Daily suspended sediment forecast by an integrated dynamic neural network

Highlights

• A signal pre-processing module is applied for feature extraction and noise deduction.

• An integrated dynamic neural network is established for sediment estimation.

• The developed model is tested for flood conditions and multistep forecast.

• The proposed method gives the most accurate predictions among the ones used.

Abstract

Suspended sediment is of importance in river and dam engineering. Due to its high nonlinearity and stochasticity, sediment prediction by conventional methods is a challenging task. Consequently, this paper establishes a new hybrid model for an improved forecast of suspended sediment concentration (SSC). It is a nonlinear autoregressive network with exogenous inputs (NARX) integrated with a data pre-processing framework (thereafter INARX). In this model, wavelet transformation (WT) is used for time series decomposition and multigene genetic programing (MGGP) for details scaling. The two incorporated modules improve time and frequency domain analysis, allowing the network to unveil the embedded characteristics and capture the non-stationarity. At a hydrological station on the upper reaches of the Yangtze River, the records of daily water stage, flow discharge and suspended sediment are collected and refer to a nine-year period during 2004–2012. The data are used to evaluate the models. Several wavelets are explored, showing that the Coif3 leads to the most accurate prediction. Compared to the sediment rating curve (SRC), the conventional MGGP, multilayer perceptron neural network (MLPNN) and NARX, the INARX demonstrates the best forecast performance. Its mean coefficient of determination (CD) increases by 7.7%–38.6% and the root mean squared error (RMSE) reduces by 15.1%–54.5%. The INARX with the Coif3 wavelet is further evaluated for flood events and multistep forecasts. Under flood conditions, the model generates satisfactory results, with CD > 0.83 and 84.7% of the simulated data falling within the ±0.1 kg/m³ error. For the multistep forecast, at a one-week lead time, the network also yields predictions with acceptable accuracy (mean CD = 0.78). The model performance deteriorates if the lead time becomes larger. The established framework is robust and reliable for real-time and multistep SSC forecasts and provides reference for time series modeling, e.g. streamflow, river temperature and salinity.

Introduction

The presence of suspended sediment in river flows is an essential issue in terms of water quality, river geological and geographical settings, channel navigability, operation of hydraulic structures, river aesthetics and fish habitats (Kişi, 2006). For instance, from the perspective of water resources exploitation, suspended sediment with high turbidity in river flows is a physical pollutant, which may act as a chemical pollutant when carrying chemicals such as phosphorous and heavy metals (Doğan et al., 2007). The transport of suspended sediment also affects erosion and deposition, leading to river morphological changes (Liu et al., 2013).

Defined as the ratio of sediment mass to volume of a sediment-laden mixture, suspended sediment concentration (SSC) characterizes a sediment transport process (Zheng et al., 2011). Accurate predictions of the SSC are of practical implications in a wide range of hydraulic issues, including design of the reservoir dead storage, environmental impact assessment, and prediction of aggradation and degradation around bridge piers (Afan et al., 2016). However, the transport is a complex phenomenon, involving both the flow and sediment motions and their interactions. From the initial detachment of sediment particles to their deposition, every stage is characterized by high nonlinearity and interplay processes, rendering the SSC forecast a challenging task.

Conventionally, the SSC in a stream is determined via either direct field measurements or already established sediment transport equations (Bayram et al., 2012). The former is an accurate approach, with however some practical and cost disadvantages. The latter refers to the use of the relationship between the SSC and flow properties, including flow velocity, discharge, etc. The approaches are usually developed based on simplified partial differential equations, assumptions and empirical correlations for erosive effects of rainfall and flow (Aytek and Kişi, 2008, Karim and Kennedy, 1990, McBean and Al‐Nassri, 1988).

Some sediment curves are also proposed for the estimation of SSC (Crowder et al., 2007, Petersen-Øverleir, 2004), which are theoretically adequate to cope with the variations in catchment properties and uneven distribution of precipitation and evapotranspiration (Aytek and Kişi, 2008). However, due to the scarcity of detailed spatial and temporal hydrological data, applications of those methods suffer from limitations (Kisi et al., 2012). Moreover, despite several established empirical models, choosing an appropriate one for a specific scenario is difficult, which is the reason why many of them do not gain expected acceptance (Afan et al., 2016). Some researchers even indicate that the sediment curves are misleading and the high goodness of fit is spurious (McBean and Al‐Nassri, 1988). As a result, efforts have been devoted to develop reliable methods for SSC predictions. Machine learning modeling offers an alternative.

In comparison with process-driven methods, machine learning models gain superiority in dealing with nonlinear issues and handling a large quantity of data. With the help of artificial intelligence (AI), they demonstrate a great potential in mapping data with high complexity, dynamism and non-stationarity, e.g. SSC time series. The recent years have witnessed a rapid growth of AI-based approaches in studying the SSC. One of the first applications is made by Jain (2001), where an integrated relation among water stage, flow discharge and SSC is established using a feedforward neural network (FFNN). The resulting model leads to better predictions than the conventional curve-fitting approach and is capable of modeling the hysteresis effects caused by unsteady flows in channels. Alp and Cigizoglu (2007) examine the performance of the FFNN and radial basis function neural network (RBFNN) in sediment load estimations. The combination of rainfall and flow data generates, as predictors, accurate results; the two evaluated models exhibit insignificant differences. Melesse et al. (2011) adopt a multilayer perceptron neural network (MLPNN) and use precipitation, river flow, and antecedent sediment data to predict the suspended sediment in three major U.S. rivers (Mississippi, Missouri and Rio Grande). Compared with the multiple linear and nonlinear regressions and autoregressive integrated moving average, the MLPNN produces more satisfactory results. Demirci and Baltaci (2013) explore the efficiency of fuzzy logic models in SSC estimations, concluding that they behave better than the multiple linear regression method. Ehteram et al. (2021) use the whale algorithm, particle swarm optimization and bat algorithm to optimize the performance of an artificial neural network (ANN). The hybrid models cut down the error up to 80% relative to the standard one. Doroudi et al. (2021) integrate the observer-teacher-learner-based optimization method into a support vector machine, which outperforms all the evaluated ones. Afan et al. (2016) provide a partial review of the relevant studies in the area.

Due to its stochastic temporal variations, time series modeling is a challenging task. Direct simulations might be inadequate to capture its features in both time and frequency domains. Consequently, for better representation, data pre-processing techniques (e.g. sampling, transformation, de-noising and normalization) are suggested to reformulate and reshape the raw signals. In a rainfall forecast study, Mehr et al. (2019) remove the non-stationary features by performing square root and standardization of the original data. Such a procedure produces a weak stationary signal that is easy to model, as the trend in the mean is separated and the variance is suppressed. For better estimation of water table fluctuations, Jeong and Park (2019) suggest a framework for detrending, deseasonalization, normalization and outlier exclusion. This method, by assuming consistency of the trends and stationarity of seasonal variability, detects, in an effective way, the process changes that occur in a groundwater system. If coupled with machine learning models, it improves the efficiency of the standalone ones. Liu et al. (2013) apply a wavelet for signal decomposition and integrate it with an ANN for SSC forecast, showing that wavelet helps better capture highly nonlinear and non-stationary SSC. A similar study by Rajaee et al. (2011) illustrates that the model is capable of obtaining useful information on various resolution levels. Shiri and Kişi (2012) combine wavelet with gene expression programming (GEP), neuro-fuzzy (NF), and ANN for sediment load prediction. It is concluded that the wavelet-based models significantly increase the accuracy of single ones.

These papers demonstrate the importance of data pre-processing for time series modeling. In most works, the main regressors are static models, e.g. ANN and NF. They are suitable for fitting problems, and a more robust model is required for time series forecast (Nanda et al., 2016). For a better SSC estimation, this paper establishes a nonlinear auto-regressive with external inputs (NARX) network and couples it with a new wavelet-based data pre-processing module. The NARX, a dynamic recurrent neural network, is a superior network for handling non-stationary issues. The data pre-processing framework takes the advantage of the discrete wavelet transformation for time and frequency analysis and the multigene genetic programming (MGGP) for feature selection, expecting to generate informative and noise-free inputs for the regressor. Time series data of daily discharge, water level and SSC during 2004–2012 collected at the Cuntan station on the upper reaches of the Yangtze River are used to test the proposed integrated NARX (INARX). Its performance is assessed statistically and compared with that of empirical and conventional data-driven models. The objective of this study is to put forward an improved neural network for real-time and multistep forecasts of the river suspended sediment. A robust prediction framework has profound engineering implications.