Methods to improve the neural network performance in suspended sediment estimation

Abstract

The effect of employment of different methods of suspended sediment estimation by artificial neural networks (ANNs) was the concern of the presented study. It was seen that the initial statistical analysis of flow and sediment data provided valuable information about the appropriate number of input nodes of the neural network, thereby avoiding redundant nodes. The k-fold partitioning of the training data set showed that similar or even superior sediment estimation performances can be obtained with quite limited data provided that the training data statistics of the subset are close to those of the testing data. The range-dependent neural network (RDNN) was found to be superior to conventional ANN applications, where only a single network is trained considering the entire training data set. It was seen that both low and high-observed sediment values were closely approximated by the RDNN.

Introduction

Estimates of sediment yield are required in a wide spectrum of problems such as design of reservoirs and dams, transport of sediment and pollutants in rivers, lakes and estuaries, design of stable channels, dams and debris basins, undertaking cleanup following floods, protection of fish and wildlife habitats, determination of the effects of watershed management, and environmental impact assessment. Fine sediment has long been identified as an important vector for the transport of nutrients and contaminants such as heavy metals and micro-organics. Suspended sediment is important in its own right, since its presence or absence exerts an important control on geomorphological and biological processes in rivers and estuaries.

Sedimentation in rivers, reservoirs and estuaries is a serious problem. The prediction of river sediment load constitutes an important issue in hydraulic and sanitary engineering. It is a well-known fact that all reservoirs are designed to contain a volume known as the dead storage to accommodate the incoming sediment that will accumulate over a specified period. The underestimation of sediment yield results in insufficient reservoir capacities while the overestimation will lead to over-capacity reservoirs. Achieving only the appropriate reservoir design is sufficient to justify every effort to determine sediment yield accurately but in sanitary engineering the prediction of river sediment load has an additional significance, especially if the particles transport pollutants. The real-time distribution of the sediment concentration is needed in this case and the sediment concentration forecast is necessary for controlling the pollution level in rivers and reservoirs.

Several factors inter-relate to determine if soil is detached or moved and these processes are difficult to predict, as is evident from the number of reservoirs where actual sedimentation rates outstrip our predicted estimates, which can be out by orders of magnitude. The traditional calculation of sediment transport rates, and hence sediment yield, relates sediment concentration to river flow values. Limited sediment data can thus be extrapolated to the length of the discharge record, although such relationships demonstrate a wide spread of points, as would be expected from a consideration of sediment transport mechanics. The classical approach of hydromechanics has not yet succeeded in modeling the complete process of sediment transport in rivers for reasons that particle movements in turbulent flow, as well as the properties of the particles, are all random. The properties of the riverbed are irregular and hence can also be considered as random. Moreover, all the processes affect each other in that the flow causes erosion and transportation of particles, while the particles transported in turn affect the flow as well as the rate of erosion. In the majority of the rivers the total sediment load is mainly constituted from suspended sediment (Morris and Fan, 1997). The bed load has a significant contribution to total sediment load only in the mountainous regions. The bed load is difficult to measure and time series for this parameter are not available in the literature. Therefore the estimation of suspended sediment is considered as the key information for the future sediment accumulation in the water reservoirs.

Sediment yield Y(t) at a given point in space (say, watershed outlet) can be represented as

$$Y(t)=\overline{Y}(t)+\epsilon (t)$$

in which $\stackrel{\_}{Y}(t)$ is the mean value or deterministic component of Y(t), and ε(t) is the error from or fluctuation around the mean value or stochastic component of Y(t). The relative contribution of$\stackrel{\_}{Y}(t)$ and ε(t) to Y(t) depends on the watershed and space-time scales. Clearly, Y(t) encompasses the full range of variability from being entirely deterministic to being entirely stochastic (Singh et al., 1988). All sediment models are special cases of (1).

The deterministic models can be distinguished as being empirical or conceptual. Most of the empirical models are related to the Universal Soil Loss Equation (USLE) and its latter modifications. These models usually require long data records, so that average annual sediment yield can be determined. The conceptual models combine the mechanics of sediment transport with empirical relationships. Both the empirical and conceptual models approximate the physical processes controlling sediment yield.

Another way to represent the complex sediment behavior is to interpret a sequence of sediment yield measurements as being random. If the processes governing sediment yield, such as soil particle detachment, entrainment, transport, and deposition, are assumed to be stochastic and thus governed by the laws of probability the sediment yield can be described by a stochastic process and associated probability distributions (pdf).

Some sediment yield models contain both deterministic and stochastic elements. A classical example is the relationship between sediment yield and runoff, represented by a line in a logarithmic plot. This is the deterministic part $\stackrel{\_}{Y}(t)$ of the model. When the measurements are plotted, they encircle this line and most often will not lie directly on it. Thus the line represents only the mean trend of sediment yield-runoff relationship, and fluctuations ε(t) above and below it may be considered stochastic. A successful model will have to include a deterministic component or fluctuations around it.

Stochastic models of sediment yield can be grouped as the regression models, time series models, entropy models and probability models. The regression models relate Y(t) empirically to rainfall R(t) and runoff Q(t). Spatial variability of these models is not considered. Stochasticity is represented by variations around the mean trend. In time series models a watershed is considered as spatially lumped system. Deterministic relationships between R(t), Q(t) and Y(t) are represented by a transfer function and stochasticity is modelled as an autoregression process. In entropy models, the pdf of Y(t) is obtained using constraints based on observed values of Y(t) and/or Q(t). Spatial variability of the variables is not accounted for. Probability models consider sediment yield Y(t) as a stochastic process, and so also may be the rainfall R(x,y,z,t) and runoff Q(t). The behaviour of Y(t) is described by its pdf or its joint probability density function with other stochastic sequences.

The application of physics-based distributed process computer simulation offers one possible method of prediction to assess the outcome of different management actions and long-term management strategies. But the application of these complex software programs is often problematic, due to the use of idealized sedimentation components, or the need for massive amounts of detailed spatial and temporal environmental data, which is not available. Simpler approaches are therefore required in the form of `conceptual` solutions or `black-box` modeling techniques.

The artificial neural network (ANN) approach, which is a non-linear black box model, would seem to be a useful alternative for modeling the complex suspended sediment series. The ANN applications in water resources are in river flow prediction (Tokar and Johnson, 1999, Khalil et al., 2001, Brikundavyi et al., 2002, Elshorbagy et al., 2002, Cigizoglu, 2003a, Cigizoglu, 2003b, Cigizoglu and Kisi, Kisi, 2004), in the rainfall-runoff relationship (Hsu et al., 1995, Minns and Hall, 1996, Fernando and Jayawardena, 1998, Dawson and Wilby, 2001), in rainfall estimation (Silverman and Dracup, 2000, Cigizoglu and Alp, 2004, Freiwan and Cigizoglu, 2005) and in the various groundwater problems (Ranjithan et al., 1993). Neural network applications in hydrology were summarized by the ASCE Task Committee (2000b) and by Govindaraju and Rao (2000).

In the majority of these studies, the feed-forward error back-propagation method (FFBP) was employed to train the neural networks. The performance of the FFBP was found to be superior to conventional statistical and stochastic methods in continuous flow series forecasting (Brikundavyi et al., 2002, Cigizoglu, 2003a). However, the FFBP algorithm has some drawbacks such as the local minima problem. In their work, Maier and Dandy (2000) summarized the methods used in the literature to overcome this problem of training a number of networks starting with different initial weights, the on-line training mode used to help the network to escape local minima, the inclusion of the addition of random noise, and the employment of second order (Newtons algorithm, Levenberg–Marquardt algorithm) or global methods (stochastic gradient algorithms, simulated annealing). In the review study of the ASCE Task Committee (2000a), other ANN methods such as conjugate gradient algorithms, the radial basis function, the cascade correlation algorithm and recurrent neural networks were briefly explained. Thirumalaiah and Deo, 1998, Thirumalaiah and Deo, 2000) used conjugate gradient and cascade correlation algorithms together with FFBPs for different hydrological applications. The Levenberg–Marquardt algorithm was employed in the FFBP applications included in the present study.

The ANN applications in suspended sediment modeling are relatively new compared with other water resources domains (Abrahart and White, 2001, Cigizoglu, 2004a). Cigizoglu (2004b) showed that the FFBP could provide negative suspended sediment estimations for some of the observed low sediment values. As the extrapolation potential of the FFBP was demonstrated by Cigizoglu (2003a), such a result can be expected. The suspended sediment records contain periods with succeeding extremely low and high sediment values (or vice versa). The ratio between overall record maximum and overall record mean $(x_{\text{max}}/\overline{x})$ is quite high and some underestimations in low values (even negative values) arise as the network faces confusion in the transition between these two extreme zones (Cigizoglu, 2004a).

Considering this difficulty in suspended sediment modeling, two methods described in the literature, previously used for river flow estimation, are employed for suspended sediment estimation in this study. The first of these is the k-fold partitioning method. Using this statistical method, as explained by Ali and Pazzani (1996), the record is divided into smaller data sets and handled separately. Thus, statistical work is carried out for each sub-set independently and the sub-set which provides the most information (even more than the whole data set) is selected. This is important because the scarcity in rainfall data is a problem faced frequently by water resources engineers. In works like water reservoir planning, the length of the observed precipitation record might be quite short making the rainfall forecasting studies difficult. Therefore, methods helping to obtain more information from the available limited data are valuable. In a recent study, it was shown that extending the ANN training sets with synthetically generated flow data noticeably increased the flow prediction performance of ANNs (Cigizoglu, 2003a). Cigizoglu and Kisi (2005) successfully applied k-fold partitioning to flow data for neural network training.

The second method employed in this study for suspended sediment estimation is the range-dependent neural network (RDNN). This method was applied to the river flow time series by Hu et al. (2001). Based on a proposed clustering algorithm for the training pairs, RDNN has been developed for better accuracy in hydrologic time series prediction. In this method, the training data are clustered using different ranges such as different proportions of x_mean (mean of the whole series). Flow data falling within each range are trained by a separate neural network. Hence, each of the networks has its own training pairs obtained by the flowing clustering algorithm and serves different magnitudes of flow predictions.