Langmuir Parameterizations

Baylor Fox-Kemper and Adrean Webb CIRES/University of Colorado at Boulder

In preparation for continued research with Keith Julien, CU-Boulder; Greg Chini, UNH; E. Knobloch, UCB

13th CCSM Meeting--OMWG Session Thurs. 6/19/08 11:25-11:40 Langmuir, What?

January 31, 2008 3:55 Geophysical and Astrophysical Fluid Dynamics cjkLC

2 Fox-Kemper et al.: Windrows 12 March 2008 2 Reduced Model of Langmuir Turbulence

Figure 1. Images of Langmuir circulation windrows: (a) a photograph of Rodeo Lagoon in CA (Szeri 1996), (b) an infrared image of Figure 1theImsuragesface ooff TLangmampa Bauiry (ccirculourtesationy of G.windroMarmows:rino, (a)NRLa, Dphotograph.C.), and (c) oftheReovodeolutioLagon of sonurfaince CAtracer(froms in a LSzeri,ES of L1996),angmuir : turbulence (McWilliams et al. 1997). (b) an infrared image of the surface of Tampa Bay (courtesy of G. Marmorino, NRL, D.C.), and (c) the evolution of surface tracers in a LES of Langmuir turbulence (McWilliams et al., 1997). Reproduced from Chini et al. (2008). 1 Introduction

by theLaco-inngmvuesirtigatorscirculati(Chini,on (LC)2008;is a wChiniind aetnd al.,surface-willwavbeeddorivcumenen conted,vectandive fltheow groundwthat comorkmofornlyimple-occurs in 2008).thHoe uwpepveer,r labyeforeers ofsplaendingkes, rivtimeers anond oacecom-ans (Leibmenovictationh 1983of, Ta hfullorpparameterizatione 2004). When thwille wbinedlaid.s exceed a plex mofewdelmiteteisrsimpperortansecontdto, LdetermineC exhibitsthea ralikngelye of length and times scales, from centimetres to hundreds of magnitudemeterofs aclimatend secoimndpacs tot.hTheoursresearc. The ehmplanergenis:ce of a4.broaBudgetd spectrum of scales prompted McWilliams et al. (1997) to dub this phenomenon “Langmuir turbulence,” both to emphasize that LC is properly viewed as Formpartulateof thane upalgebraic,per oceanequilibratedturbulence aapprond toxi-distingProf.uish itFforx-Kempom waller-borequestsunded sh1.5earmonflowthsturofbusummelence. Evr en • mationunder ofuntheconLangmtrolled,uirstrcirculationongly superduecrititocaChinil environmsalaryental cforondhimselfitions, handowe1.5ver,monLCthsis doofmsuppinateortd bfory enoneergetic (2008).counterThis-rotaparameterizationting streamwise vowillrticaincludel structtheures. Thpre-compsese structuappliedres are emathlongatgraduateed in the wstudenind ditreatctio50%n when mixedthe wilanyder-drdeepivenesninghear scalingand surfofaceLi-wandave SGar-tokes dri(approft are ximatelythemselve$18ks aligtotalned wincludingith the wifringend or btoenefitsthe right rettof th(1997)e windanddirecbteioconsistenn when Ctorwithiolis eLangmffects auirre signibutficannott. Inindirecview tofcosts).this evident anisotropy, the aim of the turbulencepresent stusimdyulationsis to de(re.g.ive ,aMcWilliamscoarse-graineted,al.,quasi-three-dimensional description of Langmuir turbulence. REFERENCES 1997).Figure 1 shows several illustrations of the hallmark surface signature of LC: a series of roughly parallel, Chini, G. P.: 2008, Strongly nonlinear Langmuir circulation Implemenwind-aligtnthised stapproreaks.ximateThese “parameterizationwindrows” are evident visuaandllyRa(fiyleiggurh–eB1éna(a)rd), coinnvinectiofran.resubd amittend adctoouJournalstic imofagery • in(tofiguthere 1NCAR(b)), anCommd in fuunitll thyreClimatee-dimensSystemional (3D) directFluidnumMeerichanicscal an.d large-eddy simulations (DNS and MoLESdel., respectively – figure 1(c)). To date, the vast mCahini,joritG.y Po.,f K.nuJulien,mericaalndsiE.muKnolatbloioncsh:o2f00L8C, Anhaavsyme eptompti-loyed cally reduced model of Langmuir turbulence. submitted to Pterformhe Craiak–sensitivitLeibovicyh (testCL)ineqaualotiw-resolution,ons, a surface-wave filtGeereophysicd versalioandn ofAstrthophysice NavialerFluid–StokDynamices (NSs). equations; • ocean-onlysee Craik,anconfigurationd Leibovich (with1976)simplified, Craik (19w77a)vaend LeiCbraoik,vicA.h (D.19D.:77)1. 9T77h,eGeCneraL eqtiounatoifoLansngamreuirfocircularmalltioy insdebnytical to the instantaneous NS equations apart from the occuanrrinstaencebilitofyamvecohartnismex-f.orJournalce termof gFluidivenMebychanicthe sc,ross forcing. 81, 209–223. product of the Stokes (or Lagrangian mass) drift velocity, associated with the high-frequency waves, and Continue sensitivity testing including higher- Fox-Kemper, B., G. Danabasoglu, R. Ferrari, and R. W. Hall- • resolution,the filteredrealisticvorticitwyavecforcing,tor in thande wacoupledter column. ThebCergL: 2v0o0r8t,ePxarafomreterizingce captsubmesoures thscae lerephctysicsifiedinegffloebactls of the filtered waves on the time-averaged dynamics. Numclimaeroutes imonvdels.estigCLIVatorARs, inExcsphangeired sb,y13t,h3e–5a.ppearance of models as necessary based on early results. Fox-Kemper, B. and R. Ferrari: 2008, Parameterization of the locally parallel windrows, have carried out theoretmicixedal stlauyderieeddies.s andII:nuPromegnoricsisal asndimimpaulatct.ionJournals of thofe 2D It should(genbeeraplossiblely downtowicompletend invariathisnt) proCLjectequawithintions; see e.g. LPhysiceibovialchOc(e1ano985gr)aphy, Le,ibinovpress.ich et al. (1989), Cox et al. a short(1time992a)frame,, Cox ewitht al. preliminary(1992b), Coxresultsand Lbeyibothevich (19La94ng),mCuir,hinI.:i a1n93d8,LSurfaeibocevimchotio(2n00of3w),aterChinducedini andbyLweiind.bovich (2005), Li and Garrett (1993), Gnanadesikan and WelScleier nc(1e9, 9875,) 1a19n–d123L.i and Garrett (1997). With the end of summer, 2008. Large, W., J. McWilliams, and S. Doney: 1994, Oceanic ver- exception of the secondary stability analysis of TandonticaanldmixingLeib:ovAicreviewh (199a5nd), ahomwoedelverw,ithinvaevsterticaigatliok-ns of the stability of 2D roll solutions of the CL equations topro3fileD dboisundaturbryanlacyeers paharavme eterizabeentioren.strRiecvt.edGetophys.o we,akly 3. Summarysupercritical forcing conditions, where weakly nonlinear36o3r–4s0m3.all wavenumber (i.e. large cell aspect-ratio) Leibovich, S.: 1977, Convective instability of stably stratified An estimationapproximaoftiothens ceaffnectsbe uoftiliLangmzed (Cuirox acircula-nd Leibovich 1997w,aterBhinasthekaroacean n.anJournald LeibofovFluidich 2Me00c2hanic). s, 82, 561– tion on global climate is proposed. If sensitivity is 581. Li, M. and C. Garrett: 1997, Mixed layer deepening due to found in regions of climatic importance, it will sup- langmuir circulation. Journal of Physical Oceanography, port conItinn tuationhis inveofstiagahighlytion, wineterdisdevelciplinaryop a stroncol-gly nonlinear27q,u1a2s1i–-133D2. approach that relaxes the assumptions laborationof str(fourict dospwnewcialitieind insvaarerianrepresence and wtedeakbysuthepercriticaMcWilliality yemt s,exJ.ploCi.,tsPt.hPe. sSullivlow adn,owanndwiCn.-H.d vaMoriaengbi:lit1y99o7f, the Langmuir turbulence in the ocean. Journal of Fluid Me- investigators),appropriaandtely bringcoarsedev-graelopmenined flotsw.atSptheecificut-cally, we obtacihanicsn a re, d334uc,e1d–3d0.escription of Langmuir turbulence ting edge of applied mathematics into practical use Smith, J.: 1998, Evolution of Langmuir circulation during a in the world of global climate modeling. A novel cli- storm. Journal of Geophysical Research-Oceans, 103, 12649–12668. mate sensitivity with potentially substantial impact Deep.Sea Research, Vol. 35, No. 5, pp. 711-747, 1988. 0198-0149188$ 3.00 + 0.00 Printed in Great Britain. ~) 1988 PergamonP ress plc.

Langm*REPORTSuir, do we care?

Role of Langmuir Circulation in the Deepening Abwater,is theh isbuoyancythe depthjumpof theatmixedthe baselayer,of andthe Langmuir circulatiofonthe wiOceanthin thSurfacee oceanMixedic miLayerxed layer layer. Using model results for Wdfn/U*, this means that Langmuir circulation will deep- Maybe: Ming Li,* Konstantin Zahariev, Chris Garrett en the mixed layer until ROBEHelicalRT Amotions,. WEknownLLEasR*Langmuir a n d circulation,JAMES areF.a keyPRphysicalICE* process in the upper Ab = cu*/h (2) ocean but have not yet been incorporated into ocean models. Here, surface mixed layer where c = 0.72SJ(v1); values for v were deepening by Langmuir circulation was added to that due to convection or velocity adjusted to match vertical velocities be- shear; Langmuir circulation is more important than shear if the velocity difference tween the model results and observations (Received 15 June 1987across; in revisedthe mixed-layer form base23 Novemberis less than about 1987;1 percent acceptedof the wind 27 Novemberspeed. In an upper 1987) (9-12). We estimate that c 50 for fully ocean data set, evidence was found for the deepening of the mixed layer by both developed seas, although it may be signifi- Deep.Sea Research, Vol. 35, No. 5, pp. 711-747, 1988. 0198-0149188$ 3.00 + 0.00 Printed in Greatmechanisms. Britain. Thus, Langmuir circulation influences upper ocean diurnal and~) 198seasonal8 PergamonP rescantlys plc. smaller in developing seas (1 1). Equa- changes in stratification. tion 2 is similar to that of an entrainment Abstract--The three-dimensional flow in the mixed layer associated with Langmuir circulatmodelion based on u* (13), but our formula is was studied with a new instrument capable of directly measuring the three componentsbased of on process modeling of Langmuir circulation (which was not present in the lab- velocity. Regions of converItgehasnt beensurfoverace 50floyearsw wsinceere Langmuirlocated wperature.ith surHere,face wedrattemptifters.to Iestablishn thesethe regioratoryons experiments), and the coefficient c the downward vertical and describeddownwwind-inducedind horizovorticesntal cinomtheposur-nentsrole ofof thLangmuire flow wcirculationere cominpthearadeep-ble in sgivesize an explicit dependence on the sea state and, at times, in excess of 2face0 cwatersm s-1. of Toceanshis dandowlakes,nwinknownd, doaswnweningellinofg theflomixedw waslayer, jet-usinglike observa-in structuandre,turbulence parameterization. LangmuirLancirculationgmuir c(1).ircInulthis,atiothen wcoun-ithin tionsthe otoceexamineanic ma ixnewed buoyancylayer jump Enhanced shear instability may occur in wMaith thybee max imNumo t:velocityterrotating located bvorticeselow arethealigned surfacwithe. Atheway criterionfrom thderivede dowfromnwea lnumericalling regimodelons anda ihorizontallyn confined region beneath wind and have surface convergence zones (9). downwelling jets to cause further the lower half of the mixed layer beloRwOB EthReT Ac.o nWvEeLrLgEeRn* caen dz oJAnMeEs,S Fth. eP RfICloEw* associated with the deepening Langmuir cells was an ordethatr ofare maoftengnitmarkedude smby anarrowller abandsnd nooft wellWind-driven resolved ishearn thecurrentse exandperisurfacements. (9),On but further work is required to learn foam and flotsam. After a series of inge- waves are currently accepted as necessary how this should be parameterized. For the some occasions, when Lan(Receivedgniousmuiexperiments,r c15e lJunels a 1p9p87Langmuire; ainr erevisedd suconcluded fdodrme n23l yNovember, thmechanismsey w1987;ere accepted forabthele generationt 2o7 Novembermix tofheLangmuir 1987)wea k nemoment,ar- we assume that it is implicitly surface stratification that hthatad thisformphenomenoned in repconstitutesonse tothe dies-urnalcirculation heating(1O).. TTheheymean coparticleuld al(Stokes)so maintincludedain in the bulk Richardson number sential mechanism generating the surface drift of surface waves tilts the vertical (Rb) criterion used in the Price, Weller, on June 2, 2008 large shears in the wellA-mbsmixedtirxacetd-- Tlayer.fhleu ithdThisr een-edlayeriamre ntsishioethen als flinkulorwf abetweeninc eth.e Tmihxedvortexy l adyeird a linessnsoocitaof,t edha ownear-surfaceiwthe Lvaengrm, upirdownwinde cnirecutlraatioten wandithPinkel (PWP) model (6). This criterion strength to the base of rewlaisc thetst umdatmosphereiiexd ewdi thla ay enanderws oithenbstsredeepumrvenetoceand c adpuabrandlien ogf sdiujetremcttomly emproducere-alsiukrieng streamwisec tohne dthirteieo vorticityncosm oporn teonwitht st hoef bstatesase that further deepening will not occur of deeper, more isothermvelaodirectlycli,t ym. Riexgaffectseiodn sl oathefy ceoair-searnsve rogbenfluxesste sruvrfeaofcdemomen- fdlouwr winerge lsosurfacetcoatredm wyconvergenceit hc sounrfdaciet idoratinftsether.s . Ijetn thmaximum;ese regions if the dtum,ownwheat,ard vanderticgasesal and(2). dowItnwisinalsod hoofrizgreatontal comtheponjetentsis ofthen the floreinforcedw were combyparcontinuedable in size Ab 2 0.65 (3) and,importance at times, infor excbiologicaless of 20 cmproductivity s-1. This doandwnwindacceleration,, downwellingby flowthe waswind jet-likstress,e in strofucttheure, AU12/h withmarine the maxpollutionimum vel(3).ocity located below the surfaceconverging. Away fromsurface the dowflow.nwelling regions and in where Au is the velocity difference across the lowDespiteer half oLangmuir'sf the mixed pioneeringlayer below work,the convergeUsingnce zothenes, Craik-Leibovichthe flow associatemodel,d with tLihe the base of the mixed layer. Comparison of Langthemuiroler cellofs wLangmuiras an ordecirculationr of magnituinde form-smaller anandd noGarrettt well resexaminedolved in ththeese einteractionxperiments.be- On Eqs. 2 and 3 suggests that engulfment by someing occtheasionmixeds, whenlayer Langandmuirin celdistributingls appeared sudtweendenly, Langmuirthey were circulationable to mixand thepreexisting weak near- Langmuir circulation dominates the deep- www.sciencemag.org surfaheatce standratifmomentumicat1io. n thIaNt hwithinTadR fOormitDehasdU inCnot rTepyetIoOnseN to stratification diurnal heati(9).ng. TThehey windcould stressalso misaiesti-ntain ening if largebeen sheadeterminedrs in the we(4).ll-miMostxed flmodelsuid nearof ththee surfamatedce. Thefromy didthe notwind, howspeedever, penethroughtrate wiath = strength to the base of relict mixed layers observed during summer-like conditionsU, or to the base lAul 9u. 0.01U, (4) of dmixedeeper, mlayerore iaresotheone-dimensional.rmal, mixed layersIn obso-served dragdurincoefficientg stormy cowithndititheons.water friction ve- LANGMUIR (1938) observedcalled lon"bulk"g, nmodelsarrow(5, 6),rochangesws ofin selocityaweu*ed1.3 oxn10-3 thUe . sTheeaStokes surdriftfacethat alis,igifntheedvelocity difference across the the depth and average velocity and densi- current u= 2SO exp (21z) is assumed to base of the mixed layer is no greater than nearly parallel to the wind itynof tthehemixed opelayern Aaretspecifiedlanticin. termsIntrigdecreaseued exponentiallyby the nwithotidepthon tz,hasafort atheabout pat1t%erofnthe wind speed, and less in of the surface buoyancy flux and some monochromatic wave of wave number 13; developing seas. of the seaweed indicated thcombinatione preseofncthee windof ostressr1g. aandInN iTzRtheeO dD U, CfortThIfullyOrNe edeveloped-dimenseas,siothenasurfacel flodriftw withThein PWPthe model can be modified to Downloaded from difference of the velocity and density be- velocity 2SO 0.015UW and the Stokes allow for the mixed layer to deepen if near-surface layer ofL tAhNeG MoUctweenIRe (1938)anthe, LlayeroAbsNeandrGveMdthe UlonIwaterRg,(1938) nabelowrrow it.rcowasrdrift roife scurrentdea oweuetde-folding ao ns tehredepthi esesa os1/(21)ufr ffalcoe wali gvniesdu ablizma- 2 0 AU12 These bulk models, as well as models that 0.12U2jg, where g is the gravitational ac- Ab < max(50u*/h, 0.65 1h) (5) tion experiments in Lnaekarely Gpatreateraollreturbulencelg teo .t hTe hwineinsdmoree in e tdetailxhep oep(7),reinm Asufferetlnanttsic celerationc. Ionntrfigiurem(11).d beyd Effectst hthe eno ofptiorturbulencene stheant tcheeare poaftt ecInstead,ron untweerdirectly- examined this buoy- of the sefromaweenotd inexplicitlydicated incorporatingthe presencthee okeyf orgaparameterizednized, threeby-diconstantmensioeddynal fviscositylow witvhin tancyhe jump criterion using measurements of rotating vortices whosnea ra-sxuerfsphysicala cwe learyeprocesses,r aofl itghen suchoecdea asnn,eLangmuir LaArNlGyM pUcir-aIRr(1938) allandel eddy ctaorr diffusivityitehde o uwt aiK. nsedr;ie fs loof tfsloawm vi saunaldithez as- uoceanrfamixedce layer. We used the data tion expeculation,riments thatin Laareke responsibleGeorge. Tforhesmixede experimeNumericalnts confimodelingrmed thshowse presthatenccounter-e of countfromer- the Long-Term Upper Ocean Study films formed rows when swlayerepdeepening,t into tandheit cis onotnvateallrgclearent rrotatingegionLangmuirs betwcellseearen generatedadjacandent v(LOTUS)ortice(14).s. The 2-year-long experi- These vortices are nrootawtin gc vthataorltliectheireds wLhoparameterizationasne agxmes uwierre acleiimplicitlyglnlesd, neaanrldymay p atrerodeahllee l thetfol otstratifiedhwe w iandsfluid;s foloctthroughsiaamte adnen-d swuriftament-fromhce theseMay 1982 to May 1984-had films formmodelsed rothesews wprocesseshen swecorrectly.pt into Eventhe caf-onvergulfmentgent reandgionmixing.s betwLangmuireen adjcirculationacent vorticfoures. periods within which simultaneous somewhat regularly sTphaescee dvoter rctiecarefulcellss a isrcalibratione cnoawll ecdaofl lempiricaleLd aLnagngmcoeffi-muuiirr ccelgeneratesilrs,c uanlda verticalttihoen f.lvelocities ow assoincitheatefluid,d wibutth thetemperaturese and current profile data were cients, the mixed layer models often over- vertical penetration is inhibited by stratifi- available for periods of 68, 50, 8, and 11 Such relatively largseom, eowrhgapredictat rneigzutheleadrlsea-surfacey, stpharcede c-temperatureedllism is ecanllsineidothe Lnaanglmcation. fuloirw cTheisrc sucellslhatoioustopnl. dpenetrating play a intosigthenificdays.antThe rofirstle period was chosen for our Such resummerlativelandy launderpredictrge, organiitzeind,the thrfallee-(8),dimenstratifiedsional fwaterlows sifhtheoulFrouded playnumber a significant roanalysisle as it had the best vertical resolu- in the transport of heaint ,th me troaalthoughnmspeonrt toufthese hmea at,discrepancies nmdo moetnhtuemr mayapnrdo oalsoptheerr tpireopse rdtioesw dnow fnr foromm thhee a iar-isre-a sinetaer fiation.ncet eTherfadata,ce obtained from a buoy lo- arise from errors in surface fluxes or from w,ncated at 34°N and 70°W, 300 km from the into the interior. Theinyt oa tlhseo iadvection nstehriooru. lTofdh watereayf afleswithoc sth taohudifferentled adffiesctem-ttr tihbe udtisitorinbu toiofn poFrlf apnl(hAb)"12atnsts aanndd a naimnailms(1), ablosth,mean ibn otpathh inof the Gulf Stream in the the near-surface ______region (Summv, 1983) and on the surface (FALLERa nd AUER, 1987),~~~Sargasso Sea, consisted of readings of tem- the near-surface regiaonnd t(hSe uCentreaimr-smforeaEarthv e,x andc1983)hOceanangeResearch, ofa ngadsUniversitye so (nFA ofLtVic-hLEeR sareachesnudr fPaEaRccriticalIeN I,( F1983)AvalueL LofaEn0.9dR (9).oa tnhHere,edr mAwdlnaUtteEr. RperatureIn, 1987),and ocean currents (eastward and toria, Victoria, British Columbia, V8W 2Y2, Canada. is the maximum downwelling velocity gen- northward) at depths of 5, 10, 15, 20, 25, and the air-sea exchadadnitgioen, *To othwhomfe yg pcorrespondencearosbeasb ly( FcoAshouldmLpLlibeEcaaddressed.Rte aattnemdp tPs EtocratedR sIaNmIbyp, leLangmuir 1983)mean p cellsroapneinrdti homogeneouseso tohf tehre smurfaa35,cttee 50,r. 65,In75, and 100 m, available at layer with Lagrangian drifters. addition, they probablAy ncuommbepr loifc ianvtees tiagtatieomns,p intscl utdoin gs tahmeoSCIENCErpeltiec aml, le*abaVOL.onra tpo270rryo a*pned22 rfDECEMBERtieileds s tuodfi1995e st,h hea vse urface 1955 layer with Lagrangiantr ieddr tiof tdeertesr.m ine the role of Langmuir circulation in various upper ocean processes; LEmOVICH (1983) and POLLARD (1977) provide good reviews of the efforts completed A number of invesptriogra toti 1o9n8s3., Hionwcelvuerd, iin gsp itteh oefo threstei sctaudli,e sl iat bhaodr raetmoarinye da unndcl efari ewlhde tshetur odri neost, have tried to determine the role of Langmuir circulation in various upper ocean processes; LEmOVICH (1983) and * PWOooLdsL HAoleR ODce a(1977)nographic Inpstritoutvioni,d Weo odgs oHooled, MrAe 0v2i54e3w, Us.S .oA.f the efforts completed prior to 1983. However, in spite of these studies it 711ha d remained unclear whether or not

* Woods Hole Oceanographic Institution, Woods Hole, MA 02543, U.S.A.

711 Waves+Wind != Wind Langmuir is ‘in’ KPP, but only based on wind

Really Langmuir depends on both u* and us Radar Altimetry Tutorial Is there data? Altimeters Radardo Altimetryboth Tutorial 3.1.2.2. Altimetric measurements over the ocean 3.1.1. Basicsim uPrincipleltaneously TheLea basic dinschematicg outlinesSlo of pa returne->Swel echo over the oceanl are as follows::

OverIn anv oceanerse surface, Ar the echoea->Ca waveform haspil a characteristiclarie shapes that can be described analytically (the Brown model). From this shape, six parameters can be deduced, by comparing the real (averaged) waveform with the theoretical curve: Thus, Local wind The principle of altimetry ! epoch at mid-height: this gives the time delay of the expected return of the radar pulse (estimated by the (Credits CNES/D. Ducros) tracker algorithm) and thus the time the radar pulse took to travel the satellite-surface distance (or 'range') and back again. Satellite-to-surface distance: Range ! P: the amplitude of the useful signal. This amplitude with respect to the emission amplitude gives the backscatter coefficient, sigma0. Radar altimeters on board the satellite transmit signals at high frequencies (over 1,700 pulses per second) to ! Po: thermal noise Earth, and receive the echo from the surface (the "waveform"). (the 'waveform'). This is analysed to derive a ! leading edge slope: this can be related to the significant wave height (SWH) precise measurement of the time taken to make the round trip between the satellite and the surface. This time measurement, scaled to the speed of light (the speed at which electromagnetic! skewness:waves travel), the yields leading a range edge curvature R measurement (see From radar pulse to altimetry measurements for Further! details). trailing edge slope: this is linked to any mispointing of the radar antenna (i.e. any deviation from nadir of However, as electromagnetic waves travel through the atmosphere, they can bethe decelerated radar pointing). by water vapour or ionisation. Once these phenomena have been corrected for, the final range can be estimated with great accuracy (see data processing). The ultimate aim is to measure surface height relative to a terrestrial reference frame. This requires independent measurements of the satellite's orbital trajectory, i.e. exact latitude, longitude and altitude coordinates.

Satellite Altitude

The critical orbital parameters for satellite altimeter missions are altitude, inclination and period. The altitude of a satellite depends upon a number of constraints (e.g. inclination, atmospheric drag, gravity forces acting on the satellite, area of the world to be mapped, etc). The period, or 'repeat orbit' is the time needed for the satellite to pass over the same position on the ground, uniformly sampling the Earth's surface. Inclination gives the highest latitude at which the satellite can take measurements. The radar altimeter receives the reflected wave (or echo), which varies in intensity over time. Where the sea surface is flat (a), the reflected wave's amplitude increases sharply from the moment the leading edge of the radar signal strikes the surface. However, in sea swell or rough seas (b), the wave strikes the crest of one wave and then a series of other crests which cause the reflected wave's amplitude to increase more gradually. We can derive ocean wave height from the information in this reflected wave, since the slope of the curve representing its amplitude over time is proportional to Waves+Wind != Wind Langmuir is ‘in’ KPP, but only based on wind

Really Langmuir depends on both u* and us

Is there data? Altimeters do both simultaneously

Fully!Developed Waves of 3.5 Pierson!Moskowitz (1964) 3

2.5

1.5 Probability Density

0.5

0 0 0.2 0.4 0.6 0.8 1 Turbulent Langmuir Number (u*/u )1/2 s

Aviso Merged Satellite Dataset, 11/12/05-05/27/08 Langmuir Circulations: Observing and Modeling on a Global Scale

B. Fox-Kemper, G. Chini, K. Julien, E. Knobloch June 18, 2008

NASA ROSES08: Physical Oceanography Research Proposal

1 Background and Motivation

Unlike the atmosphere, the ocean is forced primarily near the surface. The exchange of crucial quantities–momentum, vorticity, energy, gasses, freshwater, and heat–with the atmosphere and cryosphere is filtered through the action of the ocean surface boundary layer. It is thus no surprise that ocean models are sensitive to boundary layer processes (CITATIONS??). Improvement of the model representation of these processes (Large et al., 1994; Fox-Kemper et al., 2008) has proved an important way to improve the reliability and accuracy of climate models. This layer is only O(100m) deep, but through its influence on ocean-atmosphere exchange of these quantities the whole of the climate system is affected. Li & Garrett (1997) Almost all phytoplankton live within the mixed layer (where the light is), this biology w us combined with the saturation of water leads to an important role for the mixed laFyerr in= the 0.6 carbon cycle. Likewise, the air-sea exchange of other gasses is strongly affected by mixedNH ≈ 4NH ∼ layer depth (CITATIONS–ask Synte). Furthermore, mixed layer depth has a strong effect on hurricane strength through its role in setting the readily available ocean heat content (Emanuel, 1988). Estimate Importance from LES scalings Li and Garrett (1997) McWilliams & Sullivan (2000) 2 1/2 W V √usu u F r = ∗ 0.6 κ κ 1 + 0.08 s NH ≈ 1.5NH ≈ 1.5NH ≈ → u 2 ! ∗ " The mixed layer depth is the depth over which wind, waves, nightly convection, and 0.5 seasonal cooling have made a relatively unstratified75% surface layer. Often this1 layer is diag- 0.45 nosed as the depth over whichmedianthe potentialmeantemperature remains within 0.2K ofmodethe surface 5 3 temperature or the p0.4otential density remains within 3 10− kg/m . This small stratifica- · 0.8 median 75% tion is indicative of a0.35buoyancy frequency roughly twenty times smallerTextthan typical in themean

0.3 0.6 0.25 1

0.2 0.4 Probability Density 0.15 Probability Density

0.1 0.2 0.05

0 0 0 2 4 6 8 10 0 2 4 6 8 10 Langmuir Mixing Depth/Climatology ML Depth McWilliams and Sullivan Scaleup (1+0.08*(u /u*)4)1/2 s

N, MLD Based on Argo Climatology (Speer & Wienders)

Aviso Merged Satellite Dataset, 11/12/05-05/27/08, Assuming 120m Wavelength

1 Langmuir Circulations: Observing and Modeling on a Global Scale Li & Garrett (1997) w u F r = s 0.6 B. Fox-Kemper, G. Chini, K. Julien, E. Knobloch NH ≈ 4NH ∼ June 18, 2008

NASA ROSES08: Physical Oceanography Research Proposal McWilliams & Sullivan (2000) 1 Background and Motivation u2 1/2 κ κ 1 + 0.08 s → u 2 Unlike the atmosphere, the ocean is forced primarily near the surface. The excha!nge ∗ " of crucial quantities–momentum, vorticity, energy, gasses, freshwater, and heat–with the atmosphere and cryosphere is filtered through the action of the ocean surface boundary layer. It is thus no surprise that ocean models are sensitive to boundary layer processes (CITATIONS??). Improvement of the model representation of these processes (Large et al., 1994; Fox-Kemper et al., 2008) has proved an important way to improve the reliability and accuracy of climate models. This layer is only O(100m) deep, but through its influence on ocean-atmosphere exchange of these quantities the whole of the climate system isLiaff&ected.Garrett (1997) w u Almost all phytoplankton live within the mixed layer (where the light is), Fthisr =biology s 0.6 combined with the saturation of water leads to an important role for the mixed layer inNtheH ≈ 4NH ∼ carbon cycle. Likewise, the air-sea exchange of other gasses is strongly affected by mixed layer depth (CITATIONS–ask Synte). Furthermore, mixed layer depth has a strong effect on hurricane strength through its role in setting the readily available ocean heat content (Emanuel, 1988). Estimate Importance from LES scalings Li and Garrett (1997) McWilliams & Sullivan (2000)

4 1/2 us W V √usu∗ 1 + 0.08 | | 2 : u∗ us > 0 F r = 0.6 κ κ (u∗ us) ∀ · NH ≈ 1.5NH ≈ 1.5NH ≈ → · # $1 % : u∗ us < 0 ∀ · The mixed layer depth is the depth over which wind, waves, nightly convection, and 0.5 seasonal cooling have made a relatively unstratiﬁed surface layer. Often this1 layer is diag- nosed as the depth ov0.45er which the potential temperature remains within 0.2K of the surface 5 3 temperature or the poten0.4 tial density remains within 3 10− kg/m . This small stratiﬁca- · 0.8 tion is indicative of a0.35buoyancy frequency roughly twenty times smaller than typical in the 75% 0.3 median mean Stok0.6 es’ Drift is sensitive to wave period. 0.25 1 1 mode 75% 0.2 0.4 median Probability Density Probability Density 0.15

0.1 0.2 0.05

0 0 0 2 4 6 8 10 0 2 4 6 8 10 Langmuir Mixing Depth/Climatology ML Depth McWilliams and Sullivan Scaleup (1+0.08*(u /u*)4)1/2 s

N, MLD Based on Argo Climatology (Speer & Wienders)

WaveWatch III Data-Assimilating Wave Model Li & Garrett (1997) w u F r = s 0.6 NH ≈ 4NH ∼

McWilliams & Sullivan (2000) u2 1/2 κ κ 1 + 0.08 s → u 2 ! ∗ " Satellite versus Model

Stokes’ Drift is sensitive to wave period. 3 2 π Hs us 3 ≈ gTw 4 4 Fully!Developed Waves of 3.5 3.5 Pierson!Moskowitz (1964)

3 3 No Direction Info

2.5 2.5 Synth. Direction 2 2 Info 1.5 1.5 Probability Density Probability Density No Direction or 1 1 Period Info

0.5 0.5

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 * 2 1/2 Turbulent Langmuir Number (u*/u )1/2 Turbulent Langmuir Number (u.u /u ) s s s

WaveWatch III Data-Assimilating Wave Model Aviso Merged Satellite Dataset, 11/12/05-05/27/08 (attempted to rescale ﬁnd surface wind-stress) 1 State of the Art: n io t

a Applied Model t

Fundamental en Hierarchy em Model Hierarchy Wave Resolving Model Wave Resolving 3d DNS Impl C-L Equations 3d C-L LES Full Wave Model Asymptotic-3d PDEs Asymptotic-2d PDEs Simple Wave Model Single Mode PDEs Climatology Forcing Equilibrated Scaling Wind-Only Forcing Our Goal: n io t

a Applied Model t

Different Drag

Same Wind Conclusions

Langmuir turbulence may play an important role in mixed layer mixing and deepening

Langmuir scaling requires wind & waves

Proper parameterization requires development of theory, as well as implementation of a wave model

Once we’ve got the wave model, it will be useful for other things!