Journal of Water Resource and Protection, 2012, 4, 891-897 Published Online October 2012 (
Artificial Neural Networks for Event Based
Rainfall-Runoff Modeling
Archana Sarkar, Rakesh Kumar
National Institute of Hydrology, Roorkee, India
Received March 11, 2012; revised May 19, 2012; accepted August 12, 2012
The Artificial Neural Network (ANN) approach has been successfully used in many hydrological studies especially the
rainfall-runoff modeling using continuous data. The present study examines its applicability to model the event-based
rainfall-runoff process. A case study has been done for Ajay river basin to develop event-based rainfall-runoff model
for the basin to simulate the hourly runoff at Sarath gauging site. The results demonstrate that ANN mod els are able to
provide a good r epresentation of an even t-based rainfa ll-runo ff process. The two impor tant pa rameters, when predictin g
a flood hydrograph, are the magnitude of the peak discharge and the time to peak discharge. The developed ANN mod-
els have been able to predict this information with great accuracy. This shows that ANNs can be very efficient in mod-
eling an even t-based rainfall-runoff process for determining the peak discharge and time to the peak discharge very ac-
curately. This is important in water resources design and management applications, where peak discharge and time to
peak discharge are important input variables.
Keywords: Artificial Neural Networks (ANNs); Event Based Rainfall-Runoff Process; Error Back Propagation; Neural
1. Introduction
Rainfall-runoff is important in activities such as flood
control and management, design of hydraulic structures
in a watershed, and likewise. Historically, researchers
have relied on conventional techniques, either determi-
nistic models, which consider the physics of the under-
lying process, or systems theoretic/black-box models,
which do not. Determi ni s t i c m odels of varying degrees of
complexity have been employed in the past for the rain-
fall runoff process with varying degrees of success. The
rainfall runoff is a complex, dynamic, and non-linear
process, which is affected by many and often interrelated,
physical factors. The influence of these factors and many
of their combinations in generating runoff is an ex-
tremely complex physical process, and is not clearly un-
derstood [1]. Moreover, many of the deterministic rain-
fall-runoff models need a large amount of data for cali-
bration and validation purposes, and are computationally
expensive. As a result, the use of deterministic models of
the rainfall-runoff process is viewed rather skeptically by
researchers and consequently has not become very popu-
lar [2].
Artificial Neural Networks (ANNs) have been pro-
posed as efficient tools for and prediction in hydrology,
as black-box models. ANNs are supposed to posses the
capability to reprodu ce the unknown relationsh ip ex isting
between a set of input variables (e.g., rainfall) of the sys-
tem and one or more output variables (e .g., runoff) [3]. In
recent years ANNs have shown exceptional performance
as regression tools, especially when used for pattern rec-
ognition and function estimation. They are highly non-
linear, and can capture complex interactions among the
input variables in a system without any prior knowledge
about the nature of these interactions [4]. The main ad-
vantage of ANNs is that one does not have to explicitly
assume a model form, which is a prerequisite in conven-
tional approaches. Ind eed, in ANNs the data poin ts them-
selves generate a relationship of possibly complicated or
orthodox shape. In comparison to the conventio nal meth-
ods, ANNs tolerate imprecise or incomplete data, ap-
proximate results, and are less vulnerable to outliers [5].
They are highly parallel, i.e., their numerous independent
operations can be executed simultaneously. These char-
acteristics render ANNs to be very suitable tools for han-
dling various hydrological problems. Although applica-
tion of ANN approach for rainfall-runoff process is re-
cent, it has already produced very encouraging results.
Among various hydrological problems, rainfall-runoff
has perhaps received the maximum attention from ANN
researchers. In an earlier study, Halff et al. [6] design ed a
three-layer feedforward ANN using the observed rainfall
opyright © 2012 SciRes. JWARP
hyetographs as inputs and hydrographs recorded by the
US Geological Survey (USGS) at Bellvue, Washington,
as outputs. This study opened up several possibilities for
rainfall-runoff application using neural networks. Hjelm-
felt and Wang [7] developed a neural network based on
the unit hydrograph theory for the Goodwater Creek wa-
tershed in central Missouri. In an application using two
neural networks, Zhu et al. [8] predicted upper and lower
bounds on the flood hydrograph in Butter Creek, New
York. Smith [9] used a back-propagation ANN model to
predict the peak discharge and the time to peak resulting
from a single rainfall pattern. Carriere et al. [10] de-
signed and developed a Virtual Runoff Hydrograph Sys-
tem (VROHS) based on ANN to generate runoff hydro-
graph. Lange [11] introduced a method which generates a
spe cial hydrograph (comparable with the unit hydrograph)
by using an ANN. Anmala et al. [12] utilized ANNs for
runoff predictions in three watersheds in Kansas. The
authors found that a direct use of feed forward ANNs
without time delayed input does not prov ide a significant
improvement over other regression techniques. Sudheer
et al. [13] worked on a data driven algorithm for con-
structing Artificial Neural Network Rainfall-Runoff
Models. Quebec. Chibanga et al. [14] modeled the de-
rived flow series (by simple reservoir routing) and the
time series of historic flow measured at the Kafue Hook
Bridge (KHB), Kafue River basin in Vietnam, separately
using ANNs. Chiang et al. [15] presented a system com-
parison of two basic types of neural networks, static and
dynamic in their study. Jy S. Wu et al. [16] demonstrated
the application of ANNs for watershed-runoff and
stream-flow forecasts. Sarkar et al. [17] developed back
propagation ANN runof f models to simulate and forecast
daily runoff for a part of the Satluj river basin of India.
Kisi [18] presented a comparison of different artificial
neural network algorithms for short term daily stream-
flow forecasting. Kalteh [19] developed rainfall-runoff
model using ANN and described different approaches
including Neural Interpretation Diagram, Garson’s algo-
rithm, and randomization approach to understand the
relationship learned by the ANN model. Modarres [20]
carried out a comprehensive multicriteria validation test
for rainfall-runoff by artificial neural networks with 17
global statistics and 3 additional non-parametric tests
through a case study of the Plasjan Basin in the western
region of the Zayandehrud watershed, Iran. Dorum et al.
[21] tried to set up rainfall-runoff relationship by using
ANN and Adaptive Neuro Fuzzy Interference Systems
(ANFIS) models at Flow Observation Stations on seven
sites in Susurluk Basin.
A rainfall-runoff model can be one of two types—an
event based rainfall-runoff model or a continuous rain-
fall-runoff model. Application of ANN approach for the
continuous rainfall-runoff process is numerous but that of
the event based process are limited. The present study
focuses on the of an event-based rainfall-runoff process.
Such ANN models are very useful in real time flood
2. Methodology
An ANN is a computing system made up of a highly in-
terconnected set of simple information processing ele-
ments, analogous to a neuron, called units. The neuron
collects inputs from both a single and multiple sources
and produces output in accordance with a predetermined
non-linear function. An ANN model is created by inter-
connection of many of the neurons in a known configu-
ration. The primary elements characterising the neural
network are the distributed representation of information,
local operations and non-linear processing. The theory of
ANN has been described in many books such as Haykin
[5] and Yegnanar ayana [22].
The main principle of neural computing is the decom-
position of the input-output relationship into series of
linearly separable steps using hidden layers [5]. Gener-
ally there are four distinct steps in developing an ANN-
based solution. The first step is the data transformation or
scaling. The second step is the network architecture defi-
nition, where the number of hidden layers, the number of
neurons in each layer, and the connectivity between the
neurons are set. In the third step, a learning algorithm is
used to train the network to respond correctly to a given
set of inputs. Lastly, comes the validation step in which
the performance of the trained ANN model is tested
through some selected statistical criteria.
Large variation in the input data can slow down or
even prevent the training of the network. To overcome
this potential problem, the data are usually scaled using
linear, logarithmic, or normal transformations. It is also
important that the absolute input values are scaled to
avoid asymptotic issues [5]. In the present study, the in-
put data for a variable x were standardised through the
ANN software, Neural Power [23].
There are three basic layers or levels of data process-
ing units viz., the input layer, the hidden layer and the
output layer. Each of these layers consists of processing
units called nodes of the neural network. The number of
input nodes, output nodes and the nodes in the hidden
layer depend upon the problem being studied. If the
number of nodes in the hidden layer is small, the network
may not have sufficient degrees of freedom to learn the
process correctly. If the number is too high, the training
will take a long time and the network may sometimes
over-fit the data [24].
The process of determining ANN weights is called
training, which forms the interconnection between neu-
rons. The ANNs are trained with a training set of input
Copyright © 2012 SciRes. JWARP
Copyright © 2012 SciRes. JWARP
and known output data. At the beginning of training, the
initial value of weights can be assigned randomly or
based on experience. The learning algorithm systemati-
cally changes the weights such that for a given input, the
differen ce between the ANN ou tput and th e actual outpu t
is small. Many learning examples are repeatedly pre-
sented to the network, and the process is terminated
when this difference is less than a specified value. At this
stage, the ANN is considered trained. An ANN is better
trained as more input data are used. Several learning al-
gorithms have been reported in the literature. In the pre-
sent study, the most widely used three layer feed forward
error back propagation algorithm [25] has been used for
After training is over, the ANN performance is vali-
dated. Depe nding on the outcome, either th e ANN has to
be re-trained or it can be implemented for its intended
use. A large number of statistical criteria are available to
compare the goodness of any given model. The perfor-
mance evaluation statistics used for ANN training in the
present work are root mean square error (RMSE), coeffi-
cient of correlation (R) and coefficient of determination
(DC). These parameters have been determined using the
following equations [23].
RMSE (1)
 
where 1
, 1
Q = observed discharge (cumec), q = calculated dis-
charge (cumec).
3. Study Area and Data Used
For the present study, Ajay river basin up to Sarath
gauging site forms the study area. The catchment of the
Ajay river spreads between Latitude 23˚25'N to 24˚35'N
and Longitude 86˚15'E to 88˚15'E. The Ajay river system
originates in the low hills near Deoghar in the Santhal
Pargana district of Jharkhand state and flows in a South-
Easterly direction passing through Monghyr district of
Jharkhand state and Birbhum and Burdwan district of
West Bengal. Ajay River ultimately falls into the river
Bhagirathi at Katwa about 216 km upstream of Calcutta.
The Sarath gauging site, established near village Sarath
and about 160 m upstream of Sarath-Madhupur Road
Bridge, is maintained by Water Resources Department,
Govt of Jharkhand. The geographical location of the site
is 24˚13'45''N latitude and 86˚50'43''E longitude. The
catchment area up to the site is 1191.40 sq·km. The
length of Ajay River up to Sarath gauging site is 82.18
sq·km. Figure 1 shows the index map of the part of Ajay
river basin lying in Jharkhand state along with the
catchment defined by Sarath gauging site which forms
the study area. Table 1 gives the details of periods of
various storms whose rainfall-runoff data have been used
in the study.
Figure 1. Index map of part of Ajay River Basin in Jharkhand (India) with catchment defined by Sarath Gauging Site.
Table 1. Periods of various rainfall-runoff events. Table 2. Description of various ANN models for training
and testing.
S. No. Period of the Events
1 13.08.1977 at 09 hrs. to 13.08.1977 at 20 hrs.
2 05.08.1978 at 21 hrs. to 06.08.1978 at 02 hrs.
3 16.08.1979 at 05 hrs. to 16.08.1979 at 16 hrs.
4 26.08.1980 at 15 hrs. to 27.08.1980 at 07 hrs.
5 22.08.1982 at 24 hrs. to 23.08.1982 at 06 hrs.
6 12.09.1987 at 13 hrs. to 12.09.1987 at 24 hrs.
4. Case Study
4.1. Input Variables
The first step in developing an ANN model is to identify
the input and output variables. The output from the
model is the runoff at time step t, Rt. The input variables
have been selected based on the concepts of time of con-
centration and recession of a storm hydrograph. The time
of concentration of the Ajay river basin was observed to
lie between 21 to 22 hours. With a time of concentration
of 22 hours and a time interval of 1 hour, the number of
time steps for the past for which rainfall must be consid-
ered as input in the ANN models should be 22 (=22/1).
Further it was found that th e runoff in the immediate p ast
was a more significant variable compared to the runoff in
the distant past, and hence it has been applied in all the
ANN models. Therefore, there were 26 input variables
(Pt, Pt–1, Pt–2, ······ Pt–22, Rt–1, Rt–2) and one output vari-
able (Rt).
4.2. ANN Model Development
In estimation of parameters of a hydrologic model, the
available data are divided in two parts. The first part is
used to calibrate the model and the second, to validate it.
This practice is known as “split-sample” test. The length
of calibration data depends upon the number of parame-
ters to be estimated. The general practice is to use half to
two-third of the data for calibration and the remaining for
Six isolated storm events were chosen for the study.
The 1-hourly rainfall runoff data were available for flood
seasons. ANN models have been developed considering
hourly data for four flood events for training and two
flood events for testing. On a rotation basis, data from
four storms have been used for training, while data from
two storms have been used for testing network perform-
ance. Various combinations of the flood events consid-
ered for training and testing are given in Table 2.
A back-propagation ANN with the generalized delta
rule as the training algorithm has been employed in this
study. The ANN package Neural Power downloaded
from the internet has been used for the ANN model de-
velopment. The structure for all simulation models are
three layer BPANN which utilizes a non-linear sigmoid
activation function uniformly between the layers. Nodes
ANN Model Events used in Trainin g
(Calibration) Events used in Testing
ANN-1 Events 1, 2, 3, 4 Events 5, 6
ANN-2 Events 2, 3, 4, 5, Events 6, 1
ANN-3 Events 3, 4, 5, 6 Events 1, 2
ANN-4 Events 4, 5, 6, 1 Events 2, 3
ANN-5 Events 5, 6, 1, 2 Events 3, 4
ANN-6 Events 6, 1, 2, 3 Events 4, 5
in the input layer are equal to number of input variables,
nodes in hidden layer are varied from 18 (default value
by the NP package for 26 input nodes) to approximately
double of input nodes [8] and the nodes in the output
layer is one as the models provide single output. It was
found that 18 hidden nodes give the best results. So for
all the ANN models, 18 nodes in the hidden layer have
been considered.
Number of input nodes in input layer = 26
Number of hidden layers = 1
Number of hidden nodes = 18
Number of nodes in output layer = 1
According to Hsu et al. [26], three-layer feed forward
ANNs can be used to model real-world functional rela-
tionships that may be of unknown or poorly defined form
and complexity. Therefore, only three-layer networks
were tried in this study.
The modeling of ANN initiated with the normalization
(re-scaling) of all inputs and output with the maximum
value of respective variable reducing the data in the
range 0 to 1 to avoid any saturation effect that may be
caused by the use of sigmoid function (accomplished
through the Neural Power package). All interconnecting
links between nodes of successive layers were assigned
random values called weights. A constant value of 0.15
and 0.8 respectively has been considered for learning rate
and momentum term
selected after hit and trials. The
quick propagation (QP) learning algorithm has been
adopted for the training of all the ANN models. QP is a
heuristic modification of the standard back propagation
and is very fast. The network weights were updated after
presenting each pattern from the learning data set, rather
than once per iteration. The criteria selected to avoid
over training was through generalization of ANN for
which the developed model was simultaneously checked
for its improvement on verification data on each iteration.
The training was continued until there was an improve-
ment in the performance of the model in both calibration
and verification periods. The performance of the model
was tested through the criterion discussed earlier.
5. Results and Discussion
The values of the performance criteria from various
models for both training (calibration) and testing (valida-
Copyright © 2012 SciRes. JWARP
tion) data sets are presented in Table 3. It can be seen
from Table 3 that, in general, RMSE is found to be
smaller (lowest for ANN-4) and the ANN estimates are
closer to the observed values. Coefficient of correlation
(R) is another indicator of goodness of fit and it is seen
from Table 3 that, R is also quite high in all the cases of
training and tested data sets (highest for ANN-2). The
determination coefficient (DC) is also closer to unity, for
all the cases of training test data (highest for ANN-2).
Thus, the estimations by ANN are found to yield all the
three indices with acceptable accuracy.
From Table 3, it is clear that the ANN-2 model out-
performs all the other models. This model consists of
four flood events namely, events 2, 3, 4, and 5 for train-
ing and events 6 and 1 for testing. It is to be noted that
the flood event 2 consists of the lowest as well as the
highest numerical values of runoff. Moreover, the patterns
covered by the four flood events of ANN-2 for training
are also highest (270) compared to all the other models.
So the performance of ANN-2 model is the best. This
conforms to the general fact that an ANN is better trained
as more input data are used.
Figure 2 presents a plot between observed and simu-
lated runoff for ANN-2 model during testing and shows a
Table 3. Comparative performance of various ANN models.
Calibration (Training) Verification (Testing)
ANN Model RMSE (cumec) R DC R DC
ANN-1 16.382 0.9980.996 0.8320.61
ANN-2 8.375 0.9990.999 0.9890.977
ANN-3 11.685 0.9990.997 0.9410.675
ANN-4 7.775 0.9990.998 0.9750.933
ANN-5 12.78 0.9980.997 0.9680.934
ANN-6 11.913 0.9990.998 0.9520.766
high correlation between the two. The errors are more for
the lower discharge values and there are no errors in the
peak values.
The observed and simulated flood hydrographs for the
events 1 to 6 are shown in Figure 3. These simulated
flood hydrographs are based on the best performing
ANN model, i.e., ANN-2 model. It can be seen that there
is a perfect match between the observed and simulated
flood hydrographs for the flood events 2, 3, 4 and 5. This
is because these four events together have been used for
training the ANN-2 model. However, very good match
between the observed and simulated flood hydrographs is
also there for the events 1 and 6 which were not used for
the training. The coefficient of correlation is as high as
0.925 and 0.927 for flood events 1 and 6 respectively.
The results demonstrate the capability of ANN technique
in simulating the event-based rainfall-runoff process of
the Ajay river basin accurately. The results of the present
study comply with the demonstrated capability of ANN
technique as presented by various investigato rs.
6. Conclusion
The application of artificial neural network (ANN) meth-
odology for modeling events of rainfall-runoff in a me-
dium size catchment of the Ajay River in Jharkhand (In-
dia) is presented. Back propagation models have been
designed and developed for the hourly runoff simulation
of Ajay river basin at Sarath gauging site. Various com-
binations of the flood events have been considered dur-
ing training. The performance of each model structure
has been evaluated using common performance criteria,
namely, root mean square error (RMSE), coefficient of
Figure 2. Observed v/s simulated runoff at Sarath from ANN-2 during testing.
Copyright © 2012 SciRes. JWARP
Even t 1
1357911 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Time (hours)
Discharge (cumec)
Observed Esimated (ANN)
Event 2
Time (hours)
Discharge (cumec)
Observed Estimated(ANN)
Event 3
159 13172125293337414549535761656973778185899397101105
Time (hours)
Discharge (cumec)
Observed Estimated (ANN)
Event 4
Time (hours)
ObservedEstimated (ANN)
Event 5
1 2345678 910111213141516171819
Time (hours)
Discharge (cumec)
ObservedEstimated (ANN)
Event 6
Time (hours)
Discharge (cumec)
Observed Estimated (ANN)
Figure 3. Runoff hydrographs various flood events from ANN-2 during testing.
correlation (R), and coefficient of determination (DC).
The results obtained in the present study have been able
to demonstrate that the ANN models are able to provide
a good representation of an event-based rainfall-runoff
7. Acknowledgements
We thank the Maroochy Shire project working group, led
by Damian McGarry, who provided the wide range of
data and analysis for the analysis. We also thank Dr.
Heinz Schandl of CSIRO for suggestions to improve the
[1] B. Zhang and S. Govindaraju, “Prediction of Watershed
Runoff Using Bayesian Concepts and Modular Neural
Networks,” Water Resources Research, Vol. 36, No. 3,
2000, pp. 753-762. doi:10.1029/1999WR900264
[2] R. B. Grayson, I. D. Moore and T. A. McMahon, “Physi-
cally Based Hydrologic-2. Is the Concept Realistic?”
Copyright © 2012 SciRes. JWARP
Water Resources Research, Vol. 28, No. 10, 1992, pp.
2659-2666. doi:10.1029/92WR01259
[3] K. Chakraborty, K. Mehrotra, C. K. Mohan and S. Ranka,
“Neural Networks and Their Applications,” Review of
Scientific Instruments, Vol. 65, 1992, pp. 1803-1832.
[4] D. Hammerstrom, “Neural Networks at Work,” IEEE
Spectrum, Vol. 30, No. 7, 1993, pp. 46-53.
[5] S. Haykin, “Neural NetworksA Comprehensive Foun-
dation,” Macmillan, New York, 1994.
[6] A. H. Halff, H. M. Halff and M. Azmoodeh, “Predicting
Runoff from Rainfall Using Neural Network,” Proceed-
ings Engineering Hydrolgy, American Society of Civil
Engineers, New York, 1993, pp. 760-765.
[7] A. T. Hjelmfelt and M. Wang, “Artificial Neural Net-
works as Unit Hydrograph applications,” Proceedings
Engineering Hydrolgy, American Society of Civil Engi-
neers, New York, 1998, pp. 760-765.
[8] M. Zhu, M. Fujita and N. Hashimoto, “Application of
Neural Networks to Runoff Prediction,” In: K. W. Hipel,
et al., Eds., Stochastic and Statistical Method in Hydrol-
ogy and Environmental Engineering, Vol. 3, Kluwer,
Dordrecht, 1994, pp. 205-216.
[9] J. Smith and R. N. Eli, “Neural Network Models of Rain-
fall-Runoff Processes,” Journal of Water Resources Plan-
ning & Management, American Society of Civil Engi-
neers, Vol. 121, No. 6, 1995, pp. 499-508.
[10] P. Carriere, S. Mohaghegh and R. Gaskari, “Performance
of a Virtual Run off Hydrograph Sy stem,” Journal of Com-
puting in Civil Engineering, American Society of Civil
Engineers, Vol. 122, No. 6, 1996, pp. 421-427.
[11] N. T. G. Lange, “Advantages of Unit Hydrograph Deriva-
tion by Neural Networks,” In: V. Babovic and C. L. Lar-
sen, Eds., Hydroinformatics, Vol. 2, Balkema, Rotterdam,
[12] J. Anmala, B. Zhang and R. S. Govindraju, “Comparison
of ANNs and Empirical Approaches for Predicting Wa-
tershed Runoff,” Journal of Water Resources Planning &
Management, American Society of Civil Engineers, Vol.
126, No. 3, 2000, pp. 156-166.
[13] K. P. Sudheer, A. K. Gosain and K. S. Ramasastri, “A
Data Driven Algorithm for Constructing Artificial Neural
Network Rainfall-Runoff Models,” Hydrological Proc-
esses, Vol. 16, No. 6, 2002, pp. 1325-1330.
[14] R. Chibanga, J. Berlamont and J. Vandewalle, “Model-
ling and Forecasting of Hydrological Variables Using Ar-
tificial Neural Networks: The Kafue River Sub-Basin,”
Hydrological Sciences Journal, Vol. 48, No. 3, 2003, pp.
363-379. doi:10.1623/hysj.48.3.363.45282
[15] Y. Chiang, L. Chang and F. Chang, “Comparison of
Static Feed Forward and Dynamic-Feedback Neural Net-
works for Rainfall-Runoff,” Journal of Hydrology, Vol.
290, 2004, pp. 297-211
[16] J. S. Wu, P. E. Han, J. Annambhotla and S. Bryant, “Arti-
ficial Neural Networks for Forecasting Watershed Runoff
and Stream Flows,” Journal of Hydrologic Engineering,
ASCE, Vol. 10, No. 3, 2005, pp. 216-222.
[17] A. Sarkar, A. Agarwal and R. D. Singh, “Artificial Neural
Network Models for Rainfall-Runoff Forecasting in a
Hilly Catchment,” Journal of Indian Water Resources
Society, Vol. 26, No. 3-4, 2006, pp. 1-4.
[18] O. Kisi, “Streamflow Forecasting Using Different Artifi-
cial Neural Network Algorithms,” Journal of Hydrologic
Engineering, American Society of Civil Engineers, Vol.
12, No. 5, pp. 532-539.
[19] A. M. Kalteh, “Rainfall-Runoff Using Artificial Neural
Networks (ANNs) and Understanding,” Caspian Journal
of Environmental Science, Vol. 6, No. 1, 2008. pp. 53-58.
[20] R. Modarres, “Multi-Criteria Validation of Artificial Neu-
ral Network Rainfall-Runoff,” Hydrology and Earth Sys-
tem Sciences, Vol. 13, 2009, pp. 411-421.
[21] A. Dorum, A. Yarar, M. F. Sevimli and M. Onucyildiz,
“The Rainfall-Runoff Data of Susurluk Basin,” Expert
Systems with Applications: An International Journal, Vol.
37, No. 9, 2010, pp. 6587-6593.
[22] B. Yegnanarayana, “Artificial Neural Networks,” Pren-
tice-Hall of India Pvt. Ltd., New Delhi, 1999.
[23] Neural Power, “Neural Networks Professional Version
2.0,” CPC-X Software, 2003.
[24] N. Karunanithi, W. J. Grenney, D. Whitley and K. Bovee,
“Neural Networks for River Flow Prediction,” Journal of
Computing in Civil Engineering, ASCE, Vol. 8, No. 2,
1994, pp. 201-220.
[25] D. E. Rumelhart, G. E. Hinton and R. J. Williams, “Le arn -
ing Internal Representations by Error Propagation: Paral-
lel Distributed Processing, Vol. I ,” MIT Press, Cambridge,
1986, pp. 318-362.
[26] K. Hsu, H. V. Gupta and S. Sorooshian, “Artificial Neural
Network of the Rainfall-Runoff Process,” Water Resourc-
es Research, Vol. 31, No. 10, 1995, pp. 2517-2530.
Copyright © 2012 SciRes. JWARP