Journal of Water Resource and Protection, 2012, 4, 1024-1028 Published Online December 2012 (
Dual Artificial Neural Network for Rainfall-Runoff
Pallavi Mittal, Swaptik Chowdhury, Sangeeta Roy, Nikhil Bhatia, Roshan Srivastav
SMBS, Vellore Institute of Technology, Vellore, India
Received October 1, 2012; revised November 3, 2012; accepted November 14, 2012
One of the principal issues related to hydrologic models for prediction of runoff is the estimation of extreme values
(floods). It is well understood that unless the models capture the dynamics of rainfall-runoff process, the improvement
in prediction of such extremes is far from reality. In this paper, it is proposed to develop a dual (combined and paral-
leled) artificial neural network (D-ANN), which aims to improve the models performance, especially in terms of ex-
treme values. The performance of the proposed dual-ANN model is compared with that of feed forward ANN (FF-ANN)
model, the later being the most common ANN model used in hydrologic literature. The forecasting exercise is carried
out for hourly river flow data of Kolar Basin, India. The results of the comparison indicate that the D-ANN model per-
forms better than the FF-ANN model.
Keywords: Forecasting; Hybrid Model; ANN; Floods; Non Linear
1. Introduction
One of the most important topics in water resources de-
velopment and management is rainfall-runoff forecasting.
A future aspect of this modelling is to reduce flood risks
by providing a flood warning system which includes a
complex relationship between precipitation and runoff.
This complexity is occurred due to inconsistency of wa-
tershed characteristics, non uniformity in precipitation, as
well several other factors involved in runoff generation
where dominant ones are evaporation, infiltration, soil
moisture, overland flow and channel flow [1].
To enhance the understanding of rainfall-runoff proc-
ess a large number of studies conducted till now used
models developed either on physical deliberation (physi-
cal considerations) of the process or on the basis of a
theoretic approach (systems operation). In spite of pro-
viding appropriate accuracy, the implementation of such
models can generally result in different complications [2];
hence requiring ambiguous statistical implements, and
some extent of proficiency and experience with the
model. Usual theoretic models like autoregressive mod-
els and their variations [3] experiences from being based
on the linear systems theory and may only be slightly
appropriate in capturing the highly complex, vibrant, and
nonlinear rainfall-runoff process [4,5]. Hence due to the
complexity associated with parameter optimization in
nonlinear systems, the progress of nonlinear system
theoretic models are very restricted [6] and are not very
popular in terms of flood forecasting.
Recently the application of artificial neural networks
(ANNs) has marked an impact in the area of hydrological
modelling. ANNs are fundamentally semi-parametric
regression estimators which are well-matched for hydro-
logical modelling, as they can predict virtually any
(measurable) function up to a random degree of precision
[7]. Major benefit of this approach over previous meth-
ods is the lack of complexity in the statistical form rep-
resentation i.e. no precise process for algorithmically
converting an input to an output is required. The only
requirement of this network is a collection of representa-
tive examples for the required mapping. The ANN then
adapts itself to reproduce the desired output when acces-
sible with training model input. The demonstration of
neural network technology has provided many remarking
results in the area of hydrology and water resources
Drawback of this vast amount of network theory has
been indicated as their incapability of predicting extreme
values in the river flow [8-10] which has given rise to
record-breaking downpour and famine conditions. Imrie
et al. [11] argue that there may be a number of reasons
why ANN models are incapable of predicting extreme
values, and a range of remedies have been planned
This paper addresses this drawback of extreme value
forecast in ANN-based runoff flow modelling through
opyright © 2012 SciRes. JWARP
discussion of the probable causes, and thereby develop-
ing a new dual ANN (D-ANN) based rainfall-runoff
modelling. The performance of this proposed model is
illustrated by a real case study of Kolar basin, India. The
performance of the proposed D-ANN is compared with a
feed forward neural network (FF-ANN) model developed
for the same basin and is discussed in the following sec-
The subsequent paper is organised as follows. In Sec-
tion 2, proposed modelling framework is presented and
also a brief introduction on ANN. Following this, in Sec-
tion 3 the case study on Kolar basin is presented. Section
4 outlines the results and discussions of the present study.
Section 5 includes summary and conclusions of the pre-
sent study and scope for future work.
2. Model Development
In this section basic ANN framework has been discussed
which is followed by proposed methodology of D-ANN
2.1. Artificial Neural Networks
ANNs are highly simplified mathematical models and
computing techniques inspired by biological neural net-
works. It can be categorized as interconnected groups of
simple neurons that function as a combined system for
processing information and model complex relationships
between inputs and outputs by finding patterns in data.
The FF-ANN trained with the back propagation algo-
rithm is perhaps the most popular network for hydrologic
modelling [13,14]. This network topology which acts an
adaptive system consists of simple artificial nodes (neu-
rons) connected together by links to form a network of
nodes usually organized in a number of layers hence the
term artificial neural network. Weighted input from pre-
vious layer is received and processed output is transmit-
ted to following layer through links. Mostly ANNs have
three or more layers: an input layer for presenting data to
network, an output layer for producing an appropriate
response and intermediate (hidden) layer for collecting
feature detectors. Present study highlights on a model
back propagation algorithm for training, and the number
of hidden neurons is optimized by a trial and error proc-
ess. The basic structure of the ANN model is shown in
Figure 1.
Let y and be the actual and the predicted value of
ANN model respectively and are related by,
 (1)
is the residual error in the forecast of the run-
off value.
The predicted value of runoff y can be obtained from
the following general form of the ANN equation
Input LayerHidden Layer
yg hx
Figure 1. Structure of the feed forward ANN model.
xi is the input variables;
α is a weight connecting input node to hidden node;
β is a weight connecting hidden node to output node;
, φ are the biases at hidden and output nodes respec-
and g(), h() are the activation functions at hidden and
output layers respectively.
2.2. Proposed Dual-ANN Model
The main aim of a D-ANN model is to estimate the error
along with the predicted value. The general form of the
predicted value is given by
YfX (3)
X is an n-dimensional input vector consisting of vari-
ables x1···xi, ···, xn;
Y is a m-dimensional output vector consisting of re-
sultant variables y1···yi···ym.
In the current modelling vector X comprises of both
rainfall and runoff values at recurrent priory time lags
and the vector Y is usually the flow for a consecutive
period or at a different particular site.
Information is processed in D-ANN on the basis of
learning method which is a nonlinear alteration of link
weights so that the network can produce an approximate
output. In general, in this process the network changes its
structure and the strength of the existing matrix of nodal
weights is increased. Hence, the probability of achieving
similar outputs for same inputs increases. In addition to
develop a relation between the input vector and output
vector, it is suggested to use another subsequent rela-
tionship between the input variables and the errors from
the earlier network. The detail steps involved in dual-
ANN model are as follows.
Copyright © 2012 SciRes. JWARP
Copyright © 2012 SciRes. JWARP
7 1 2
 
Step 1: Compilation of the statistics of rainfall (R) and
the corresponding runoff (Q). The subsequent relation
can be derived,
as the model is tested using validation set. The cones-
quential hydrographs from the model is analyzed statis-
tically using an assortment of assessment measures. In
this study areal average value of rainfall data for three
upstream gauging stations have been used.
Step 2: Allotment of the patterns in the calibration data
set and the validation data set. Evaluation and estimation
of the predicted values and errors of the runoff values (of
calibration data set),
4. Results and Discussions
7 1 2
 
As discussed previously, the performance of the pro-
posed D-ANN model is compared with a FF-ANN model
for forecasting the runoff of Kolar River at a lead time of
1 hour. The results of the study are discussed in detail in
the following paragraphs.
where, ε-Value of Error, y-Observed value of runoff and
-redicted value of runoff.
Step 3: Development of the relation,
fR R
(6) One of the most important steps in the ANN hydro-
logical model development is determination of signifi-
cant input variables which requires prior knowledge and
generating an analytical approach of cross correlation to
find the dependence (linear) between these variables
[6,17,18]. The foremost drawback related with this
method is that the correlation can be nonlinear but it is
only capable of identifying linear dependency between
two variables. The present study uses a statistical ap-
proach of data series which is based on the scrutiny that
the input variables analogous to different time lags can
be acknowledged using cross correlations, autocorrela-
tions and partial autocorrelations. To certify good over-
view by ANN model, many associations between
weighted inputs and output samples have been recom-
mended in the literature [19]. The input variables se-
lected in this study are R(t 9), R(t 8), R(t 7), Q(t 2)
and Q(t 1), where R and Q represent the rainfall and
runoff values, respectively at time “t”. The hidden nodes
are identified by various trials.
Now an additional model is trained, to estimate the
value of error corresponding to the predicted runoff, the
value of
. After validating the model, D-ANN can be
used for the forecast of the runoff value () associated
to the specified inputs using the relation,
Figure 2 illustrates the methodology of the D-ANN
3. Case Example
The application of the proposed D-ANN model is carried
out on a real case study on Kolar river basin, in India
(Figure 3). The Kolar basin is a descendant of the river
Narmada. The basin has a total drainage area of about
1350 km2 which constitutes an area of 903.87 km2 lies
between north latitude 21˚90' - 23˚17' and east longitude
77˚10' - 77˚29'. The climate of the basin is humid and
landscape of the Kolar basin is hilly consisting of mainly
black soil. The basin can be divided into three distinct
zones: low land areas, hilly slopes or semi hilly areas,
and upland or hilly areas.
The performance of the proposed D-ANN model is
compared with that of the feed-forward neural network
by means of a variety of statistical criteria coefficient of
correlation (R), coefficient of efficiency (E), Root-mean-
square error (RMSE) between the calculated and com-
puted flow values. The statistics of the above criteria for
D-ANN and FF-ANN model is presented in Table 1.
Data are collected during monsoon season during
years 1987 to 1989. This available data is divided into
two sets, calibration set (data during years 1987-1988)
and validation set (data during year 1989). Parameters of
the model are obtained using calibration data set where
Input Values
987 1
ttt t
 
Model 1 Model 2
Values of ε
and ε
Estimation of the values of
Estimation of the values of
Values of
Estimation of the values of
Figure 2. Methodology of D-ANN.
Figure 3. Map of Kolar Basin [15].
Table1. Statistical indices—comparison between D-ANN
and FF-ANN model.
Coefficient of
correlation (R) 0.99 0.99
Coefficient of efficiency (E) 0.98 0.98
Error (RMSE) 27.16 23.24
1E (9)
RMSE (10)
where y and be the actual and the predicted value of
ANN model respectively.
It is observed from the Table 1 that performance of
both the models in terms of statistical indices is very
similar and satisfactory. The correlation statistics, for
evaluating the linear correlation between the observed
and predicted runoff, is persistent for all models during
calibration as well as validation period. While evaluating
capability of the model for predicting runoff values away
from the mean, efficiency of both the models is found to
be greater than 90%, which according to Shamseldin [20]
is very reasonable. Similarly RMSE statistic for indicat-
ing quantitative measure of the model error in units of
the variable was also found good for all models as is
Figure 4. Model computed flows for a typical event during
validation showing historical flows and predicted flows
from D-ANN and FF-ANN.
evidenced by the low values. Further, it can be observed
from Figure 4 that both the models are able to predict the
flows. However, it is observed (Figure 4) that the
D-ANN model is able to predict the peak flows better
than the FF-ANN model. In general it is observed that
the D-ANN model although has a similar statistical per-
formance in comparison to FF-ANN, it outperforms the
later in terms of prediction of high flows.
5. Summary and Conclusion
This paper presents a dual-ANN model to improve the
performance of the model in terms of prediction of high
flows. The performance of the model is compared with
that of the feed-forward ANN model in terms of statisti-
cal indices such as coefficient of correlation, coefficient
of efficiency and root means square error. The exercise
was carried out for the hourly data in Kolar river basin,
India. It is observed that the proposed D-ANN model and
the FF-ANN model show similar performances in terms
of statistical indices. However, the D-ANN model out-
performs the FF-ANN model in prediction of high flows
(extremes). The performance of the D-ANN models has
to be tested on various time scales. Further extensions of
this model can be examined to improve the forecasting
6. Acknowledgements
The authors thank the Vellore Institute of Technology
Vellore, India, for providing the necessary facilities to
carry out this research work.
[1] K. J. Beven, “Rainfall-Runoff Modelling: The Primer,”
Copyright © 2012 SciRes. JWARP
John Wiley, Hoboken, 2000.
[2] Q. Duan, S. Sorooshian and V. K. Gupta, “Effective and
Efficient Global Optimization for Conceptual Rainfall
Runoff Models,” Water Resources Research, Vol. 28, No.
4, 1992, pp. 1015-1031.
[3] G. E. P. Box and G. M. Jenkins, “Time Series Analysis:
Forecasting and Control,” Holden Day Inc., San Fran-
cisco, 1976.
[4] A. Jain, and S. Srinivasulu, “Development of Effective
and Efficient Rainfall-Runoff Models Using Integration
of Deterministic, Real-Coded Genetic Algorithms and
Artificial Neural Network Techniques,” Water Resources
Research, Vol. 40, No. 4, 2004, Article ID: W04302.
[5] R. K. Srivastav, K. P. Sudheer and I. Chaubey, “A Sim-
plified Approach to Quantifying Predictive and Paramet-
ric Uncertainty in Artificial Neural Network Hydrologic
Models,” Water Resources Research, Vol. 31, No. 10,
2007, pp. 2517-2530.
[6] K. Hsu, V. H. Gupta and S. Sorooshian, “Artificial Neural
Network Modelling of the Rainfall-Runoff Process,” Wa-
ter Resources Research, Vol. 31, No. 10, 1995, pp. 2517-
2530. doi:10.1029/95WR01955
[7] K. Hornik, M. Stichcombe and H. White, “Multi Layer
Feed forward Networks Are Universal Approximators,”
Neural Networks, Vol. 2, 1989, pp. 359-366.
[8] A. W. Minns and M. J. Hall, “Artificial Neural Networks
as Rainfall-Runoff Models,” Journal of Hydrology Sci-
ence, Vol. 41, No. 1, 1996, pp. 399-417.
[9] C. W. Dawson and R. Wilby, “An Artificial Neural Net-
work Approach to Rainfall Runoff Modelling,” Hydro-
logical Science, Vol. 43, No. 1, 1998, pp. 47-66.
[10] M. Campolo, P. Andreussi and A. Soldati, “River Flood
Forecasting with a Neural Network Model,” Water Re-
sources Research, Vol. 35, No. 4, 1999, pp. 1191-1197.
[11] C. E. Imrie, S. Durucan and A. Korre, “River Flow Pre-
diction Using Artificial Neural Networks: Generalization
beyond the Calibration Range,” Journal of Hydrology,
Vol. 233, 2000, pp. 138-153.
[12] N. Karunanithi, W. J. Grenney, D. Whitley and K. Bovee,
“Neural Networks for River Flow Prediction,” Journal of
Computing in Civil Engineering, Vol. 8, No. 2, 1994, pp.
201-220. doi:10.1061/(ASCE)0887-3801(1994)8:2(201)
[13] ASCE Task Committee, “Artificial Neural Networks in
Hydrology-I: Preliminary Concepts,” Journal of Hydro-
logic Engineering, Vol. 5, No. 2, 2000, pp. 115-123.
[14] ASCE Task Committee, “Artificial Neural Networks in
Hydrology-II: Hydrologic Applications,” Journal of Hy-
drologic Engineering, Vol. 5, No. 2, 2000, pp. 124-137.
[15] P. C. Nayak, K. P. Sudheer, D. M. Rangan and K. S.
Ramasastri, “Short-Term Flood Forecasting with a Neu-
rofuzzy Model,” Water Resources Research, Vol. 41,
2005, Article ID: W04004. doi:10.1029/2004WR003562
[16] G. J. Bowden, G. C. Dandy and H. R. Maier, “Input De-
termination for Neural Network Models in Water Re-
sources Applications: 1. Background and Methodology,”
Journal of Hydrology, Vol. 301, No. 1-4, 2004, pp. 75-92.
[17] G. J. Bowden, G. C. Dandy and H. R. Maier, “Input de-
termination for Neural Network Models in Water Re-
sources Applications: 2. Background and Methodology,”
Journal of Hydrology, Vol. 301, No. 1-4, 2004, pp. 93-
107. doi:10.1016/j.jhydrol.2004.06.020
[18] 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, 1325-1330.
[19] H. R. Maier and G. C. Dandy, “Neural Networks for the
Prediction and Forecasting of Water Resources Variables:
A Review of Modelling Issues and Applications,” Envi-
ronmental Modelling & Software, Vol. 15, No. 1, 2000,
pp. 101-124. doi:10.1016/S1364-8152(99)00007-9
[20] A. Y. Shamseldin, “Application of a Neural Network
Technique to Rainfall-Runoff Modelling,” Journal of
Hydrology, Vol. 199, No. 3-4, 1997, pp. 272-294.
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