DSpace at VNU: Extremum sea levels in VietNam coast
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VMU. JOURNAL QF SCIENCE, Nat., Sci., & Tech., T XIX. NọỊ, 2003___________________________________________
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 tr a c t : A revievv ()f tho in v e s tig a tio n s on t.hcì sea levol changcỉS in S o uth
rh in a
soa is
presenUỉíl
and
th e
methods o f approxim ate
e a U u la tio n
of
th eoretical 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 stations vvith
fu ll
sot
o f harm onic constants
(le tcrm in o tl
thc
theoretical extrem o heights o f tiíỉa l level by p re d ictin g h o u rly ti do h e ig h ts in a
2 0 -year ptỉriod. lf,or o th e r ninctecn stations w ith 1 1 harm onic constants o f m ain
tid a l co n stitu 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.
The e n ip irica 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 also show ed th a t tho tiđ a l extreines and đcsign le vol valuos ()f 20-
year rc 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 tro 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 cu rre n ce p r o b a b ilitie s a re ta k e n in to
a cco 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 iffe 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 ].
The
m a in
c o n ccp ts
of
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 rve d se ries 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 ce d u re s
of
e x tre m e
a n a ly s is
th e o ry ,
th a t
u s ụ a lly
happen
in
th e
d e sig n
in v e s tig a tio n s in th 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 ve 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 re 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 ve 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 som 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 se rie s o f tic ỉa l h e ig h ts 1 9 -y o a r
22
ềÍÊề
E x tv e m u m s c a lc v e ls i n
23
long, one choose th e lovvest h e ig h t n m o n g a ll lo w vvatồrs in th e se 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
of
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 tr 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 es 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 tric te d
n u m b e r o f t id e c o n s titu e n ts ìn to c o n s id e ra tio n [G]. S e ctio 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 re s u lts to o b ta in m a x im a l c h a ra c te ris tic s o f sea le v e l in som 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 st 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 ra lly
s p e a k in g u p to novv th e n u m b e r o f tiđ 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 iric a l e a lc u la tic m s ơf
level e x tre m e s in s p e c ia l.
In so m e r a re 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 tre 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 me y e a rs long. T h e s p e c tru m a n a ly s is [2] s h o w e d th a t
besiđes
th e
s e m ia n n u a l
and
annual
p e rio d s ,
in
th e
a lm o s t
o f t id 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 and lo n g e r e x is t (íìg u re 1 ).
8
0.(1»
0.0»
0.030
(k*.'ỉ
•>.0'i?
o.c»«
0.024
0 .0 5 6
0.071
txtrb
r4 j,
0.019
Hon 0*1.
0.0*0
Nhon
0.015
n .tX ‘ 2
o.m:
ao:-*
ỉ L
0 t
mo4
0 .0
ii.ođ
\ __
'. 5
p‘«ni>dirtiìntt)
Jỡ
100
rtẠ
0 .0 0 3
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 and Q u y N h o n
T a b le 1 lis ts 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 th 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 te o f lc v e l
riíe a b o u t 14-3 m tn p e r y e a r.
P h a m Van H u an
24
T a b le 1. R a te o f sea le v e l ris e a t some p o in ts a lo n g V ie tn a m c o a s t
Gauge
C o-o rd ina 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 on D au
20°4 0’ N - 106°4 9’ E
1957-1994
2 ,1
C ua Cam
20o4 5 'N -1 0 6 °õ 0 'E
1 9 61 -1 9 92
2,7
Da N an g
16°06,N -1 0 8 °1 3 ,E
1978-1994
1,2
Q u y N ho n
1 3 °4 õ 'N -1 0 9 o13'E
1976-1994
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
re p o rt í ir s t ly lis te d s e rie s o f m o n th ly ave rag 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 was
c a rrie 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 ssum e
VỊ th e
v a lu e s o f in c ic ỉe n ta l v a r ia b le
A'
V
a t t im e / a n d
x (m) = m in { F ,,F 2 , ...,Vm
.
O ne is o fte n in te 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 inim aỉ value exceeds a th resh o ld , Iì{Xim > x} or P{X(m) < x } . If th e observations
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 te d iffe r e n tly
due to d istribu tion function F{x) - P{Vị < x ) , th e precise d istrib u tio n of m axim um
an d m in im u m ca n be cxp re ssed :
/ ’ { A '('n) < x } = |/- - ( .v ) f
< x ) = 1 - |1 - /<-(x)|m
and
(1)
The extrem es an alysis theory says that with the enough length of sam ple m ,
the
p rob ab ili ty
distribution
of the
norm alized
m axim um
Y (m)= ( X ' m
bm > 0 c a n be 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 íơllovving 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)
0*3(v) = c x p |- ( - v ) 1 k K v < 0 . k > 0
(Wcibull function)
(2)
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 .
These d iffe r e n t forms 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 shape o f
th e t r a il 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 ) . In
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 ro 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 tre 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 - loca 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 tin g th e d is t r ib u tio 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 qu antile
p
of extrem e distribution. Besides, one converts the
probability of th e design v a lu e Xp to r e tu r n period T = 1/(1 - p ) , w h ere 7 - th e tinie
to b e e x p e c te 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 fo r t h e f i r s t ti m e , o r t h e a v e r a g e tim e
betvveen tvvo above th r e s h o ld e ve 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 tio n th e d c s ig n v a lu e s can be e a s ily
e xpresseđ. K o re x a m p le , v v itlì G u m b e l d is tr ib u tio n , one has:
y p
=G\ '(/>) = - log (- log
p )
.
(5)
Consequently, design v a lu e estim ate vvith return period T = ( ! - / ; )
e x tre m e
years of the
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 ,
where y
(6 )
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
of
convergence of precise d is trib u tio n of ex trem es i ,r’ to th e asym ptotic one, in
p ractical
aspect, th e
p recision of design value 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 rea 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 tim 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 iffe r e n t m e th o d s to e s tin ia te th 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 se 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 ga ug cs a lo n g V ie tn a m coast.
2. 2.
M e t h o d o f c o ìì i p u ti n f í e x t r e m e v a lu e s o f tid c
T h e t id a l h e ig h t a b ove 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 rm u la
zt =
C0S
I
(7)
vvhere f t - th e re d u c e c o e ffic ie n ts de pe 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 th e t i d a l íe a tu re , 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
s e m id iu r n a l
tid e ) .
In
th e s e
c o n d itio n s
(fo r d iu r n a l tid e ) o r N = 1800
(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 se 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'
ĩ t + 2h - 2s - gMf
0,963
1,038
2t - g
1,000
1,000
2r + 2h - 3 s + p - g V;
0,963
1,037
*>
2/ + 2h
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/ +
0.894
1.1 IX
•w.
.
- g Ki
6h - 6 s - g Kf
Sa
h ~Sso
1.000
1.000
SSa
2h - Kssa
1.000
1.000
E x tv c tỉiu tti sca lc v c ls iti
III ta b le 2 Ị S un;
27
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 M o o n ;
V
p e rig ro ; fỉ
p-
a v e ra g e lo n g itu d e o f th e
a v e ra g e lo n g itu d e o f lu n a r o r b it
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 ticle 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 ra m e te rs í. lì. V a n d />, vvhich fo rm a c o m b in a tio n c o rre s p o n d in g to
an e x t I ^ m e c o n d itio n , a re k n o w n . In 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 tre m e c o n d itio n o f th e t id a l h c ig h t:
IM
2
sin
Kị SI n
+ 4 M S Ằ sin
s
i
n
+ 6 M 6 sin
=0
2 M ■>sin
+
sm (pK 4*
+ 0 | sinv?£> + 4iV/ 4 sin$?A/ +
+ 6.A/, sin
+ .Sí7 sin y>ViJ + 2.V.Ví/ sin
2 A /: sin (pSỊy -f 3 iV , S1I1 (ps% + 2 0 Ị sin (p(ỉ + 3 (/ị sin ^
4A/ 4 sin
4- 2A/.V4 sin
>
(pSỊSị+ 6 A /Ố sin
(8)
- 0
+
- 0
A,r: sin
If
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 ra m e te rs
c o rre s p o n d in g
to
e x trc 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 rm
by
T a v lo r
e x p a n s io n .
W hcn
a p p ro x im a te
v a lu o s
of
th e
unknovvn
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 rrc 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 ra 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 tr ix :
/l,v + /1 = 0 ,
vvhcre
(9)
P h a m V an ỉ ỉu an
a\
bị
h í,
Cj
d]
c ,í
í
dĩ
Cj
zl/
A
/ƯJ
;
A" =
;
zlv
A =
/ ,£
/,
/4
a ) - 4 M 2 cos<
p ' m + 4 S 2 cos (p's + 4 N 2 cos (p's + 4 K 2 cos
+16 M S4 cos
+ 1 6 A /4 cos
•
/?ị = 4jV/2 cos
- 1\ cos ợ?), + Ọj cos
+
+ 3 6 M ỗ cos
Cị = - 4 A / , COS0>Ú - 6 ^ 2 cos (p'Ni - 2 0 ì cos
í/, = 2 N 2 cos
/j =
2 M 2 sin
+ 2 5 2 sin
+
01 cos
;
(p's + 2 / V 2 s i n
+ K x sin (p'K + 0 ] sin
+ l\ sin
+ 4A* 4 sin ^ ; Í4 + 4M S 4 sin ^
b 2 = 4 A / : C0S(p's1 + 4 jV 2 cosợ?v
(p'K +
+ 2AT2 s i n
+ (>! sin
+
+ 6 M 6 sin
+ 4 /^ c o s ộ \
+ Ả'j c o s p í
+
+ ƠJ cosọ>'0 +!\ cos (p'j. +Qị cos
+ 36 M ố cos
+ 4MV4 cos
c 2 = -4 A /: c o s ọ h
+ Sa cos
- 6 N 2 co s^ v
- 16A /4 cos
-2 ơ |
cos
-3 (P ị C0SỘ?£
- 4MV4 cos
d 2 = 2 iV: cos{?v + (?! cosỌọ ;
/ 2 = 2 A / 2 sin
+ 2/V-, sin
+ ()] sin
+ 2/w 2 sin
+ Áf| sin
sin ự Ị, + Qx sin (pQ 4- 4A / 4 sin
+ 6 A/ 6 sin (pu + .SV/ sin
+ 2M V 4 sin
c 3 = 4 A / 2 c o s (p M
f
+ 16Af 4 cos
+ 9 N : c a s ọ 's
+
+
-f- 2 XVc7 sin
;
+ 4 Ơ , c o s tp ý + 9 Q ị c o s (p ọ
+ 4M V 4 cos ^ /5 + 3 6A /Ốcos ạ>X
Ệi ,
J 3 = - 3 W 2 cos (p\^ - 3 ( ^ J cos
/, = - 2 A / : sin^>v/j ” 3^2 s in f v 2 - 20j s i n ^ -3Ợj s i n ^
- 4 A í 4 sin - 2A/.V4 sin
J4
= /v 2 cos
- 6 jW() sin
;
;
/ 4 = N z costpl/ + Q \ cos
a s tr 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 .
In
29
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 th e ite ratio n m ethod m ay be used. 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
the coefficients of e q u a tio n s (9) vve will use the p h a ses (p' com puted th r o u g h thc
va lu e s c o rre c te d o f a s tro n o m ic a l p a ra m e te rs :
.v" = .v' + Av', h n = h ' + A h '% p* = p ' + Ap'
/' = /' + A/'
T he loop is repeated 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 tro 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
M a x im a l leve l
c o n d itio n
t[ = 90” + 0,5 g St
í, '= 180’ + 0 , 5 ^
t-j -
r
t'2 = 270“ + 0 , 5 ^
w
0 .5 (g JCj - g S i)
s1
0,5ị g Kỉ - g M i )
p'
° M z Kị - 3 g Mj + 2 g N ì )
ÒQ
t/}
M in im a l level
c o n d itio n
»
o
A s tro n o m ic a l
p a ra m e te rs
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 he 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 rre 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 tid 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 titu e n ts
and
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 xp re ssio n s:
- F o r s e m id iu r n a l tid e :
- F o r d a u rn a l tid e :
ỌK = (pQ =
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 ro x im a te
va lu e s
of
a s tr o n o m ic a l
c c n d itio n s ( ta b le s 3 -6 ).
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
P ham Van H u an
30
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 tim e / ' th e r e a re tw o
e xp re ssio 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 ra te ly , s in c e fo r
s e m iđ iu rn a l tid e one day has tw o ' h ig h w a te rs a n d tw o lo w vvaters. T h e ch o ice 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 ry
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 cosơị +1\ cosa 2 +Q\
J
COSƠ3
+ K cosa4|
J
c = ƠJ sin ơ| + p I sin a 2 + Q\ sin a 3 + 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 ° , a 4 = 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 leve l
C o n d itio n s o f th e h ig h e s t leve l
/j
w hen c > 0
t2 w h e n c < 0
w hen 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 ro 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
t§
C o n d itio n s o f th e low e st
level
- gp, )
C o n d itio n s o f th e
h ig h e s t le v e l
0 , 5 ( ^ , + g P|) + 18(r
/r
0,5 (gKi - g Pi)+ 90"
5'
0,5 (gKí - g o , ) + 90”
p'
0.5(«r , - 3So, + 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) For s e m id iu m a l
tide, i f { h £ + H G ) ỵ H M < 0,5 then 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 mixed tide, if 0,5 < [h K + HQ )ỵ H Kí < 1,5 then we must use 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 astronomical 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 tid 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 vvill 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
of
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 tre 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 tid 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 ch o osin g v a lu e s (pK in th e in te r v a l fro m 0° to 3G0°:
H = A'j cosỌị
+ K . co s(2 Ọ K + a A ) +|/ỈJ 4- 7Ỉ, 4- / Ỉ 3Ị
(12 )
/. = Ả' jC 0 s ^ A + K : cos(2
/í, =y[MỈ +()■' + 2 M , O x c o s r J
;
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
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 tid c
w it h d iu r n a l tid e
p e río rm e d w ith
f
is chosen fo r
///
/
is also macỉe as th e
is chosen fo r yV ^lX O ,
N = 0 . W ith m ix e d tid e th e c o m p u ta tio n is
f fo 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 be 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 tly fr o m th e e x p re s sio 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
(
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 ve l:
P h a m Van H u a n
32
' = ° - 5 [ ( Ế' : L x
h
=
b>K> L
J= w
p = w , L
+
x
+ s *.
L
2*.
+
+ S
■ ° ’5 t a
í
3 1
L »
" ° ’5^ '
+
)■ « + * « .
~
+gs,
] - 9 0 ’ i
] " 90° ’
]+ t a
)m ax
+ * A f, ] - 9 0 ' ’
w h e re
O, s»n(r, )min-mjx
= a r c l8
M 2 +Qt c o s í r , ) ^ ^ ’
(f :L a n u x = a rc ts
yv2 +£;, cos(r3)min,max'
*
) min. max
II
II
( r 3 ) min. maX
Ồ.
( r 2 ^min. max
) min. max
+
a\ >
) min, max + * 2 ;
>c
(h
g l s ị^ ìU o m ạ x
II
U
\)
= arctg
V 3 /m m . max
sin(r2)miamax
S2 +/> cos(r,)mmm„ ■
) 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 tio 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
th a n
V la d im ir s k y
m e th o d
vvhen
by ío rm u la e in ta b le s 3 a n d 5 is m u c h s im p le r
th e
c o m p u ta tio n
in v o lv e
m o re
th 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 rm 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
V la d im ir s k y
m e th o d . C o m p u te
m e th o d
a n d c o rre c t th e m
by th e
it e r a tio n
by
th e
e x tre m e le ve ls by e q u a tio n (7).
In some 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 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 m p u te d
by
ío 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 in s u f fic ie n tly clo se 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 ve rg e n ce o f th e ite r a tio n process in s o lu tio n
E x t r c m u m sca ic v c is i i ì
33
System (7). I f a g i von n u m b e r o f it e r a tio 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 re 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
(13)
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 rm in g a n d s o lv in g s y s te m (9) a n d
ite 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 ive 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 ; íu r th e r , th e ir v a lu e s o b ta in e d
in each ste p s a re u se 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
n
f in ổecond s te p -
- 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 th 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 ts
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 we h a d used a se rie s o f h o u rly
ob serve 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 ll 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 ean sea leve 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
-10
397
Cua G ia n h
17°42’N - 106°28'E
107
-1 6
201
Da N a n g
16 °0 6 ’N -1 0 8 ° 13' E
93
11
175
Q uv N h o n
13o4 5 'N -1 0 9 o13'E
160
74
248
N ha T ra n g
^ “ lõ ^ N - lO ^ ir õ E
121
8
227
V ung Tau
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
P h a rn Van H u an
34
3.2. T i d a l t h c o r c t i c a l extrerncs coĩìiputcci by i te 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
se rie s o f h o u r ly o b se rve d le v e ls o f c ỉu ra tio n o f some 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 tid a l c o n s titu e n ts (by D a rw in m e th o d o r by th e le a s t sq uares
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 we 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 ra c te ris tic s o f th e tid a l leve ls.
T h e re 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 co 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 xtrem es o f tid e fo r some s ta tio n s by ite r a tio n m ethod
S ta tio n
Ite ra tio n m ethod
M e a n sea
le v e l (cm)
Lo w e st
C ua O ng
H ig h e s t
P re d ic te d 2 0 ye a r
p e rio d
Low est
H ig h e s t
ề2aế
470
2150
0
472
204
-10
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
133
57
214
58
214
P hu Le
41
-9 7
171
-9 7
169
N hu Tan
83
3
166
4
166
6
-1 0 8
126
-1 0 7
125
M u i Da
81
-6 4
207
-6 4
206
Vam Lau
30
-1 1 9
92
-1 1 7
107
Co To
K in h K h e
Ba L a t
3.3. R e s u l t s o f c o m p u t i n g d c s ig n lcv els f r o m o b s e r v e d d a t a
In th is s e c tio n vve use se 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 ve 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 tu 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 one 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 se rie s.
T h e a u th o r o f [ 1 ] has b u ilt th e e m p iric a l d is t r ib u tio 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 tig 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 tio n
c u rv e s
and
th e
íì 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 th a t we p e rfo rm e d by u s in g d if fe 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 tio n p a ra m e te rs p re s e n te đ in [5 ].
35
E xt rem u m sca ỉcvcỉs in
The
a n a ly z in g
p ro c e d u re
vvas c a rrie d
out
fo r
a ll
th e
s ta tio n s
w ith
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 tin 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 )
H e ig h t (cn i) re la te d to r e tu r n p e rio d
A n a ly s is m e th o d s
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)
- M e th o d o f m o m e n ts (e m p iric a l)
- M e th o d o f q u a n tile s
l.in e a r u n b ia s e d e s tim a te s
- M e th o ci o f p ro b a b ilitv
w e ig h te d
- M a x im u m lik e lỉh o o d m e th o d
T h re e p a ra m e te rs m e th o ds (J p n k in s o n ):
M e th o d o f q u a n tile s
- M e th o d o f p ro b a b ility - w e ig h te d
- M a x im u m lik e lih o o d m e th o d
406
409
412
411
418
410
426
424
435
424
428
432
436
435
448
434
404
414
404
413
424
413
419
434
419
A v e ra g e o f a ll m ethods:
410
422
431
419
499
b) C h a ra c te ris tic s o f e m p iric a l sa m p le
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Scries mcmbcr
Prohabililv
Nonnali/cd
Sorled
-1,3G9
0,020
347
349
0018
-1,112
350
-0,916
0,076
351
0,104
-0,815
351
0 133
-0,703
353
0 161
-0,603
354
-0,510
0,189
0,217
362
-0,423
36õ
-0,339
0,246
365
-0,258
0,274
366
-0,180
0,302
367
0,330
-0,102
367
0,359
-0,025
0,387
368
0,052
369
0,129 . 0,415
0,207
371
0,443
371
0,286
0,472
372
0,367
0,500
Peiiod
N
1,020
1,050
1,082
1,117
1,153
1,192
1,233
1,278
1 326
1 377
1 433
1,494
1,559
1,631
1,710
1,797
1 893
2.000
19
20
21
(ycunỉ)
99
•m
éw
23
24
25
26
27
28
29
30
31
32
33
34
35
Serỉcs mcmbcr
Probablỉỉlv 1’criod
(>cars)
Sortcd Nonnali/id
377
0.449
0,028
2,120
0,534
0,507
2,255
378
379
0,623
0,Õ8Õ
2 408
0,715
379
2,581
0.G13
380
0,811
0,641
2,788
380
0,913
0,G70
3,026
3,309
382
1,022
0,698
1,139
382
0,726
3 651
4,071
384
1,266
0,754
386
0,783
1,406
4,600
390
0,811
5,287
1,562
391
0,839
1,741
6 216
395
1,950
0,867
7,540
398
0,896
2,200
9,582
2,536
400
0,924
13,140
400
3,015
0.952
20,901
421
3923
0,980
51,062
36
P h a rn V an H u an
T a b le 9. R e su lts o f e x tre m e leve l a n a ly s is (a ve ra g e o f a ll m e th o d s )
D e s ig n levels (cm ) re la te d to r e tu r n p e rio d
S ta tio n
N um ber of
o b s e rv a tio n
y e a rs
2 0 ve a rs
H ig h e s t
C ua O n g
Õ0 y e a rs
Lovvest
1 0 0 y e a rs
H ig h e s t
Lovvest
H ig h e s t
Lovvest
491
481
464
452
422
192
319
230
-1 4
-2 5
-2 7
7
-1 4
-1 8 8
-1 7 0
-1 4 7
499
491
473
460
431
203
347
248
_22
250
421
281
-202
_2
480
467
452
440
410
178
-1 7 9
H oang Tan
Lach Sung
32
35
31
33
35
33
26
25
284
207
-1 6 3
-1 3 6
C ua H o i
H on N gu
H o Do
32
25
27
221
393
237
-1 8 2
-7
-1 3 2
238
409
262
-1 9 4
-21
-1 3 8
C am
N huong
C u a G ia n h
D o n g H oi
C ua V ie t
Da N ang
H oi A n
Q uy N hon
Phu Q uy
V u n g Tau
32
242
-9 8
272
-1 0 4
300
-1 0 8
31
33
17
15
18
16
14
15
15
15
163
192
313
287
350
290
324
434
150
202
151
152
126
-1 4 8
-1 4 4
-1
9
186
217
357
-3 4
27
64
-4 6
-3 2 5
-1 6 1
323
401
299
331
440
168
207
-1 5 3
-1 5 2
-5
3
-3 8
20
58
-5 5
-3 3 7
-1 6 8
-6 1
-2 5 3
-6 1
168
157
136
-6 4
-2 6 4
r,l
204
236
396
349
441
306
335
445
182
2 10
181
161
144
-1 5 7
-1 5 8
-7
-3
-4 1
15
53
-6 1
-3 4 5
-1 7 3
-6 7
-9 7 2
Co T o
H on G ai
C u a C am
H on D au
Ba L a t
V a m K in h
C ho L a ch
Ca M a u
Phu A n
R ach G ia
16
16
16
-1 4
-1 4
17
-6
-3 2
-3 7
-1
-20
-1 9 4
-1 7 6
-1 5 5
-3 1
-1 4 2
-66
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 (less 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 re tic a l e x tre m e
h e ig h ts o f tid 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 ite r a tio n m e th o c i g iv e s close to
each 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 om puter tim e , w h ile
th e
ite r a tio n
m e th o d
allovvs
m o re
ra p id
c a lc u la tio n .
T h e re fo re
in
p ra c tic a l
in v e s tig a tio n a t th e re g io n vvhere no gauges set u p we sh o u lcỉ 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 ts .
Than
vvith th e
ite r a tio n
m e th o d a p p lie d , we c a n c o m p u te
e x tre m e s , vvhich h a ve a c c r ta in p r a c tic a l u s e íu ln e s s .
th e
tid e
th e o r e tic a l
37
E x t r c m n m scn lc v c ls in
T h e re s u lts o f a n a lv s is sho 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 tio 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 re s tr ic te d le n g th o f used s a m p le s .
The
th e o r e tic a l e x tre m e s
o f tid c
ha ve
th e sense o f e x tre m e
le v e ls .
For
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 fro 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 rio 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; 422) 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 fe 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 sa m e tim e th e h ig h e s t le v e ls d iffe r fro m each o th e r u p to 30 cm , th 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, ta k in g in to 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 , th 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 give 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 ith th e m e th o d o f a v c ra g in g 9 v a r ia n ts t h a t we
d id , th e p a irs 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 ; 410), 50 y e a rs : (-1 4 ;
422), 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 20 to 30 cm.
T h e d iffe re n c e b e tw e e n v a r ia n ts 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 iffe r e n t m e th o d and
a v e ra g in g re s u lts is th e b e s t w ay to p ro v id e re a l d e s ig n le v e ls in th e ca sc o f s h o rt
se rie s.
F ro m th e a b ove 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 ilit y . F o r th e s ta tio n s w ith 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 ra c te ris 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 arinc 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 Khước, N g h iê n cứ u sự b iế n
th 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 tr ạ m q u a n trắ c , Dáo cáo thực hiện chuyên
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
th u ậ t b iê n , số 1 , H à N ộ i, 1993.
B ù i Đ ìn h Khước, Xác đ ịn h th ê m về x u th ê mực nưóc b iể n tạ i m ộ t sô đ iể m ve n bờ
b iể n V iệ t N a m , Báo cáo thực hiện chuyên để, Đổ t à i cấ p n h à nước K T -0 3 -0 3 ,
1993.
38
5.
P h a m V a n Ị ỉ ti a n
T ib o r K a ra g o , R ic h a rd
vv.
K a ts , E xtrem es a n d d e ssig 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
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vpoeHỉi
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rHJ3pOMCTCoH3jI3T., JIcHHHrpa.a, 1961
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TAP CHỈ KHOA HQC ĐHQGHN, KHTN & CN, T XIX, Nọ 1, 2003________
M ự c NƯỚC
cực
TRỊ ở VÙNG B I E N v i ệ t n a m
Phạm V ăn H uân
Khoa K h í tượng T h ủ y văn & H ải d ư ơ n g học
Đại học Khoa học T ự nhiên , Đ H Q G Hà Nội
G iớ i th iệ u tổ n g q u a n n h ữ n g k ế t quả n g h iê n cứ u về b iế n th 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 iế 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
th u ỷ t r iề u ỉý th u y ế t.
B iế n th iê n m ực nước b iể n gần 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 đến 3 m m m ộ t n ă m .
V ớ i b ả y tr 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 tí n h các độ cao m ực t r iề u từ n g g iò tro n g
ch u k ỳ 20 n ă m . V ó i 19 tr 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 th iê n v ă n lý th u y ế t dược ưỏc lư ợ n g b ằ n g p hư ơ ng p h á p lặ p . So
s á n h cho th ấ y h a i phư ơ ng p h á p cho k ỏ t q uả k h á p h ù hợp.
P hép 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 25 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 iế t k ế ứ ng v ỏ i các tà n x u ấ t h iế m
khác nhau.
P h â n tíc 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 với ch u k ỷ
lặ p lạ i d à i hơ n bị ả n h hương c h ủ yế u bơi h iệ n tư ợ ng lủ v à nước d â n g .
