Propagation of Big Island eddies


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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. C1, PAGES , JANUARY 15, 2001 Propagaton of Bg Island eddes Chrstna L. Holland and Gary T. Mtchum College of Marne Scence, Unversty of South Florda, St. Petersburg, Florda Abstract. Usng satellte altmetry data, we have observed a seres of antcyclonc eddes as they form at the Bg Island of Hawa and have tracked them as they move away from the sland. Whle smlar eddes have been observed near the Hawaan Islands n prevous studes, the fate of the antcyclonc eddes has prevously been unclear. The eddes that we observed ntally propagated to the southwest but consstently changed propagaton drecton to the northwest later n ther lfetmes. Ths was ntrgung to us, as theoretcally, the decay of solated antcyclonc eddes on a/3 plane should cause them to contnually move toward the southwest. Such solated eddy dynamcs are unable to account for the observed change to northwestward eddy propagaton, and the presence of the westward flowng North Equatoral Current turns out to be mportant to the Bg Island eddy dynamcs. The eddes are not passvely advected by the North Equatoral Current; rather, the mean flow changes the propagaton characterstcs of the eddes. An exstng theory that ncludes merdonally varyng, purely zonal mean flow s shown to account for the observed propagaton of the Bg Island eddes f the zonal varaton of the mean flow s consdered. 1. Introducton It has been known for some tme [Patzert, 1969; Wyrtk, 1982] that there s an actve area of eddy generaton n the lee of the Bg Island of Hawa. The eddy feld s comprsed of both cyclonc and antcyclonc eddy events, and several of these Hawaan eddes were descrbed n detal by Patzert [1969], although that study focused manly on the cyclonc events. The cyclonc eddes moved away from the Bg Island n a west/ northwestward drecton and essentally stayed near the Hawaan Island chan throughout ther lfetmes. There was a rather dstnct boundary between the areas west of the Bg Island that were domnated by cyclonc eddes (to the north) and by antcyclonc eddes (to the south). Whle the cyclonc eddes have been relatvely well studed, the fate of the antcyclonc eddes after leavng the vcnty of the Bg Island s unclear. Snce mesoscale eddes carry both water mass and energy wth them as they propagate, the speed and drecton of ther propagaton as well as the length of ther lfe could have mportant mplcatons for the crculaton and varablty far away from ther formaton at the Hawaan Islands. It was just such a potental longdstanceffect that ntally prompted the present nvestgaton nto the propagaton of these antcyclonc Bg Island eddes. A seres of epsodc 90 day events was observed n the tde gauge sea level tme seres at Wake Island [Mtchurn, 1995], whch s located km due west of the Bg Island of Hawa at øN, 165øE. It was shown that the 90day sgnals at Wake Island were consstent wth an energy source at the Hawaan Rdge, and t was further hypotheszed that the 90day sgnals mght be the remnants of the antcyclonc eddes generated at the Bg Island. It was not known, however, f the eddes could persst and propagate from Hawa to Wake Island and thus be responsble for the observatons there. For ths to occur, the net merdonal propagaton of the eddes would have to be essentally zero. Copyrght 2001 by the Amercan Geophyscal Unon. Paper number 2000JC /01/2000JC In addton to the eddy feld, the Hawaan Islands le on the northern boundary of the equatoral current system and at the northern edge of the North Equatoral Current (NEC), specfcally. The mean structure of the NEC was surveyed and descrbed as part of the HawatoTaht shuttle experment by Wyrtk and Klonsky [1984], who reported NEC flow between 9 ø and 18øN wth an annual mean speed of 8.2 cm s . We note as well that the NEC has strong seasonal varablty, varyng from cm s n the boreal fall to 5 cm s 1 n the boreal sprng [Seckel, 1975]. In addton, the NEC s home to other mesoscale eddy varablty, as descrbed by Wyrtk [1982]. Wyrtk [1982] was most nterested n a subset of the eddes that appeared to be formed wthn the NEC tself, at lattudes between 14 ø and 19øN. The NEC eddes were farly frequent events, occurrng n 50% of the cruse sectons across the NEC. These eddes moved km/day, whch s smlar to both the zonal speed of advecton by the NEC and the baroclnc long Rossby wave propagaton speed. As wll be descrbed n secton 2, we observed a consstently westward component of propagaton for the antcyclonc Bg Island eddes usng TOPEX/Posedon (T/P) altmetry data. Intally, the eddes moved to the southwest. Eddy dynamcs on a/3 plane predct a southward component of propagaton for antcyclonc eddes, as we wll also dscuss later. Of course, eddes propagatng contnually southwest from the Bg Island of Hawa could never reach Wake Island, as the two slands are at approxmately the same lattude. When we tracked the eddes for longer perods of tme, however, we were surprsed to see them change drecton. The early propagaton was to the southwest, but somewhere between the longtudes of 170øE and 170øW, every one of the observed eddes stopped movng to the south. In fact, after reachng that crtcal regon, they all began to propagate to the northwest. There was sgnfcant varaton n detal between the ndvdual eddy tracks, but ths change n drecton from southwestward to northwestward was a consstent feature of all of the eddy tracks (Fgure 1). Ths turn to northwestward propagaton means that t mght be possble for some of the Bg Island eddes, or at least some 935
2 936 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES Eddy # 1 Eddy # 5 20 N 20 N 140 E 16 ) E 18'0 16 W 140 E 16 ) E 18'0 166 W Eddy # 2 Eddy # 6 2O N 20 N ! 140 E 160 E ( W 140 E 160 E W Eddy # 3 Eddy # 7 2O N 2O N ! 140 E 160 E W 140 E 160 E W 2O N Eddy # 4 2O N Eddy # 8 '4. I 140 E 160 E W 140 E 160 E 18'0 160W Fgure 1. The observed tracks of the Bg Island eddes. The postons of the eddes are plotted every 5 days from the tme of ther formaton at the Bg Island of Hawa. The tracks were obtaned usng maps of grdded TOPEX/Posedon altmetry data. Supermposed on the tracks s a composteddy track, whch was computed by averagng the eddy lattudes n 1 ø bns and smoothng by fttng a sum of snusodal functons to that curve by least squares. resdual sgnal assocated wth ther decay, to have reached Wake Island. Only one of the eght observed eddes could be tracked to the vcnty of Wake Island. At ths tme, gven the avalable data, we cannot determne whether or not the energy assocated wth the antcyclonc Bg Island eddes mght explan the sea level varablty at Wake Island observed by Mtchurn [1995]. Ths northwestward turn n the observed eddy trajectores does, however, ntroduce an entrely new puzzle. Dynamcs for an solated antcyclonc eddy (n the Northern Hemsphere) predct that on a/3 plane t should contnue to move southwestward throughout ts lfetme. The underlyng cause of the change we observed n the eddy propagaton drecton s therefore an ntrgung queston. Obvously, though, eddes n the real world are unlkely to exst n complete solaton, and there are other processes to consder. In ths case, an mportant factor s lkely to be nteracton wth the NEC. After the eddes form at the Bg Island of Hawa, they propagate southwestward and approach the west ward flowng NEC, and nteracton wth the mean current mght affect the propagaton behavor. We have chosen to smplfy the problem, treatng the eddes as f they were solated except for the NEC, to explore the possbltes afforded by those dynamcs. In ths study, we wll examne the dynamcs of nteracton wth a mean current lke the NEC to determne whether that can account for the change n the merdonal component of the observed eddy propagaton. In so dong, prevou studes of nteractons between vortces and varous types of mean flows wll be partcularly useful and these studes are brefly revewed below. Future work n ths area should nclude other nterestng possbltes, such as nteractons between the antcyclonc eddes and the cyclonc eddes whch also form at the Bg Island. Secton 2 descrbes the observatons and the analyss that led to the eddy tracks shown n Fgure 1. Followng that s a dscusson of some of the dynamcal studes relevant to the problem of eddy propagaton n Secton 3. Specfcally, we wll
3 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 937 dscuss both the propagaton of solated eddes on a/3 plane and the possbl effects of eddes nteractng wth a mean zonal current. Fnally, we wll present calculatons from clmatologcal data n an attempt to dagnose the dynamcs behnd the observed eddy propagaton. temperature were used. There were stll only a lmted set of AVHRR maps for the relevant regon and tme perod wth enough data to be useful. The set of AVHRR maps was nsuffcent for trackng the eddes from AVHRR alone, but comparsons could be made between the AVHRR and T/P maps at 2. Observed Eddy Paths a number of specfc tmes. The mesoscale features n these monthly AVHRR maps were qualtatvely smlar to those n the T/P grdded maps. The eddes can be seen n the same The ntal observatons of the Bg Island eddes by Patzert [1969] were made from hydrographc surveys, but such data are not avalable for trackng the eddes over long dstances and tmes. The eddes, do, however, have readly observable sea surface heght sgnatures and can therefore be observed at tde gauges or by satellte altmeters. The altmeters have an obvlocaton n each data set and are of the same approxmate sze. As a second ndependent check, sea level data from the tde gauge at Johnston Island (16.7øN, 169.5øW) was examned n relaton to the T/P grdded maps. Fve of the observed eddes passed wthn 100 km of the Johnston Island staton. Postve sea level anomales, whch correspond to antcyclonc features, ous advantage due to the global spatal and quassynoptc of the correct ampltude are observed n the tde gauge tme coverage provded by TOPEX/Posedon (T/P) and other satellte altmeters. Thus T/P s the prmary tool that we used to observe the eddes as they propagated away from the Bg Island. There s a problem, though, n that the average dstance between the T/P passes at 19øN s 150 km, whch s comparable to the sze of the eddes, so that reconstructng the eddy sgnatures n tme and space can be dffcult. Ths problem can be partally overcome by usng data from multple altmeters, and we also used data from the European Space Agency's ERS1 msson n the early phases of our work. Vsualzaton of the eddy propagaton s acheved wth grdded sea surface maps. Intally, altmetrc data from T/P and ERS1 were merged and grdded to form a seres of 5day sea surface heght anomaly maps. Whle the ERS1 data set has a longer repeat perod, 35 days, than does the T/P data set, the spatal resoluton s much better than that of T/P, so that the two complement one another. Usng ths blended data set, we were able to track ndvdual eddes wthout dffculty, owng seres at the tmes at whch these eddes passed Johnston Island (Fgure 2). Note that the seasonal varaton has been removed from the sea level seres n Fgure 2 n order to emphasze the mesoscale events. Also note that there are clearly many other smlar features n the Johnston record, but our man concern s that the tde gauge records the passage of the Bg Island eddes at the same tmes as the T/P grdded felds do. The other events n the tde gauge record are also observed n the T/P maps (.e., the tme seres correlate well), but these events are not of nterest n the present context. Gven the lack of senstvty to the data used to make the maps and the corroboratng evdence from the AVHRR and tde gauge data, we concluded that we could safely track the Bg Island eddes from the grdded sea surface heght maps. Usng these maps, we were able to track eght antcyclonc eddes from the Bg Island. These eght eddes formed between November of 1992 and July of 1996, whch mples an average rate of just over two eddes per year. Intally, all of the obpartly to the relatvely large dameters and ampltudes assoc served eddes moved off to the southwest from the Bg Island ated wth the Bg Island eddes. We also made maps from the T/P data alone, and whle the maps from only T/P data appeared rougher than those comprsed of both T/P and ERS1 of Hawa, although the ndvdual trajectores were rather vared. Later, all eght of the eddes turned to the northwest between the longtudes of 170øE and 170øW and contnued to data, the observed postons of the eddy tracks were nsenstve propagate northwestward from that pont (Fgure 1). It s natto ths dfference. Also, regardless of whether we use T/P and ERS1 or T/P alone, t s mportant to take care n grddng the data to be sure that the analyzed heght feld s not unduly dstorted. Several dfferent grddng methods were therefore used n ths analyss, and we found that the postons of the eddy tracks were nsenstve to the partcular scheme used. Snce T/P has a longer data record than ERS1, the fnal grdded map seres was made usng only the T/P data, whch enabled us to observe a larger total number of eddes. In addton to testng the grdded sea surface heght felds by evaluatng the senstvty of our results to whch data was ncluded (.e., T/P and ERS1 or T/P alone) and to what type of grddng algorthm was used, we also attempted to verfy the eddy locatons usng ndependent data. Frst, satellte sea surural to ask whether these eght eddes that we tracked were all that were formed or whether our sample mght be based n some fashon. To address ths queston, we note that Patzert [1969] used data from a number of cruses near the Hawaan Islands between 1949 and Three cruses between September 1952 and August 1953 each observed a sngle antcyclonc eddy. Then between May 1965 and May 1967 a total of fve antcyclonc eddes were observed out of measurements made by eght dfferent cruses. The frequency of antcyclonc eddes at the Bg Island of Hawa appears from these data to be approxmately two to three eddes per year. We are therefore reasonably confdent that wth the T/P grdded data we were able to observe all of the antcyclonc eddes that were formed durng our study perod. face temperature from the advanced very hgh resoluton radometer (AVHRR) satelltes was examned for ndependent confrmaton of what the grdded T/P maps showed. The 3. Dynamcs of Eddy Propagaton AVHRR data, unlke data from T/P and other mcrowave Several studes have dscussed the effects of a/3 plane and altmeters, are receved n a wde swath beneath the satellte rather than along a narrow nadr track. These data can be dsplayed as a map wthout any artfcal grddng, whch makes t a useful data set wth whch to evaluate the grdded T/P maps. The usefulness of the AVHRR data are lmted, though, by large data gaps whenever clouds were n the sky. For ths reason, monthly composte maps of the AVHRR sea surface nonlneartes on the zonal and merdonal propagaton of solated eddes [Flerl, 1977; McWllams and Flerl, 1979; Flerl, 1984; McWllams et al., 1986]. None of these studes consdered the potental effect of any mean flow on the eddy propagaton; they dealt nstead wth the behavor of solated eddes. A study by Chang and Phlander [1989] addresses ths gap. These authors consdered the propagaton of packets of
4 938 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 3OO 2OO IO0 IO02OO ! 1994 Eddy # 3 I I oo 2oo loo 0 loo 2oo 300 Eddy # 7 Eddy # 8 19' Fgure 2. Fve of the Bg Island eddy events as seen n the tme seres of sea surface heght taken from the tde gauge staton at Johnston Island (16.7øN, 169.5øW). The best ft (n the least square sense) of the annual cycle has been removed from the sea surface heght tme seres. The tmes at whch the eddes, as observed n the TOPEX/Posedon grdded maps, most closely approached Johnston Island are shown as thn vertcal lnes. Rossby waves n the presence of a mean, purely zonal, geostrophc current. Eddes can be vewed as a packet of Rossby waves, and the results of Chang and Phlander [1989] are thus relevant to the case currently under consderaton, that of an eddy approachng the NEC. We wll frst summarze the solated eddy dynamcs and then turn to the case of an eddy n a merdonally varyng zonal mean flow. and Fled, 1979; Fled, 1984; McWllams et al., 1986; Sutyrn and Fled, 1994]. Frst, the speed of westward propagaton ncreases more rapdly than n the lnear case and more closely approaches the expected long Rossby wave speed Cx = tx n whch X s the Rossby radus of deformaton wrtten as 3.1. An Isolated Eddy X = (g'h/f ) /2, (2) An solated eddy wll propagate westward on a/3 plane, even where #' and H are the reduced gravty and the upper layer under lnear dynamcs [Fled, 1977]. In the study of Fled thckness. Second, nonlnearty also nduces a merdonal com [1977], mesoscale eddes are thought of as packets of Rossby ponent of propagaton, through the development of a beta gyre waves, and as the ndvdual Rossby wave components propa [Sutyrn and Fled, 1994]. The potental vortcty of the eddy gate westward, so does the complete eddy. The speed of the eddy's westward moton s smply the group speed of the Rossby waves makng up the eddy. Intally the eddy s com Q = (f + )/H, (3) prsed of many dfferent Rossby waves, and whle all travel westward, ther phase speeds are vared. Intally, then the where (7 s the relatve vortcty, s conserved. The nonvortex part of the flow conssts of the beta gyre, formed prmarly by westward propagaton of the eddy s found to be at only 30% the advecton of planetary vortcty and secondarly by dstorof the long Rossby wave speed. Ths varety of propagaton tons n the shape of the vortex. The merdonal eddy propaspeeds n the wave components of the eddy causes the eddy to gaton s controlled by the sgn of the eddy's vortcty. An be dspersve and therefore to decay. As t propagates, t antcyclonc eddy propagates to the southwest under these evolves, leavng behnd a tral of slower Rossby waves. As those dynamcs n the absence of any mean flow. The maxmum slower wave components are shed, the eddy ampltude de magntude of the merdonal propagaton speed, for ether creases, and the westward propagaton speed of the eddy n cyclonc or antcyclonc eddes, s gven by creases toward the long Rossby wave speed. Everythng dslev: (1/4)/3x 2 (4) cussed here thus far s true even for a lnear eddy, but nonlnear effects can change the eddy evoluton and propaga [McWllams and Fled, 1979]. Fo; cyclonc eddes, Cy ton substantally. The nonlnear case, whle t s a bt more complcated, s also more true to the real world of eddy propagaton dynamcs than the lnear, so t s approprate that we now address the effects of nonlnearty on the propagaton of an solated eddy. Nonlnear effects change the propagaton tve, whle for antcyclonc eddes t s a negatve quantty. Nothng about the dynamcs of an solated eddy, however, offers any explanaton for antcyclonc eddes propagatng to the northwest. If the eddes were only very weakly nonlnear, then ther southward translaton mght be nearly nonexstent. behavor of antcyclonc eddes n two man ways [McWllams Even f that were so, however, there s no reason n the theory s pos
5 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 939 dscussed up to ths pont for the eddes' merdonal propagaton to change drecton as was observed. As dscussed n secton l, though, the presence of the NEC probably cannot be gnored, so we wll now consder mean flow effects on eddy propagaton characterstcs Effect of a Mean Current Chang and Phlander [1989] use essentally the same equatons as the studes dscussed above. Ther model s nonlnear, on a/3 plane, and quasgeostrophc for a sngle actve layer above a lower layer assumed to be at rest. They use these dynamcs to consder packets of Rossby waves nteractng wth a background mean flow. The mean flow U o s constraned to be geostrophc, purely zonal, and only varable merdonally; that s, = r0(y). (5) The exstence of a mean current ntroduces a quantty B, whch Chang and Phlander term the "effectve"/3. The quantty B s defned as B  (f/q)oq/oy = [f/(f OUo/Oy)] ß [13 (02Uo/Oy 2)  Q(OHo/Oy)], (6) where Q s the mean state potental vortcty, Q  [(f OUo/Oy)/Ho], (7) whch s dependent upon the planetary vortcty f, the mean relatve vortcty OUo(y)/Oy, and the merdonally varable part of the mean thermoclne depth Ho(y ). If the length scale L o over whch the flow speed changes s large compared to the Rossby radus X, (6) can be smplfed. The term f/[ f  0 Uo/ Oy] reduces to one, and the last term wthn the brackets n (6) s Q(OHo/Oy), where Q, the potental vortcty, s approxmately equal to f/ho. If the mean flow s assumed to be geostrophc, then ths term can be approxmated as Q(OHo/Oy)  (f/ho)oho/oy (f2/#'ho)uo U0 x2, (8) where X agan represents the Rossby radus of deformaton, so (6) becomes B = 1302eo/Oy 2 + x2e0. (9) Recall from (19) that the merdonal speed s drectly propor The above dscusson n terms of packets of Rossby waves tonal to/3'. If the mean flow s eastward, then the/3' s larger encounterng a background current. It s more approprate, than/3, and the merdonal propagaton speed s ncreased. If however, to dscuss nonlnear vortex dynamcs n the context of an eddy were approachng such an eastward current from a the eddycurrent nteractons rather than smply treatng the regon of slower or nonexstent mean flow, then ths ncrease n eddes as packets of Rossby waves. The followng dscusson merdonal propagaton would serve to carry t further nto the starts from these nonlnear vortex dynamcs [McWllams and current, thus ncreasng the mean flow t feels even more and Flerl, 1979; Sutyrn and Flerl, 1994] and wll show that the so on. On the other hand, f the mean flow s westward lke same effectve /3 can be derved. Startng wth the quas NEC,/3' s less than/3, and the merdonal propagaton speed geostrophc equaton for the streamfuncton q, s therefore decreased and eventually goes to zero at the lat (V 2 X2)Oqt/Ot + J(qt, V2qt) + 130qt/Ox = 0 (10) [Sutyrn and Flerl, 1994], where X s the Rossby radus of deformaton and J s the Jacoban, expressed as J(q,, v q,) _(oq,/ox)[o/oy(v q,)]  (oq,/oy)[o/ox(v q,)], t can easly be shown that the relatve vortcty of the flow, r = (v:  x:) q,, ( 2) obeys the relatonshp DF/Dt = OF/Ot + J(q,, F) = t Oq,/Ox. (13) Wth the ntroducton of a zonal mean flow Uo(y), such that the vortcty equaton becomes Oq /Oy = Oq '/Oy Uo, (14) DF'/Dt = ar'/at + J(q,, r') = t 'aq,/ax, (15) F'= (V 2 A2)½ ' (16) 13' _ Uo/Oy 2 + X2Uo. (17) Expresson (17) s dentcal to (9) for the effectve/3, B, from the Chang and Phlander [1989] dscusson for packets of Rossby waves. Expresson (15) for conservaton of potental vortcty for the anomalous flow (wth respecto a mean flow) s dentcal to (13) for the no mean flow case, wth the substtuton of/3' for/3, so that the eddy propagaton speeds (1) and (4) now become Cx U0 = /3'X 2 (18) cy = 1/4/3'A 2 (19) for an antcyclonc eddy. Clearly, the speed and drecton of propagaton s dependent on the magntude and sgn of/3', the effectve/3. Understandng the merdonal propagaton of the Bg Island eddes requres an understandng of the value of/3' and how t changes throughout the lfetmes of the eddes. To that end, we wll now consder some smplfcatons to (17), the expresson for/3'. If L o s larger than A, the shear of the mean flow s small and the secondterm the rghthand sde of (9), 02Uo/Oy 2, can be neglected. In most cases ths s reasonable. At 10øN, for example, f s 2.5 x 10 s, and f the nternal gravty wave speed s taken as 2.7 m s 1 (a reasonable value but used here only for llustraton), then the Rossby radus of deformaton s 107 km, or just under 1 ø of lattude. The wdth of the mean flow, on the other hand, s usually several degrees. Except n regons of hghest mean flow shear, the second term can be neglected, and/3' can be approxmated as /3' /3 + U0 x2. (20) tude where/3' = 0. The degree to whch the merdonal propagaton s slowed depends manly on the strength of the cur rents, except as noted earler n regons of very strong merdonal shear n the mean flow. The expresson for the zonal propagaton speed (18) has two terms, one equal to the mean flow and one analogous to the long Rossby wave speed at whch t propagates n the no mean flow case. The second term, lke the expresson for the merdonal propagaton speed, s drectly proportonal to/3' rather than/3, as t would be n the no mean flow case. As the strength
6 940 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 20 I 19 o oo o o, , ,, Levtus zonal flow, 18 at 135.5øE, ø E, and 154.5øW. 'o., Zonal flow from 17 I WOCE surface drfters. 0 0 Observed eddy zonal 16 I propagaton, ths study.!,! ~ l] ll Eddy zonal propagaton, I from Lumpkn, Zonal Speed (m/s) Fgure 3. The zonal speed of the eddes, computed from the observed trajectores wth a tme step of 2 months. Also shown are the zonal eddy speeds computed by Lumpkn [1998], the Levtus et al. [1994] geostrophc U0, and the mean zonal speeds of the World Ocean Crculaton Experment (WOCE) surface drfters between ø and 160øW, between 160 ø and 168øW, and between 170 ø and 180øW [Lumpkn, 1998]. of the westward mean flow that the eddy encounters ncreases, are faster than the geostrophc U0 computed from the Levtus the value of the parameter/3' decreases, and as ths happens, et al. [1994] clmatologcal dynamc heghts owng to the the zonal propagaton speed approaches the lmt of smooth nature of the clmatology. As can be seen n Fgure 3, however, the eddy propagaton speeds do agree well wth the Cx = u0 World Ocean Crculaton Experment (WOCE) surface drfter at the same lattude where the merdonal propagaton com derved zonal speeds [Lumpkn, 1998]. Chang and Phlander ponent goes to zero. In a westward mean flow, t s therefore [1989] suggesthat the Rossby waves should be absorbed nto possble for the eddy paths to asymptote toward a crtcal the mean flow at the crtcal lattude as they cannot propagate lattude, whch s smply the lattude where /3'  0. After away from t. In our observatons, however, the eddes conreachng ths pont, the zonal propagaton contnues at a con tnue to be vsble as dstnct features n the sea surface heght stant rate equal to the mean flow speed at that lattude. The anomaly felds. merdonal speed s zero, and so the eddes are unable to leave As dscussed earler, the Bg Island eddes propagate to the that crtcal lattude. If the eddy s thought of as a packet of southwest ntally. Later, the southward component of ther Rossby waves as descrbed by Chang and Phlander [1989], all moton decreases, comes to a halt, and n fact, reverses, so that of the Rossby wave components of a packet of waves such as a these antcyclonc eddes propagate to the northwest. On the mesoscaleddy would then be travelng at the same speed, that bass of the above theory, nteracton wth a strong westward of the mean current at the crtcal lattude. The zonal propa mean current such as the NEC seems to be a lkely cause for gaton speeds of the antcyclonc eddes obs6rved n ths study ths haltng of the southward moton, but the northwestward
7 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 941 1ON 140 E 160 E W Fgure 4. The composte eddy track compared to vrtual drfter trajectores. The vector feld s the surface geostrophc flow computed from the clmatologcal [Levtus et al., 1994] dynamc heght relatve to 1000 m. The thckest lne s the compost eddy track, as n Fgure 1. Vrtual drfters were nserted nto the clmatologcal surface geostrophc flow at several locatons along the composte eddy tracks. The daly postons of these vrtual drfters, as nferred by the clmatologcal flow, are shown. propagaton that follows that wll requre addtonal consderaton Advecton by the North Equatoral Current The effectve/3 from Sutyrn and Flerl [1994] and Chang and Phlander [1989] appears to offer a possble explanaton for at least some of the observed propagaton characterstcs of the Bg Island eddes, and later we wll address the effect of a more complcated mean flow that s allowed to vary zonally n sze and strength. Frst, though, t s natural to wonder whether there mght be another, smpler way to account for the observed propagaton. One possblty s that the eddes do not actvely propagate at all but are smply advected passvely to the northwest by the mean flow. We wll therefore dgress brefly to determne whether the eddy propagaton mght nstead be accounted for by a smple advecton processes. From Secton 3.2 [Chang and Phlander, 1989; Sutyrn and Flerl, 1994] we know that for the case where Uo, Ho, and/3' are all functons of lattude only, the eddy propagaton speeds at the pont where/3' approaches zero can be wrtten as Cx = Uo Cy = 0. (22) In ths scenaro, the eddy can be thought of as nondspersve and freely propagatng at exactly the mean flow speed. Con versely, t could be magned that the eddy s not freely propagatng at all but rather s smply beng advected along by the mean current after the pont when t reaches the crtcal lattude. If the mean flow s a functon of lattude only, t s mpossble to test whch of these vews s correct. If, on the other hand, the mean flow Uo vares wth both lattude and longtude, then these two hypotheses can be easly tested aganst one another. All eght of the eddes observed n ths study were ncorporated nto a composteddy track (Fgure 1) n order to more easly compare the eddy propagaton to the mean flow. The mean flow used s the geostrophc flow at the surface, relatve to the 1000 m depth level, computed from the Levtus et al. [1994] clmatology. We nserted vrtual drfters nto ths mean feld at several locatons along the composte eddy track and plotted the drfter locatons every day (Fgure 4). If one supposes that the eddes, n movng northwestward, were smply advected by the mean flow of the NEC, then the vrtual drfter trajectores should also turn to the northwest. Those trajectores should, n fact, le alongsde the eddy path, but ths does not appear to be true for any part of the eddes' lfetme. Instead, the clmatologcal drfters move consstently to the southwest even after the eddy path has turned to the northwest. Ths does not elmnate the possblty that nstantaneous varatons n the NEC could advect eddes to the northwest, but for ths to be a reasonable explanaton for the very consstent northwestward turn of all of the observed eddes, we would expect to see some ndcaton of northwest flow n the clmatologcal current. Smple advecton processes appear to be unable to account for the northwestward eddy moton, and so we now return to/3', the effectve/3, and dscuss the case where the zonal flow s allowed to vary wth longtude Zonal Varaton n the Mean Flow To attempt to explan why an antcyclonc eddy mght move northwestward, we want to take the deas of Sutyrn and Flcrl [1994] and Chang and Phlander [1989] a step further. That s, can these dynamcs, when extended to a mean flow that s nether purely zonal nor varyng solely n the merdonal d recton, account for the observed change n the eddy propagaton drecton? Zonal varaton n the mean flow alters/3', the effectve /3 parameter, and therefore can further affect the propagaton of mesoscal eddes. The NEC does n fact have spatal varablty, wth zonal varatons n the flow speeds and n the lattude of the strongest flow (Fgure 5). The speeds shown are the geostrophc speeds at the surface relatve to 1000 m, agan computed from the Levtus et al. [1994] clmatologcal dynamc heght data. Recall that Sutyrn and Flerl [1994] and Chang and Phlander [1989] deal only wth a purely zonal and purely merdonally varyng flow Uo(y), whch s n geostrophc balance wth the merdonally varyng nterface depth Ho(y ). Exposed to such a mean flow, the merdonal moton of antcyclonc eddy depends on the effectve/3 parameter,/3', whch was shown above to be approxmately 13' (y) = 13  Q(y)OHo(y)/Oy. (23) The lattude at whch/3' = 0 was of partcular nterest, as that defned the expected path of the eddes n the presence of the mean flow. A more realstc case to consder s a current that
8 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES ø E ø E ø W! 20 2 '"15 lo 1 1 5_ ' o U(y) n m/s Fgure 5. Zonal varaton n the surface geostrophc flow of the NEC computed from the Levms et al. [1994] clmatologcal dynamc heght relatve to 1000 m. The x axs of each panel s the strength of the zonal component of the mean flow Uo(y) (n m s ). The y axs n every case s lattude. The panelshow the mean flow at (left) 135.5øE, (mddle) 170.5øE, and (rght) 154.5øW. can vary n strength and wdth wth longtude. The NEC, for nstance, wdens and strengthens as t moves westward. In ths case, the lattude at whch/3' s approxmately zero s no longer constant but rather vares wth longtude; that s, there s a curve y (x) defned by compute rro profles versus depth at each lattude and longtude. Inspecton of these profles suggested that rro values of between 26.0 and 26.2 kg m 3 serve as a reasonable defnton of the pycnoclne n our study area, and the depth of these sopycnals are therefore used to defne Ho(y) at each grd 13'[x, y(x)] = 0. (24) pont n the Levtus clmatology. These Ho(y) can then be merdonally dfferentated at each zonal poston to obtan By analogy wth the smpler/3' (y) case, we expecthat fy(x) s slowly changng zonally, then the eddy placed n such a mean flow feld should follow the/3' = 0 contour, once reachng t, for the remander of ts lfetme. The NEC has both zonal and merdonal flow, but t s stll prmarly a zonal current, as can be seen n a vector map of geostrophc flow relatve to 1000 m, computed from the Levtus et al. [1994] clmatology (Fgure 4). Ths greatly smplfes matters; f the NEC were not prmarly a zonal current, the dsperson relaton would dffer from the estmates of/3' at each grd pont. In determnng the postons at each longtude where/3' = 0, whch defne the y(x) curve that we need, we frst dentfed the regon where/3' decreases from 2 to 0 x m  s  as we approach the core of the NEC from the north. These regons are shown on Fgure 6 for two calculatons: one uses rro = 26.0 kg m 3 and the other uses rro = 26.2 kg m 3 as the defnton of the pycnoclne. There can, of course, be zero contours of B on both the north and south flanks of the NEC, but snce the eddes are approachng form dscussed earler and would be much more complcated. the NEC from the north sde, only the contours of/3' on the As t stands, contours of/3' and thus the expected path y(x) north sde of the core of the NEC are shown because these are can be estmated from the Levtus et al. [1994] clmatology. In order to make ths estmate, we recall that the mean flow potental vortcty Q s approxmately f/ho. Ths allows us to wrte (23) as consdered to be the dynamcally mportant ones. For comparson, the composte of the observed eddy tracks s also ncluded on Fgure 6, and the close correspondence between the average eddy path and the y(x) estmates sup 13' 13  (f/ho)oho/oy, (25) ports the dea that the basc Sutyrn and Flerl [1994] and Chang and Phlander [1989] theory can account for the general propwhch s a more convenent form snce t only nvolves the nterface depth. Ths quantty can be estmated from the Levtus et al. [1994] clmatology. We could have nferred Ho from the dynamc heght relatve to 1000 m from Levtus et al. [1994]. A better choce, however, s to use the actual depth of the agaton characterstcs of the Bg Island eddes. In fact, t appears from ths analyss that the Bg Island eddes are never truly solated; they are formed n close proxmty to the/3' = 0 contour and reman wth t throughout ther lfetmes. It does not appear to be necessary to nvoke/3 plane dynamcs for an pycnoclne or at least the best estmate of that depth possble solated'eddy all to explan the zonal propagaton n ths from the clmatologcal data. The clmatologcal values of temperature and salnty from Levtus et al. [1994] were used to case. The zonal propagaton s controlled, along the zero /3' contour, by the mean zonal flow component. The merdonal
9 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES 943 Contours for 0 < B < 2xl 012(ms) I I I I... oe = 26.0 kg/m 3 '120N E 170 E W 160 W 150 W longtude Fgure 6. The composte eddy track compared to the zero contour of B, the effectve /3 of Chang and Phlander [1989]./3' s computed from the Levtus et al. [1994] clmatology of temperature and salnty accordng to/3' = /3  (f/ho)oho/oy, where H o s the thermoclne depth, estmated from the depths of cr o contours. The sold lne s the compost eddy track, and the medum and lght shaded lnes curves are the zero contours of B on the north sde of the north equatoral current based on the depths of cr o equal to 26.0 and 26.2 kg m 3, respectvely. propagaton, on the other hand, depends on the zonally varable poston of the gradent of the Corols parameter and of the poston, strength, and lattudnal shear of the background mean current. From the pont of ther formaton at the Bg Island of Hawa the eddes appear to reman on the zero contour of/3' through much, f not most, of ther lfetmes. 4. Future Work The propagaton of the antcyclonc Bg Island eddes can be explaned by ther followng the/ ' = 0 contour, where/ ' s the effectve/. Ths effectve/ dffers from the planetary/ owng to the presence of a mean background current, the NEC. Ths s, of course, not the only possble explanaton, and further research s needed. One topc requrng further study s the stablty of the NEC. It s possble that for a largescale current, such as the NEC, f t s stable, the merdonal gradent of potental vortcty and the advecton effects balance, producng only small net effects on vortex propagaton. Snce we found that/3' has a zero contour, though, the NEC may be an unstable current. In fact, the CharneyStern condton for nstablty of a flow s that the merdonal gradent of the potental vortcty, whch has been desgnated here as/3', must change sgn somewhere wthn the flow [Charney and Stem, 1962]. Ths s a necessary but not a suffcent condton of nstablty, so we cannot say from ths alone whether or not the NEC s unstable. The queston of the stablty or nstablty of the NEC could have mportant consequences when eddycurrent nteractons and subsequent eddy propagaton are consdered. The data for the mean NEC avalable at the tme of ths study [Levtus et al., 1994] are not suffcent owng, n partcular, to ther heavly smoothed nature to determne whether the NEC s stable or unstable. Better clmatologcal data sets, such as the recently released World Ocean Database [Levtus et al., 1998] may allow ths queston to be answered. Another approach to the nsght nto the nature of the eddycurrent nteractons and the stablty of the mean current. The altmetrc data used n ths study, whle suffcent for determnng the poston of the eddes as they propagate, wll not allow such detaled plots of the eddy structure as would be requred for ths purpose owng to the crosstrack resoluton of the altmeter and the dffculty of separatng the eddes from the surroundng varablty. New data products, such as the recent hghresoluton mappng usng combnatons of T/P, ERS1, and ERS2 [Ducet et al., 2000], may make ths a practcal approach. Another nterestng area for future work s the possblty of nteractons between ndvdual eddes. In ths study, we have focused exclusvely on the effect of the NEC on the eddy propagaton, treatng these antcyclonc eddes as f they were otherwse solated, n order to see how much of ther behavor could be explaned n that way. These eddes are not solated, however, and eddyeddy nteractons may be an mportant factor n the eddy propagaton. One possblty s that the antcyclonc eddes may be nteractng wth one another. Two vortces of the same sgn, otherwse solated and wth all moton except for the vortex rrotatonal and nvscd, wll tend to rotate about a statonary pont between the two [Kundu, 1990]. Under the rght crcumstances n a rotatng basn, two vortces of the same rotatonal sense wll merge nto one [Nof and Smon, 1987]. Cyclonc eddes are also formed at the Bg Island, and nteractons between the antcyclonc eddes and the cyclonc eddes are also possble, although the cyclonc eddes, unlke the antcyclonc eddes, ntally move to the northwest from the Bg Island. Vortces of opposte sgn n close proxmty to one another tend to mantan ther dstance, wth the weaker rotatng about the stronger, or movng n parallel lnes f they are of smlar strength [Kundu, 1990]. On a /3 plane, there s the added tendency for southward and northward merdonal moton for antcyclonc and cyclonc eddes, respecproblem would be to examne the sea surface heght expresson tvely, so the relatve poston of the eddes s mportant to of the eddes n detal as they propagate and evolve. The consder. All of the above vortex nteractons could complcate evoluton of the structure of the eddes would provde further the propagaton of the antcyclonc Bg Island eddes, along
10 944 HOLLAND AND MITCHUM: PROPAGATION OF BIG ISLAND EDDIES wth the /3 plane dynamcs and the effect of the mean NEC. References Improved altmetrc products such as that of Ducet et al. [2000], Chang, P., and S. G. H. Phlander, Rossby wave packets n baroclnc wth fne enough resoluton to capture the detaled structure of mean currents, Deep Sea Res., Part A, 36, 1737, the varous vortces and any evolutons as they nteract, mght Charney, J. G., and M. E. Stern, On the stablty of nternal baroclnc allow one to address ths possblty n future studes. jets n a rotatng atmosphere, J. Atmos. Sc., 19, , Ducet, N., P. Y. Le Traon, and G. Reverdn, Global hghresoluton Ths study was ntally concerned wth determnng whether mappng of ocean crculaton from TOPEX/Posedon and ERS1 or not the antcyclonc Bg Island eddes could account for the and 2, J. Geophys. Res., 105, 19,47719,498, sea level varablty at Wake Island noted by Mtchum [1995]. Flerl, G. R., The applcaton of lnear quasgeostrophc dynamcs to Of the eght eddes observed n ths study, only one (number 2) Gulf Stream rngs, J. Phys. Oceanogr., 7, , was tracked to the vcnty of Wake Island. In the tde gauge Flerl, G. R., Rossby wave radaton from a strongly nonlnear warm eddy, J. Phys. Oceanogr., 14, 4758, sea level tme seres at Wake Island, wth the annual cycle Kundu, P. K., Flud Mechancs, 638 pp., Academc, San Dego, Calf., removed, there s a peak at the tme suggested by the eddy trajectory. Ths provdes some addtonal valdaton of the eddy Levtus, S., R. Gelfeld, T. Boyer, and D. Johnson, Results of the trackng, as wth the tme seres at Johnston Island, dscussed NODC and IOC Oceanographc Data Archaeology and Rescue Projects, Key to Oceanographc Records Documentaton 19, Natl. prevously, but ths s only one peak among all the varablty of Oceanogr. Data Center, Washngton, D.C., the Wake Island sea level tme seres. We cannot conclude Levtus, S., T. P. Boyer, M. E. Conkrght, T. O'Bren, J. Antonov, C. from the currently avalable data whether or not the antcy Stephens, L. Stathoplos, D. Johnson, and R. Gelfeld, World Ocean clonc Bg Island eddes or energy assocated wth ther decay Database 1998, vol. 1, Introducton, NOAA Atlas NESDIS 18, Natl. reach Wake Island, but ths queston should be reconsdered as Oceanc and Atmos. Admn., Slver Sprng, Md., Lumpkn, C. F., Eddes and Currents of the Hawaan Islands, Ph.D. better data become avalable, such as the Ducet et al. [2000] dssertaton, 281 pp., Unv. of Hawa at Manoa, Honolulu, mappng. We have found that the eddy propagaton s conss McWllams, J. C., and G. R. Flerl, On the evoluton of solated, tent wth movement along the/3' = 0 contour, and as Fgure 6 shows, ths contour does not curve suffcently northward for nonlnear vortces, J. Phys. Oceanogr., 9, , McWllams, J. C., P. R. Gent, and N.J. Norton, The evoluton of balanced, lowmode vortces on the/3plane, J. Phys. Oceanogr., 16, the eddes to reach Wake Island f they follow t. In ths study, , however, /3' was computed from the Levtus et al. [1994] cl Mtchum, G. T., The source of 90day oscllatons at Wake Island, J. matologcal felds, and t s apparent n Fgure 3 that Geophys. Res., 100, , geostrophc veloctes computed from ths data set can be Nof, D., and L. M. Smon, Laboratory experments on the Mergg of much slower than nstantaneous measurements from such nonlnear antcyclonc eddes, J. Phys. Oceanogr., 17, , Patzert, W. C., Eddes n Hawaan waters, Rep. HIG698, Hawa Inst. sources as the WOCE surface drfters. The strength, posof Geophys., Unv. of Hawa at Manoa, Honolulu, ton, and shear of the mean current affect the value of/3'. Seckel, G. R., Seasonal varablty and parameterzaton of the Pacfc Better estmates of/3' and the locaton of the/3' = 0 contour may be avalable from the World Ocean Database [Levtus et al., 1998] or from other clmatologcal data sets, and ths mght allow future studes to address whether or not the hypothess presented here, that the eddes follow the/3' = 0 contour, s consstent wth the Bg Island eddes reachng Wake Island. North Equatoral Current, Deep Sea Res., 22, , Sutyrn, G. G., and G. R. Flerl, Intense vortex moton on the beta plane: Development of the beta gyres, J. Atmos. Sc., 51, , Wyrtk, K., Eddes n the Pacfc North Equatoral Current, J. Phys. Oceanogr., 12, , Wyrtk, K., and B. Klonsky, Mean water and current structure durng the HawatoTaht Shuttle Experment, J. Phys. Oceanogr., 14, , Acknowledgments. Ths work was supported by NASA through the Jet Propulson Laboratory as part of the TOPEX Altmeter Research n Ocean Crculaton Msson. Conversatons wth several people n the Department of Oceanography at the Unversty of Hawa and n the College of Marne Scence at the Unversty of South Florda were very helpful. The paper was also sgnfcantly mproved by suggestons from two anonymous revewers. C. L. Holland and G. T. Mtchum, College of Marne Scence, Unversty of South Florda, 140 Seventh Avenue South, St. Petersburg, FL (Receved January 14, 2000; revsed August 21, 2000; accepted August 31, 2000.)
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