FLOOD FORECASTING MODEL FOR HUAI RIVER IN CHINA USING TIME DELAY NEURAL NETWORK

Xue Yunpeng

The Yellow River Conservancy Commission, Zhengzhou, China

 Yonas B. Dibike

International Institute for Infrastructural, Hydraulic and Environmental Engineering,

Delft, The Netherlands

 Xue Yunpeng, Ihe, Westvest 7, P.O. Box 3015, 2601 DA Delft, The Netherlands

Tel: 31 (0)15-2151841, Fax: 31 (0)15-2122921, Email: xue@ihe.nl

Abstract: Time delay neural network, which is time lagged feed-forward network with delayed memory processing elements at the input layer, is applied to predict the discharge at Wangjiaba station, which is a reference station for the control of a important flood detention basin in Huai River in China. The network topology is using multiple inputs, which includes the time lagged discharges at upstream of the main trunk of the river and tributaries as input to the network, and a single output, which is the discharge at Wangjiaba station. Different types of input representations, such as the measured discharge, modified discharges, and the rate of changes in discharges have been considered by pre-processing the data. It was found that using multiple input with modified changes in discharge give the best result for prediction horizon of 12 hours. Moreover, including precipitation as input helped to improve the prediction for a longer (24 hours) prediction horizon.

Keywords: flood forecasting, artificial neural networks

1   INTRODUCTION

The Huai River Basin is located in the eastern part of China between the two major rivers, Yellow River and Yangtze River. The Huai River Basin is quite a complicated water system composed of a large number of tributaries, lakes, and canals. The upper reaches of the river is a mountainous area with a lot of tributaries while the middle reaches of the river is very flat with flood plain. After passing through a big lake which bed is high than the river bed, the Huai River discharges into the Yangtze River and the sea separately through different canals. However, the flood caused by the frequent and intensive stormy rainfall in summer can not flow into the sea or to Yangtze River quickly, and as a result, the Huai River basin is one of the heavy flood disaster areas in China. To minimise this problem, a huge and complicated flood control system has been constructed, which consists of river channels, natural lakes, reservoirs, dikes, flood detention and diversion areas.

Among the entire flood detention basin, the Mengwa flood detention basin which locate at the boundary of two provinces is the most crucial one, and it is controlled based on the water level at Wangjiaba gauging station. As it is shown in Figure 1, the flow condition at Wangjiaba station is a bit complicated, there are 3 main tributaries which discharge into the main trunk of the Huai River between the Wangjiaba (Q) gauging station and upstream station Xixian (Q1). There is also a flood-diverting gate to divert the flood into the detention basin and a spillway at the upstream section of Wangjiaba. So it is very difficult to predict the water level and discharge accurately during the flood period at Wangjiaba, while it is extremely important for flood control.

In general, there are two stages in the process of flood forecasting at Wangjiaba station. The first one is rainfall-runoff forecasting at each tributary and the other is flood routing in the main river systems. In practice, the traditional hydrological methods such as unit hydrograph and Muskingum methods are still being used while the possibility of using rainfall-runoff and 1D hydrodynamic models is under review. The main objective of this study is, however, to investigate the possibility of using the time delay neural network (TDNN) to improve the flood forecasting accuracy and prediction horizon at the Wangjiaba station.

2    METHODOLOGIES

River flood forecasting is one of the most important components in many flood control systems and flood forecasting models are becoming very essential tools to predict future flood events early enough in order to take appropriate control action to minimise damage. There are different types of flood forecasting methods, and they can be classified into three types: empirical (or black box) models, lumped conceptual (or grey box) models, and Distributed physically based (or white box) models. Black box model may also be divided into sub groups according to their origin, namely empirical hydrological methods (such as unit hydrograph model), statistically based methods (such as ARMA, gauge to gauge correlation methods) and artificial intelligence based methods (such as artificial neural networks, evolutionary algorithms, and chaos theory). Physically based models usually give more insight about the nature of the system to be modelled. The advantage of such model is that it can predict the events that might not have occurred before, such as extreme flood events or the effects of building of a hydraulic structure. However, they needs considerable amount of topographic and other site-specific data which usual (and for the present study specifically) may not be available. Moreover, physically based models require very long computational time, which is a disadvantage for real time flood forecasting and control. In such cases, data-driven models such as artificial neural networks (ANNs) which can discover relationships form data without having the complete physical understanding of the system, might be preferable. The models can learn from observed data, as well as data generated by physically based models. They usually run very fast in application, although they may take longer time to learn (to be trained). A number of research papers in the past few years  (Minns and Hall, 1997, Dibike and solomatine, 1999; khondker and Wilson, 2000; Solomatine and Rojas, 2000) have shown that using data-driven techniques to model hydrologic processes, such as rainfall-runoff forecasting, flush flood forecasting and prediction surge water levels, are promising. Among these technique, ANN seems more popular because of its superior ability to resolve the non-linear nature of the relationships so that the dynamic behaviour can be reconstructed adaptively [Liu and Lin, 2000]. In particular, the time lagged recurrent network (TDNN) topology (as implemented in the software package NeuroSolutions ) is found to be very suitable to deal with time series analysis and was chosen to be used in the present flood forecasting problem.

3    ARTIFICIAL NEURAL NETWORKS

Artificial Neural Network is an information processing system that tries to replicate the behaviour of a human brain by emulating the operations and connectivity of biological neurons (Tsoukalas and Uhrig, 1997). It performs a human-like reasoning, learns the attitude and stores the relationship of the processes on the basis of a representative data set that already exists. ANNs exhibit three features, namely, distributed processing, adaptation and non-linearity, and have been mathematically proven to be universal approximators of functions and their derivatives. This means that neural networks can approximate any function that best characterises a time series. It is this property that has stimulated civil engineers to adapt, investigate, and improve the performance of neural networks associated with their applications.

Multi-layer perseptron (MLP)has been well proven as a possible network topology in many time series prediction studies. However, it processes all the delayed signals explicitly in the input layer (Figure 2 ), and as a result, a very large network is usually required if all the relevant signals from the past are to be considered. This usually makes training very difficult (particularly if the data is noisy) [NeuroSolutions, 1995]. Moreover, since the expected time delay is obtained by trial-and-error, the network topology has to be modified every time and that is not very convenient.

Different from MLPs, a time delay neural network (TDNN) uses the so-called memory processing elements (PEs) to solve this problem. TDNN’s memory structure is simply a cascade of ideal delays and the signal and its time delay information are stored in a memory PE, which is processed as an input variable in the input layer. The number of time delay (also called taps) is a parameter of memory PEs, which can be adjusted manually or automatically depending on the memory structure type chosen without any changes of the network topology (shown Figure 3). The advantage of TDNNs is that they share some of the nice properties of feed-forward neural networks (such as trivial stability), but they can capture the information present in the input time signals. A one input TDNN with taps d (time delay d-1) is equivalent to a MLP with d inputs in the input layer to represent the signal and its d-1 lags. Therefore, TDNN can still use back propagation learning algorithm while it has an additional advantage that the optimal lag time for the input signal can be found through trial by changing the number of taps and tap delay instead of building a new network for each trial.

To discuss the performance of different models for simulation and forecasting by the TDNN, the following three statistical indices are evaluated (Lachtermacher & Fuller 1994).

(1) Mean absolute error (MAE)

where is number of data, is the observed data and  is the estimated one.

(2) Root mean square error (RMSE)

(3) Correlation coefficient (R)

where is the mean of observed data and  is the mean of estimated data.

The best performance is when these values are close to zero for MAE and RMSE, but close to one for R.

4    DATA PRE-PROCESSING AND ANALYSIS

At the study area of Huai Rive, 10 years (1979-1988) of historical precipitation and discharge data are available. There are 37 rainfall station data available, which could be too many for ANN to learn. So, they are classified into 3 regions according to their distance from the station where discharge is to be predicted, and the average rainfall data of each region is used as a input to ANN. Moreover, data about operation of the get for the flood detention basin shows that it has been used twice in 1982 and once in 1983. A Boolean variable was used to identify whether the flood detention basin was used at a particular time or not, which is not only important for the ANN to distinguish the input data, but also a very useful approach for future decision-making to compare the effect using or not using the flood detention basin during a particular flood event. The whole data was then divided into training set (1981-1986), cross-validation set (1987-1988), and testing set (1979-1980).

In order to prepare the data for TDNN, the optimum time delay has to be determined by using correlation analysis. The correlation between discharges at the forecast station (Q) and the other three upstream stations (Q1, Q2, Q3) and their time lags are calculated (table1, figure 4). The result shows that maximal correlation coefficients of Q1 and Q2 with Q are obtained with lag times of 28h and 32h respectively. However, the correlation between the present and antecedent rainfalls and the corresponding discharges was found to be insignificant (table1).

Preliminary investigation shows how difficult it is to obtain acceptable discharge forecast at Wangjiaba station by using the upstream discharges and their antecedents as input to the network. To improve this result, magnitudes of the upstream discharges were modified by multiplying their values with the corresponding average correlation coefficient. These modified discharge values where then were used as input to the TDNN. Moreover, the hourly changes in discharge value, both at the upstream and downstream measuring points, instead of the absolute values of discharges were used as alternative data sets. The correlation between these changes in discharge at each station with that of the change in discharge at the forecast station has also been calculated (Figure 5) for selecting the optimum lag time.

5   FORECASTING RESULTS

In this study, the TDNN memory processing elements (PE) was used in the input layer, while hyperbolic tangent activation function and linear activation function were used in the hidden and output layers respectively. The Input-output data to the TDNN were represented in five different ways: In the 1^st case, the absolute discharges both at upstream and forecast points were considered; 2^nd case, the upstream discharges were modified by multiply their value by the average correlation coefficient with the downstream discharge; (Note: unlike in MLPs, the input variable and its lags in TDNN are processed as one input variable inside memory PEs. As a result the input variables are modified by multiplying their values with the averaged correlation coefficient for all possible lags); 3^rd case, hourly change in the discharge values were used instead of the absolute values; 4^th case, the hourly change in the discharge were modified by multiply their value by the correlation coefficient with the downstream change in discharge; 5^th case, the 4^th case together with precipitation values as additional inputs. All these cases are summarised in table 2.

TDNNs were trained for each of the different cases described in Table 2 and the results have been compared with each other and with that of the so called ‘naive’ model which is obtained by assuming the future discharge to be the same as what is at present. In general, it has been found that the input - output data representation to the network has significant effect to the performance of the network during training and also to the subsequent performance of the network. Using the absolute discharge values at the upstream stations as input did not provide networks that can forecast better than the naive model (figure 6). Using modified discharges instead of the absolute values as input to the network has shown some improvement in prediction (figure 7). However, as shown in Table 3, using the values of changes in discharge modified by multiplying with the average correlation coefficients with the downstream changes in discharge has shown reasonable improvement for the 12h prediction horizon. The RMSE, MAE, and absolute maximal error are all decreased significantly. The reason for this could be that the changes in discharge represent the rate of change in the discharge, which is bigger at flood periods, and small in dry season. Since flood periods constitute a smaller portion of the whole time series, the use of the change in discharge instead of the absolute value increases the importance of the flood events specially when one uses RMSE as criterion to learn. By using changes in discharge as input, the dry season data is discriminated, and as a result, the network get more information about flood events, thus increasing the overall prediction performance of the network as shown in Figure 8.

Including the precipitation data as input did not improve the networks performance for the 12 hour prediction horizon. However for prediction horizon of 24 hours, using average precipitation data as input together with changes in discharge was found to be useful. As shown in table 4, for the prediction horizon of 24hours, the RMSE error is significantly bigger than 12 hours, but when precipitation data is included as input, the result is improved as can be seen Table 4, and Figure 9.

6    CONCLUSIONS AND RECOMMENDATIONS

This study shows the possibility of using TDNN for the prediction of discharge at Wangjiaba station, which is necessary for controlling the flood detention basin in Huai River in China. It has also showed that using the hourly changes in discharge as input-output pair is more appropriate than using the absolute values of discharges. Moreover, multiplying the inputs by the average correlation coefficients with the output shows significant improvement on the capability of the network to predict downstream discharges. This may be due to the fact that upstream discharges with higher correlation coefficient with the downstream discharges are given more weight during the training than the one with lower correlation coefficients. Even though using precipitation data as additional input to the network was not helpful to improve the 12-hour prediction, it gave a slight improvement in the case of 24-hour prediction. In general, the prediction of downstream discharge at Wangjiaba station using TDNN was reasonably good, especially in terms of RMSE or MAE. However, higher values of maximum absolute errors indicate that the network still has a problem in predicting some of the discharges. One of the reasons for this could be the fact that the upstream discharge of the Hong rive and some other small tributaries were not considered since the data was not available.

The study also shows that pre-processing the input-output data to an appropriate format has a significant effect on the performance of the network. Moreover, using TDNN instead of MLPs made the simulation experiment faster since the optimal lag time for the input data can be found easily by changing the memory depth in a single network instead of building a new network every time we want to change the lag time. More over, MLPs usually needs bigger network size compared to TDNN. Other neural network topologies, such as the network with Gamma or Lagueere memory processing elements and backpropagation through time (BPTT) learning algorithm, which can automatically change the memory parameter to find the best compromise between memory depth and resolution for the task, may further improve the prediction performance.

References

[1] Chang-ling Liu & Shu-Chen Lin, 2000. Artificial Neural Network Forecasting for Chaotic Dynamical Process in Hydrology.

[2] Jean-Philippe DRECOURT, Application of Neural Networks and Genetic Programming to Rainfall Runoff modelling, D2K Technical Report, 1999 website: http://www.dk2k.dk.

[3] Khondker Msood-UI-Hassan, Geoffrey Wilson and Anders Klinting, 2000, Application of Neural Networks in Real Time Flash Flood Forecasting, the 4-th International Conference on Hydroinformatics, Iowa, USA, Balkema, Rotterdam.

[4] Lachtermacher G. & Fuller J.D., 1994. Bcakpropagation in Hydrological Time Series Forecasting. In: Hipel K. W., Mcleod A.I., Panu U.S. & Singh V.P.  (eds), Stochastic and Statistical Methods in Hydrology and Environmental Engineering , vol.3, time series analysis in hydrology and environmental engineering: 229-242. Kluwer: Dordrecht.

[5] Minns, A.W. & Hall, M.J., 1996. Artificial Neural Networks as Rainfall-runoff Models, Hydrological Sciences Journal, Vol.41, NO.3, pp399-417.

[6] NeuroSolution, 1995. 'User Guide and Manual', Third Edition, Manual vol.II,  version 2.1, E-mail: ns-techsupport@nd.com.

[7] Principe J.C. & Lefebvre W.C., 1999 Neural and Adptive Systems: Fundamentals through Simulations John Wiley & Sons, INC.

[8] Solomatine D.P., Rojas C.J., Velickov S., Wust J.C., 2000. Chaos Theory in Predicting Surge Water Levels in the North Sea, the 4-th International Conference on Hydroinformatics, Iowa,USA, Balkema,Rotterdam.

[9] Tsoukalas, L.H.& Uhrig. R.E., 1997 Fuzzy and neural approach in engineering, John Wiley, INC.

[10] Yonus B.Dibike & Solomatine D.P., 1999. River Flow Forecasting Using Artificial Neural Networks, European Geophysical Society (EGS) XXIV General Assembly, The Hague, the Netherlands.

Table 1    The time lags of max correlation coefficient of discharges and precipitation

Table 2    The list of the different input representation in this study 

Table 3    The results of TDNN for predict horizon of 12h

Table 4    Significance of using precipitation data as input for discharge prediction with 24h horizon

  Fig.1   The sketch map of study area of Huai River

Fig.2    Example of processing of time delay signals in MLPs  [Principe, et al, 1999]

Fig.3    The time delay paradigm for processing time series data [adapted from Principe, et al, 1999]

Fig.4  The correllogram of discharge

Fig.5  The correllogram of changes in discharge

Fig.6  The 12-hours predicted result of using discharge as input

Fig.7  The 12-hours predicted result of using modified discharge as input

Fig.8  The 12-hours predicted result of using modified changes in discharge as input

Fig. 9  The 24-hours predicted result of using precipitation as additional input