Division-based rainfall-runoff simulations with BP neural networks and Xinanjiang model
Introduction
Since the Stanford Watershed Model was developed by Crawford and Linsley in 1966 [45], there has been much research on the numerical hydrologic modeling in watershed hydrology. This activity has been enhanced by the ever-expanding computing power and growing capability to observe, store, retrieve, and manage hydrologic data (i.e., rainfall and streamflow). These enhancements result in a significant revolution in watershed models. Not only do these models simulate watershed hydrology more accurately, but they also simulate other components in the ecobiological system [40] and socio-economic continuum [9]. In addition to the simulation of various hydrologic components, models have been used for the simulation of water quality [21], ecology study [53], risk and uncertainty analysis [55], and environmental impact assessment within watersheds [57], [58]. Many models have been developed over years for different purposes. Nevertheless, many of these models share structural similarities because their underlying physical laws and assumptions are the same while some of other models possess distinct differences. Based on the description of various processes and characteristics in watersheds, models can be classified as lumped or distributed. Conceptual lumped models, which are expressed with ordinary differential equations based on simplified hydraulic laws, and taking no account of spatial variability of processes, can aim at predicting streamflow over a watershed. On the other hand, physically based distributed models, which rely on conservation equations of mass and momentum of the watershed, take an explicit account of spatial variability of processes. Depending upon the way that the processes are described, watershed models can be classified as fully deterministic or fully stochastic or mixed [46].
The research in artificial intelligence increased dramatically during the 1990s which has been widely used in many hydrologic fields such as artificial neural networks, chaos theory, genetic algorithm, fuzzy theory, and wavelet theory. Luk et al. [31] used an ANN (artificial neural network) to forecast short-term rainfall for an urban catchment and investigated the effect of temporal and spatial information on short-term rainfall forecasting. Singh and Datta [44] developed a method which links the numerical simulation model with the genetic algorithm for optimal identification of unknown groundwater pollution sources. Jacquin and Shamseldin [26] applied the Takagi–Sugeno fuzzy inference systems to rainfall-runoff modeling. Ju et al. [29] employed a loose type of wavelet neural network model which utilizes the merits of the wavelet analysis method and artificial neural network to simulate daily streamflow. Ng et al. [38] found that chaotic approach can determine the level of complexity of a system after they applied the chaotic analytical techniques to daily hydrologic series comprising of outliers. Numerous studies have concluded that the artificial intelligence can provide an alternative approach for hydrologic problems that are difficult to be solved with conventional approaches.
The artificial neural network (ANN) was originally developed to mimic basic biological neural systems-the human brain. In general, ANN is composed of a number of interconnected simple processing elements called neurons or nodes with the attractive attribute of information processing characteristics such as nonlinearity, parallelism, noise tolerance, and learning and generalization capability. Contrary to the traditional model-based methods, ANN is a data-driven, self-adaptive method in which there are few a priori assumptions about the models for problems in the study. They learn from examples and capture subtle functional relationships among the data even if the underlying relationships are unknown or difficult to be described. Thus, ANN is well suited for problems whose solutions require knowledge that is difficult to specify and which there are enough data or observations. In this sense, they can be treated as one of the multivariate nonlinear non-parametric statistical methods. Due to its highly parallel structure, high speed self-leaning ability, self-adaptable processing ability, arbitrary function mapping ability, powerful pattern classification and pattern recognition capabilities for modeling complex nonlinear systems [24], the application of ANN to various aspects of hydrologic modeling has undergone many investigations in recent years [6], [10], [11], [12], [13], [24], [25], [28], [36], [43]. To obtain a higher successful prediction rate, many researchers attempt to employ hybrid approaches combining ANN and other theory, such as conceptual models [7], chaos theory [47], wavelet theory [29], [30], and clustering analysis [1].
As mentioned above, although ANN has provided many promising and exciting results in rainfall-runoff forecasting, it is difficult to obtain satisfying results by using raw data for direct predictions, particularly in high and low flow periods [25], [28], [36], [42], [50]. As we all know, rainfall-runoff processes are dynamic, seasonal and nonlinear time series as well the underlying mechanisms of streamflow generation are likely to be quite different during high and low flow periods. All the above mentioned factors make ANN difficult to obtain a stable and reliable prediction when faced with complex problems like rainfall-runoff processes. So, how to achieve better performance in high and low flow regions is a key problem for hydrologic simulations. Many researchers attempt to decompose the data corresponding to flow hydrograph for the purpose of improving time series forecasting accuracy. Amold et al. [3] applied automated base flow separation and recession analyses techniques partitioning the total flow data into surface flow and base flow. Furundzic [20], Abrahart and See [1], Jain and Srinivasulu [27] have proposed a self-organizing map (SOM) classifier to decompose the whole data set into different number of clusters and develop separate ANN models for each cluster of data. Hu et al. [25] employed the range-dependent neural network (RDNN) to the river flow time series. Zhang and Govindaraju [60] have demonstrated that the performance of the developed MNN which divides the data set into three classes of low, medium, and high flows, and an expert ANN is developed for each class to be better than these of a single ANN. Labat et al. [30] developed wavelet transforms to identify varying characteristics in the rainfall and runoff time series analysis. Cigizoglu and Kisi [14] successfully applied k-fold partitioning to flow data for neural network training.
Most of these studies have indicated that an integrated approach coupled with data decomposing techniques which divides the data set into different number of clusters using separate ANN models for each cluster of data can achieve better performance as compared with a single ANN when faced with a complex rainfall-runoff process. This performance could perhaps be attributed that the hydrologic rules for generating runoff are apparently different for average and extreme events and sub-cluster data sets containing more homogeneity than the whole data. It is generally accepted that the daily streamflow time series indicated strong seasonal effects. According to this, a novel time series prediction method is proposed in this paper, which combines the advantage of the divided-period analysis and BP neural network. First, all samples are divided into two groups: flood period and non-flood period. Then, two different neural networks are constructed and data in each group is used to train BP neural network separately. Finally, a comparison of the division-based BP (DBP) model to the primitive BP model and the Xinanjiang model is also conducted to evaluate the performance of the DBP model.
The remaining paper is organized as follows. Section 2 provides a brief review of the BP Neural Network model and Xinanjiang model. In Section 3, the study area and data set are described. The approaches and techniques of applying the division-based BP (DBP) on the streamflow simulation are presented. The relative performance of DBP over traditional BP model and Xinanjiang model is reported in Section 4. Some concluding remarks are drawn in Section 5.
Section snippets
Back-propagation (BP) neural network model
After the first simple neural network was developed by McCulloch and Pitts in 1943 [35], many types of ANN have been proposed. The neural network model with multi-layer perceptron is the most mature, widely used model among ANN models. Research in these studies shows promising results in hydrology [29], [31]. The BP neural network is the most widely used ANN in hydrologic modeling and is used in this study. The BP network has all the functions of the neural network and its unique advantages
Study area and data sets
The study area shown in Fig. 3 is in the upper area of Nangao Reservoir with a drainage area of 152.7 km2, located in the Luo River, Shanwei City, Guangdong Province, China. It is characterized with frequent storms with the highest annual rainfall reaching 2328 mm. The precipitation events during the flood season can be classified as low pressure troughs, or as cyclones. Four hydrologic control stations were selected in the main streams of the basins: Nangao, Luoyan, Dingyang, and Nanwan. Thus,
Results and discussion
The performance of DBP model evaluation results during the flood and non-flood testing periods is presented in Table 4, Table 5 respectively. It can be seen that three models have the high practicability and accurate ability for streamflow forecasting. For a comparison on the values of performance evaluation criteria CE and , it is evident from Table 4, Table 5 that the prediction error of BP and DBP models are lower than these of the Xinanjiang model for the testing stage—its coefficient of
Conclusions
In this paper, a novel method is applied to daily streamflow simulations, which combines the advantages of the divided-period analysis and BP neural network. BP neural network is used to train separately after all data are divided into flood and non-flood categories. The comparison study of ANN with Xinanjiang model indicates that ANN performs well on the streamflow simulation and grouping can improve the simulations, especially on base-flow. However, the effect on peak forecast performance is
Acknowledgments
This study was funded by the National Natural Science Foundation of China (Grant no. 40830639, 50679018, 50879016 and 40730634), the program for Changjiang Scholars and Innovative Research Team in University (IRT0717) and the 111 project under Grant B08048, Ministry of Education and State Administration of Foreign Experts Affairs, PR China. We are very grateful to four anonymous reviewers whose comments helped improve the paper considerably.
Qin Ju received her B.S. and M.S. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, in 2002 and 2005, respectively. Since then, she has studied for Ph.D. at the same university up to the present. Her main research interests include numerical hydrological modeling and developing models using neural network.
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Qin Ju received her B.S. and M.S. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, in 2002 and 2005, respectively. Since then, she has studied for Ph.D. at the same university up to the present. Her main research interests include numerical hydrological modeling and developing models using neural network.
Zhongbo Yu is a Professor in the Department of Geoscience, University of Nevada Las Vegas, USA and in the College of Hydrology and Water Resources, Hohai University in Nanjing, China. His research interests include watershed hydrological modeling, flow and contaminant transport, and impacts of climate change and land use-land cover change on ecological and hydrological systems. He received his Ph.D. in Hydrology/Hydrogeology from Ohio State University, USA in 1996, his M.S. in Hydrogeology from University of Southern Mississippi, USA in 1992 and his B.S. in Hydrogeology and Engineering Geology from Hohai University, China in 1983.
Zhenchun Hao received his B.S. and M.S. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, in 1981 and 1984, respectively. He continued his education at the same university where he received a Ph.D. in Hydrology in 1988. Now he is a Professor of Hydrology at the College of Hydrology and Water Resources, Hohai University in Nanjing, China. His research interests include large-scale hydrological modeling, watershed hydrological modeling and ecological hydrology.
Gengxin Ou is going to study in Hydrologic Science as a Ph.D. candidate at the School of Natural Resources, the University of Nebraska-Lincoln, USA. He received his B.S. and M.S. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, in 2006 and 2008, respectively. His interests include development and application of hydrologic models and groundwater models, and interaction between surface water and groundwater.
Jian Zhao received the B.S. and M.S. in the College of Water Conservancy and Hydropower Engineering, Hohai University in Nanjing, China, in 1981 and 1989, respectively. He received his Ph.D. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, 2006. Now he is a Professor of Hydrology at the College of Water Conservancy and Hydropower Engineering, Hohai University in Nanjing, China. His main research interests are in ground Water environmental protection and watershed hydrological modeling.
Dedong Liu received the B.S. degree in College of Hydraulic Engineering Economy and the M.S. degree in the College of Water Resources from North China University of Water Conservancy and Electric Power, in 2002 and 2005, respectively. Since then, he has been studying for Ph.D. in the College of Hydrology and Water Resources, Hohai University in Nanjing, China, up to the present. His main research interests are in numerical hydrological modeling.