EFFICACY OF NEURAL NETWORK IN RAINFALL-RUNOFF MODELLING OF BAGMATI RIVER BASIN

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 9, Issue 11, November 2018, pp. 37–46, Article ID: IJCIET_09_11_003
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=10
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
©IAEME Publication Scopus Indexed
EFFICACY OF NEURAL NETWORK IN
RAINFALL-RUNOFF MODELLING OF
BAGMATI RIVER BASIN
Keshav Kumar
Ph.D. Research Scholar, Dept. of Civil Engg.,
National Institute of Technology Patna, Bihar, India
Vivekanand Singh
Professor, Dept. of Civil Engg.,
Thendiyath. Roshni
Asst. Professor, Dept. of Civil Engg.,
ABSTRACT
In this paper, rainfall-runoff model of Bagmati river basin has been developed
using the ANN Technique. Three-layered fced forward network structure with back
propagation algorithm was used to train the ANN model. Different combinations of
rainfall and runoff were considered as input to the network and trained by BP
algorithm with different error tolerance, learning parameter, number of cycles and
number of hidden layers. The sensitivity of the prediction accuracy to the number of
hidden layer neurons in a back error propagation algorithm was used for the study.
The monthly rainfall and runoff data from 2000 to 2009 of Bagmati river basin has
been considered for the development of ANN model. Performance evaluation of the
model has been done by using statistical parameters. Three sets of data have been
used to make several combination of year keeping in view the highest peaks of
hydrographs. First set of data used was from 2000 to 2006 for the calibration and
from 2007 to 2009 for validation. The second set of data was from 2004 to 2009 for
calibration and from 2000 to 2003 for validation. The Third set of data was from 2000
to 2009 for calibration and from 2007 to 2009 for validation. It was found that the
third set of data gave better result than other two sets of data. The study demonstrates
the applicability of ANN approach in developing effective non-linear models of
Rainfall-Runoff process without the need to explicitly representing the internal
hydraulic structure of the watershed
Key words: Rainfall-Runoff modelling, ANN Techniques Bagmati River, Neural
Network.

Keshav Kumar, Vivekanand Singh and Thendiyath. Roshni
Cite this Article: Keshav Kumar, Vivekanand Singh and Thendiyath. Roshni,
Efficacy of Neural Network in Rainfall-Runoff Modelling of Bagmati River Basin,
International Journal of Civil Engineering and Technology (IJCIET) 9(11), 2018, pp.
37–46.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=11
1. INTRODUCTION
The rainfall-runoff process is highly nonlinear, time varying, spatially distributed, and not
easily described by simple models. A considerable amount of research effort in the area of
hydrology during the past few decades has been devoted towards development of computer
based models of rainfall-runoff processes. A rainfall-runoff model is used to simulate the
hydrologic response of a catchment to rainfall input. The estimation of runoff from a
catchment is required for the purposes such as design of storage facilities to assess the flood,
assessment of water available for municipal, agricultural or industrial purposes, planning
irrigation operations, estimating future dependable water supplies for power generation, wild
life protection etc. Many rainfall-runoff models have been developed over the years. These
models can be broadly divided in three categories: Black box models, Conceptual models and
physically based models.
The Black box models are based on transfer functions which relate inputs with outputs
and generally do not have any physical basis. The success of these models can be attributed
mainly to simple mathematics, minimum computational requirements and acceptable results.
Conceptual models require large computation for calibrating the parameters involved.
Application of distributed models requires large quantity of data compared to lumped models
and large computer resources for successful implementation. The time required to construct
these models is enormous and thus an alternative modeling technique is needed when detailed
modeling is not required. The linear time series models such as ARMA (Auto Regressive
Moving Average) have been developed to handle such situations because they are relatively
easy to implement.
In recent years, Artificial Neural Networks (ANNs) have become very popular for
prediction and forecasting in a number of areas including finance, power generation,
medicine, water resources and environmental science. The main reason is that ANNs can
represent any arbitrary nonlinear function given sufficient complexity of the trained neural
network (Dawson and Wilby, 1998). ANNs can find relationship between different input
samples and can group samples in similar way to cluster analysis. ANNs are able to
generalize a relationship from small sample of data, are robust in the presence of noisy or
missing inputs and can learn in response to changing environments. ANNs have been applied
widely in various aspects of hydrology such as rainfall-runoff modelling, stream flow
forecasting, ground water modeling, water quality, water management policy, precipitation
forecasting, hydrological time series, and reservoir operations (ASCE, 2000a). ASCE (2000a,
2000b) reported the applications of ANN in hydrology and water resources. ANN models
provided better results when compared with other conceptual SAC-SMA (Sacramento soil
moisture accounting) model (Hsu et al., 1995), autoregressive models (Raman and
Sunilkumar, 1995), ARMAX model (Fernando and Jayawardena, 1998), Volterra type
Functional Series Model (Sajikumar and Thandaveswara, 1999), multiple regression models
(Thirumalaiah and Dco, 2000) linear and non-linear regressive model (Elshorbagy et al.,
2000), and Conceptual models(Tokar and Markus, 2000) Sudhir et al. (2001), Kumar et al.
(2008), Kaltech (2008), Solaimani (2009), Nourani et al. (2011), Nourani et al. (2014);
Asadnia et al. (2014) have used the ANN model for the rainfall-runoff studies. Sudhir et al.
(2001), used ANN technique with back propagation algorithm for the development of rainfall

Efficacy of Neural Network in Rainfall-Runoff Modelling of Bagmati River Basin
runoff model. The statistical properties of data series such as auto, partial and cross
correlation values were used to select and appropriate input vector for the model
development. Kumar et al. (2008) examined the effectiveness of the rainfall runoff modeling
with ANNs by comparing their results with AREVIA model and concluded that ANN could
provide more accurate discharge forecasts than the traditional mentioned model. Kaltech
(2008) has introduced the interpretation diagram, Garson's algorithm, and randomization
approaches to understand the relationship learned by ANN model. The results indicated that
ANNs are promising tools not only in accurate modeling of complex processes but also in
providing insight from the learned relationship. Solaimani (2009) has demonstrated the
application of the feed forward back propagation for the rainfall forecasting with various
algorithms with performance of multi-layer perceptions.
Rajkumar et al. (2002), Tayfur and Singh (2006), S M Chen et al. (2013), Chen and Liu
(2013) have used the ANN model for the flood estimation. Rajkumar et al. (2002) applied
ANN for modelling daily flows during monsoon flood events for a catchment in India using
daily rainfall data as input vector of the network model. Tayfur and Singh (2006) used three-
layered feed forward neural network using sigmoid function with back propagation algorithm
to forecast the runoff and compared with fuzzy inference method. S M Chen et al. (2013) used
ANN technique with feed forward Natural network with back propagation algorithm for
runoff estimation and compared with Conventional Regression Analysis (CRA). They found
that Feed Forward Back Propagation network (FFBP) gave superior result than Conventional
Regression Analysis (CRA). Chen and Liu (2013) developed artificial neural network models
using back propagation algorithm and compared with multi-linear regression (MLR) model.
They found that ANN model gave better result than multi-linear regression MLR) model.
The results of any model application depend upon the quality of input data. In
undeveloped and developing countries, one frequently encounters a situation the input data
are of poor quality and inconsistent. Typically rain gauge network is inadequate which means
that the spatial variation of rainfall is poorly represented Enough secondary information may
not be available to improve the quality of input data or to remove inconsistency. Nevertheless,
modeling has to be carried out for a variety of purposes such as river basin planning,
hydrologic design of projects, flood forecasting, etc. ANN models are built using the input
and output observations without the detailed understanding of the complex physical laws
governing the process under investigation. It is also able to provide reasonably accurate model
for the process under investigation, as a large number of the applications in hydrology along
with the comparison of their predictive performance with other methods (Kaltech, 2008). The
results of various ANN models indicate that ANNs can be powerful tools in modeling the
rainfall-runoff process for various time scale, topography, and climatic patterns.
2. STUDY AREA AND DATA USED
The Bagmati River is a perennial river of Nepal and India, particularly of North Bihar It
originates from the Shivpuri range of hills in Nepal at latitude 270
47' N and longitude 850
17'E, and 16 km North-East of Kathmandu at an elevation of 1500 m above MSL. The
Bagmati flows southwesterly for about ten kilometres along the Kathmandu Valley which is
predominately rice-patties in terraces up the slopes. A number of resistant rock strata interrupt
the flow down the valley, among these, is the outcrop that the Pashupatinath Temple is built
upon. After passing the temple, the river flows south across the plain where it is joined by the
larger Monahara River and turns westward. In Kathmandu the river flows past several
important places. The river mixes with the Vishnumati (Bishnumati) after a number of curves
enters the Chobar Gorge.

For this study, monthly rainfall data of 10 years i.e. from 2000 to 2009 at five rain gauge
stations namely Dheng, Kamtaul, Muzzafarpur, Benibag and Hayaghat in Bagmati river basin
have been used. Theisen polygons were drawn using these rain gauge stations to compute the
average depth of monthly rainfall. The discharge data measured at Hayaghat gauging site by
Central Water Commission (Central Water Commission) was used. These monthly rainfall
and runoff data were used to calibrate and validate the ANNs monthly model. Three sets of
data have been used for different combination of years. First set of data used is from 2000 to
2006 for the calibration and from 2007 to 2009 for validation. The second set of data is from
2004 to 2009 for calibration and from 2000 to 2003 for validation. The Third set of data is
from 2000 to 2009 for calibration and from 2007 to 2009 for validation.
3. METHODOLOGY
3.1. Artificial Neural Network Models
A typical ANN model consists of number of layers and nodes that are organized to a
particular structure. The commonly used neural network is three layered feed forward network
due to its general applicability to a variety of different problems (Hsu et al., 1995). The first
layer is input layer and its role is to pass the input variables onto the subsequent layers of the
network. The last layer consists of the output variables and is called as output layer. The
layers) in between the input and output layer are called as hidden layer(s) and the introduction
of this layer enhances the network's ability to model complex functions. The processing
elements in cach layer are called nodes. The information flow and processing in this network
is from input layer to hidden layer and from hidden layer to output layer. The number of
nodes in input and output layers is decided by the problem to be addressed. The number of
hidden layers and the number of nodes in each hidden layer are problem dependent and are
usually determined by a trial and error procedure. A synaptic weight is assigned to each link
to represent the relative connection strength of two nodes at both ends in predicting the input-
output relationship. The output yi of any node j, is given by






 
j
m
i
iij bWXfy
1
. (3.1)
where Xi is the input received at node j, W, is the input connection pat way weights, m is
the total numbers of inputs to node j, bj is the node threshold and function f is called an
activation function. It determines the response of a node to the total input signal it receives
and is given as the sigmoid function (Dawson and Wilby, 1998).
xe
xf


1
1
)( (3.2)
The characteristics of a sigmoid function are that it is bounded above and below, it is
monotonically increasing, and it is continuous and differentiable everywhere. Any nonlinear
process can be mapped using this sigmoidal function (ASCE, 2000a). Back propagation, the
most popular algorithm used for the training of the Feed Forward ANNs by Hsu et al., (1995)
and Burian et al., 2001), is used for training the ANN. In this process, each input pattern of
the training data set is passed through the network from the input layer to output layer. The
network output is compared with the desired target output, and an error is computed as
  
P P
i
t
i
yE 2
(3.3)
Where, P is the number of training patterns; ti is a component of the desired output T; p is
the number of output nodes; and yi is the relevant output of ANN.

This error is propagated backward through the network to each node, and correspondingly
the connection weights are adjusted based on the equation (ASCE, 2000a)
   1


 nw
w
E
nw ij
ij
ij  (3.4)
Where, )(nwij and )1(  nwij are weight increments between node i and j during nth and
(n-1)th epoch or pass.
Due to the boundation of the sigmoid function between 0 and 1, all input values should be
converted to the range between 0 and 1 before passing into a neural network (Smith and Eli,
1995). The output from the ANN should be denormalized to provide meaningful results.
Equation used to normalize the data set is
)()( b
i
Mina
i
Max
R
i
N i

 (3.5)
Where, Ni is the subsequent standardized value calculated for node i; Ri is the real value
applied to node i; Maxi is the maximum value of all values applied to node i; Mini is the
minimum value of all values applied to node i. The a and b are constants to define the range
of normalization.
3.2. Model Performance Evaluation Criteria
The performance of a model can be evaluated in terms of several characteristics. Root
mean square error (RMSE) and coefficient of correlation (R) are the numerical
performance indicators used to compare the models. They are defined as follows:
 
K
K
k
yt
RMSE



 1
2
(3.6)


22
)(
YT
TY
RncorrelatiooftCoefficien (3.7)
Where, t is the observed data; y is computed data; K is the number of observations;
yyY  in which y is the mean of the computed data and ttT  in which t is the mean
of the observed data.
To get the optimized structure for the neural network model, several combinations of
inputs were trained, but the best one is: rainfall (t-2), rainfall (t-I) and rainfall (t). In this case
the output neuron was runoff (t). It was noticed that the best convergence was achieved for the
above combination with the error tolerance, the learning parameter, neurons in hidden layer
and number of cycles as 0.1, 0.9, 9 and 9000 respectively. The coefficient of correlation was
0.910 and root mean square error (RMSE) was 119. Then the weights for this best trained
structure were frozen to evaluate the trained network. The weights for the best trained
network structure were collected from the training module of the Back Propagation simulator.
The monthly rainfall and runoff data were normalized and the data set of input vector was
prepared according to the best trained neural network structure. The runoff was computed
using this network and the weight vector for this trained network structure. The computed
runoff values were denormalized and compared with the observed runoff values.

4. RESULTS AND DISCUSSIONS
First of all, the first set of data used for the calibration is from the years 2000 to 2006 and for
the validation from the years 2007 to 2009 for the development of model. The calibration and
validation of first data set is shown in figure 4.1 and figure 4.2 respectively. From the
calibrated result of first set of data, it was found that all the peaks of the computed runoff
hydrograph were not matching well with the observed peaks. The coefficient of correlation
was 0.910 and RMSE was 119. The coefficient of correlation was good, but the root mean
square error was large.
Figure 4.1 Calibrated Results of the best combination of ANN by BP algorithm for 2000 to 2006.
Figure 4.2 Validation result of discharge by ANN model for 2007 to 2009
The model was validated with this set of data and it was found that all the peaks of the
computed runoff data are not matching with the observed peaks, but first computed peak is
nearly same whereas the second peak is high and there is slight lag in third observed peak.
This lag shows some error in the observed discharge data. The coefficient of correlation and
RMSE were 0.949 and 83 respectively. Coefficient of correlation was satisfactory and root
0
100
200
300
400
500
600
700
800
900
1000
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84
Discharge(cumec)
Time (months)
Observed Computed
0
100
200
300
400
500
600
700
800
900
1000
0 6 12 18 24 30 36
Discharge(cumec)
Time (months)
Observed Computed

mean square error was low, so the matching was not satisfactory in the validation period, and
the peaks of computed hydrograph were not matched well, so another set of data were used.
Model was then calibrated with the second set of data from the years 2004 to 2009 and for
the validation from the years 2000 to 2003. The calibration and validation of second data set
is shown in figure 4.3 and figure 4.4 respectively. It was found that again all the computed
peaks are not matching well but results are more closure to the observed peaks of runoff
hydrograph. The coefficient of correlation between the observed and computed runoff was
0.957 and root mean square error was correlation is high and the root mean square error is
also low.
In the case of validation, it was found that all the peaks of the computed runoff data were
not matching satisfactorily with the observed peaks. The coefficient of correlation was 0.896
whereas the RMSE was 119. Coefficient of correlation is satisfactory but root mean square
error is high. From the above two sets of data it was concluded that there was some problem
in the beginning stage of the data and that is why the RMSE were high, whereas the statistical
parameters show very good results in the last stage of the data. This may be due to the small
span of the data used due to non-availability.
Figure 4.4 Validation result of discharge by ANN model for 2000 to 2003
0
100
200
300
400
500
600
700
800
900
1000
0 6 12 18 24 30 36 42 48 54 60 66 72 78
Discharge(cumec)
Time(months)
Observed Computed
0
100
200
300
400
500
600
700
800
900
1000
0 6 12 18 24 30 36 42 48
Discharge(cumec)
Time (months)
Observed Computed

Then, third set of data from the years 2000 to 2009 and from the years 2007 to 2009 were
used for calibration and validation. The calibration and validation of third data set is shown in
figure 4.5 and figure 4.6 respectively. It was found that this set of data gave good result in
calibration as well as in validation as compared to the first two set of data. Figure 4.5 presents
the computed and observed hydrographs for calibration and Figure 4.6 presents the computed
hydrograph for validation. From Fig. 4.6, it can be seen that the calibrated peaks are more or
less same and coefficient of correlation was 0.915 and RMSE was 97. The coefficient of
correlation is satisfactory and the root mean square error is small. For validation, the
coefficient of correlation was 0.947 whereas RMSE was 81. Coefficient of correlation is again
satisfactory but root mean square error is little bit high. It was also observed that the matching
of the peaks was good in the validation period as compared to the earlier two set of data. The
finally the third set of data were used for the model development.
Figure Error! No text of specified style in document..6 Validation result of discharge by ANN model
for 2007 to 2009
0
100
200
300
400
500
600
700
800
900
1000
0 12 24 36 48 60 72 84 96 108 120
Discharge(Cumec)
Time (months)
Observed Computed
0
100
200
300
400
500
600
700
800
900
1000
0 6 12 18 24 30 36
Discharge(cumec)
Time (Months)
Observed Computed

5. CONCLUSIONS
In this study, an ANN model for the rainfall-runoff process was developed for Bagmati basin.
Three layered feed forward network structure was used to model the process. Back
propagation algorithm was used to train the ANN model. Fifteen different combinations of
rainfall and runoff were considered as input to the network and trained by BP algorithm with
different error tolerance, learning parameter, number of cycles and number of hidden layers. It
was observed from the training results that the combination of rainfall(t-2), rainfallt-1) and
rainfall(t) as input and runoffit) as output was the best combination compared to other
combinations with high coefficient of correlation and low root mean square error. In the
training of objective is to achieve a global minimum error on the whole length of the data.
Training the model with long record of data, which contain more extreme events, can reduce
the large variations in the statistical parameter. It was observed from the training and
validation results that ANNs are good in learning the underlying process in rainfall runoff
relationship. The study demonstrates the applicability of ANN approach in developing
effective non-linear models of Rainfall-Runoff process without the need to
explicitly representing the internal hydraulic structure of the watershed. However, the entire
study was based oi a short period of data. If a proper, longer data set is available, it will be
better to model rainfall-runoff processes for longer periods in seasonal and annual scales. The
phenomena can be modelled and studied for watersheds where rainfall and stage data are
measured directly and independently.
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