Extreme values and rising tendencies of sea levels along Vietnam coast

For stations with 11 harmonic constants o f main tidal constituents the theoretical astronomical extreme tide levels were calculated by the Peresipkin iteration metho[r]

VNU Ịournal of Science, Earth Sciences 25 (2009) 116-124

E xtrem e values and rising tendencies o f sea levels along

V ietnam coast

-Hoang Trung Thanh, Pham V an Huan*

College o f Science, VNU

Received 5 August 2009; received in revised form 23 August 2009

A bsỉract A revievv o f the investigations on the sea leveỉ changes in South-china sea is presented

The full set o f yearly sea level data at 25 tide gauges along Vietnam coast is used for extreme

analysis and trend analysis Based on the level data collection up to year 2007 the empirical

extreme analysis yields new estimates o f the design values o f sea ievel with different rare

ữequencies

The results o f extreme analysis are compared wilh the theoretical exừem e heights o f tide

obtained by predicting hourly tide heights in a 20-year period For stations with 11 harmonic

constants o f main tidal constituents the theoretical astronomical extreme tide levels were

calculated by the Peresipkin iteration method The comparison showed a good agreement between

two methods The analysis also showed that the tidal extremes and design level values o f 20-year

retum period are o f the same range The ỉeveỉ values o f longer retum period are affected mainỉy by

tloods and surges at a decreasingly extent

The rate o f yearly changes o f sea ỉevel due to global vvarming and other eíĩects is evaỉuated to

bc about 1 mm per year

Keywords: Extreme analysis; Trend analysis; Retum period, Design ỉevels, Sea level rise.

ỉ In tro d u ctio n

T h e e x tre m e sea levels are research su bject

o f m any pu rp oses T h e m ax im al an d m inim al

v alu es o f sea levels an d th e ir occu rren ce

p ro b a b ilitie s are taken into a c c o u n t in d esig ning

h y d ro -te c h n ic a l in stallation s an d in build ing

n a v ig atio n m aps, w ith m inim um se a level being

th e z e ro o f th e navigation m aps

T h e issu es o f sea level c h an g e ab len e ss are

o f a co m m o n interest, esp ecially in the context

o f th e g lo b al vvarming

T h e o b serv atio n o f sea level alo n g V ietnam

co ast is m ain ly carried o u t by a system o f tidal

# Tel.: 84-912116661

E-mail: huanpv@vnu.edu.vn

gau g es o f th e V ietn am H yd ro-m eteoro lo gical

S ervice G en erally sp eak in g, up to no w the

nu m ber o f tid al g au g es th at belo ng s to V ietn am

w aters is n o t large and th e perio d o f observ ation years is n o t lo n g en o u g h So th e re is no m uch

d eal vvith th e b eh av io r o f sea level in general

an d w ith th e em p irical calcu la tio n s o f level

ex trem es in particular

T he th e o ry o f e x tre m e an aly sis o f statistical

m ath em a tic s is ap p lied to the h y d ro m eteoro lo gy vvith d iíĩe r e n t d istrib u tio n s o f th e o bserved series o f c lim a tic an d hyd ro lo gical param eters [6,8] T h e m ain co ncep ts o f th ese m ethods and

th e ir p ractical realizatio n h av e been presented

in details in [2 ]

In th e c a s e th at ob serv ed series o f sea level

is n o t lo n g en o u g h to apply th e p ro ced u res o f

ex trem e a n a ly sis th eo ry , w hich usu ally happens 116

H T Thanh, p.v H uan / V N U Ịoum al o f Science, Earth Sciences 25 (2009) 116-124 117

in th e design inv estig atio n s in th e Coastal zone

and estu aries, o n e m ay use th eo retical extrem e

v alu es o f so ly tidal levels

In m any practical p ro b lem s th e m inim al

theoretical level is assu m ed to be th e zero depth

in tidal seas T his level c an be calcu lated by

su b tractin g m axim al lovv h e ig h t o f tid e d u e to

astro no m ical co n d itio n s from th e m ean sea

level In som e co u n trie s th is v alu e is

dcterm in ed by an aly zin g a predicted series o f

20-y ear lo n g tidal heig hts, on e choose the

low est h eig h t am o n g all lovv w aters in the series

as a zero depth In R u ssia th e m inim al

theoretical level is d eterm in e d by know n

V ladim irsk y m ethod V lad im irsk y m ethod

gives an an aly tic al so lu tio n o f th e problem with

harm o nic co n stan ts o f 8 m ain tid al constituents

T h e rest tidal c o n stitu en ts are tak en into

account ap p ro x im ately R ecen tly the

calculatio ns can be p erfo rm e d rap id ly by

com puters, ev alu atin g ex tre m e h cig h ts o f tide

can b e carried o u t by m o re d etailed schem es

and th e accu racy is im p ro v ed by ta k in g a non-

restricted n u m b e r o f tid e co n stitu en ts into

con sideration [7] A d etailc d ex p lan atio n o f a

schem e to im p lem en t th is m eth o d in practice

and the results o f its ap p licatio n fo r 25 tid e

gau g es a lo n g V ietnam co ast h av e been presented b y Pham V an H uan [2]

A full cu m b crso m e calcu la tio n o f level

ex trem es h a s been p eríò rm ed by N g u y en Tai

H oi since 1995 [1] T h at rep ort íirs tly listed series o f m o n th ly av erag e, m a x im al and

m inim al le v e ls m easured a t all g au g es along

V ietnam c o a st u p to m id d le o f th e ninetieth

T h e e x ữ e m e an aly sis w as th en carried o u t by using an asy m p to tic G u m b el íu n c tio n o f

p ro b ab ility d istrib u tio n o f th e extrem es

In so m e rare w orks there re p o rte d th e results o f a n a ly z in g c h an g e ab len e ss o f sea level and th e estim atin g th e trend o f s e a level rise in

th e base o f an aly sis o f ob served s e rie s o f sea Ievel som e y e a rs long T h e sp ectru m an aly sis [3] sho w ed th a t b esid es th e sem ian n u al and annual p erio d s, in th e m o st o f tid al g au g es oscillation s o f p erio d o f 6 to 10 y ears and lon g er exist

T h e tre n d an aly sis u sin g m o n th ly m ean lev els c o llected u p to m id d le o f th e n in e tieth [2 - 5] show ed th a t th e sum m ary e íĩe c t b y the global vvarm ing and o scillatio n s o f sea b ed in region o f V ietn am c o a st cau ses a ra te o f level rise (tren d ) a b o u t 1 to 3 m m p er y e a r (T a b le 1)

Table 1 The rate o f sea level rise along Vietnam coast [2]

Tidal gauge Co-ordinatcs Observation years Samplc sizc (ycars) Trend (mm/year)

Đ ased o n th e y e a rly m ean level data

coliected u p to th e y e a r 2 0 0 7 nevv evaluation s

o f th e d esig n v alu es o f se a level o f d iíĩe re n t

rarỉ íreq u e n cies are p resen ted in section 3 T he

re silts o f ex tre m e an aly sis are co m p ared with

th e th eo retical ex trem e h eig h ts o f tid e o b tained

b y p red ic tin g ho urly tid e h eig h ts in a 2 0 -year period F or o th er statio n s w ith 11 o r 8 h arm onic

co nstants o f m ain tidal c o n stitu en ts th e theoretical astro n o m ical ex trem e lev els w ere

118 H T Thanh, p.v H uan Ị V N U Ịoum al o f Science, Earth Sciences 25 (2009) 116-124

calcu la ted by th e Peresipkin iteration method

T h e c o m p ariso n show ed a g o o d agreem ent

betvveen tw o m ethods T h e analysis also

sh o w e d th a t the tidal extrem es and design level

v alu es o f 2 0 -y e a r re tu m period are o f the same

range T h e level values o f longer retum period

are a íĩe c te d m a in ly by Aoods a n d surges at a

m o d e st extent

2 D ata an d m etb o d s

2.1 Data

All the analy se s are based on sea levels

collected at 25 tidal gauges T h re e types o f data

are considered: y e arly m ean sea levels, yearly

m a x im u m an d m in im u m levels T he observation

period and th e length o f d a t a series a t points are diíĩeren t a n d r a n g e s from 2 7 to 4 6 years (see Table 2) It is s een th a t the lengths o f the sam ples are m u c h better than those in the

m iddle o f th e n inetieth vvhen th e design levels had been e s tim a te d b y us [2] for the íìrst tim e ( s e e T a b l e 1)

T he h a r m o n ic co n s la n ts o f a large n um ber

o f stations are u s e d a s the input data for the tide prediction to fin d th e e x tre m e tide levels For

m any a m o n g th e s e stations th e set o f harm onic constants are o b ta in e d from the observed hourly levels series o f o n e - y e a r o r longer F o r one-year series the n u m b e r o f h a rm o n ic constants equals

30 S tations w ith a tw o -y e a r o r longer series have the n u m b e r o f h a rm o n ic constants up to 114

Table 2 The characteristics o f the data samples Tide Gauge Co-ordinates Observation years Sample size (years)

Côn Đào 8 ° 4 r N - 1 0 6 ° 3 6 ’E 1980-2007 28

H.T Thanh, p.v H uan ị V N U Ịoum al oỊSàence, Earth Sciences 25 (2009) 116-124 119

2.2 Extremes anaỉysis with empirical daía

A question o f principle in the application o f

extrem es analysis th e o ry is the precision o f the

approxim ation, i.e the q u e s tio n o n the rate o f

co nvergence o f precise distribution o f extrem es

to the asym ptotic on e, in p ractical aspect, the

precision o f desig n valu es estim ated by

asym ptotic distribution in c o m p a ris o n vvith its

real value (but often unknovvn)

T he m e thods o f e s tim a tio n o f extrem e

distribution a im a t the settlem en t o f the

question on the initial series, th e relatively short

length o f initial series T i b o r Farago and

Richarđ w K ats [6] e x p la in e d different

methods for th e estim ation o f the distribution

param eters ( k - shape param eter, u m - local param eter a n d bm - scale p aram eter) a n d for

the d eterm ination o f design valu es a n d their estim ate accuracy Section 3.3 presents the results o bta ined by applying th e se m eth o d s to series o f an nually m a xim al a n d m inim al levels

o f 25 tidal g au g e s alo n g V ie tn a m coast

B ecause o f th e short length an d the unknow n

p arent distribution o f the em pirical sam ples, all nine m ethods o f estim ation are applied to each level series t o investigate a n d c om pare T o avoid a risk o f o v er-estim ation o r under- estim ation the design values o f e x ừ e m e levels

o f different re tu m periods are o btained as the averages o f n in e m eth o d s (an e x a m p le o f the calculations m a y be seen in T a b le

3).-Table 3 The example o f extreme value analysis for yearly maximal level at Hòn Dấu

Mean = 378.50; Standard Deviaíion = 21.70; Maximum = 421.00; M in im u m = 332.00 (cm)

2-parameter methods (Gumbeỉ):

Linear unbiased estimates (Lieblein) 414.24 429.16 448.46 462.92

Method o f probability-weighted moments 413.51 428.57 448.07 462.68

3-parameíer melhods (Jenkinson):

Method o f probabiIity-weighted moments 412.04 420.16 428.25 432.91

2.3 M e th o d o f c o m p u íin g tid a l extrem es

Extrem e valu es o f tid e (so call the

theoretical astro n o m ical levels o f tide or

simply, the tid al e x tre m e s ) are c o m p u ted by

two m ethods First One is t o p re d ic t th e hourly

tidal levels for the period o f 2 0 -y e a r long The

highest from all high w a te r s will be the

maximal value o f tide a n d th e lo w est from all

low w aters w ill be the m in im a l v alu e o f tide

T h is m ethod h a s a disad v an tag e in req u ire m en t

o f large co m p u tin g time

T he Peresipkin iteration m e th o d o f estim ation o f th e tidal e x ừ e m e s is tested to exam in e its efficiency T h is m e th o d o f

a p proxim ate calculation o f tid al e x ừ e m e s and the appropriate Computer pro g ram fo r its realization h a v e been ex plained in detail in [2]

120 H.T Thanh, p.v H uan / V N U Ịoum al o f Science, Earlh Sãences 25 (2009) 116-124

In contrast to the m eth o d o f predicting level

series 2 0-year long said above, th e iteration

m eth o d has a distinctive advantage in

req u irc m en t o f less c o m p u tin g time

2.4 T ren d analysis

T rend analysis is applied t o th e series o f

y e arly m c an sea levels a t 25 tidal gauges listed

in T able 2 T h e rate o f sea level rise (ram per

y e a r) at eac h tidal gauge is obtaincd by

regression m eth o d o f finding an equation o f sea

le vels d ep ending o n tim e (year)

3 T h e r c s u lts a n d d is c u s s io n

3.1 Tidal exírem es f o r th e g a u g e s w ith f u l l set

o f h a rm o n ic constants

For the hydrographic stations with tidal

gauges w e used a series o f ho u rly observed

levels o f o n e y e a r duration to co m p u te the full

set o f h arm onic constants (30 constituents or more) T h e hourly levels w e re predicted for a period o f 2 0 years ( 1 9 8 9 - 2 0 0 8 ) T he lowest and highest levels chosen for so m e stations are listed in colum ns 4 and 5 o f T able 4 in the order from the north to the South alo n g V ietnam coast

3.2 T id a l exírem es e s tim a te d b y Vìadim irsky

m e th o d o r P eresip kin itera tio n m e th o d

For the stations w ith n o systematic observations on sea levels vve used series o f hourly o b serv ed levels o f duration o f so m e days

to co m p u te harm onic constan ts o f main tidal constituents (by Darvvin m eth o d o r b y the least squares m ethod) T h an , from these restricted sets o f the harm onic constan ts w e used the iteration m eth o d đealt vvith in section 2.3 to get the cxtrem e characteristics o f the tidal levels

T he results o f co m p u tin g are \vritten in Table 4

T a b le 4 T id a l e x ữ e m e s a lo n g V ie tn a m c o a s t e stim a te d b y p r e d ic tin g 2 0 - y e a r s e rie s a n d b y th e ite ra tio n m eth o d

-S ta tio n Co-ordinatcs M can lcvcl (cm)

Prcdicted 20-year pcriod Iteration method Lovvest tidc H ighcst tidc Lovvest tidc H ighest tide

C át Hải 20°.47’2 (T E -1 0 6 o5 r i 8 ”

E

H.T Thanh!, p v H uan ỉ V N U Ịoum al oỊSàence, Earth Sáences 25 (2009) 116-124 121

It is seen from T ab le 4 that the results o f

tw o m ethods o f c o m p u tatio n s are in good

agreement T h e m ean absolute declination

between two estim ates eq u als 2.1 cm for the

lowest tides an d 3.9 cm for the highest tides

T he m ean squ are declination eq u als 3.7 c m for

the lovvest tides a n d 8.5 cm for the highest ones

T he rare m axim al d iíĩe re n c e s (1 0 c m o r more)

bet\veen tw o m e th o d s o f estim ation o ccu r only

for stations w h ic h have a considerably high

value o f am p litu d e harm onic constants o f tidal

c o n stitu e n ts S a a n d S s a T h u s , h a rm o n ic

co n sta n ts S a a n d S s a f o r s ta tio n C ử a G ia n h

equal 21 and 8 cm respectively; for Sơn T rà -

18 a n d 12 cm ; for Q u y N h ơ n - 10 a n d 7; for

Vũr.g T àu - 2 0 a n d 6; for R ạch G iá - 12 an d 2

and for Bạch H ổ - 17 and 3 cm It is know n that

constituents S a a n d S s a have n o t only purely

tidal nature b u t also m eteorological one These

two constituents are a íĩe c te d b y seasonal

o s c ỉla tio n s o f th e m eteorological processes and

espccially by flo o d s in estuaries In th is case the

tidal extrem es ch o s e n from a 20-year series o f predicted levels a re m ore exact

F rom th e se experim en ts íòllovved a rule o f

th u m b th a t for a station vvhich h a s high

h arm onic constants o f annual and semi-annual periods th e e x ừ e m e tid es m ust be determ ined

b y both t w o m e th o d s - procedure o f predicting 20-year series an d V ladim irsky m ethod, the lesser a m o n g tw o e s ừ e m e values w ill be the Iowest tide a n d the bigger am o n g tw o extreme values - h ig h e st tiđe

3.3 R esu ỉts o f c o m p u tin g d esig n v a lu es fr o m

o b se rv e d y e a r ly m a xim u m a n d m in im u m se a levels

In th is section w e u s e series o f th e yearly

m inim al a n d m axim al levels a t stations listed in

T able 2 t o ev alu ate th e design levels with different re tu m perio d s b y extrem e analysis In eac h y e a r o n e low est level (or o n e highest level)

w a s ch o s e n to establish the sam ple series

122 H.T Thanh, p.v Huan / V N U Ịoum al o f Science, Earth Sciences 25 (2009) 116-124

Tabỉe 5 Design leveỉs (cm) at 25 tidal gauges along Vietnam coast

Tidal gauge

Retum period (ycar)

Trend o f MSL (mm/year)

T a b l e 3 is an e x a m p le o f calculations

p e rfo rm e d for estim ating distribution

p aram eters a n d determ in in g the design values

dis c u s s e d in [6] T he an alo g o u s analyzing

p ro c e d u re w a s carried out for all the stations

w ith th e observation p erio d 2 7 to 4 6 years long

(T a b le 2) F o r each station the design levels

w e re c o m p u ted by 9 estim atin g methods

Further, nine values w ere averaged and

su m m a riz e d in T ab le 5

N o w w e co m pare th e desig n levels o f retum

period 2 0 y e ars (colu m n s 3 a n d 7 in T a b le 5)

w ith tidal extrem es (colum ns 4 a n d 5 in Table 4)

K e e p in m ind th a t the reference level o f

eac h tidal gauge in T a b le 4 d iíĩe rs from th a t in

T a b le 5 W ith station C ử a c ấ m , for ex am ple, if

w e su bstitute a zero o f th is station (217 cm)

from the tid e m i n im u m 30 c m in T a b le 4, then the value o f th e tiđ e m in im u m referenced to

m ean s e a level w ill be - 1 9 3 cm S ubstitution

217 cm íí o m th e tid e m a x im u m 4 0 6 c m yields a tide m a x im u m 189 cm I f w e d o th e sam e with station C ử a H ội, th e tide extrem es referenced to

m ean sea level o f this station w ilỉ be -151 and

120 cm respectively

F ro m t h e c o m p a r is o n betw ee n the m inim um design leveỉs o f 2 0 -y e a r re tu m period and the tide m in im a for s o m e stations follo w s that these design levels d i í ĩ e r from tide m in im a lesser than ab o u t 60 cm T h is d iíĩe re n c e is caused by the surge oscillations in the Coastal zo n e and the analysis errors as w h en

S urges also affect the m a x im u m design levels in the s a m e w ay H ow e v er, for the

H.T Thanh, p v H uan / V N U Ịoum al o f Science, Earlh Sciences 25 <2009) 116-124 123

m a x im u m design levels, th e ir differe n ces to the

tide m a x im a arc much la rger at th o s e stations

vvhich locateđ in river m o u th s, such as Ba Lạt

(189 cm ), H oàng T ân (122 c m ) a n d C ừ a Hội

(110 cm ) T h is is the w ork o f floods

This rem ark has a n important

m ethodological signiíìcance in th e practice o f

calculations o f low est sea levels for the regions

w hich lack o f long o bservations In th is case the

lovvest sea level can be th e tid e m inim um

substituted b y a surge co rre c tio n , and the

highest sea level - the tide m a x im u m added by a

surge correction and a m a x im a l h e ig h t o f flood

3.4 R esu ỉts o f tr e n d a n a ly sis w ith y e a r ly m ean

s e a levels

T he regression eq uation o f m e an sea level

relative to tim e (years) is d e te rm in e d for each

station in T ab le 2 From th e se eq u a tio n s follows

the estim ates o f the rate o f s e a level rise

(colum n 10 in Tab!e 5) O b v io u s ly , the obtained

here sea level trends h a v e the diíĩeren t

reliability, d ep e n d in g on the s a m p le length and

the precision o f data collected

As secn from T ab le 5, the rate o f level rise

is different from station to station, ev en by sign

T h e average for all stations is 0.6 m m /y ear (~1

mm/year)

4 C o n clu d in g rcm arks

Evaluating theoretical e x tre m e heights o f

tide by the m eth o d o f p re d ic tin g 2 0 -y e a r series

o f h íu rly h eig h t a n d b y th e iteration m ethod

gives close to eac h o th e r results

Predicting tide in 2 0 -y e a r p erio d takes great

C o m p u te r tim e, vvhile the iteration method

a llo v s m o re rapid calculation T herefore in

praciical investigation at th e reg io n vvhere no

gauges set up w e should fu 1 fĩ 11 the m e asure m ent

o f to u rly levels in so m e d a y s to derive the

h a m o n ic constan ts o f m a in tid e constituents

Than vvith th e V ladim irsky m eth o d o r the Peresipkin iteration m eth o d applied, w e can com pute the tide theoretical extrem es, vvhich have a certain practical useíulness

T h e differences betw een e x tre m e levels in 20-year du ratio n and the design levels o f 20- year re tu m period are not larger then the analysis errors in the case o f restricted length o f used samples

T he theoretical e x tre m es o f tid e hav e the sense o f e x tre m e levels I f th e surge correction

is know n, One should substitute this v alu e from the m in im u m tide height to obtain a more reliable lovvest sea level a n d add it to the

m axim um tid e height to hav e a h ig h e st sea level F o r e s tu ary stations, the highest sea level

m ust be corrected b y the flood height

T h e o bta ined design levels hav e the different reliability H ow e v er, for th e stations with o b servation m ore than 30 y e ars the design levels in T able 5 can be considered as satisfactory

T he rate o f yearly changes o f sea level along

V ietnam c o a s t d u e to global vvarming a n d other effects is ev aluated to be ab o u t 1 m m p e r year

A ck n o w led g em en ts

T h is report w as com plete d w ith in the fram ew ork o f the R eserch Project Q G -08-11 íunded by V ie tn a m N ational ư n iv e rs ity , H anoi

R eíe r en ces

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M arine H ydrom eteorological C entre, Vietnam

VA Project, Hanoi, 1995

[2] Pham Van Huan, Exừemum sea levels in

Victnam coast, VNU Journal o f Science T XIX,

N o l (2003) 22-38

[3] Sludy ọ f the changeability and the correlalion o f sea levels a l the tid a l gauges a lo n g Vietnam

124 H T Thanh, p.v Huatt / V N U Ịoum aỉ o f Sàence, Earth Sciences 25 (2009) 116-124

coast a n d the possibiỉitỵ o f reconstruction o f sea

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B ui Dinh K huoc/Them e K T - 0 3 -0 3 , 1995 (in

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technoỉogy, N o l (1993), H anoi (in Vietnamese)

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coasí, Item report by Bui D inh Khuoc/Theme

K T - 0 3 - 0 3 , 1995, 1993 (in Vietnam ese)

[6] T ibor F aragot R ichard w K ats, Extremes and design vaỉues in cỉimatoỉogy, W C A P -14,

W M O /T D -N o 386, W orld M eteorological

O rganization, 1990

[7] V.I P eresipkin, The analystìc methods Ịo r the calcuỉation o f the oscilỉations o f sea levels,

H ydrom eteoizdat., Leningrad, 1961 (in Russian) [8] Guidance on the calcuỉaíion o f hydrological parameters fo r the investigation and research in Coastal zones a n d estuarìesy P ub “Science”, Moscovv, 1973 (in R ussian)