Modeling discharge–sediment relationship using neural networks with artificial bee colony algorithm
Highlights
► We use ANN with artificial bee colony (ANN–ABC) algorithm to model sediment load. ► The ANN–ABC is compared with other soft computational methods and rating curve models. ► These methods are neural differential evolution, adaptive neuro-fuzzy and ANN. ► Comparison results indicate that the ANN–ABC models performed better than the others. ► The logarithm transform is also found to significantly increase models’ accuracy.
Introduction
Estimation of suspended sediment concentration carried by a river is required for many water resources projects related with channel navigability, reservoir filling, hydroelectric-equipment longevity, river aesthetics, fish habitat and scientific interests. All surface water reservoirs are designed to a volume known as “the dead storage” to accommodate the sediment income that will accumulate over a specified period called the economic life. The underestimation of sediment yield results in insufficient reservoir capacity. To achieve an appropriate reservoir design and operation it is essential to determine sediment yield accurately. In environmental engineering, if sediment particles also transport pollutants, the estimation of river sediment load has additional significance (Kisi, 2010). The estimation of suspended sediment is an extremely difficult task because it is closely related to flow and the mechanism of their relationship is non-linear and they have complex interactions to each other (Sivakumar and Wallender, 2005).
The physically-based distributed models are based on the simplified partial differential equations of flow and sediment flux. The models are also based on some unrealistic simplifying assumptions for flow and empirical relationships for erosive effects of rainfall and flow. Examples of such models are reported by Wicks and Bathurst, 1996, Refsgaard, 1997 and others. These are highly complex and sophisticated models having components that correspond to physical processes. These models are able to consider theoretically the effects of spatial variation of catchment properties as well as uneven distribution of precipitation and evapotranspiration. Because the real spatial distribution of most of the variables such as precipitation is not presently measurable for much of the world, process-oriented distributed models are not practical as much as lumped models and have many disadvantages (Guldal and Muftuoglu, 2001). Lumped models are preferred since they only need a limited data need. However, it should be noted that (it should be emphasized that) they require lengthy calibration and parameterization processes (Haghizadeh et al., 2010). The advantages of artificial neural network (ANN) over deterministic models is that it needs fewer data and they are well suited for forecasting. However, the disadvantage of the ANN is that it is based on a ‘black box’ approach because their internal structure is generally not known and must be developed by a trial and error process. In spite of the black-box nature of the ANN, it is flexible in capturing the non-linearity of rainfall–runoff–sediment yield processes. Thus, it is more attractive for modeling hydrological processes (Coulibaly et al., 2000). The main advantage of the ANN method over the traditional approaches is that it does not require to explicitly describe the complex nature of the underlying process in a mathematical form (Nayak et al., 2005).
In last decades, the ANN has been successfully used in hydrological sciences (Lohani et al., 2011, Huo et al., 2010, Chen et al., 2010, Agarwal et al., 2006, Panagoulia, 2006; Wainwright and Mulligan, 2004; Govindaraju, 2000). Recent experiments have indicated that ANN may offer a promising results for estimating suspended sediment (Jain, 2001, Tayfur, 2002, Cigizoglu, 2004, Kisi, 2004, Kisi, 2008, Agarwal et al., 2006, Cigizoglu and Kisi, 2006, Tayfur and Guldal, 2006, Alp and Cigizoglu, 2007, Ardiclioglu et al., 2007; Zhu et al., 2007, Kisi et al., 2008, Kisi, 2010). Jain (2001) established sediment-discharge relationships by using ANN approach and found that the ANN model could perform better than the sediment rating curve. Tayfur (2002) used ANN in modeling sheet sediment transport and indicated that the ANN could perform as well as, in some cases better than, physically-based models. Cigizoglu (2004) examined the ability of ANN models in the estimation and forecasting of daily suspended sediments. Kisi (2004) used three different ANN techniques for predicting and estimating daily suspended sediment concentration, and he indicated that multi-layer perceptron models performed better than the generalized regression and radial basis function neural networks. Kisi (2008) successfully applied a data-driven algorithm for constructing ANN based sediment estimation models. Agarwal et al. (2006) simulated daily, weekly, ten-daily, and monthly monsoon runoff and sediment yield from an Indian catchment using back propagation ANN technique. Cigizoglu and Kisi (2006) developed methods to improve ANN accuracy in estimating suspended sediments. Tayfur and Guldal (2006) predicted total suspended sediment using daily precipitation and discharge data. Alp and Cigizoglu (2007) estimated suspended sediments by two different ANN techniques, feed forward neural networks and radial basis function, using hydrometeorological data. Ardiclioglu et al. (2007) investigated the accuracy of two different ANN algorithms in estimation monthly suspended sediments. Zhu et al. (2007) used ANN to model the monthly suspended sediment flux in the Longchuanjiang River, the Upper Yangtze Catchment, China. Kisi et al. (2008) employed different ANN techniques in suspended sediment modeling and compared their accuracy with sediment rating curves. All these studies used conventional ANN models with back-propagation (BP) algorithms for modeling suspended sediments. The main disadvantage of the BP algorithms is that it has the danger of getting stuck into local minima. Recently, Kisi (2010) proposed neural differential evolution models as an alternative to BP algorithms for suspended sediment estimation. In this study, an ANN model with a new novel algorithm, which is the artificial bee colony (ABC) algorithm, is used for modeling daily suspended sediment concentrations. ABC algorithm has a balanced exploration and exploitation capability and therefore it does not get stuck into local minima. To the knowledge of the authors, there is not any published study indicating the input–output mapping capability of ANN–ABC technique in modeling of suspended sediments.
Neuro-fuzzy networks have also been successfully used to model suspended sediments in last decades (Kisi, 2005, Kisi et al., 2006, Kisi et al., 2008, Kisi et al., 2009, Rajaee et al., 2009, Cobaner et al., 2009, Firat and Gungor, 2010). Kisi (2005) used a neuro-fuzzy model for daily suspended sediment estimation. Kisi et al. (2008) employed a neuro-fuzzy technique for estimating daily suspended sediment of rivers in Turkey and compared it with three different ANN techniques. Kisi et al. (2009) compared ANN and neuro-fuzzy models in estimation of monthly suspended sediments. Rajaee et al. (2009) examined the accuracy of a neuro-fuzzy model for suspended sediment concentration simulation and compared it with ANN, rating curves and multiple linear regression models. Cobaner et al. (2009) compared the ability of neuro-fuzzy and different ANN techniques for modeling daily suspended sediment concentration. Firat and Gungor (2010) used a neuro-fuzzy approach in modeling monthly suspended sediments.
The main purpose of this study is to develop ANN–ABC models for accurately estimation of suspended sediment concentration. The accuracy of ANN–ABC models is compared with those of the neural differential evolution, adaptive neuro-fuzzy, neural networks and rating curve models employed in the previous work of Kisi, 2005, Kisi, 2010).
Section snippets
Artificial neural network
The artificial neural networks (ANNs) may have one or more hidden layers. ANN is a massively parallel system comprising many processing elements connected by links of weights. Among the many ANN paradigms, the feed-forward back-propagation network (FFBP) is by far the most popular (Haykin, 1998). This network includes layers of parallel processing elements, called neurons, with each layer being fully connected to the proceeding layer by interconnection weights. Initially assigned weight values
Case study
The daily stream flow and suspended sediment concentration data of Rio Valenciano Station and Quebrada Blanca Station operated by the US Geological Survey (USGS) were used in the study. The drainage areas at these sites are 43.57 km2 and 8.63 km2, respectively. The same data were also used by Kisi, 2005, Kisi, 2010. The gauge datum of the Rio Valenciano and Quebrada Blanca are 98 and 130 m above sea level, respectively. Daily time series of stream flow and sediment concentration were downloaded
Methodology
Kisi (2005) developed neuro-fuzzy (NF) models to estimate the suspended sediment load for the Rio Valenciano and Quebrada Blanca stations. They used four input combinations: (1) Qt; (2) Qt and Qt−1; (3) Qt and St−1; (4) Qt, Qt−1 and St−1. Here, the Qt and St indicate the flow and suspended sediment at time t. He used mean square error (MSE) and the determination coefficient (R2) for the evaluation of NF models in the test period and compared the accuracy of NF with those of the ANN and sediment
Conclusions
The study investigated the ability of artificial neural networks (ANN) with artificial bee colony (ABC) algorithm for modeling daily discharge-suspended sediment relationship. The accuracy of the ANN–ABC models were compared with those of the neural differential evolution, adaptive neuro-fuzzy, neural networks and sediment rating curve models obtained from the previous studies (Kisi, 2005, Kisi, 2010). Mean square error and determination coefficient criteria were used as comparison criteria.
Acknowledgements
The data used in this study were downloaded from the web server of the USGS. The author wishes to thank the staff of the USGS who are associated with data observation, processing, and management of USGS Web sites.
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