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Neural networks forecasting of flood discharge at an unmeasured station using river upstream information
Advances in Engineering Software 37 (2006) 533–543 www.elsevier.com/locate/advengsoft
Neural networks forecasting of flood discharge at an unmeasured station using river upstream information Tienfuan Kerh *, C.S. Lee Department of Civil Engineering, National Pingtung University of Science and Technology, 1 Hseuh Fu Road, Pingtung 91207, Taiwan Received 7 October 2004; accepted 19 November 2005 Available online 7 February 2006
Abstract Based upon information at stations upstream of a river, a back-propagation neural network model was employed in this study to forecast flood discharge at station downstream of the river which lacks measurement. The performance of the neural network model was evaluated from the indices of root mean square error, coefficient of efficiency, error of peak discharge, and error of time to peak. The verification results showed that the neural network model is preferable, which performs relatively better than that of the conventional Muskingum method. Furthermore, the developed model with different input parameters was trained to check the sensitivity of physiographical factors. The results exhibited that flood discharge and water stage, are two factors to dominate the accuracy of estimation. Meanwhile, the physiographical factors had a slight and positive influence on the accuracy of the prediction. The time varied flood discharge forecasting at an unmeasured station might provide a valuable reference for designing an engineering project in the vicinity of the investigation region. 2005 Elsevier Ltd. All rights reserved. Keywords: Flood discharge estimation; Unmeasured station; Neural network model; Evaluation index; Physiographical factor
1. Introduction In the field of civil and hydraulic engineering, the information of a river flood discharge is related to flood control, and may be used to evaluate the performance of water resource planning and management. Therefore, how to accurately analyze the flood discharge based on measuring records at a specified flow domain becomes a crucial issue either from academic or practical standpoints. Typhoons generated in the usual fashion, affect flood discharge by several time and space factors. This may cause a difficulty in describing this hydrological phenomenon with the use of conventional statistical models. In general, the deterministic method and the stochastic method are frequently used to develop a model for estimating the flood discharge [1,2]. However, the former method assumes the occurrence obeys certain physical properties, and simulates the complicated *
Corresponding author. Tel.: +886 933 325188; fax: +886 877 40122. E-mail address: [email protected] (T. Kerh).
0965-9978/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2005.11.002
hydrological process to as a simplified model. This may not correctly reflect the actual conditions of flow domain, and thus may reduce the accuracy of flood discharge estimations. The latter method takes a time series of statistical data as the basis, and then a flood discharge estimation model is developed according to the principle of random probability. This may require a very complicated calculation procedure, and may become a tedious task if the data information is not well recorded. The approach of neural network has the advantages of using field recorded data directly without simplification and is not like regression analysis, which needs to make an assumption of equation in advance. Furthermore, this method is capable of executing parallel computations, and can simulate a nonlinear system which is hard to describe by traditional physical modeling. This has allowed for a wide range of applications in civil and hydraulic engineering to be extensively published in recent years [3–14]. Among these research reports, the issues related to flood discharge were mainly focused on the prediction of flood
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stage or discharge at a specified river station or section based on previously recorded time series data structures. The results were effectively estimated by neural network models, but there are only very few papers that dealt with flood discharge estimation, including a location which has an important engineering concern, but lacks measurement due to insufficient measuring time periods or device installation difficulties. Hence, this relative topic is still open and the neural network model may be applied to solve the problem of interest in a particular river flow domain. Located in southern part of Taiwan, the main Kaoping river basin consists of several branches, three major branches, Yailiao river (R1), Laonumg river (R2) and Chisan river (R3) are considered (see Fig. 1). This main river has the total length of 176.6 km, the area in flow domain of 3257 km2, and that is the largest in the whole island of Taiwan [15,16]. To evaluate the variation of flood discharge at an important place downstream of this river, which has incomplete or no measurement. A back-propagation neural network model has been developed at the
present to perform the task. At first, by collecting time historical records of flood discharge, water stage and physiographical factor at three measuring stations, Sanlin bridge (B2), Shinfa bridge (B3) and Sandimen (B4) in each river branch, upstream of the main river as the input data sets. Also, by taking the measuring station, Lilin bridge (B1), at merging place of the above mentioned three branches and downstream of the main river, as the verification target output. Then, four cases of flood records caused by typhoons are used for training basis, another four cases of typhoon records are taken to verify the estimations of the neural network model, and make comparisons with the calculation results of the conventional Muskingum method. Finally, two important locations, Kaoping bridge (B5) and Wanta bridge (B6), downstream of the river, lack measurement and have different physiographical factors, chosen to estimate the variation of flood discharge in accordance with the developed neural network model. The estimated results may provide a valuable reference for designing an engineering project, and may increase
Fig. 1. Sketch of the research area at Kaoping river basin.
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the performance of water resource management in these regions. 2. Neural network model and evaluation criteria Basically, the neural networks can be classified into four types according to its learning law, which are: (1) supervised learning nets, (2) unsupervised learning nets, (3) associate learning nets, and (4) optimization application nets. Among these nets, the back-propagation neural network is properly the most common used methods in solving various engineering problems [17–21]. The computational algorithm of this model has been well programmed in a couple of software packages. Thus in this study, the neural network toolbox MATLAB [22], is taken to develop the flood discharge estimating model for the sake of convenience. As the theoretical background of back-propagation neural network is simple and may be seen in many of relative references (e.g. [23–25]), the details are not included in this section, but some of the key points such as evaluation indices of accuracy are discussed properly. For estimating flood discharge varied with time in each typhoon case, two neural network models are considered here through numerical experiments. The first model ANN(A) as shown in Fig. 2, there exists 21 neurons in the input layer, 15 neurons in the hidden layer and 1 neuron in the output layer (I21H15O1). The input parameters are important as they may have an influence on the accuracy of estimation (e.g. [26]). For this model, the inputs include four time steps (t-3, t-2, t-1, t) of discharge information at three upstream measuring stations, Sanlin bridge, Shinfa bridge and Sandimen, respectively. In addition, the studied river basin may be considered as an open
Input layer
535
physical system. Basically the physiographical factors to affect river discharge may include nine items. They are the basin area (A), length of the main stream (L), mean slope (S), mean width (W), form factor (F), perimeter (P), circularity ratio (R), compactness (C), and elongation (E) for three branches, the Yailiao river, the Laonumg river and the Chisan river [27,28]. Note that the output layer is the estimation of discharge of Lilin bridge at time step t. Since the water stage is strongly related to the discharge in a river, three time steps (t-2, t-1, t) of the river stage at the same measuring stations are included in the input layer of the second model ANN(B). With the same numbers of hidden layers and output layers as the first model, this model (I30H15O1) is further used to check the difference in neural network calculations. To evaluate the results of neural network training and estimations, the following are some of the commonly used indices for checking the accuracy of estimated flood discharge. The first one is root mean square error (RMSE), and its definition is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 n ðT n Y n Þ RMSE ¼ ð1Þ N where Tn denotes the actual observed value, Yn is the estimated value from neural network output, and N is the training number. The second index is the coefficient of efficiency (CE), and the definition is P 2 ðQ Qest Þ CE ¼ 1 P obs ð2Þ 2 ðQobs Qobs Þ where Qobs is the observed discharge value, Qobs is the averaged discharge of observation, and Qest is the neural
Hidden layer
Output layer
Shinfa Bridge Discharge records at t, t-1, t-2, t-3
Sanlin Bridge Discharge records at t, t-1, t-2, t-3 Lilin Bridge Estimating discharge at t Santimen Discharge records at t, t-1, t-2, t-3
Physiographical factors at each station region Fig. 2. Neural network model (I21H15O1) for flood discharge estimation.
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Herb, occurred on 03/08/1994, 08/06/1995, 25/07/1996, and 31/07/1996, respectively. With the input of physiographical data in these regions (Table 1), and the discharge recorded at downstream station (B1) is taken as the target output. Then, by using the Levenberg–Marquardt algorithm in the learning process, the convergent tendency of error in training for both models ANN(A) and ANN(B) is displayed in Fig. 3. For both models, a total of 100 times of calculation are included for each epoch, the curve shows that the learning error is converged after 600 epochs. The neural network training result shows that the performance of model ANN(A) is acceptable. The root mean square error is RMSE = 0.186, and the square of correlation coefficient is R2 = 0.912 for this model. In other words, the neural network estimation is in reasonable agreement with observation. Now by adding observed river stage information at upstream stations in the input layer, the neural network model ANN(B) exhibits better performance than that of the model ANN(A), as the root mean square error becomes RMSE = 0.017, and the square of correlation coefficient becomes R2 = 0.988 in this preferred model. Displayed in Figs. 4 and 5 are error distribution and the approaching tendency of estimation and observation for both models. These complete the training process of the neural network model, and the model will be applied to verify its capability in the next typhoon event. Now by taking the same weighting coefficients and bias terms in the developed neural network models, and by replacing flood discharges and river stages, caused from another four different types of typhoon in the input layer.
network estimated discharge. The more the CE value approaches one, the higher the consistency of the simulation result with actual information. The third index is the error of peak discharge (EQp), and the definition is EQp ¼
Qpest Qpobs 100% Qpobs
ð3Þ
where Qpobs is the observed peak flood discharge, and Qpest is the estimated peak flood discharge. If EQp > 0, it represents to us that the estimated result is larger than the observed result, while if EQp < 0, it means the estimated result is less than the observed result. The last index of error is time to peak (ETp), and the definition is ETp ¼ jT pest T pobs j
ð4Þ
where Tpobs is the observed arrival time of peak flood discharge, and Tpest is the estimated arrival time of peak flood discharge. The less of ETp value represents more accurately the estimated arrival time of peak flood discharge. 3. Neural network training and verification To fit in transfer functions and to treat data information in the neural network calculation, the normalization of input data may be required to reduce the effect of extreme values in parameters. Thus after data normalization, the discharges of a 3 h ahead time and the present time at the upstream stations (B2, B3 and B4) of the Kaoping river are used as the input in the training process. These data sets result from four typhoons, Caitlin, Deanna, Gloria, and Table 1 Physiographical factors for station at each branch river region River (station)
A (km2)
L (km)
S
W (km)
F
P (km)
R
C
E
Yailiao Laonumg Chisan
642 1373 802
68.5 137 117
0.0340 0.0402 0.0410
9.37 10.02 6.85
0.137 0.073 0.059
121 277 225
0.55 0.22 0.20
0.74 0.47 0.45
0.42 0.31 0.27
0.6 ANN(A)
0.5
ANN(B)
RMSE
0.4 0.3 0.2 0.1 0 0
100
200
300
400
500
600
Epochs Fig. 3. Convergent tendency of learning errors for both the neural network models.
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537
2000 Discharge difference (cms)
ANN(A)
1000
0
-1000
-2000 0
48
96
144
192
240
288 336 Time (hrs)
384
432
480
528
576
624
Discharge difference (cms)
2000 ANN(B)
1000
0
-1000
-2000 0
48
96
144
192
240
288 336 Time (hrs)
384
432
480
528
576
624
Fig. 4. Error distributions in neural network training for both models.
20000
20000 ANN(A) R 2 = 0.912
15000 ANN (cms)
ANN (cms)
15000
ANN(B) R 2 = 0.988
10000
5000
10000
5000
0 0
5000 10000 15000 Observation (cms)
20000
0 0
5000 10000 15000 Observation (cms)
20000
Fig. 5. Scatter plots of estimation versus observation for both models.
The estimations are compared with the results of conventional Muskingum method and measuring records for typhoon, Bilis, Toraji, Nari, and Lekima, occurred on 22/08/2000, 30/07/2001, 17/09/2001, and 26/09/2001, and are shown in Figs. 6–9, respectively. Additionally, the comparison result of evaluation indices for four typhoon types are shown in Table 2. The obtained plots and data may clearly reflect the performance of estimation models in this type of problem.
For the ANN(A) model, excluding the simulation in uprising section of discharge has significantly underestimated the results of the Bilis and Lekima typhoons. The errors are small for the other two cases. All four cases have good performance in the coefficient of efficiency, which ranges from 0.919 to 0.973. The estimated results of peak flood discharge for typhoons Bilis and Toraji are smaller than the observations, and the differences are 0.6% and 1.7%. But for multi-peak type of typhoons such as Nari
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12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
72
48
96 Time (hrs)
120
144
168
192
Fig. 6. Estimation compared with observation at Lilin bridge for typhoon Bilis.
12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 7. Estimation compared with observation at Lilin bridge for typhoon Toraji.
and Lekima, the estimated peak flood discharges are larger than the observations, and the differences are 4.6% and 2.6%. Excluding that the case of typhoon Nari which has a 2 h difference in error of time to peak, there are no differences for the other cases. For the ANN(B) model, only very small errors are found in the uprising section of discharge, and the coefficients of efficiency have values that range from 0.967 to 0.989. Those are close to the value of one for all typhoons. The estimated peak flood discharges are smaller than the observations, and the difference is ranged from 2.1% to 0.75%. There are no differences in error of time to peak for all cases except typhoon Bilis which has a 2 h difference.
For the conventional Muskingum method, the continuity equation may be used to deal with the relationship between water storage (S), flood inlet discharge (I), and flood outlet discharge (O). The basic equation is as follows: S ¼ K½xI þ ðI xÞO
ð5Þ
where K is the time of propagation, and x is the weighted parameter. The accuracy of this conventional method is strongly dependent upon the length of historical data and the choice of weighting factors. In this study, the averaged coefficients of the storage time and the weighting factor are in accordance with previous research report in this region [16]. The coefficients of storage time are 3.13, 3.49, 3.58, and 4.53; and the weighting factors are 0.493, 0.493,
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12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 8. Estimation compared with observation at Lilin bridge for typhoon Nari.
12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 9. Estimation compared with observation at Lilin bridge for typhoon Lekima.
0.495, and 0.500, for typhoons Bilis, Tozaji, Nari, and Lekima, respectively. It can be found that the estimated flood discharge for each typhoon case by this conventional approach has a significant underestimations and errors. The coefficient of efficiency for typhoon Tozaji is only 0.630, is the best among the other typhoons. The estimated peak flood discharge has a very large error, which is up to 51.92% for typhoon Nari. For the error of time to peak, the best case is typhoon Bilis, which has a 2 h difference, while the worst case is typhoon Toraji, which has a 6 h difference. Above all, it can be found that the neural network model ANN(B) has the best ability for estimating flood discharge in four typhoons. This model can obtain a more accurate prediction than that of neural network model ANN(A), but this model requires more input items and
that may require more time in computation. The use of the Muskingum method is case independent, and the accuracy of calculation may rely on regional characteristics of the river basin. That is, this method may be good in estimation for one river case, but it may not have to be the same level of accuracy for the other one river case. In the present Kaoping river case, this conventional method performs a poor estimation as the result is not very consistent with the observation. Although it is possible to improve the accuracy of estimation by trying some other sets of coefficients for this method, it may require tedious work, which is not a good choice from an economical point of view. Note that many parameters are considered in the input layer of neural network models, which may increase the complexity in calculation process. Also because the previous records of flood discharge and river stage are two
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Table 2 Evaluation indices for flood discharge estimation using different models
Table 4 Square values of correlation coefficient and root mean square errors
Model
Typhoon
Index
Model
R2
RMSE
ANN(A)
Bilis Toraji Nari Lekima
0.966 0.953 0.973 0.919
0.6 1.7 2.6 4.6
0 2 0 0
ANN(B)
Bilis Toraji Nari Lekima
0.974 0.989 0.986 0.967
0.32 2.1 0.75 0.56
2 0 0 0
ANN(A) ANN(B) ANN(1) ANN(2) ANN(3) ANN(4) ANN(5)
0.912 0.988 0.921 0.926 0.963 0.970 0.954
0.186 0.017 0.150 0.139 0.034 0.022 0.054
Muskingum
Bilis Toraji Nari Lekima
0.565 0.630 0.523 0.499
28.98 44.89 51.92 30.73
2 6 5 3
CE
EQp (%)
ETp (h)
primary consideration factors, which may not be neglected in the discharge estimation. So in this study, it is worthy to check the sensitivity of hydrological factors in the present neural network models. Originally, nine physiographical factors are taken in the input layer, but some of them are related to each other and may be divided into two groups. Group (A) includes five physical parameters, which are basin area, main stream length, mean slope, mean width, and perimeter. Group (B) contains four shape parameters of river flow domain, which are form factor, circularity ratio, compactness, and elongation. Shown in Table 3 are the modifications of input parameters for different neural network models, where the neurons in the input layer, the hidden layer, and the output layer are I17H15O1, I16H15O1, I26H15O1, I25H15O1, and I21H15O1 for the model from ANN(1) to ANN(5), respectively. Shown in Table 4 is the comparison result of neural network calculations, it can be seen that discharge and water stage do dominate the accuracy of flood discharge estimation. The physiographical factors in either group have a slight influence on the prediction accuracy, but both of the two groups do have a positive contribution in the neural network estimations. Therefore, to obtain the highest accuracy possible, the neural network model ANN(B) is a relatively good option for further flood discharge estimation at stations with insufficient data or without records.
4. Flood discharge forecasting at unmeasured station Downstream of the Kaoping river, the Kaoping bridge and the Wanta bridge, are two important connection places for many agricultural and import/export developments in this region. Even at the present time, there exists a new bridge under construction in the neighborhood of Kaoping bridge. The original measurement device for flood discharge and river stage has been removed, and the recorded data such as peak flood discharge and time to peak, are no longer sufficient to provide the needs for various hydraulic engineering designs in this area. Now by taking physiographical information (Table 5) at the above mentioned places as the input in the neural network model ANN(B), with historical discharge and water stage inputs, the simulation results for four typhoon events show that there is no too much difference in peak discharge, about an hour more or less slight difference in peak arrival time for Kaoping and Wanta bridges as shown in Figs. 10 and 11. These plots also present the hydrograph of each case which is similar for both places, due to the fact that the distance between these two bridge is not too far (about 4.5 km), and the physiographical factors are similar at this region downstream. For a type of short time to peak typhoon like Bilis, the estimated peak discharge at Kaoping bridge is 5809 cms, and the peak arrival time is 12 h. At Wanta bridge, the peak values are 5963 cms and 13 h. For typhoon Toraji, a high peak discharge type, the estimated peak discharge at Kaoping bridge is 10,624 cms, and the peak arrival time is 33 h. At Wanta bridge, the peak values are 10,745 cms and 33 h. For typhoon Nari, the estimated peak discharge and time to peak are 7181 cms and 54 h for Kaoping
Table 3 Input parameters for different neural network models Model
Input Discharge
ANN(A) ANN(B) ANN(1) ANN(2) ANN(3) ANN(4) ANN(5)
• • • • • • •
Water stage
Physiographical factors (A)
Physiographical factors (B)
•
• • •
• • •
• • •
• •
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Table 5 Physiographical factors for unmeasured station at the main river region River (station)
A (km2)
L (km)
S
W (km)
F
P (km)
R
C
E
Kaoping Wanta
3075.5 3110.7
165.3 169.8
0.0067 0.0067
1.786 1.721
0.113 0.100
334.3 357.7
0.35 0.31
0.587 0.552
0.37 0.35
12000 Bilis Toraji
10000
Nari
Discharge (cms)
Lekima
8000
6000
4000
2000
0 0
24
48
72 96 Time (hrs)
120
144
168
Fig. 10. Flood discharge estimation at Kaoping bridge for four typhoon events.
12000 Bilis
10000
Toraji
Discharge (cms)
Nari Lekima
8000
6000
4000
2000
0
0
24
48
72
96 Time (hrs)
120
144
168
Fig. 11. Flood discharge estimation at Wanta bridge for four typhoon events.
bridge, and 7307 cms and 54 h for Wanta bridge, respectively. For a multi-peak type of typhoon like Lekima, the peak results are 6089 cms at 86 h for the former place and 6071 cm at 85 h for the latter place. According to the hydraulic division report of the government, the highest historical record of peak discharge at Kaoping bridge is 18,100 cms, and the highest value is
19,700 cms for the entire Kaoping river basin. These historical records with the estimated results are less than 24,200 cms of the flood designed value, so that no damages are reported at both places for the four different types of typhoon studied herein. However, because of some manmade reasons such as unauthorized excavation of river aggregates or unauthorized construction in the river bank,
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which may decrease the strength of bridge foundations and may affect the natural balance of the river, so that precautions should be taken for these problems and they should check from time to time to avoid unwanted damage. It is noted that in each typhoon incident, the rainfall is not distributed uniformly in the river basin. And from the characteristics of the Kaoping river basin, the experiences showed that the discharges at downstream station in general have about 3 h delay of discharges at upstream station. Therefore in the present study, it can be found that the discharges of a 3 h ahead time and a present time is used in the input layer, but there exists only one estimation in the output layer at the same present time. This model arrangement seems inhomogeneous from mathematical standpoint and which is not a forecast from the sense of time step. However, this study is aimed at the prediction of flood discharge at a river downstream location which has incomplete or no measurement. The obtained results may still be considered as a forecast problem from spatial coordinate relationship. In addition, the drawback of using neural networks is that the so-called ‘‘black box’’ operation in the developed model, which may lack a series of logical explanation. Furthermore, the actual effect of physiographical factors is hard to analyze as they may have been resulted in the measured flood discharge at a station. Thus, many computational experiments are required for various input parameters in the neural network model to find out a way for better performance in estimation. Anyway, the neural network method is useful as long as the estimated result is within an acceptable range from practical point of view. 5. Summary and conclusion In accordance with information at stations upstream of the Kaoping river, the back-propagation neural network models have been developed in this study to estimate flood discharge at stations downstream of the river, which lacks measurement. In the computational models, three factors were included in the structure of the input layer. The first one was discharge factor, which might describe the condition of channel storage and represents the hydrograph of flood discharge; the second one was water stage factor, which might describe the river sectional elevation; and the third one was physiographical factor, which might describe the shape and feature of the river basin. As a result, the estimated discharge in the output layer was expected to fit in the actual hydrologic spatial system. The developed models with different input parameters have been trained to check the sensitivity of physiographical factors. Basically, the factors of discharge and water stage did dominate the accuracy of flood discharge estimation. The physiographical factors had a slight and positive influence on the accuracy of prediction. But in fact these factors might have been resulted in the measured flood discharge at a station, thus these factors could be neglected from the practical point of view.
The performance of neural network models have been evaluated from the indices including root mean square error, coefficient of efficiency, error of peak discharge, and error of time to peak. The verification results showed that the neural network models have a relatively better capability of estimating flood discharge than the conventional Muskingum method. The neural network model with time series of flood discharge, river stage, and sufficient physiographical factors could obtain the highest accuracy in estimation, but this model might require more computational time as more parameters were inputted in the calculation process. On 2 July 2004, typhoon Mindulle attacked Taiwan and brought very large amounts of rain in a short period of time, which have caused tremendous property losses and road system damages in both the central and southern parts of the island. The Kaoping river basin also suffered from a huge flood. More than 50% of bridges were shut down in this area during the high peak flood level. The problem of flood control was brought a new attention, and many of engineering projects were proposed to rebuild or to repair the flood damages. The obtained results of flood discharge at the Kaoping river by the present developed neural network model might provide useful references for further hydraulic engineering designs in this region. Acknowledgements The authors wish to thank Mr. Liam Briggs, a Canadian who teaches at Schoolhouse Language Center of Taiwan, for correcting the usage of English through out this paper. References [1] Hsu YL. Applied hydrology. Taiwan: Great China Book Company; 1995. [2] Wang RY, Yee Z. Applied hydrology (I) and (II). Taiwan: National Publishing Corporation; 1999. [3] Adeli H. Neural network in civil engineering: 1989–2000. ComputAided Civ Infrastruct Eng 2001;16:126–42. [4] Baratti R, Cannas B, Fanni A, Pintus M, Sechi GM, Toreno N. River flow forecast for reservoir management through neural networks. Neurocomputing 2003;55:421–37. [5] Bodri L, Cermik V. Prediction of extreme precipitation using a neural network: application to summer flood occurrence in Moravia. Adv Eng Software 2000;31:311–21. [6] Chang FJ, Chen YC. A counter propagation fuzzy-neural network modeling approach to real-time streamflow prediction. J Hydrol 2001;245:153–64. [7] Flood I, Kartam N. Neural networks in civil engineering I: principles and understanding. J Comput Civ Eng, ASCE 1994;8(2):131–48. [8] Flood I, Kartam N. Neural networks in civil engineering II: systems and applications. J Comput Civ Eng, ASCE 1994;8(2):149–62. [9] Imrie CE, Durucan S, Korre A. River flow prediction using artificial neural networks: generalization beyond the calibration range. J Hydrol 2000;233:138–53. [10] Kim G, Barros AP. Quantitative flood forecasting using multisensor data and neural networks. J Hydrol 2001;246:45–62. [11] Liong SY, Lim WH, Paudyal GN. River stage forecasting in Bangladesh: neural network approach. J Comput Civil Eng, ASCE 2000;14(1):1–8.
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Neural networks forecasting of flood discharge at an unmeasured station using river upstream information Tienfuan Kerh *, C.S. Lee Department of Civil Engineering, National Pingtung University of Science and Technology, 1 Hseuh Fu Road, Pingtung 91207, Taiwan Received 7 October 2004; accepted 19 November 2005 Available online 7 February 2006
Abstract Based upon information at stations upstream of a river, a back-propagation neural network model was employed in this study to forecast flood discharge at station downstream of the river which lacks measurement. The performance of the neural network model was evaluated from the indices of root mean square error, coefficient of efficiency, error of peak discharge, and error of time to peak. The verification results showed that the neural network model is preferable, which performs relatively better than that of the conventional Muskingum method. Furthermore, the developed model with different input parameters was trained to check the sensitivity of physiographical factors. The results exhibited that flood discharge and water stage, are two factors to dominate the accuracy of estimation. Meanwhile, the physiographical factors had a slight and positive influence on the accuracy of the prediction. The time varied flood discharge forecasting at an unmeasured station might provide a valuable reference for designing an engineering project in the vicinity of the investigation region. 2005 Elsevier Ltd. All rights reserved. Keywords: Flood discharge estimation; Unmeasured station; Neural network model; Evaluation index; Physiographical factor
1. Introduction In the field of civil and hydraulic engineering, the information of a river flood discharge is related to flood control, and may be used to evaluate the performance of water resource planning and management. Therefore, how to accurately analyze the flood discharge based on measuring records at a specified flow domain becomes a crucial issue either from academic or practical standpoints. Typhoons generated in the usual fashion, affect flood discharge by several time and space factors. This may cause a difficulty in describing this hydrological phenomenon with the use of conventional statistical models. In general, the deterministic method and the stochastic method are frequently used to develop a model for estimating the flood discharge [1,2]. However, the former method assumes the occurrence obeys certain physical properties, and simulates the complicated *
Corresponding author. Tel.: +886 933 325188; fax: +886 877 40122. E-mail address: [email protected] (T. Kerh).
0965-9978/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2005.11.002
hydrological process to as a simplified model. This may not correctly reflect the actual conditions of flow domain, and thus may reduce the accuracy of flood discharge estimations. The latter method takes a time series of statistical data as the basis, and then a flood discharge estimation model is developed according to the principle of random probability. This may require a very complicated calculation procedure, and may become a tedious task if the data information is not well recorded. The approach of neural network has the advantages of using field recorded data directly without simplification and is not like regression analysis, which needs to make an assumption of equation in advance. Furthermore, this method is capable of executing parallel computations, and can simulate a nonlinear system which is hard to describe by traditional physical modeling. This has allowed for a wide range of applications in civil and hydraulic engineering to be extensively published in recent years [3–14]. Among these research reports, the issues related to flood discharge were mainly focused on the prediction of flood
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stage or discharge at a specified river station or section based on previously recorded time series data structures. The results were effectively estimated by neural network models, but there are only very few papers that dealt with flood discharge estimation, including a location which has an important engineering concern, but lacks measurement due to insufficient measuring time periods or device installation difficulties. Hence, this relative topic is still open and the neural network model may be applied to solve the problem of interest in a particular river flow domain. Located in southern part of Taiwan, the main Kaoping river basin consists of several branches, three major branches, Yailiao river (R1), Laonumg river (R2) and Chisan river (R3) are considered (see Fig. 1). This main river has the total length of 176.6 km, the area in flow domain of 3257 km2, and that is the largest in the whole island of Taiwan [15,16]. To evaluate the variation of flood discharge at an important place downstream of this river, which has incomplete or no measurement. A back-propagation neural network model has been developed at the
present to perform the task. At first, by collecting time historical records of flood discharge, water stage and physiographical factor at three measuring stations, Sanlin bridge (B2), Shinfa bridge (B3) and Sandimen (B4) in each river branch, upstream of the main river as the input data sets. Also, by taking the measuring station, Lilin bridge (B1), at merging place of the above mentioned three branches and downstream of the main river, as the verification target output. Then, four cases of flood records caused by typhoons are used for training basis, another four cases of typhoon records are taken to verify the estimations of the neural network model, and make comparisons with the calculation results of the conventional Muskingum method. Finally, two important locations, Kaoping bridge (B5) and Wanta bridge (B6), downstream of the river, lack measurement and have different physiographical factors, chosen to estimate the variation of flood discharge in accordance with the developed neural network model. The estimated results may provide a valuable reference for designing an engineering project, and may increase
Fig. 1. Sketch of the research area at Kaoping river basin.
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the performance of water resource management in these regions. 2. Neural network model and evaluation criteria Basically, the neural networks can be classified into four types according to its learning law, which are: (1) supervised learning nets, (2) unsupervised learning nets, (3) associate learning nets, and (4) optimization application nets. Among these nets, the back-propagation neural network is properly the most common used methods in solving various engineering problems [17–21]. The computational algorithm of this model has been well programmed in a couple of software packages. Thus in this study, the neural network toolbox MATLAB [22], is taken to develop the flood discharge estimating model for the sake of convenience. As the theoretical background of back-propagation neural network is simple and may be seen in many of relative references (e.g. [23–25]), the details are not included in this section, but some of the key points such as evaluation indices of accuracy are discussed properly. For estimating flood discharge varied with time in each typhoon case, two neural network models are considered here through numerical experiments. The first model ANN(A) as shown in Fig. 2, there exists 21 neurons in the input layer, 15 neurons in the hidden layer and 1 neuron in the output layer (I21H15O1). The input parameters are important as they may have an influence on the accuracy of estimation (e.g. [26]). For this model, the inputs include four time steps (t-3, t-2, t-1, t) of discharge information at three upstream measuring stations, Sanlin bridge, Shinfa bridge and Sandimen, respectively. In addition, the studied river basin may be considered as an open
Input layer
535
physical system. Basically the physiographical factors to affect river discharge may include nine items. They are the basin area (A), length of the main stream (L), mean slope (S), mean width (W), form factor (F), perimeter (P), circularity ratio (R), compactness (C), and elongation (E) for three branches, the Yailiao river, the Laonumg river and the Chisan river [27,28]. Note that the output layer is the estimation of discharge of Lilin bridge at time step t. Since the water stage is strongly related to the discharge in a river, three time steps (t-2, t-1, t) of the river stage at the same measuring stations are included in the input layer of the second model ANN(B). With the same numbers of hidden layers and output layers as the first model, this model (I30H15O1) is further used to check the difference in neural network calculations. To evaluate the results of neural network training and estimations, the following are some of the commonly used indices for checking the accuracy of estimated flood discharge. The first one is root mean square error (RMSE), and its definition is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 n ðT n Y n Þ RMSE ¼ ð1Þ N where Tn denotes the actual observed value, Yn is the estimated value from neural network output, and N is the training number. The second index is the coefficient of efficiency (CE), and the definition is P 2 ðQ Qest Þ CE ¼ 1 P obs ð2Þ 2 ðQobs Qobs Þ where Qobs is the observed discharge value, Qobs is the averaged discharge of observation, and Qest is the neural
Hidden layer
Output layer
Shinfa Bridge Discharge records at t, t-1, t-2, t-3
Sanlin Bridge Discharge records at t, t-1, t-2, t-3 Lilin Bridge Estimating discharge at t Santimen Discharge records at t, t-1, t-2, t-3
Physiographical factors at each station region Fig. 2. Neural network model (I21H15O1) for flood discharge estimation.
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Herb, occurred on 03/08/1994, 08/06/1995, 25/07/1996, and 31/07/1996, respectively. With the input of physiographical data in these regions (Table 1), and the discharge recorded at downstream station (B1) is taken as the target output. Then, by using the Levenberg–Marquardt algorithm in the learning process, the convergent tendency of error in training for both models ANN(A) and ANN(B) is displayed in Fig. 3. For both models, a total of 100 times of calculation are included for each epoch, the curve shows that the learning error is converged after 600 epochs. The neural network training result shows that the performance of model ANN(A) is acceptable. The root mean square error is RMSE = 0.186, and the square of correlation coefficient is R2 = 0.912 for this model. In other words, the neural network estimation is in reasonable agreement with observation. Now by adding observed river stage information at upstream stations in the input layer, the neural network model ANN(B) exhibits better performance than that of the model ANN(A), as the root mean square error becomes RMSE = 0.017, and the square of correlation coefficient becomes R2 = 0.988 in this preferred model. Displayed in Figs. 4 and 5 are error distribution and the approaching tendency of estimation and observation for both models. These complete the training process of the neural network model, and the model will be applied to verify its capability in the next typhoon event. Now by taking the same weighting coefficients and bias terms in the developed neural network models, and by replacing flood discharges and river stages, caused from another four different types of typhoon in the input layer.
network estimated discharge. The more the CE value approaches one, the higher the consistency of the simulation result with actual information. The third index is the error of peak discharge (EQp), and the definition is EQp ¼
Qpest Qpobs 100% Qpobs
ð3Þ
where Qpobs is the observed peak flood discharge, and Qpest is the estimated peak flood discharge. If EQp > 0, it represents to us that the estimated result is larger than the observed result, while if EQp < 0, it means the estimated result is less than the observed result. The last index of error is time to peak (ETp), and the definition is ETp ¼ jT pest T pobs j
ð4Þ
where Tpobs is the observed arrival time of peak flood discharge, and Tpest is the estimated arrival time of peak flood discharge. The less of ETp value represents more accurately the estimated arrival time of peak flood discharge. 3. Neural network training and verification To fit in transfer functions and to treat data information in the neural network calculation, the normalization of input data may be required to reduce the effect of extreme values in parameters. Thus after data normalization, the discharges of a 3 h ahead time and the present time at the upstream stations (B2, B3 and B4) of the Kaoping river are used as the input in the training process. These data sets result from four typhoons, Caitlin, Deanna, Gloria, and Table 1 Physiographical factors for station at each branch river region River (station)
A (km2)
L (km)
S
W (km)
F
P (km)
R
C
E
Yailiao Laonumg Chisan
642 1373 802
68.5 137 117
0.0340 0.0402 0.0410
9.37 10.02 6.85
0.137 0.073 0.059
121 277 225
0.55 0.22 0.20
0.74 0.47 0.45
0.42 0.31 0.27
0.6 ANN(A)
0.5
ANN(B)
RMSE
0.4 0.3 0.2 0.1 0 0
100
200
300
400
500
600
Epochs Fig. 3. Convergent tendency of learning errors for both the neural network models.
700
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537
2000 Discharge difference (cms)
ANN(A)
1000
0
-1000
-2000 0
48
96
144
192
240
288 336 Time (hrs)
384
432
480
528
576
624
Discharge difference (cms)
2000 ANN(B)
1000
0
-1000
-2000 0
48
96
144
192
240
288 336 Time (hrs)
384
432
480
528
576
624
Fig. 4. Error distributions in neural network training for both models.
20000
20000 ANN(A) R 2 = 0.912
15000 ANN (cms)
ANN (cms)
15000
ANN(B) R 2 = 0.988
10000
5000
10000
5000
0 0
5000 10000 15000 Observation (cms)
20000
0 0
5000 10000 15000 Observation (cms)
20000
Fig. 5. Scatter plots of estimation versus observation for both models.
The estimations are compared with the results of conventional Muskingum method and measuring records for typhoon, Bilis, Toraji, Nari, and Lekima, occurred on 22/08/2000, 30/07/2001, 17/09/2001, and 26/09/2001, and are shown in Figs. 6–9, respectively. Additionally, the comparison result of evaluation indices for four typhoon types are shown in Table 2. The obtained plots and data may clearly reflect the performance of estimation models in this type of problem.
For the ANN(A) model, excluding the simulation in uprising section of discharge has significantly underestimated the results of the Bilis and Lekima typhoons. The errors are small for the other two cases. All four cases have good performance in the coefficient of efficiency, which ranges from 0.919 to 0.973. The estimated results of peak flood discharge for typhoons Bilis and Toraji are smaller than the observations, and the differences are 0.6% and 1.7%. But for multi-peak type of typhoons such as Nari
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12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
72
48
96 Time (hrs)
120
144
168
192
Fig. 6. Estimation compared with observation at Lilin bridge for typhoon Bilis.
12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 7. Estimation compared with observation at Lilin bridge for typhoon Toraji.
and Lekima, the estimated peak flood discharges are larger than the observations, and the differences are 4.6% and 2.6%. Excluding that the case of typhoon Nari which has a 2 h difference in error of time to peak, there are no differences for the other cases. For the ANN(B) model, only very small errors are found in the uprising section of discharge, and the coefficients of efficiency have values that range from 0.967 to 0.989. Those are close to the value of one for all typhoons. The estimated peak flood discharges are smaller than the observations, and the difference is ranged from 2.1% to 0.75%. There are no differences in error of time to peak for all cases except typhoon Bilis which has a 2 h difference.
For the conventional Muskingum method, the continuity equation may be used to deal with the relationship between water storage (S), flood inlet discharge (I), and flood outlet discharge (O). The basic equation is as follows: S ¼ K½xI þ ðI xÞO
ð5Þ
where K is the time of propagation, and x is the weighted parameter. The accuracy of this conventional method is strongly dependent upon the length of historical data and the choice of weighting factors. In this study, the averaged coefficients of the storage time and the weighting factor are in accordance with previous research report in this region [16]. The coefficients of storage time are 3.13, 3.49, 3.58, and 4.53; and the weighting factors are 0.493, 0.493,
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539
12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 8. Estimation compared with observation at Lilin bridge for typhoon Nari.
12000 ANN(A) ANN(B) Muskingum Observation
Discharge (cms)
10000
8000
6000
4000
2000
0 0
24
48
72 Time (hrs)
96
120
144
Fig. 9. Estimation compared with observation at Lilin bridge for typhoon Lekima.
0.495, and 0.500, for typhoons Bilis, Tozaji, Nari, and Lekima, respectively. It can be found that the estimated flood discharge for each typhoon case by this conventional approach has a significant underestimations and errors. The coefficient of efficiency for typhoon Tozaji is only 0.630, is the best among the other typhoons. The estimated peak flood discharge has a very large error, which is up to 51.92% for typhoon Nari. For the error of time to peak, the best case is typhoon Bilis, which has a 2 h difference, while the worst case is typhoon Toraji, which has a 6 h difference. Above all, it can be found that the neural network model ANN(B) has the best ability for estimating flood discharge in four typhoons. This model can obtain a more accurate prediction than that of neural network model ANN(A), but this model requires more input items and
that may require more time in computation. The use of the Muskingum method is case independent, and the accuracy of calculation may rely on regional characteristics of the river basin. That is, this method may be good in estimation for one river case, but it may not have to be the same level of accuracy for the other one river case. In the present Kaoping river case, this conventional method performs a poor estimation as the result is not very consistent with the observation. Although it is possible to improve the accuracy of estimation by trying some other sets of coefficients for this method, it may require tedious work, which is not a good choice from an economical point of view. Note that many parameters are considered in the input layer of neural network models, which may increase the complexity in calculation process. Also because the previous records of flood discharge and river stage are two
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Table 2 Evaluation indices for flood discharge estimation using different models
Table 4 Square values of correlation coefficient and root mean square errors
Model
Typhoon
Index
Model
R2
RMSE
ANN(A)
Bilis Toraji Nari Lekima
0.966 0.953 0.973 0.919
0.6 1.7 2.6 4.6
0 2 0 0
ANN(B)
Bilis Toraji Nari Lekima
0.974 0.989 0.986 0.967
0.32 2.1 0.75 0.56
2 0 0 0
ANN(A) ANN(B) ANN(1) ANN(2) ANN(3) ANN(4) ANN(5)
0.912 0.988 0.921 0.926 0.963 0.970 0.954
0.186 0.017 0.150 0.139 0.034 0.022 0.054
Muskingum
Bilis Toraji Nari Lekima
0.565 0.630 0.523 0.499
28.98 44.89 51.92 30.73
2 6 5 3
CE
EQp (%)
ETp (h)
primary consideration factors, which may not be neglected in the discharge estimation. So in this study, it is worthy to check the sensitivity of hydrological factors in the present neural network models. Originally, nine physiographical factors are taken in the input layer, but some of them are related to each other and may be divided into two groups. Group (A) includes five physical parameters, which are basin area, main stream length, mean slope, mean width, and perimeter. Group (B) contains four shape parameters of river flow domain, which are form factor, circularity ratio, compactness, and elongation. Shown in Table 3 are the modifications of input parameters for different neural network models, where the neurons in the input layer, the hidden layer, and the output layer are I17H15O1, I16H15O1, I26H15O1, I25H15O1, and I21H15O1 for the model from ANN(1) to ANN(5), respectively. Shown in Table 4 is the comparison result of neural network calculations, it can be seen that discharge and water stage do dominate the accuracy of flood discharge estimation. The physiographical factors in either group have a slight influence on the prediction accuracy, but both of the two groups do have a positive contribution in the neural network estimations. Therefore, to obtain the highest accuracy possible, the neural network model ANN(B) is a relatively good option for further flood discharge estimation at stations with insufficient data or without records.
4. Flood discharge forecasting at unmeasured station Downstream of the Kaoping river, the Kaoping bridge and the Wanta bridge, are two important connection places for many agricultural and import/export developments in this region. Even at the present time, there exists a new bridge under construction in the neighborhood of Kaoping bridge. The original measurement device for flood discharge and river stage has been removed, and the recorded data such as peak flood discharge and time to peak, are no longer sufficient to provide the needs for various hydraulic engineering designs in this area. Now by taking physiographical information (Table 5) at the above mentioned places as the input in the neural network model ANN(B), with historical discharge and water stage inputs, the simulation results for four typhoon events show that there is no too much difference in peak discharge, about an hour more or less slight difference in peak arrival time for Kaoping and Wanta bridges as shown in Figs. 10 and 11. These plots also present the hydrograph of each case which is similar for both places, due to the fact that the distance between these two bridge is not too far (about 4.5 km), and the physiographical factors are similar at this region downstream. For a type of short time to peak typhoon like Bilis, the estimated peak discharge at Kaoping bridge is 5809 cms, and the peak arrival time is 12 h. At Wanta bridge, the peak values are 5963 cms and 13 h. For typhoon Toraji, a high peak discharge type, the estimated peak discharge at Kaoping bridge is 10,624 cms, and the peak arrival time is 33 h. At Wanta bridge, the peak values are 10,745 cms and 33 h. For typhoon Nari, the estimated peak discharge and time to peak are 7181 cms and 54 h for Kaoping
Table 3 Input parameters for different neural network models Model
Input Discharge
ANN(A) ANN(B) ANN(1) ANN(2) ANN(3) ANN(4) ANN(5)
• • • • • • •
Water stage
Physiographical factors (A)
Physiographical factors (B)
•
• • •
• • •
• • •
• •
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541
Table 5 Physiographical factors for unmeasured station at the main river region River (station)
A (km2)
L (km)
S
W (km)
F
P (km)
R
C
E
Kaoping Wanta
3075.5 3110.7
165.3 169.8
0.0067 0.0067
1.786 1.721
0.113 0.100
334.3 357.7
0.35 0.31
0.587 0.552
0.37 0.35
12000 Bilis Toraji
10000
Nari
Discharge (cms)
Lekima
8000
6000
4000
2000
0 0
24
48
72 96 Time (hrs)
120
144
168
Fig. 10. Flood discharge estimation at Kaoping bridge for four typhoon events.
12000 Bilis
10000
Toraji
Discharge (cms)
Nari Lekima
8000
6000
4000
2000
0
0
24
48
72
96 Time (hrs)
120
144
168
Fig. 11. Flood discharge estimation at Wanta bridge for four typhoon events.
bridge, and 7307 cms and 54 h for Wanta bridge, respectively. For a multi-peak type of typhoon like Lekima, the peak results are 6089 cms at 86 h for the former place and 6071 cm at 85 h for the latter place. According to the hydraulic division report of the government, the highest historical record of peak discharge at Kaoping bridge is 18,100 cms, and the highest value is
19,700 cms for the entire Kaoping river basin. These historical records with the estimated results are less than 24,200 cms of the flood designed value, so that no damages are reported at both places for the four different types of typhoon studied herein. However, because of some manmade reasons such as unauthorized excavation of river aggregates or unauthorized construction in the river bank,
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which may decrease the strength of bridge foundations and may affect the natural balance of the river, so that precautions should be taken for these problems and they should check from time to time to avoid unwanted damage. It is noted that in each typhoon incident, the rainfall is not distributed uniformly in the river basin. And from the characteristics of the Kaoping river basin, the experiences showed that the discharges at downstream station in general have about 3 h delay of discharges at upstream station. Therefore in the present study, it can be found that the discharges of a 3 h ahead time and a present time is used in the input layer, but there exists only one estimation in the output layer at the same present time. This model arrangement seems inhomogeneous from mathematical standpoint and which is not a forecast from the sense of time step. However, this study is aimed at the prediction of flood discharge at a river downstream location which has incomplete or no measurement. The obtained results may still be considered as a forecast problem from spatial coordinate relationship. In addition, the drawback of using neural networks is that the so-called ‘‘black box’’ operation in the developed model, which may lack a series of logical explanation. Furthermore, the actual effect of physiographical factors is hard to analyze as they may have been resulted in the measured flood discharge at a station. Thus, many computational experiments are required for various input parameters in the neural network model to find out a way for better performance in estimation. Anyway, the neural network method is useful as long as the estimated result is within an acceptable range from practical point of view. 5. Summary and conclusion In accordance with information at stations upstream of the Kaoping river, the back-propagation neural network models have been developed in this study to estimate flood discharge at stations downstream of the river, which lacks measurement. In the computational models, three factors were included in the structure of the input layer. The first one was discharge factor, which might describe the condition of channel storage and represents the hydrograph of flood discharge; the second one was water stage factor, which might describe the river sectional elevation; and the third one was physiographical factor, which might describe the shape and feature of the river basin. As a result, the estimated discharge in the output layer was expected to fit in the actual hydrologic spatial system. The developed models with different input parameters have been trained to check the sensitivity of physiographical factors. Basically, the factors of discharge and water stage did dominate the accuracy of flood discharge estimation. The physiographical factors had a slight and positive influence on the accuracy of prediction. But in fact these factors might have been resulted in the measured flood discharge at a station, thus these factors could be neglected from the practical point of view.
The performance of neural network models have been evaluated from the indices including root mean square error, coefficient of efficiency, error of peak discharge, and error of time to peak. The verification results showed that the neural network models have a relatively better capability of estimating flood discharge than the conventional Muskingum method. The neural network model with time series of flood discharge, river stage, and sufficient physiographical factors could obtain the highest accuracy in estimation, but this model might require more computational time as more parameters were inputted in the calculation process. On 2 July 2004, typhoon Mindulle attacked Taiwan and brought very large amounts of rain in a short period of time, which have caused tremendous property losses and road system damages in both the central and southern parts of the island. The Kaoping river basin also suffered from a huge flood. More than 50% of bridges were shut down in this area during the high peak flood level. The problem of flood control was brought a new attention, and many of engineering projects were proposed to rebuild or to repair the flood damages. The obtained results of flood discharge at the Kaoping river by the present developed neural network model might provide useful references for further hydraulic engineering designs in this region. Acknowledgements The authors wish to thank Mr. Liam Briggs, a Canadian who teaches at Schoolhouse Language Center of Taiwan, for correcting the usage of English through out this paper. References [1] Hsu YL. Applied hydrology. Taiwan: Great China Book Company; 1995. [2] Wang RY, Yee Z. Applied hydrology (I) and (II). Taiwan: National Publishing Corporation; 1999. [3] Adeli H. Neural network in civil engineering: 1989–2000. ComputAided Civ Infrastruct Eng 2001;16:126–42. [4] Baratti R, Cannas B, Fanni A, Pintus M, Sechi GM, Toreno N. River flow forecast for reservoir management through neural networks. Neurocomputing 2003;55:421–37. [5] Bodri L, Cermik V. Prediction of extreme precipitation using a neural network: application to summer flood occurrence in Moravia. Adv Eng Software 2000;31:311–21. [6] Chang FJ, Chen YC. A counter propagation fuzzy-neural network modeling approach to real-time streamflow prediction. J Hydrol 2001;245:153–64. [7] Flood I, Kartam N. Neural networks in civil engineering I: principles and understanding. J Comput Civ Eng, ASCE 1994;8(2):131–48. [8] Flood I, Kartam N. Neural networks in civil engineering II: systems and applications. J Comput Civ Eng, ASCE 1994;8(2):149–62. [9] Imrie CE, Durucan S, Korre A. River flow prediction using artificial neural networks: generalization beyond the calibration range. J Hydrol 2000;233:138–53. [10] Kim G, Barros AP. Quantitative flood forecasting using multisensor data and neural networks. J Hydrol 2001;246:45–62. [11] Liong SY, Lim WH, Paudyal GN. River stage forecasting in Bangladesh: neural network approach. J Comput Civil Eng, ASCE 2000;14(1):1–8.
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