- Email: [email protected]
Cyclogenesis and Forecast of Dramatic Water Elevations in Venice
427
CYCLOGENESIS A N D FORECAST OF DRAMATIC WATER ELEVATIONS I N VENICE
A.
TOMASIN' a n d R . FRASSETTO
1
' L a b o r a t o r i o p e r l o S t u d i o d e l l a Dinamica d e l l e Grandi Masse, C.N.R.,Venezia
(Italy)
ABSTRACT The o c e a n o g r a p h i c and m e t e o r o l o g i c a l a s p e c t s o f t n ? A d r i a t i c s u r g e s are invest i g a t e d . S i n c e V e n i c e f l o o d s a r e only d u e t o s u c h a n o m a l o u s t i d e s , t h e i r f o r e c a s t is o b v i o u s l y r e q u e s t e d f o r p r a c t i c a l p u r p o s e s . S h o r t term w a r n i n g ( a b o u t s i x h o u r s a h e a d ) i s now p o s s i b l e w i t h good a c c u r a c y , t h a n k s t o p r e s e n t u n d e r s t a n d i n g o f t h e s u r g e g e n e r a t i o n . The s t u d y o f t h e c y c l o g e n e s i s i n t h e a t m o s p h e r e o v e r t h e w e s t e r n Alps c a n e x t e n d t h e time f r e e b o a r d f o r alarm. TNTRODUCTION A N D HISTORICAL REMARKS I n t h e h i s t o r y o f Venice, f l o o d s are r e p o r t e d a s a r e c u r r e n t c a l a m i t y f o r t h e c i t y ( U n e s c o , 1 9 6 9 , pp. 3 4 - 6 6 ) .
T h i s i s n o t s u r p r i s i n g when c o n s i d e r i n g t h a t
s t r e e t s a r e n o r m a l l y l e s s t h a n o n e meter o v e r mean w a t e r l e v e l a n d t h e t i d a l range is comparable t o t h i s f i g u r e .
Troubles can c l e a r l y arise even w i t h a s u r g e
h a l f a meter h i g h , w h i c h i s a r a t h e r common o c c u r r e n c e .
F i g u r e 1 shows a n e x -
ample. Even t h o u g h
V e n i c e is l o c a t e d i n a l a g o o n , a n d n o t d i r e c t l y e x p o s e d t o t h e
s e a , f r o m t h e p o i n t o f v i e w o f t i d e s a n d s u r g e s no d i f f e r e n c e i s o b s e r v e d , e x c e p t
f o r a d e l a y o f a b o u t a n h o u r f r o m t h e o p e n sea t o t h e town.
The s i t u a t i o n i n
t h i s c e n t u r y i s c e r t a i n l y w o r s e t h a n i n t h e p a s t , as f a r a s t h e f r e q u e n c y o f f l o o d s 1s c o n c e r n e d .
T h i s is d u e t o v a r i o u s r e a s o n s :
t h e town h a s s u n k a b o u t 2 0 cm
s i n c e t h e l a s t c e n t u r y ( w h i c h is c o m p a r a b l e , p r e s u m a b l y , t o t h e t o t a l s i n k i n g i n the previous millennium).
Also, t h e c o m m u n i c a t i o n b e t w e e n t h e sea a n d t h e l a g o o n
is larger now t h a n Z C O y e a r s a g o , d u e t o e x t e n s i v e d r e d g i n g i n t h e l a g o o n i n l e t s . I n t h o s e d a y s , t h e p e a k l e v e l s o f t h e e x t e r n a l sea were p r e s u m a b l y " c u t " by t h e n a r r o w o p e n i n g s o f t h e l a g o o n , e x c e p t f o r s u r g e s o f long d u r a t i o n ( a n d t h e most t r e m e n d o u s f l o o d , i n 1 9 6 6 , was o f t h i s k i n d ) .
428
.
6
12
18
0
6
12
18
0
6
12
F i g . 1. R e c o r d e d water l e v e l i n V e n i c e , s t a r t i n g A p r i l 20, 1967. r i s e a t t h e e n d o f t h e s e c o n d d a y i s e v i d e n t ( T i m e i s GMT + 1 ) .
18
0
The a n o m a l o u s
ADRIATIC DYNAMICS O n l y t h e A d r i a t i c phenomena ( t i d e s a n d s u r g e s ) w i l l b e c o n s i d e r e d now, s i n c e ,
a s i t was s t a t e d a b o v e , t h e r e is n o s i g n i f i c a n t c h a n g e ( o t h e r t h a n a time l a g ) i n t h e t r a n s i t i o n f r o m t h e o p e n sea t o V e n i c e (Goldmann e t a l . , 1 9 7 5 ) . t a n t f e a t u r e is t h e i n d e p e n d e n c e o f t i d e a n d s u r g e i n t h i s area.
t o h a v e a n y i n t e r a c t i o n , a n d s i m p l y b u i l d up.
An impor-
They seem n o t
A t a first g l a n c e , t h i s c a n be
s u r p r i s i n g , s i n c e t h e n o r t h e r n " h a l f " o f t h e sea i s a p l a t e a u s l o w l y d e c l i n i n g s o u t h w a r d s , u p t o 100 m d e p t h ( s e e F i g . 2 ) . I n s u c h a s h a l l o w a r e a , o c e a n o g r a p h e r s would e x p e c t s u b s t a n t i a l n o n l i n e a r i t i e s i n t h e t i d a l c o n s t i t u e n t s and r e l a t e d i n t e r a c t i o n s between t i d e and s u r g e .
In-
d e e d , t h e r a t i o o f t h e d e p t h t o t h e t i d a l r a n g e i s s t i l l v e r y l a r g e , a n d t h i s accounts f o r t h e observed l i n e a r i t y . S i n c e t i d e a n d s u r g e &re i n d e p e n d e n t , o n e c a n e a s i l y i m a g i n e t h e v a r i o u s rnixt u r e s t h a t can appear.
There can be a c o i n c i d e n c e o f f l o o d t i d e and s u r g e , s o
t h a t t h e l e v e l rises t o d a n g e r o u s v a l u e s , or t h e y c a n o t h e r w i s e c a n c e l e a c h o t h e r . What is i m p o r t a n t f o r n u m e r i c a l a n a l y s i s i s t h a t , g i v e n t h e t i d a l r e c o r d , by s u b t r a c t i n g t h e ordinary astronomical t i d e one obtains a kind of meteorological t i d e
t o be s t u d i e d s e p a r a t e l y .
429
N
40' N
F i g . 2.
The A d r i a t i c S e a .
D e p t h s are i n meters
TIDES A N D SEICHES T h e r a n g e o f t h e a s t r o n o m i c a l t i d e i n c r e a s e s from t h e SE o p e n i n g o f t h e A d r i a t i c t h r o u g h t h e NW e n d w h e r e V e n i c e i s : t h e s p r i n g r a n g e 80 cm ( a b o u t ) ( S t e r n e c k , 1 9 1 9 ) .
2(M2+S )
2
rises from 25 t o
This is consistent with t h e c l a s s i c a l picture
a c c o r d i n g t o w h i c h t h e t i d e , a s o b s e r v e d i n t h e A d r i a t i c , i s f o r c e d by t h e o s c i l l a t i o n o f t h e M e d i t e r r a n e a n by t h e O t r a n t o C h a n n e l , w i t h l i t t l e r e l e v a n c e o f t h e direct lunisolar attraction.
It s h o u l d b e r e m a r k e d t h a t r e c e n t c a l c u l a t i o n s t e n d
t o c h a n g e t h i s p i c t u r e (Tomasin, 1976). 8
A t least for t h e d i u r n a l p a r t of t h e t i d e ,
c o n t r i b u t i o n n o t l e s s t o 30% o f t h e o b s e r v e d r a n g e s h o u l d b e a t t r i b u t e d t o t h e
direct l o c a l f o r c i n g o f the astronomical effects. theoretical interest.
Indeed, t h i s should have only
Much more i m p o r t a n t , i n p r a c t i c e ,
is a n o t h e r r e m a r k :
the
d o m i n a n t t i d a l p e r i o d s , 12 a n d 2 4 h o u r s , a r e c l o s e t o t h e r e s o n a n t p e r i o d s o f t h i s
sea.
The s t u d y o f i t s e i g e n m o d e s i s c r u c i a l , s i n c e f r e e o s c i l l a t i o n s a r e o b s e r v e d
f r e q u e n t l y and w i t h r e l e v a n t amplitude.
T h i s way a common m e c h a n i s m i s f o u n d f o r
a r e g u l a r phenomenon, t h e t i d e , c o n s t a n t t h r o u g h t h e c e n t u r i e s , a n d f o r t h e random b u r s t s o f e n e r g y s t i m u l a t i n g t h e s e a i n t h e storms.
430
The f u n d a m e n t a l mode o f o s c i l l a t i o n ( " s e i c h e " ) o f t h e sea h a s a p e r i o d o f app r o x i m a t e l y 22 h o u r s ( K e s s l i t z , 1 9 1 0 ) .
O r d i n a r y s t o r m s h a v e a much s h o r t e r d u r a -
t i o n , b e i n g s h a r p a t m o s p h e r i c f r o n t s t h a t c r o s s t h e s e a moving e a s t w a r d s .
r e a c t s l i k e a pendulum h i t by a q u i c k p u l s e and s t a r t s o s c i l l a t i n g .
The sea
The r a t h e r
p e c u l i a r s h a p e o f t h e A d r i a t i c makes it as a n o r g a n p i p e , w e l l t u n e d o n i t s t o n e and w i t h l i t t l e d i s s i p a t i o n (Robinson e t a l . ,
1973).
Indeed, one can b e l i e v e
t h a t t h e r e i s l i t t l e i n t e r n a l f r i c t i o n f o r t h e same r e a s o n o f t h e l i n e a r i t y o f T h e r e is a l s o l i t t l e e x t e r n a l r a d i a t i o n o f e n e r g y s i n c e , a f t e r t h e g a t e ,
the tide.
t h e M e d i t e r r a n e a n i m m e d i a t e l y o f f e r s a wi de a n d d e e p b a s i n , v e r y c l o s e t o a n i d e a l i n f i n i t e o c e a n wh ere no e n e r g y c a n b e r a d i a t e d ( T o m a s i n , 1 9 7 1 ) .
A v e r y s l o w damp-
i n g o f t h e f r e e o s c i l l a t i o n s is o b s e r v e d , i f t h e r e i s no f u r t h e r p e r t u r b a t i o n . The 9 - v a l u e ( t h e f i g u r e o f m e r i t ) i s l a r g e r t h a n 1 0 0 , a n d t h e o s c i l l a t i o n s p e r -
s i s t f o r many d a y s ( s e e F i g . 3 ) .
100
-50
-I
16
I
I
17
18
I
19
A s i m i l a r b e h a v i o u r i s shown by t h e f i r s t h a r m o n i c ,
a l l y ( b u t n o t a l w a y s ) smaller i n a m p l i t u d e .
20
*
time (days)
11-hour o s c i l l a t i o n , u s u -
For t h i s f r e q u e n c y a n amphidromy i s
observed i n t h e n o r t h e r n A d r i a t i c , b o t h i n t i d e s and s e i c h e s ( A r t e g i a n i e t a l . , 1972).
I t i s now c l e a r t h a t a s u r g e h a s u s u a l l y a p e c u l i a r s h a p e , s i n c e , d u e t o s e i c h e s , i t is f o l l o w e d by many r e p l i c a s o f s u b s t a n t i a l h e i g h t , s p a c e d l e s s t h a n o n e da y.
It may o c c u r t h a t t h e f i r s t a r r i v a l o f t h e s u r g e d o e s n o t c o i n c i d e w i t h t h e f l o o d t i d e , while t h e second one does: was t h e case i n F e b r u a r y 1972.
p e o p l e f o r g e t t h e s t o r m and t h e f l o o d c o m e s , a s
A s an i n t e r e s t i n g c u r i o s i t y , cases c a n h e found
o f " n e g a t i v e " s u r g e s , c a u s e d by r e v e r s e m e t e o r o l o g i c a l c o n d i t i o n s , r e g u l a r l y f o l lo w e d by a s e i c h e s e q u e n c e (e.g. J u n e 3 0 , 1 9 7 5 ) . t h e problem, c a n b e f a c e d a t t h i s p o i n t .
Storm s u r g e s , t h e r e a l c o r e o f
431 O R I G I N OF SURGES
It t u r n s o u t from t h e r e c o r d s t h a t t h e s e a s o n a l p l o t o f t h e f l o o d s h a s a peak i n November and a c e r t a i n r e l e v a n c e i n December a n d J a n u a r y .
Since t h e r e is
l i t t l e d i f f e r e n c e i n t h e t i d a l p a t t e r n through t h e seasons, s p e c i a l meteorologic a l c o n d i t i o n s must f a v o u r t h e s u r g e s .
By a n a l y z i n g c a s e a f t e r c a s e , o n e s e e s
t h a t p u l s e s o f SE wind a l o n g t h e A d r i a t i c a r e t h e t r u e c a u s e . A more d e t a i l e d a n a l y s i s o f t h e m e t e o r o l o g i c a l d y n a m i c s g i v i n g o r i g i n t o f l o o d s
shows t h a t t h e L i g u r i a n S e a , f a c i n g t h e n o r t h w e s t e r n r e g i o n s o f I t a l y , i s a n i m p o r t a n t r e f e r e n c e p o i n t , s i n c e sometimes t h e storm i s born t h e r e .
More f r e q u e n t l y ,
m o d e r a t e p e r t u r b a t i o n s from t h e A t l a n t i c r e a c h i n g t h e L i g u r i a n a r e a become much s t r o n g e r , a s i f a l o c a l mechanism were t r i g g e r e d .
One c a n s a y t h a t t h i s p l a c e i s
subject t o cyclogenesis, o r formation o f depressions, t h a t eventually migrate eastward.
There a r e important s t u d i e s concerning t h i s weather f e a t u r e (Speranza,
1975; B u z z i e t a l . , 1 9 7 8 ) .
It can b e mentioned h e r e t h a t t h e s u r g e sket ched i n
f i g u r e 1 was s e l e c t e d t o i l l u s t r a t e a s p e c i f i c case o f c y c l o g e n e s i s a n a l y z e d i n t h e l i t e r a t u r e , whose w e a t h e r maps a r e shown i n f i g . 4 .
The e f f o r t t o f o r e c a s t
t h e f l o o d s w i l l o b v i o u s l y t a k e a d v a n t a g e o f t h i s knowledge.
April 21, 1067, 1x00 GMI' F i g . 4. A t y p i c a l case of cyclogenesis. end o f t h e Alps.
April 22, 1967, 0000 GMT A d e p r e s s i o n is formed a t t h e w e s t e r n
PREDICTION BY STATISTICAL METHODS A b i g e f f o r t f o r t h e f o r e c a s t o f t h e f l o o d s was made i n t h e l a s t t e n y e a r s .
432 The p u r p o s e i s w a r n i n g t h e c i t y i n o r d e r t o r e d u c e t h e d a m a g e s o f t h e f l o o d .
Also, i f t h e p l a n n e d p r o t e c t i o n s f o r t h e l a g o o n w i l l b e b u i l t ( l i k e s l u i c e s a t t h e i n l e t s , t o b e c l o s e d o n l y when a s u r g e i s c o m i n g ) , a w a r n i n g s y s t e m w i l l b e vital. A v a r i e t y o f p r e d i c t i v e s c h e m e s was d e v e l o p e d , u s i n g e i t h e r s t a t i s t i c a l o r
d e t e r m i n i s t i c methods
-
o r both.
A d i s t i n c t i o n c o u l d a l s o b e made b e t w e e n s i m p l e
l o w a c c u r a c y s c h e m e s ( f r e q u e n t l y u s e f u l f o r a l o n g term f o r e c a s t ) a n d more s o p h i s t i c a t e d and p r e c i s e methods. An i d e a f o r t h e f o r m e r o n e s c o m e s from t h e a b o v e c o n s i d e r a t i o n s a b o u t s e i c h e s . They p e r s i s t f o r many d a y s , a n d t h i s means t h a t t h e A d r i a t i c h a s a g o o d memory. T r o u b l e s c o m i n g f r o m t h e s u r g e " r e t u r n s " c a n b e p r e d i c t e d by s i m p l y o b s e r v i n g t h e t i d e of t h e l a s t h o u r s .
On t h e s e a s s u m p t i o n s , a s i m p l e s c h e m e was d e v e l o p e d
( T o m a s i n , 1 9 7 2 ) w h e r e t h e f u t u r e l e v e l o f t h e sea i s e s t i m a t e d by a p r e d i c t i v e l i n e a r filter applied to t h e observed t i d e .
The f i l t e r w e i g h t s were s t a t i s t i c a l l y
o b t a i n e d from t h e r e c o r d i n g s of t h e p a s t . I n m a t h e m a t i c a l s y m b o l s , t h e estimate o f t h e sea l e v e l i n V e n i c e , a t time t , s; , i s o b t a i n e d a s t h e i n n e r p r o d u c t o f t w o v e c t o r s b u i l t by p r o p e r f i l t e r w e i g h t s
(f.
f,
, f, ,
... , f
) a n d sea l e v e l s ( 2 ~t - T s
T h o u r s b e f o r e t h e p r e d i c t e d time.
Then S*
t
' s t-T-1 ' ...' t-T-n ) o b s e r v e d u p t o
r s - f
-
-
The l e n g t h o f t h e f i l t e r , n + 1 , was f o u n d t o b e c o n v e n i e n t a t a b o u t 6 0 h c u r s . S t a t i s t i c s o f f e r another simple idea f o r an approximate expectation:
since the
w e a t h e r b e h a l f i o w i s somehow d e t e r m i n e d i n t h e cases o f i n t e r e s t , t h e s i m p l e s t
l o c a l a t m o s p h e r i c p a r a n e t e r , t h e p r e s s u r e , c o u l d g i v e some i n d i c a t i o n .
A numeri-
cal f i l t e r was b u i l t , l i k e t h e o n e d e s c r i b e d a b o v e , b u t now u s i n g a l s o p r e s s u r e f i g u r e s of t h e last hours.
- L2
Now s* = 2 f, +E , where p is t h e v e c t o r o f t h e observed p r e s s u r e values. t The l e n g t h o f t h e f i l t e r was now r e d u c e d t o 2 4 h o u r s . I n s p i t e of its s i m p l i c i t y ( a n y i n t e r e s t e d V e n e t i a n c o u l d u s e i t by h i m s e l f ) , t h e a d v a n t a g e i s r e m a r k a b l e . F i g u r e 5 s h o w s , f o r t h e c a s e a l r e a d y c o n s i d e r e d ( A p r i l 2 1 , 1 9 6 7 ) how t h e s i m p l e s c h e m e w o u l d h a v e p r e d i c t e d t h e f l o o d s i x h o u r s in a d v a n c e .
(Obviously, t h e
w e i g h t s o f t h e f i l t e r were o b t a i n e d f r o m a s a m p l e w h i c h d i d n o t i n c l u d e t h i s c a s e ) . F u r t h e r a d v a n c e s for t h e l a t t e r method ( w h i c h is s t i l l i n p r o g r e s s ) a r e exp e c t e d by r e l a x i n g t h e l i n e a r i t y of t h e method. A s s t a t e d a b o v e , more c o m p l i c a t e m e t h o d s are r e q u i r e d f o r b e t t e r r e l i a b i l i t y ,
a n d t h e p r e c i s e d y n a m i c s o f t h e sea m u s t b e s t u d i e d .
What r e a l l y g i v e s o r i g i n
t o s u r g e s i s t h e SE w i n d a n d , w i t h smaller e f f e c t , t h e low p r e s s u r e o r more p r e cisely a certain pressure gradient along the Adriatic.
The g o o d c o v e r a g e o f
w e a t h e r s t a t i o n s a l o n g t h e s h o r e s is o b v i o u s l y a f a v o u r a b l e f e a t u r e .
T h e i r re-
p o r t s c a n b e c o r r e l a t e d t o sea l e v e l e i t h e r v i a s t a t i s t i c s o r u s i n g storm s u r g e
433
6
10
12
0
6
12
0
10
F i g . 5. An e x a m p l e o f t h e p r e d i c t i o n o f a f l o o d u s i n g a s i m p l e s t a t i s t i c a l reg r e s s i o n . P r e d i c t . o r s a r e a v a i l a b l e f o r t h e s c h e m e u p t o 1 6 . 0 0 , A p r i l 2 1 , 1967. equations. The s t a t i s t i c a l a p p r o a c h ( S g u a z z e r o e t a l . , above t o t h e whole A d r i a t i c .
1972) e x t e n d s t h e method d e s c r i b e d
T h e r e are more i n d e p e n d e n t v a r i a b l e s :
not the sim-
p l e a t m o s p h e r i c p r e s s u r e i n V e n i c e , b u t e s t i m a t e s o f t h e p r e s s u r e g r a d i e n t a n d wind
stress i n c e r t a i n i d e a l p o i n t s i n t h e m i d d l e o f t h e A d r i a t i c . s;. ' 2
' f + P l ' F , + P * - E 2+
..... ' + -1w ' G-1 + E 2 - G 2 + ....
Here 2 is a g a i n t h e v e c t o r o f t h e sea l e v e l s i n V e n i c e s t-T
t h e v e c t o r ( P l. , t - T ,
P l,t-T-l .
,...)
In formula
9
s t-T-
, . . - ; pi
is
of t h e p r e s s u r e v d u e s i n t h e i - t h s t a n d a r d
p o i n t . W . i s t h e v e c t o r o f t h e wind s t r e s s f i g u r e s i n t h e j - t h s t a n d a r d p o i n t , . ' -J F G a n d f a r e o b v i o u s " f i l t e r " v e c t o r s . More s p e c i f i c a l l y , t h i s model u s e d -k , -k f i v e p o i n t s for g r a d i e n t and stress estimates ( e q u a l l y s p a c e d a l o n g t h e axis o f t h e A d r i a t i c ) a n d t h i s f i e l d r e c o n s t r u c t i o n was made u s i n g s e v e n c o a s t a l s t a t i s m .
Data were t h e o r d i n a r y s y n o p t i c t h r e e - h o u r l y m e a s u r e m e n t s .
The " p a s t " d a t a en-
t e r i n g t h e f o r m u l a r e f e r r e d t o two d a y s f o r l e v e l a n d o n e d a y f o r w e a t h e r .
It
s h o u l d b e r e m a r k e d t h a t g r a d i e n t a n d s t r e s s were t a k e n o n l y i n t h e c o m p o n e n t al o n g t h e a x i s of t h e A d r i a t i c .
T h i s is a p o i n t o f i n t e r e s t , s i n c e i t emphasizes
t h a t t h e A d r i a t i c d y n a m i c s i s almost c o m p l e t e l y o n e - d i m e n s i o n a l f o r s u r g e s .
In t h e r a n g e o f f o r e c a s t o f s i x h o u r s ( T : 6 i n t h e p r e v i o u s f o r m u l a ) f l o o d s were p r e d i c t e d w i t h i n a few c e n t i m e t e r s i n t h e d o z e n s o f cases when t h e model
was t e s t e d (many o f t h e m i n r e a l t i m e ) .
Fig. 6 g i v e s a n example.
434
F i g . 6. An e x a mpl e o f p r e d i c t i o n u s i n g t h e s t a t i s t i c a l me thod by S g u a z z e r o e t a l . The s u r g e ( i . e . t h e d e v i a t i o n from o r d i n a r y t i d e ) i s shown by t h e s o l i d l i n e . Dashed c u r v e i s t h e f o r e c a s t , e a c h p o i n t b e i n g g i v e n s i x h o u r s i n a d v a n c e . ( s t a r t i n g p o i n t F e b r u a r y 1 2 , 1 9 7 2 , 0300 GMT). One c a n c o n c l u d e t h a t u s i n g o n l y t h e w e a t h e r r e p o r t s from t h e A d r i a t i c c o a s t a n d t h e o b s e r v e d t i d a l l e v e l s , t h e p r e d i c t i o n i s p o s s i b l e f o r a b o u t s i x h o u r s ahead.
( F u r t h e r f o r e c a s t i n g is p r o g r e s s i v e l y u n r e l i a b l e , due t o t h e a r r i v a l o f
o t h e r a t m o s p h e r i c phenomena i n t h e m e a n t i m e ) .
PREDICTION BY DETERMINISTIC MODELS
B e t t e r s a t i s f a c t i o n comes from a d e t a i l e d i n s p e c t i o n o f w ha t h a p p e n s i n t h e A d r i a t i c when t h e a t m o s p h e r e
forces it.
More o r less t h e same i n f o r m a t i o n ( i . e .
w e a t h e r r e p o r t s from c o a s t a l s t a t i o n s ) c a n be u s e d f o r t h e i n t e g r a t i o n o f t h e s t o r m s u r g e e q u a t i o n s where t h e d r i v i n g f o r c e s a r e , a g a i n , t h e wind stress a nd the pressure gradients.
It i s o b v i o u s l y n o t o n l y a matter o f s a t i s f a c t i o n b u t
a l s o a b e t t e r k n owl edge o f t h e p h y s i c s o f t h e s u r g e a n d a more c o m p l e t e i n f o r m a t i o n f o r t h e various places.
1954)
The s t o r m s u r g e e q u a t i o n s c a n b e w r i t t e n (Proudma n,
435
a (UCOS -
a cos Ip ad
p)
+
av + a< = ax a t
where Q and X are l a t i t u d e and e a s t - l o n g i t u d e ,
0,
t is t i m e , 5 t h e e l e v a t i o n o f t h e
sea s u r f a c e , U a n d V t h e c o m p o n e n t s o f t h e t o t a l s t r e a m , i . e .
v e l o c i t y times
d e p t h , Fs a n d Gs t h e c o m p o n e n t s o f t h e f r i c t i o n o f t h e wind o n t h e sea s u r f a c e , FB a n d G B t h e c o m p o n e n t s o f t h e water f r i c t i o n on t h e s e a b o t t o m , pa t h e a t m o s p h e r i c p r e s s u r e o n t h e s e a , h t h e water d e p t h ,
P
t h e d e n s i t y o f t h e water ( a s-
sumed u n i f o r m ) , a t h e mean r a d i u s o f t h e e a r t h , 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 , w t h e a n g u i a r s p e e d of t h e e a r t h ’ s r o t a t i o n .
T h e s e e q u a t i o n s are l i n e a r i z e d a n d i n t e g r a t e d w i t h r e s p e c t t o d e p t h . c a n b e s a f e l y assumed after t h e above r e m a r k s .
Linearity
This accounts for t h e suppression
o f a l l non l i n e a r terms i n d e r i v i n g t h e s e e q u a t i o n s a n d a l l o w s t h e a s s u m p t i o n o f a l i n e a r i z e d b o t t o m f r i c t i o n , as i t was d o n e i n p r a c t i c e . A v a r i e t y o f w o r k s were d e v e l o p e d ( T o m a s i n , 1971; S t r a v i s i , 1972;’ A c c e r b o n i e t a l . ,
1973) u s i n g t h e above b a s i c e q u a t i o n s , c o r r e c t l y r e p r o d u c i n g t i d e s , s e i c h e s and surges.
I n t e g r a t i o n t e c h n i q u e s were e s s e n t i a l l y a l r e a d y known f r o m t h e l i t e r a -
t u r e of h y d r o d y n a m i c a l n u m e r i c a l m o d e l s ( H a n s e n , 1 9 5 6 ; H e a p s , 1 9 6 9 ) .
In particu-
l a r , r e d u c t i o n t o o n e d i m e n s i o n was p o s s i b l e d u e t o t h e s h a p e o f t h e A d r i a t i c . And t h i s was r e a l l y t h e s c h e m e more e x t e n s i v e l y t e s t e d i n p r a c t i c e ( F i n i z i o , 1970; Tomasin, 1973).
I n formula
w h e r e t h e x a x i s i s d i r e c t e d a l o n g t h e s e a , w is t h e w i d t h o f t h e c r o s s s e c t i o n a n d Q t h e d i s c h a r g e a c r o s s i t , o r , s a y , t h e a v e r a g e v e l o c i t y times t h e a r e a o f the section. The e q u a t i o n s are c l e a r l y s i m p l i f i e d a l s o b e c a u s e t h e e a r t h c u r v a t u r e i s d i s regarded:
n e e d l e s s t o s a y , a l l t h e s e s i m p l i f i c a t i o n s would n o t b e p o s s i b l e f o r
o t h e r a r e a s , l i k e f o r e x a m p l e t h e M e d i t e r r a n e a n , whose m o d e l l i n g i s m e n t i o n e d below.
436 I n f o r e c a s t i n g , t h e o n e d i m e n s i o n a l s c h e m e was u s e d o n t h e f i e l d , u s i n g s y n o p t i c m e t e o r o l o g i c a l d a t a a n d i n t e g r a t i n g t h e e q u a t i o n s by a n e x p l i c i t f i n i t e - d i f f e r e n c e s scheme. issued:
The w e a t h e r f i e l d i s known u p t o t h e time when t h e f o r e c a s t i s
t h e s i t u a t i o n is s u p p o s e d c o n s t a n t f o r t h e f o l l o w i n g h o u r s and t h e equa-
t i o n s g i v e f u t u r e sea l e v e l u n d e r
this
hypothesis.
Consistent with the statis-
t i c a l a p p r o a c h , i t t u r n s o u t t h a t a t a n y time t h e r e i s e n o u g h i n f o r m a t i o n t o p r e d i c t s a f e l y t h e sea l e v e l f o r a b o u t s i x h o u r s .
A s expected, the
a b o v e method
t u r n e d o u t t o b e s a t i s f a c t o r y as a p r e d i c t o r . FURTHER DEVELOPMENTS I m p r o v e m e n t s o f t h e p r e d i c t i o n a r e e x p e c t e d by w i d e n i n g t h e l i m i t s i n r e s e a r c h h a s been confined so far. p r e d i c t i o n s was a v o i d e d .
which
It w i l l b e r e m a r k e d t h a t t h e u s e o f w e a t h e r
Over t h e M e d i t e r r a n e a n t h e y a r e made d i f f i c u l t by t h e
i n f l u e n c e o f o r o g r a p h y w h i c h c o m p l i c a t e s t h e f l o w o f a i r masses a n d g e n e r a t e s l o c a l effects:
c y c l o g e n e s i s on t h e w e s t e r n l e e o f t h e A l p s was m e n t i o n e d a b o v e .
The G l o b a l A t m o s p h e r i c R e s e a r c h P r o g r a m (GARPI h a s c r e a t e d a s u b p r o g r a m o n Air Flow Over a n d Around M o u n t a i n s a n d t h e f i r s t e x p e r i m e n t a r o u n d t h e A l p i n e b a r r i e r ( A l p e x ) i s p r o p o s e d f o r 1981.
This e f f o r t should help i n understanding the dy-
namics o f p e r t u r b a t i o n s i n t h e M e d i t e r r a n e a n , w i t h t h e f i n a l o b j e c t i v e o f a n a c c u r a t e p r e d i c t i o n 12 t o 24 h o u r s a h e a d :
Venice, I t a l y and s e v e r a l c o u n t r i e s w i l l
substantially benefit. For t h e s p e c i f i c w a r n i n g o f f l o o d s , a wind f o r e c a s t i n g model is b e i n g d e v e l o p e d
(Palmieri a t a l . , 1 9 7 6 ) .
S t a t i s t i c a l m e t h o d s a l s o are b e i n g i m p l e m e n t e d i n V e n i c e
for the prediction o f the'pressure f i e l d i n the central Mediterranean. From t h e h y d r o d y n a m i c a l p o i n t o f v i e w , i t i s n o t i c e a b l e t h a t n o a t t e m p t was made t o f o r e c a s t e x t e r n a l s u r g e s , i . e . phenomena o r i g i n a t i n g o u t o f t h e A d r i a t i c , b u t g i v i n g s i g n i f i c a n t e f f e c t i n it.
From e x p e r i e n c e , t h e y seem n o t t o e x i s t ; s o
f a r t h e l o w f r e q u e n c y c h a n g e s i n t h e l e v e l o f t h e M e d i t e r r a n e a n h a v e b e e n monit o r e d c l o s e t o t h e O t r a n t o Channel and t r a n s m i t t e d t o Venice f o r a d i r e c t u s e i n t h e p r e d i c t i v e models (Mazzoldi et a l . ,
1973).
For a b e t t e r i n s i g h t i n t h e s e
large s c a l e phenomena a f f e c t i n g t h e M e d i t e r r a n e a n , a s p e c i f i c n u m e r i c a l model i s b e i n g d e v e l o p e d , t o f i l l u p t h e t h e o r e t i c a l g a p t h a t was s o f a r o v e r c o m e by d i -
rect i n s p e c t i o n . Time i s r i p e f o r w i d e r a n a l y s i s , w h e r e t h e M e d i t e r r a n e a n i s f u l l y c o n s i d e r e d f o r its hydrodynamical c o n t r i b u t i o n s and f o r t h e m e t e o r o l o g i c a l p a t t e r n s t h a t develop over it.
The g o a l o f a w a r n i n g f o r V e n i c e f l o o d s w i t h a n a d v a n c e o f
t w e l v e h o u r s o r o n e d a y seems n o t t o b e c h i m e r i c a l .
437 ACKNOWLEDGEMENTS The h e l p o f R .
D a z z i , G . A l d i g h i e r i , and Mrs. J . Z a n i n , o f t h e CNR l a b o r a t o r y ,
h a s b e e n o f u t t e r i m p o r t a n c e f o r t h i s work.
P r e c i o u s s u p p o r t was g i v e n by t h e
C e n t r o S c i e n t i f i c 0 IBM o f Veni ce and t h e CRIS-ENEL b r a n c h o f V e nic e -Me s tre . REFERENCES A c c e r b o n i , E. a n d Manca, B., 1973. S t orm s u r g e s f o r e c a s t i n g i n t h e A d r i a t i c Se a by means o f a t wo-di mensi onal h y d r o d y n a m i c a l n u m e r i c a l mode l. B o l l . G e o f i s . Teor . Appl . , 15: 3-22. A r t e g i a n i , A . , Tomasi n, A . and Goldmann, A . , 1972. Sur l a dyna mique d e l a mer A d r i a t i q u e d u e aux e x c i t a t i o n s m & t & o r o l o g i q u e s . Rapp. Comm. I n t . Mer MGdit., 21:181-183. B u z z i , A . a n d T i b a l d i , S . , 1978. C y c l o g e n e s i s i n t h e l e e o f t h e A l p s : A c a s e s t u d y . Q u a r t . J . R . Met. SOC., 104:271-287. F i n i z i o , C . , Palmieri, S. and R i c c u c c i , A . , 1970. A n u m e r i c a l model o f t h e Adria t i c S e a f o r t h e s t u d y and p r e d i c t i o n o f sea t i d e s a t V e n i c e . 1st. F i s . At mo sf ., STR 12. Goldmann, A . , R a b a g l i a t i , R . and S g u a z z e r o , P . , 1975. P r o p a g a z i o n e d e l l a marea n e l l a l a g u n a d i Venezia: a n a l i s i d e i d a t i r i l e v a t i d a l l a r e t e m a r e o g r a f i c a l a g u n a r e n e g l i a n n i 1972-73. R i v. I t a l . G e o f i s . , 2:119-124. Hansen, W . , 1956. T h e o r i e z u r E r r e c h n u n g d e s W a s s e r s t a n d e s und d e r Stromungen i n Randmeeren n e b s t Anwendungen. T e l l u s , 8:287-300. P h y l . T r a n s . A 265: Heaps, N.S., 1969. A t wo-di mensi onal n u m e r i c a l sea model. 93-137. 1910. Das Gezei t enphanomen i n Hafen von P o l a . Mittl. Geb. K e s s l i t z , W.V., S e e w e s e n s , 38: H . V - V I . M a z z o l d i , A . , D a l l a p o r t a , G . , G a s p a r i , A . , C u r i o t t o , A . a nd P e r u z z o , G . , 1973. S i s t e m a d i t e l e m i s u r e d a s t a z i o n i a u t o m a t i c h e f i s s e . CNR-LSDGM, V e n e z i a , R a p p o r t 0 T e c n i c o n . 37. P a l m i e r i , S., F i n i z i o , C. and C o z z i , R . , 1976. The c o n t r i b u t i o n of m e t e o r o l o g y B o l l . Geofis. t o t h e s t u d y a nd p r e d i c t i o n o f h i g h t i d e s i n t h e A d r i a t i c . T e o r . Ap p l ., 19:191-198. Mon. N ot. R . a s t r . Proudman, J . , 1954. Note on t h e dynami cs o f s t o r m - s u r g e s . S OC . Geophys. S u p p l . , 7:44-48. R o b i n s o n , A . R . , T omasi n, A. a n d A r t e g i a n i , A . , 1973. F l o o d i n g o f V e n i c e : Phenomenology a n d p r e d i c t i o n o f t h e A d r i a t i c s t o r m s u r g e . Q u a r t . J . R . Met. S O C . , 99~688-692. S g u a z z e r o , P . , Giommoni, A . and Goldmann, A . , 1972. An e m p i r i c a l model f o r t h e IBM I t a l i a T e c h . Rep. CSVOO6. p r e d i c t i o n o f t h e sea l e v e l i n Veni ce. S p e r a n z a , A . , 1975. The f o r m a t i o n o f b a r i c d e p r e s s i o n s n e a r t h e A l p s . Ann. d i G e o f i s . , 28:177-217. 1919. Die G e z e i t e n e r s c h e i n u n g e n i n d e r A d r i a . D e ns c hr. Akad. Sterneck, R.V., Wiss. Wien, 96:277-324. S t r a v i s i , F . , 1972. A n u m e r i c a l e x p e r i m e n t on wind e f f e c t s i n t h e A d r i a t i c Se a . Acc. Naz. L i n c e i , Rend. S c. F i s . , m a t . , n a t . , 52:187-196. To ma sin , A . , 1971. A p p l i c a t i o n o f t h e h y d r o d y n a m i c a l n u m e r i c a l i n t e g r a t i o n method t o t h e A d r i a t i c S e a . P h y s i c s o f t h e S e a , T r i e s t e , 13-16 O c t . , Accad. Naz. L i n c e i , Quad. n . 2 0 6 , 119-121. Tomasin, A . , 1972. A u t o r e g r e s s i v e P r e d i c t i o n o f S e a L e v e l i n t h e N o r t h e r n Adria t i c . R i v . I t a l . G e o f i s . , 21:211-214. To ma sin , A . , 1973. A comput er s i m u l a t i o n o f t h e A d r i a t i c S e a f o r t h e s t u d y o f i t s d y n a mic s and f o r t h e f o r e c a s t i n g o f f l o o d s i n t h e town o f V e n i c e . Comp. Phys. Comm., 5: 51-55.
438 T o m a s i n , A . , 1 9 7 6 . The d y n a m i c s o f t h e d i u r n a l t i d e i n t h e A d r i a t i c S e a : p r e l i m i n a r y r e s u l t o f a r e v i s i t i n g a n a l y s i s . Rapp. Comm. I n t . Mer M d d i t . , 2 3 : 4 9 . U n e s c o , 1969. R a p p o r t 0 s u V e n e z i a . M o n d a d o r i , M i l a n o , 348 p p .
CYCLOGENESIS A N D FORECAST OF DRAMATIC WATER ELEVATIONS I N VENICE
A.
TOMASIN' a n d R . FRASSETTO
1
' L a b o r a t o r i o p e r l o S t u d i o d e l l a Dinamica d e l l e Grandi Masse, C.N.R.,Venezia
(Italy)
ABSTRACT The o c e a n o g r a p h i c and m e t e o r o l o g i c a l a s p e c t s o f t n ? A d r i a t i c s u r g e s are invest i g a t e d . S i n c e V e n i c e f l o o d s a r e only d u e t o s u c h a n o m a l o u s t i d e s , t h e i r f o r e c a s t is o b v i o u s l y r e q u e s t e d f o r p r a c t i c a l p u r p o s e s . S h o r t term w a r n i n g ( a b o u t s i x h o u r s a h e a d ) i s now p o s s i b l e w i t h good a c c u r a c y , t h a n k s t o p r e s e n t u n d e r s t a n d i n g o f t h e s u r g e g e n e r a t i o n . The s t u d y o f t h e c y c l o g e n e s i s i n t h e a t m o s p h e r e o v e r t h e w e s t e r n Alps c a n e x t e n d t h e time f r e e b o a r d f o r alarm. TNTRODUCTION A N D HISTORICAL REMARKS I n t h e h i s t o r y o f Venice, f l o o d s are r e p o r t e d a s a r e c u r r e n t c a l a m i t y f o r t h e c i t y ( U n e s c o , 1 9 6 9 , pp. 3 4 - 6 6 ) .
T h i s i s n o t s u r p r i s i n g when c o n s i d e r i n g t h a t
s t r e e t s a r e n o r m a l l y l e s s t h a n o n e meter o v e r mean w a t e r l e v e l a n d t h e t i d a l range is comparable t o t h i s f i g u r e .
Troubles can c l e a r l y arise even w i t h a s u r g e
h a l f a meter h i g h , w h i c h i s a r a t h e r common o c c u r r e n c e .
F i g u r e 1 shows a n e x -
ample. Even t h o u g h
V e n i c e is l o c a t e d i n a l a g o o n , a n d n o t d i r e c t l y e x p o s e d t o t h e
s e a , f r o m t h e p o i n t o f v i e w o f t i d e s a n d s u r g e s no d i f f e r e n c e i s o b s e r v e d , e x c e p t
f o r a d e l a y o f a b o u t a n h o u r f r o m t h e o p e n sea t o t h e town.
The s i t u a t i o n i n
t h i s c e n t u r y i s c e r t a i n l y w o r s e t h a n i n t h e p a s t , as f a r a s t h e f r e q u e n c y o f f l o o d s 1s c o n c e r n e d .
T h i s is d u e t o v a r i o u s r e a s o n s :
t h e town h a s s u n k a b o u t 2 0 cm
s i n c e t h e l a s t c e n t u r y ( w h i c h is c o m p a r a b l e , p r e s u m a b l y , t o t h e t o t a l s i n k i n g i n the previous millennium).
Also, t h e c o m m u n i c a t i o n b e t w e e n t h e sea a n d t h e l a g o o n
is larger now t h a n Z C O y e a r s a g o , d u e t o e x t e n s i v e d r e d g i n g i n t h e l a g o o n i n l e t s . I n t h o s e d a y s , t h e p e a k l e v e l s o f t h e e x t e r n a l sea were p r e s u m a b l y " c u t " by t h e n a r r o w o p e n i n g s o f t h e l a g o o n , e x c e p t f o r s u r g e s o f long d u r a t i o n ( a n d t h e most t r e m e n d o u s f l o o d , i n 1 9 6 6 , was o f t h i s k i n d ) .
428
.
6
12
18
0
6
12
18
0
6
12
F i g . 1. R e c o r d e d water l e v e l i n V e n i c e , s t a r t i n g A p r i l 20, 1967. r i s e a t t h e e n d o f t h e s e c o n d d a y i s e v i d e n t ( T i m e i s GMT + 1 ) .
18
0
The a n o m a l o u s
ADRIATIC DYNAMICS O n l y t h e A d r i a t i c phenomena ( t i d e s a n d s u r g e s ) w i l l b e c o n s i d e r e d now, s i n c e ,
a s i t was s t a t e d a b o v e , t h e r e is n o s i g n i f i c a n t c h a n g e ( o t h e r t h a n a time l a g ) i n t h e t r a n s i t i o n f r o m t h e o p e n sea t o V e n i c e (Goldmann e t a l . , 1 9 7 5 ) . t a n t f e a t u r e is t h e i n d e p e n d e n c e o f t i d e a n d s u r g e i n t h i s area.
t o h a v e a n y i n t e r a c t i o n , a n d s i m p l y b u i l d up.
An impor-
They seem n o t
A t a first g l a n c e , t h i s c a n be
s u r p r i s i n g , s i n c e t h e n o r t h e r n " h a l f " o f t h e sea i s a p l a t e a u s l o w l y d e c l i n i n g s o u t h w a r d s , u p t o 100 m d e p t h ( s e e F i g . 2 ) . I n s u c h a s h a l l o w a r e a , o c e a n o g r a p h e r s would e x p e c t s u b s t a n t i a l n o n l i n e a r i t i e s i n t h e t i d a l c o n s t i t u e n t s and r e l a t e d i n t e r a c t i o n s between t i d e and s u r g e .
In-
d e e d , t h e r a t i o o f t h e d e p t h t o t h e t i d a l r a n g e i s s t i l l v e r y l a r g e , a n d t h i s accounts f o r t h e observed l i n e a r i t y . S i n c e t i d e a n d s u r g e &re i n d e p e n d e n t , o n e c a n e a s i l y i m a g i n e t h e v a r i o u s rnixt u r e s t h a t can appear.
There can be a c o i n c i d e n c e o f f l o o d t i d e and s u r g e , s o
t h a t t h e l e v e l rises t o d a n g e r o u s v a l u e s , or t h e y c a n o t h e r w i s e c a n c e l e a c h o t h e r . What is i m p o r t a n t f o r n u m e r i c a l a n a l y s i s i s t h a t , g i v e n t h e t i d a l r e c o r d , by s u b t r a c t i n g t h e ordinary astronomical t i d e one obtains a kind of meteorological t i d e
t o be s t u d i e d s e p a r a t e l y .
429
N
40' N
F i g . 2.
The A d r i a t i c S e a .
D e p t h s are i n meters
TIDES A N D SEICHES T h e r a n g e o f t h e a s t r o n o m i c a l t i d e i n c r e a s e s from t h e SE o p e n i n g o f t h e A d r i a t i c t h r o u g h t h e NW e n d w h e r e V e n i c e i s : t h e s p r i n g r a n g e 80 cm ( a b o u t ) ( S t e r n e c k , 1 9 1 9 ) .
2(M2+S )
2
rises from 25 t o
This is consistent with t h e c l a s s i c a l picture
a c c o r d i n g t o w h i c h t h e t i d e , a s o b s e r v e d i n t h e A d r i a t i c , i s f o r c e d by t h e o s c i l l a t i o n o f t h e M e d i t e r r a n e a n by t h e O t r a n t o C h a n n e l , w i t h l i t t l e r e l e v a n c e o f t h e direct lunisolar attraction.
It s h o u l d b e r e m a r k e d t h a t r e c e n t c a l c u l a t i o n s t e n d
t o c h a n g e t h i s p i c t u r e (Tomasin, 1976). 8
A t least for t h e d i u r n a l p a r t of t h e t i d e ,
c o n t r i b u t i o n n o t l e s s t o 30% o f t h e o b s e r v e d r a n g e s h o u l d b e a t t r i b u t e d t o t h e
direct l o c a l f o r c i n g o f the astronomical effects. theoretical interest.
Indeed, t h i s should have only
Much more i m p o r t a n t , i n p r a c t i c e ,
is a n o t h e r r e m a r k :
the
d o m i n a n t t i d a l p e r i o d s , 12 a n d 2 4 h o u r s , a r e c l o s e t o t h e r e s o n a n t p e r i o d s o f t h i s
sea.
The s t u d y o f i t s e i g e n m o d e s i s c r u c i a l , s i n c e f r e e o s c i l l a t i o n s a r e o b s e r v e d
f r e q u e n t l y and w i t h r e l e v a n t amplitude.
T h i s way a common m e c h a n i s m i s f o u n d f o r
a r e g u l a r phenomenon, t h e t i d e , c o n s t a n t t h r o u g h t h e c e n t u r i e s , a n d f o r t h e random b u r s t s o f e n e r g y s t i m u l a t i n g t h e s e a i n t h e storms.
430
The f u n d a m e n t a l mode o f o s c i l l a t i o n ( " s e i c h e " ) o f t h e sea h a s a p e r i o d o f app r o x i m a t e l y 22 h o u r s ( K e s s l i t z , 1 9 1 0 ) .
O r d i n a r y s t o r m s h a v e a much s h o r t e r d u r a -
t i o n , b e i n g s h a r p a t m o s p h e r i c f r o n t s t h a t c r o s s t h e s e a moving e a s t w a r d s .
r e a c t s l i k e a pendulum h i t by a q u i c k p u l s e and s t a r t s o s c i l l a t i n g .
The sea
The r a t h e r
p e c u l i a r s h a p e o f t h e A d r i a t i c makes it as a n o r g a n p i p e , w e l l t u n e d o n i t s t o n e and w i t h l i t t l e d i s s i p a t i o n (Robinson e t a l . ,
1973).
Indeed, one can b e l i e v e
t h a t t h e r e i s l i t t l e i n t e r n a l f r i c t i o n f o r t h e same r e a s o n o f t h e l i n e a r i t y o f T h e r e is a l s o l i t t l e e x t e r n a l r a d i a t i o n o f e n e r g y s i n c e , a f t e r t h e g a t e ,
the tide.
t h e M e d i t e r r a n e a n i m m e d i a t e l y o f f e r s a wi de a n d d e e p b a s i n , v e r y c l o s e t o a n i d e a l i n f i n i t e o c e a n wh ere no e n e r g y c a n b e r a d i a t e d ( T o m a s i n , 1 9 7 1 ) .
A v e r y s l o w damp-
i n g o f t h e f r e e o s c i l l a t i o n s is o b s e r v e d , i f t h e r e i s no f u r t h e r p e r t u r b a t i o n . The 9 - v a l u e ( t h e f i g u r e o f m e r i t ) i s l a r g e r t h a n 1 0 0 , a n d t h e o s c i l l a t i o n s p e r -
s i s t f o r many d a y s ( s e e F i g . 3 ) .
100
-50
-I
16
I
I
17
18
I
19
A s i m i l a r b e h a v i o u r i s shown by t h e f i r s t h a r m o n i c ,
a l l y ( b u t n o t a l w a y s ) smaller i n a m p l i t u d e .
20
*
time (days)
11-hour o s c i l l a t i o n , u s u -
For t h i s f r e q u e n c y a n amphidromy i s
observed i n t h e n o r t h e r n A d r i a t i c , b o t h i n t i d e s and s e i c h e s ( A r t e g i a n i e t a l . , 1972).
I t i s now c l e a r t h a t a s u r g e h a s u s u a l l y a p e c u l i a r s h a p e , s i n c e , d u e t o s e i c h e s , i t is f o l l o w e d by many r e p l i c a s o f s u b s t a n t i a l h e i g h t , s p a c e d l e s s t h a n o n e da y.
It may o c c u r t h a t t h e f i r s t a r r i v a l o f t h e s u r g e d o e s n o t c o i n c i d e w i t h t h e f l o o d t i d e , while t h e second one does: was t h e case i n F e b r u a r y 1972.
p e o p l e f o r g e t t h e s t o r m and t h e f l o o d c o m e s , a s
A s an i n t e r e s t i n g c u r i o s i t y , cases c a n h e found
o f " n e g a t i v e " s u r g e s , c a u s e d by r e v e r s e m e t e o r o l o g i c a l c o n d i t i o n s , r e g u l a r l y f o l lo w e d by a s e i c h e s e q u e n c e (e.g. J u n e 3 0 , 1 9 7 5 ) . t h e problem, c a n b e f a c e d a t t h i s p o i n t .
Storm s u r g e s , t h e r e a l c o r e o f
431 O R I G I N OF SURGES
It t u r n s o u t from t h e r e c o r d s t h a t t h e s e a s o n a l p l o t o f t h e f l o o d s h a s a peak i n November and a c e r t a i n r e l e v a n c e i n December a n d J a n u a r y .
Since t h e r e is
l i t t l e d i f f e r e n c e i n t h e t i d a l p a t t e r n through t h e seasons, s p e c i a l meteorologic a l c o n d i t i o n s must f a v o u r t h e s u r g e s .
By a n a l y z i n g c a s e a f t e r c a s e , o n e s e e s
t h a t p u l s e s o f SE wind a l o n g t h e A d r i a t i c a r e t h e t r u e c a u s e . A more d e t a i l e d a n a l y s i s o f t h e m e t e o r o l o g i c a l d y n a m i c s g i v i n g o r i g i n t o f l o o d s
shows t h a t t h e L i g u r i a n S e a , f a c i n g t h e n o r t h w e s t e r n r e g i o n s o f I t a l y , i s a n i m p o r t a n t r e f e r e n c e p o i n t , s i n c e sometimes t h e storm i s born t h e r e .
More f r e q u e n t l y ,
m o d e r a t e p e r t u r b a t i o n s from t h e A t l a n t i c r e a c h i n g t h e L i g u r i a n a r e a become much s t r o n g e r , a s i f a l o c a l mechanism were t r i g g e r e d .
One c a n s a y t h a t t h i s p l a c e i s
subject t o cyclogenesis, o r formation o f depressions, t h a t eventually migrate eastward.
There a r e important s t u d i e s concerning t h i s weather f e a t u r e (Speranza,
1975; B u z z i e t a l . , 1 9 7 8 ) .
It can b e mentioned h e r e t h a t t h e s u r g e sket ched i n
f i g u r e 1 was s e l e c t e d t o i l l u s t r a t e a s p e c i f i c case o f c y c l o g e n e s i s a n a l y z e d i n t h e l i t e r a t u r e , whose w e a t h e r maps a r e shown i n f i g . 4 .
The e f f o r t t o f o r e c a s t
t h e f l o o d s w i l l o b v i o u s l y t a k e a d v a n t a g e o f t h i s knowledge.
April 21, 1067, 1x00 GMI' F i g . 4. A t y p i c a l case of cyclogenesis. end o f t h e Alps.
April 22, 1967, 0000 GMT A d e p r e s s i o n is formed a t t h e w e s t e r n
PREDICTION BY STATISTICAL METHODS A b i g e f f o r t f o r t h e f o r e c a s t o f t h e f l o o d s was made i n t h e l a s t t e n y e a r s .
432 The p u r p o s e i s w a r n i n g t h e c i t y i n o r d e r t o r e d u c e t h e d a m a g e s o f t h e f l o o d .
Also, i f t h e p l a n n e d p r o t e c t i o n s f o r t h e l a g o o n w i l l b e b u i l t ( l i k e s l u i c e s a t t h e i n l e t s , t o b e c l o s e d o n l y when a s u r g e i s c o m i n g ) , a w a r n i n g s y s t e m w i l l b e vital. A v a r i e t y o f p r e d i c t i v e s c h e m e s was d e v e l o p e d , u s i n g e i t h e r s t a t i s t i c a l o r
d e t e r m i n i s t i c methods
-
o r both.
A d i s t i n c t i o n c o u l d a l s o b e made b e t w e e n s i m p l e
l o w a c c u r a c y s c h e m e s ( f r e q u e n t l y u s e f u l f o r a l o n g term f o r e c a s t ) a n d more s o p h i s t i c a t e d and p r e c i s e methods. An i d e a f o r t h e f o r m e r o n e s c o m e s from t h e a b o v e c o n s i d e r a t i o n s a b o u t s e i c h e s . They p e r s i s t f o r many d a y s , a n d t h i s means t h a t t h e A d r i a t i c h a s a g o o d memory. T r o u b l e s c o m i n g f r o m t h e s u r g e " r e t u r n s " c a n b e p r e d i c t e d by s i m p l y o b s e r v i n g t h e t i d e of t h e l a s t h o u r s .
On t h e s e a s s u m p t i o n s , a s i m p l e s c h e m e was d e v e l o p e d
( T o m a s i n , 1 9 7 2 ) w h e r e t h e f u t u r e l e v e l o f t h e sea i s e s t i m a t e d by a p r e d i c t i v e l i n e a r filter applied to t h e observed t i d e .
The f i l t e r w e i g h t s were s t a t i s t i c a l l y
o b t a i n e d from t h e r e c o r d i n g s of t h e p a s t . I n m a t h e m a t i c a l s y m b o l s , t h e estimate o f t h e sea l e v e l i n V e n i c e , a t time t , s; , i s o b t a i n e d a s t h e i n n e r p r o d u c t o f t w o v e c t o r s b u i l t by p r o p e r f i l t e r w e i g h t s
(f.
f,
, f, ,
... , f
) a n d sea l e v e l s ( 2 ~t - T s
T h o u r s b e f o r e t h e p r e d i c t e d time.
Then S*
t
' s t-T-1 ' ...' t-T-n ) o b s e r v e d u p t o
r s - f
-
-
The l e n g t h o f t h e f i l t e r , n + 1 , was f o u n d t o b e c o n v e n i e n t a t a b o u t 6 0 h c u r s . S t a t i s t i c s o f f e r another simple idea f o r an approximate expectation:
since the
w e a t h e r b e h a l f i o w i s somehow d e t e r m i n e d i n t h e cases o f i n t e r e s t , t h e s i m p l e s t
l o c a l a t m o s p h e r i c p a r a n e t e r , t h e p r e s s u r e , c o u l d g i v e some i n d i c a t i o n .
A numeri-
cal f i l t e r was b u i l t , l i k e t h e o n e d e s c r i b e d a b o v e , b u t now u s i n g a l s o p r e s s u r e f i g u r e s of t h e last hours.
- L2
Now s* = 2 f, +E , where p is t h e v e c t o r o f t h e observed p r e s s u r e values. t The l e n g t h o f t h e f i l t e r was now r e d u c e d t o 2 4 h o u r s . I n s p i t e of its s i m p l i c i t y ( a n y i n t e r e s t e d V e n e t i a n c o u l d u s e i t by h i m s e l f ) , t h e a d v a n t a g e i s r e m a r k a b l e . F i g u r e 5 s h o w s , f o r t h e c a s e a l r e a d y c o n s i d e r e d ( A p r i l 2 1 , 1 9 6 7 ) how t h e s i m p l e s c h e m e w o u l d h a v e p r e d i c t e d t h e f l o o d s i x h o u r s in a d v a n c e .
(Obviously, t h e
w e i g h t s o f t h e f i l t e r were o b t a i n e d f r o m a s a m p l e w h i c h d i d n o t i n c l u d e t h i s c a s e ) . F u r t h e r a d v a n c e s for t h e l a t t e r method ( w h i c h is s t i l l i n p r o g r e s s ) a r e exp e c t e d by r e l a x i n g t h e l i n e a r i t y of t h e method. A s s t a t e d a b o v e , more c o m p l i c a t e m e t h o d s are r e q u i r e d f o r b e t t e r r e l i a b i l i t y ,
a n d t h e p r e c i s e d y n a m i c s o f t h e sea m u s t b e s t u d i e d .
What r e a l l y g i v e s o r i g i n
t o s u r g e s i s t h e SE w i n d a n d , w i t h smaller e f f e c t , t h e low p r e s s u r e o r more p r e cisely a certain pressure gradient along the Adriatic.
The g o o d c o v e r a g e o f
w e a t h e r s t a t i o n s a l o n g t h e s h o r e s is o b v i o u s l y a f a v o u r a b l e f e a t u r e .
T h e i r re-
p o r t s c a n b e c o r r e l a t e d t o sea l e v e l e i t h e r v i a s t a t i s t i c s o r u s i n g storm s u r g e
433
6
10
12
0
6
12
0
10
F i g . 5. An e x a m p l e o f t h e p r e d i c t i o n o f a f l o o d u s i n g a s i m p l e s t a t i s t i c a l reg r e s s i o n . P r e d i c t . o r s a r e a v a i l a b l e f o r t h e s c h e m e u p t o 1 6 . 0 0 , A p r i l 2 1 , 1967. equations. The s t a t i s t i c a l a p p r o a c h ( S g u a z z e r o e t a l . , above t o t h e whole A d r i a t i c .
1972) e x t e n d s t h e method d e s c r i b e d
T h e r e are more i n d e p e n d e n t v a r i a b l e s :
not the sim-
p l e a t m o s p h e r i c p r e s s u r e i n V e n i c e , b u t e s t i m a t e s o f t h e p r e s s u r e g r a d i e n t a n d wind
stress i n c e r t a i n i d e a l p o i n t s i n t h e m i d d l e o f t h e A d r i a t i c . s;. ' 2
' f + P l ' F , + P * - E 2+
..... ' + -1w ' G-1 + E 2 - G 2 + ....
Here 2 is a g a i n t h e v e c t o r o f t h e sea l e v e l s i n V e n i c e s t-T
t h e v e c t o r ( P l. , t - T ,
P l,t-T-l .
,...)
In formula
9
s t-T-
, . . - ; pi
is
of t h e p r e s s u r e v d u e s i n t h e i - t h s t a n d a r d
p o i n t . W . i s t h e v e c t o r o f t h e wind s t r e s s f i g u r e s i n t h e j - t h s t a n d a r d p o i n t , . ' -J F G a n d f a r e o b v i o u s " f i l t e r " v e c t o r s . More s p e c i f i c a l l y , t h i s model u s e d -k , -k f i v e p o i n t s for g r a d i e n t and stress estimates ( e q u a l l y s p a c e d a l o n g t h e axis o f t h e A d r i a t i c ) a n d t h i s f i e l d r e c o n s t r u c t i o n was made u s i n g s e v e n c o a s t a l s t a t i s m .
Data were t h e o r d i n a r y s y n o p t i c t h r e e - h o u r l y m e a s u r e m e n t s .
The " p a s t " d a t a en-
t e r i n g t h e f o r m u l a r e f e r r e d t o two d a y s f o r l e v e l a n d o n e d a y f o r w e a t h e r .
It
s h o u l d b e r e m a r k e d t h a t g r a d i e n t a n d s t r e s s were t a k e n o n l y i n t h e c o m p o n e n t al o n g t h e a x i s of t h e A d r i a t i c .
T h i s is a p o i n t o f i n t e r e s t , s i n c e i t emphasizes
t h a t t h e A d r i a t i c d y n a m i c s i s almost c o m p l e t e l y o n e - d i m e n s i o n a l f o r s u r g e s .
In t h e r a n g e o f f o r e c a s t o f s i x h o u r s ( T : 6 i n t h e p r e v i o u s f o r m u l a ) f l o o d s were p r e d i c t e d w i t h i n a few c e n t i m e t e r s i n t h e d o z e n s o f cases when t h e model
was t e s t e d (many o f t h e m i n r e a l t i m e ) .
Fig. 6 g i v e s a n example.
434
F i g . 6. An e x a mpl e o f p r e d i c t i o n u s i n g t h e s t a t i s t i c a l me thod by S g u a z z e r o e t a l . The s u r g e ( i . e . t h e d e v i a t i o n from o r d i n a r y t i d e ) i s shown by t h e s o l i d l i n e . Dashed c u r v e i s t h e f o r e c a s t , e a c h p o i n t b e i n g g i v e n s i x h o u r s i n a d v a n c e . ( s t a r t i n g p o i n t F e b r u a r y 1 2 , 1 9 7 2 , 0300 GMT). One c a n c o n c l u d e t h a t u s i n g o n l y t h e w e a t h e r r e p o r t s from t h e A d r i a t i c c o a s t a n d t h e o b s e r v e d t i d a l l e v e l s , t h e p r e d i c t i o n i s p o s s i b l e f o r a b o u t s i x h o u r s ahead.
( F u r t h e r f o r e c a s t i n g is p r o g r e s s i v e l y u n r e l i a b l e , due t o t h e a r r i v a l o f
o t h e r a t m o s p h e r i c phenomena i n t h e m e a n t i m e ) .
PREDICTION BY DETERMINISTIC MODELS
B e t t e r s a t i s f a c t i o n comes from a d e t a i l e d i n s p e c t i o n o f w ha t h a p p e n s i n t h e A d r i a t i c when t h e a t m o s p h e r e
forces it.
More o r less t h e same i n f o r m a t i o n ( i . e .
w e a t h e r r e p o r t s from c o a s t a l s t a t i o n s ) c a n be u s e d f o r t h e i n t e g r a t i o n o f t h e s t o r m s u r g e e q u a t i o n s where t h e d r i v i n g f o r c e s a r e , a g a i n , t h e wind stress a nd the pressure gradients.
It i s o b v i o u s l y n o t o n l y a matter o f s a t i s f a c t i o n b u t
a l s o a b e t t e r k n owl edge o f t h e p h y s i c s o f t h e s u r g e a n d a more c o m p l e t e i n f o r m a t i o n f o r t h e various places.
1954)
The s t o r m s u r g e e q u a t i o n s c a n b e w r i t t e n (Proudma n,
435
a (UCOS -
a cos Ip ad
p)
+
av + a< = ax a t
where Q and X are l a t i t u d e and e a s t - l o n g i t u d e ,
0,
t is t i m e , 5 t h e e l e v a t i o n o f t h e
sea s u r f a c e , U a n d V t h e c o m p o n e n t s o f t h e t o t a l s t r e a m , i . e .
v e l o c i t y times
d e p t h , Fs a n d Gs t h e c o m p o n e n t s o f t h e f r i c t i o n o f t h e wind o n t h e sea s u r f a c e , FB a n d G B t h e c o m p o n e n t s o f t h e water f r i c t i o n on t h e s e a b o t t o m , pa t h e a t m o s p h e r i c p r e s s u r e o n t h e s e a , h t h e water d e p t h ,
P
t h e d e n s i t y o f t h e water ( a s-
sumed u n i f o r m ) , a t h e mean r a d i u s o f t h e e a r t h , 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 , w t h e a n g u i a r s p e e d of t h e e a r t h ’ s r o t a t i o n .
T h e s e e q u a t i o n s are l i n e a r i z e d a n d i n t e g r a t e d w i t h r e s p e c t t o d e p t h . c a n b e s a f e l y assumed after t h e above r e m a r k s .
Linearity
This accounts for t h e suppression
o f a l l non l i n e a r terms i n d e r i v i n g t h e s e e q u a t i o n s a n d a l l o w s t h e a s s u m p t i o n o f a l i n e a r i z e d b o t t o m f r i c t i o n , as i t was d o n e i n p r a c t i c e . A v a r i e t y o f w o r k s were d e v e l o p e d ( T o m a s i n , 1971; S t r a v i s i , 1972;’ A c c e r b o n i e t a l . ,
1973) u s i n g t h e above b a s i c e q u a t i o n s , c o r r e c t l y r e p r o d u c i n g t i d e s , s e i c h e s and surges.
I n t e g r a t i o n t e c h n i q u e s were e s s e n t i a l l y a l r e a d y known f r o m t h e l i t e r a -
t u r e of h y d r o d y n a m i c a l n u m e r i c a l m o d e l s ( H a n s e n , 1 9 5 6 ; H e a p s , 1 9 6 9 ) .
In particu-
l a r , r e d u c t i o n t o o n e d i m e n s i o n was p o s s i b l e d u e t o t h e s h a p e o f t h e A d r i a t i c . And t h i s was r e a l l y t h e s c h e m e more e x t e n s i v e l y t e s t e d i n p r a c t i c e ( F i n i z i o , 1970; Tomasin, 1973).
I n formula
w h e r e t h e x a x i s i s d i r e c t e d a l o n g t h e s e a , w is t h e w i d t h o f t h e c r o s s s e c t i o n a n d Q t h e d i s c h a r g e a c r o s s i t , o r , s a y , t h e a v e r a g e v e l o c i t y times t h e a r e a o f the section. The e q u a t i o n s are c l e a r l y s i m p l i f i e d a l s o b e c a u s e t h e e a r t h c u r v a t u r e i s d i s regarded:
n e e d l e s s t o s a y , a l l t h e s e s i m p l i f i c a t i o n s would n o t b e p o s s i b l e f o r
o t h e r a r e a s , l i k e f o r e x a m p l e t h e M e d i t e r r a n e a n , whose m o d e l l i n g i s m e n t i o n e d below.
436 I n f o r e c a s t i n g , t h e o n e d i m e n s i o n a l s c h e m e was u s e d o n t h e f i e l d , u s i n g s y n o p t i c m e t e o r o l o g i c a l d a t a a n d i n t e g r a t i n g t h e e q u a t i o n s by a n e x p l i c i t f i n i t e - d i f f e r e n c e s scheme. issued:
The w e a t h e r f i e l d i s known u p t o t h e time when t h e f o r e c a s t i s
t h e s i t u a t i o n is s u p p o s e d c o n s t a n t f o r t h e f o l l o w i n g h o u r s and t h e equa-
t i o n s g i v e f u t u r e sea l e v e l u n d e r
this
hypothesis.
Consistent with the statis-
t i c a l a p p r o a c h , i t t u r n s o u t t h a t a t a n y time t h e r e i s e n o u g h i n f o r m a t i o n t o p r e d i c t s a f e l y t h e sea l e v e l f o r a b o u t s i x h o u r s .
A s expected, the
a b o v e method
t u r n e d o u t t o b e s a t i s f a c t o r y as a p r e d i c t o r . FURTHER DEVELOPMENTS I m p r o v e m e n t s o f t h e p r e d i c t i o n a r e e x p e c t e d by w i d e n i n g t h e l i m i t s i n r e s e a r c h h a s been confined so far. p r e d i c t i o n s was a v o i d e d .
which
It w i l l b e r e m a r k e d t h a t t h e u s e o f w e a t h e r
Over t h e M e d i t e r r a n e a n t h e y a r e made d i f f i c u l t by t h e
i n f l u e n c e o f o r o g r a p h y w h i c h c o m p l i c a t e s t h e f l o w o f a i r masses a n d g e n e r a t e s l o c a l effects:
c y c l o g e n e s i s on t h e w e s t e r n l e e o f t h e A l p s was m e n t i o n e d a b o v e .
The G l o b a l A t m o s p h e r i c R e s e a r c h P r o g r a m (GARPI h a s c r e a t e d a s u b p r o g r a m o n Air Flow Over a n d Around M o u n t a i n s a n d t h e f i r s t e x p e r i m e n t a r o u n d t h e A l p i n e b a r r i e r ( A l p e x ) i s p r o p o s e d f o r 1981.
This e f f o r t should help i n understanding the dy-
namics o f p e r t u r b a t i o n s i n t h e M e d i t e r r a n e a n , w i t h t h e f i n a l o b j e c t i v e o f a n a c c u r a t e p r e d i c t i o n 12 t o 24 h o u r s a h e a d :
Venice, I t a l y and s e v e r a l c o u n t r i e s w i l l
substantially benefit. For t h e s p e c i f i c w a r n i n g o f f l o o d s , a wind f o r e c a s t i n g model is b e i n g d e v e l o p e d
(Palmieri a t a l . , 1 9 7 6 ) .
S t a t i s t i c a l m e t h o d s a l s o are b e i n g i m p l e m e n t e d i n V e n i c e
for the prediction o f the'pressure f i e l d i n the central Mediterranean. From t h e h y d r o d y n a m i c a l p o i n t o f v i e w , i t i s n o t i c e a b l e t h a t n o a t t e m p t was made t o f o r e c a s t e x t e r n a l s u r g e s , i . e . phenomena o r i g i n a t i n g o u t o f t h e A d r i a t i c , b u t g i v i n g s i g n i f i c a n t e f f e c t i n it.
From e x p e r i e n c e , t h e y seem n o t t o e x i s t ; s o
f a r t h e l o w f r e q u e n c y c h a n g e s i n t h e l e v e l o f t h e M e d i t e r r a n e a n h a v e b e e n monit o r e d c l o s e t o t h e O t r a n t o Channel and t r a n s m i t t e d t o Venice f o r a d i r e c t u s e i n t h e p r e d i c t i v e models (Mazzoldi et a l . ,
1973).
For a b e t t e r i n s i g h t i n t h e s e
large s c a l e phenomena a f f e c t i n g t h e M e d i t e r r a n e a n , a s p e c i f i c n u m e r i c a l model i s b e i n g d e v e l o p e d , t o f i l l u p t h e t h e o r e t i c a l g a p t h a t was s o f a r o v e r c o m e by d i -
rect i n s p e c t i o n . Time i s r i p e f o r w i d e r a n a l y s i s , w h e r e t h e M e d i t e r r a n e a n i s f u l l y c o n s i d e r e d f o r its hydrodynamical c o n t r i b u t i o n s and f o r t h e m e t e o r o l o g i c a l p a t t e r n s t h a t develop over it.
The g o a l o f a w a r n i n g f o r V e n i c e f l o o d s w i t h a n a d v a n c e o f
t w e l v e h o u r s o r o n e d a y seems n o t t o b e c h i m e r i c a l .
437 ACKNOWLEDGEMENTS The h e l p o f R .
D a z z i , G . A l d i g h i e r i , and Mrs. J . Z a n i n , o f t h e CNR l a b o r a t o r y ,
h a s b e e n o f u t t e r i m p o r t a n c e f o r t h i s work.
P r e c i o u s s u p p o r t was g i v e n by t h e
C e n t r o S c i e n t i f i c 0 IBM o f Veni ce and t h e CRIS-ENEL b r a n c h o f V e nic e -Me s tre . REFERENCES A c c e r b o n i , E. a n d Manca, B., 1973. S t orm s u r g e s f o r e c a s t i n g i n t h e A d r i a t i c Se a by means o f a t wo-di mensi onal h y d r o d y n a m i c a l n u m e r i c a l mode l. B o l l . G e o f i s . Teor . Appl . , 15: 3-22. A r t e g i a n i , A . , Tomasi n, A . and Goldmann, A . , 1972. Sur l a dyna mique d e l a mer A d r i a t i q u e d u e aux e x c i t a t i o n s m & t & o r o l o g i q u e s . Rapp. Comm. I n t . Mer MGdit., 21:181-183. B u z z i , A . a n d T i b a l d i , S . , 1978. C y c l o g e n e s i s i n t h e l e e o f t h e A l p s : A c a s e s t u d y . Q u a r t . J . R . Met. SOC., 104:271-287. F i n i z i o , C . , Palmieri, S. and R i c c u c c i , A . , 1970. A n u m e r i c a l model o f t h e Adria t i c S e a f o r t h e s t u d y and p r e d i c t i o n o f sea t i d e s a t V e n i c e . 1st. F i s . At mo sf ., STR 12. Goldmann, A . , R a b a g l i a t i , R . and S g u a z z e r o , P . , 1975. P r o p a g a z i o n e d e l l a marea n e l l a l a g u n a d i Venezia: a n a l i s i d e i d a t i r i l e v a t i d a l l a r e t e m a r e o g r a f i c a l a g u n a r e n e g l i a n n i 1972-73. R i v. I t a l . G e o f i s . , 2:119-124. Hansen, W . , 1956. T h e o r i e z u r E r r e c h n u n g d e s W a s s e r s t a n d e s und d e r Stromungen i n Randmeeren n e b s t Anwendungen. T e l l u s , 8:287-300. P h y l . T r a n s . A 265: Heaps, N.S., 1969. A t wo-di mensi onal n u m e r i c a l sea model. 93-137. 1910. Das Gezei t enphanomen i n Hafen von P o l a . Mittl. Geb. K e s s l i t z , W.V., S e e w e s e n s , 38: H . V - V I . M a z z o l d i , A . , D a l l a p o r t a , G . , G a s p a r i , A . , C u r i o t t o , A . a nd P e r u z z o , G . , 1973. S i s t e m a d i t e l e m i s u r e d a s t a z i o n i a u t o m a t i c h e f i s s e . CNR-LSDGM, V e n e z i a , R a p p o r t 0 T e c n i c o n . 37. P a l m i e r i , S., F i n i z i o , C. and C o z z i , R . , 1976. The c o n t r i b u t i o n of m e t e o r o l o g y B o l l . Geofis. t o t h e s t u d y a nd p r e d i c t i o n o f h i g h t i d e s i n t h e A d r i a t i c . T e o r . Ap p l ., 19:191-198. Mon. N ot. R . a s t r . Proudman, J . , 1954. Note on t h e dynami cs o f s t o r m - s u r g e s . S OC . Geophys. S u p p l . , 7:44-48. R o b i n s o n , A . R . , T omasi n, A. a n d A r t e g i a n i , A . , 1973. F l o o d i n g o f V e n i c e : Phenomenology a n d p r e d i c t i o n o f t h e A d r i a t i c s t o r m s u r g e . Q u a r t . J . R . Met. S O C . , 99~688-692. S g u a z z e r o , P . , Giommoni, A . and Goldmann, A . , 1972. An e m p i r i c a l model f o r t h e IBM I t a l i a T e c h . Rep. CSVOO6. p r e d i c t i o n o f t h e sea l e v e l i n Veni ce. S p e r a n z a , A . , 1975. The f o r m a t i o n o f b a r i c d e p r e s s i o n s n e a r t h e A l p s . Ann. d i G e o f i s . , 28:177-217. 1919. Die G e z e i t e n e r s c h e i n u n g e n i n d e r A d r i a . D e ns c hr. Akad. Sterneck, R.V., Wiss. Wien, 96:277-324. S t r a v i s i , F . , 1972. A n u m e r i c a l e x p e r i m e n t on wind e f f e c t s i n t h e A d r i a t i c Se a . Acc. Naz. L i n c e i , Rend. S c. F i s . , m a t . , n a t . , 52:187-196. To ma sin , A . , 1971. A p p l i c a t i o n o f t h e h y d r o d y n a m i c a l n u m e r i c a l i n t e g r a t i o n method t o t h e A d r i a t i c S e a . P h y s i c s o f t h e S e a , T r i e s t e , 13-16 O c t . , Accad. Naz. L i n c e i , Quad. n . 2 0 6 , 119-121. Tomasin, A . , 1972. A u t o r e g r e s s i v e P r e d i c t i o n o f S e a L e v e l i n t h e N o r t h e r n Adria t i c . R i v . I t a l . G e o f i s . , 21:211-214. To ma sin , A . , 1973. A comput er s i m u l a t i o n o f t h e A d r i a t i c S e a f o r t h e s t u d y o f i t s d y n a mic s and f o r t h e f o r e c a s t i n g o f f l o o d s i n t h e town o f V e n i c e . Comp. Phys. Comm., 5: 51-55.
438 T o m a s i n , A . , 1 9 7 6 . The d y n a m i c s o f t h e d i u r n a l t i d e i n t h e A d r i a t i c S e a : p r e l i m i n a r y r e s u l t o f a r e v i s i t i n g a n a l y s i s . Rapp. Comm. I n t . Mer M d d i t . , 2 3 : 4 9 . U n e s c o , 1969. R a p p o r t 0 s u V e n e z i a . M o n d a d o r i , M i l a n o , 348 p p .