Rainfall-Runoff Model Using.pdf

8/12/2019 Rainfall-Runoff Model Using.pdf

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vailable onl ine at www sciencedirect corn M A T H E M A T I C A LAND8 C I n N C E ~ D I FI E (~'11" OMPUT ER

M O E L L I N GMathemat ica l and Computer Model l ing 40 (2004) 839-846 w w w . e l s e v i e r . c om/ l oc a t e / mc m

R a i n f a l l R u n o f f M o d e l U s i n ga n A r t i f i c i a l N e u r a l N e t w o r k A p p r o a c hS . R I A D A N D J . M A N I AU n i v e rs i t4 d e s S c ie n c es e t T e ch n o l o g ie s d e L i ll e - U S T L - L M L - E P U L . U M R C N R S 8 1 0 7

E c o l e P o l y t e c h n i q u e U n i v e r s i t a i r e d e L i l l e , D 6 p a r t e m e n t d e g ~ o t e c h n i q u e e t g 6 n i e c i v i lC i t ~ s c i e n t i f i q u e , A v e n u e P a u l L a n g e v i n , 5 9 6 5 5 V i l l e n e u v e d ' A s c q C e d e x , F r a n c e polyt ech-lille fr rsouad_ 2OO4ya hoo fr

L BOUCH OUU n i v e r s i t 6 I b n Z o h r , F a c u l t ~ d e s s c i e n c e s , D 6 p a r t e m e n t d e G 6 o l o g i eL a b o r a t o i r e d e G ~ o lo g ie A p p li q u 6 e e t G ~ o e n v i r o n n e m e n t ( G . A . G . E )E q u i p e d ' H y d r o g ~ o l o g ie , B P 2 8 / S , 8 0 0 0 0 A g a d i r, M a r o cB o u c h a o u l c a r a ~ a i l . co m

Y . N A J J A RK a n s a s S t a t e U n i v e r s i t y D e p a r t m e n t o f C i v i l E n g i n e e r i n g

M a n h a t t a n K S 6 6 5 0 5 U . S . A .e a 4 1 4 6 k s u e u

Received March 2003; revised and accepted October 2003)A b s t r a c t - - T h e u se o f a rt if ic ia l ne u r a l ne t w orks ( A N N s) i s be c omi ng i nc re as ing ly c om mon in t heana lys i s of hydro logy and wate r resources problems . In th i s research , an A NN w as deve loped and usedto m ode l the ra infa l l - runoff re la tionship , in a ca tchme nt loca ted in a semiar id c l imate in M orocco.Th e m ul t i layer percept ron (ML P) neura l ne twork was chosen for use in the cur rent s tudy. Th e resul t sand com para t ive s tudy indica te tha t the a r t if ic ia l neura l ne twork m ethod i s mo re su i t able to predic triver runo ff th an classical regression mod el. (~) 2004 Elsevier Ltd. All righ ts reserved.K e y w or d s - - R a i n f a l l - r u no f f , C a t c hme n t , S emi ar id c l ima te , M L P , M ode ll ing , A rt if ic ia l ne u r a l ne t -work, Multiple regression, Morocco.

1 I N T R O D U C T I O NT h e A N N s m o d e l s a r e p o w e r f u l p r e d i ct i o n t o o l s fo r t h e r e l a t io n b e t w e e n r a in f a ll a n d r u n o f fp a r a m e t e r s . T h e r e s u l ts w i ll s u p p o r t d e c i s io n m a k i n g i n th e a r e a o f w a t e r r e s o u r ce s p l a n n i n g a n dm a n a g e m e n t . B e s id e s , t h e y a s si st u r b a n p l a n n e r s a n d m a n a g e r s u n d e r t a k e t h e n e c e s s a r y m e a s u r e st o fa c e t h e b a d p r e d i c t i o n s . T h u s , t h e y h e lp a v o i d l o ss e s i n p u b l i c a n d p r i v a t e p r o p e r t i e s , a n dh e a l t h a n d e c o l o g i c a l h a z a r d s t h a t a r e l ik e l y t o o c c u r d u e t o f l o o d i n g .

M o r e o v e r , t h e A N N m o d e l s h a v e b e e n u s e d i n c r e a s i n g l y i n v a r i o u s a s p e c t s o f s c i en c e a n d e n -g i n e e ri n g b e c a u s e o f i ts a b i l i ty t o m o d e l b o t h l in e a r a n d n o n l i n e a r s y s t e m s w i t h o u t t h e n e e d t om a k e a n y a s s u m p t i o n s a s a r e im p l i c it i n m o s t t r a d i t i o n a l s t a t i s t i c a l a p p r o a c h e s . I n s o m e o f t h eh y d r o l o g i c p r o b l e m s , A N N s h a v e a l r e a d y b e e n s u c c e s s fu l l y u s e d f o r r i v e r f lo w p r e d i c t i o n [ 1 -8 ] ,089 5-71 77/0 4/ - see front m at te r (~) 2004 Elsevier Ltd. All r ights reserved. Ty pe set by .Ah/tS-TEXdoi:10.1016/j.mcm.2004.10.012


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840 S RIAD et al

for rainfall-runoff process [9-11], for the prediction of water quality parameters [12] and for char-acterizat ion of soil pollu tion [13]. In addition, ANNs are applied for prediction of evaporation [14],for rainfa ll-runoff forecasting [15-19], for predict ion of flood disas ter [20], and for river flow timeseries prediction [21].

In these hydrological applications, a multilayer feed-forward backpropagation algorithm isused [22]. It usually is composed of a large number of interconnected nodes, arranged in aninput layer, an ou tpu t layer, and one or more hidden layers. The t ransfer function selected forthe network was the sigmoid function.

The aim of this paper is to model the rainfall-runoff relationship in the Ourika catchmentlocated in semiarid climate in Morocco using a black box type model based on ANN methodology.

2 T H E A R T I F I C I A L N E U R A L N E T W O R K S A P P R O A C H

2.1. Overview of AN NThe ANN technology is an alternate computational approach inspired by studies of the brainand nervous systems [23]. It is based on theories of the massive interconnection and parallel

processing architecture of biological neural systems. The main theme of ANN research focuseson modelling of the brain as a parallel computational device for various computational tasks t hatwere performed poorly by traditional serial computers.

ANNs have a number of interconnected processing elements PEs) t ha t usually operate inparallel and are configured in regular architectures. The collective behavior of ANN, like ahuman brain, demonstrates the ability to learn, recall, and generalize from training patterns ordata. The advantage of neural networks is they are capable of modelling linear and nonlinearsystems.

In the present study, we use an MLP trained with a backpropagation algorithm to predict thedrainage basin runoff. The MLP consists of an input layer consisting of node s) represent ingvarious input variable s), the hidden layer consisting of many hidden nodes, and an output layerconsisting of ou tput variable s). The input nodes pass on the input signal values to the nodesin the h idden layer unprocessed. The values are dist ributed to all the nodes in the hidden layerdepending on the connection weights W~j and jk [24-26] between the input node and the hiddennodes. Connection weights are the interconnecting links between the neurons in successive layers.Each neuron in a certain layer is connected to every single neuron in the next layer by links havingan appropriate and an adjustable connection weight.

We ight sA Wi ~ W e i g h t so ti 6

P t ~Input la y e r idde n la y e r O ut put la y e r

Input Neuron Outputt ~ ) ~

X.S

Figure 1 Archi tectur e of the neural network model used in this study


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Rainfa ll-Runof f Model 841

T h e a r c h i t e c t u r e o f t h e n e u r a l n e t w o r k u s e d in th i s s t u d y a n d t h e s c h e m a t i c r e p r e s e n t a t i o no f a n e u r o n a r e s h o w n i n F i g u r e 1 . E a c h n o d e j r e c ei v e s i n c o m i n g s i g n a l s f r o m e v e r y n o d e i i nt h e p r e v i o u s la y e r . A s s o c i a t e d w i t h e a c h i n c o m i n g s i g n a l ( X i ) i s a w e i g h t ( W i j ) . T h e e f f ec t iv ei n c o m i n g s i g n a l ( S j ) t o n o d e j i s t h e w e i g h t e d s u m o f a ll t h e i n c o m i n g s i g n al s a n d b j is t h e n e u r o nt h r e s h o l d v a l ue .

s j = x i w q + b . 1)i l

T h e e f fe c ti v e i n c o m i n g s i g n a l, S y , is p a s s e d t h r o u g h a n o n l i n e a r a c t i v a t i o n f u n c t i o n t o p r o d u c e t h eo u t g o i n g s i g n a l yj) o f t h e n o d e . T h e m o s t c o m m o n l y u s e d in t h i s t y p e o f n e tw o r k s is t h e l o g i st ics i g m o i d f u n c t i o n . T h i s t r a n s f e r f u n c t i o n is c o n t in u o u s l y d i f f er e n t ia b l e , m o n o t o n i c , s y m m e t r i c ,b o u n d e d b e t w e e n 0 a n d 1 [ 27 ]. I t i s e x p r e s se d m a t h e m a t i c a l l y a s:

1f S j ) - 1 + e - s j 2 )2 .] . . A N N P e r f o r m a n c e

I n t h i s s t u d y , b o t h s t a t i s ti c a l a n d g r a p h i c a l c r it e r ia w e r e a d o p t e d t o s e l ec t th e d e s i re d o p t i m a ln e t w o r k m o d e l . T h e s t a t i s t i c a l c r i t e r i a c o n s i s t o f a v e r a g e s q u a r e d o f e r r o r ( A S E ) , c o e f f ic i e n t o fd e t e r m i n a t i o n ( R 2 ) a n d t h e m e a n a b s o l u t e re l a ti v e e r r o r ( M A R E ) . T h e y a r e g iv e n b y

N 2A SE = 4=1 Y (3)

N ( Q ~ ) 2E t~ - Qt~i lR 2 = 1 - N , 4 )

E Q t i - Q t 0 2i=1N

M A R E = ~=1 l o o , 5 )Nw h e r e Qti a n d Qti a r e r es p e c t i v e ly , t h e a c t u a l a n d p r e d i c t e d v a l u e o f f lo w ( n o r m a l i z e d b e t w e e n0 a n d 1 ) , ( ~ t i i s t h e m e a n o f Qti v a l u e s a n d N i s t h e t o t a l n u m b e r o f d a t a s e t s.

T h e R 2 s t a ti s t i c m e a s u r e s t h e l in e a r c o r r e l a ti o n b e t w e e n t h e a c t u a l a n d p r e d i c t e d f lo w s v a lu e s.T h e A S E a n d M A R E s t a t i s ti c m e a s u r e s a re u s ed to q u a n t i f y t h e e r r o r b e tw e e n o b s e r v e d a n dp r e d i c t e d v a l u es . T h e o p t i m a l v a l u e fo r R 2 is eq u a l t o 1 .0 a n d f o r A S E a n d M A R E i s e q u a lto 0.0.T h e g r a p h i c a l p e r f o r m a n c e i n d i c a t o r g i v es b e t t e r r e s u l ts w h e n t h e d a t a p a i r s a r e c l o si n g t o 4 5 l in e a n d t h e g o o d s u p e r p o s i t i o n b e t w e e n t h e d e s i re d a n d c a l c u l a t e d f lo w v a l u es i n t h e t r a i n i n ga n d t e s t i n g p h a s e s .

F o r t h e d a t a s e t c o n s i d e r e d i n t h e p r e s e n t s t u d y , t h e i n p u t v a r i a b l e s a s w e l l a s t h e t a r g e tv a r i a b l e s a r e f i r st n o r m a l i z e d l i n e a r l y in t h e r a n g e o f 0 a n d 1 . T h i s r a n g e i s s e l e c t e d b e c a u s e o ft h e u s e o f t h e l o g is t ic f u n c t i o n ( w h i c h i s b o u n d e d b e t w e e n 0 . 0 a n d 1 .0 ) a s t h e a c t i v a t i o n f u n c t i o nf o r t h e o u t p u t l a y er , i. e. , e q u a t i o n ( 2) . T h e n o r m a l i z a t i o n is d o n e u s i n g t h e f o ll o w i n g e q u a t i o n .

.,~ = X -- Xm i n .Xmax - - Xmin (6)

w h e r e . ~ is t h e s t a n d a r d i z e d v a l u e o f t h e i n p u t , Xm i n a n d X m a x a r e r e s p e c t i v e l y , t h e m i n i m u ma n d m a x i m u m o f t h e a c t u a l v a lu e s , in a ll o b s e r v a t io n s a n d X i s t h e o r i g i n a l d a t a s e t .

T h e m a i n r e a s o n f o r s t a n d a r d i z i n g t h e d a t a m a t r i x i s t h a t t h e v a r i a b l e s a r e u s u a l l y m e a s u r e di n d i f fe r e n t u n i t s . B y s t a n d a r d i z i n g t h e v a r i a b le s a n d r e c a s ti n g t h e m i n d i m e n s i o n le s s u n i ts , t h ea r b i t r a r y e f fe c t o f s i m i l a r i t y b e t w e e n o b j e c t s is r e m o v e d .


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842 S RIAD e t a l

3 T H E S T U D Y C A T C H M E N T A N D D A T A B A S EI n t h e p r e s e n t s t u d y , t h e f lo w a n d r a i n fa l l s e ri es o b s e r v ed i n O u r i k a b a s i n a t A g h b a l o u s t a t i o n i n

M o r o c c o is a n a ly z e d u s in g th e A N N m o d e l . T h e O u r i k a b a s in i s t h e m o s t i m p o r t a n t s u b c a t c h m e n to f T e n s i f t b a s i n d r a i n a g e l o c a t e d i n s e m i - a r id r e g i o n o f M a r r a k e c h , w h i c h is d r a i n i n g a n a r e a o fa b o u t 5 0 3 k m 2 . S e e F i g u r e 2 .)

ensift drainage basin

\ t ) / / /

/t . _ .~

CIH ~[AOUA

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1 2 3 K m k\ \ ,

t

/ / _ , _ / / ~ G a u g e s t a t i o nFigure 2 Location of Ourika Wadi in the Tensift basin

T h e R a i n f a l l a n d R u n o f f d a i l y d a t a a t t h e A g h b a l o u s t a t i o n w a s u s e d f o r m o d e l i n v e s ti g a t io n .T h e d a t a c o n t a i n s i n f o r m a t i o n f o r a p e r i o d o f s e v e n y e a r s 1 9 90 t o 1 9 9 6 ). T h e e n t i r e d a t a b a s e isr e p r e s e n t e d b y 2 5 5 0 d a i l y va l u es o f r a i n fa l l a n d r u n o f f p a i rs . T h e A N N m o d e l w a s t r a i n e d u s i n gt h e r e s u l t i n g r u n o f f a n d r a in f a ll d a i l y d a t a . T h e d a t a b a s e w a s c o l le c t ed b y t h e R a b a t h y d r a u l i ca d m i n i s t r a t i o n .

T h e i n p u t v e c t o r is r e p r e s e n t e d b y r a i n f a l l a n d r u n o f f v a l u e s f o r t h e p r e c e d i n g s e v e n d a y s , i .e .,t - 1 , t - 2 , t - 3 , t - 4 , t - 5 , t - 6 , t - 7) as we l l as the r a inf a l l va lue ex pe c te d fo r d ay t .A c c o r d i n g l y , t h e o u t p u t v e c t o r re p r e s e n ts t h e e x p e c t e d r u n o f f v a l u e f o r d a y t Q t ) .

4 R E S U L T S A N D D I S C U S S I O N ST h e d a t a b a s e c o m p i l e d r e p r e s e n t s s e v e n y e a r s d a i l y s e ts o f r a i n f ai l - ru n o f f v a l u e s f o r t h e O u r i k a

W a d i b a s in . I n t h i s p a p e r , w e u s e d th e d a t a f o r t h e l a s t y e a r 1 9 96 ) f o r m o d e l t e s ti n g , w h i l e t h eo t h e r r e m a i n i n g d a t a 1 9 90 t o 1 99 5) w a s u s ed fo r m o d e l t r a i n i n g / c a l i b r a t i o n . T h e t r a i n i n g p h a s eo f A N N m o d e l w a s t e r m i n a t e d w h e n t h e a v e ra g e s q u a r ed e r r o r A S E ) o n t h e t e s ti n g d a t a b a s esw a s m i n i m a l .

T h e g o a l o f t h e t r a i n i n g p r o c es s i s t o r e a c h a n o p t i m a l s o l u t i o n b a s e d o n s o m e p e r f o r m a n c em e a s u r e m e n t s s u c h a s A S E , c o e f fi c ie n t o f d e t e r m i n a t i o n k n o w n a s R - s q u a r e v a l u e R 2 ) , a n d t h eM A R E .

T h e r e f o r e , re q u i r e d A N N m o d e l w a s d e v e lo p e d in t w o p h a se s : t r a i n i n g c a l i b r a ti o n ) p h a s e , a n dt e s t i n g g e n e r a l i z a t i o n o r v a l i d a t i o n ) p h a s e .

I n th e t r a i n i n g p h a s e , a la r g e r p a r t f o r d a t a b a s e s ix y ea r s ) w a s u s e d t o t r a i n t h e n e t w o r ka n d t h e r e m a i n i n g p a r t o f t h e d a t a b a s e o n e y e a r ) is u s e d i n t h e t e s t i n g p h a s e . T e s t i n g se t s ar e


5/8

R a i n f a l l - R u n o f f M o d e l 8 43T a b l e 1 . S t a t i s t i c a l a c c u r a c y m e a s u r e s o f t h i s n e t w o r k m o d e l a t te s t i n g a n d t r a i n i n gpha s e s . A S E R 2 M A R E

Tr a i n i ng Ph a s e 0 .000076 0 .948 1 .029Te s t i ng Ph a s e 0 .000007 0 .917 1 .524

180160

120

~ 8o, - 60

4 02 0

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. , ~ 4o~ 120

,~ 100~ 60

4 0

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' . ~ i l r a .: IR-- 0 948u . o i 0 2 0 4 0 6 0 8 0 I 0 0 1 2 0 1 4 0 1 6 0 1 8 0

Actual flow l~/S)~ r a in i n g p h a s e l . . . . . . . P r ed ic te d f l ow

Actual f low

A c t u a l f l o w ( m 3 / s )F i g u r e 3. C o m p a r i s o n b e t w e e n t h e a c t u a l a n d A N N p r e d i c t e d f l ow v a l u e s .

3 02 52 0

q~ 15 ~~ lO

[ T e s t ln g p h a s e l .s e ~ . j / E q u a l i t y l i n e

le ~ mI I mm ~ * [R=0 917

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5 I 0 15 2 0 2 5 3 0A c tu a l f lo w m 3 /s )


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302 52 0

~ 15

I T e s t i n g p h a s e ] . . . . . . . Predicted flowActual flow

, . .: ( ~ . b

Table 2.testing phases.(a) Training Phase

A c t u a l f l o w ( m ~ / s )Figure 3. (cont.)

Statistical parameters of the predicted and actual flow at training and

Statistical Actual Flow Predicted FlowParameters (ma/s) (ma/s)Average 9.79 9.70

Standard of 18.93 17.81DeviationMinimum 0 1.37Maximum 184 187.17

Coefficient of 1.93 1.84Variation

(b) Testing PhaseStatistical Actual Flow Predicted FlowParameters (ma/s) m a / s )Average 2,71 3.25

Standard of 4.33 3.96DeviationMinimum 0.10 1.38Maximum 31.90 31.16

Coefficient of 1.60 1.22Variation

usually used to select the best per forming network model. In this research, the ANN was opti malat 600 iterations with 12 hidden nodes. The corresponding accuracy measures of this networkmodel on tes ting and tra ini ng data are given in the following table (Table 1). Generally, accuracymeasures on t ra in ing da ta a re be t te r th an those on tes t ing da ta.

18016 . ,140 120l o o . ~ . . .

8 0 . . ,_~ . ; . , ._~.. 2 . ~ ~ -6 0 . . . X ~ . .

4 0 1 - * 0 . , 1 1 *2 0 . * ~ . I R = 0 , 92 4F- - - I I I I I I I

0 20 40 60 80 100 120 140 160 180Actual flow (m~/s)

Figure 4. Comparison between the a~tual and predicted flow values by mult iple linearregression (MLR).


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Rainfall-Runoff M odel 845

3O,,,~, 25

~ o5

E q u a l i t y l in e 0e . e ~

O .. o~r

0 ~ [ R = 0 ,8 8 8u a u , ,

0 5 10 15 20 25 30Actual flow m 3/s)Figure 4. (cont.)

Table 3 . Com parison of correlat ion coefficients between ac tual a nd predicted f low byANN and MLR models .A N N t ML R

R2Training Phase 0 .9 48 I 0 .924Testing Phase 0 . 91 7 i 0 .888

The comparison between the predicted and actual flow values at training and testing phasesshow excellent agreement with the R 2 are respectively 0,948 and 0,917 see Figure 3). Note tha t,dat a pairs closer to the 45 line represent be tte r prediction cases. The good performance andconvergence of the model are illustrated in Figure 3. The statistical parameters of the predictedand ac tual values of flow for the en tire database are practica lly identical see Table 2).

]In order to evaluate the performance of the ANN, the multiple linear regression MLR) tech-nique was applied with the same da ta sets used in the ANN model. Figure 4 shows the compara-tive results obtained by MLR technique. The R 2 values for MLR and ANN models are presentedin Table 3. Apparently, the ANN approach gives much better prediction th an the tradit ionalmethod MLR).

5 . C O N C L U S I O NT h e a r ti f ic i a l n e u r a l n e t w o r k ( A N N ) m o d e l s s h o w g o o d c a p a b i l i t y t o m o d e l h y d r o l o g ic a l p r o -

c e ss . T h e y a r e u se f u l a n d p o w e r f u l t o o ls t o h a n d l e c o m p l e x p r o b l e m s c o m p a r e d w i t h t h e o t h e rt r a d i t i o n a l m o d e l s . I n t h i s s t u d y , th e r e s u l t s o b t a i n e d s h o w c l e a r l y t h a t t h e a r t if i c ia l n e u r a l n e t -w o r k s a r e c a p a b l e o f m o d e l r a i n f a l l - r u n o f f r e l a t i o n s h i p i n t h e a r i d a n d s e m i a r i d r e g i o n s i n w h i c ht h e r a i n f a l l a n d r u n o f f a r e v e r y i r r e g u l a r , t h u s , c o n f i r m i n g t h e g e n e r a l e n h a n c e m e n t a c h i e v e d b yu s i n g n e u r a l n e t w o r k s i n m a n y o t h e r h y d r o l o g i c a l fi el ds .

T h e r e s u l ts a n d c o m p a r a t i v e s t u d y i n d i c a te t h a t t h e a r ti fi c ia l n eu r a l n e t w o r k m e t h o d is m o r es u i t a b le t o p r e d i c t r i v er r u n o f f t h a n c l as s ic a l r e g r e s si o n m o d e l . T h e A N N a p p r o a c h c o u ld p r o v i d ea v e r y u se f u l a n d a c c u r a t e t o o l t o s ol ve p r o b l e m s i n w a t e r r e s o u rc e s s t u d ie s a n d m a n a g e m e n t .

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