Hydro-morphological study

ADMINISTRAQAO-GERAL DO PORTO DE LISBOA

Hydro-morphological study

Tagys Estuary

Part 1

Wave penetration model

Volume 1.1

Text & figures

June 1982 / P473

PORT AND WATERWAY ENGINEERS

-CONTENTS 1 . I n t r o d u c t i o n 2 . S e t - u p o f t h e s t u d y 3 . D e t e r m i n a t i o n o f i n p u t d a t a k. C o m p u t a t i o n s 5 . D i s c u s s i o n s o f t h e r e s u l t s 6 . C o n c l u s i o n s FIGURES TABLES

1 . INTRODUCTION The a i m o f t h e t o t a l s t u d y i s t o h a v e an o p e r a t i o n a l m a t h e m a t i c a l model w i t h w h i c h i t i s p o s s i b l e t o s t u d y t h e h y d r a u l i c and m o r p h o l o g i c a l c o n s e q u e n c e s o f v a r i o u s i n t e r v e n t i o n s i n t h e p r e s e n t s t a t e . T h i s f i r s t p a r t o f t h e s t u d y i s d e a l i n g w i t h t h e w a v e p e n e t r a t i o n i n t h e B u g i o -reg i o n .

The r e s u l t s p r e s e n t e d i n t h i s r e p o r t can be used as a b a s i s f o r

f u r t h e r c a l c u l a t i o n s l a t e r i n t h i s s t u d y , e s p e c i a l l y t h e m o r p h o l o g i c a l c a l c u l a t i o n s . But t h e y can a l s o be used as b o u n d a r y v a l u e s f o r t h e d e s i g n p a r a m e t e r s f o r c o n s t r u c t i o n s p l a n n e d i n t h e B u g i o - a r e a . H a v i n g an i d e a o f t h e w a v e - c l i m a t e i n t h e o u t e r e s t u a r y , t h e l a y - o u t o f h a r b o u r - b a s i n s , b e r t h s and j e t t i e s can be d e t e r m i n e d . A l s o t h e d e s i g n o f b r e a k w a t e r s d e p e n d s on t h e waves t o be e x p e c t e d i n t h e a r e a . T h i s r e p o r t g i v e s a s h o r t r e v i e w o f t h e a p p r o a c h t o t h e p r o b l e m , t h e used b o u n d a r y v a l u e s ( d e e p w a t e r wave d a t a , c a l i b r a t i o n d a t a , g e o m e t r y ) , a d i s c u s s i o n o f t h e r e s u l t s and a c o n c l u s i o n . A d e s c r i p t i o n o f t h e

m a t h e m a t i c a l b a c k g r o u n d o f t h e model i s p r e s e n t e d i n Annex A. In Annex B t h e g r a p h i c a l o u t p u t o f t h e c a l c u l a t i o n i s g i v e n .

2 . SET-UP OF THE STUDY The s t u d y i s s p l i t - u p i n t o 3 d i f f e r e n t t y p e s o f m o d e l s : - wave p e n e t r a t i o n m o d e l s - t i d a l c u r r e n t m o d e l s - s e d i m e n t o l o g i c a l m o d e l s T h i s r e p o r t d e s c r i b e s t h e r e s u l t s o f t h e m a i n wave p e n e t r a t i o n m o d e l , w h i c h g i v e s a d e s c r i p t i o n o f t h e way o c e a n waves p e n e t r a t e i n t o t h e e s t u a r y . The c a l c u l a t i o n has been c a r r i e d o u t w i t h t h e use o f t h e c o m p u t e r p r o g r a m s a v a i l a b l e i n o u r o f f i c e . T h e s e p r o g r a m s a r e u s i n g

l i n e a r wave t h e o r y and t h e B o u w s / B a t t j e s m e t h o d t o o v e r c o m e t h e c a u s t i c s p r o b l e m . A d e t a i l e d d e s c r i p t i o n o f t h e m a t h e m a t i c a l b a c k -g r o u n d o f t h e s e p r o -g r a m s i s -g i v e n i n a n n e x A t o t h i s r e p o r t . The d e t a i l e d wave model i s n o t y e t r u n , b e c a u s e i t p r o v e d f r o m t h e o v e r a l l m o d e l , t h a t r u n n i n g t h i s model i s o n l y u s e f u l ! , i f t h e p l a n n e d p o r t - l a y - o u t f o r t h e B u g i o a r e a i s e n t e r e d c o r r e c t l y i n t h e m o d e l . For a d e s c r i p t i o n o f t h e nowadays s i t u a t i o n t h e o v e r a l l m e t h o d p r o v i d e s e n o u g h i n f o r m a t i o n . T h e r e f o r e a l s o w a v e - h e i g h t c h a r t s and w a v e - d i r e c t i o n c h a r t s w e r e made o f a l l t h e r u n s o f t h e o v e r a l l m o d e l ; t h i s i n a d d i t i o n t o t h e r a y d i a g r a m s , as m e n t i o n e d i n t h e t e r m s o f r e f e r e n c e . For t h e l o c a t i o n o f t h e o v e r a l l m o d e l , see f i g . 1 . i t i s s u g g e s t e d t h a t t h e r u n s f o r t h e d e t a i l e d model s h o u l d be d e t e r m i n e d i n d i s c u s s i o n w i t h t h e c l i e n t . In t h i s r e p o r t a d e s c r i p t i o n o f t h e used i n p u t d a t a f o r t h e wave p e n e t r a t i o n model i s g i v e n and a d i s c u s s i o n o f t h e r e s u l t s . F i n a l l y , some c o n c l u s i o n s a r e d r a w n .

3 .

3 . DETERMINATION OF INPUT DATA

Wave d a t a

B a s i s f o r t h e c a l c u l a t i o n a r e t h e d e e p - w a t e r wave d a t a as p r e s e n t e d by t h e I n s t i t u t e H i d r o g r a f i c o . These d a t a c o n s i s t o f m e a s u r e m e n t s n e a r C o s t a C a p a r i c a and L a r g o a de I ' A l b u f e i r a .

Because t h e d a t a o f A l b u f e i r a a r e m e a s u r e d on r e l a t i v i l y deep ^ater, t h e y a r e used as i n p u t f o r t h e m o d e l , w h i l e t h e C a p a r i c a d a t a a r e used f o r c a l i b r a t i o n . From A l b u f e i r a 702 o b s e r v a t i o n s a r e a v a i l a b l e , f r o m A u g u s t 2 7 t h , 1979 u n t i l A p r i l 3 0 t h , 1 9 8 0 . A l t h o u g h t h e s e d a t a do n o t c o v e r a f u l l y e a r , one may assume, t h a t t h e s e d a t a a r e , as a f i r s t a p p r o x i m a t i o n r e p r e s e n t a t i v e f o r t h e wave c l i m a t e i n t h e a r e a .

When a f t e r some y e a r s more l o n g t e r m wave m e a s u r e m e n t s a r e a v a i l a b l e i t i s p o s s i b l e t o r e a d j u s t t h e r e s u l t s o f t h e s e c a l c u l a t i o n s .

For such a r e a d j u s t m e n t i t i s n o t n e c e s s a r y t o make a l l t h e c o m p u t e r -r u n s a g a i n . The -r e s u l t s o f t h e d a t a p -r e s e n t e d i n t h i s -r e p o -r t can be u s e d , when some a d d i t i o n a l r u n s a r e made f o r s p e c i a l c a s e s , f o l l o w i n g f r o m t h e new m e a s u r e m e n t s .

The r e q u i r e d i n p u t - v a l u e s f o r t h e model a r e w a v e - h e i g h t , w a v e - p e r i o d and w a v e - d i r e c t i o n . For t h e w a v e - h e i g h t t h e s i g n i f i c a n t w a v e h e i g h t f r o m t h e measurements i s u s e d . The z e r o - c r o s s i n g p e r i o d i s used as i n p u t f o r t h e p e r i o d .

In t h e t a b l e b e l o w t h e r e l a t i o n b e t w e e n H and T i s g i v e n , ( t a b l e c o p i e d f r o m d a t a I . H . ) H 3 k 5 6 7 8 9 10 11 12 13 14 15 0 m O.kl 2 . 4 2 1.99 2 . 8 5 2 . 2 7 1.57 1.28 0 . 4 3 0 . 4 3 0 . 1 4 0 . 5 m 1.^+2 5•k^ 5 . 5 6 4 . 4 2 3 . 4 2 3 . 2 8 2 . 1 4 1.57 0 . 4 3 0 . 1 4 0 . 1 4 1.0 m O . I A 3 . 9 9 4 . 9 9 5 . 7 0 5 . 7 0 3 . 8 5 2 . 7 1 0 . 8 5 0 . 1 4 0 . 1 4 0 . 1 4 1.5 m 0 . 4 3 3 . 4 2 3 . 7 0 2 . 8 5 2 . 1 4 1.71 0 . 4 3 0 . 1 4 2 . 0 m 1 . 2 8 1.85 1.57 1.57 0 . 5 7 0 . 4 3 0 . 1 4 2 . 5 m 0 . 4 3 0 . 4 3 0 . 5 7 0 . 4 3 0 . 1 4 3 . 0 m 0 . 4 3 0 . 1 4 3 . 5 m 0 . 1 4 i t . 0

_{£ J 1}

f r e q u e n c y o f o c c u r r a n e e ( ^ ) In t h i s way t h e w a v e - c l i m a t e i s s p l i t up i n 59 e l e m e n t s . Because t h i s number o f e l e m e n t s i s t o o l a r g e , t h e e l e m e n t s a r e g r o u p e d . For c a l c u l a t i n g t h e a v e r a g e v a l u e o f e a c h g r o u p f o r t h e w a v e - h e i g h t t h e ( w e i g h e d ) r o o t - m e a n - s q u a r e v a l u e i s u s e d . For t h e p e r i o d s t h e n o r m a l a r i t h m e t i c ( w e i g h e d ) mean i s u s e d . T h i s o p e r a t i o n r e s u l t s i n t h e f o l l o w i n g t a b l e : H T % (m) ( s e c ) 0 . 5 3 . 8 6 . 8 2 1 . 0 4 . 0 4 . 1 3

1

0 . 8 5 . 0 9 . 8 3 1.6 5 . 0 4 . 7 0 i 0 . 8 1 6 . 0 1 1 . 2 6 1.7 6 . 0 5 . 9 8 i 0 . 8 7 . 0 1 0 . 1 2

i

' - 7 7 . 0 4 . 4 2

5 . H T % (m) ( s e c ) 0 . 8 ! 8 . 0 ' 1.11 1.6 8 . 0 3 . 7 3 0 . 8 9 . 0 5 . 9 9 ' 1.6 9 . 0 2 . 2 7 2 . 8 7 - 7 2 . 2 8 0 . 6 1 0 . 5 5 . 2 7 3 . 5 1 0 . 2 1.28 0 . 7 1 4 . 3 0 . 4 3 The d a t a o f t h i s t a b l e a r e a l s o p r e s e n t e d i n an e x c e e d a n c e - d i a g r a m (see f i g . 2 )

W i t h t h e s e 16 e l e m e n t s a l a r g e number o f c a l c u l a t i o n s has been made. D u r i n g t h e c a l c u l a t i o n s i t p r o v e d h o w e v e r t h a t s p l i t t i n g up t h e wave c l i m a t e i n 16 e l e m e n t s i s n o t n e c e s s a r y . T h e r e f o r e t h e l a s t c a l c u l a t i o n s have been made w i t h o n l y 8 e l e m e n t s , v i z :

H T (m) ( s e c ) 0 . 7 2 3 . 8 1 0 . 9 6 0 , 7 9 3 . 5 21 .09 1.71 5 . 6 1 0 . 6 8 1.15 7 . 8 3 3 . 7 9 2 . 8 0 1.1 2 . 1 8 0 . 6 0 1 0 . 5 5 . 2 7 3 . 5 0 1 0 . 2 1.28 0 . 7 0 1 4 . 3 0 . 4 3

6 . A c c o r d i n g t h e i n f o r m a t i o n f r o m t h e I n s t i t u t e H i d r o g r a f i c o , t h e w a v e -d i r e c t i o n s a r e -d i s t r i b u t e -d as f o l l o w s : 2 3 0 ° - 2 6 0 ° 8 2 °/ '0 2 6 5 ° 13 9 °/ 2 7 0 ° 24 6 °/ 'a 2 7 5 ° 19 0 °/ '0 2 8 0 ° 21 3 9 2 8 5 ° - 3 2 0 ° 12 9 9 '0

I t can be seen t h a t n e a r l y 8 0 ^ o f t h e waves come f r o m t h e d i r e c t i o n s 2 6 5 ° , 2 7 0 ° , 2 7 5 ° , 2 8 0 ° . T h e r e f o r e , i n . f i r s t i n s t a n c e o n l y t h e s e s i t u a t i o n s have been c o n s i d e r e d . A n a l y s i s o f t h e r e l a t i o n b e t w e e n w a v e - p e r i o d and w a v e - h e i g h t i n d i c a t e d t h a t t h e r e i s a r a t h e r u n i f o r m d i s t r i b u t i o n o f p e r i o d s and w a v e - h e i g h t s o v e r t h e d i r e c t i o n . So, i n f i r s t i n t a n c e 4 x 16= 64 w a v e - p e n e t r a t i o n r u n s w e r e made, ( r u n s TG01 u n t i 1 T G 6 4 ) .

The f a c t t h a t a l l t h e waves come f r o m w e s t e r n d i r e c t i o n s i m p l i e s however t h a t t h e r e a r e no waves f r o m o t h e r d i r e c t i o n s . And b e c a u s e t h e s e d a t a a r e s u p p o s e d t o be deep w a t e r wave d a t a , i t i m p l i e s t h a t on t h e w e s t e r n A t l a n t i c Ocean t h e r e a r e no waves f r o m o t h e r d i r e c t i o n s t h a n w e s t . Of c o u r s e t h i s c a n n o t be t r u e . An e x p l a n a t i o n f o r t h i s c o n t r a d i c t i o n can be f o u n d i n t h e f a c t t h a t t h e o b s e r v a t i o n s o f w a v e - h e i g h t and w a v e - p e r i o d a r e made w i t h a w a v e - r i d e r b u o y , w h i c h as l o c a t e d a t r e l a t i v e l y deep w a t e r , w h i l e t h e wave d i r e c t i o n s w e r e o b s e r v e d v i s u a l l y f r o m t h e s h o r e .

T h u s : w a v e - h e i g h t s and w a v e - p e r i o d s a r e deep w a t e r d a t a and wave d i r e c t i o n s a r e s h a l l o w w a t e r d a t a .

To i l l u s t r a t e t h e e f f e c t o f t h e d e p t h on t h e wave d i r e c t i o n s i x l a r g e s c a l e w a v e - p e n e t r a t i on c a l c u l a t i o n s have been made ( s e e f i g . 2 0 - 2 5 ) •

I t can be seen t h a t n e a r t h e m e a s u r i n g s t a t i o n t h e wave i s n o t v e r y much r e f r a c t e d , b u t t h a t n e a r t h e c o a s t a l l t h e waves come f r o m w e s t e r n d i r e c t i o n s .

Because o f t h i s f a c t i t i s n o t p o s s i b l e t o use t h e d i r e c t i o n a l i n f o r m a t i o n f r o m t h e I . H . - d a t a . As a r e p l a c e m e n t t h e d a t a f r o m t h e "Ocean Wave S t a t i s t i c s " (Hogben & Lumb, HMSO L o n d o n , I 9 6 7 ) h a v e been u s e d ; d i r . % 1 8 0 ° ^% 2 1 0 ° / 2 3 5 ° 3.2^0 2 4 0 ° 2 4 0 ° 5 . 6 ^ 2 7 0 ° lk% \ 2 4 5 ° 4 . 3 ^ 3 0 0 ° 2 0 ^ \ 2 5 0 ° 4.9°^ 3 3 0 ° 2 0 ^ Because d e t a i l e d c a l c u l a t i o n s f o r t h e d i r e c t i o n s 235 - 250 w e r e a v a i l a b l e f r o m i n i t i a l r u n s t h e 18^ f r o m 2 4 0 ° has been s p l i t up i n more d e t a i 1 . Because waves f r o m t h e s o u t h o c c u r r e l a t i v e l y s e l d o m , no s p e c i a l c a l c u l a t i o n s has been made f o r t h i s d i r e c t i o n . But i n o r d e r t o g e t t h e r i g h t r e s u l t s t h e o c c u r r a n c e o f t h e 2 1 0 ° - w a v e s has been i n c r e a s e d w i t h 8 ^ . From f i g . 24 and 27 f o l l o w s c l e a r l y t h a t waves f r o m 3 0 0 °

and 3 3 0 ° do n o t r e a c h t h e s t u d i e d a r e a , so t h e y a r e o m i t t e d t o o . The t o t a l number o f wave p e n e t r a t i o n c a l c u l a t i o n s i s t h e r e f o r e 8 0 , n o t i n c l u d e d t h e 6 c a l c u l a t i o n s i n t h e l a r g e s c a l e m o d e l . C a l i b r a t i o n d a t a Because n o t v e r y much w a v e - m e a s u r e m e n t s w e r e a v a i l a b l e f r o m t h e a r e a i t s e l f , i t was d i f f i c u l t t o f i n d wave d a t a f o r c a l i b r a t i o n o f t h e m o d e l . The b e s t d a t a f o r t h i s p u r p o s e w e r e w a v e - m e a s u r e m e n t s made by t h e I n s t i t u t e H i d r o g r a f i c o j u s t o f f C o s t a C a p a r i c a (426 o b s e r v a t i o n f r o m 1 0 - 0 7 - 1 9 7 9 u n t i l 1 5 - 0 4 - 1 9 8 0 ) . The d a t a p r o v i d e d w e r e r e p r o c e s s e d and a r e p r e s e n t e d i n f i g . 3 . The d i r e c t i o n o f a l l t h e waves was 2 4 0 ° . Geometry The l o c a t i o n o f t h e m o d e l e d a r e a i s p r e s e n t e d i n f i g u r e 1 . T h i s a r e a i s d e v i d e d i n t o 40 x 66 = 2640 mesh p o i n t s , e a c h on a d i s t a n c e o f 250 The d e p t h i n f o r m a t i o n used i s t a k e n f r o m t h e h y d r o g r a p h i c c h a r t s ,

s u r v e y e d by t h e I n s t l t u t o H i d r o g r a f i c o i n 1965 ( s c a l e 1 : 5 0 0 0 ) . For t h e B u g i o a r e a a s u r v e y f r o m 197^ has been u s e d . The d a t a w e r e e n t e r e d i n t o t h e c o m p u t e r , w i t h an a c c u r a c y o f 0 . 1 m. A p r i n t - o u t o f t h e e n t e r e d d a t a i s added a t t h e b a c k o f t h i s r e p o r t ( t a b l e 1 ) .

9 . k. COMPUTATIONS F i r s t a l i m i t e d number o f t e s t r u n s w e r e made i n o r d e r t o c h e c k i f a i l p r o g r a m s d i d t h e i r j o b i n t h e c o r r e c t w a y . Then f o r a l l t h e 80 c a s e s a w a v e - p e n e t r a t i o n c a l c u l a t i o n was c a r r i e d o u t , r e s u l t i n g i n w a v e - h e i g h t d a t a a l o n g t h e v a r i o u s w a v e - r a y s . For l a t e r r e f e r e n c e t h e s e d a t a w e r e p r i n t e d o u t and s t o r e d on c o m p u t e r d i s c . The d a t a on d i s c w e r e p l o t t e d , w h i c h r e s u l t e d i n t h e w a v e - r a y d i a g r a m s as p r e s e n t e d i n Annex B. Because t h e r a y s do c r o s s e a c h o t h e r , f r e q u e n t l y , t h e b e h a v i o u r o f t h e waves i n s u c h c a u s t i c s c a n n o t be d e r i v e d f r o m t h e r a y - d i a g r a m s . T h e r e f o r e t h e s t o r e d d a t a w e r e p r o c e s s e d a g a i n a c c o r d i n g t h e Bouws S B a t t j e s m e t h o d , w h i c h r e s u l t e d i n t o t w o m a t r i c e s . The f i r s t m a t r i x c o n t a i n s t h e a v e r a g e d i r e c t i o n i n e a c h m e s h - p o i n t , t h e s e c o n d o n e t h e a v e r a g e w a v e - h e i g h t i n e a c h m e s h - p o i n t . T h e s e two m a t r i c e s w e r e a l s o p l o t t e d . P l o t s a r e p r e s e n t e d i n Annex B. The p r i n t e d c o m p u t e r o u t p u t ( a p p r o x . 200 pages p e r r u n , t h u s i n t o t a l a p p r o x . 14000 p a g e s ) a r e n o t added t o t h e r e p o r t , b u t a r e a v a i l a b l e upon r e q u e s t . In t e n s e p e r a t e p o i n t s ( f o r t h e i r l o c a t i o n s see f i g . 4 ) t h e w a v e -c l i m a t e i s d e t e r m i n e d . The r e s u l t s w e r e p r i n t e d o u t ( s e e t a b l e 2 : " w a v e f r e q u e n c i e s i n s e l e c t e d p o i n t s " a t t h e e n d o f t h i s r e p o r t ) and p l o t t e d ( f i g . 5 - l 4 ) The r e s u l t s o f p o i n t 10 s h o u l d be more o r l e s s i d e n t i c a l t o t h e m e a s u r e d w a v e - c l i m a t e f r o m C o s t a C a p a r i c a . B o t h c u r v e s a r e p l o t t e d i n f i g u r e

15From t h i s f i g u i t e one may c o n c l u d e t h a t t h e model d e s c r i b e s t h e w a v e -p e n e t r a t i o n i n t h e B u g i o a r e a r a t h e r w e l l .

1 2 .

6 . CONCLUSIONS

The wave c l i m a t e i n t h e B u g i o - a r e a i s v e r y i r r e g u l a r due t o t h e

i r r e g u l a r b o t t o m - t o p o g r a p h y . Rough seas may be e x p e c t e d a t any p o i n t s o u t h and s o u t h w e s t o f B u g i o . The n o r t h e r n s l o p e o f t h e B u g i o - b a n l < i s h a r d l y e x p o s e d t o w a v e - i n f 1 u e n c e . P o r t f a c i l i t i e s on t h i s s l o p e a r e n o t v e r y much i n f l u e n c e d by o c e a n w a v e s . i n t h e A l p e i d a o r e g i o n a v e r y t u r b u l e n t a r e a i s . e x p e c t e d . Much s e d i m e n t w i l l be b r o u g h t i n t o s u s p e n s i o n i n t h i s a r e a . Wave . l e i g h t s on t h e B u g i o - b a n k i t s e l f a r e v e r y l i m i t e d due t o s m a l l w a t e r d e p t h s , a l t h o u g h d u r i n g h i g h w a t e r t h e w a v e h e i g h t may r i s e t o a c o n s i d e r a b l e v a l u e .

1 0 0 . 0 0 ^

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0.00

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WAVE-HEIGHT

A. G. P. L-

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n d m i o

-aliadnooht holland

CALCULATED WAVE HEIGHTS

ALBUFEIRA

h y ö R o n d m i o

WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n d m i c

-a i i ednooht ho11-and

CALCULATED WAVE HEIGHTS

COSTA CAPARICA

h y ö R o n d m i c

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

K

^

^

^

^

eliodroohfc holland

CALCULATED WAVE HEIGHTS

POINT 1

K

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

hyöRondmiQ

bv

oliodn«oh-fc holland

CALCULATED WAVE HEIGHTS

POINT 2

1 0 0 . 0 a _

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n d m i c

-«liedr'soh't holland

CALCULATED WAVE HEIGHTS

POINT 3

h y ö R o n d m i c

100.00_

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

h v ó R o n d m i c

-s 1 i edn®oh"fc ho 11 and

CALCULATED WAVE HEIGHTS

POINT 4

h v ó R o n d m i c

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WAVE-HEIGHT

A. G. P. L.

h y ö R o n d m i c

-sliedr-eoht. holland

MATHEMATICAL MODEL TAGUS ESTUARY

CALCULATED WAVE HEIGHTS

POINT 5

oJ CO ^

WAVE-HEIGHT

A- G. P« L.

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n A m i c

-®1

iedneoht

holland

CALCULATED WAVE HEIGHTS

POINT 6

h y ö R o n A m i c

1 0 0 , 0 0 ^

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n d m i o

-® 1

i «dneohfc ho11and

CALCULATED WAVE HEIGHTS

POINT 7

h y ö R o n d m i o

1 0 0 . 0 0 _ „

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

h y ö R o n d m i o

-® 1

i edr-tsoht holland

CALCULATED WAVE HEIGHTS

POINT 8

h y ö R o n d m i o

100.00.

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

CALCULATED WAVE HEIGHTS

h y ö R o n d m i c

-«liedneoht holland

POINT 9

h y ö R o n d m i c

100.00,

8 0 . 0 0 _

Lü

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WAVE-HEIGHT

A. G. P. L.

MATHEMATICAL MODEL TAGUS ESTUARY

hvóRondmic-sla sdneoht ho11and

CALCULATED WAVE HEIGHTS

POINT 10

100.0a_

Lü U Z < • UJ UJ

u

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CALCULATED

MEASURED

s)

S 3 O J c a «

00

S 3

WAVE-HEIGHT

A. G. P. L.

bv

hyöRondmiQ

s

1

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1 1

and

MATHEMATICAL MODEL TAGUS ESTUARY

MEASURED AND CALCULATED DATA

COSTA CAPARICA

n --^ X 3 X — 7^ 3 ~ ••^ 23 X = - i - — - ^ — 7 — 7 — 7 — 7 — 1 — i — i . ' N i ^ ' i " ^ ' — 7 i 7 - 7 - 7 - T ' . - - 7 ^ 7 - N 7 - N 7 - j 7 ^ 7 — T — I — I — I — I ^ I -s- I .•SI I I — 7 ^ 7 = • 7 " I — t — I ^ • I ^ f -"^ ' — I -1 = I — I _ I _ I i = _ï- = • O C c *. — :s' .N _ I _ 1 _ 1 _ I I rM I M 1 ,N I N I ^ - c c -•! •r c c .-5 - 3 c -^ = o — 1 _ I „ 1 _ I — I r I rJ I r< I >i I C S I — 7 — 7 — 7 — I I " i I ~ J 1 N I I :N I r- ^ = ; -1 1-0 -n ; 's; e s : r - .1 x J rM —. - i ' i ' - ' O rs' - s j - I s, I -.1 5- ^ 3 ~ ci; - .~ O- — X r- .-N ^ ts; X r^i c- ,-s- r -r r^ — _ _ >i ^ ^ .-M e w s j s^ — IC r- O -r O D — = N — S 1 3 - - J " ,-N* — f^.- — r-i r>; rs. j • r- c rs; r* c IN — — vN --^ fsf — ^ « r s — .-N — r s — *n ^ - r , - • 3 — -1 — • _ _ « rsi — rM . r ^ w"' r r ^ ^- „ SI „ ^ _

T A B L E i l ( c o n t . )

T G A 0 1 T G A 0 2 T G A G 3 T G A 0 4 T G A 0 5 T G A 0 6 T G A 0 7 TGA08 T G A Q 9 T G A 1 G T G A 1 1 T G A 1 2 T G A 1 3 T G A 1 4 T G A 1 5 T G A 1 6 TGA17 TGA18 TGA19 T G A 2 0 T G A 2 1 T G A 2 2 TGA23 T G A 2 4 T G A 2 5 T G A 2 6 TGA27 T G A 2 8 TGA29 TGA30 TGA31 T G A 3 2 TGA33 TGA34 TGA35 TGA36 TGA37 T G A 3 8 TGA39 T G A A O T G A 4 1 T G A 4 2 T G A 4 3 T G A A A T G A 4 5 TGA46 TGAA7 T G A A 8 T G A 4 9 T G A 5 0 T G A 5 1 T G A 5 2 T G A 5 3 . 2 2 ^ . 1 3 ? ; . 3 1 ? ; .3É>5ó . 1 9 ^ . 3 2 % .23%

.

]2% . 1 9 % . 0 7 % . 0 7 % . 1 7 % . 0 4 % . 0 1 % . 3 8 % . 2 3 % . 5 5 % . 2 6 % . 6 3 % . 3 3 % .57% . 2 5 % . 4 1 % . 2 1 % . 3 3 % . 1 3 % . 1 3 % . 3 0 % . 0 7 % . 0 2 % . 2 9 % . 1 8 % . 4 2 % . 2 0 % . 4 8 % . 2 6 % . 4 4 % , 19% . 3 1 % . 1 6 % . 2 6 % . 10% . 10% . 2 3 % . 0 5 % . 0 2 % . 3 3 % . 2 0 % . 4 8 % . 2 3 % .55% 1 2 3 4 5 6 ₇ 8 9 . 5 0 . 5 0 " .k3 . 4 7 .^^9 . 5 2 . 4 2 . 4 8 1 . 0 0 . 9 9 . 9 7 . 9 2 . 9 8 1 . 1 2 . 5 1 . 8 7 . 9 0 . 8 0 . 7 4 . 8 1 . 5 9 . 7 2 . 7 1 . 4 1 . 4 3 . 5 5 1 . 6 0 1 . 4 9 1 . 6 3 1 . 1 9 1 . 4 4 1 . 5 9 . 8 0 . 8 7 1 . 10 . 8 0 . 7 2 . 6 3 . 5 6 . 7 0 . 6 2 . 0 0 . 0 0 . 4 7 1 . 7 0 1 . 5 3 1 . 3 3 1 . 1 8 1 . 4 8 . 9 4 . 0 0 . 0 0 1 . 10 . 7 9 . 7 5 . 7 5 . 4 7 . 7 6 . 7 9 . 0 0 . 0 0 . 6 9 1 . 6 8 1 . 5 9 1 . 6 0 1 . 0 0 1 . 6 2 1 . 0 8 . 0 0 . 0 0 . 7 4 . 7 6 . 6 9 . 3 6 . 3 1 . 9 1 . 6 2 . 0 0 . 0 0 . 6 6 1 . 5 3 1 . 3 8 . 5 3 . 6 2 1 . 8 2 1 . 2 2 . 0 0 . 0 0 . 8 2 . 7 4 . 8 5 . 2 4 . 2 5 . 5 1 . 6 2 . 0 0 . 0 0 . 6 3 1 . 4 8 1 . 7 0 . 3 9 . 5 0 1 . 0 2 . 5 7 . 0 0 . 0 0 . 7 7 2 . 7 0 2 . 5 8 1 . 2 0 1 . 2 9 3 . 5 7 . 7 7 . 0 0 . 0 0 . 7 7 . 5 6 . 9 0 . 4 1 . 0 0 1 . 3 6 . 8 7 . 0 0 . 0 0 . 5 8 3 . 2 4 3 . 3 6 . 9 8 1 . 2 3 2 . 0 0 1 . 1 4 . 0 0 . 0 0 . 7 9 . 7 1 1 . 3 4 . 0 0 . 3 4 . 4 8 . 8 5 . 0 0 . 0 0 . 8 8 . 5 0 . 4 9 . 5 0 . 4 9 . 5 0 . 4 7 . 3 8 . 4 1 . 7 0 1 . 0 0 . 9 6 . 9 9 1 . 0 0 . 9 8 . 9 3 . 4 3 . 7 7 1 . 0 2 . 8 0 . 7 6 . 7 9 , 8 8 . 7 4 . 9 7 . 3 9 . 5 6 . 5 0 1 . 6 0 1 . 5 1 1 . 5 8 1 . 7 7 1 . 4 9 1 . 2 9 . 7 6 1 . 1 3 . . 8 1 . 8 0 . 7 4 . 6 4 1 . 0 3 . 6 6 . 7 9 . 0 0 . 0 0 . 9 7 1 . 6 9 1 . 5 7 1 . 3 6 2 . 1 8 1 . 4 0 . 9 2 . 0 0 . 0 0 . 8 0 . 7 9 . 7 2 1 . 6 2 1 . 0 2 . 7 6 . 7 2 . 0 0 . 0 0 . 7 1 1 . 5 7 1 . 4 4 3 . 2 3 2 . 0 5 1 . 5 2 1 . 0 3 . 3 0 . 2 9 . 5 5 . 7 6 . 8 9 1 . 0 9 . 0 0 . 6 9 . 7 1 . 0 0 . 0 0 . 5 4 1 . 5 2 1 . 7 7 2 . 1 8 . 0 0 1 . 3 7 1 . 0 2 . 0 0 . 0 0 . 5 8 . 7 3 . 7 4 . 4 2 . 0 0 . 7 8 . 9 5 . 0 0 . 0 0 . 5 2 1 . 4 7 1 . 4 7 . 6 9 . 0 0 1 . 5 7 1 . 0 7 . 0 0 . 0 0 . 5 4 2 . 7 0 3 . 0 2 3 . 0 9 . 0 0 2 . 12 1..38 . 0 0 . 0 0 . 5 9 . 5 3 . 5 7 . 3 8 . 4 0 . 3 9 1 . 4 4 . 0 0 . 0 0 . 5 4 3 . 1 1 3 . 2 1 1 . 0 3 . 0 0 . 8 8 1 . 2 1 . 0 0 . 0 0 . 8 2 . 6 6 . 7 0 . 3 7 . 0 0 . 4 1 . 8 2 . 0 0 . 0 0 . 6 8 . 5 0 . 4 9 . 5 1 . 4 8 . 4 9 . 4 9 . 0 0 . 4 5 . 7 9 1 . 0 0 . 9 6 1 . 0 7 1 . 0 2 . 9 7 . 9 9 . 0 0 1 . 0 3 1 . 1 5 . 8 0 . 6 9 . 7 8 . 6 5 . 7 5 1 . 1 7 . 4 4 . 0 0 1 . 6 5 1 . 6 0 1 . 3 7 1 . 5 6 1 . 2 9 1 . 5 0 1 . 9 9 . 8 7 . 0 0 1 . 6 7 - . 8 0 . 6 6 1 . 1 5 . 7 3 . 6 8 1 . 6 4 . 0 0 . 0 0 . 4 8 1 . 7 0 1 . 4 0 2 . 4 5 1 . 5 5 1 . 4 5 1 . 1 3 . 0 0 . 0 0 . 5 5 . 7 9 . 8 5 1 . 7 5 . 5 5 . 6 3 1 . 2 5 . 0 0 . 0 0 . 9 7 1 . 6 7 1 . 8 0 2 . 8 3 1 . 1 5 1 . 3 3 1 . 1 3 . 0 0 . 0 0 . 6 7 . 7 6 . 6 9 . 7 8 . 3 8 1 . 0 2 . 9 0 . 0 0 . 0 0 . 7 4 1 . 5 3 1 . 3 7 1 . 5 5 . 7 7 2 . 0 4 . 7 8 . 0 0 . 0 0 . 5 9 . 7 4 . 8 2 . 7 6 . 0 0 1 . 0 1 . 8 2 . 0 0 . 0 0 . 7 0 1 . 4 3 1 . 6 3 1 . 2 8 . 0 0 2 . 0 2 . 9 1 . 0 0 . 0 0 . 6 5 2 . 7 0 2 . 7 2 3 . 2 4 . 0 0 2 . 8 1 . 9 8 . 0 0 . 0 0 . 3 7 . 5 3 1 . 0 6 . 6 7 . 0 0 . 4 5 . 5 0 . 0 0 . 0 0 . 5 4 3 . 1 1 3 . 3 4 1 . 8 5 1 . 1 0 2 . 5 3 2 . 0 5 . 0 0 . 0 0 . 9 3 . 6 1 1 . 0 4 . 4 9 . 0 0 . 6 0 . 8 7 . 0 0 . 0 0 . 0 0 . 5 0 . 5 0 . 4 9 . 5 0 . 4 9 . 4 8 . 5 4 . 4 4 . 3 3 1 . 0 0 . 9 9 . 9 7 . 9 8 . 9 8 . 9 6 . 3 9 . 8 0 . 6 0 . 8 0 . 7 9 . 6 6 . 7 2 . 7 5 . 7 9 1 . 4 8 . 3 6 . 6 6 1 . 6 0 1 . 5 8 1 . 3 2 1 . 4 3 1 . 5 0 1 . 5 8 . 5 9 . 7 2 1 . 3 1 . 8 0 . 7 6 . 5 0 . 5 5 . 7 2 1 . 0 1 . 0 0 . 3 3 . 7 3 10 . 9 4 . 6 7 1 . 3 4 . 5 5 1 . 1 8 1 . 5 5 3 . 2 9 . 4 4 . 8 8 . 3 8 . 7 6 1 . 7 2 . 3 2 2 . 8 6 . 0 0 . 5 3 1 . 0 1 . 7 7 1 . 5 6 . 7 3 1 . 5 5 . 7 4 1 . 4 8 . 6 7 1 . 3 4 . 3 3 . 6 6 2 . 6 0 . 2 6 1 . 4 8 . 4 4 . 5 0 1 . 0 5 1 . 2 8 2 . 5 5 . 7 3 1 . 5 6 . 6 9 1 . 4 7 . 6 4 1 . 2 9 . 5 6 1 . 1 2 1 . 8 7 . 3 3 . 7 1 . 0 0 . 4 9 . 9 6 . 6 4 1 . 2 8 . 7 5

T A B L E : 2

TGA54 .29% 1.70 1.62 1.06 1.16 TGA55 .50% . 7 9 1.05 . 4 7 1.17 TGA56 .22% 1.67 2 . 2 3 1.01 _1.57 TGA57 .36% . 7 7 1.60 . 4 7 . 7 0 TGA58 . 1 8 % 1.54 3 . 1 9 . 9 4 1.21 TGA59 .29% . 7 6 1.85 . 5 9 . 9 2 TGA60 . 1 1 % 1.51 2 . 3 6 1.17 1.83 TGA61 . 1 1 % 2 , 7 2 3 . 3 3 1.46 1.41 TGA62 .26% . 5 6 . 8 6 . 0 0 1.46 TGA63 .06% 3 . 2 6 2 . 4 3 . 0 0 2 . 7 8 TGA64 .02%

.68

. 7 6 . 0 0 1.71 TGA65 1.97% . 0 0 . 7 1 . 7 2 . 7 6 TGA66 3.80% . 0 0 . 7 1 .74 1.01 TGA67 1.92% . 0 0 1.55 1.64 1.97 TGA68 6.08% . 0 0 . 6 9 . 8 2 , 7 0 TGA69 . 4 1 % . 0 0 1.86 1.93 1.02 TGA70 .95% . 0 0 . 4 3 .63 . 4 9 TGA71 .23% . 0 0 2 . 2 2 1.88 2 . 4 5 TGA72 . 0 8 % . 0 0 . 5 4 . 6 7 . 6 0 TGA73 2.63% . 0 0 . 7 2 . 7 1 . 6 5 TGA74 5.06% . 0 0 . 8 9 . 8 6 2 . 6 2 TGA75 2.56% . 0 0 1.88 2 . 1 3 8 . 2 2 TGA76 8 . 1 1 % . 0 0 1.49 1.33 1.70 TGA77 .55% . 0 0 3 . 8 3 3 . 2 0 1.44

TGA78

1.27% . 0 0 . 6 5 . 8 0 . 2 5 TGA79 . 3 1 % . 0 0 3 . 9 0 4 . 6 3 . 0 0 TGA80 . 10% . 0 0 .91 1.53 . 4 0

WAVE FREQUENCIES IN SELECTED PIONTS

1.53 . 9 4 . 0 0 . 7 2 1.28 1.60 . 7 6 1.03 2 . 0 6 . 0 0 . 6 0 . 6 3 1.61 1.16 . 8 0 . 0 0 . 7 9 1.33 1.33 . 8 5 . 0 0 , 0 0 . 7 3 . 3 8 2 . 6 5 . 9 9 . 8 9 . 0 0 . 7 0 . 7 7 . 5 2 . 5 6 . 0 0 . 0 0 . 6 7 . 4 6 1.04 . 5 3 . 0 0 . 0 0 . 8 6 1.24 4 . 2 4 1.54 . 2 7 . 0 0 . 7 7 1.34 . 3 6 . 0 0 . 0 0 . 0 0 . 6 7 . 5 2 2 . 0 0 1.26 . 0 0 . 0 0 .83 1.51 . 6 7 . 5 1 . 0 0 . 0 0 . 0 0 . 5 8 .71 . 7 0 . 6 0 . 6 7 . 5 9 . 7 0 .73 1.00 . 6 4 . 7 0 . 8 2 . 7 3 1.57 2 . 3 2 . 8 8 . 7 7 1.18 1.53 1.06 1.17 . 0 0 . 0 0 1.14 . 8 8 2 . 5 8 1.65 . 0 0 . 0 0 . 6 4 2 . 5 3 . 5 7 . 6 4 . 8 1 . 0 0 . 3 9 . 4 0 3 . 1 9 1.70 . 0 0 . 0 0 .93 2 . 1 3 . 7 4 . 9 1 . 0 0 , 0 0 . 0 0 . 5 4 . 7 0 . 6 3 . 0 0 1.07 . 8 3 . 6 7 . 7 1 . 9 2 . 0 0 . 4 9 . 9 6 . 3 3 1.29 1.61 . 0 0 . 4 4 . 5 3 . 6 1 2 . 4 4 1.36 . 4 8 . 7 9 . 8 4 3 . 0 6 ' 1.66 . 6 3 . 0 0 4 . 0 0 . . 6 9 1.58 . 3 2 . 6 2 . 3 3 . 2 4 . 0 0 . 4 5 1,91 1.37 . 4 9 . 8 9 . 3 5 . 9 0 . 6 6 1 . 2 6 . 0 0 . 0 0 . 0 0 . 8 6

T A B L E : 2 (cont.)