JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. B9, PAGES 20,151-20,163, SEPTEMBER 10, 1996 Diurnal/semidiurnal polar motion excited by oceanic tidal angular momentum B.F. Chao,1 R. D. Ray,2 J.M. Gipson,3 G. D. Egbert,4 and C. Ma I Abstract. The axialcomponent of the oceanictidal angularmomentum (OTAM) hasbeen demonstratedto be responsiblefor mostof thediurnal and semidiurnal variations in Earth's rotationalrate. In thispaper we studythe equatorial components of OTAM andtheir correspondingeffects on the orientationof Earth'srotational axis, or polarmotion. Three oceantide models derived from TOPEX/Poseidonsatellite altimetry are employed to predict thepolar motion excited by eightmajor diurnal/semidiurnal tides (Q1, O1, P1, K1, N2, M2, $2, K2).The predictions are compared with geodetic measurements of polar motion from both long-termobservations and during the intensivecampaign Cont94. The progradediurnal and progradeand retrograde semidiurnal periods are treated, whereas the retrograde diurnal polar motionis not treated(because it cannotbe observeddirectly and uniquely.) The comparison showsgenerally good agreement, with discrepanciestypically within 10-30micro-arc- secondsfor thelargest tides. The eightfides collectively explain nearly 60% of the total variancein subdailypolar motion during Cont94. This establishesthe dominant role of OTAM in excitingthe diurnal/semidiurnalpolar motion and paves the way for detailed studiesof short-periodnontidal polar motion. The presentaccuracy, however, is inadequate to shedlight on the progradediurnal polar libration. Introduction excitationvia the conservationof angularmomentum by the ocean tides. Two mechanisms are involved in this excitation Earth'srotation varies slightly with time dueto geophysical process [e.g., Munk and MacDonald, 1960]: (1) tidal processesthat involve mass movement on or withinthe Earth. deformationin the form of tidal heightvariation that changes We say that these geophysicalprocesses "excite" Earth Earth'sinertia tensor (referred to as the "mass"term); and (2) rotationalvariations, which manifestthemselves as changesin tidal motionrepresented by tidal currentthat evokesangular boththe rotational speed and the rotational axis orientation.The momentumrelative to the solid Earth as a whole (referred to as scalarvariation in the rotationalspeed is usuallyexpressed in the "motion"term). Connectedby the conservationof mass, termsof thetime derivativeof the universal time UT1 (or often theyare collectively called the oceanic tidal angularmomentum the length-of-dayif the variationin questionis longerthan a (OTAM). In the presenceof OTAM the conservationof the day). The vectorialvariation in the rotationalaxis orientation total angular momentumof the solid Earth-oceansystem relativeto the terrestrialreference frame is known as the polar dictateschanges in the solidEarth' s rotation. motion. Thispaper compares the polar motion observed by thespace One importantexcitation source is the luni-solartides, as geodetic techniquesof very-long-baselineinterferometry they influenceEarth's rotation in a variety of ways [e.g., (VLBI) and satellite laser ranging (SLR), with model Lambeck, 1980]. The one under considerationhere is the predictionsof diurnaland semidiurnal OTAM derivedfrom the TOPEX/Poseidonaltimetry data [e.g., Fu et al., 1994; Le Provostet al., 1995]. At any givenperiodicity (such as tidal) the polar motioncan be decomposedinto the progradeand 1LaboratoryforTerrestrial Physics, NASA Goddard Space Flight Center,Greenbelt, Maryland. retrogradecomponents (or "wobbles") [Munk and Mac- 2HughesSTX, NASA Goddard Space Flight Center, Greenbelt, Donald, 1960]. Here we treatboth componentsat the diurnal Maryland. and semidiurnalperiods, except the retrogradediurnal polar 3NVI, Inc.,NASA Goddard Space Flight Center, Greenbelt, motion for which, for reasonsdescribed below, only the tide Maryland. modelpredictions will be presented.In addition,results for 4Collegeof Oceanicand Atmospheric Sciences, Oregon State UT1 thatare updated fxom Chao et al. [1995]will be presented University,Corvallis. for comparison. Copyright1996 by theAmerican Geophysical Union. Polar Motion Excitation Dynamics Papernumber 96JB01649. Both kinematic and dynamic complicationsset the polar 0148- 0227/96/96JB-0164959.00 motionproblem apart from the UT1 problem.Kinematically, 20,151 20,152 CHAOET AL.:DIURNAL/SEM•IURNAL POLAR MOTION UT1 is a scalarquantity and all observersagree on its value in a right-handedterrestrial coordinate system. Its physical independentof the referenceframe. The rotationalaxis excitationconsists of (1) the massterm: the complex-valued orientation,however, is a referenceframe-dependent vectorial quantityc whosereal andimaginary parts are the variationin quantity:While methods that are sensitive to absoluterotation thexz andyz componentsof theEarth's inertia tensor due to the (suchas those based on gravimetryor gyroscopicprinciples) massredistribution; (2) the motionterm: the complex-valued can potentiallymake direct measurement of the "true"polar relativeangular momentum h whosereal andimaginary parts motion[Chao, 1991], presentprecise measurements of Earth are simply the x and y componentsof the relative angular rotation have been solely obtained from space geodetic momentum.Here ctoo andh collectivelyrepresent the oceanic techniqueswhich measurethe relativerotation. The space tidal angularmomentum (OTAM). When normalizedagainst geodetictechniques do not determinethe polar motion A too as expressedin equation (1), they representthe uniquely;instead, they observe the orientationof thecelestial (dimensionless)excitation for the polarmotion. ephemerispole [e.g., Eubanks,1993; Soverset al., 1993; The first term in (1) arises from the Chandler wobble Herring and Dong, 1994]. As a result,the retrogradepolar resonance. The numerical factors are the transfer functions motion at the diurnaltidal periodsis observationallyaliased [Munkand MacDonald, 1960] accountingfor Earth'selastic with andhence inseparable from thecorresponding nutations. yielding effect and the decouplingof the fluid core from the Theseterms are relativelylarge as theyinclude the nutations mantle. The second term arises from the FCN resonance. driven by the externaltidal torquesand the polar motion Except in the retrogradediurnal band near the resonance,its resultingfrom the largesolid Earth fides. transfer functions are much smaller than their Chandler Dynamically,in contrastto the simplesystem function for counterpart(especially for the motionterm), so thatthe FCN UT1 excitation,the polar motion systemfunction can be term generallycontributes much less to the polar motion characterizedby a linearoscillatory system with two distinct excitationthan the Chandlerterm, and possibleerrors in the natural frequenciesof resonance:the progradeChandler FCN transferfunctions become numerically unimportant. wobblewith a periodof about434 days,and the retrograde free The mass term c in OTAM arisesfrom the tidal height, core nutation (FCN) of the fluid core manifesting as a whereas the motion term h arises from the tidal current: retrogradenearly diurnal free wobble with frequency -(1+1/430) cycleper siderealday (cpsd)in the terrestrial frame [e.g., Herring et al., 1986; Merriam, 1994]. In the c<t)=-a4p f f ocean;(•,t)sinOcosOet•'d• (2a) retrogradediurnal band the near-resonanceeffect is very sensitiveto the FCN period and Q [e.g., Wahr, 1981] (especiallyfor componentsclosest to FCN periodsuch as K1), h<t)=-aSpf f o•ean [u<f•,t)cos0 +iv<fLt)lH(f•)ea'df•<2b) sothat detailed knowledge about the OTAM excitationof polar motionand nutation can in principleprovide useful constraints Inthese equations, a isEarth's mean radius; p = 1035kg m '3 is onnutation models and the determination of FCN periodand Q. the mean densityof seawater;f• is an abbreviationfor the For the abovetwo reasons,we shallnot treatthe retrograde diurnalpolar motions per sein thispaper but will onlypresent element for the integral over the oceans.The tidal height thetide-height and current model predictions in thiscase. relative to the seabedis (; u and v are the eastwardand Theequation of motion for polar motion can be derivedfrom northwardspeed, respectively, of the tidal currentassumed to the Liouvilleequation based on the conservationof angular be barotropicand hence uniform over the water columnwith momentum [Munk and MacDonald, 1960]. Written in the depth H. These tidal variablesare providedby tide models frequency(to) domain, it is [Sasaoand Wahr,1981 ] describedin the next section.Thus our studyof polar motion procxedsby simpleapplication of theprinciple of conservation (DO of angularmomentum; the natureof the torquesthat give rise + 0.772 p(6o) = 1.124h(to) c(tø)tøo to this motion need not concern us here. Aa>o Aa>o •cw - (• Ocean Tide Convention and Models {DO 6.17x10'4 h(6o) + 0.0734 c(60)60oß (1) Atoo Atoo fit)fcn - O0 To evaluatec(t) and h(t) of equation(2) requiresglobal modelsof oceantidal height and current fields. As is traditional, whereA is theEarth's equatorial moment of inertia,o) o is the thesemodels are decomposedinto a setof discretefrequency meanangular rate of rotation,tOcw is the positiveChandler components,or constituents,thus enabling evaluation of c(to) angularfrequency corresponding to prograde434.45 sidereal andh(to) in (1). This paperconsiders in detailthe eight major dayswith a Q of 170 adoptedfrom Wilsonand Vicente[1990] diurnaland semidiurnal tidal constituents listed in Table1 (Q•, (butsee Furuya and Chao[1996]), and (.Ofca is