2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012)

Flood Water Level Modelling and Prediction Using Artificial Neural Network : Case Study of Sungai Batu Pahat in Johor Ramli Adnan #1, Fazlina Ahmat Ruslan #2, Abd Manan Samad*3, Zainazlan Md Zain #4 #

*

Faculty of Electrical Engineering Center for Surveying Science and Geomatics, Faculty of Arc., Planning and Surveying Universiti Teknologi MARA 40450, Shah Alam, Selangor, Malaysia 1 [email protected] 2 [email protected]

Abstract— Flood water level prediction has long been the earliest forecasting problems that have attracted the interest of many researchers. Accurate prediction of flood water level is extremely importance as an early warning system to the public to inform them about the possible incoming flood disaster. Using the collected data at the upstream and downstream station of a river, this paper proposes a modelling of flood water level at downstream station using back propagation neural network (BPN). In order to improve the prediction values, an extended Kalman filter was introduced at the output of the BPN. The introduction of extended Kalman filter at the output of BPN shows significant improvement to the prediction and tracking performance of the actual flood water level.

applied back propagation neural network with typhoon characteristics and tide level as the input factors to develop a typhoon surge forecasting model. Lin and Wu [8] proposed rainfall prediction using hybrid ANN model where multilayer networks are employed to map the relationship between input and output. This paper proposes a modelling of flood water level at downstream station using back propagation neural network (BPN). In order to improve the prediction values, an extended Kalman filter was introduced at the output of the BPN. This paper was organized in the following manner: Section II describes the methodology; Section III is on results and discussion; and finally, Section IV is on conclusions.

Keywords — Back Propagation Neural Network, Flood Water Level Forecasting, Mean Squared Error, Correlation Coefficient, Error Goal

II.

A. Study Area and Data The case study was done to a Sungai Batu Pahat that located at Batu Pahat, Johor. A major contribution of water level at Sungai Batu Pahat basin comes from four upstream rivers as depicted in Figure 1. The upstream river level measuring station names are Station 1929401(Sg Simpang Kiri at Sri Medan), Station 2130422 (Sg Bekok Bt 77 Jln Yong Peng), Station 1831480 (Sg Sembrong at Parit Karjo) and Station 2030402 (Sg Bekok at Yong Peng). The water level measuring station for Sungai Batu Pahat is Station 1829478 (Sg Batu Pahat at Batu Pahat). The water level data is in meters, starting from May 2, 2012 until May 8, 2012. This real-time data is available online from website www.water.gov.my. The water level data is measured using Supervisory Control and Data Acquisition System (SCADA) by Department of Irrigation and Drainage Malaysia.

I. INTRODUCTION Flood water level prediction has long been the earliest forecasting problems that have attracted the interest of many researchers [1]. Accurate prediction of flood water level is extremely important as an early warning system to the public to inform them about the possible incoming flood disaster. Flood water levels at downstream areas are strongly affected by upstream conditions [2]. The artificial neural network (ANN) is capable of articulate the underlying relationship between downstream and upstream conditions because of its ability to represent a complex nonlinear system without any priori knowledge of the physical systems itself [3]. McCulloch and Pitts [4] introduced ANN as a representative of the synaptic processes in brain. ANN became popular in the early 1980s with the advent of microprocessors and by late 1990s ANN starts to be used in hydrological modelling. Recently, ANN has been widely applied in various areas to overcome the problem of nonlinear relationship in geographical system. For example, ANN is able to predict all India summer monsoon rainfall with varieties of model inputs [5]. Tsung-Lin Lee [6] successfully forecast the storm surge and surge deviation in coastal areas using back propagation neural network approach. Lee [7]

978-1-4673-2036-8/12/$31.00 ©2012 IEEE

METHODOLOGY

22

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012)

levels are expected to be a good downstream river levels predictor in the same river system [12]. Singh et al. [13] reported that the data sets range from 0.1-0.9 or 0.2-0.8 can improve generalization of ANN architecture. Figure 3 illustrates the basic structure of BPN water level prediction model of this study. The input variable of this model is water level at the upstream river whereas the output variable is the peak water level at the downstream river, Sungai Batu Pahat. The number of neuron in hidden layer is only representative and not the actual number in the model. Input Layer

Hidden Layer

Output Layer

Station 1929401 Station 2130422

Figure 1. The location of Sungai Batu Pahat basin and its upstream river (http://telemetryjohor.com/Pages/StationStatus.aspx)

Station 1829478

B. Artificial Neural Network ANN is a mathematical system that emulates the ability of connecting simple neurons and represents it in a biological neural network. In general, ANN contains input layers, hidden layers and output layers. This is illustrated in Figure 2. Input layers receive input signals and then passed to each hidden layer. Hidden layer then represent relationship between input and output layer and finally output layer releases the output signals.

Station 1831480

Station 2030402

Figure 3. BPN model for flood water level modelling

C. Extended Kalman Filter (EKF) The EKF algorithm has two main stages: prediction step; and update (filtering) step. In prediction steps, previous state estimate of the system is being used and in the update step, the predicted state is corrected by using feedback correction step. The feedback correction step contains the weight of the measured and estimated output signals. In EKF, by calculating the stochastic properties of the noise, the initial values of the matrices can be arranged correctly. Furthermore, a critical part of EKF is to apply correct initial values for various covariance matrices. Covariance matrices have an important effects on converge time and filter stability. The summary of EKF algorithm is given in Figure 4.

Figure 2. Structure of artificial neural network

The back propagation neural network (BPN) is the most popular supervised model of artificial neural networks which is developed by Rumelhart et al. [9]. BPN repeatedly adjust the parameters (weights and biases) to minimize the error between target output and estimated output according to “generalized delta rule”. The parameter modification stops when the performance error goal is met [10]. The crucial factor that leads to the success of ANN model is the selection of appropriate inputs. Too many inputs that are redundant will contribute to the problem of local minima [11]. By understanding the physical system to be model, the good choice of input can be guided. For example, upstream river

23

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012)

According to 10, 0000 cycles of training, the error goal is set at 1.00e-05. The training algorithm used is traincgp, conjugate gradient with Polak Ribiere updates. The verification results are given in Figure 5. The BPN verification result shows that the model cannot be considered good because there is slight difference in the simulated and actual water level results. Furthermore, overshoot occurs at the end of the graph. This is maybe because that the training is stop after the minimum step size is reached. However the value of mean squared error (MSE) is 8.89e-05 which is still close to the error goal that is 1.00e-05, so the result is still acceptable.

Time Update (“Predict”) (1) Project the state ahead

xˆ − k = f (xˆ k −1,uk −1, 0)

(2) Project the error covariance ahead

P − k = Ak Pk −1 AT k + Wk Qk −1W T k

Measurement Update (“Correct”) (1) Compute the Kalman Gain

(

)

1.5

zk

1.4

−1

K k = P − k H T k H k P − k H T k + Vk RkV T k (2) Update estimate with measurement

(

(

xˆk = xˆ − k + K k z k − h xˆ − k , 0

))

BPN estimates versus actual value

1.3

Pk = (I − K k H k )P

water level(meter)

(3) Update the error covariance −

k

Figure 4. Extended Kalman Filter (EKF) Loop

Figure 4 summarizes the overall operation of EKF algorithm. The prediction stage starts by projecting the state and error covariance ahead using the present value of Jacobian matrix and prior value of error covariance. Then, based on the projected error covariance value, the Kalman gain is calculated and measurement xˆ k is estimated. Finally, the

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5

0

2

4

6

8

10

12

hours Figure 5. The verification results of the flood water level

error covariance value is updated. The loop will continue until the desired error covariance value is achieved. III.

simulated water level actual water level

In order to improve the prediction results, an Extended Kalman Filter (EKF) is introduced at the output of BPN. EKF is the most commonly used nonlinear Bayesian estimator which is able to filter and track the nonlinear output based on assumptions that are: perturbations from the mean trajectory are small; and the conditional density function of the state is Gaussian [15]. Figure 6 shows the results after the EKF being applied. From the graph, it is clearly shown that the results are improved as the overshoot is reduced and the pattern of the simulated and actual water level between 0— 6 hours is nearly the same as compared to Figure 5.

RESULTS AND DISCUSSION

The water levels at the upstream and downstream rivers station at Sungai Batu Pahat is applied in the BPN model. Station 1929401, 2130422, 1821480 and 2030402 acts as a feeder to the BPN model because it is located at upstream location whereas Station 1829478 is the output of the model because it is the target station. The nodes of both input and output layers are set as 1.The number of nodes for hidden layer were set to be 15, in following the law of Kolmogorov [14]. Kolmogorov’s law state that the number of nodes in the hidden layer is at least 2n+1, where n is the number of nodes in the input layer. Thus, the topology structure of BPN flood modelling and forecasting in this study is (1,15,1). In order to accelerate the convergence, it is necessary to normalize the original data, but need to remember to denormalize it back to obtain the desired data. After the normalization process, the training parameters used were learning rate η at 0.55 and momentum constant α is fixed at 1. Learning rate and momentum constant is used to accelerate convergence of ANN training process and the value of η and α is selected in the range of 0 and 1.

24

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012) [5]

BPN estimates(with EKF)versus actual value 1.5 simulated water level with EKF actual water level

1.4

[6]

water level(meter)

1.3 1.2

[7]

1.1

[8]

1 0.9

[9]

0.8

[10]

0.7

[11]

0.6 0.5

0

2

4

6

8

10

[12]

12

hours [13] Figure 6. The verification results of the flood water level with EKF

IV.

CONCLUSIONS

[14]

Accurate prediction of flood water level is important as an early warning system to the public to inform them about the possible incoming flood disaster. This paper proposed ANN model to predict the flood water level. A supervised neural network with the back propagation model is adopted in this study. The performances of BPN model have been evaluated but yet the result is not that satisfactory. Hence, Extended Kalman Filter is proposed to improve the results. In conclusion, Extended Kalman Filter is able to provide better result compared with actual result without application of Extended Kalman Filter. The water level is only the parameter in this Back Propagation Neural Network model. So, for future works, more parameters can be added in the model such as rainfall and water flow so that more accurate and realistic prediction results can be achieved.

[15]

ACKNOWLEDGEMENT The authors would like to thanks and acknowledge the financial support from the Faculty of Electrical Engineering and Research Management Institute (RMI) under Excellence Fund No. 600-RMI-ST-DANA 5/3/Dst(33/2011), Universiti Teknologi MARA, Shah Alam. REFERENCES [1]

[2]

[3]

[4]

Amir F. Atita et al, “A comparison between neural network forecasting techniques – case study: river flow forecasting,” IEEE Transactions on Neural Networks, vol. 10, no.2, pp.402-409, 1999. Chang-Shian Chen et al, “Development and application of a decision group Back-Propagation Neural Network for flood forecasting,” ELSEVIER Journal of Hydrology, vol. 385, pp. 173-182, 2010. Paul Leahy, Ger Kiely & Gearoid Corcoran, “Structural optimisation and input selection of an artificial neural network for river level prediction,” ELSEVIER Journal of Hydrology, vol. 355, pp. 192-201, 2008. McCulloch, W., Ps, W.H., “A logical calculus of the ideas immanent in nervous activity,” Bull. Math. Biophys. 5, pp. 115-133, 1943.

25

Venkatesan et al, “Prediction of all India summer monsoon rainfall using error back propagation neural networks,” Meteorology and Atmospheric Physics, vol. 62(3-4), pp.225-240, 1997. Tsung-Lin Lee, “Predictions of tyhphoon storm surge in Taiwan using artificial neural networks,” ELSEVIER Advances in Engineering Software, vol. 40, pp.1200-1206, 2009. Lee, T.L, “Neural network prediction of a storm surge,” Ocean Engineering, vol.33, pp.483-494, 2006. Lin, G.F., Wu. M.C., “A hybrid neural network model for typhoon rainfall forecasting ,” Journal of Hydrology, vol. 375(3-4), pp.450-458, 2009. Rumelhart et al., “Learning representations by back propagating errors,” Nature, 323:533-6, 1986. Hsiao, T.R., Lin, C.W., Chiang,H.K., “Partial least-squares algorithm for weights initialization of back propagation network,” Neurocomputing, vol. 50, pp. 237-247, 2003. Govindaraju, R., “Artificial neural networks in hydrology : preliminary concepts,” Journal of Hydrology, vol. 5(2), pp. 115-123, 2000. Govindaraju, R., “Artificial neural networks in hydrology : hydrologic applications,” Journal of Hydrology, vol. 5(2), pp. 124-137, 2000. Singh et al, “Appropriate data normalization range for daily river flow forecasting using an artificial neural networks,” Hydroinformatics in Hydrology, Hydrogeology and Water Resources. International Association of Hydrological Sciences Publication, Uk, pp. 51-57, 2009. Wabgaonkar,H., Stubberud,A., “The Kolmogorov superposition theorem and functional approximation in neural networks,” 24th Asilomar Conference on Signals, Systems and Computers, vol. 2, 1990. Jangho Yoon, Yunjun Xu & Prakash Vedula, “A direct quadrature based nonlinear filtering with Extended Kalman Filter update for orbit determination,” 2010 American Control Conference Marriot Waterfront, Baltimore, MD, USA, June 30-July 02, 2010.

Flood Water Level Modelling and Prediction Using Artificial Neural Network : Case Study of Sungai Batu Pahat in Johor Ramli Adnan #1, Fazlina Ahmat Ruslan #2, Abd Manan Samad*3, Zainazlan Md Zain #4 #

*

Faculty of Electrical Engineering Center for Surveying Science and Geomatics, Faculty of Arc., Planning and Surveying Universiti Teknologi MARA 40450, Shah Alam, Selangor, Malaysia 1 [email protected] 2 [email protected]

Abstract— Flood water level prediction has long been the earliest forecasting problems that have attracted the interest of many researchers. Accurate prediction of flood water level is extremely importance as an early warning system to the public to inform them about the possible incoming flood disaster. Using the collected data at the upstream and downstream station of a river, this paper proposes a modelling of flood water level at downstream station using back propagation neural network (BPN). In order to improve the prediction values, an extended Kalman filter was introduced at the output of the BPN. The introduction of extended Kalman filter at the output of BPN shows significant improvement to the prediction and tracking performance of the actual flood water level.

applied back propagation neural network with typhoon characteristics and tide level as the input factors to develop a typhoon surge forecasting model. Lin and Wu [8] proposed rainfall prediction using hybrid ANN model where multilayer networks are employed to map the relationship between input and output. This paper proposes a modelling of flood water level at downstream station using back propagation neural network (BPN). In order to improve the prediction values, an extended Kalman filter was introduced at the output of the BPN. This paper was organized in the following manner: Section II describes the methodology; Section III is on results and discussion; and finally, Section IV is on conclusions.

Keywords — Back Propagation Neural Network, Flood Water Level Forecasting, Mean Squared Error, Correlation Coefficient, Error Goal

II.

A. Study Area and Data The case study was done to a Sungai Batu Pahat that located at Batu Pahat, Johor. A major contribution of water level at Sungai Batu Pahat basin comes from four upstream rivers as depicted in Figure 1. The upstream river level measuring station names are Station 1929401(Sg Simpang Kiri at Sri Medan), Station 2130422 (Sg Bekok Bt 77 Jln Yong Peng), Station 1831480 (Sg Sembrong at Parit Karjo) and Station 2030402 (Sg Bekok at Yong Peng). The water level measuring station for Sungai Batu Pahat is Station 1829478 (Sg Batu Pahat at Batu Pahat). The water level data is in meters, starting from May 2, 2012 until May 8, 2012. This real-time data is available online from website www.water.gov.my. The water level data is measured using Supervisory Control and Data Acquisition System (SCADA) by Department of Irrigation and Drainage Malaysia.

I. INTRODUCTION Flood water level prediction has long been the earliest forecasting problems that have attracted the interest of many researchers [1]. Accurate prediction of flood water level is extremely important as an early warning system to the public to inform them about the possible incoming flood disaster. Flood water levels at downstream areas are strongly affected by upstream conditions [2]. The artificial neural network (ANN) is capable of articulate the underlying relationship between downstream and upstream conditions because of its ability to represent a complex nonlinear system without any priori knowledge of the physical systems itself [3]. McCulloch and Pitts [4] introduced ANN as a representative of the synaptic processes in brain. ANN became popular in the early 1980s with the advent of microprocessors and by late 1990s ANN starts to be used in hydrological modelling. Recently, ANN has been widely applied in various areas to overcome the problem of nonlinear relationship in geographical system. For example, ANN is able to predict all India summer monsoon rainfall with varieties of model inputs [5]. Tsung-Lin Lee [6] successfully forecast the storm surge and surge deviation in coastal areas using back propagation neural network approach. Lee [7]

978-1-4673-2036-8/12/$31.00 ©2012 IEEE

METHODOLOGY

22

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012)

levels are expected to be a good downstream river levels predictor in the same river system [12]. Singh et al. [13] reported that the data sets range from 0.1-0.9 or 0.2-0.8 can improve generalization of ANN architecture. Figure 3 illustrates the basic structure of BPN water level prediction model of this study. The input variable of this model is water level at the upstream river whereas the output variable is the peak water level at the downstream river, Sungai Batu Pahat. The number of neuron in hidden layer is only representative and not the actual number in the model. Input Layer

Hidden Layer

Output Layer

Station 1929401 Station 2130422

Figure 1. The location of Sungai Batu Pahat basin and its upstream river (http://telemetryjohor.com/Pages/StationStatus.aspx)

Station 1829478

B. Artificial Neural Network ANN is a mathematical system that emulates the ability of connecting simple neurons and represents it in a biological neural network. In general, ANN contains input layers, hidden layers and output layers. This is illustrated in Figure 2. Input layers receive input signals and then passed to each hidden layer. Hidden layer then represent relationship between input and output layer and finally output layer releases the output signals.

Station 1831480

Station 2030402

Figure 3. BPN model for flood water level modelling

C. Extended Kalman Filter (EKF) The EKF algorithm has two main stages: prediction step; and update (filtering) step. In prediction steps, previous state estimate of the system is being used and in the update step, the predicted state is corrected by using feedback correction step. The feedback correction step contains the weight of the measured and estimated output signals. In EKF, by calculating the stochastic properties of the noise, the initial values of the matrices can be arranged correctly. Furthermore, a critical part of EKF is to apply correct initial values for various covariance matrices. Covariance matrices have an important effects on converge time and filter stability. The summary of EKF algorithm is given in Figure 4.

Figure 2. Structure of artificial neural network

The back propagation neural network (BPN) is the most popular supervised model of artificial neural networks which is developed by Rumelhart et al. [9]. BPN repeatedly adjust the parameters (weights and biases) to minimize the error between target output and estimated output according to “generalized delta rule”. The parameter modification stops when the performance error goal is met [10]. The crucial factor that leads to the success of ANN model is the selection of appropriate inputs. Too many inputs that are redundant will contribute to the problem of local minima [11]. By understanding the physical system to be model, the good choice of input can be guided. For example, upstream river

23

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012)

According to 10, 0000 cycles of training, the error goal is set at 1.00e-05. The training algorithm used is traincgp, conjugate gradient with Polak Ribiere updates. The verification results are given in Figure 5. The BPN verification result shows that the model cannot be considered good because there is slight difference in the simulated and actual water level results. Furthermore, overshoot occurs at the end of the graph. This is maybe because that the training is stop after the minimum step size is reached. However the value of mean squared error (MSE) is 8.89e-05 which is still close to the error goal that is 1.00e-05, so the result is still acceptable.

Time Update (“Predict”) (1) Project the state ahead

xˆ − k = f (xˆ k −1,uk −1, 0)

(2) Project the error covariance ahead

P − k = Ak Pk −1 AT k + Wk Qk −1W T k

Measurement Update (“Correct”) (1) Compute the Kalman Gain

(

)

1.5

zk

1.4

−1

K k = P − k H T k H k P − k H T k + Vk RkV T k (2) Update estimate with measurement

(

(

xˆk = xˆ − k + K k z k − h xˆ − k , 0

))

BPN estimates versus actual value

1.3

Pk = (I − K k H k )P

water level(meter)

(3) Update the error covariance −

k

Figure 4. Extended Kalman Filter (EKF) Loop

Figure 4 summarizes the overall operation of EKF algorithm. The prediction stage starts by projecting the state and error covariance ahead using the present value of Jacobian matrix and prior value of error covariance. Then, based on the projected error covariance value, the Kalman gain is calculated and measurement xˆ k is estimated. Finally, the

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5

0

2

4

6

8

10

12

hours Figure 5. The verification results of the flood water level

error covariance value is updated. The loop will continue until the desired error covariance value is achieved. III.

simulated water level actual water level

In order to improve the prediction results, an Extended Kalman Filter (EKF) is introduced at the output of BPN. EKF is the most commonly used nonlinear Bayesian estimator which is able to filter and track the nonlinear output based on assumptions that are: perturbations from the mean trajectory are small; and the conditional density function of the state is Gaussian [15]. Figure 6 shows the results after the EKF being applied. From the graph, it is clearly shown that the results are improved as the overshoot is reduced and the pattern of the simulated and actual water level between 0— 6 hours is nearly the same as compared to Figure 5.

RESULTS AND DISCUSSION

The water levels at the upstream and downstream rivers station at Sungai Batu Pahat is applied in the BPN model. Station 1929401, 2130422, 1821480 and 2030402 acts as a feeder to the BPN model because it is located at upstream location whereas Station 1829478 is the output of the model because it is the target station. The nodes of both input and output layers are set as 1.The number of nodes for hidden layer were set to be 15, in following the law of Kolmogorov [14]. Kolmogorov’s law state that the number of nodes in the hidden layer is at least 2n+1, where n is the number of nodes in the input layer. Thus, the topology structure of BPN flood modelling and forecasting in this study is (1,15,1). In order to accelerate the convergence, it is necessary to normalize the original data, but need to remember to denormalize it back to obtain the desired data. After the normalization process, the training parameters used were learning rate η at 0.55 and momentum constant α is fixed at 1. Learning rate and momentum constant is used to accelerate convergence of ANN training process and the value of η and α is selected in the range of 0 and 1.

24

2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012) [5]

BPN estimates(with EKF)versus actual value 1.5 simulated water level with EKF actual water level

1.4

[6]

water level(meter)

1.3 1.2

[7]

1.1

[8]

1 0.9

[9]

0.8

[10]

0.7

[11]

0.6 0.5

0

2

4

6

8

10

[12]

12

hours [13] Figure 6. The verification results of the flood water level with EKF

IV.

CONCLUSIONS

[14]

Accurate prediction of flood water level is important as an early warning system to the public to inform them about the possible incoming flood disaster. This paper proposed ANN model to predict the flood water level. A supervised neural network with the back propagation model is adopted in this study. The performances of BPN model have been evaluated but yet the result is not that satisfactory. Hence, Extended Kalman Filter is proposed to improve the results. In conclusion, Extended Kalman Filter is able to provide better result compared with actual result without application of Extended Kalman Filter. The water level is only the parameter in this Back Propagation Neural Network model. So, for future works, more parameters can be added in the model such as rainfall and water flow so that more accurate and realistic prediction results can be achieved.

[15]

ACKNOWLEDGEMENT The authors would like to thanks and acknowledge the financial support from the Faculty of Electrical Engineering and Research Management Institute (RMI) under Excellence Fund No. 600-RMI-ST-DANA 5/3/Dst(33/2011), Universiti Teknologi MARA, Shah Alam. REFERENCES [1]

[2]

[3]

[4]

Amir F. Atita et al, “A comparison between neural network forecasting techniques – case study: river flow forecasting,” IEEE Transactions on Neural Networks, vol. 10, no.2, pp.402-409, 1999. Chang-Shian Chen et al, “Development and application of a decision group Back-Propagation Neural Network for flood forecasting,” ELSEVIER Journal of Hydrology, vol. 385, pp. 173-182, 2010. Paul Leahy, Ger Kiely & Gearoid Corcoran, “Structural optimisation and input selection of an artificial neural network for river level prediction,” ELSEVIER Journal of Hydrology, vol. 355, pp. 192-201, 2008. McCulloch, W., Ps, W.H., “A logical calculus of the ideas immanent in nervous activity,” Bull. Math. Biophys. 5, pp. 115-133, 1943.

25

Venkatesan et al, “Prediction of all India summer monsoon rainfall using error back propagation neural networks,” Meteorology and Atmospheric Physics, vol. 62(3-4), pp.225-240, 1997. Tsung-Lin Lee, “Predictions of tyhphoon storm surge in Taiwan using artificial neural networks,” ELSEVIER Advances in Engineering Software, vol. 40, pp.1200-1206, 2009. Lee, T.L, “Neural network prediction of a storm surge,” Ocean Engineering, vol.33, pp.483-494, 2006. Lin, G.F., Wu. M.C., “A hybrid neural network model for typhoon rainfall forecasting ,” Journal of Hydrology, vol. 375(3-4), pp.450-458, 2009. Rumelhart et al., “Learning representations by back propagating errors,” Nature, 323:533-6, 1986. Hsiao, T.R., Lin, C.W., Chiang,H.K., “Partial least-squares algorithm for weights initialization of back propagation network,” Neurocomputing, vol. 50, pp. 237-247, 2003. Govindaraju, R., “Artificial neural networks in hydrology : preliminary concepts,” Journal of Hydrology, vol. 5(2), pp. 115-123, 2000. Govindaraju, R., “Artificial neural networks in hydrology : hydrologic applications,” Journal of Hydrology, vol. 5(2), pp. 124-137, 2000. Singh et al, “Appropriate data normalization range for daily river flow forecasting using an artificial neural networks,” Hydroinformatics in Hydrology, Hydrogeology and Water Resources. International Association of Hydrological Sciences Publication, Uk, pp. 51-57, 2009. Wabgaonkar,H., Stubberud,A., “The Kolmogorov superposition theorem and functional approximation in neural networks,” 24th Asilomar Conference on Signals, Systems and Computers, vol. 2, 1990. Jangho Yoon, Yunjun Xu & Prakash Vedula, “A direct quadrature based nonlinear filtering with Extended Kalman Filter update for orbit determination,” 2010 American Control Conference Marriot Waterfront, Baltimore, MD, USA, June 30-July 02, 2010.