing the terminal and the set of functions. In the current research, the terminal sets include the river flow records (with various lag times) and meteorological variables. The selection of the appropriate function was done based on the viewpoints of the user. Here, various mathematical functions (i.e., ⁠) were used based on the previous pieces of experience (Karimi et al. 2018). The next step is to select the linking function. In the present investigation, an ‘addition’ function was used to link genes as applied by Karimi et al. (2018). The final step is to select the genetic operators. Table 3 illustrates the GEP genetic operators.

In this study, two hybrid AI techniques were developed by combining DWT with two AI models, i.e., GEP and M5P. The WGEP and WM5P models, which use the sub-time-series components, compute through DWT on original data. For processing the input variables (i.e., hydrological data with different lags), the original time series were decomposed into a certain number of sub-time-series components (Ds) using the algorithm proposed by Mallat (1989). The hybrid models were built in which the Ds of the original time series are considered as input variables of the AI techniques, and the original output time series are the output of the WGEP and WM5P. Figure 4 provides a schematic representation of both hybrid AI models that are used in the current study.

In this paper, Khoshkroud and Polroud Rivers have been selected to determine whether the performance of the AI models (GEP, WGEP, M5P, and WM5P) can satisfy the sufficiency of statistical criteria. GEP and M5P have been considered due to the representation of mathematical functions which simplify the analysis of their performance. Furthermore, their mathematical expressions determine the relationships among input variables and their relative importance in modeling. As indicated in Table 4, seven combinations (I₁ to I₇) were composed of hydrological (H) and climatic (M) attributes to demonstrate the benefits of attributes on the precision level of hybrid AI models.

In the hybrid AI models (WGEP and WM5P), in order to explore the effectiveness of two wavelet features on the wavelet modeling ability, three mother wavelets (haar, db7, and dmey) with four decomposition levels (3–6) have been employed to preprocess streamflow time series. M5P is a linear technique that has required more delay times to satisfy classification bands, while GEP is a nonlinear method that could have been run in a global space with every shape. According to this, all seven combinations (I₁–I₇) have been prepared in five frame times as seen in Table 4.

According to the linear structure of M5, the use of all input variables needs a large number of lags for the time series of streamflow. Additionally, the high capability of wavelet functions in the detection of time series caused a low number of lags. Accordingly, M5P and WM5P have been modeled for ‘T₁–T₅’ (35 scenarios), GEP for ‘T₁–T₃’ (21 scenarios), and WGEP for ‘T₂–T₃’ (14 scenarios).

All mentioned scenarios have been investigated for three lead times, including 1-, 2-, and 3-month-ahead (L1, L2, and L3). Additionally, 70% of samples were considered for the training phase and the remaining samples (30%) were employed for the testing phase. The methods have utilized the Polroud and Khoshkroud data based on 504 and 269 months for the training phase, and 216 and 115 months for the testing phase, respectively. Finally, the performance of AI techniques was assessed by statistical indices and diagrams. Table 4 shows all scenarios' properties used in this study.

The scenarios presented in this study were operated with their optimized results for both rivers. in Tables 5 and 6, the best results are highlighted in each lead time. From Tables 5 and 6, GEP and M5P had a poor performance with regard to hydrological factors in the multi-month-ahead, notably when the Khoshkroud River datasets were examined. In addition, as meteorological data is merged to the hydrologic data, the capabilities of both AI methods in streamflow forecasting increase. Adding the meteorological elements (i.e., T_m, T_d, P, and P_r) to hydrological input (Q) has no tangible variations in the accuracy level of hybrid AI models (WM5P and WGEP), whereas this is remarkable for GEP and M5P especially in high values of lead time. Furthermore, Tables 5 and 6 indicated that the precision level of AI models has an inverse direction with an increase in the number of lead times. Furthermore, it can be seen from Figure 5 that both graphical performances of M5P_Polroud and GEP_Polroud illustrated convergence toward the 45° line, while M5P_Khoshkroud and GEP_Khoshkroud were scattered in a horizontal area. Careful consideration of the time-series length for both rivers demonstrated that the effects of time-series length on the performance of the M5P technique are higher than the GEP model. In the case of M5P efficiency, the streamflow forecasting for Polroud River (I_{a(M5P, Polroud, L1)} = 0.85) with a 720-month time series is more accurate than that predicted for Khoshkroud River (I_{a(M5P, Khoshkroud, L1)} = 0.42) with a 360-month time series.

It can be inferred from the results of M5P and GEP techniques that wavelets had a significant effect on the performance of these AI methods, which were changeable in their WT properties. In the case of the case study basins, discrete and step Haar functions have made a marginal impact compared to other mother wavelet functions (i.e., dmey and db) and could have not dominated frequencies correctly, out of discontinues shape and dissimilar style to oscillation flow series and short band length (NSE_{Khoshkroud, haar-GEP, M5P, L1-3} > 0.27 and NSE_{Polroud, haar-GEP, M5P, L1-3} > 0.35). In the preference, db7 and dmey have had a notable role in improving the performance of GEP and M5P techniques, in order for the NSE greater than 50% of all the lead times (NSE_{Khoshkroud, GEP, M5P, L1-3} > 0.49 and NSE_{Polroud, GEP,M5P, L1-3} > 0.68). Dmey and db7 functions had almost the same impacts on GEP and M5P approaches; nonetheless, a decrease in differences between RMSE and MAE values has attracted attention and has observed less contrast with Koshkroud River, in particular GEP technique. Dmey wavelet function includes a lengthier band than db7 (7.7 times) and focused on extremes as well as sudden jumps primarily; however, db7 has a smooth and expandable curve shape and behaves closely toward the entire time series. These differences discovered how the db7-GEP could have forecasted the 10 m³/s maximum discharges (low flow) of Khoshkroud River as well as dmey-GEP; however, dmey-M5P has grown results toward db7-M5P which M5P has recognized patterns of extreme flow simulations. Figure 6 illustrates the better graphical performance of M5P for the 1-month-ahead, where WM5P has decreased the RMSE index 78% toward the GEP technique and could simulate peak flows accurately as same as the GEP model.

Figure 7 illustrates that higher confidence of WM5P model associated to the Polroud River performed in 5% confident area (for 1-month-ahead), and additionally, this issue has been efficiently approved by the WGEP hybrid model. The second wavelet property is the decomposition level. M5P and GEP techniques have reacted to variations in the decomposition level values, and mother wavelets were highly sensitive to scales for these two-time series, notably Polroud River. Figures 8 and 9 illustrate variations of statistical criteria for the best hybrid AI models versus decomposition levels and scenarios of input combinations for both Khoshkroud and Polroud Rivers, respectively. From Figures 8 and 9, it can be inferred that in a short lead time (1-month-ahead), the hybrid AI models provided satisfying efficiency for low values of decomposition level, whereas for the higher values of lead time (3-month-ahead), higher values of decomposition level (5 and 6) are required to boost the accuracy level of AI models.

Furthermore, hybrid AI techniques have the potential of modeling time-series flow, and especially applying the DWT could improve the performance of hybrid AI models significantly at 3-month-ahead for both rivers (RI_{(WM5P, Khoshkroud, L3)} = 0.48, RI_{(WM5P, Polroud, L3)} = 0.57). For both basins, WM5 has yielded an equation that stood relatively at the same accuracy level provided by the WGEP model. In the case of extreme values of streamflow, WM5P provided more accurate results than the WGEP technique. Figure 10 demonstrates that hybrid AI approaches estimated discharges for 3-month-ahead with R values greater than 70%. According to the above-mentioned results, although meteorological variables might suffer from proper localization (i.e., meteorological stations are not at the near vicinity of hydrometric station) and noises of time series, they could provide a significant improvement in the efficiency level of stand-alone AI techniques (M5P and GEP). For instance, the M5P technique had the worst performance for both case study rivers (NSE_{Khoshkroud, M5P, I5, L3} = −0.06, NSE_{Khoshkroud, M5P, I1, L3} = −0.07, NSE_{Polroud, M5P, I7, L3} = 0.46, NSE_{Polroud, M5P, I1, L3} = 0.05) when M5P is not fed by meteorological data. In this way, the effect of wavelet function usage on the performance of AI techniques is more efficient than that of typical datasets (i.e., M and L). Based on the RI index, the largest improvement in model capability was observed in WM5P-dmey at L1 compared to stand-alone AI approaches (GEP and M5P) for both case study rivers.

In this study, stand-alone AI models and hybrid AI techniques were performed 336 and 3,528 times, respectively. Essentially, the length of time series is an influential factor in the complexity degree of M5P and GEP models. It can be generally said that the increase of time-series length and number of input variables caused to present a complicated M5P formulation, whereas simpler equations by the GEP model were obtained owing to the existence of nonlinear mathematical expression in GEP formulation. Furthermore, meteorological data have had a substantial effect on the efficiency of AI models, which can be treated as a piece of axillary information especially during long lead time. The confidence level is dependent on the type of mother wavelet and is not a constraint to the decomposition level extremely. In fact, the wavelet mother function extracted important properties of time series such as decomposition level of time series, scale, and delimited frequencies. Widening the band of wavelet mother caused to boost the capability of preprocessing in time series and extraction of main properties. As a result, there exists high sensitivity to the variations in the decomposition level and scenarios of inputs combination. This issue is the reason why dmey wavelet is more robust than other typical wavelet functions. According to Tables 5 and 6, the performance of preprocessing time series decreased both the number of rules applied in the M5P and the complexity of the linear equation by M5P; therefore, the accuracy level of Equations (14) and (15) booted. In general, it can be said that the increase in the number of meteorological variables and preprocessing the time series led to bring the forecasting results for both distinctive basins at the same level of precision. On the contrary, once AI models were not fed by meteorological data, the results of AI models for Polroud River were more accurate than those for Khoshkroud River.

Accurate forecasting of streamflow is a vital issue in hydrology and water resources management. Intelligence computing is a satisfactory solution to increase confidence in river flow modeling. Thus, in the current research, the monthly streamflow of two distinctive rivers (Khoshkroud and Polroud) was forecasted by WGEP, WM5P model tree, and their stand-alone AI models (GEP and M5P). To understand the influence of preprocessing on the performance of hybrid AI models, meteorological (M) variables and long lead time (L) have been considered within several input scenarios. Results indicated that the accuracy level of all the AI techniques was in close connection with properties of time series such as being long-term persistence and having extreme values. In fact, these characterizations of time series mean comprehensiveness of streamflow datasets. WT functions were capable of eradicating limitations of time series; then, the results of hybrid AI models were accurate. More specifically, although time series associated with Khoshkroud River had lower comprehensiveness in terms of missing information and length of time series compared with Polroud River, the accuracy level of hybrid AI models fed by Khoshkroud River was approximately equal to the those obtained by Poulroud River. Additionally, meteorological information had the capability to cover deficits of input time series, although effects of meteorological data on the performance of stand-alone AI technique was more tangible than those of hybrid AI models. Due to the existence of more complexity and unknown patterns of time series in longer lead times, the AI models benefited from climatic variables and higher decomposition levels. WM5P with piece-wise linear structure has been considered as the most accurate hybrid AI model owing to its higher compatibility of hybrid M5P technique to various basins. Although WM5P has a simpler structure than the WGEP model, the WM5P technique has the higher capability (NSE_{(Polroud, WM5P, H, L3)} = 0.88 and NSE_{(Khoshkroud, WM5P, H, L3} = 0.74) in the simulation of river flow even for extreme values and long lead times. Ultimately, the most significant improvement in the AI models' capability was related to the WM5p-dmey3 in comparison with the stand-alone GEP approach. One of the limitations of this study is the lack of meteorological stations in the location of the hydrometric stations. Also, since the modeling period is monthly, another limitation is accurate forecasting for long-term periods (more than 3 months). It is suggested that the effect of catchment area on the performance of the proposed models be evaluated, and additionally, the proposed hybrid AI models can be combined with other intelligent methods or time-series models such as ARMA and ARIMA for the streamflow forecasting.

The authors are grateful to the editor and three anonymous reviewers for their constructive and insightful comments, which help enhance the quality of the manuscript.

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