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RAINFALL—RUNOFF MODELLINGUSING ARTIFICIAL NEURALNETWORKSP. Mallikarjuna M.ISH a , C. H. Suresh Babu b & A.Jagan Mohan Reddy ca Dept. of Civil Engineering , S. V. U College ofEngineering , Tirupati , A.P. , 517502b Dept. of Civil Engineering , N. B. K. R. Institute ofScience & Technology , Vidyanagar , A.P. , 524413c S. V. U. College of Engineering , Tirupati , A.P. ,517502Published online: 07 Jun 2012.

To cite this article: P. Mallikarjuna M.ISH , C. H. Suresh Babu & A. Jagan Mohan Reddy(2009) RAINFALL—RUNOFF MODELLING USING ARTIFICIAL NEURAL NETWORKS, ISHJournal of Hydraulic Engineering, 15:1, 24-33, DOI: 10.1080/09715010.2009.10514928

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THE INDIAN SOCIETY FOR HYDRAULICS JOURNAL OF HYDRAULIC ENGINEERING

VOL. 15, (I)

RAINFALL- RUNOFF MODELLING USING ARTIFICIAL NEURAL NETWORKS

by

P. Mallikarjuna1, M.ISH, C. H. Suresh Babu2 and A. Jagan Mohan Reddy3

ABSTRACT

Runoff simulation and forecasting is essential for planning, designing and operation of water resources projects. In the present study, the rainfall - runoff process is modelled by coupling simple time- series (STS) and linear autoregressive (ARX) models with Artificial Neural Networks (ANN). The study uses the monthly data at Keesara. Damarcherla and Madhira gauging sites of Krishna basin. The study reveals that the performance of ANN model in the simulation and forecasting of monthly runoff during monsoon period can be improved considerably by including the residuals derived from STS and ARX models as additional inputs together with rainfall.

KEYWORDS : Simple time-series model, Linear autoregressive model, Artificial neural network, Combination, Performance evaluation.

INTRODUCTION

Accurate estimation of runoff in streams is essential for the development, regulation and efficient management of water resources for different activities such as .irrigation, water supply, hydropower development, land drainage and flood control. The process of transformation of rainfall into runoff over a catchment is complex, nonlinear and exhibits both temporal and spatial variability. The models developed to simulate the process can be categorized as empirical black- box, conceptual and physically based distributed models. However, these models fail to represent the inherent nonlinear dynamics in the process of rainfall - runoff transformation. The Artificial Neural Network (ANN) technique which is capable of representing complex nonlinear process has been applied in the recent years, as a successful tool, in the rainfall - runoff modelling.

A number of researchers have investigated the capability of artificial neural

l. Professor, Dept. of Civil Engineering, S. V. U College of Engineering, Tirupati (A.P) -517502

2. Associate Professor, Dept. of Civil Engineering, N. B. K. R. Institute of Science &Technology, Vidyanagar (A.P)-524413

3. M.Tech. Student, S. V. U. College of Engineering, Tirupati (A.P) -517502.

Note: Written discussion of this paper will be open until 30th June 2009.

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networks in the rainfall - runoff modelling process (Halff et al. 1993, Zhu et al. 1994, Karunanithi et al. 1994, Smith and Eli 1995. Hsu et al. 1995, Minns and Hall 1996, Jayawardena and Fernando 1996, Shamseldin, 1997, Fernando and Jayawardena 1998, Dawson and Wilby 1998, Tokar and Johnson 1999, Campolo et al. 1999, Sajikurnar and Thandaveswara 1999, Tokar and Markus 2000, Thirumalaiah and Deo 2000. Imrie et al. 2000, Elshorbagy 2000, Zhang and Govindaraju 2000, Birkundavyi et al. 2002, Rajurkar et al.· 2004, Senthil kumar et al. 2005, Wu et al. 2005, Nilsson et al. 2006, Garbrecht 2005 and Archama Sarkar et al. 2006).

In most of the recent rainfall -runoff modelling studies, the ANN was used as an independent model and its performance was compared with the other conventional models. The present study aims to apply the combination of empirical models such as simple linear time - series (STS) and linear autoregressive (ARX) with ANN models to enhance the forecasting ability of ANN models in the simulation and prediction of monthly runoff during monsoon period (June to December) at Keesara, Damarcherla and Madhira gauging sites of Krishna basin.

DESCRIPTION OF STUDY AREA AND DATA

The stream gauging sites selected for the present study are Keesara, Damarcherla and Madhira of Krishna basin. The locations of influencing rain gauge stations and gauging sites are shown in Fig. 1. A brief description of the gauging sites is presented in Table 1.

TABLE-1

BRIEF DESCRIPTION OF GAUGING SITES

Gauging site Latitude Longitude Catchment Mean monthly Mean monthly area rainfall during runoff during (kml) monsoon monsoon

period (em) period (Mm3)

Keesara 16°42' N 80019' E 688.75 13.80 261.82

Damarcherla 16°45' N 7go53' N 236.50 11.83 98.18

Madhira 16°50' N 80029' N 203.50 14.69 81.17

The monthly rainfall data during monsoon period at rain gauge stations influencing the catchments of gauging sites for the period 1985- 1999 were collected from the Irrigation department, A.P. The average monthly rainfall during monsoon period over these catchments has been computed using Thiessen polygon method. The corresponding monthly runoff data for the period at gauging sites were obtained from the Central Water Commission (CWC).

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FIG. 1 INDEX MAP OF STUDY AREA

METHODOLOGY

The combination of the following models is adopted in the present study.

SIMPLE TIME-SERIES MODEL (STS)

The model is generally expressed as simple equation based on summation components as

m m

R, = C + L a; Pt-i+t + L b;R,_; (1) i=l i=l

where a. and b. are empirical parameters and P and R are rainfall and runoff in the I I , t t

time period 't'.

In this model, P1

and R1•

1 are only considered for the present study.

LINEAR AUTOREGRESSIVE MODEL (ARX)

The discrete linear autoregressive model structure is generally expressed as

m m

R, + L a;R,_; = L /3;P,-; + e, (2) i=l i=l

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PERFORMANCE EVALUATION CRITERIA

The evaluation criteria used in the present study are coefficient of determination (R2), root mean square error (RMSE). efficiency coefficient (EC) and volumetric error (EV).

COEFFICIENT OF DETERMINATION (R2)

It is the square of the correlation coefficient (R) and the correlation coefficient is expressed as

n

L(Yi- y)(yi- y) R = i=l xiOO

~ t<Yi -y) 2 t<Yi -y) 2]

112

L •=I 1=1

(3)

where, Y; and Y; are the observed and predicted values respectively and, y and Y; are the means of observed and predicted values.

ROOT MEAN SQUARE ERROR (RMSE)

It yields the residual error in terms of the mean square error expressed as (Yu, [1994]).

I (yi- Y; )2

RMSE= _i=_l ___ _ (4) 1l

where , n = number of observations.

EFFICIENCY COEFFICIENT (EC)

It is used to assess the performance of different models (Nash and Sutcliffe, 1970). It is a better choice than RMSE statistic when the calibration and verification periods have different lengths (Liang et al., 1994 ). It is expressed as

EC+-:, }100 (5)

n n

where, F0

= L (Y; - Y) 2 and F = L (Y;- Y; )2

i=l i=l

A value ofEC of90% generally indicates a very satisfactory model while a value

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in the range 80-90%, a fairly good model. Values of EC in the range 60-80% would indicate an unsatisfactory model fit.

VOLUMETRIC ERROR (EV)

It is an absolute prediction error (Yu, [1994] ) expressed as

(6)

The negative EV value indicates underestimation of the output variable.

RESULTS AND DISCUSSION

The runoff at each of the gauging sites has been estimated using STS, ARX and ANN models independently. Evidently the runoff predicted from ANN has yielded fairly good results. These results have then been refined using the residuals, regressors and runoffs estimated from STS and/or ARX models as additional inputs. The runoff values predicted using ANN models with residuals derived and runoffs predicted from STS and ARX models as additional inputs compared well with the observed values. As the improvement in the performance of ANN models when the residuals derived from STS and ARX models are used as additional inputs is more significant, these results are only presented in this paper. The performance indices of ANN models with different inputs are presented in Table 2. ANN 1, ANN2 and ANN3 models simulate the runoff at Keesara, Damarcherla and, Madhira gauging sites respectively with only rainfall as the input variable. ANN 4, ANN 5 and ANN 6 simulate the runoff at the gauging sites with residuals derived from STS model as additional input. ANN 7, ANN 8 and ANN 9 simulate the runoff with an additional input of residuals derived from ARX model. ANN 10, ANN 11 and ANN 12 models use the inputs of rainfall and residuals derived from both STS and ARX models. Ten years' data (1985 - 1994) have been used for calibration and the rest (1995- 1999) for verification of the models.

It may be observed from the results presented in Table 2 that the performance of ANN models with rainfall as the input in terms of R2 and EC is fairly good. EV values indicate either overestimation or underestimation of runoff. The possible reason for this tendency in the ANN is due to small number of low and high values in the time series during the monsoon period that it makes is more difficult for the network to learn such events. However the performance has improved considerably and satisfactorily with additional inputs of residuals derived from STS and ARX models. The R.\1SE has also reduced significantly. Figures 2 and 3 show the scatter and

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comparison plots of observed and predicted runoff values for the ANN 10, ANN 11 and ANN 12 models for the testing period. Theses models which considered the additional inputs of residuals derived from STS and ARX models depict the closeness of the values and thereby reflect the appropriateness of the modelling technique.

TABLE-2

PERFORMANCE INDICES OF ANN MODELS

Model Training data set Testing data set

R2 RMSE EC EV R2 RMSE EC EV (Mm3/month) (Mm3/month)

ANN1 0.88 125.66 88.30 -0.21 0.79 160.47 79.20 +35.20 (1,2,1)

ANN2 0.87 48.06 87.50 -8.72 0.78 67.75 78.65 -13.28 (1,2,1)

ANN3 0.76 55.96 76.23 -2.03 0.70 44.53 70.62 +17.66 (1,2,1)

ANN4 0.98 48.65 98.25 -1.16 0.95 77.02 95.26 +11.82 (2,4,1)

ANN5 0.89 44.74 89.20 -8.96 0.87 52.22 87.02 -12.65 (2,4, 1)

ANN6 0.82 48.62 82.06 -1.71 0.67 47.91 66.75 +8.57 (2,4,1)

ANN7 0.97 63.47 97.20 +7.42 0.94 85.87 94.20 +11.01 (2,4, I)

ANN8 0.86 53.61 85.62 -4.79 0.85 56.91 84.50 -7.95 (2,4,1)

ANN9 0.82 48.79 82.20 +1.79 0.66 48.37 66.10 +6.94 (2,4, 1)

ANN10 0.99 39.47 98.85 -0.22 0.97 66.41 97.40 +8.38 (3,6,1)

ANNll 0.94 34.94 93.68 -7.42 0.91 42.98 91.44 -16.01 (3,6, 1)

ANN12 0.90 36.88 89.73 -4.08 0.86 31.33 85.66 +9.02 (3,6, 1)

This may be due to the fact that the residuals derived from STS and ARX models which exhibit the nonlinearity present in the rainfall-runoff process reinforce the

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l~r-------------------~ Glluglng tn•' KHUU

1200 ModeU,HN10

200

0~------------------~ 0 200 ~ 600 800 1000 IZOO 1.oiX

Obsuwd Runolf(Mm 'h11Qr1111J

Gauging llll!:l•llldhll'a Moxl>ei:AnN12

0~~--------------~ 0 100

OIIMIVK Runo"!Mm"'month)

VOL. 15. (I l

FIG. 2 SCATTER PLOTS OF OBSERVED AND PREDICTED RUNOFFS DURING TESTING PERIOD

,,.XI 1m

E !! 1()00

J fiOO ~

l flOO t:

~ ~ .. :00

c

o. :~~o

--~J ......... .,_,.,.,

4 7 l·C 'l >f) 19 1Z 45 l·~ ~~ M

Mlonlto

~r-----------------~ •:iiAc~ ~ .. Lt,.,. .. it ---~,.~ "'·-Pr~•,.y.J

1 4 1 ~0 13 Ui 19 :2 ~e; ~~ l~ 34 Jt -

_.._,~I'Jr.¢

~~<ott)(ldf!:!tj:

FIG. 3 COMPARISON OF OBSERVED AND PREDICTED RUNOFFS DURING TESTING PERIOD

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input to yield satisfactory model output. This modelling technique not only improves the performance but also completes the process with less computational effort (only 100 epochs used). Therefore, the ANN models coupled with STS and ARX models with inputs of rainfall, residuals from STS model and residuals from ARX model can be adopted for the simulation and forecasting of monthly runoff at the gauging sites of Krishna basin.

CONCLUSIONS

ANN model coupled with simple time - series and linear autoregressive models for rainfall -runoff modelling at Keesara. Damarcherla and Madhira gauging sites of Krishna basin is presented. The residuals derived from STS and ARX models are used as additional inputs along with rainfall to improve the performance of ANN model. The results obtained based on the performance evaluation criteria indicate that the ANN model coupled with STS and ARX models can be used satisfactorily in the simulation and forecasting of runoff.

ACKNOWLEDGEMENT

The authors are thankful to the authorities of S. V. University for the facilities provided during the investigation.

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