Dual Artificial Neural Network for Rainfall-Runoff Forecasting

doi:10.4236/jwarp.2012.412118

Paper Menu >>

Journal Menu >>

Journal of Water Resource and Protection, 2012, 4, 1024-1028

http://dx.doi.org/10.4236/jwarp.2012.412118 Published Online December 2012 (http://www.SciRP.org/journal/jwarp)

Dual Artificial Neural Network for Rainfall-Runoff

Forecasting

Pallavi Mittal, Swaptik Chowdhury, Sangeeta Roy, Nikhil Bhatia, Roshan Srivastav

SMBS, Vellore Institute of Technology, Vellore, India

Email: [email protected]

Received October 1, 2012; revised November 3, 2012; accepted November 14, 2012

ABSTRACT

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

model.

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

[6,12].

This paper addresses this drawback of extreme value

forecast in ANN-based runoff flow modelling through

P. MITTAL ET AL. 1025

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-

tions.

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

model.

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)

where,



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

Output

Layer

ˆ+

iii

yg hx

Figure 1. Structure of the feed forward ANN model.

























 (2)



where,

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-

tively;

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)

where

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.

P. MITTAL ET AL.

1026



7 1 2

,,,

ttt

RQQ

 

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.

ttt

QfRR



 (4)

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

ttt

RQ Q

 

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.

(5)

where, ε-Value of Error, y-Observed value of runoff and

-redicted value of runoff.

Step 3: Development of the relation,



ttt

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,

ˆˆ





(7)

Figure 2 illustrates the methodology of the D-ANN

pictorially.

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

RRRQ

 

and



Model 1 Model 2

Values of ε

and ε

Estimation of the values of



Values of

Estimation of the values of

Figure 2. Methodology of D-ANN.

P. MITTAL ET AL. 1027

Figure 3. Map of Kolar Basin [15].

Table1. Statistical indices—comparison between D-ANN

and FF-ANN model.

D-ANN FF-ANN

Coefficient of

correlation (R) 0.99 0.99

Coefficient of efficiency (E) 0.98 0.98

Root-Mean-Square

Error (RMSE) 27.16 23.24



















ˆˆ





 













(8)











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

accuracy.

6. Acknowledgements

The authors thank the Vellore Institute of Technology

Vellore, India, for providing the necessary facilities to

carry out this research work.

REFERENCES

[1] K. J. Beven, “Rainfall-Runoff Modelling: The Primer,”

P. MITTAL ET AL.

1028

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.

doi:10.1029/2003WR002355

[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.

doi:10.1029/1998WR900086

[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.

doi:10.1016/S0022-1694(00)00228-6

[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.

doi:10.1061/(ASCE)1084-0699(2000)5:2(115)

[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.

doi:10.1061/(ASCE)1084-0699(2000)5:2(124)

[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.

doi:10.1016/j.jhydrol.2004.06.021

[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.

doi:10.1002/hyp.554

[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.

doi:10.1016/S0022-1694(96)03330-6