Short- and long-term streamflow forecasting using wavelet neural networks for complex watersheds: A case study in the Mahanadi River, India
Graphical abstract
Introduction
In regions where data is scarce, such as the Mahanadi River basin in Odisha State (India), streamflow forecasting studies are essential for efficient water management and water resources protection and planning (Mishra et al., 2022; Rai et al., 2020; Santos et al., 2021). A dam, for example, needs such forecasts for planning the operation, preventing droughts and floods, and contributing to the conservation of ecosystems (Park et al., 2018). However, streamflow is hard to predict. Besides its complexity, it presents abnormalities and nonlinear properties, which makes it difficult to identify patterns (Thomas et al., 2021).
Since 1970, hydrologists have been using classic time series models (black box) for forecasting streamflows, such as methods based on regression and the moving average (e.g., auto-regressive, moving average, auto-regressive moving average, auto-regressive integrated moving average, auto-regressive integrated moving average with exogenous input, linear regression, and multiple linear regression models) (Cho and Kim, 2022; Ibrahim et al., 2022; Salas et al., 1980; Valipour and Montaza, 2012; Wu et al., 2009a).
However, conventional linear models have difficulties dealing with the non-stationarity and nonlinearity of the hydrological parameters. Therefore, researchers have sought to develop streamflow forecasting models capable of overcoming the inherent disadvantages of conventional models (Saraiva et al., 2021; Yaseen et al., 2015). Machine learning (ML) techniques have been present in various fields of science and engineering since the mid-20th century (Niu and Feng, 2021; Park et al., 2018). Thus, many ML methods have already been developed, for example, for mathematical optimization, statistical and probabilistic classification, and learning.
According to Hsu et al. (1995) and Li et al. (2022), artificial neural networks (NN) are tools capable of distinguishing complex nonlinear relationships between input and output data. They are appropriate for solving problems when it is difficult to describe the processes using physical equations. Hence, neural networks are acceptable ML methods for performing input/output simulations and streamflow forecasting.
Recently, Kisi et al. (2019) showed the superiority of the Least Squares Support Vector Machine over other ML methods when incorporating climate signal information for modeling monthly streamflows in the Mediterranean region. In 2020, Cui et al. (2020) contributed to the state-of-the-art of river engineering by exploring the Emotional Neural Network to estimate hourly streamflows at Mary River, Australia. Along the same lines, Choubin et al. (2019) and Mosavi et al. (2021) applied the Fuzzy Clustering Approach to streamflow regionalization in ungauged watersheds in Iran.
Despite the NN's capabilities of processing nonlinear data, high-frequency components in the hydrological time series may impair the quality of the forecasts. It is often the case that such high-frequency components can be considered noise or nonimportant information in the original signal. One of the tools used to reduce noise is the wavelet transform (WT) (Chong et al., 2022; Freire et al., 2019). When applied to input data, WT can improve accuracy and prolong the forecasting time (Wu et al., 2009b).
Some researchers combined NN and WT to simulate hydrological processes. Dalkiliç and Hashimi (2020), for example, proved that wavelet neural networks (WNN) were superior to NN alone and the adaptive neuro-fuzzy inference system (ANFIS) for daily streamflow estimation. Other authors have investigated short-term streamflow forecasting models based on WT and NN (Freire et al., 2019; Saraiva et al., 2021). Similarly, applications of WNN to long-term forecastings, such as the works of Li et al. (2019) and Yilmaz et al. (2022), have been carried out. However, the proposal of a unique WNN methodology for short- and long-term forecasting, especially in complex watersheds (i.e., with diverse streams and many competing needs), is still being addressed in the literature.
Knowledge about the behavior and interaction of rivers is vital for managing the available water resources (Loucks and Van Beek, 2017). Data-driven approaches appear more suitable and easier to use when dealing with complex systems than physical-based models (do Nascimento et al., 2022;Freire et al., 2019; Hsu et al., 1995; Wu et al., 2009b). In this context, the present work proposes WNN models to predict short- (daily) and long-term (weekly, fortnightly, and monthly) streamflows in the Mahanadi River basin, a major watershed in East Central India.
Section snippets
Materials and methods
Fig. 1 shows a flowchart with a brief description of the methodology steps, as described in the following sections.
Forecasting using streamflow data
In this application, NN models used previous streamflows to predict the current streamflow. In some cases, the input data comprised previous streamflows from upstream stations. Table 5 describes the models for each station, detailing: the used stations, the number of antecedent days (inputs), the forecasting horizon, the number of nodes, and the performance results for the test dataset.
The models provided the best results for short-term forecasting (one day ahead), losing efficiency when
Conclusions
This paper is innovative as it applies and evaluates WNN for improving short- (daily) and long-term (weekly, fortnightly, and monthly) streamflow forecasting. The approach investigated and validated NN models using data from ten stations of the Mahanadi River basin, an important watershed in India. In this study, we compared results for the following sets of inputs: (a) only previous streamflows, (b) previous streamflows and rainfalls, and (c) wavelet-based approximations of previous
Author contributions
C.A.G.S. and M.M. designed the research; G.R.N., C.A.G.S. and C.A.S.F. wrote the original draft; and G.R.N., C.A.G.S., C.A.S.F., R.M.S. and M.M. conducted the manuscript review, edited, and wrote the final paper. All authors have read and agreed to the published version of the manuscript.
Declaration of Competing Interest
None.
Acknowledgments
This study was financed in part by the Brazilian Federal Agency for the Support and Evaluation of Graduate Education (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES) – Finance Code 001, the National Council for Scientific and Technological Development, Brazil – CNPq (Grant No. 313358/2021-4 and 309330/2021-1) and Federal University of Paraíba.
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