Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 2 M may , . The 1 2 1 , S − Q 4 , 1 airs and O ff , 1 K , A. Setiawan 1 , B. Fan 4 , T. R. Adi 3 2832 2831 1 has the largest amplitude, exceeding 50 cm, whereas 1 K , R. D. Susanto 1,2 , and X. M. Gao are smaller than 5 cm at all stations. The amplitudes of 1,2 2 M , G. H. Fang in Karimata and Gaspar Straits. Tidal currents are mostly of rectilinear type at five stations in this area have been analyzed using in-situ observational 2 , and those of the semi-diurnal tidal currents are smaller than 5 cms 1,2 2 1 , Y. G. Wang M N − 1 and 2 This discussion paper is/has beenPlease under refer review to for the the corresponding journal final Ocean paper Science in (OS). OS if available. The First Institute of Oceanography, StateLaboratory Oceanic for Administration, Regional Qingdao, Oceanography China and Numerical Modeling, Qingdao National Department of Atmospheric and OceanicAgency Science, for University Marine of Maryland, & Fisheries College Park, Research USA and Development, Ministry of Marine A the amplitudes of exceed in this area. The major10 cms semi axis lengths of the diurnal tidal current ellipses are about data. The results show thatstudy the diurnal area. tides The are constituent the dominant constituents in the entire 1 Introduction Tidal system in therugged Indonesian bottom seas topography, is complicated the coastline,propagating most and from complex the the one interference Pacific in ofearliest Ocean, reports tidal the Indian of waves world, Ocean tidal due characteristics andcolonial in to South period the its China Indonesian in seas Sea the can (SCS). early be twentieth The traced back century, to which the were recompiled by Wyrtki (1961) diurnal tidal energy flowsfrom from the the SCS SCS to to the theern JS Natuna JS. Sea through The but the semi-diurnal flows Karimata tidalpart in Strait the energy of opposite and flows direction the the in eastern southernvation the part Gaspar Natuna also Strait of suggest Sea. and the that the Harmonic south- waves, western the analysis and study in of area the sea is nodalthe level located band existing and in of models current the the are loop obser- semi-diurnalimprovements basically band tidal are consistent of waves. necessary. with Comparisons the the show diurnal observational that tidal results, but further Abstract The South China Seamata (SCS) Strait, and Gaspar the Java Strait,used Sea and as (JS) open the are boundary southern connectedTides, condition tidal Natuna through currents for Sea, the and tidal tidal Kari- where simulation energy the fluxes in of tides the the principle SCS are constituents or often Indonesian seas. S. J. Li 1 2 Laboratory for Marine3 Science and Technology, Qingdao, China 4 S Fisheries, Jakarta, Received: 10 October 2015 – Accepted: 28Correspondence October to: 2015 Z. – X. Published: Wei 20 (weizx@fio.org.cn) November 2015 Published by Copernicus Publications on behalf of the European Geosciences Union. Tidal elevation, current and energythe flux area in between the Southand China Sea Z. X. Wei Ocean Sci. Discuss., 12, 2831–2861, 2015 www.ocean-sci-discuss.net/12/2831/2015/ doi:10.5194/osd-12-2831-2015 © Author(s) 2015. CC Attribution 3.0 License. 5 10 25 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2 M shore ff erent models, ff in the Indonesian airs and Fisheries, 1 ff K and 2 M tides propagate in an opposite direction. tides and tidal currents in the Indonesian 1 1 O K 2834 2833 and and 1 2 K M . The results show that semidiurnal tides originate from both 1 E; and diurnal type west of the Kalimantan . Using the O ◦ and 1 K , 2 S , constituents in the Indonesian seas. Their results are further reported by 2 1 M K and In this study, long-term water level and current profile observations at five stations The junction area between the SCS and the JS, comprising the southern Natuna Egbert and Erofeeva (2002) have assimilated satellite altimeter data into an in- 2 Indonesia, and the Lamont-Doherty Earth Observatory (LDEO), Columbia University, eries Research and Development (AMFRD), Ministry of Marine A 2 Data The data used in thisSouth study were China obtained Sea under – the Indonesian trilateralsonal seas collaborative Fish project Transport/Exchange Migration” (SITE) “The which and wasraphy Impacts established on (FIO), in Sea- 2006 State by Oceanic the First Administration, Institute China, of the Oceanog- Agency for Marine and Fish- local dynamics buttidal also simulation useful of the for SCSfollows: the or Sect. Indonesian 2 determination seas. gives of a The descriptionresults rest open of of of the boundary the observed tides, paper data; condition “is” Sect. tidalgiven organized in 3 in currents as presents Sect. the 4. and analyzed tidal energy fluxes; summary and discussion are (Fig. 1) are used toflux investigate the between characteristics the of tidal SCS elevation, current and and JS. energy The results are not only important for understanding observations are needed toand provide to assess a the clearer existing recognition model results. about the Indonesian tides even the satellite altimeterpossibly data due have to been the assimilatedone into coarse descending the altimeter track pass models. track through This separation this is (only region; most one Ray ascending et al., track 2005). and Therefore, o Sea, the , andIndonesian the Gaspar seas Strait, (Fig. is 1). awaves Furthermore, throat that connecting this propagate the from area SCS the is and SCSthat the also or the the the JS convergent simulated (Hatayama region et tidal al., of 1996). currents tidal It in is worth this noting area are discrepant among di still not well determineddependent. as reflected by the fact that the simulated results are model seas using inversion method.investigated Using the characteristics a of barotropic tide model, Hatayama et al. (1996) tide mainly propagates from theern Indian Indonesian Ocean seas, into whereas the the Pacific Ocean through the east- verse barotropic ocean tideM model, providing the cotidal charts and tidal currents for to construct diurnal and semidiurnal cotidalland charts observations. based Although on the all results available ofthe coastal Wyrtki Indonesian and (1961) is- seas, are mapping impressively of reasonableof the in observations. Indonesian During tides are the still pasttidal incomplete decades, phenomena owing remarkable to is progress lack benefited of investigations byolution about use numerical of simulation, satellite and altimeter withtide measurements no gauge and exception high observations in res- and the TOPEX/Poseidonand (T/P) Indonesian Berge satellite seas. (1994) altimeter Based data, have on Mazzega produced the cotidal charts of seas, which shows thatnarrow the straits, tidal i.e. currents the Lombok in and the Java Strait, Sea are (JS) relatively strong. and in the vicinities of Ray et al. (2005),semidiurnal showing that tides there dominated aredonesian but three with seas types significant of and tides diurnalthe its in region inequality adjoining the west in region Indonesian of the seas: of 118 eastern the In- Pacific Ocean;simulated the mixed barotropic diurnal and tides baroclinicstituents tides in in the Indonesian seas for four tidal con- Regional Ocean Modeling System (ROMS), Robertson and Ffield (2005, 2008) have the Pacific and IndianOcean. Oceans; These whereas results the are confirmed diurnal by tides Teng et are al. mainly (2013), from which the suggests that Pacific the Although the characteristics ofmore Indonesian accurate geometry, tides and have thesouthern results been are SCS simulated indeed and with better JS, than particularly more before, in and the the tides junction in region the between the SCS and JS, are 5 5 25 20 15 10 25 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , 1 1 1 K O Q and and , 1 1 1 vs. P K O 1 , P 1 on K 1 P has the largest N) was used as 1 ). In the present ◦ 2 K are equal to 0.286 S erence of 2 ff S and E, 1.26 ◦ vs. 2 K 2 K using the conventional harmonic 2 N at Stations B1, B2 and B3. For all of the , respectively, listed in the table using the , and 2 2 , and between 2 1 S S S 2836 2835 K , 2 and M and 1 , K 1 1 P Q , respectively, and those of 1 ◦ O , 10 1 − K at five stations are listed in Table 3. The harmonic constants of 2 erences between ff N are corrected through introducing inference quantities (amplitude ratios and respectively. 2 ◦ , and S 2 2 − S can be derived from those of on , while they are greater than 5 cm for , The obtained amplitudes and Greenwich phase-lags for the constituents Current and sea level measurements were made from December 2007 to Septem- 2 2 2 2 exceeding 30 cm. For semidiurnalM tides, the amplitudesfive stations, are it all is found smaller thatof than the semidiurnal amplitudes 5 tides, of cm suggesting diurnal for that tidesarea. diurnal are Meanwhile, much tides the greater are results than the also those increase dominant show from constituents that Section in the A this phase-lags tosemidiurnal of Sections the B1 tides and diurnal dramatically B2. tides increase Onresented slightly the from by contrary, the Station the phase-lags eastern A2) ofof to segment the Section Section of A B2, (represented Section by and Alocated Station from in (rep- A1). the Section These loop B1 results (anti-nodal)the to suggest band semidiurnal that the of tidal the the waves. western As study diurnal segment athose area tidal result, is waves of the but amplitudes semidiurnal in of tides, the diurnalthose tides nodal whereas of are band the semidiurnal greater of phase-lags than tides. The ofposition semidiurnal diurnal of tidal the tides waves incident in change waves this2005; propagating less area Teng from et than appear the al., as 2013). SCS a These andopposite two super- Indian incident phase, Ocean waves happen (Ray resulting to et a have al., diurnal similar nodal intensity tidal band and waves here. in this In area contrast appear to as the a semidiurnal superposition tides, of the the incident waves propa- K inference relations. It can be seenamplitude, from exceeding the 50 table cm. that the The constituent second largest amplitude is that of constituent are equal to 0.296 and study a nearest tidal gaugean station inference at station, Keppel where harbor the (103.82 amplitude ratio andand phase-lag di M phase-lag di K rion for separating these six constituents is satisfied. The influences of 3.1 Tides Based on the observedciple sea level tidal data, constituents we extract the harmonic constants of six prin- the present paper we focuslower on panel of the Fig. tides 1. and TheA measurements tidal were is currents conducted located in along three in the sections.Island. area the Section as Section southern shown Natuna B1 in SeaIsland. the is between Section in the B2 the Bangka is IslandKalimantan Gaspar located and Island. Strait The in Kalimantan between mean theB1, water the Karimata B2 depths Bangka and Strait of B3 Island between the are 36.6,vational five the and 48.0, lengths TRBM Belitung 44.2, of stations 42.8 Island the labeled and and sea 49.0 A1,in m, Table level A2, respectively 2. and (Table 1). current The profile obser- vary from 33 to 960 days3 as listed Analyzed results from observations ber 2011 in the southern NatunaResistant Sea, Bottom Gaspar Mounts Strait (TRBMs). and The KarimataCurrent TRBMs Strait Profilers by were (ADCPs) using equipped and Trawl- with pressure Acoustic gaugeslevels. Doppler The for measuring volume, current heat, profiles and andseas freshwater sea have transports been between previously the reported SCS by Fang and et Indonesian al. (2010) and Susanto et al. (2013). In USA. The study area oftitle the of project the was collaborative extended programseas to was the Transport/Exchange changed Sunda (SITE) to Strait “The and inTheir South Impacts 2008, Dynamics China on and Sea of Seasonal the – Fish Sunda Indonesian Migration”. and Lombok Straits, and analysis method developed by Wang andformance Fang (1981), as which those is nearly developed ofthe by the Foreman shortest same (1977) per- record and length Pawlowicz is et 33 al. days (2002). (current Since observation at A1), the Rayleigh crite- 5 5 15 20 25 10 15 20 10 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the and h ) and 2 1 M K ) and di- . Figure 2 ϕ 2 N are generally 2 S ect of the strait. In ff slightly smaller than and . The major semi axis , (1) 1 2 ] 1 ) O M − G the amplitude and phase- − , north component of energy η x G , with ( the gravity acceleration, F 1 the water density (taken to be g the east and north components O cos ) and ρ ), Greenwich phase-lag ( v V r , , H and ) u we choose the one that is aligned with . At Station A2 the tidal currents rotate ( 1 . We can see that all stations show the G 2 2 K θ N S (in degrees measured clockwise from the − ∆ ξ θ ( and 2838 2837 the time, 2 cos ), ellipticity ( can approach to 20 cms t C and a salinity of 33 which are roughly equal to M U ◦ [ w 1 , 1 O the phase-lags of the corresponding components of O ) , and η 1 ρghH , and the principal semi-diurnal tidal constituents K W ξ 2 1 the tidal elevation, , and direction . At Station B1 the tidal currents rotate counterclockwise ( 1 2 F erences between the current major axis and the energy flux = ζ O S ff t d the amplitudes of the east and north components of vertically ) for diurnal constituents at all stations. and v ) 1 1 , − 1 V − u , . At Station B2 the diurnal tidal currents rotate counterclockwise, the ( K 2 U ζ ( the period of the tidal constituent, T N Z 0 ) are the east and north components of the tidal energy flux density , magnitude T y y for a temperature of 28 F F T 3 and , are also given in Table 5 (Since the current ellipse has two major semi-axes ρgh − x ) of the maximum current speed, are given in Tables 4a–e. In the tables, signs 2 F θ λ = M ∆ ) y F in the most cases. At Station B1, however, which is located in the , , . From Table 5 and Fig. 3, it is found that for diurnal tides, the tidal energy flows from Table 5 lists the east component of energy flux density x 1 2 F S the SCS to the JS at all stations. Maximum energy flux densities of 11.6 (for the energy flux). Figure 3tidal shows constituents the tidal energy flux densities of the principal diurnal with opposite directions, in the calculation of vector true north) atMoreover, Stations the direction A1, di A2, B1, B2 and B3 from observed harmonic constants. where, ( tidal current. flux density respectively, 1021 kgm undisturbed water depth, lag of the tide, the mean temperature and salinity in the study area), of vertically averaged tidal currents, averaged tidal current, and smaller than 5 cms K diurnal tidal currents are significantly increased by the narrowing e 3.3 Tidal energy flux density The energy fluxconstituent across it a can section becurrent of by calculated the unit from following width formula harmonic is constants called of flux tidal density. elevation For and a( tidal specific characteristics of rectilinear tidal currents.ellipses The are major 10 cms semi axis lengths of tidal current lengths of tidal current ellipses of the semi-diurnal constituents rection ( of the ellipticity representterclockwise the and sense negative of forflatness clockwise the of an (the current ellipse, term vector herein it of rotation, Fang is and ellipticity positive defined Ichiye, as for generally 1983 the and coun- referstidal ratio Beardsley currents of to et rotate minor al., the counterclockwise axis 2004). except vs. Wecounterclockwise can major see axis except that as at done Station A1 the particular, the maximum speed of except gating from the SCS andtwo the incident Pacific Ocean waves have (Ray basically et the al., 2005; same Teng phase, et resulting al.,3.2 in 2013). a These loop band Tidal here. currents The conventional harmonic method is appliedthe to harmonic the current constants data of analysiselevation principle for in extracting tidal Sect. constituents, 3.1. asmajor Parameters done and of minor in the semi-axes the vertically ( analysis averaged of current tidal ellipse, including semi-diurnal currents rotate clockwise.counterclockwise, At while the Station semi-diurnal B3 currents the rotate clockwise diurnal except tidal currents rotate shows the current ellipses of 5 5 25 20 15 10 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | p q (Ray ) are wave , (4) and q 1 2 ( − p M p are elevation ) is called the 0.078m) b ζ , ∂ ∂y = a 2 = S into Eqs. (5) and (6) b C v 0.070m) , = ∂ζ ∂y 1 and amphidromic point should O = u C 2 b M , we have 0.168m, , ζ ω = ∂ ∂x has been adjusted for the earth’s 2 ζ = M C a 0.104m, , = waves from the SCS are slightly stronger 1 ∂ζ ∂x K 2 waves from the JS; and (2) the southward , (7) = C S 2 a 2840 2839 S ωt ωt ωt ωt ωt ωt erences between energy flux and current major ff sin sin sin sin sin sin 00 00 00 (positive for northward) directions are respectively: 00 00 00 H H P Q U V y + + + + + + ), respectively. ωt ωt ωt ωt ν ωt ωt cient and is taken to be 0.0025 in this study. The values of )for semi-diurnal tides ( tidal energy flows oppositely from the JS to the SCS. But for cos cos ffi )for diurnal tides ( λ cos cos cos cos , (3) 2 0 0 0 and λ tide is quite small and flows to the JS only in the eastern pas- 2 0 0 0 q H H , (2) M P 2 Q V U + + , (6) , (5) Q appear at Station B1 in the Gaspar Strait. On the other hand, the p − ( v = = u = M = = = 1 ) 2 2 ) ) − ) ωt ωt µ − ) ) ) / / b ) 1 ν 1 µ G G ξ η ) ) a − are longitude and latitude respectively. In the Eqs. (2) and (3), 2 2 − − − − − − − b cos( v v cos( and ( ϕ a + ωt + ϕ ωt ωt ωt g ϕ ωt ( ωt P wave from the SCS is slightly stronger than the northward incident ) kWm 2 2 2 g 1 ). The amplitudes and phase-lags of the obtained constituents of is the drag coe − 2 u u v and is the Coriolis parameter, and O ( ( − D M cos( cos( cos( cos( sin2 cos( cos( cos D f u D λ f C can be obtained by inserting the observed values of Q P C C U H H V f v C − C (positive for eastward) and and 1 q h 1 h ======x = tide, the tidal energy flux flows from SCS to JS at all station except B2. In the In- u For a given constituent with angular speed equal to ζ ζ q p ζ ζ v u = = 2 ∂t ∂t ∂v ∂u where and respectively, and can be decomposedto into various corresponding constituents tidal with constituents frequenciesof through equal harmonic analysis (similar to the analysis elastic response, and is equal to( (see e.g., Fang et al., 1999) tidal elevation gradient vector. The equilibrium tide where, represent the east and north components of bottom friction: p q than the northward incident diurnal and from the JS inern the eastern passage. passage, The and feature is (2) slightly further weaker indicates than that the latter the in the west- where gradients of tides and equilibrium tides respectively. The vector of ( denoted as 14.7 (for sage of the study area, includingthe the Gaspar Karimata Strait, Strait. the In the western passage, including axis are generally small.that From (1) directions the of southward incident energy diurnal fluxes and shown Fig. 3incident we can judge be located between theshould A1–B1 rotate line clockwise. and the A2–B2 line and3.4 the amphidromic system Tidal elevation gradients Based on the tidal currents, theshallow gradients water of equations, sea as surface done height bythe can Proudman be and derived Doodson from (1924). the The equations in                    tidal energy flux for S donesian seas, the magnitudes of tidal energy densities may exceed 100 kWm et al., 2005; Teng etsmall. al., Table 5 2013), shows thus that the direction energy di fluxes in the study area are relatively 5 5 15 10 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ◦ 2 2 M M ). The at the 00 2 H S , 0 may exceed H , tide, the tidal 1 00 and 2 O may exceed H 2 S , 2 0 M S H , ( ). The tidal elevation for diurnal tides, with 1 ∂ 00 ∂y 1 O V − , , = 0 1 ) at all stations. V K are larger than 50 cm at all 00 ; 1 1 B 00 − , K 0 U , B 0 ) can be obtained from Eq. (4). , 00 U 00 B B on the cotidal chart lies between 0 , , 0 0 G B B . In comparison, the amplitudes of , ◦ 00 ) in the same way as the calculation of 00 A , B 0 , 0 A 2842 2841 ), and ( B 00 ; tides, the tidal elevation gradient vectors rotate 00 H , A 0 1 energy flux flows southward in the Karimata Strait , , (9) 0 , (8) O 2 H (the rest are similar). Inserting Eq. (7) into Eqs.2) ( 1 1 A , at Station B1. The maximum speeds of semi-diurnal 1 1 ). The tidal elevation gradient ellipse parameters can − − M 00 − − 00 1 ξ − H B to the vector grad and /g /g , /g /g , 0 ) ) 0 ) ) sin 0 0 1 00 00 H H in the most cases. But in the Gaspar Strait, B Q U ) into Eqs. (8) and (9), we can get the values of the tidal ( P K ; Q P 1 00 00 − ∂ are greater than eight at all stations, suggesting predominance − = − ∂x K are generally smaller than 5 cms − ). B 0 A 0 ◦  , 00 , 00 00 2 0 0 2 = U S S f U f V B A ) f U , f V , H 00 180 − + 00 ξ A − + + − 00 00 A , 0 2 0 and 0 , 0 M 2 A cos A ωV , ωU H ωV appearing at Station B1. The tidal energy flux distributions of semidiur- ωU and M 00 ( U ( − − ◦ tide, the tidal elevation gradient vectors rotate counterclockwise at Stations ( 1 ( / A + = + , −  2 0 (0 + + 0 1 00 00 0 0 ◦ A K M U B A B A H = = + = = 1 0 00 00 0 slightly smaller than and approaches to 20 cms O By examining the tidal energy fluxes at each station, we found that the diurnal From the known tidal elevation gradient we have calculated the directions of the co- Figure 4 shows the tidal elevation gradient ellipses of The tidal currents are analyzed based on the ADCP observations on board of B A B A 1 1 H A1 and A2, andelevation rotate gradient clockwise vectors at rotate Stationsclockwise counterclockwise at B1, at Stations B2 Stations A2, and B2 A1 B3. and and B3. But B1, for and rotate counterclockwise at Stations A1,B3. A2 For and B2, and rotate clockwise at Stations B1 and observation stations. For and (3) yields ( K constituents nal tides are quite complicated: tidal energy flows from14.7 kWm the SCS to the JS with the maximum energy flux density of of the diurnal tides instations the with study the area. The phase-lags amplitudes being of around 30 are smaller than 5 cm.in It the is Karimata worth and mentioning Gaspar thatlag Straits. the changes The amplitudes of greater of diurnal amplitudes and tidesstudy smaller compared area spatial with is phase- those located of innodal semidiurnal band the tides of loop indicate the that (anti-nodal) semidiurnal the band tidal of waves. the diurnal tidal5 waves TRBMs, but showing in that the the jor tidal semi currents axis are lengths of of rectilinearO tidal type at current all ellipses stations. are The about ma- 10 cms tidal and co-amplitude lines asco-tidal done by charts Proudman of and Doodson the (1924)struct North in co-tidal Sea. constructing charts Since in the the purpose study area, of the the obtained present results work are is not4 not shown to here. con- Summary and discussion The sea level and currentthe data SCS and obtained JS at are fivethis analyzed stations region. to The along reveal results the three show characteristics sections that of between the tides ratios and of tidal diurnal currents in vs. semidiurnal tides amplitudes be obtained from the values of ( and 180 and ( where, ( elevation gradients ( tidal current ellipse parametersgradient from ellipse the has values a ofco-amplitude close ( and relationship co-phase-lag to contours theparticular, if tidal (see the regime, Appendix tidal that elevation B gradientangle is, for ellipse from the rotates detailed the counterclockwise distribution derivation). (clockwise) vector of the grad In where, elevation gradients of equilibriumBy tides inserting ( ( 5 5 20 25 20 10 15 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ). Table A2 ◦ 0.125 the angular speed. × ◦ ω , (B4) , (B3)   ) ) G G − − ωt ωt ( ( i i ), NAO.99b (Matsumoto et al., − − ◦ e e   0.5 × ◦ ∂y ∂x H∂G H∂G i i + + , (B5)  ) ∂y ∂x ∂H ∂H β 2844 2843 −   energy flux generally flows from the SCS to JS G 2 − + + ) ) S ωt G G ( i − − − ωt ωt ( ( i i Be e e +   ). (B2) ) ) α G + − G ∂y ∂x − H∂G H∂G ωt ( i i ort of assimilating the in situ observations into numerical model in i ωt ( ff − − i − e ), (B1) ) and DTU10 (Cheng and Andersen, 2011; 0.125 + Ae are its amplitude and phase-lag respectively, and ◦ ∂y G components of the tidal elevation gradient are ∂x ) ∂H ∂H  G G − y 1 2 resolution), GOT00.2 (Ray, 1999; 0.5 − 0.5   ◦ ωt = × ωt 2 1 ( 1 2 i ◦ and and e = ib = ( 0.25 x H cos( + H × ◦ ∂ζ ∂y a ∂ζ ∂x 1 2 H The With these long-term observational results, we can make an accuracy assessment = ≡ ≡ = = The equivalent complex form of Eq. (B1) is ζ respectively. The gradient vector on the complex plane is thus equalS to Appendix B: Relationship betweenthe the tidal rotation regime of tidal elevation gradient and The tidal regime forcalled a co-tidal specific constituent chart, is showingtidal conventionally elevation its illustrated of co-amplitude with the contours constituent a can and diagram, be co-phase written contours. as ζ The a where b that the relativeTherefore, discrepancies further are e generallythe greater future than is those worthwhilethe in for study providing tidal area. more Since elevations. accurate theing knowledge study tides of in area the the is SCS tidal oftenobservational or results systems chosen of Indonesian as in this seas an study (e. open are g., expected boundary Fang to in et be simulat- useful al., in 1999; improving Gao model et results. Appendix al., A: 2015) the Comparison with existing model results Table A1 showsvations the and comparison the0.25 of global the ocean tidal2000; tide 0.5 harmonic models constants TPXO7.2 between (Egbert obser- and Erofeeva, 2002; on the existingTPXO7.2, tidal GOT00.2, NAO.99b, models andtides for DTU10, (see the are Appendix A). compared study Thethe with comparison model area. our shows results that Four observations are the generallycies for representative amplitudes consistent of and with tidal the phase-lags model the of models, results observations.the from However, model discrepan- the TPXO7.2 observations are areGOT00.2, also not NAO.99b, and ignorable. compared The DTU10 with tidal do observations not currents in contain of tidal Appendix currents). A The (the comparison models shows except at Station B2. shows the comparison ofand the TPXO7.2. tidal The Cressman current interpolation harmonic method constants (Cressman, between 1959) is observations used here. but northward in the Gaspar Strait; 5 5 10 15 10 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , 2 2 β / / 1 1 (B6) (B7) ) ) and   α , ∂x ∂x B H∂G H∂G , can be further A ∂y ∂y ∂H ∂H B . Therefore, the − − G and ∂y ∂y A H∂G H∂G ce of Naval Research of the ∂x ∂x ∂H ∂H ffi ; it rotates counterclockwise ◦   2 2 . Their sum divided by 2 is the ). The directions of the vectors ◦ − + B # , (B14) , (B15) # 2 2 2 2 180 / /   0 or 180 1 1 rotates counterclockwise (clockwise) − to the vector grad = ), (B12) S ∂y H ∂y sin) sin) α . (B9) , (B8) ψ | | , and the second term represents a vector H∂G H∂G − A G G     (0 and β ). (B13) + + ( 2845 2846 ◦ β 2 2 1 2 grad grad ∂y ∂y   + + H∂G H∂G H H α || || can be readily obtained from the co-amplitude and ( G − + H H ∂x 1 2 ∂x ψ = H∂G H∂G whose tip traces an ellipse, called tidal elevation gra- = ∂x ∂x   ∂H ∂H , (B10) S grad grad " " | |   B 2 2 + + + . . ), (B11) + − # # A   2 2 2 B 2 | |   = + G G ∂x ∂x A ( H∂G ∂y H∂G ∂y ∂H ∂H This study was supported by the International Cooperation Program of and the angle / ). From Eqs. (B6) and (B7) the magnitudes of ) grad grad   + − G B lies between 0 and 180 H H + + | | ); it reduces to a straight line if 2 2 − ◦ ∂y ∂y ∂H ∂H ψ + +   A A < B 2 2 | | ( 90 (   − H is the angle from the vector grad H ∂x = ∂x ∂H ∂H ( ◦   and grad ψ 90 A > B grad grad | H | ( (" arctan arctan ( (" = = The first term on the right-hand side of Eq. (B5) represents a vector rotating counter- From Eq. (B5) we can see that the vector Yang, Y. J., andOceanic Fang, Eng., 29, G. 1075–1086, H.: 2004. Barotropic tide insea area the and northeast its adjacent South southwest1997 waters, (in China Oceanologia Chinese et Sea, with Limnologia English Sinica, IEEE 28, abstract). 198–208, J. = = = = = ψ B phase-lag of maximum gradient clockwise with its tip along arotating circle clockwise of radius with its tip along a circle of radius (Godin, 1972, § 2.6.1; Fang, 1984): semimajor axis length ellipticity β tidal elevation gradient vector dient ellipse. The parameters of the ellipse can be readily derived from grad co-phase contours in the co-tidal chart. Acknowledgements. China (grant no. 2010DFB23580),gram) the (grant National no. Basic 2011CB403502),search Research the Centers Program NSFC-Shandong of (grantopment China Joint no. (973 Program Fund U1406404), Pro- for (863 theFoundation Marine National Program) of Science China High (grant Re- (grant Technology no.of nos. Research 2013AA09A506), China 41476025 and and (grant the 41306031), Devel- Oceanography, no. State National the Oceanic 2200207), State Administration Natural the (grant Oceanic Science no.dation Basic Administration 2014G26), of the Research the National United Operating Science States Foun- Funds (grant no. of OCE-07-25935), and the the First O Institute of Cao, D. M., Fang, G. H., Huang, Q. Z., Yu, K. J., and Wang, X. Y.: Tidal regime in the Nansha United States (grant no. N00014-08-1-0618). References Beardsley, R. C., Duda, T. F., Lynch, J. F., Irish, J. D., Ramp, S. R., Chiu, C. S., Tang, T. Y., where tidal elevation gradient ellipse becomesif a counterclockwise (clockwise)(clockwise) rotating if circle direction of maximum gradient written as A when B α where A 5 5 10 15 10 15 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ect ff 2848 2847 cient inverse modeling of barotropic ocean tides, J. Atmos. ffi baroclinic tides in the Indonesian seas, Oceanography, 18, 2 M 62–73, 2005. isons to observations, J. Geophys. Res., 113, C07031, doi:10.1029/2007JC004677,Karimata 2008. Strait througflow from December1–6, 2007 2013. to November 2008, Acta Oceanol. Sin., 32, tidal constituents in the179, Indonesian 2013 (in adjacent Chinese seas, with Advances English abstract). in Marine3, Science, 193–210, 31, 1981 166– (in Chinese with English abstract). investigations of the SouthScripps China Institute Sea of and Oceanography, La the Jolla, Gulf CA, of USA, Thailand 195 pp., 1959–1961, 1961. NAGA Rep. 2, NASA/TM-1999–209478, Goddard Space Flight Centre, Greenbelt, MD, USA, 1999. Oceanography, 18, 74–79, 2005. Ocean. Tech., 19, 183–204, 2002. theory and observations, Marine Sciences, 8, 1–11, 1984 (in ChineseGeophys. with J. English abstract). Roy. Astr. S., 73, 65–82, 1983. constituents in the South19, China 845–869, Sea, 1999. Gulf of Tonkin and Gulf ofSulistiyo, Thailand, B., Cont. Shelf and Res., Li,Sea S. to Indonesian J.: seas Volume, in,doi:10.1029/2010JC006225 heat, the 2010. and boreal winter freshwater of transports 2007–2008, from J. Geophys. the Res.,Report South 115, 77-10, C12020, China Institute of Ocean Science, Victoria, B. C.,in Canada, the 101 South pp., China 1977. Sea with adjoint method, Ocean Model., 92, 101–114, 2015. waters and polar seas, J. Geophys. Res., 116, C11001,, doi:10.1029/2011JC007172 1959. 2011. on transport and mixing, J. Geophys. Res., 101, 12353–12373,TOPEX/POSEIDON 1996. altimeter data into hydrodynamical model:model a around global model Japan, and J. a Oceanogr., regional 56, 567–581, 2000. TOPEX/POSEIDON, J. Geophys. Res., 99, 24867–24881, 1994. estimates in MATLAB using T_TIDE, Comput. Geosci., 28, 929–937, 2002. T. Roy. Soc. A., 224, 185–219, 1924. Robertson, R. and Ffield, A.: Baroclinic tides inSusanto, the R. Indonesian D., Wei, seas: Z. tidal X., fields Adi, and R. compar- T., Fan, B., Li,Teng, F., S. Fang, G. J., H., and Wang, X. Fang, Y., Wei, G. Z. X., H.: and Observations Wang, Y. of G.: Numerical the simulation of principal Wang, J. and Fang, G. H.: An analysisWyrtki, of incomplete K.: hourly Physical tidal oceanography records, of Acta the Oceanol. Southeast Sin., Asian waters, scientific results of marine Ray, R. D.: A GlobalRay, R. D., Ocean Egbert, G. Tide D., and Model Erofeeva, S. Y.: from ARobertson, brief R. overview TOPEX/POSEIDON of and tides Altimetry: Ffield, in A.: the GOT99.2, Indonesian seas, Fang, G. H.: Basic characteristics of the verticalFang, structure G. of H. tidal and currents Ichiye, – T.: A On comparison theFang, of vertical G. structure H., of Kwok, tidal Y. currents K., in Yu, a K. homogeneous sea, J., andFang, G. Zhu, H., Y. Susanto, H.: R. Numerical D., simulation Wirasantosa, S., of Qiao, principal F. L., tidal Supangat, A., Fan, B.,Foreman, Wei, M. Z. G. X., G.: Manual for tidalGao, heights X. M, analysis Wei, Z. and X., Lv, prediction, X. Q., Pacific Wang, Marine Y. G., andGodin, Science Fang, G.: G. The H.: Numerical Analysis study ofHatayama, of Tides, T., tidal Awaji, University dynamics T., of and Toronto Akitomo, Press, K.: Toronto, 264 Tidal pp, currents 1972. in the Indonesian seas and their e Cheng, Y. C. and Andersen, O.Cressman, B.: G. Multimission P.: An empirical operational ocean objective analysis tide system, modeling Mon.Egbert, Weather G. for Rev., D. 87, and shallow Erofeeva, 367–374, S. Y.: E Matsumoto, K., Takanezawa, T., and Ooe, M.: Ocean tide models developedMazzega, by assimilating P. andPawlowicz, Berge, R., Beardsley, B., M.: and Lentz, Ocean S.: ClassicalProudman, J. tides tidal and harmonic Doodson, A. analysis T.: in The including principal constituent error of the the tides of the Asian North Sea, Philos. semienclosed seas from 5 5 15 10 20 10 15 25 30 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 671Nv2008 2009–12 Nov 2010 301 1687–15Nov 96019Oct S 36.6 S 48.0 S 44.2 S 42.8 S 49.0 0 0 0 0 0 40.0 05.5 46.8 17.0 54.9 ◦ ◦ ◦ ◦ ◦ 4 Dec 2007–12 Jan 2008 15 Feb–1 Nov 2008 12 May–11 Oct 2008 19–24 Oct 2009 7 Nov 2008–17 Oct 2009 17 Feb–29 Sep 2011 2850 2849 E 1 E 1 E 2 E 2 E 1 0 0 0 0 0 50.1 59.2 09.6 15.0 33.0 ◦ ◦ ◦ ◦ ◦ Station LongitudeA1 Latitude Depth 106 (m) A2 107 B1 107 B2 108 B3 108 Sea levelCurrent profile Sea level 2 DecCurrent 2007–5 profile May 2008Sea levelCurrent profile 2 Nov 12 2008–11 May–3 Nov Nov 156 2010 2008Sea level 18 Oct 2009–11 Nov 2010 740 176 390 6 Nov 2008–9 Sep 2009 308 Current profileSea levelCurrent profile 13 Jan–14 Feb 2008 13 Jan–5 May 2008 33 114 B1 B2 B3 Station Measuring parameterA1 Starting and ending dates Length (d) A2 Record length of the obtained data. Locations and water depths of the observational stations. Table 2. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) ◦ ( ) ◦ G ( have λ λ B3 192.6 175.2 158.0 333.4 338.0 338.1 168.8 159.9 155.8 356.7 343.3 180.2 / / / / / / / / / / / / and 2.28.7 68.5 0.5 96.5 8.7 35.211.7 343.9 339.4 57.2 36.2 (cm) ϕ H ) ◦ ( ) G ◦ ( B2 316.6 12.6 324.9 348.8 294.2 355.2 288.0 338.0 308.9 153.4 272.1 158.1 293.3 158.1 300.3 339.9 283.4 335.8 188.7 176.7 198.5 163.3 344.3 0.2 7.31.9 335.0 117.5 5.60.6 123.8 192.6 / / / / / / / / / / / / 54.436.5 45.4 354.7 (cm) H ) ◦ ( : Greenwich phase-lag of the maximum G r ϕ ϕ B1 0.19 113.3 0.35 18.5 : length of minor semi axis (i.e. minimum 7.44.3 324.3 236.4 5.32.0 160.0 206.6 − − w 59.639.6 33.3 344.7 (cm) H ) 1 2852 2851 − ) ◦ ( with signs representing the direction of the current vector G (cms w/W A2 w respectively. 7.24.4 305.4 322.9 2.70.8 62.2 284.9 ◦ 50.837.4 27.0 326.8 (cm) ) H 1 − ) 9.63 0.70 0.07 136.6 8.02 3.34 0.42 114.2 2.252.341.830.97 0.58 0.38 0.26 0.16 108.0 0.16 0.19 128.9 0.092.41 92.1 3.002.280.80 0.16 0.58 0.06 0.79 103.4 0.19 0.30 8.7 0.37 164.3 ◦ ( 11.51 1.89 0.16 144.9 10.31 1.97 0.19 120.3 G (cms erence of 180 ff W A1 2.60.4 82.3 306.6 3.8 341.3 7.8 306.1 : direction of the major semi axis measured clockwise from north. Both 59.1 30.0 42.4 329.1 (cm) λ H : ellipticity, equal to the ratio r Station A2 Station A1 2 2 1 1 2 2 1 1 1 1 2 2 Vertically averaged tidal current ellipse. Tidal harmonic constants at the observation stations. : length of major semi axis (i.e. maximum speed); Constituent (a) K (b) K O Q M S N O Q M S N 2 1 2 1 1 2 rotation (positive/negative for counterclockwise/clockwise); speed); W current speed; two values with a di S N Constituent K Q M O Table 4. Table 3. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) ◦ ( 8.0 0.7 ) λ / / 85.3 ◦ ( 325.5 326.9 147.7 324.5 296.1 144.6 347.4 352.2 174.0 357.4 299.3 308.5 129.5 307.9 / 305.5 5.8 4.8 1.5 5.5 / / / / / / / / / / / / / / / θ 16.2 13.8 17.2 − − − − ∆ − − − ) ◦ ( θ ) ◦ ( ) 264.0 145.5 184.8 146.9 326.4 327.7 205.1 144.5 187.8 116.1 358.6 324.6 262.5 167.4 289.7 119.3 193.5 172.2 342.9 354.0 269.0 177.4 292.5269.1 188.0 180.7 205.9 128.5 349.4 309.5 217.8 127.9 337.4185.0 265.3 125.5 1 / / / / / / / / / / / / / / / / / / − (kWm F r ϕ ) 0.010.36 25.1 7.8 0.20 89.0 0.21 89.1 0.080.04 37.8 157.4 0.05 5.0 1 − − − − − − − − : north component of energy flux density; ) y 0.0807 0.0865 158.9 0.8 0.0079 0.0093 212.6 32.4 0.1135 0.1135 181.6 18.3 0.2759 0.3091 153.2 0.2249 0.2270 187.9 11.2 0.3507 0.3893 154.3 5.0011 5.3576 159.0 7.5581 8.3789 154.4 6.0846 6.9176 151.6 3.0800 3.0806 178.8 1 2854 2853 F − − − − − − − − − − − (kWm y : direction of energy flux density, measured clockwise F θ (cms ) w 1 − ) 1 ). − 0.0023 0.0066 0.0069 340.7 2.6 0.0312 0.0050 0.0746 0.1175 0.1392 327.6 0.0032 0.1394 0.0310 0.1690 1.9216 3.6167 3.2910 0.0628 λ 2.254.301.100.86 0.04 0.06 0.02 0.40 146.4 0.08 0.10 178.6 7.77 0.15 0.02 84.0 4.325.414.341.40 0.39 1.07 0.09 0.67 162.9 0.30 0.16 112.6 2.324.051.100.86 0.36 0.31 0.16 0.04 169.4 0.05 − − − − − − (kWm 10.26 0.24 0.02 4.8 13.32 0.05 0.00 82.4 12.25 1.27 0.10 109.7 19.08 0.77 0.04 13.5 11.56 1.55 0.13 25.9 θ x (cms F = W : direction of energy flux density, measured clockwise from the major axis of θ ∆ Station A2 Station A1 2 2 1 1 2 2 1 1 1 1 2 2 Station B2 : east component of energy flux density; Station B3 Station B1 N S N M S Q M Q O O (b) K (a) K Constituent : magnitude of energy flux density; x 2 2 2 1 1 1 2 2 2 1 1 1 from north; the current ellipse ( F F 1 1 1 2 2 2 Tidal energy flux density. Continued. O Q M S N (e) K Constituent (c) K (d) K O Q M S N O Q M S N Table 5. Table 4. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (cm) ∆ ) ) ◦ ( 2 ◦ ( S G 0.9 1.5 0.2 9.6 7.3 θ 22.4 − − − − − ∆ − 1.73.0 123.90.9 93.60.6 168.1 1.7 2.6 53.4 0.7 2.7 82.3 2.30.5 2.1 8.80.2 135.31.6 216.12.7 2.3 2.6 40.2 2.9 62.2 3.64.8 159.1 1.4 7.9 156.06.1 190.4 1.7 5.3 178.8 0.6 160.0 4.3 3.5 2.0 5.4 97.62.7 146.54.0 19.5 2.9 5.6 2.2 94.1 123.8 3.2 6.8 5.2 2.9 85.84.5 146.74.5 5.6 8.08.7 6.7 97.1 96.5 9.7 4.2 (cm) ) H ◦ ( θ (cm) ∆ ) ) ◦ 1 ( 2 − M G 2.21.9 76.9 117.5 2.22.0 1.4 3.36.6 69.32.3 353.12.2 2.4 63.5 0.2 6.4 68.5 0.2 5.46.4 18.0 357.54.44.8 339.1 3.3 3.8 346.4 2.9 341.3 0.6 7.6 1.1 5.7 314.37.3 325.65.4 305.3 3.3 318.44.4 1.3 322.9 3.4 1.8 1.1 1.0 235.74.0 285.14.2 231.6 2.5 4.3 254.6 3.7 236.4 0.5 2.8 1.3 2.6 13.24.2 93.1 3.8 9.7 1.2 5.1 (cm) (kWm H F ) (cm) 1 ∆ − ) ◦ ( 1 0.0084 0.0104 143.7 0.0787 0.0853 202.6 86.5 0.0120 0.1109 263.8 0.1394 0.1696 145.3 0.8 0.0282 0.0323 150.8 22.9 0.5330 0.6319 147.5 0.3511 0.3512 178.4 0.2354 0.3530 131.8 2.3 7.0172 8.3251 147.4 0.5 5.3376 7.8035 133.2 4.7 6.1473 7.3562 146.7 1.2 0.6735 0.6754 175.7 1.7 4.2226 6.3772 131.5 12.2 O 2856 2855 G 11.290014.6383 11.5554 14.7337 167.7 173.5 0.3 1.3 − − − − − − − − − − − − − erence, with subscripts m and o representing model and observation respectively. (kWm ff − − y F 37.936.5 339.5 354.7 36.6 9.9 35.3 337.836.8 335.337.9 335.3 4.1 35.2 338.4 5.3 343.9 5.6 4.4 45.242.0 323.9 325.341.541.4 325.6 4.9 42.4 328.6 2.8 329.1 2.7 38.3 1.1 37.8 325.237.4 323.838.4 322.2 1.4 327.237.4 2.0 326.8 3.0 40.3 1.0 36.6 348.040.3 337.537.4 337.5 2.4 39.6 343.1 5.6 344.7 5.1 38.1 2.4 35.3 338.035.9 335.3 10.9 337.1 12.2 11.1 (cm) H ) 1 is the vector di − 2 / 1 i (cm) 2 ) o ∆ 0.0062 0.0089 0.0065 0.0110 305.90.0328 0.4 0.1103 0.0966 0.0115 0.0289 0.03110.0157 338.3 0.3395 0.0098 0.2630 4.4794 0.0752 0.4329 0.43945.6926 350.1 4.0403 2.4623 1.6738 0.0506 4.7790 G ) − − − − − sin ◦ (kWm o 1 ( H K x G − F m G sin m (cm) H ( H + 2 ) o G cos Station B2 Station B3 Station B1 o H 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 − m N N S S M N M Q S Q O M O (e) K (d) K Constituent (c) K O Q TPXO7.2 55.3 34.2TPXO7.2 10.7 51.8 34.6 5.6 TPXO7.2GOT00.2NAO.99b 66.7DTU10 61.5 23.0observation 56.6 26.5TPXO7.2 10.8 25.5 59.1GOT00.2 59.0 30.0 4.4 NAO.99b 26.8 5.2 51.0DTU10 53.4 28.1observation 3.3 50.8 24.3TPXO7.2 22.8 50.8 1.0 GOT00.2 52.6 27.0 3.6 NAO.99b 24.5 3.7 64.6DTU10 61.5 43.8observation 2.9 61.8 30.5 12.4 30.8 59.6GOT00.2 59.8 33.3 3.5 NAO.99b 33.4 3.4 DTU10 54.4observation 0.2 52.5 27.8 30.3 54.4GOT00.2 55.0 16.6 45.4 NAO.99b 31.0 14.2 DTU10 54.3observation 13.7 53.7 27.4 30.1 57.2 54.6 36.2 9.0 30.1 6.9 6.5 Comparison between four tidal models and observations. G Continued. cos m H ( h B2 B3 Station Source A1 A2 B1 ∆ = Table A1. Table 5. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) 1 − (cms ∆ ) ◦ ( η ) 1 − 1 2 S O (cms V ) ◦ ( ξ ) 1 − 0.70.9 318.5 244.70.81.1 295.1 337.6 1.10.7 4.3 323.31.0 359.0 293.8 357.7 0.7 0.1 212.7 311.5 3.5 1.0 0.6 215.3 224.2 1.0 0.5 4.5 322.63.4 12.83.24.0 311.4 11.8 327.83.6 86.52.7 114.5 8.0 112.2 9.0 30.05.6 9.79.1 74.0 21.1 116.3 6.7 6.2 32.06.3 18.9 146.15.6 360.0 193.2 6.9 1.8 6.8 7.3 159.6 16.0 0.7 196.3 2.40.7 244.3 163.0 104.10.9 8.6 7.0 1.0 255.6 183.9 329.4 1.0 6.5 1.7 229.6 270.1 1.8 2.2 201.5 204.4 1.7 1.2 2 / (cms 1 i 2 U ) o η ) 1 sin − o V − m (cms η ∆ sin m V ( ) ◦ 2858 2857 + ( 2 ) η o η cos ) o 1 V − − 2 1 m K η M (cms cos V m V ( ) + ◦ 2 ( ) o ξ ξ sin o ) U 1 − − m ξ sin (cms m U U ( + 2 ) o ξ cos o U − Comparison between TPXO7.2 tidal currents and observations. m The map of the Indonesian seas (upper), and observational stations (lower). Isobaths TPXO7.2TPXO7.2observation 2.1TPXO7.2 175.1observation 2.1 1.1TPXO7.2 311.0observation 12.0 2.8 1.2 3.2 142.2 34.4 1.3 4.1 2.6 2.5 5.4 310.8 269.5 31.2 23.9 3.2 2.5 1.4 223.5 179.2 4.0 2.6 3.5 180.8 205.7 2.9 1.6 TPXO7.2TPXO7.2 8.2TPXO7.2 25.1 5.3TPXO7.2 23.5 19.7 5.9TPXO7.2 143.0 158.8 13.7 9.5 120.5 13.5 87.6TPXO7.2 9.0 8.9 180.9 75.1 6.1 2.2 206.1 15.8 3.3 160.3 2.2 237.7 7.4 1.6 6.5 13.2 3.1 observationobservation 2.2 118.5observation 2.9observation 4.5 9.4 2.9 137.5 observation 83.5 10.7 11.3 113.0 143.0 13.0 4.4observation 262.4 85.6 6.1 279.2 observation 1.1 146.7 6.4 263.3 0.6 82.0 2.1 304.3 3.0 188.1 ξ cos m U ( h A2 B1 B2 B3 Station Source A1 A2 B1 B2 B3 A1 ∆ = Figure 1. are in meters. Table A2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 1 O , 1 K 2860 2859 at the observational stations. Red/blue color indicates counterclockwise/clockwise The vertically averaged tidal current ellipses of principle tidal constituents Horizontal tidal energy flux density. 2 S and 2 Figure 3. M rotation. Dots on the ellipses represent the tips of the tidal current vectors at 00:00 GMT. Figure 2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | at the observational stations. 2 S and 2 M , 1 O , 1 K 2861 The tidal elevation gradient ellipses of Red/blue color indicates counterclockwise/clockwise rotation. Figure 4.