RREDICTION OF UPPER CITARUM RIVER BASIN …blogs.unpad.ac.id/ruminta/files/2012/07/Makalah-BMKG.pdf · *) Presented in Internasional Workshop on Climate Information Services in Supporting

*) Presented in Internasional Workshop on Climate Information Services in Supporting Mitigation and Adaption to Climate Change in Energy and Water Sectors,. Jakarta, 2009..

RREDICTION OF UPPER CITARUM RIVER BASIN DISCHARGE

BASED ON ANFIS

Ruminta

Padjadjaran University

Abstract Water resources availability for meeting reservoir storages, water supply diversion and

environmental in stream flow requirements must be assessed on various premises regarding future water used as well as climatic and hydrologic conditions. Reliable discharge predictions are particularly important for warning against dangerous flood and inundation. This study, therefore, investigates temporal dynamical model and predicts discharge in the Upper Citarum River Basin, West Java, Indonesia. The investigations and predictions based on pentad observations data of the rainfall, rainday, evapotranspiration, and discharge from January 1994 to December 2001. Modeling and prediction of the river discharge based on Adaptive Neuro-Fuzzy Inference System (ANFIS). A hybrid learning algorithm, which combines the least square method and the back propagation algorithm, is used to identify the parameters of the ANFIS. The rainfall, rainday, evapotranspiration, and discharge at time t-1 (one pentad before) should be included in the ANFIS input variables are determined by statistical methods, i.e. correlation coefficient between the that input variables and output variable or discharge at time t. Prediction of discharge was done for 1-pentad until 72-pertad ahead in orders to compare the models generalization at higher horizons. The results shows that temporal dynamical model of the discharge based on ANFIS can simulate the observations data successfully and provide high accuracy and reliability for river discharge prediction. The model is capable to minimize the bias and root mean squared error (RMSE=21.817 m3/sec.) and mean absolute percentage error (MAPE=2.05%). The model exhibits satisfactory agreements between observed and prediction data (r = 0.975). Prediction of river discharge has high precision (E=97.94%). The information gathered from the preliminary results provides useful information for flood early warning system design in which the magnitude and the timing of a potential extreme flood are indicated, for hydropower operation, and for improvement of an integrated water management in the Upper Citarum River Basin.

Key words: rainfall, number of rain day, evapotranspiration, discharge, prediction, ANFIS

1. Introduction

The design, planning, and operating of river system depend largely on relevant

information derived from extreme event forecasting and estimation. Reliable river discharge

and rainfall forecasts are particularly important for warning against dangerous flood or


inundation and drought as well as in the case of multi-purpose reservoirs. Variability of river

discharge in Indonesian had been changed as consequences of global climate changes and

ENSO variability (Peel, et al., 2001, Hendon, 2002). The river discharge has high relationship

with rainfall. The rainfall in South East Asian had been changed significantly (Burn and Hag,

2002, Leon, 2002).

There are many forecasting techniques have been developed to simulate the climatic

and hydrologic time series such as empirical black box, conceptual, and physically based

distributed models. Conceptual and physically based distributed models are designed to

simulate the physical mechanisms that determine the hydrological circle, and use to involve

water transference physical laws, and parameters associated with the characteristics of the

catchment's area (Sorooshian and Gupta, 1995). Such models may require sophisticated

mathematical tools, a significant amount of calibration data, and some degree of expertise and

experience with the model.

In practical situations, the uses of a simple model such as linear system models (black

box models) more commonly used. However, these simpler models normally fail to represent

the non-linear dynamics, which are inherent in the process of rainfall-discharge

transformation. By considering the complexity of phenomena involved there is a strong need

to explore alternative solutions through modeling direct relationship between the input and

output data without having the complete physical understanding of the system. While data-

driven models do not provide any physics of the climatic and hydrologic processes, they are

in particular, very useful for modeling hydrological time series where the main concern is to

predict accurate flows at specific watershed locations (Nayak et al., 2005; Sudheer, et al.,

2002). Recently, intelligent computation methods have been adopted in water resources

forecasting studies as a powerful alternative modeling tools. These methods offer advantages

over conventional modeling, including the ability to handle large amounts of noisy data from

dynamic and nonlinear systems, especially where the underlying physical relationships are not

fully understood (Aqil et al., 2006)). Other associated benefits include improvement of model

performance, faster model development and calculation times, and improved opportunities to

provide estimates of prediction confidence through comprehensive bootstrapping operations

(Openshaw and Openshaw, 1997).


The application of ANFIS to various aspects of hydro meteorological modeling has

undergone much investigation in recent years (Franc and Panigrahi, 1997; Mashudi, 2002;

Ozelkan and Duckstein, 2001). ANFIS is mostly suited to the modeling of nonlinear system.

Zhu (2000) and Shapiro (2002) have indicated that ANFIS is the best modeling to analysis

numerical data, because in training process based on minimize value of root mean square

error (RMSE). The others investigation show ANFIS can predict better than back propagation

multilayer preceptor (BPMP) or auto-regression. This computational methods offers real

advantages over conventional modeling, especially when the underlying physical relationship

are not fully understood ( Nayak et al., 2004; Cigizoghu, 2003; Tokar and Markus, 2000).

The other successful applications of adaptive network-based fuzzy inference system

based modeling in water resources forecasting have been widely reported such as used neuro

fuzzy and neural networks model for short-term water level prediction (Bazartseren, 2003), a

fuzzy neural network model for inflow forecast into electric power plant (Valenca and

Ludermir, 2000). Also, the performance of the adaptive network-based fuzzy inference

system is significantly improved if the input data are transformed into the normal domain

prior to model building (Nayak et al., 2004). Demonstration on the use of Takagi-Sugeno

models for predicting discharge from rainfall time series by comparing grid partitioning,

subtractive clustering and Gustafson-Kessel clustering identification method for constructing

the models (Vernieuwe et al., 2005).

The Citarum river basin is a complex basin containing most of the feature of water

system: storage, uncontrolled sources, multi purposes, and potential for all forms of

operational management. Information of temporal models, predictions, persistence (wet and

dry periods), and long-term trends of the hydro meteorological components have the potential

to drastically improve the effective use of available water resources in this basin.

The current paper reports an outcome of a study aims at applying ANFIS as a

modeling tool to predict and estimate the discharge of the Upper Citarum River Basin in West

Java. The ANFIS applications was used to predict river discharge for 1-pentad to 72-pentad

ahead. The purposes of this study are investigates temporal dynamical model and predicts

river discharge in the Upper Citarum River Basin, West Java. The results of these studies can

give information for warning system design in which the magnitude and the timing of a


potential extreme flood are indicated, for hydropower operation, for improvement of an

integrated water management in the Citarum River Basin.

2. Adaptive Neuro-Fuzzy Inference System

ANFIS is a type biologically inspired computational model. The functioning of

ANFIS is based on learning process (Jang, 1993). A network of this model is made up of a

member interconnected nodes arranged into three basic layers: input, hidden, and output. The

input nodes perform no computation but are used to distribute input to network. In this

network an information passed one way through the network from the input layers, through

the hidden layers and finally to the output layer. The ANFIS was trained by the standard back

propagation algorithm which uses a set of input and output pattern was applied. An input

pattern is used by the system to produce an output, which then is compared with the actual

output. If these no difference, then no learning takes place.

Adaptive network-based fuzzy inference system (ANFIS) used a feed forward network

to search for fuzzy decision rules that perform well on a given task. In this study, using a

given input-output data set, ANFIS creates a FIS whose membership function parameters are

adjusted using a combination between a back propagation algorithm with a least squares

method.

This allows the fuzzy systems to learn from the data being modeled. ANFIS provide a

method for the fuzzy modeling procedure to learn information from the data set, followed by

creating the membership function parameters that best allow the associated FIS to well

perform the given task (Jang, 1997). Then the equivalent ANFIS architecture of the first order

Takagi-Sugeno inference system is shown in Fig.1. Consider a first order Takagi-Sugeno

fuzzy model with a two input, one output system having three membership functions for each

input (Fig.2.).


Fig.1. The ANFIS Architecture for the Takagi-Sugeno Fuzzy Model.

Fig.2. Fuzzy Reasoning Of the ANFIS with a Two Input.

The functioning of ANFIS is a five layered feed forward neural structure and the

functionality of the nodes in these layers can be summarized as follows:

Layer 1: Every node i in this layer is an adaptive node with a node output function

defined by,

)(,1 xAO ii µ=

)(2,1 yBO ii −= µ

Premise parameters

Consequent parameters

A2

B1

w1

w2

w1*f1

w2*f2

wi*fi

Π

N

N

x y

w1

w2

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

Π

Σ

x

y

A1

B2

(2)

(1)

A1 B1

A2 B2

x=3

X

X

Y

Yy=2

W1

W2

z1 = p1*x+q1*y+r1

z =

z2 = p2*x+q2*y+r2

w1+w2

w1*z1+w2*z2

∏


where x(or y) is the input to the node i; Ai (or Bi-2) is a fuzzy set associated with this node,

characterized by the shape of the membership function in this node and can be any

appropriate functions that are continuous and piecewise differentiable such as Gaussian,

generalized bell shaped, trapezoidal shaped and triangular shaped functions. Assuming a

Generalized Bell function as the membership function, Ai can be computed as,

ib

i

i

Ai

acx

xO 2,1

1

1)(1

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+

== µ

where {ai, bi, ci} are the parameter set. Parameters in this layer are referred to as premise

(antecedent) parameters.

Layer 2: Every node in this layer is a fixed node labeled Π, whose output is outputs

the product multiplies the incoming signals,

)()(,2 yxO

ii BAii µµω ×==

Each node output represents the firing strength of a rule.

Layer 3: Every node in this layer is a circle node labeled N. The i-th node calculates

the ratio of the i-th rule's firing strength to the sum of all rule's firing strengths. Output of this

layer will be called normalized firing strengths.

21,3 ωω

ωϖ+

== iiiO

Layer 4: Node i in this layer compute the contribution of the i-th rule towards the

model output, with the following node functions,

)(,4 iiiiiii ryqxpfO ++== ϖϖ

(3)

(4)

(5)

(6)


where iw is the output of layer 3 and {pi, qi, ri) is the parameter set. Parameters in this layer

will be referred to as consequent parameters.

Layer 5: The single node in this layer is a fixed node labeled ∑ that computes the

overall output as the summation of all incoming signals.

21

22115 ωω

ωωω

ωϖ

++

=∑

∑=∑=

ffffO

ii

iii

iii

The learning algorithm for ANFIS is a hybrid algorithm, which is a combination

between gradient descent and least squares method. For simplicity, the adaptive network has

only one output

The application of the ANFIS to the time series data consisted of two steps. The first

step was the training of the ANFIS, which comprised the time series data describing the input

and output to the network and obtaining the inter-connection weight. Once the training stage

was complete the ANFIS were applied to the testing data. The best training of the ANFIS is

the lowest root mean square error (RMSE) and the lowest mean absolute percentage error

(MAPE).

4. Data and Methodology

This study was carried out at Upper Citarum River Basin. The upper Citarum river

basin is located in West Java Indonesia, with a geographical position of about 6o43’-7o04’

southern latitude and 107o15’-107o55’ eastern latitude. The total drainage area of the river

basin is approximately 2.283 km2. The investigations based on pentad (every five days)

observations data of the rainfall, number of rain day, evapotranspiration, and discharge from

January 1994 to December 2001. The discharge was observed at Nanjung that show an inflow

of the Saguling dam. Total of data set is 576 pentads (Fig. 3 and 4). The data were divided

into three independent subsets: a training subset includes 288 data sets; the verification subset

has 216 data sets; and the testing subset has the remaining 72 data sets.

(7)


-3

-2

-1

0

1

2

3

4

1 72 143 214 285 356 427 498 569

Pentad

Stan

dard

ized

Rainfall Rainday Evapotranspiration Discharge

Fig.3. Standardized of Climatic and Hydrologic Observation Data.


02040

6080

100120140

160180200

1 72 143 214 285 356 427 498 569

Rai

nfal

l (m

m)

0

1

2

3

4

5

6

7

1 72 143 214 285 356 427 498 569

Rai

nday

(day

s)

0

10

20

30

40

50

60

70

1 72 143 214 285 356 427 498 569

Evap

otra

nspi

ratio

n (m

m)

0200400600800

10001200140016001800

1 72 143 214 285 356 427 498 569

Pentad

Dis

char

ge (m

^3 /s

ec.)

Fig.4. Climatic and Hydrologic Observation Data of the Citarum River Basin.


Prediction of the river discharge based on Adaptive Neuro-Fuzzy Inference System

(ANFIS). In this study, input of ANFIS model are rainfall, number of rain day,

evapotranspiration, and river discharge at time t-1 and output of ANFIS model is river

discharge at time t. Using a given input/ output data set, we construct a fuzzy inference in

which partition the input space to reflect the premise part of the fuzzy inference system. We

created an initial set of membership functions using grid partition method.

In the common grid partitioning method, at the beginning of training, a uniformly

partitioned grid is taken as the initial state. In this study, grid partition method was used to

create the initial membership function matrix using the generalized bell functions for each of

the input variables. We selected three membership functions for each input at low, medium,

and high. As the parameters in the premise membership functions are adjusted, the grid

evolves. After computing the gradient vector of the parameters of the membership functions,

ANFIS employed an optimization technique to adjust the parameters to reduce some error

measure.

The ANFIS model applied in this study uses the hybrid learning algorithm, a

combination of least square estimation and back propagation, for membership function

parameter estimation. In the forward pass of the hybrid learning algorithm, node outputs go

forward until layer 4 and the consequent parameters are identified by the least-squares

method. In the backward pass, the error signals propagate backward and the premise

parameters are updated by gradient descent. The final fuzzy inference system model would

ordinary be the one associated with minimum training error. The performances of the models

developed in this study were assessed using various standard statistical performance

evaluation criteria.

The statistical measures considered were (RMSE), mean absolute percentage error

(MAPE), precision (E), and correlation coefficient (r),

∑=

−=N

ttt QQ

NRMSE

1

2' )(1 (8)


%100)(11

'

⎥⎦

⎤⎢⎣

⎡ −= ∑

=

N

t t

tt

QQQ

NMAPE

where Q’t is the predicted discharge; Qt is the observed discharge; and N is the number of

data points.

The degree of the discharge prediction precision (also was used to evaluate general

quality of the ANFIS model) is defined as E,

2

2

1o

cEσσ

−=

where oσ is the variation of the observed discharge and cσ is the variation of the difference

between the observed discharge and predicted discharge.

The relationship between the observed discharge and predicted discharge was evaluated

by correlation coefficient (r),

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

−−=

∑∑

∑

−−

−

n

iPPi

n

iOOi

n

iPPiOOi

QQQQ

QQQQr

1

2

1

2

1

)()(

))((

where OiQ and PiQ are the observed and predicted discharge at time t respectively; OiQ and

PiQ are the mean of the observed and predicted discharge; and n is the number of data.

4. Results and Discussion

Input of ANFIS model are rainfall, number of rain day, evapotranspiration, and river

discharge at time t-1 and output of ANFIS model is river discharge at time t. Before training

process in ANFIS, relationship between the each input and output model was evaluated by

correlation coefficient (r). The results demonstrate that correlation coefficient of the each

input and output ANFIS are significant (Table 1). This fact indicated direct relationship

between the input (rainfall, number of rain day, evapotranspiration, and river discharge at

(9)

.(10)

(11)


time t-1) and output (river discharge at time t) data, although without having the complete

physical understanding of the system.

Table 1. Correlation Coefficient of Input and Output ANFIS Before of Training Process.

Input of ANFIS

Rainfall (Pt-1)

Rainday (Dt-1)

Evapotranspiration (ETt-1)

Discharge (Qt-1)

Output of ANFIS

0.491o* 0.546o* -0.235o* 0.837o* Discharge (Qt)

0.708m* 0.697m* -0.430m* 0.978m* Discharge (Qt) * : significant at α = 0.05 t : time (pentad, every five days); o : original data; m : non noise data.

In this study, identification and prediction of ANFIS model used two categories data,

i.e. original data and non noise data. Non noise data was generated by moving average (every

6 pentads) and was useful to minimize root mean square error (RMSE) and to increase

performance of the river discharge prediction.

The fuzzy inference system has a total of 81 rules, and all of the rules include all the

four input variables and three membership function. In order to find the optimum membership

parameters for the input models, the Sugeno-style ANFIS is employed. Therefore, the model

contains 81 (3x3x3x3) rules (Fig. 5).

The training RMSE, MAPE, E, and r for the ANFIS model is shown in Table 2. For

original data, the model is capable to minimize the bias and root mean squared error

(RMSE=93.469 m3/sec.) and mean absolute percentage error (MAPE=16.41%). The model

exhibits satisfactory agreements between observed and prediction data (r = 0.934). Prediction

of river discharge has high precision (E=98.54%). And for non noise data, RMSE and MAPE

are 27.13 m3/sec and 0.84% respectively. Correlation coefficient (r) and precision (E) are

98.54% and 0.993 respectively. The ANFIS model that was used non noise input data shows

the best performance and high accuracy and reliability to simulate observation data.

The membership functions of river discharge after training are shown in Fig. 6. The

membership function matrix using the generalized bell functions. There are selected three

membership functions for each input at low, medium, and high. From Fig. 6 we see how the


final membership functions are trying to catch the local features of the training set.

Performance of the ANFIS model is compared in three data sets: (1) training sets, (2)

verification sets, and (3) testing sets. Fig. 7 and 8 shows the observed, simulated, and

predicted discharge on x-axis during the training for original and non noise data respectively.

In each of the scatter diagrams, the more perfectly the model was tested, the closer the points

fall on the same line. As could be concluded from those figures, the ANFIS was successful in

learning the relationship between the input and output data. As shown in Fig. 7 and 8, the

result of forecasting using the ANFIS model falls relatively close to actual data line. The

results indicate that the generalization properties of the ANFIS model during the training,

verification, and testing are comparable.

Fig. 5. ANFIS Architecture of the River Discharge Prediction


In identification and prediction the pentad temporal dynamical model of the river

discharge show that for the simulation during training and testing stages have the lowest

RMSE and the highest values E (precision) to forecasts the river discharge. The prediction

and scatter plot for the training period are compared with the observed data of the river

discharge. The statistical measures exhibit satisfactory agreements between observed and

predicted data

0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

1

Rainfall,(mm)

Deg

ree

of m

embe

rshi

p

Low Medium High

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

Rainday,(days)

Deg

ree

of m

embe

rshi

p

Low Medium High

20 25 30 35

0

0.2

0.4

0.6

0.8

1

Evapotranspiration,(mm)

Deg

ree

of m

embe

rshi

p

Low Medium High

200 400 600 800 1000

0

0.2

0.4

0.6

0.8

1

Discharge,(m3/sec.)

Deg

ree

of m

embe

rshi

p

Low Medium High

Fig. 6. The Membership Functions for Input of the River Discharge ANFIS Model.

A comparative prediction accuracy of the ANFIS model using four statistical indices

(RMSE, MAPE, precision, and correlation) indicates that the ANFIS model is accurate and


consistent in different subsets (Fig. 8), where the value of RMSE are smaller (original

data=78.948 m3/sec and non noise data=21.817 m3/sec) whereas value of MAPE are smaller

(original data=10.22% and non noise data =2.05%) (Table 3). The correlation values are also

close to unity (original data=0.876 and non noise data=0.975). Precision of the river

discharge prediction are bigger (original data=72.4% and non noise data=97.94%) (Table 4).

For a prediction of river discharge in 72 pentad ahead, the performance indices of non

noise data model were comparable to each other and resulted in high prediction accuracy as

shown in Fig. 8. This result might suggest that the ANFIS has a great ability to learn from

input output patterns, which only represent three antecedent value of water level to produce a

good generalization.

Table 2. Statistics of the ANFIS Training

Training Model ANFIS

RMSE MAPE

Precision (E) (%)

r t_ test

Discharge 93.469 16.41% 87.28 0.934* 0.00002* Discharge (non noise) 27.130 0.84% 98.54 0.993* 0.000006*

Critical value of the t distribution: t0.05 (2), 576 =1.963 * = Significant (Acceptable); r = correlation coefficient Table 3. RMSE and MAPE of the River Discharge Prediction.

Predicted Data Model ANFIS

RMSE MAPE Discharge 78.948 10.22% Discharge (non noise) 21.817 2.05%

Table 4. Statistics of the River Discharge Prediction

Observed Data Predicted Data Model ANFIS Min. Mean Max. Min. Mean Max.

(E) (%) r t_ test

Discharge 78.87 312.46 645.06 74.31 334.29 679.42 72.36 0.876* 0.299* Discharge (non noise) 78.87 312.46 645.06 74.30 319.35 682.20 97.94 0.975* 0.252*


Critical value of the t distribution: t0.05 (2), 72 =1.994 * = Significant (Acceptable); E = Precision; r = correlation coefficient; Min. = Minimum; Max. = Maximum

Relationship between input and output of the river discharge models show in Fig. 9

and 10. Rainfall and river discharge at time t-1 had strong response to river discharge at time

t, in especially at above 60 mm and 800 m3/ sec for rainfall and river discharge respectively.

In other side, number of rain day and evapotranspiration at time t-1 had no persistence

response to river discharge at time t. This fact indicated that rainfall and river discharge at

time t-1 are the best predictor for river discharge at time t, where t is lead time in pentad..

0200400600800

10001200140016001800

1 72 143 214 285 356 427 498 569 640

Pentad

Dis

char

ge (m

^3 /s

ec.)

Observed Simulated Predicted

Fig.7. Prediction of the River Discharge.


0200400600800

1000120014001600

1 72 143 214 285 356 427 498 569 640

Pentad

Dis

char

ge (m

^3/s

ec.)

Observed Simulated Predicted

Fig. 8. Prediction of the River Discharge (non noise).


0

50

100

0

2

4

0

5

10

15

x 104

Rainfall,(mm)Rainday,(days)

Dis

char

ge,(m

3 /sec

.)

0

50

100

2025

3035

0

1

2

x 105

Rainfall,(mm)Evapotrans-

piration,(mm)

Dis

char

ge,(m

3 /sec

.)

01

23

45

2025

3035

0

2

4

6

0

2

Rainday,(days)Evapotrans-

piration,(mm)

Dis

char

ge,(m

3 /sec

.)

200400

600800

1000

0

50

100-2

0

2

4

6x 105

Discharge,(m3/sec.)Rainfall,(mm)

Dis

char

ge,(m

3 /sec

.)

200400

600800

1000

0

2

4

0

Discharge,(m3/sec.)Rainday,(days)

Dis

char

ge,(m

3 /sec

.)

200400

600800

1000

2025

3035

0

5

Discharge,(m3/sec.)

Evapotrans-piration,(mm)

Dis

char

ge,(m

3 /sec

.)

Fig. 9. Response of Two-Input to the River Discharge.


0 20 40 60 80 100 1200

2000

4000

6000

8000

10000

12000

Rainfall,(mm)

Dis

char

ge,(m

3 /sec

.)

1 1.5 2 2.5 3 3.5 4 4.5 50

100

200

300

400

500

600

700

800

900

1000

Rainday,(days)

Dis

char

ge,(m

3 /sec

.)

0 200 400 600 800 1000 12000

1000

2000

3000

4000

5000

6000

Discharge,(m3/sec.)

Dis

char

ge,(m

3 /sec

.)

10 20 30 40 50 60 70-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5 x 106

Evapotranspiration,(mm)

Dis

char

ge,(m

3 /sec

.0

Fig.10. Response of One-Input to the River Discharge.

5. Conclusions

The conclusion obtained in this study shows that temporal dynamical model of the river

discharge based on ANFIS can simulate the observation data accurately. Adaptive network-

based fuzzy inference system model can be applied successfully and provide high accuracy

and reliability for river discharge estimation. This model can potentially use to predict the

river discharge in Upper Citarum River Basin. The results demonstrate that the in general, the

adaptive network-based fuzzy inference system provide accurate and reliable river discharge

prediction where the MAPE=2.05%, correlation=0.975 and precision=97.94% as achieved.

Up to 72-pentad ahead prediction, the adaptive network-based fuzzy inference system still


shows relatively good performance where the error of prediction resulted was less than

10.22%. Therefore we conclude that the information gathered from the preliminary results

provide a useful guidance or reference for flood early warning system design in which the

magnitude and the timing of a potential extreme flood, for hydropower operation, and for

improvement of an integrated water management in the Upper Citarum River Basin.

6. References

Aqil, M., Ichiro Kita, and Moses Macalinao, 2006: A Preliminary Study on the Suitability of Data Driven Approach for Continuous Water Level Modeling, International Journal of Computer Science, Vol 1(4), ISSN 1306-4428.

Bazartseren, B., G. Hildebrandt, and K.P. Holz, 2003: Short-term Water Level Prediction Using Neural Networks and Neuro-Fuzzy Approach, Neurocomputting., vol. 55, pp. 439-450.

Burn, D.H. and E. Hag, 2002: Detection of Hydrologic Trends and Variability. Journal of Hydrology, 255(1-4), 107-122.

Cigizoghu, H.K., 2003: Estimation, Forecasting, and Extrapolation of River Flows by Artificial Neural Networks. Hydrology Science Journal, 48(3), 349-361.

Duan, Q., S. Sorooshian, and V.K. Gupta, 1992: Effective and Efficient Global Optimization for Conceptual Rainfall-Runoff Models, Water Resour. Res., vol. 28, pp. 1015–1031.

Franc, J.L. and S. Panigrahi, 1997: Artificial Neural Network Models of Wheat Leaf Wetness. Journal of Agricultural and Forest Meteorology, 88(1-4), 57-65.

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