Probabilistic determination of Design Waterlevels in the Eastern Scheldt

ministerie van verkeer en waterstaat

rijkswaterstaat

ministerie van verkeer en waterstaat

rijkswaterstaat

nota

Roos

samenvatting: A probabilistic coitiputation method for the determination

of the design waterlevel of a dam or dyke is presented.

The results of the application of the method in the

Eastern Scheldt estuary are shown.

REF.NR.

i S]QM. !1

Cs^

DATUM

o.oo

PROBABJLISTIC D E T E R M I N A T I O N Ó F DESIGN W A T E R L E V E L S I N THE E A S T E R N SCHELDT

b y N i e k PraagmanC»tD and Ary RoosC+D

A b s t r a c t : A p r o b a b i l i s t i c c o m p u t a t i o n method f o r t h e d e t e r m i n a t i o n o f t h e d e s i g n - w a t e r l e v e l o f a dam o r d y k e i s p r e s e n t e d . R e s u l t s o f t h e a p p l i c a t i o n o f t h e m e t h o d i n t h e E a s t e r n S c h e l d t e s t u a r y a r e s h o w n . l.INTRODUCTION The d e s i g n w a t e r l e v e l i s a s s o c i a t e d w i t h t h e a s t r o n o m i c a l t i d e a n d s t o r m s u r g e s . I n d e t e r m i n i n g t h e c r e s t l e v e l o f a d y k e o r dam t h e w a v e r u n - u p a n d s o m e " e x t r a — h e i g h t " s h o u l d b e a d d e d t o t h e d e s i g n w a t e r l e v e l . T h e " e x t r a - h e i g h t " a c c o u n t s f o r t h e r e l a t i v e r i s i n g o f t h e s e a l e v e l and s h r i n k i n g o f t h e d y k e body. A l o n g t h e c o a s t o f t h e S o u t h W e s t e r n p a r t o f t h e N e t h e r l a n d s t h e d e s i g n w a t e r l e v e l i s d e f i n e d a s t h e w a t e r l e v e l w i t h a n e x c e s s - f r e q u e n c y o f 2.5»»10C-43 t i m e s p e r y e a r . N o r m a l l y t h i s w a t e r l e v e l i s o b t a i n e d from e x c e s s - f r e q u e n c y c u r v e s w h i c h a r e d e t e r m i n e d u t i l i z i n g h i s t o r i c a l o b s e r v a t i o n s . T h i s m e t h o d i s d e s c r i b e d i n c h a p t e r 2 a n d w i l l b e r e f e r r e d t o a s t h e " C l a s s i c a l Method". For l o c a t i o n s i n t h e E a s t e r n S c h e l d t e s t u a r y C s e e f i g u r e ID t h i s method i s n o t a p p l i c a b l e s i n e e i n t h e mouth o f t h e e s t u a r y a s t o r m s u r g e b a r r i e r h a s b e e n c o n s t r u c t e d . T h i s b a r r i e r i s p a r t o f t h e s o c a l l e d " D e l t a P l a n " , i n i t i a t e d a f t e r t h é f l o o d d i s a s t e r o f 1 9 5 3 . The b a r r i e r w i l l b e o p e n under nor mal c o n d i t i o n s , s o t h a t t h e t i d a l movement - i m p o r t a n t f o r t h e e c o l o g y o f t h e e s t u a r y - w i l l r e m a i n . O n l y when s e v e r e s t o r m s a r e e x p e c t e d t h e b a r r i e r w i l l b e c l o s e d . To s e p a r a t e t h e i n l a n d s h i p p i n g r o u t e b e t w e e n Antwerp a n d R o t t e r d a m from t h e t i d a l e s t u a r y a n d t o c r e a t e a f r e s h w a t e r l a k e t w o c o m p a r t m e n t dams a r e b u i l t . T h e s e a r e c a l l e d t h e P h i l i p s d a m and t h e O e s t e r d a m C s e e f i g u r e ID. The d e s i g n w a t e r l e v e l s o f t h o s e dams c a n n o t b e o b t a i n e d f r o m e x i s t i n g f r e q u e n c y c u r v e s b e c a u s e t h e w a t e r l e v e l s i n t h e E a s t e r n S c h e l d t w i l l c h a n g e d u e t o t h e b a r r i e r a n d t h e dams t h e m s e l v e s . T h e b a r r i e r i n f l u e n c e s t h e w a t e r l e v e l s i n t w o ways : t h e a p e r t u r e i n t h e mouth o f t h e e s t u a r y w i l l b e r e d u c e d and d u r i n g s e v e r e s t o r m s t h e b a r r i e r w i l l b e c l o s e d . I n t h i s p a p e r a method f o r t h e d e t e r m i n a t i o n o f d e s i g n w a t e r l e v e l s i n t h e m o d i f i e d E a s t e r n S c h e l d t i s d e s c r i b e d . The method w i l l b e r e f e r r e d t o a s t h e "New Methpd". The e x c e s s f r é q u e n c i e s a r e c o m p u t e d u s i n g a c o m b i n a t i o n o f h i s t o r i c a l o b s e r v a t i o n s a t t h e mouth o f t h e e s t u a r y and a m a t h e m a t h i c a l t i d a l model t h a t i n c l u d e s w i n d e f f e c t s . A l t h o u g h t h e p r o p o s e d method c a n b e a p p l i e d g e n e r a l l y , u p t o now i t h a s o n l y b e e n c a l i b r a t e d t o and u s e d f o r t h e E a s t e r n S c h e l d t a r e a . C*0 M a t h e m a t i c i a n , S v a s e k B. V. , C o a s t a l a n d Harbour E n g i n e e r i n g C o n s u l t a n t s , R o t t e r d a m , The N e t h e r l a n d s

C+Z) Engineer, Rijkswaterstaat, Tidal Waters Division, The Hague The Netherlands

2.THE CLASSICAL METHOD

At v a r i o u s l o c a t i o n s a l o n g t h e D u t c h c o a s t w a t e r l e v e l ö b s e r v a t i o n s a r e a v a i l a b l e f o r a p e r i o d o f a l m o s t 1 0 0 y e a r s . I n t h e c l a s s i c a l method an e x c e s s - f r e q u e n c y c u r v e i s made u s i n g t h e o b s e r v e d d a t a . For e a c h l o c a t i o n p o i n t s a r e p l o t t e d i n a d i a g r a m i n w h i c h t h e w a t e r l e v e l s a r e on t h e y - a x i s and t h e l o g a r i t h m o f t h e number o f e x c e e d e n c e s o f a w a t e r l e v e l p e r y e a r on t h e x — a x i s . The p l o t s h o w s a more or l e s s s t r a i g h t c u r v e . B e c a u s e o f t h e l i m i t e d p e r i o d o f ö b s e r v a t i o n s n o e s t i m a t e s f o r w a t e r l e v e l s w i t h a n e x c e s s - f r e q u e n c y l e s s t h a n 0 . 0 1 t i m e s p e r y e a r a r e d i r e c t l y a v a i l a b l e from t h e d i a g r a m . The e x t r a p o l a t i o n o f t h e c u r v e h a s b e e n t h e s u b j e c t o f e x t e n s i v e s t a t i s t i c a l r e s e a r c h . C v a n D a n t z i g & H e m e l r i j k , 1 9 6 0 3 . They s h o w e d t h a t t h e o b s e r v e d w a t e r l e v e l s c a n b e d e s c r i b e d a s ö b s e r v a t i o n s drawn f r o m a d i s t r i b u t i o n , h a v i n g i n t h e l o g a r i t h m i c s c a l e a n a s y m p t o t e t o w a r d s h i g h e r w a t e r l e v e l s . F i g u r e 2 s h o w s o b s e r v e d d a t a and t h e e x t r a p o l a t e d c u r v e f o r t h e l o c a t i o n Hook o f H o l l a n d . C W e m e l s f e l d e r , 1 9 6 0 D.

3 . THE "NEW METHOD" I n a n e s t u a r y w a t - e r l e v e l s a r e m a i n l y d e ' t e r m i n e d b y t h e a s t - r o n o m i c a l t i d e , t h e w i n d s e t - u p a t t h e m o u t h a n d t h e i n t e r n a l w i n d e f f e c t . I n t o t a l e i g h t p a r a m e t e r s c a n b e d i s t i n g u i s h e d . For t h e i n t e r n a l w i n d e f f e c t t h r e e p a r a m e t e r s : - Winddi r e e t i o n - W i n d d u r a t i o n - W i n d v e l o c i t y The w i n d s e t - u p c a n b e d e s c r i b e d b y t w o p a r a m e t e r s : - Wind s e t - u p d u r a t i p n - Wind s e t - u p l e v e l

Further one parameter for : .

- A s t r o n o m i c a l t i d e F i n a l l y , d u e t o p h a s e d i f f e r e n c e s , t w o more p a r a m e t e r s h a v e t o b e c o n s i d e r e d : - P h a s e d i f f e r e n c e b e t w e e n w i n d and w i n d s e t - u p - P h a s e d i f f e r e n c e b e t w e e n w i n d s e t - u p a n d a s t r o n o m i c a l t i d e H i s t ö r i c a l o b s e r v a t i o n s s h o w t h a t t h e s e e i g h t p a r a m e t e r s a r e n o t i n d e p e n d e n t . I n t h e f o l l o w i n g a d e s c r i p t i o n o f t h e d e p e n d e n c i e s i s g i v e n . C o n s i d e r i n g o b s e r v a t i o n s i t t u r n s o u t t h a t w i n d d i r e e t i o n a n d w i n d v e l o c i t y g i v e r i s e t o a t w o - d i m e n s i o n a l m a t r i x o f p r o b a b i l i t i e s . I n s e c t i o n 3 . 1 m o r e I n f o r m a t i o n c o n c e r n i n g t h e r e l a t i o n o f t h e s e t w o p a r a m e t e r s c a n b e f o u n d . T h e r e e x i s t s a l s o a r e l a t i o n b e t w e e n w i n d v e l o c i t y a n d w i n d d u r a t i o n . F o r s e v e r a l l o c a t i o n s i n t h e N e t h e r l a n d s a s t a t i s t i c a l i n v e s t i g a t i o n o f s t o r m s h a s b e e n m a d e t o o b t a i n a q u a n t i t a t i v e r e l a t i o n f o r t h e s e t w o p a r a m e t e r s . T h e f o r m u l a Vmax 0 . 8 4 C 1 D k = 3 6 . 8 C - 1 D Vk w i t h C s e e f i g u r e 3 D k : Number o f h o u r s d u r i n g w h i c h t h e o n e h o u r a v e r a g e w i n d v e l o e i t y V e x c e e d s t h e v e l o e i t y Vk w i t h o u t i n t e r r u p t i o n Vmax : hdaximum o n e h o u r a v e r a g e w i n d v e l o c i t y o v e r t h e t o t a l p e r i o d o f t h e s t o r m a p p l i e s f o r t h e h i s t ö r i c a l d a t a o f t h e E a s t e r n S c h e l d t a r e a . C R i j k o o r t , 1 9 6 0 D O n c e t h e maximum v e l o e i t y Vmax i s g i v e n t h e t i m e h i s t o r y o f t h e w i n d v e l o e i t y a n d s o t h e w i n d d u r a t i o n a r e f i x e d . C o n s i d e r i n g t h e h i s t ö r i c a l d a t a f o r w i n d s e t - u p d u r a . t i o n a n d w i n d s e t - u p l e v e l i t h a s b e e n s h o w n t h a t t h e e x p r e s s i o n n t C 2 D s C t D = sm »t c o s C D D

The meaning of the parameters is s C t D sm D w i n d s e t - u p a t a t t i m e t maximum w i n d s e t - u p w i n d s e t - u p d u r a t i o n E s p é c i a l l y t h e s y m m e t r i e b e h a v i o u r i n t i m e o f t h e s e t - u p s C t D w i t h r e s p e c t t o t h e d u r a t i o n D i s n o t f o u n d i n g e n e r a l . I n m a n y a p p l i c a t i o n s f o r m a n d c o e f f i c i e n t s o f b o t h f o r m u l a s C l 5 a n d C2D may d i f f e r c o n s i d e r a b l y . F o r t h e d e t e r m i n a t i o n o f s m a n e m p i r i c a l f o r m u l a V9 *t V9 C 3 D sm = CCRD *t 3 h a s b e e n u s e d . C W e e n i n k , 1 9 S 8 D H e r e CCRD : E m p i r i c a l c o ë f f i c i ë n t w h i c h e x p r e s s e s t h e r e l a t i ó n b e t w e e n t h e maximum w i n d s e t — u p a n d t h e w i n d v e l o c i t y t h a t i s e x c e e d e d f o r 9 h o u r s : V 9 . T h e R s h o w s t h a t t h i s c o ë f f i c i ë n t i s d i r e c t i o n d e p e n d e n t . F o r o u r a p p l i c a t i o n i t h a s b e e n a s s u m e d t h a t t h e w i n d i s u n i f o r m o v e r t h e w h o l e E a s t e r n S c h e l d t a r e a . T h i s a s s u m p t i o n i s r e a l i s t i c i n m o s t s i t u a t i o n s , b u t e s p é c i a l l y d u r i n g s t o r m c o n d i t i o n s w h i c h i s d u e t o t h e f a c t t h a t t h e E a s t e r n S c h e l d t a r e a h a s r a t h e r s m a l l d i m e n s i o n s c o m p a r e d t o t h e d i m e n s i o n s o f t h e w i n d f i e l d . g : T h e a c c e l e r a t i o n o f g r a v i t y . F i n a l l y i t h a s b e e n n o t i c e d t h a t t h e p h a s e d i f f e r e n c e b e t w e e n t h e maximum w i n d v e l o c i t y a n d t h e maximum w i n d s e t - u p i s a l w a y s a p p r o x i m a t e i y s i x h o u r s f o r t h e m o u t h o f t h e E a s t e r n S c h e l d t . I n o t h e r w o r d s : t h e maximum w i n d s e t - u p sm i s f o u n d t o a p p e a r s i x h o u r s l a t e r t h a n t h e maximum w i n d v e l o c i t y Vmax. I n f o r m u l a : C 4 D t = t + 6 sm Vmax C o n s i d e r i n g t h e r e l a t i o n s d e s c r i b e d s o f a r t h e h u m b e r o f d e t e r m i n i n g p a r a m e t e r s i s d e c r e a s e d t o t h e f o l l o w i n g f i v e : W i n d d i r e e t i o n W i n d v e l o c i t y Wind s e t - u p d u r a t i o n A s t r o n o m i c a l t i d e P h a s e d i f f e r e n c e b e t w e e n w i n d s e t - u p a n d a s t r o n o m i c a l t i d e

R

V

D

H

F

In order to make a discrete probabilistic model, the continuous range of values of the parameters is divided in a number of

discrete classes. For each class t-he probabili-ty of occurrence of a specia:! tidal cycle as a resul't of the con±5ination of the five parameters R, V, D, H and F may be obtained by multiplication of the probabilities of each. Since one year contains approximateiy 706 high-tides the final result has to be multiplied by 706 in order to determine the probability of occurrence of the computed high waterlevel per year. In formula

pCijklmD = 706 »t pCRi.VJD •* pCDkD a pCH15 ** pCFmD

In chapter 4 numerical values for the probabilities p are given for the mouth of the Eastern Scheldt estuary. For each combi nation of R, V, D, H and F high waterlevels in the Eastern Scheldt area have to be computed. To that pur pose a numerical

one-dimensional tidal model, called IMPLIC, is used. CCStroband &

Wijngaarden , 1977 D and CVoogt & Roos, 1980 Dl). The IMPLIC model has been calibrated and verified extensively. The model integrates the continuity equation and the momentum equation by a finite difference technique. In IMPLIC wind is included as an external driving force in the momentum equation. The estuary is schematized in a network of branches and nodal points C see figure 4 D. To each branch the finite difference equivalent of the continuity and the momentum equation holds. Because the high water levels have to be computed for the situation with compartment dams and storm sürge barrier, those elements are included in the schematization.

The high waterlevels in the estuary depend on the closing strategy of the barrier. Several closing strategies for the storm surge barrier have been considered. CRoos e. a. , 1980 3. For the design waterlevel of the compartment dams the strategy that the barrier is closed in one hour as soon as the seaside waterlevel exceeds mean sea level +3.25 meter, being the strategy which leads to the highest waterlevels in the estuary, has been adopted.

For each computation with the IMPLIC model a boundary condition at the mouth of the Eastern Scheldt and a windfield applying to the interior of the basin have to be made available. The windfield is defined by the values of the parameters R, V and D. The waterlevel at the seaside is obtained combining the astronomical tide at that location and the wind set up according to equation C2D.

High waterlevels together with their probability of occurrence are computed for several locations in the estuary. Fr om these data excess frequency curves are obtained adding for each waterlevel the probabilities of occurrence of all higher waterlevels. The discrete curve obtained in this way is transformed to a continuous one using Standard continuation processes.

6

4. PROBABILITY, DISTRI BUTTONS FOR THE EASTERN SCHELDT

In t,he design of •the classes with probabilities of occurrence an optimum has been strived for. On the one hand the classes should not be too small in order to restrict the number of combinations possible and hence the number of computations with the IMPLIC model to be made. On the other hand, small classes are desirable in order to have, especially in the region of interest, enough separating power. In the following classes and probabilities are listed together with a short justification. Also values for the coëfficiënt CCRD of formula C3D are specified.

4.1 WINDDIRECTI ON and WINDVELOCITY Vmax

For the winddirection the compass has been divided in twelve classes, each class a sector of 30 degrees. Only the classes SW,

WS, W, VU and NW Csee figure 5D are important in the case of the

Eastern Scheldt. Observations show that the distribution of the windvelocity Vmax is dependent on the directiön R. Therefore table 1 has been constructed in which for each combi nati on CRi,Vj!) a probability of occurrence is given.

For the vel oei ty ten classes VI, V 2 , VIO have been created. The range of each class is defined by

Vj = C S «CJ-ID, 5 *t j m / s

J=l,2,.

S i n c e o n l y f i v e d i r e c t i o n s a r e i m p o r t a n t t h e t a b l e h a s f i f t y e n t r i e s . The t a b l e h a s b e e n c o n s t r u c t e d by c o m b i n i n g d a t a o f t h e l i g h t v e s s e l " G o e r e e " , d u r i n g t h e p e r i o d 1951 - 1 9 6 0 . C D o r r e s t e i n , 1 9 6 7 O

4 . 2 WIND SET-UP DURATTON D

For t h e E a s t e r n S c h e l d t t h e p r o b a b i l i t y d e n s i t y o f t h e w i n d s e t - u p d u r a t i o n i s a l o g - n o r m a l f u n c t i o n . C V r i j l i n g & B r u i n s m a , 1 9 8 0 D. I n f o r m u l a : C 5 D pCDD = D C l n 1 . 4 D e x p

h-i'^^r^^f]

Since the probability of occurrence pCDD is not uniform over each interval, as follows from CSD , a weighted duration <Dk> has been

c o m p u t e d f o r e a c h c l a s s u s i n g t h e f o r m u l a k « 1 0 y D *t pCD3 C 6 D _{<Dk> =} D = Ck-i:)*»10 + 1 k *t 1 0 l PCDD D = Ck-1D»«10 + 1 R e s u l t s a r e g i v e n i n T a b l e 2 . 4 . 3 THE ASTRONOMICAL TI DE H. A l o n g t h e O u t c h c o a s t t h e t i d e i s s e m i - d i u r n a l . I t i s a l m o s t s y m m e t r i e and c a n b e a p p r o x i m a t e d b y a s i n u s - c u r v e . For t h e mouth o f t h e E a s t e r n S c h e l d t t h e f o r m u l a 2 TT t C 7 D HCtD = a *t s i n C + F D + b T a p p l i e s wi t h : a : t i d a l a m p l i t u d e T : t i d a l p e r i o d b : mean w a t e r l e v e l r e l a t e d t o mean s e a l e v e l A d i V i s i o n i n t h r e e c l a s s e s , e a c h w i t h a p r o b a b i l i t y o f o c c u r r e n c e o f p C H 3 = l / 3 h a s b e e n u s e d . The c l a s s e s c o i n c i d e a p p r o x i m a t e l y w i t h t h e a v e r a g e s p r i n g t i d e , t h e a v e r a g e mean t i d e and t h e a v e r a g e n e a p t i d e . The v a l u e s f o r a and b a r e g i v e n i n T a b l e 3 .

The v a l u e o f b d i f f e r s from z e r o f o r mean t i d e and f o r s p r i n g t i d e . T h i s i s d u e t o t h e d i f f ê r e n c e b e t w e e n t h e o b s e r v e d c u r v e and t h e a p p r o x i m a t i n g s i n u s - c u r v e .

4 . 4 THE PHASE DIFFÊRENCE F.

The phase differences of wind set-up and astronomical tide cover the interval of O hours to 12 hours and 25 minutes. Since both are totally independent a strictly mathematical division in six classes, each ha ving a length of 2 hours, 4 minutes and 10 seconds has been used. For each class the probability of occurrence is pCFi!)=l/6 and in the computations per class a mean value for the phase F is used.

4.5 THE PARAMETER CCRD.

From the observations of 54 historical storms an estimate has been made for the value of CCRD in equation C33. For the mouth of the Eastern Scheldt the following values have been found :

CCSVO = O. 0150 CCWND = O. 0250

CCWSD = O. 0175 CCNVD = O. 0300

8

S. COMPUTATIONAL RESULTS FOR THE EASTERN SCHELDT ESTUARY.

In order t,o show t-he potential power and the reliabili'ty of t.he

used formulae in the new method, t,he method has been applied t-o t-he mouth of the East-ern Scheldt, for the original situation. Furthermore the method has been used to coiiipute the excess frequency curves for the compartment dams in the Eastern Scheldt for the new situation. Results of both computations are given in this chapter.

5. 1 EXCESS FREQUENCY CURVE AT THE MOUTH OF THE EASTERN SCHELDT For the application of the méthpd for a location at the mouth of the Eastern Scheldt waterlevels had to be made available for all the combi na ti ons of the parameters R, V, D, H and F. No IMPLIC computations were needed. Computation of the waterlevels and adding their probabilities of occurrence delivers the excess frequency curve as shown in figure 6. The curve can be compared with the excess frequency curve obtained by the classical method. The two curves show a good agreement which justifies the cal i brat ion of the formulae and the division in discrete classes of the five parameters as used.

5. 2 EXCESS FREQUENCY CURVES FOR THE COMPARTMENT DAMS.

Because tidal amplification and internal wind effects do play an important role in the Eastern Scheldt estuary, computations with the IMPLIC model had to be made for all the combinations of the parameters R, V, D, H and . F for the new situation. The computation of the waterlevels with their probabilities of occurrence resulted in the curves as shown in figure 7 for the Philipsdam and figure 8 for the Oesterdam. To show the effect of the barrier and the compartment dams also curves for the original situation, obtained with the classical method, are included in the figures. The large effect of the changes on the waterlevels is clearly illustrated.

From the curves as shown in the figures 7 and 8 the design waterlevels have been derived at the excess frequency of 2.5 *t IOC-4!) times per year. Those waterlevels have been used in the design of the compartment dams.

6. DISCUSSION

A method Vo compule excess frequency curves on a probabilist-ic basis has been propos ed. Although the method can be used for general applicat-ion whenever sufficiënt data are available, up to now it has been applied and calibrated to the Eastern Scheldt area ónly. Formulae and parameters of this paper are restricted to this estuary.

For a location along the coast the method cah be used as an alternative to the classical method. The new method is not "better", because also in the new method extrapoiation, in this case of the wind, is needed. However if a new or mpdified geometry is created, as in the presented example, pnly the new method is applicabie.

10 APPENDIX I. - REFERENCES

van Dantzig, D., and Hemelrijk, J. " Extrapolatie van de over-schrijdingslijn van de hoogwaterstanden te Hoek van Holland met behulp van geselecteerde stormen"

Report of the Delta Comittee, part 3, The Hague, 1960 C In EXitch with English summary D

Etorrestein, R. "Wind and wave data of Netherlands lightvessels sinee 1949"

K. N. M.I. , Mededelingen en verhandelingen, 9 0 , 1967

Roos, A. , Remery, F. J. , and Voogt, • J. , "Strategies in barrier control"

in : Hydraulic Aspects of Coastal Structures, D. U. P., Delft, 1980

Rijkoort, P.J., "Statistisch onderzoek van Noordwester stormen" Report of the Delta Committee, part 2, The Hague, 1960

Stroband, H.J. and van Wijngaarden, N. J. , "Modelling of the Oosterschelde estuary by a hydraulic model and a mathematical model"

I.A.H.R. , Baden-Baden, 1977

Voogt, J. and Roos, A., "Effects on tidal regime"

in : Hydraulic Aspects of Coastal Structures, D. U. P., Delft, 1980

Vrijling, J.K. and Bruinsma, J., "Hydraulic boundary conditions" in : Hydraulic Aspects of Coastal Structures, D. U. P. ,

Delft, 1980

Weenink, M.P.H. , " A theory and method of calculation of wind effects on sea levels in a partly enclosed sea, with special application to the Southern coast of the North Sea"

1 1

A p p e n d i x I I . - N o t - a t i o n

The f o l l o w i n g s y m b o l s a r e u s e d i n t h i s p a p e r a = Ti d a l a m p l i t u d e

b = Mean w a t e r l e v e l , r e l a t e d •to mean s e a l e v e l C = E m p i r i c a l c o ë f f i c i ë n t f o r s e t - u p D = Wind set—up d u r a t i o n F = P h a s e d i f f e r e n c è b e t w e e n wind s e t - u p and a s t r o n o m i c a l t i d e g = A c c e l e r a t i o n o f g r a v i t y H = A s t r o n o m i c a l t i d e ' p = P r o b a b i l i t y R = Wind d i r e c t i o n s = Wind s e t - u p t = Time T = Ti d a l p e r i o d V = Wind v e l o e i t y

WINDVELOCITY V IN M/S 0.0 - 5.0 5.0 - 10.0 10.0 - 15.0 15.0 - 20.0 20.0 - 25.0 25.0 - 30.0 30.0 - 35.0 35.0 - 40.0 40.0 - 45.0 45.0 - 50.0 SW 3.76666667 3.01333333 3.31466667 1.04713333 0.11177600 0.01094171 0.00040112 0.00002186 0.00000174 0.00000016 WINDDIRECTION

ws

w

Table 1: Probability o£ occurrence of the combination windvelocity - winddrection (R^, Vj) in peccents.

Class 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Class boundaries (hrs) 1 - 10 1 1 - 2 0 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 101 - 110 111 - 120 121 - 130 131 - 140 141 - 150 151 - 160 161 - 170 171 - 180 181 - 190 191 - 200 {D,J}

(hrs)

C l a s s 1 2 3 a (m) 1.55 1.41 1.23 b (m) 0 . 0 8 0 . 0 5 0 . 0 0

Table 3; The tidal iunplitüde a and the mean water level b for the

Fig. 1: The South-Western part of the Netherlands. Zt. z - I 6 Ui > UJ —I UJ •• V ) < Ui > o "^ 3 > UJ 2 _ i er UJ

1 ,

y

TIME t

Fig. 3: Definition sketch of the time history for the windvelocity.

ws

Fig. 5: Compass-card for winddlrectipns.

T > < t/l z < UJ > o < UJ > UI - i te UI

I

y ^ |—CL A5SICAL METHOD EXTRAPOLATED

10' 10" O ' 1 0 ' 10 «-2 v-i

EXCESS FREOUENCY M TIMES PER YEAR

NEW METHOO

CLASSICAL METHOO

Fig. 6: Comparison of the excess frequency curves obtained bij the new method and the classical method at the mouth of the Eastern Scheldt for the original situation.

> UJ _ l < 5 UJ tn < UI

z

I

-^LASSICAL METHOO-ORIGINAL SITUATION

^„.""^'EH METHOO-NEW SITUATION

.^^TRATEGY BARRIER: CLOSE AT MSL • 3.25M

10"

F i g . 7;

10-' lOr* «•^ lO" 10 = 10* 10"^

EXCESS FREQUENCY IN TIMES PER YEAR Excess frequency curves for the Philipsdam.

z UJ > UJ _l < 5 lUJ tn

z

<

I

EXCESS FREQUENCY IN TIMES PER YEAR Excess frequency curves for the Oesterdam.