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: [email protected]
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 n ce p ts o f th e se m eth o d s 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 117in 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 tid al h eig h ts, o n e ch o o se 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 a in tid al co n stitu en ts.
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 e a rs 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)
Hòn Dấu 20°40 ’ N - 106°49 ’ E 1957-1994 38 2.1
Cửa Câm 20°45’N-106°50'E 1961-1992 32 2.7
Sơn Trà 16°06’N-108°13’E 1978-1994 17 1.2
Quy Nhơn \y 4 5 'H -\0 9 ° \y E 1976-1994 19 0.9
Vùng Tàu 10ữ20’N -!0 7°04’E 1979-1994 16 3.2
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 o n ic 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)
Cửa ô n g 21.o02’N-107.°22’E 1962-2007 46
Bãi Cháy 20.°5 8 ’N - 107°. 04 ’ E 1962-2007 46
Cô Tô 20.o58’N -l07.°46’E 1960-1994 35
Cửa Cấm 20°45’N -106°50’E 1961-2006 46
Hòn Dấu 20°40’N -106°49’E 196Õ2007 48
Ba Lạt 20°.19’N-106.°J I’E 1960-2006 45
Hoàng Tân 19.°.46’N-105°.52’E 1965-2005 41
Hòn Ngư 18.°.48’N - 105.°.46’E 1962-2007 42
Cửa Hội 18-°.46’N - 105.°.45’E 1962-2005 44
Cẩm Nhượng 18°.15’N-106.o06’E 1962-2007 46
Cồn Cỏ 17.°10’N-107.°22’E 1980-2007 27
Cừa Việt 16°53’N-107.°10’E 1977=2005 29
Sơn Trà 16°06’N -108°13’E 1978-2007 30
Quy Nhơn 13°45’N -109°13’E 1976-2007 32
Tuy Hòa 13.o05’N-109.° 17’E 1977-2004 28
Phú An 10.°46’N - 106 °42’E 1977-2005 29
Phú Quý 1 0 ° J r N - 1 0 8 o-56’E 1986-2007 22
Chợ Lạch 10°. 17’N-106.°07’E 1977-2005 29
Vàm Kênh 10o.16’N -I06.°44’E 1978-2005 28
Vũng Tàu 10°20’N -107°04’E 1979-2007 29
Rạch Giá 10.°00’N - 105 °05’N 1978-2005 28
Năm Căn 8°.46’N - 1 0 5 o0 r E 1980-2005 24
Cà Mau 8 o3 9 ’N -1 0 4 ° 4 5 ’E 1978-2005 28
Phú Quốc 10°.13’N-103.°58’E 1980-2007 28
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 1192.2. 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 distributionparam 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)
Methods Retum period (year)
10 20 50 100
2-parameter methods (Gumbeỉ):
Method o f moments (ưieoretical) 406.80 418.98 434.74 446.56
Method o f moments (empirical) 408.53 421.32 437.88 450.28
Method o f quantiles 420.76 437.31 458.74 474.80
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
Maximum likelihood method 414.88 430.08 449.74 464.47
3-parameíer melhods (Jenkinson):
Method o f sextiles 405.24 410.67 415.65 418.29
Method o f probabiIity-weighted moments 412.04 420.16 428.25 432.91
Maximum likelihood method 406.01 412.30 418.37 421.75
Average o f all melhods 411 423 438 448
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) 116-124In 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
(1) (2) (3) (4) (5) (6) (7L _
C ử a Ông 21 .°.02’N - 107.°22’E 215 2 469 0 472
C ô Tô 20.o5 8 ’N -1 0 7 .°4 6 ,E 204 - 7 454 - 1 0 454
C át Hải 20°.47’2 (T E -1 0 6 .o5 r i 8 ” E
180 -5 2 414 - 5 4 416
C ử a Cấm 20°45’N -1 0 6 ° 5 0 ’E 217 30 406 28 408
H òn Dấu 20°40’N - 106°49’E 194 -1 8 412 - 2 2 416
Đ a Lạt 20.°. 19 * N -106 ° 3 1 *E 6 -1 7 5 185 -1 7 7 187
N hư Tân 20.°.01 *N-106.°.06’E 83 - 6 173 - 7 174
Lạch Sùng 19.oJ 7 ’N - 1 0 5 .° i8 ’E - 1 6 -1 8 2 128 -1 8 5 130
H oàng Tân 19°.46’N -1 0 5 .°5 2 ’E 3 -1 8 8 161 -1 9 0 163
H òn Ngư 18.°48’N -1 0 5 .°4 6 ’E 182 28 317 27 318
C ử a Hội \ Z 0A 6 'H -\Q 5 ° A 5 'E 171 20 291 19 291
C ử a Gianh 17°42,N -1 0 6 ° 2 8 ’E - 3 4 -1 5 7 61 -1 6 0 37
N h ật Lộ \ 7 ° 3 0 'H - \ 0 6 ° 3 6 'E 0 -7 7 54 - 7 8 54
c ồ n Cò \ 7 oA 0 'H - \ 0 r o2 2 'E 80 36 120 36 120
C ử a Tùng 1 7 .° .0 rN -1 0 7.°.06’E 80 36 113 36 113
Thuận An 16 ° 3 4 ’N - 107.°38'E 50 25 77 25 77
H.T. Thanh!, p .v . H uan ỉ V N U Ịoum al oỊSàence, Earth Sáences 25 (2009) 116-124 121
Chơn Mây 16o.19’N -107.°59’E 80 34 115 33 115
Sơn Trà 16°06’N -108°13’E 93 10 175 10 142
Cù Lao Chàm 15.°.57’N -108.°32’E -23 - 9 9 49 -9 5 50
Sa Huỳnh 14 °.4 0 'N -109.° 04 'E - 6 -9 9 88 -9 9 90
Quy Nhơn 13°45’N -109°13’E 160 75 247 70 232
Nha Trang 12° 15 ’0 5 N -109° 11’05E 121 8 227 8 225
Cam Ranh 11 o-53’N-109-° 12’E 124 30 206 29 207
Phan Thiết 10 °-5 5 108°. 06 ’ E 0 -130 79 -131 79
Vũng Tàu 10°20’N -107°04’E 259 -2 7 413 -1 5 402
Cà Mau 8.°3 9 ’N - 104.°.45 ’ E 76 - 7 146 - 7 146
Hà Tiên 10.°22 ’ N - 104.°.28 ’ E 70 32 121 32 121
Rạch Giá 10o00’N -105°05’E 5 -4 8 90 -3 4 84
Mỏ Bạch Hổ 10 °.00’N - 107.°.00’ E 372 190 488 192 469
Mỏ Đại Hùng 8.°29*N -108.°3 8 ’ E 189 73 273 72 273
Phú Quốc 10.°. 13 103.°38’E 58 5 96 5 96
Trường Sa 8.03 8 ’N -111.°55’E 0 -9 8 87 -9 9 87
Hoàng Sa 16°33’N -111.°37’E 118 45 189 45 189
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) 116-124Tabỉe 5. Design leveỉs (cm) at 25 tidal gauges along Vietnam coast
Tidal gauge
Retum period (ycar)
Trend o f MSL (mm/year)
10 20 50 100 10 20 50 100
Minimum Maximum
(1) (2) (3) (4) (5) (6) (7) (8) (9) _ (10)
Cửa Ong 12 1 - 1 2 -2 1 477 489 504 515 1.1
Bài Cháy 1 - 1 0 -23 -3 2 440 451 464 474 1.0
C ô Tô - 1 - 1 1 -23 -3 3 450 462 477 489 1.0
Cửa Cấm -184 -193 -205 -215 216 225 237 245 0 .0
Hòn Dấu - 7 -1 3 - 2 2 -2 8 411 423 438 448 1.0
Ba Lạt -1 2 6 -133 -143 -1 4 9 314 374 467 555 0.1
Hoàng Tân -1 5 7 -1 6 2 -1 6 9 -173 256 283 320 351 0.1
Hòn Ngư - 7 -1 8 -33 -4 3 374 387 402 414 0.9
Cửa Họi -173 -1 7 8 -185 -1 9 0 213 230 253 271 0.2
Cẩm Nhượng -1 3 0 -1 3 5 -1 4 2 -146 218 235 258 275 0.4
Cồn Cỏ - 2 -5 - 8 - 1 1 180 188 199 207 0 .0
Cửa Việt -8 9 -9 2 -9 5 -98 160 177 199 216 0.5
Sơn Trà 13 9 3 - 2 226 238 253 264 0.5
Quy Nhơn 21 13 2 - 5 277 283 291 297 0 .8
Tuy Hòa -7 8 -8 5 -9 4 - 1 0 0 467 512 567 607 0.1
Phú An -2 4 7 -2 5 6 -2 6 7 -275 147 150 155 158 0.1
Phú Quý 77 70 61 55 318 325 334 340 1.1
Chợ Lạch -1 8 0 -1 8 6 -194 - 2 0 0 180 185 192 197 0.2
Vàm Kênh -2 4 8 -2 5 2 -2 5 8 -262 61 65 70 74 0.0
Vùng Tàu -3 5 -4 3 -5 3 -6 0 434 439 446 451 -0.1
Rạch Giả -6 2 -6 4 -6 7 -6 9 110 119 130 139 0.0
Năm Căn -3 2 7 -3 6 0 -403 -435 143 148 154 159 0.1
C à Mau -5 9 -6 3 -6 9 -73 120 129 140 148 0.2
Phú Quốc 4 - 1 - 7 - 1 2 169 175 184 191 0.5
Côn Đảo 16 8 - 1 - 8 415 423 434 441 1.2
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
[1] Nguyen Tai Hoi, Reporl on iidal characteristics (Sub. A5), Design water levels (Sub. A I3).
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) 116-124coast a n d the possibiỉitỵ o f reconstruction o f sea ỉeveỉ series a í some observation stations, Item report by N guyen N goe T huy, Pham Van Huan, B ui Dinh K huoc/Them e K T - 0 3 -0 3 , 1995 (in V ietnam ese)
[4] N guyen N g o e Thuy, On th e rising tendency o f sea level in Vietnam , M arìne Science and technoỉogy, N o .l (1993), H anoi (in Vietnamese).
[5] A suppỉem entary determ ination o f rising tendency o f sea leveỉ aí some points o f Vietnam 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).
