Extkemưm Sea Levels in V1etnam Coast

EXTKEMƯM SEA LEVELS IN V1ETNAM COAST

Pham Van ỉỉu a n

D epartm ent o f Hydro Meteorology a n d Oceanology CoIIegc o f Science, V N U

A b s t r a c t : A revievv ()f th o in v e s tig a tio n s on t.hcì sea le vol changcỉS in S o u th r h in a soa is presenUỉíl and th e methods o f approxim ate e a U u la tio n o f th e o retica l tid a l oxtrem cs w crc oxplaineil in (letail.

Tho soa level changes ncar V ietnam coast (ỉuo to global w a rm in g and o lh e r

<ìffccts is evaluated to be from 1 to 3 mm per ycar.

Kor sevon sta tio n s vvith fu ll sot o f harm onic constants (le tc rm in o tl thc th e o retica l extrem o heights o f tiíỉa l level by p re d ictin g h o u rly t i do h e ig h ts in a 2 0-year ptỉriod. lf,or o th e r ninctecn stations w ith 1 1 h arm onic constants o f m ain tid a l co n s titu e n ls the theoretical astronom ical cxt.rome hìvols wortĩ calculatod by the ito ra tio n mcìthod. Thtĩ coniparison showeđ a good agrcỉomen! l)c(wcM n l.wo methods.

T he e n ip iric a l oxtrem e analysis was carried out for 25 tid e gaugcs along V ie tn a n ì coast to e v a lu a tc t h r design values <)f sca lcĩvel <)f ( ỉiffo ro n t ra re fr(?qucncies.

T h o a n a lysis a lso show ed th a t th o tiđ a l e xtre in e s and đ csig n le vo l valu o s ()f 20- y ea r r c tu rn poriod arc of the samc rango.

'rhc

levcl valuos ()f longer rcĩturn p e rio d arcì affect.o(J m a in ly hy Hoods and surges.

1. In tr o d u c tio n

T h e e x tre m e sea le v e ls a re s tu d y s u b je c t o f m a n v p u rp o s e s . T h e m a x im a l a n d m in im a l v a lu e s o f sea le v e ls a n d t h e ir o c c u rre n c e p r o b a b ilitie s a re ta k e n in to a c c o n n t in d e s ig n in g h v d ro te c h n ic a l s tru c tu re s .

T h e th e o ry o f e x tre m e a n a ly s is o f s ta tis tic a l m a th e m a tic s is a p p lie d to th e h v d ro m e te o ro lo g y w it h d if fe r e n t d is tr ib u tio n s o f th e o b s e rv e d s e ric s o f c lim a tic a n d h y d ro lo g ic a l p a ra m e te rs [5 t7 ]. T h e m a in c o n c c p ts o f th e s e m e th o d s w ill be p re s e n te d in s e c tio n 2.1.

In th e case t h a t o b s e rv e d se rie s o f sea le v e l a rc n o t lo n g e n o u g h to a p p ly th e p ro c e d u re s o f e x tre m e a n a ly s is th e o ry , t h a t u s ụ a lly h a p p e n in th e d e s ig n in v e s tig a tio n s in t h c

Coastal

zone a n d e s tu a rie s , one m a y use th e o r e tic a l e x tre m e v a lu e s o f p u re ly t id a l le v e ls .

In m a n y p r a c tic a l p ro b le m s th e m in im a l th e o r e tic a l le v e l is a s s u m e d to be th e zero d e p th in t id a l seas. T h is le v e l can be c a lc u la te d by s u b tr a c tin g m a x im a l lo w h e ig h t o f tid e due to a s tro n o m ic a l c o n d itio n s fro m m e a n sea le v e l. III so m e c o u n trie s th is v a lu e is d e te rm in e d b v a n a ly z in g a p re d ic te d s e rie s o f tic ỉa l h e ig h ts 1 9 -y o a r

22^ềÍÊề

VMU. JOURNAL QF SCIENCE, Nat., Sci., & Tech., T XIX. NọỊ, 2003___________________________________________

E x tv e m u m s c a lc v e ls i n 23 long, o n e ch o ose th e lovvest h e ig h t n m o n g a ll lo w vvatồrs in th e s e rie s . III R n s s ia th o m ỉin m a l th e o r e tic a l le v e l is c le te rm in e d bv k n o w n m e th o d o f V la đ im ir.s k y .

V la d im ir s k y m e th ơ d g iv e s an a n a lv tic a l s o lu tio n o f th e p ro b le m w ith h a rm o n ic c o n s ta n ts o f 8 m a in tid a l c o n s titu e n ts . T h o r r s t tid a l c o n s titu c n ts nre ta k c n in t o a c c o u n t a p p r o x im a te ly . lỉe c e n tly th e c a lc u la tio n s can be p e ríb rm e d ra p id ly in c o m p u t r r s , e v a lu a tin g e x tro m e h e ig h ts o f tid e can be c a r r ie d o u t by m ore íie ta ile d sch e m e s a n d th e a c c u ra c y is im p ro v e d by w ith c lr a w in g a n o n - r e s tr ic te d n u m b e r o f t id e c o n s titu e n t s ìn to c o n s id e ra tio n [G]. S e c tio n 2.2 vvill e x p la in in d e ta ils a schom e to im p le m e n t th is m e th o d in p ra c tic e a n d in s e c tio n 3 vvill p re s e n te d th e n p p lic a tio n r e s u lts to o b ta in m a x im a l c h a r a c te r is tic s o f sea le v e l in so m e re g io n o f V ie tn n m c o a s t.

T h e o b s e rv a tio n o f sea le v c l a lo n g V ie tn a m co a s t is m a in ly c a r r ie d o u t by a System o f t id a l g a u g e s o f th e V ie tn a m H v d ro m e te o ro lo g ic a l S e rv ic e . G e n e r a lly s p e a k in g u p to novv t h e n u m b e r o f t iđ a l gauges th a t b e lo n g s to V ie tn a m w a te rs is not m a n v a n d th e n u m b e r o f o b s c rv a tio n y e a rs is n o t lo n g e n o u g h . So th e r e is no niuch d e a l w it h th o b e h a v io r o f sea le v e l in g e n e ra l a n d th e e m p ir ic a l e a lc u la tic m s ơf leve l e x tre m e s in s p e c ia l.

In so m e r a r e w o r k s th c r e re p o rte d th e r e s u lts o f a n a ly z in g c h a n g e a b le n e s s o f sea le v e l a n d th e e s tim a tin g th e tr e n đ o f.s e a le v e l ris e in th e base o f a n a ly s is o f observed s e rie s o f sea le v e l so m e y e a rs lon g . T h e s p e c tru m a n a ly s is [2] s h o w e d t h a t besiđes th e s e m ia n n u a l a n d a n n u a l p e rio d s , in th e a lm o s t o f t i d a l gauges o á c illa tio n s o f p e rio d o f G to lO y e a r s an d lo n g e r e x is t (íìg u re 1).

8 < p /

0.0»

(k*.'ỉ o.c»«

0 . 0 5 6

txtrb

0.0*0 n .t X ‘ 2

ao:-*

mo

4 ii.ođ

Hon 0*1.

\ __ p‘«ni>d irtiìntt)

0.(1»

0.030

•>.0

'i?

0.024

0.071

0.019 0.015

o.m:

0 t <V J

0 . 0rtẠ

0 . 0 0 3

r4 j , Nhon

ỉ L

' . 5 J ỡ 100 S.0 \b ¹⁰ lô

F igure 1.

S p e c tru m o f sea

level

a t tid a l gauges H on D a u a n d Q u y N h o n

T a b le 1 lis t s th e r e s u lts o f e s tim a tio n o f th e sea le v e l ris e by tr e n d a n a ly s is vv.th m o n th ly m ean le v e l [2 - 4 ]. It is fo llo w e d t h a t th e s u m m a ry e ffe c t b y th e g lo b a l vv.irm in g a n d o s c illa tio n s o f sea bed in re g io n o f V ie tn a m c o a s t causes a r a t e o f lc v e l riíe a b o u t 14-3 m tn p e r y e a r.

24 P h a m V a n H u a n

T a b le 1.

R a te o f sea le v e l ris e a t som e p o in ts a lo n g V ie tn a m c o a s t

Gauge C o-o rd in a te s O b s e rv a tio n

y e a rs

T re n d (

m m / y e a r

)

H o n D au 20°4 0’ N - 106°4 9’ E 19 57 -1 9 94 2 , 1

C ua Cam 20o4 5 'N -1 0 6 °õ 0 'E 1 9 6 1 -1 9 9 2 2,7

Da N an g 16°06,N -1 0 8 ° 1 3 ,E 19 78 -1 9 94 1 , 2

Q u y N ho n 1 3 °4 õ 'N -1 0 9 o13'E 19 76 -1 9 94 0,9

V u n g Tau 10°20,N -1 0 7 ° 0 4 ’ E 19 79 -1 9 94 3,2

A f u ll c u m b e rs o m e c a lc u la tio n o f le v e l e x tre m e s vvas p e ríb rm e d in [1 ]. I n th is r e p o r t í ir s t ly lis te d s e rie s o f m o n th ly a ve ra g e , m a x im a l a n d m in im a l le v e ls fo r a ll gauges a lo n g V ie tn a m co a st u p to m id d le o f n in e tie th . T h e e x tre m e a n a ly s is w as c a r r ie d o u t by an a s y m p to tic G u m b e l fu n c tio n o f p r o b a b ility d is t r ib u t io n o f th e e x tre m e s .

2. T h e m e th o d o f s t u d y

2 .1. E x t r e m e s a n a l y s i s i v i t h e m p i r i c a l d a t a

A s s u m e

VỊ

t h e v a lu e s o f in c ic ỉe n ta l v a r ia b le

V

a t t im e / a n d A'<m) = m a x {F1) F2) ...) Fm} ;

x (m)

= m in { F , ,F2,

...,Vm .

O ne is o fte n in t e r e s t in e s tim a tio n th e p r o b a b ility w it h w h ic h m a x im a l o r

m in im aỉ value exceeds a th re s h o ld , Iì{ Xim > x} or P{X(m) < x } . If t h e o b serv atio n s

on th e h y d ro m e te o ro lo g ic a l p a ra m e te rs a re in d e p e n d e n t a n d d is t r ib u t e d if fe r e n t ly

due to d istrib u tio n fu n ctio n F{x) - P{Vị < x ) , t h e p recise d is tr ib u tio n of m ax im u m

a n d m in im u m ca n be cxp re sse d :

/ ’ { A '('n) < x } = | / - - ( . v ) f a n d < x ) = 1 - |1 - /<-(x)|m (1)

The extrem es a n a ly sis theory says th at w ith th e enough length of sam ple m ,

t h e p r o b a b i l i t y d i s t r i b u t i o n o f t h e n o r m a l i z e d m a x i m u m

Y (m)= ( X ' m

bm > 0 c a n b e a p p r o x i m a t e d by o n e o f t h e t h r e e íơ ll ov vi ng f o r m s o f a s y m p t o t i c

function

G, ( v) = cxp(-ế y ) (Gumbel íunction)

G: ( v) = cxp(-V 1 k ). y > 0 , k <0 (Frechet íunction) (2)

0*3(v) = c x p |- ( - v ) 1 k K v < 0 . k > 0 (Wcibull function)

E x t rem u m SCO ie v e ỉs ỉ n

25

a n d s i m i l a r for t h e m i n i m a l v a l u e

//,(>•) = l - c x p ( - i ' v)

/ / : ( v ) = I - C \ p | - ( - v ) 1 A). V < 0 . Ả < 0 (3)

/ /,( > ’) = i - c x p ( - v 1;*),

y >

0. * > 0 ^.

T hese d if fe r e n t

form s

o f a s y m p to tic fu n c tio n s a re d e p e n d e n t to th e sh a pe o f th e t r a i l o f p r o b a b ilìty d is t r ib u t io n

F(x)

(th e r ig h t sicỉe fo r th e m a x im a a n d th e le ft s id e fo r th e m in in ia ) . I n p ra c tic c th e s a m p le c o n c ỉitio n s (th e h o m o g e n e ity , th e incỉe p en đ o n cc a n d th e d im e n s io n ) in ílu e n c e on th e p re c is io n o f th e a p p r o x im a tio n by th e above a s y m p to tic íu n c tio n s .

A s y m p to tic e x tr e m e c lis tr ib u tio n s in c lu d e th re e p a ra m e te rs :

k

- s h a p e p a ra m e te r.

u m -

lo ca l p a r a m e te r a n d

hn

- scale p a ra m e te r.

O fte n , in s te a d o f e s tim a t in g th e d is t r ib u t io n o f m a x im a (o r m i n i m a) t one e xecutes a d iv e rs e p ro b le m : d e te rm in e a d e s ig n v a lu e , i. e. a v a lu e

x fnii

such as

Othervvise

X

is the q u a n tile

p

of extrem e distribution. B esides, one converts the probability o f th e d esig n v a lu e Xp to r e t u r n period T = 1/(1 - p ) , w h e re 7 - th e tinie

to b e e x p e c t e d t h a t t h r e s h o l d X r is e x c e e d e d f o r t h e f i r s t t i m e , o r t h e a v e r a g e t i m e betvveen tvvo above th r e s h o ld e v e n ts .

U s in g th e a s y m p tọ tic e x tre m c d is t r ib u t io n th e d c s ig n v a lu e s can be e a s ily e xp resse đ . K o re x a m p le , v v itlì G u m b e l d is t r ib u t io n , one has:

y p

=

^G\

'(/>) = - log (- log

^{p )}

. (5) C onsequently, design v a lu e estim a te vvith return period T = ( ! - / ; ) years of the

e x tr e m e

variable

X m a y b e c a l c u l a t e d k n o v v in g p a r a m e te r s u a n d h :

xr = hyp

+

u

, (6)

w here y is also called f,norm alized design value".

A q u e s tio n o f p r in c ip le in th e a p p lic a tio n o f e x tre m e s a n a ly s is th e o ry is th e p re c is io n o f th c a p p r o x im a tio n (2) 01* (3), i. e. th e q u e s tio n on th e ra te o f

convergence of p recise d i s t r ib u t i o n of e x tre m e s i ,r’ to th e a sy m p to tic one, in p rac tic al aspect, th e p re c isio n of design v alu e x p e s tim a te d by asym ptotic

d i s t r i b u t i o n i n c o m p a r i s o n vvith ií's r e a l v a l u e ( b u t o f t e n u n k n o w n )

x ('"].

26

P h a t n V a tì H u n u

T h e m e th o cls o f e s t im a tio n o f e x tre m e d is t r ib u t io n a im a t s e ttle m e n t th e q u e s tio n on th o i n i t i a l s e rie s , th e r e la t iv e ly s h o r t le n g th o f i n i t i a l s e rie s . T ib o r K a ra g o a n d R ic h a rd

w .

K a ts [5 ] e x p la in d if fe r e n t m e th o d s to e s tin ia te t h e e x tre m e p a ra m e te rs a n d d e te r m in e d e s ig n v a lu e s a n d t h e ir e s tim a te a c c u ra c y . S e c tio n 3.3 p re s e n ts th e r e s u lts o b ta in e đ b y a p p ly in g th e s e m e th o d s to s e rie s o f a n n u a lly m a x im a l a n d m in im a l le v e ls o f som e t id a l g a u g cs a lo n g V ie tn a m coast.

2

^.

2

^.

M e t h o d o f c o ì ì i p u t i n f í e x t r e m e v a lu e s o f t i d c

T h e t id a l h e ig h t a b o ve th e m e a n le v e l m a y be e x p re s s e d by th e fo llo w in g íb r m u la

z t

= C0S<P, 1 ⁽⁷⁾

I

vvhere

f t -

th e re d u c e c o e ffic ie n ts d e p e n d e d o n lo n g itu d e o f th e r is in g k n o t o f lu n a r o r b it ;

/ / t

- th e a v e ra g e a m p litu d e s a n d

(pt -

th e p h a s e o f t id a l c o n s titu e n ts .

D e p e n d in g on t h e t i d a l íe a tu r e , th e h e ig h t o f tid e m a y a c h ie v e th e e x tre m e s w h c n lo n g itu d e o f th e r is in g k n o t o f lu n a r o r b it

N

= 0 (fo r d iu r n a l tid e ) o r

N

= 1800 (fo r s e m id iu r n a l tid e ) . I n th e s e c o n d itio n s (7V = 0 ,1 8 0 °) th e phases o f t id a l c o n s titu e n ts a re e x p re s s e d th r o u g h a s tro n o m ic a l p a ra m e te rs i n ta b le 2.

T a b le 2. E x p re s s io n s o f p h a s e s a n d re d u c e c o e ffic ie n ts o f t id a l c o n s titu e n ts [6] Tidal

constitucnt Phase,

(p

Rcducc cocfficicnt, /

;V = ()•

N

= 180'

•w.

ĩ t + 2h

-

2s

-

gMf

^{0,963 1,038}

2

t - g .

^{1,000 1,000}

2r

+

2h - 3 s + p -

g V; 0,963 1,037

*> 2/ + 2

h - g Ki

^{1,317 (),74X}

A',

t + h + 90' - g K]

^{1.113 0.882}

0,

1 + H - 2 S - 9 Ơ - g 0)

^{1,183 0,806}

p, 1 - h -

90° -

gpt

^{1,000 1,000}

Ỡ

t + h -

3.V

+ p -

90° -

g Qí

^{1,183 0,806}

A/,

4t + 4 h - 4 s - g M'

^{0,928 1.077}

MS, 41 + 2h - 2s - ỊỊ'KÍS'

^{0.963 1.038}

A/. 6/ +

6h -

6

s

-

g Kf

^0.894 1.1 IX

Sa h ~Sso

^{1.000 1.000}

SSa 2h - Kssa

^{1.000 1.000}

E x tv c t ỉiu tt i sca l c v c ls iti 2 7

III ta b le

2

Ị - a v e ra g e zone tim e fro m m ic ln ig h t, lì a v e ra g e lo n g itu d e o f th e S u n ; V a v e ra g e lo n g itu d e o f th e M o o n ;

p -

a v e ra g e lo n g itu d e o f lu n a r o r b it p e rig ro ;

fỉ

s p e c ia l i n i t i a l p h a s c r c la te d to th o G re e n vvich lo n g itu d e .

T h o e x tre m e h e ig h ts o f tic le m a y be c o m p u te d fro m (7) i f th e v a lu e s o f a s tro n o m ic a l p a r a m e te r s

í. lì.

V a n d />, vvhich fo rm a c o m b in a tio n c o r re s p o n d in g to an e x tI ^ m e c o n d itio n , a re k n o w n . I n v e s tig a tin g on e x tre m e s th e íu n c tio n . z ( í . h . s . p ) fro m (7 ), vve o b ta in a s y s ti m o f fo u r e q u a tio n s w it h fo u r u n k n o w n s

í . h . s

a n d /?

w hose v a lu e s d e te r m in e th e e x tr e m e c o n d itio n o f th e t id a l h c ig h t:

I f th e a p p r o x im a te v a lu e s o f a s tro n o m ic a l p a r a m e te r s c o rre s p o n d in g to e x tr c m e c o n d itio n

( t \ h \ s é % p f)

a r c knovvn, w e m a y Ie a d e q u a tio n s (8) to a lin e a r fo r m by T a v lo r e x p a n s io n . W h c n a p p r o x im a te v a lu o s o f th e u n k n o v v n are s u ffic ie n t ly close to th e €?xact

v a h ie s ụ

./? ,.V ./>,,) th e c x p a n s io n ca n be r e s tr ic te d in f ir s t o rd e r ite m s .

VVith (ie s ig n a tio n s o f c o r r c c tio n s to th e a p p r o x im a te v a lu e s o f a s tro n o m ic a l p a r a m e te rs as fo llo w in g

th o r e s u lt o f th e e x p a n s io n is a s y s te m o f fo u r lin e a r e q u a tio n s vvith d ia g o n a lỉv s y m m c tr ic c o e ffic ie n t m a t r ix :

I M

2 sin

<pu ^

4* 2.v: sin

(pSs

+ 2

N 2

sin

<PX'

+

2 K

2 sin

(pKy

+ Kị SIn<pK 4‘ (ỉ ị SIIU/9,, + ì \ s i i í ặ ? , , s i n +

4À /4 sin (pSỊ + 4M S Ằ sin <PSỊS + 6 M 6 sin <PSỊ = 0

2 M ■ >

sin

<psr

+

2;V,

sin

<p < %

+ 2Ả \ sin

(pK%

+

K

I sm

(pK

4*

(), sin<pa

+ /* sin + 0 | sinv?£> + 4iV/ 4 sin$?A/ + >

4A/.V4 sin + 6.A/, sin + .Sí7 sin y> ViJ + 2.V.Ví/ sin - 0

2 A /: sin

(pSỊy

-f 3 iV , S1I1

(ps%

+

2 0 Ị

sin

(p(ỉ

+ 3 (/ị sin ^ + 4A/ 4 sin <PA/ 4- 2A/.V4 sin

(pSỊSị

+ 6A / Ố sin - 0

A,r: sin <Pv: + 0 , sin <PC,( = 0,

( 8)

/l,v + /1 =0 , (9)

vvhcre

P h a m V a n ỉ ỉ u a n

a \ bị

Cj

d ]

z l/ A

h

,

í

c ,

í í

/ƯJ / ,

; A" = ; A =

£

Cj d ĩ

^zlv _{/ ,}

/4

a )

-

4 M 2

c o s

<

p

'

m + 4

S 2

cos

(p's + 4 N 2

cos

(p's

+ 4

K 2

co s

<p'Kĩ

+ + K | c o s ^ í + 0 ị COSỰ)'0 +P\ COS{?Ị» + ( í| COSộ?£ + + 1 6 A /4 cos +16

M S 4

cos

<p'KiS

+ 3 6 A /6 cos • /?ị = 4jV/2 cos<Pv/ + 4/V, cosợ?Y + 4 /v 2 c o s(p'K + ATj c o s(p’K +

+ ƠJ co s - 1\ co s ợ?), + Ọj cos <Pọ + 16;V/4 co s + + 8 A / S 4 c o s ọ9ms + 3 6 M ỗ cos<p'ví ;

Cị = - 4 A / , COS0>Ú - 6 ^ 2 cos

(p'Ni - 2 0 ì cos <P

q - 3 Ộ | cosợ?£

- 16A-/, CCS «?;,4 - U í S A cos íỡ;,Í4 - 3 6 M 6 cos <?;,6 ,

í/, = 2 N 2 cos +

01

^{cos ;}

/j = 2 M2 s i n + 2 5 2 s i n (p's + 2 / V 2 s i n + 2AT2 s i n (p'K + +

K x

sin

(p'K

+

0 ]

sin +

l\

sin + (>! sin +

+ 4A* 4 sin ^ ; Í4 + 4

M S 4

sin ^ +

6 M

6 sin <p;,6 ;

b 2 = 4 A / : C

0

S(p's1 + 4 j V 2 cosợ?v + 4 / ^ c o s ộ \ + Ả 'j c o s p í + + ƠJ

cosọ>'0 +!\ cos (p'j. +Qị cos<P

q + ỉ6A/ 4 cos<Pv/ + + 4MV4 cos + 36M ố cos + Sa cos <pýa + 4&SV7 cos <p'SSa;

c 2 = - 4 A / : c o s ọ h - 6 N 2 c o s ^ v - 2 ơ | cos <Po - 3 ( P ị C

0

^SỘ?£

- 16A /4 cos - 4MV4 cos <P v,v< - 3 6 A /6 cos <p v,A;

d 2

= 2iV: cos{?v + (?!

cosỌọ

;

/ 2 = 2 A / 2 sin + 2/V-, sin + 2/w 2 sin + Áf| sin + +

()]

sin sin ự Ị, +

Qx

sin

(pQ

4- 4A/ 4 sin + + 2M V4 sin + 6A/ 6 sin

(pu

+ .SV/ sin -f- 2XVc7 sin ; c 3 = 4 A / 2 c o s(p fM + 9 N : c a s ọ ' s + 4 Ơ , c o s t p ý + 9 Q ị c o s ( p ọ

+ 16A f4 cos + 4M V4 cos^ /5 + 3 6 A /Ố cos

ạ>Ệ Xi

, J 3 = - 3 W 2 c o s (p \^ - 3 ( ^ J cos<pộ ;

/, = - 2 A / : sin^>v/j ” 3^2 s i n f v 2 - 20j s i n ^ -3Ợj s i n ^

- 4 A í4 sin - 2A/.V4 sin - 6jW() sin

<p'M

; J 4 = /v 2 cos V + ộ j cos ;

/ 4 = N z costpl/ + Q \ cos<Pọt ;

p h a s e o f th e t i đ a l c o n s t it u e n ts c o m p u te d t h r o u g h a p p r o x im a te v a lu e s o f th e a s t r o n o m ic a l p a r a m e te r s í \ h \ s ' a n d p '

E x t r e m u m s c n lc v c ls i n . 2 9

I n o r d e r to c o m p u te th o v a lu e s o f a s tro n o m ic a l c o rre s p o n d in g to e x tre m c

concỉition (tt,,h0. s 0, pv) w ith a given accuracy t h e ite ra tio n m eth o d m ay be u sed . If any correction am ong [ảí% Ah. A\\ Ap) obtained from solving system (9) exceecỉs in

m a g n itu d e a g iv e n v a lu e

\ổ\

th e s o lu tio n w ill re p e a te d a n d th e n in o rd e r to c o m p u te

th e c o efficien ts of e q u a t io n s (9) vve will u se th e p h a se s (p' co m p u ted t h r o u g h th c

va lu e s c o r re c te d o f a s tr o n o m ic a l p a ra m e te rs :

/ ' = /' + A/' .v" = .v' + Av', h n =

h '

+

A h '%

p* = p ' + Ap'

T he loop is rep eated until all corrections (At, Ah, Av, Ap) obtained in solution

step k o f

system

(9)

becom e

less th a n

ổ :

T a b le 3 . V a lu e s o f a s tr o n o m ic a l p a ra m e te rs a p p ro x im a te ly c o rre s p o n đ in g e x tre m e c o n d itio n [6]

S e m id iu rn a l tid e A s tr o n o m ic a l

p a ra m e te rs

M in im a l leve l c o n d itio n

M a x im a l le ve l c o n d itio n

r

t[

=90” + 0,5 g St í, '= 180’ + 0 , 5 ^ t'2 = 270“ + 0 , 5 ^

t-j

- » o ÒQ

t/}

w 0 .5 (g JCj - gS i)

s 1 0,5ị g Kỉ

-

g M i )

p'

^{° M zKị - 3 g Mj + 2g N ì )}

I f i n i t i a l a p p r o x im a te v a lu e s

( í \ h \ s \

/ / ) close to re a l v a lu e s

(ía

,

h f)

,

s

a ,

p

a ) th e ite r a tio n r a p id ly c o n v c rg e s . T h e se v a lu e s o f a s tro n o m ic a l p a ra m e te rs c o r re s p o n d in g to e x tre m e c o n d itio n m a y be c a lc u la te th ro u g h fo u r d iu r n a l o r s e m id iu r n a l t id a l c o n s titu e n ts d e p e n d in g o n tid e fe a tu re . T h e e x tre m e c o n d itio n fo r fo u r s e m iđ iu r n a l tid a l c o n s t itu e n t s a n d d iu r n a l c o n s titu e n ts is d e te rm in e d by th e íb llo v v in g e x p re s s io n s :

- F o r s e m id iu r n a l tid e : <PKU = (ps = (pN

=(pKĩ

= <p . - F o r d a u rn a l tid e :

ỌK

=

(pQ =<pr

=

Ọọ - (p

,

w h e re

(p

= 180° +

2mi

- fo r th e lo w c s t le v e l a n d

(Ọ

= 360° + 2

7U1 -

fo r th e h ig h e s t le v e l.

F ro m th e s c e x p re s s io n s fo llo w th e ío rm u la e fo r c o m p u tin g th e a p p r o x im a te va lu e s o f a s tr o n o m ic a l p a ra m e te rs

\ i \ h \ s \ p )

c o rre s p o n d in g th e e x tre m e c c n d itio n s ( ta b le s 3 - 6 ).

30 P h a m V a n H u a n In o rd e r to c o m p u te a p p ro x im a te v a lu e o f a ve ra g e zone t im e / ' th e r e a re tw o e x p re s s io n s fo r th e lovvest c o n d itio n a n d h ig h e s t c o n đ itio n s e p a r a te ly , s in c e fo r s e m iđ iu r n a l tid e o n e day has tw o ' h ig h w a te rs a n d tw o lo w vvaters. T h e ch o ic e o f ío rm u la used in c o n c re te case m u s t be re fe re n c e to th e s ig n o f s u p p le m e n ta r y c o e ffic ie n ts

B

a n d c (ta b le 4). C o e ffic ie n ts

tì

a n d

c

a re c o m p u te d b y

following

fo rm u la e :

t ì - 0

^J

cosơị +1\ cos a 2 +Q\

COSƠ3

+ K

^J

cosa4|

c

= ƠJ sin ơ| +

p

I sin

a 2

+

Q\

sin a3 +

K ]

sin

ữ A

J

= g Mỉ

c,

- g o ,

" 9 0 °;

a ì= s.w , - ° ’58

k

, - g Ql

- 9 0 ^ |

(

11

)

« 2 = «5, - 0 f5 g JCi - g p> - 9 0 ° , a4 = 0 , 5 * ^ - g ^ + 9 0 c

T a b le 4 . C o n d itio n s o f th e lo w e s t a n d h ig h e s t le v e l [6]

C o n d itio n s o f th e lovvest le ve l C o n d itio n s o f th e h ig h e s t le ve l w h e n c > 0

t 2

w h e n

c

< 0

/j w h e n

B <

0 /2 w h e n

B >

0

T a b le 5. V a lu e s o f a s tro n o m ic a l p a ra m e te rs a p p r o x im a te ly c o rre s p o n d in g to e x trc m e c o n d itio n [6]

D iu r n a l tid e

A s tro n o m ic a l p a ra m e te rs C o n d itio n s o f th e lo w e st leve l

C o n d itio n s o f th e h ig h e s t le v e l

t§ - gp,

) 0 , 5 ( ^ , + g P|) + 18(r

/r 0,5

(g Ki - g Pi)+

90"

5' 0,5

(g Kí - g o , ) +

90”

p'

0.5(«r , - 3

So,

+ 2

g ữ))

+ 90"

T h e choice o f re d u c e c o e ffỉc ie n ts to c o m p u te v a lu e s / / / is d e p e n d e d o n th e tid e íe a tu re :

1) F or s e m id iu m a l

tide,

i f { h £ + H G ) ỵ H M < 0,5

th en

f is chosen fo r iV = 180 ; 2) F o r d iu r n a l tic ỉc , i f

[

h

K

+ / / ỡ ) /

H K1 >

1,5 th e n

f

is chosen fo r

N = 0*;

3) For m ixed tide, if 0,5 < [

h

K + HQ )ỵ H Kí < 1,5 th en we m ust u se th e values

o f a s tro n o m ic a l p a ra m e te rs fo r b o th s e m id iu r n a l tid e (ta b le 3) a n d d iu r n a l tid e

(table 5). YVhen com pute vvith astronom ical param eters of diurnal tide choose f for

E x t r c r n u r n s e o l c v c l s ỉ tì 31

;V = 0 , vvhen c o m p u te w it h a s tro n o m ic a l p a ra m e te rs o f s e m id iu r n a l t id e choose / fo r

N

0 a n d

N =

180 . T h e h ig h o s t le v e l a n d th e lo w e s t le v e l o b ta in e d by th re e v a r ia n ts vv ill bo a c c e p te d to be th e e xtre m e s.

\V e also c o m p u tc th e a p p ro x im a te v a lu e s o f a s tro n o m ic a l p a ra m e te rs c o rre s p o n d in g th e e x tr e m e c o n đ itio n s by V la c ỉim ir s k y m e th o d ; t h is m e th o d a p p lie d fo r 8 t id e c o n s titu e n ts . In V la d im ir s k y m e th o d th e e x tre m e h e ig h ts o f tid e is d e te rm in e d by c o n s e q u e n tlv c h o o sin g v a lu e s

(pK

in th e in t e r v a l fro m 0° to 3G0°:

T h e choice o f re d u c e c o e ffic ie n ts to c o m p u te v a lu e s / / / is also macỉe as th e above re c o m m e n d a tio n s , i. e. w it h th e s e m id iu r n a l t id c / is chosen fo r yV ^lX O , w it h d iu r n a l tid e

f

is chosen fo r

N

= 0 . W it h m ix e d t id e th e c o m p u ta tio n is p e río rm e d w it h

f

f o r

N

= 180 a n d /V = 0 a n d th a n th e lovvest a n d h ig h e s t va ỉu e s in tw o v a r ia n ts w il l b e th e e x tre m e lc v e ls .

I f c o m p u te e x tr e m e le v e ls vvith 8 tid e c o n s titu e n ts th e n th e la s t re s u lts are o b ta in e d d ir e c t ly fr o m th e e x p re s s io n s (1 2). In th e case o th e r c o n s titu e n ts a re ta k e n in t o th e c o m p u ta tio n s , we m u s t re íe re n c e to v a lu e s

(<pK

)mm a n d

((pK )mxx

fro m a n a ly z in g (1 2) to c o m p u te th e a s tro n o m ic a l p a ra m e te rs c o rre s p o n d in g e x tre m e c o n d itio n s

í j ụ s \ p

a n d u s c th e m as th e a p p ro x im a tio n s to c o m p u te th e c o e ffíc ie n ts o f e q u a tio n s (9).

T h e c o n d itio n s o f th e lovvest le v e l:

H = A'j

cosỌị

+ K . c o s(2Ọ K + a A ) +|/ỈJ 4- 7Ỉ, 4- / Ỉ 3Ị /. = Ả' jC0s ^ A

+ K : cos(2<pk

+ ơ4) - | / {1+ / ỉ2+ / ỉ 5|

(12⁾

w h e re

/í,

=y[M Ỉ +()■'

+ 2

M , O x

c o s r J ;

3 2 P h a m V a n H u a n

' = ° - 5 [ ( Ế' : L x + S í3 1

h ⁼ b>K> L x + s * . ■ ° ’ 5 t a L » + g s , ] - 9 0 ’ i

J =

w

L + " ° ’5^ ' + ] " 9 0 ° ’

p = w , ^{L +} 2 * . ^~ ) ■ « + * « . ^{] + t a )m ax} + * A f, ] - 9 0 ' ’ w h e re

O, s»n(r, )min-mjx

M 2

+Qt

c o s í r , ) ^ ^ ’

sin(r2)miamax S2 +/> cos(r,)mm m„ ■

g l s ị ^ ì U o m ạ x

yv2 +£;, cos(r3)min,max'

( h ) min. max II * ) min. max + a \ >

( r 2 ^min. max

Ồ.

II

) min, max + * 2 ;

( r 3 ) min. maX II >c ) min. max + a , .

T h e la s t e x tre m e v a lu e s o f tid e vvith a r b it r a r y n u m b e r o f c o n s titu e n ts a re c ỉe te rm in e d fro m e q ư a tio n (7) u s in g th e v a lu e s o f th e a s tro n o m ic a l p a ra m e te rs

/ơ,

h0yS0j po

c o rre c te d b y th e ite r a t io n m e th o d .

H ovvever, i t is w o r th to m a k e a n o te t h a t c o m p u ta tio n o f a p p r o x im a te v a lu e s o f a s tro n o m ic a l p a ra m e te rs

t \ h \ s \ p

by ío r m u la e in ta b le s 3 a n d 5 is m u c h s im p le r t h a n V la d im ir s k y m e th o d vvhen th e c o m p u ta tio n in v o lv e m o re t h a n 8 tid e c o n s titu e n ts

T h u s th e p ro c e d u re o f c o m p u tin g e x tre m e le v e ls m a y be p e rfo rm e d d u e to tvvo fo llo w in g schem es:

1) R egarciless w h a t is th e n u m b e r o f t id a l c o n s titu e n ts , d u e to íb r m u la e in ta b le s 3 a n d 6 d e te r m in e th e a p p ro x im a te v a lu e s o f th e a s tro n o m ic a l p a ra m e te rs c o rre s p o n d ig to e x tre m e c o n d itio n s , th a n c o rre c t th e s e v a lu e s by th e ite r a tio n m e th o d . C o m p u te th e e x tre m e le v e ls by e q u a tio n (7).

2) C o m p u te th e e x tre m e le v e ls w it h 8 tic ia l c o n s titu e n ts by V la d im ir s k y m e th o d . I f th e n u m b e r o f c o n s titu e n ts is b ig g e r 8 th e n c o m p u te th e a p p ro x im a te v a lu e s o f a s tro n o m ic a l p a ra m e te rs o f e x tre m e c o n d itio n fo r 8 c o n s titu e n ts by V la d im ir s k y m e th o d a n d c o rre c t th e m by th e it e r a t io n m e th o d . C o m p u te th e e x tre m e le v e ls by e q u a tio n (7).

In som e cases vvhen s h a llo w w a te r c o n s titu e n ts h a ve su ch a b ig m a g n itu d e t h a t causes th e a p p r o x im a te v a lu e s o f a s tr o n o m ic a l p a ra m e te rs c o m p u te d by ío r m u la e in ta b le s 3 a n d 5 o r by V la d im ir s k y m e th o d in s u f f ic ie n t ly c lo s e d to re a l v a lu e s ( ỉ{f

% hư , s a

,

p u

) to m e e t th e co n v e rg e n c e o f th e ite r a tio n process in s o lu tio n

U \ )

=

arctg

V 3 /m m . max

(f : L a n u x = a rc ts

= a r c l8

E x t r c m u m s c a ic v c is i i ì 3 3

S ystem (7). I f a g i von n u m b e r o f it e r a t io n s tc p s (fo r e x a m p le , 8 o r 10 s te p s ) do n o t p ro v id e th e c o n v e rg e n c e o f th e r e s u lts , one m a y use th e m e th o d o f c o n s e q u e n t a p p ro x im a tio n s .

E ach s h a llo v v w a te r c o n s titu e n t o f b ig m a g n itu d e is decom posed in to a n u m b e r o f c o n s titu e n ts o f th e s m a lle r m a g n itu d e :

f \ H t Q Q sọì = n— / j / / , COS0V ( 1 3 )

n

T h e n u m b c r

n

is s ta te d d e p e n d in g on th e m a g n itu d e o f t id a l c o n s titu e n ts . T h e s o lu tio n is p e rfo rm e đ i n som e s te p s , each step in c lu d e a ll th e c a lc u la tio n s to c o rre c t th e va lu e s o f a s tro n o m ic a l p a ra m e te rs , i. e. íb r m in g a n d s o lv in g s y s te m (9) a n d it e r a tiv e c a lc u la tio n s as w h e n to c o rre c t th e a s tro n o m ic a l e x tre m e c o n d itio n s a t a g iv e n ste p . F o r s o lv in g in f i r s t s te p a s tro n o m ic a l p a ra m e te rs a re c o m p u te d by th e fo rm u la e in ta b le s 3 a n d 5 o r by V la d im ir s k y m e th o d ; í u r th e r , t h e ir v a lu e s o b ta in e d in each s te p s a re u s e d as i n i t i a l v a lu e s íb r th e n e x t ste p . T h e m a g n itu d e o f shallovv

\v a te r c o n s titu e n ts is in c re a s e d fro m s te p to s tc p to th e f u ll m a g n itu d e (fo r e x a m p le , in íì r s t a p p r o x im a tio n s te p th e m a g n itu d e is chosen as f in ổecond s te p -

n - f ' H ,

, in s te p

n -

/ ; / / , .

n

3. The re s u lts o f c o m p u tin g e x tre m e levels in V ie tn a m coast

3.1. T i d a l t h e o r e t i c a l c x t r e m e s f o r t h e g a u g e s w i t h f u l ỉ set o f h a r m o n i c c o n s t a n t s

F o r th e h y d r o g r a p h ic s ta tio n s vvith tid a l gauges w e h a d used a s e rie s o f h o u r ly o b se rve d le v e ls o f one y e a r d u r a t io n to c o m p u te th e f u l l set o f h a rm o n ic c o n s ta n ts (30 c o n s titu e n ts o r m o re ). T h e h o u r ly le v e ls w c re p re d ic tc d fo r a p e rio d o f 20 y e a rs (1 9 8 0 -2 0 0 0 ). T h e lovvest a n d h ig h e s t le v e ls chosen a re p re s e n te d in ta b le 6.

T a b le 6. T h e o re tic a l e x tre m e s o f tid e a t «ome s ta tio n s a lo n g V ie tn a m coast

S ta tio n C o -o rd in a te s M e a n sea le ve l (cm)

T h e o re tic a l e x tre m e s (cm ) L o w e st H ig h e s t

Mon D au 2 0 ° 4 0 'N -1 0 6 ° 4 9 ’ E 185 - 1 0 397

Cua G ia n h 17°42’N - 106°28'E 107 - 1 6 2 0 1

Da N a n g 16 °0 6 ’N -1 0 8 ° 13' E 93 1 1 175

Q uv N h o n 13o4 5 'N - 1 0 9 o13'E 160 74 248

N ha T ra n g ^ “ l õ ^ N - l O ^ i r õ E 1 2 1 8 227

V u n g T a u 10°20’N -1 0 7 ° 0 4 ’ E 258 - 2 6 412

Rach G ia l0 ° 0 0 ’N - 1 0 5 o0 õ 'E 5 - 4 8 90

34 P h a r n V a n H u a n

3.2. T i d a l t h c o r c t i c a l e xtre rn c s coĩìiputcci by i t e r a t i o n m e t h o d

F o r th e s ta tio n s w it h no s y s te m a tic o b s e rv a tio n on sea le v e ls w e had used s e rie s o f h o u r ly o b s e rv e d le v e ls o f c ỉu ra tio n o f som e cỉays to c o m p u te h a rm o n ic c o n s ta n ts o f m a in t id a l c o n s titu e n ts (by D a r w in m e th o d o r by th e le a s t sq u are s m e th o d ). T h a n , fro m th e se r e s tr ic te d h a rm o n ic c o n s ta n ts w e used th e ite r a tio n m e th o d p re s e n te d in s e c tio n 2 to g e t th e e x tre m e c h a r a c te r is tic s o f th e t id a l le ve ls.

T h e r e s u lts a re w r it t e n in ta b le 7. In th is ta b le a re also v v ritte n th e th e o re tic a l e x tre m e s o f tid e c o m p u te d fo r a p e rio d o f 2 0 y e a rs to c o m p a re . I t is shovved th a t fo r th e case o f r e s tr ic te d h a rm o n ic c o n s ta n ts ( 1 1 c o n s titu e n ts ) th e r e s u lts by tw o c o m p u ta tio n s a re th e sam e.

T a b le 7. R e s u lts o f c o m p u tin g e xtre m e s o f tid e fo r some s ta tio n s by ite r a tio n m ethod

S t a t i o n

M e a n sea le v e l (cm)

Ite r a tio n m ethod P re d ic te d 2 0 y e a r p e rio d

Lo w e st H ig h e s t L o w e s t H ig h e s t

C ua O ng 2150 0 472

ềaế

2

470

Co To

204

- 1 0 454 - 7 454

K ie n A n 98 -1 4 215 -1 4 214

D ong X u y e n 91 -1 4 206 - 1 3 204

D in h C u 58 -4 7 176 - 4 6 174

K in h K h e 133 57 214 58 214

P hu Le 41 -9 7 171 - 9 7 169

N h u T a n 83 3 166 4 166

Ba L a t 6 -1 0 8 126 -1 0 7 125

M u i Da 81 -6 4 207 -6 4 206

V a m L a u 30 -1 1 9 92 -1 1 7 107

3.3. R e s u l t s o f c o m p u t i n g d c s i g n lc v e ls f r o m o b s e r v e d d a t a

In t h is s e c tio n vve use s e rie s o f th e y e a rly m in im a l a n d m a x im a l le v e ls a t s ta tio n s to e v a lu a te th e d e s ig n le v e ls vvith d iffe r e n t r e t u r n p e rio d s . In each y e a r one lo w e s t le v e l (o r on e h ig h e s t le v e l) vvas chosen to e s ta b lis h th e s a m p le s e rie s .

T h e a u th o r o f [1] has b u il t th e e m p ir ic a l d is t r ib u t io n c u rv e s b y g ra p h ic a l m e th o d fo r 24 s ta tio n s a lo n g V ie tn a m coast. T h e re s u lts o f th e in v e s t ig a tio n shovveđ a good a g re e m e n t betvveen th e e m p iric a l d is t r ib u t io n c u rv e s a n d th e í ì r s t a s y m p to tic d is t r ib u t io n íu n c tio n (G u ín b e l íu n c tio n ). F ro m t h a t th e r e c o m p u te d th e le v e l e x tre m e s vvith r a r e fre q u e n c ie s .

T a b le 8 p re s e n ts a n e x a m p le t h a t w e p e rfo rm e d by u s in g d if f e r e n t m e th o d s o f e v a lu a tio n fo r d is t r ib u t io n p a ra m e te rs p re s e n te đ in [5 ].

E x t r e m u m s c a ỉ c v c ỉ s i n

35

T h e a n a ly z in g p ro c e d u re vvas c a r r ie d o u t fo r a ll th e s ta tio n s w it h th e o b s c rv a tio n o f 15 to 35 y e a rs lo n g . F o r each s ta tio n th e d o s ig n le v e ls w e re c o m p u te d by 9 e s tim a t in g m e th o d s . K u r th e r , 9 v a lu e s vvcre a v e ra g c d (ta b le 9).

T a b le H. E x a m p le o f e x tre m c s a n a ly s is fo r s ta tio n H on D a u bv d iffe r e n t m ethocls a) V a lu e s o f desigĩì le v e ls (m a x im u m )

A n a ly s is m e th o d s

H e ig h t (c n i) re la te d to r e t u r n p e rio d 2 0 ye a rs 50 ye a rs 1 0 0 y e a rs T w o p a ra m e te rs m e th o d s (G u m b e l):

M e th o d o f m o m e n ts (tk e o re tic a l) 406 419 428

- M e th o d o f m o m e n ts (e m p iric a l) 409 ^{4 9 9} 432

- M e th o d o f q u a n tile s 412 426 436

l.in e a r u n b ia s e d e s tim a te s 411 424 435

- M e th o c i o f p r o b a b ilitv w e ig h te d 418 435 448

- M a x im u m lik e lỉh o o d m e th o d 410 424 434

T h re e p a ra m e te rs m e th o d s (J p n k in s o n ):

M e th o d o f q u a n tile s 404 413 419

- M e th o d o f p r o b a b ility - w e ig h te d 414 424 434

- M a x im u m lik e lih o o d m e th o d 404 413 419

A v e ra g e o f a ll m ethods: 410 422 431

b) C h a ra c te ris tic s o f e m p iric a l s a m p le

N Scries mcmbcr

Prohabililv Peiiod

(ycunỉ)

N Serỉcs mcmbcr Probablỉỉlv 1’criod (>cars)

Sorled

Nonnali/cd Sortcd Nonnali/id

1 347 -1,3G9 0,020 1,020 19 377 0.449 0,028 2,120

2 349 -1,112 0 0 1 8 1,050 20 378 0,534 0,507 2,255

3 350 -0,916 0,076 1,082 21 379 0,623 0,Õ8Õ 2 408

4 351 -0,815 0,104 1,117

^{9 9•mé w}

379 0,715 0.G13 2,581

5 351 -0,703 0 133 1,153 23 380 0,811 0,641 2,788

6 353 -0,603 0 161 1,192 24 380 0,913 0,G70 3,026

7 354 -0,510 0,189 1,233 25 382 1,022 0,698 3,309

8 362 -0,423 0,217 1,278 26 382 1,139 0,726 3 651

9 36õ -0,339 0,246 1 326 27 384 1,266 0,754 4,071

10 365 -0,258 0,274 1 377 28 386 1,406 0,783 4,600

11 366 -0,180 0,302 1 433 29 390 1,562 0,811 5,287

12 367 -0,102 0,330 1,494 30 391 1,741 0,839 6 216

13 367 -0,025 0,359 1,559 31 395 1,950 0,867 7,540

14 368 0,052 0,387 1,631 32 398 2,200 0,896 9,582

15 369 0,129 . 0,415 1,710 33 400 2,536 0,924 13,140

16 371 0,207 0,443 1,797 34 400 3,015 0.952 20,901

17 371 0,286 0,472 1 893 35 421 3 9 2 3 0,980 51,062

18 372 0,367 0,500 2.000

36

P h a r n V a n H u a n

T a b le 9. R e s u lts o f e x tre m e le ve l a n a ly s is (a ve ra g e o f a ll m e th o d s )

N u m b e r o f o b s e rv a tio n

D e s ig n leve ls (cm ) re la te d to r e t u r n p e rio d

S ta tio n 2 0 v e a rs Õ0 y e a rs 1 0 0 y e a rs

y e a rs

H ig h e s t Lovvest H ig h e s t Lovvest H ig h e s t Lovvest

C ua O n g 32 480 _ 2 491 - 1 4 499 _ 2 2

Co T o 35 467 - 1 4 481 - 2 5 491 - 3 2

H o n G a i 31 452 -1 4 464 - 2 7 473 - 3 7

C u a C am 33 440 17 452 7 4 60 - 1

H o n D a u 35 410 - 6 422 - 1 4 431 - 2 0

Ba L a t 33 178 -1 7 9 192 - 1 8 8 203 -1 9 4

H o a n g T a n 26 284 -1 6 3 319 - 1 7 0 347 -1 7 6

L a c h S u n g 25 207 -1 3 6 230 - 1 4 7 248 -1 5 5

C ua H o i 32 2 2 1 -1 8 2 238 -1 9 4 2 5 0 - 2 0 2

H o n N g u 25 393 - 7 409 - 2 1 421 -3 1

H o Do 27 237 -1 3 2 262 - 1 3 8 281 - 1 4 2

C am 32 242 - 9 8 272 -1 0 4 300 -1 0 8

N h u o n g

C u a G ia n h 31 163 - 1 4 8 186 -1 5 3 204 -1 5 7

D o n g H o i 33 192 -1 4 4 217 -1 5 2 236 - 1 5 8

C ua V ie t 17 313 - 1 357 - 5 396 - 7

D a N a n g 15 287 9 323 3 349 - 3

H o i A n 18 350 - 3 4 401 - 3 8 441 -4 1

Q u y N h o n 16 290 27 299 2 0 306 15

P h u Q u y 14 324 64 331 58 335 53

V u n g T a u 15 434 - 4 6 440 - 5 5 445 -6 1

V a m K in h 15 150 -3 2 5 168 -3 3 7 182 - 3 4 5

C ho L a c h 15 2 0 2 -1 6 1 207 - 1 6 8 2 1 0 -1 7 3

Ca M a u 16 151 -6 1 168 - 6 4 181 - 6 7

P h u A n 16 152 -2 5 3 157 -2 6 4 161 - 9 7 2

R a ch G ia 16 126 -6 1 136 r,l 144 - 6 6

4. Rem arks and conclusions

F o r th e s ta tio n s w it h r e s tr ic te d se t o f h a rm o n ic c o n s ta n ts (le ss th a n 1 1 tid e c o n s titu e n ts ) e v a lu a tin g th e o r e tic a l e x tre m e h e ig h ts o f t id e b y th e m e th o d o f p r e d ic tin g 2 0-y e a r s e rie s o f h o u r lv le v e l a n d by th e it e r a t io n m e th o c i g iv e s clo se to e ach o th e r r e s u lts (see ta b le 7).

N o te t h a t p r e d ic tin g tid e in 2 0 -y e a r p e rio d ta k e s g re a t

C o m p u ter

tim e , w h ile th e ite r a tio n m e th o d allovvs m o re r a p id c a lc u la tio n . T h e r e fo r e in p r a c tic a l in v e s t ig a tio n a t th e re g io n vvhere no gauges set u p we sh o u lc ỉ f u l f i l m c a s u re h o u r ly le v e ls in som e d a y s to d e riv e th e h a rm o n ic c o n s ta n ts o f m a in tid e c o n s titu e n t s . T h a n vvith th e it e r a t io n m e th o d a p p lie d , we c a n c o m p u te th e tid e th e o r e tic a l e x tre m e s , vvhich h a v e a c c r ta in p r a c tic a l u s e íu ln e s s .

E x t r c m n m s c n l c v c l s i n 37 T h e r e s u lts o f a n a lv s is sh o w e d th a t t.he d iffe re n c e b e tw e e n e x tre m e le v e ls in 2 0-y e a r d u r a t io n a n d th e d e s ig n le v e ls o f 2 0-y e a r r e tu r n p e rio d is n o t b ig g e r th a n th e n n a ly s is e r r o r in th e case o f r e s tr ic te d le n g th o f used s a m p le s .

T h e th e o r e tic a l e x tre m e s o f t id c h a ve th e sense o f e x tre m e le v e ls . F o r e x a m p le , in ta b le 6, th e lovvest le v e l a t H on D a u in p e rio d 20 y e a rs is “ 10 c m , th e h ig h e s t is 397 c m . D ue to r e s u lts o f e v a iu a tin g e x tre m e s fr o m e m p ir ic a l d a ta th e d e s ig n le v e ls fo r r e t u r n p e rio d 20 y e a rs are - 6 và 410 cm re s p e c tiv e lv ( ta b le 9). F o r th e r c t u r n p c r io d 50 y c a rs

u n d

100 y c a rs th c p a ir s o f v a lu c s a r c ( 14; 4 2 2) a n d ( 20;

431) re s p e c tiv e lv . O b v io u s lv th e lo w c s t le v e ls d if f e r no m u c h , c o n s is t o f a b o u t lO cm . A t th e s a m e tim e th e h ig h e s t le v e ls d if fe r fro m each o th e r u p to 30 cm , t h is re íle c ts th o in A u e n c e o f ílo o d s a n d vvind su rg e s . H o w e v e r, t a k in g in t o a c c o u n t th e la rg e d is p e rs io n o f th e e s tim a te s by d iffe r e n t m e th o d s , t h is d iffe re n c e cỉoes n o t exceed th e e r r o r o f e s tim a tio n . F o r e x a m p le , fo r s ta tio n H o n D a u , in [1] th e e s tim a tio n by g r a p h ic a l m e th o cỉ g ive s re s u lts : fo r r e tu r n p e rio d 20 y e a rs : ( - 1 1 ; 4 3 5 ), 50 y e a rs : (- 19; 4 5 1 ), 100 y e a rs : ( “ 25; 462). W it h th e m e th o d o f a v c r a g in g 9 v a r ia n ts t h a t we d id , th e p a ir s o f v a lu e s a re : fo r r e t u r n p e rio d 20 y e a rs : ( -6; 4 1 0), 50 y e a rs : (-1 4 ; 42 2), 100 y e a rs : ( - 2 0 ; 4 3 1 ) (ta b le 9). T h e d iffe re n c e s b y novv a c h ie v e 2 0 to 30 cm . T h e d iffe re n c e b e tw e e n v a r ia n t s o f e s tim a tio n m ay be m o re s u b s ta n tia l vvith th e s h o r te r s e rie s . T h e re íb re , th e e s tim a tio n o f d e s ig n le v e ls b y d if fe r e n t m e th o d and a v e ra g in g r e s u lts is th e b e s t w a y to p ro v id e re a l d e s ig n le v e ls i n th e ca sc o f s h o rt s e rie s .

F r o m th e a b o ve a n a ly s is fo llo w s t h a t th e o b ta in e d h e re d e s ig n le v e ls h a v e th e d if fe r e n t r e lia b il i t y . F o r th e s ta tio n s w it h o b s e rv a tio n m o re th a n 30 y e a rs th e d e s ig n le v e ls in ta b le 9 c a n be c o n s id e re d as s a tis ía c to ry .

R o ío r e n c e s

1. N g u y ê n T a i H o i, R e p o rt on t id a l c h a r a c te r is tic s (S u b . A 5 ), D e s ig n vva te r le v e ls (S u b . A 1 3 ),

M a rin c H ydrom eteorological C entre

, V ie tn a m V A P ro je c t, H a n o i, 1995.

ì.

N g u y ề n N gọc T h ụ y , P h ạ m V ă n H u ấ n , B ù i D in h K hước, N g h iê n cứ u sự b iế n t h iê n và tư ơ ng q u a n c ủ a mực nưóc các tr ạ m cỉọc bò V iệ t N a m v à k h ả n ă n g k h ỏ i p h ụ c các c h u ỗ i m ục nưóc ờ m ộ t

số

t r ạ m q u a n trắ c ,

Dáo cáo thực h iện ch u yên dể,

Đ ề t à i cấp n h à nưốc K T - 0 3 -0 3 , 1995.

I. N g u y ễ n N gọc T h ụ y , v ề xu t h ế nưỏc b iể n d â n g ở V iệ t N a m , T ạ p

c h í K hoa học Kỹ t h u ậ t b iê n

, số 1, H à N ộ i, 1993.

B ù i Đ ìn h K hước, Xác đ ịn h th ê m về x u th ê m ực nưóc b iể n t ạ i m ộ t sô đ iể m ve n bờ b iể n V iệ t N a m ,

Báo cáo thực hiện c h u yên để,

Đổ t à i cấ p n h à nước K T -0 3 -0 3 ,

1993.

38

P h a m V a n Ị ỉ ti a n

5. T ib o r K a ra g o , R ic h a r d

vv.

K a ts ,

E xtrem es a n d d e s s ig n v a lu e s in c lim a to lo g ỵ

, W C A P - 1 4 , W M O /T D - N o 386, W o r ld M e te o ro lo g ic a l O r g a n iz a tio n , 1990.

1 ílcpccbinKHH tì H A n a m tm m e c K u e Mưmoỏbi p a c u e m a K oneỗaĩiuủ vpoeHỉi MopH, rHJ3pOMCTCoH3jI3T., JIcHHHrpa.a, 1961

7 P yK oeoờ cm eo n o p a c u e m v ĩu d p0Ji0ỉu u ecK u x xapaK m epucm uK (h u uccA edoeattuù u U3MCKCIHUÙ fí ỗ e p e ĩO d h ĩx 30ỈỈCIX u 3 c m \a p u e (i. H a y ic a , M o c K B a , 1 9 7 3

TAP CHỈ KHOA HQC ĐHQGHN, KHTN & CN, T XIX, Nọ 1, 2003________

M ự c NƯ Ớ C c ự c TRỊ ở VÙNG B I E N v i ệ t n a m

P h ạ m V ă n H u â n

K hoa K h í tượng T h ủ y văn & H ả i d ư ơ n g học Đại học Khoa học T ự n hiên

,

Đ H Q G H à Nội

G iớ i th iệ u tổ n g q u a n n h ữ n g k ế t q u ả n g h iê n cứ u về b iế n t h iê n mực nưốc b iể n ở b iể n Đ ô n g v à t r ì n h b à y c h i t i ế t v ề các phư ơ ng p h á p t í n h to á n g ầ n đ ú n g các cực t r ị t h u ỷ t r iề u ỉý th u y ế t.

B iế n t h iê n m ực nước b iể n g ầ n bò V iệ t N a m do sự n ó n g lê n to à n cầ u và các h iệ u ứ ng k h á c dược ưỏc lư ợ ng b ằ n g k h o ả n g từ 1 đ ế n 3 m m m ộ t n ă m .

V ớ i b ả y t r ạ m h ả i v ă n có bộ h ằ n g sô* đ iể u hoà t h ủ y t r iề u đ ầ y đ ủ đã xác đ ịn h được các độ cao mực t r iề u cực t r ị b ằ n g cách t í n h các độ cao m ự c t r iề u từ n g g iò tro n g c h u k ỳ 20 n ă m . V ó i 19 t r ạ m k h á c có 1 1 h ằ n g s ố đ iề u h o à c ủ a các p h â n t r iề u c h ín h , các m ực nước cực t r ị t h iê n v ă n lý th u y ế t dược ưỏc lư ợ n g b ằ n g p h ư ơ n g p h á p lặ p . So s á n h cho th ấ y h a i p h ư ơ n g p h á p cho k ỏ t q u ả k h á p h ù hợp.

P h é p p h â n tíc h cực t r ị th ự c n g h iệ m được th ự c h iệ n c h o 2 5 t r ạ m m ực nước (lọc bò V iệ t N a m đế ưóc lư ơ ng các t r ị số m ực nưỏc t h i ế t k ế ứ ng v ỏ i các tà n x u ấ t h iế m k h á c n h a u .

P h â n tí c h so s á n h c h ỉ ra rằ n g các cực t r ị th ủ y t r iề u và m ực nước t h i ế t ke ch u k ỳ lậ p lạ i 20 n ă m có dộ lớn n h ư n h a u . C òn n h ữ n g t r ị sô* m ự c nước t h iế t kê vớ i ch u k ỷ lặ p lạ i d à i hơ n bị ả n h hươ ng c h ủ y ế u bơi h iệ n tư ợ ng lủ v à nước d â n g .