JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 89, NO. C1, PAGES 607-615, JANUARY 20, 1984 Numerical Simulations of the Ross Sea Tides DOUGLAS REED MACAYEAL1 GeophysicalFluid DynamicsProgram, Princeton University Tidal currentsbelow the floating Ross Ice shelfare reconstructedby using a numericaltidal model. They are predominantlydiurnal, achievemaximum strengthin regionsnear where the ice shelf runs aground,and are significantlyenhanced by topographicRossby wave propagationalong the ice front. A comparisonwith observationsof the vertical motion of the ice shelf surfaceindicates that the model reproducesthe diurnal tidal characteristicswithin 20%. Similar agreementfor the relatively weak semi- diurnal tideswas not obtained,and this calls attentionto possibleerrors of the open boundaryforcing obtained from global-oceantidal simulationsand to possibleerrors in mapping zones of ice shelf grounding.Air-sea contact below the ice shelf is eliminated by the thick ice cover. The dominant sub-ice-shelfcirculation may thus be tidally induced.A preliminaryassessment of sub-ice-shelfconditions basedon the numericaltidal simulationssuggests that (1) strongbarotropic circulation is driven along the ice front and (2) tidal fronts may form in the sub-ice-shelfcavity where the water column is thin and wherethe buoyancyinput is weak. INTRODUCTION in Figure2), wherea bore hole was openedfor severaldays Tidal currents are the strongestobserved form of seawater [Cloughand Hansen, 1979; Jacobs and Haines, 1982]. motion in the cavity below the floatingice shelfin the south- Tidal currents can be difficult to reconstruct on the basis of ern Ross Sea [Williams and Robinson,1979, 1980; Jacobs and observedtidal amplitudeand phasealone because of complex Haines,1982]. The thickice platform shown in Figure1 elimi- basinshape and topography[Williams, 1976]; hence,the scar- nates air-sea contact; thus sub-ice-shelf ocean circulation and city of reliabletidal currentmeasurements presents a serious heat transport may be forced primarily by tidal currentsor by obstacleto the investigationof sub-ice-shelfoceanography. related processessuch as tidal current rectification and tidal Basintopography, for example,may exerta particularlyinflu- front formation [MacAyeal, 1983]. Given presentice flow pat- entialcontrol on the currentsbecause, in polarlatitudes, topo- terns,approximately 25% of the snow that accumulatesover graphic Rossbywaves can be excited by the diurnal tide. Antarctica flows through the Ross Ice Shelf and ablates into Thesewaves are commonlyobserved in the Arcticalong con- the Ross Sea by basal melting or by icebergcalving [Hughes, tinentalslopes and aboveisolated seabed bumps [Cartwright, 1975]. The Ross Sea tidal regime may thus provide a direct 1969;Huthnance, 1974, 1981; Cartwright et al., 1980;Thomson and influential li•k between the ocean and the earth's largest and Crawford,1982]. It is thereforereasonable to expectsuch ice mass..This paper presentsthe results of numerical tidal wavesalong sectionsof the ice front, along various seabed simulations undertaken to reconstruct the Ross Sea tidal cur- ridgesbelow the ice shelf,and along the continentalslope rents and to estimate their influence throughout the sub-ice- north of the Ross Sea. As a result of their strong currents, shelfcavity. thesewaves could induce significantstirring in the sub-ice- The Ross Ice Shelf is an integratedice massthat is flexible shelfenvironment. Current meter records, however, are gener- when deformed over large horizontal length scalessuch as ally requiredto detecttopographic Rossby waves [Cartwright, those imposedby tides in the water below. As a result of its 1969]; thus, to detect them below the ice shelf, the available slow horizontal movement,the ice shelf has provided a natu- observationsof tidal amplitudeand phasemust be coordi- ral platform upon which the tidal amplitude and phase have natedwith numericalsimulations capable of accuratelyrecon- been measured (the 10 observation stations are shown in structingthe tidal currents. Figure 2) [Williams and Robinson,1979, 1980; Williams, 1976, The numericaltidal simulationsconducted in this studyare 1979' Thiel, 1960; Thiel et al., 1960].These measurements intended to amplifythe existingobservations by calculating show that the diurnal tide is stronger than the semidiurnal the sub-ice-shelftidal currentsand by extendingthe mapsof tide and that the tidal amplitudesare largest in areas near tidal amplitudeand phaseacross regions not coveredby the data collection network. where the ice shelfruns aground. In contrastwith the tidal amplitudeand phase,tidal cur- MODEL EQUATIONSAND PROCEDURE rents and their effect on the sub-ice-shelf water column have not been measuredreliably becauseof the thick and impen- The governing equations for barotropic tidal motion em- etrable ice cover. The few available tidal current measure- ployedin this studyare [Nihoul, 1975,p. 51] ments come from north of the ice front (MCM and "current •(Du)/•t + V-(Duu)= -gDV(rl- •]e)-fDez x u- klulu meter" in Figure 2) [Heath, 1977; Gilmouret al., 1962; Jacobs and Haines, 1982] and from a singlesub-ice-shelf location (J9 + vDV2u (1) and •Now at Departmentof the GeophysicalSciences, The University •rl/•t + V-(Du) = 0 (2) of Chicago. where u is the depth-averagedhorizontal velocity, r/ is the Copyright 1984 by the American Geophysical Union. departureof the sea surfaceor ice shelfbase from the level of Paper number 3C 1414. rest,D is the instantaneousdepth of the water layer (extending 0148-0227/84/003 C- 1414505.00 from the seabedto either the sea surfaceor the ice shelf base), 607 608 MACAYEAL' SIMULATION OF Ross SEA TIDES 100øW 110øW 120øW 150øWl 80 ø 150øE 120øE 110øE 100øE 80øS OOOE 30øS WestAntarctica .• • EastAntarctica / 11 • / "'.:•:•;:y-•,i•-,:... '- 10øE ......... 120øW , ..'1.-:'•'•' '•'-..••••'::•,•,•':J'•' :•...•?"•T ......tarctic Mountains 20øE ß.:.:-,:•. -•7.--:....: •.. '":":•:•:•f:f.:::':"::f:-'::''BCF::::':::-'...... ....."-: '. :.':•'•".."::ii?::: ........ •:..e. :•... :i:;•::.:::-•;i:::i:i::•::;:!:.:..:.::.::.i:::i::•:..:......,...... =====================.'.... '- '.:---::L:-u:y•5:-:..',•.:.-.,• . :.'.:.:....:::;.';::•::;::;:::5::-::.:;;.::::..:;;•f:: ..:•.::•'::::........ :-:..::L::::.:•: .... .. 130øW 130øE :..?-'.•'i:•.t•?.....:...e. •.9.....c...•.....i..• :..'•:"d?:•i.":':::.•:?!.:i':.:'':-'-•.'-!;• ....... ::::.-'•"':::i!i!:Y:":"?::?:.?'-•:sd':•:::::::::::::::::::::::::::::::::::::::i:..:- '....!•: ":!•:'..'"':i:::::::::11111;i!:i•;!•:i,•11:i::,:.; :.:-:ii':i::7:::.'•:•il;i;:!i'::ii::;•ii:.':':::;:......... ...'.. --:.:::.-'f.:.. •:•:-::.:-._ %-.•:: •:-'•. :•: L•.•?i:...•:% :.:%:,::.--,-... ß • ' """ '"• '"" '•' ""• '"--'••'••••••••••••'••,-•"• •.:c.•-•:-.t;.:. .• • ...... :-:• ::...--• •,, ... ß.... ......... --:y-.:..- -.-:.-.::::.:.:: ...... •:...: ::.-:•-•-;:;.:..... - - ......:'•&•'- '•..• .;' .z•-.'-.-.•' '"';:,,• .........•,,,,,,,"• .....;........... ,•...... '.'"'.::":':'.; ":•......'•-•'. '•c• '•'•:'•'•t";'%:.%:?•¾. .....--' 140øE 140øW / .... :t•.- -...;-.•-:.:::: • .......;....... •....... -,.-' ...:......: ..::::..:.::::•::•.'..• ,••• • o::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: o-•• • 500 ,ooo ] o Bank ß • •o • .2 50øE 150øW / oo 70øS• RossSea • • ••/Ca•e__t) '• ,0os lO• 160øW 1 70øW W180øE 1-70øE 160øE Fig. 1. At themargins ofthe West Antarctic Ice Sheet, large floating ice shelves (indicated byshading) extend seaward from wherethe ice floatsfree of the seabed.The RossIce Shelf,shown above, occupies the southernhalf of the RossSea. It rangesin thicknessfrom 1100to 100m, coversan areaof 580,000km :, and flowstoward the openocean at ratesof up to 1200m/yr. Air-sea contact is prohibitedwithin the sub-ice-shelf cavity; hence, tidal currents and related tidally driven processesmay contribute to oceancirculation below the i•e shelfand associated basal-ice ablation. Although observations of the tidal amplitudesand phaseshave been made at 10 locationsdistributed across the ice shelfcovered portion of the RossSea (indicated above by dots)[Williams and Robinson,1979, 1980], this paperpresents the resultsof numericaltidal simulationsconducted to-investigate the sub-ice-shelftidal currents.This map is tracedfrom the polar-stereographic projectionof the AmericanGeographical Society of New York [ 1970]. lie is the equilibriumtidal elevationspecifying forcing by the significant influence within several kilometers of coasts sun and moon [Dietrich,1963, p. 443], g = 9.81 m/s2 is the [Hughes,1977; Holdsworth,1977; MacAyeal, 1983], its effect gravitationalacceleration, f-- 1.42 x 10-½ s-• is the Co- on tidal propagationthrough the centralpart of the basinis riolis parameterat the meanlatitude of the RossSea (78øS), k thoughtto be minor [Williamsand Robinson, 1981]. is the nondimensionalquadratic bottom-frictionparameter Boundaryconditions applied at coastsare u-e, = 0, where equalto 2.5 x 10-3 in ppenwater and 5.0 x 10-3 in iceshelf e, is the outwardpointing unit vectorthat is perpendicularto coveredwater [Rhmming and Kowalik,1980, p. 17], v = 100 the coastand •(u- e•)/•n + (2/Ax)uß e, = 0, wheree, is the unit m2/sis the eddyviscosity (selected arbitrarily to supressnu- vector tangent to the coast, •(u-et)/c•n is the gradient of the mericalnoise, but otherwiseof small importance),and e• is a longshoreflow in the direction of e., and fix is the finite unit vectorthat is perpendicularto the geoid. differencegrid point spacing(10 km). The first conditionlisted The elastic strength of the ice shelf and its inertia