rssN 1560-7496
POCCI{I4CKA'I AKA NEMVIS., HAYK CI,IE I4PCKOE OTNEJIEH HE
KPMOC$EPA SEMJIW
OKTgEPb_NEKAEPb TOM Xr.2007
(oTAEJrbHnilA OTTT4CK)
HOBOCHb14PCK
AKAAEMI4qECKOE H3AATEJIbCTBO <fEO)
MonElrupoBAnun asunuruult rEMnEpAwpHofo n rnlpoloruqEcKoto pDKnMoB MEP3lIorbI Pa6ora BbrrroJrHeHa npl4 rloAAepxre P(DOZ
(rpaHru Nb 06-05-64502, 05-05-64907), rpaHra llpe- 3r{AeHra PO (HIX-4166.2006.5) u nporpauu Or4e-
JreHus. HayK o 3err.rne PAH.
Jlureparypa
Anrcuuon O.A. 06 ouenKe rlyBcrBvreJrbtrocrz reuHoft uepa- Jrorbr K r43MeueHr,rro r.no6a.nlnoro repMrlrrecKoro pexvMa 3eM- noft nonepxuocrn / / Me'reopororus u rqporlorr4f, 1989, N 1, c.79-84.
Auncuuor 0.A., Ee.no.ryqraa M.A. Mo4enuponanfie soaAeft- cTBr{fi aHTporroreEHoro noTeIIJIeHI4fi Ha BeqHyIo Mep3JIoTy: yrreT Brrvrsanns. pacrzreJrbnocru / / MercopoJlon4s fi r'trI'polrorvs, 2004.}s lI.c.73-82.
Bo;roAsn E. M., Jlrrrcocor B. H. flapauerpl43arll4t npo[eccoB TenJro- 14 sraroo6rn{eHa B cr{creMe pacrl,ITeJrbHocrb-noqBa AJrt MoaeJrr.rpoBanr4r o6uefi uzpxy.txuun arrvrocQeprr. Ouucauue ra pacrrerbr c ficnoJrb3oBaHI.reM JroKaJIbHbrx aanrrhrx na6rro4e- uuir // Zgn. PAH. (Drier.rKa aruocSepn,I oKeaua, 1998, r.34, N 4, c.453-465.
Io.nm$m LC. K reoprau KoHBeKuI{I{ Bepxuefi rr,ranrzlr / / Aoxn.
AH CCCB 1977,r.234, N 3,c.552-555.
,{eu.renrco [I.(D., Be;rn.mo A.A., E;rrceen A.B, u ap.
3aaucr.rldocrr yc.ronuft paclpocrpateura.a ne.ruoft MepsJIorbl or ypoBHr rro6aarnoro rlorenJIeEI,Is: cpaBrIeHlIe rraoAelefi, crleuaprleB r{ AaEHbIx naJreopeKoncrpyruufi // I4zn. PAH.
(Dr.raura aruocQepu r oKeaHa, 2002,r.38, N! 2, c.165-174.
Heqaes B.[I. O uexoropbrx coorHorlenruIx MOKAy Mep3Jrornbr Mr4 lr KJrLlMarrlqecKI,IMr4 fiapaMerpaMrr r{ nx na;reoreorpaQrauec- xoe snauenue / / Bonpocrr ra;reoreorpaSlrra n.teftcroqena leA- HrrKoBbrx u nepfiulsuraJrbrblxo6tacreir / Pe.q. A.A. Be;ruuro, B.II. fpr.rvyrc. M., Hayra, 1981, c. 211-220.
Ilanaos A.B. Mep3JrorHo-KJII4MaTI{qecKI'Ie IlaMeHeHI,I{ Ha ceBe- pe Pocczu: valrtorewrs, npofno3 // I4sz. PAH. Cep. reorp.,
2003, N! 6, c.39-50.
Ila{encrrfi fl.A., IlaqencrcaaJI.E., Mnpouenlco E.B.' Ko- nrapor A.C. Mo4e.nlrpoaawle BoAno-coJreBoro pexr,IMa rtoq- BorpylrroB c licrloJll,3oBanaeu 3BM. M., Hayxa, 1976,
140 c.
Cuuonon B.B. O srlattuu Bnyrpl{roaoBbrx Mexce3oulrblx cBt- eefi na repuxry rpyuroB r paftonax se.Inofi Mep3JIorbI / / Me- reopoJror't4r rr ilrApoJrorru, 2000, }s 5, c. 15-22.
Goodrich L.E. Efficient numerical technique for one-dimen- sional thermal problems with phase change / / Intern. J. Heat.
Mass Transfer, 1982, No. 5, p. 160-163.
Nelson EE., Outcalt S.I. A computational method for predic- tion and regionalization of permahost / / Arctic. Alp. Res., 1987, vol. 19, No.3, p. 279-288.
Uppala S.M., Krillberg P.W, Simmons AJ. et al. The ERA- 40 re-analysis // Q,tarten J. Roy. Meteorol. Soc., 2005, vol. 131, p.2961-3012.
Zhang T., Barry R.G., Knowles K. et al. Statistics and characteristics ofpermafrost and ground-ice distribution in the Northern Hemisphere // PoIar. Geogr., 1999, vol.23, No. 2, p. 132-154.
Ilocrngmua o pedarc4uto 29 noa6pa 2006 z.
69
HAYTIHbIfi XCYPHAJI
K P I , I O C ( D E P A S E M J I 1 4
Kpuocifepa 3ennu,2007, r. XI, N 4, c.70-79 http : / / ww w.izdatgeo. ru
CHDITHhII;I NOKPOB U JIENHUKN
yAK 910.1 551.8
JTATPAHIICEB METOA PACTTETA BOSPACTA r{ IISOTOIIHOTO COCTABA JIbAA B TPEXMEPHO IZ MONEJII,I AHTAPKTI,ITIECKOTO JIEAHI,IKO B O TO qIITA
O.O. Pu6arcl'2, (D. X66pexrc2'3
1 Co"am&ratil uayuuo-uccneOoaamenocrcuil qeump PAH,354000, Couu, gn. Teampanouaa, Sa, Pocan, snic@sochi'ru 2 Llucmumgm nonapttbw u ntopcrcur uccae)oeauttiun. A. Bezeuepa,,[-27515, BpenepxaQen, lepnauua
3 Cao6odaod gnulepqtmem Eproccena, zeozpaQuuecrcuil Q-m, 8-1050, Eproccena, Een zun
A'.g onucauug. a"{BeKrlrrr{ B MareMarr4qecKlx MoAeJffrx Jre,{Er{KoBbrx lqvroB l4crloJrb3yrorcg ABa noAxoAa - efi.nepoa rr JrarpaxxeB. B uacrosqefi pa6ore cpannuBaercs rpa,qr{Ilraouur,rfi aiiaepon MeroA c ortocl'IreJrbr{o HoBbIM B rJrgrlr4oJroruqecKnx flpltroxenusx rarparrxenrru. JIarpaHriKeB Meroa, 3arrlorrarol[uitcxs otcrexura' Hnrr rpae6Topuft yc;ronntrx qacrr.ru .nlAa (rpaccepon) nny"rpz JIeAHI4KoBoro turrra, Moxer rIp[MeInITbct AJIf perrreHr{fl 3aAaq Aar[poBKI{ JIbAa, BoccTaHoBJreE[g ero r{3oronHoro cocTaBa il AJIfi nocTpoenfis norf rro6ofi rorceptaruunofi xaparrepucrr,tKlr, Koroparr rrepetocr.rrcg c rloro(oM JIbAa. OAux rr3 aJIropI,ITMoB JIafpaHXeBa Mero,Ia, uo.nyvurmrafi HaBBaHrre Particle-in-Cell (PIC), cocrorrr B nocJreAoBareJrbnoM BoccranoBJretrrrr rpaeK- Topnrr rpaccepa rro Mepe ero fiepeMeueHr,rf, B aBoJrroqrronl,tpylorleM JIeAHr4KoBoM IrII{re I4 Qlarcuponanzz xor- cepnarnnuofi xapa4repr,rcrr4Kr,r BAoJrb rpaeKropr,rrn. Sror a.nroprrrM,{ocraroqro npocr B npurr,reneHrau n eQ$ex- Tr{BeH, oAgarco rpe6yer 3fiaqr.rrerbroro pacxoAa Maurrunoro BpeMeurr. OcnonHoe ero fipeltMyrrlecrBo rlo cpaB- nenuro c afireposlrM noArogoM 3arofioqaercr B roM, uro on ne rpe6yer BBeAeHns AoIroJrHI,ITeJIbHofi auQQyeuu na guxnefi lpaHrrrle Ns cra6unutaq[r,r Bbltrr4cnenufi, vro cyilIecrBeHuo noBbllrraer ero rorrnocrb n nzxnefi rracr[ rearr4KoBoro qr4Ta. Mero,q PIC Aaer Bo3Moxnocrb HenocpeAcrBeggo fioryqurb rpaeKTopt4lo rIacrI'IIIbI, rrro BaiKHo a.rrs BoccranoB;rerrns oco6ennocrefi rroroKa, rr HerrocpeAcrBeHHoe pacnpeAe.Irerl,le ucron'roft xapar- Tepr/rcrrrKr,r Ha n3oxpogr{ofi noaepxnocru. Onrranta.lrrnoe ucIIoJlbgoBauue JlarparlxeBa noAxo.4a 3axJlloqaerct B co6nroAenr.rrz pa3yMuoro 6a.naHca uexAy Bbrrrr4crurerbnblMfi 3arpararr.tlr z rpe6yervror? ro'rnocrl]o'
Jledmtrcoewil uptm, Bospacm nada, usomonnoni cocmaa noda, ilame.ntamuLtecrcaa nodettt, Aumaptcmuda LAGRANGIAN METHOD FOR THE CAI.]CULATION OFAGEAND ISOTOPIC COMPOSITION
OF ICE IN A3D ANTARCTIC ICE.SHEETMODEL O.O. Rybakl'', Ph. Huybrechts2'3
1 Sochi Scientific Research Centre 1."1.5,354000, Sochi, Tbatralnaga str.,8a, Russia, mic@sochi.ru tAlfnd Wegener Insiitutfi)r Polar- und Meeresforschung, Postfach 120161, D-27515, Bremerhanten, Germang'
fDepartement-Geografie, Vrije Unioersiteit Brussel, Pleinlaan 2, 8-1050, Brussels, Belgium
Two basic approaches exist for describing advection in the ice sheet model. We proceed with.comparing traditional Euleriin approach with a rather new in glaciological applications Lagrangian one. Particle tracing in the ice sheet is requiied to deal with such problems as detailed ice dating,establishing itf isotopical cornposition, or distribution of any other conservative ciaracteristic, which is advected with the ice flow. Within the frame of the Particle-in-Cell-(PlC) algorithm, a particle's trajectory is construited by numerical-interpolation as it moves through "n .uoluing ici sheet within a regular 3D grid. The algorithm !" conceptually straightforward, but demandiig in terms of"its practical implemenlation. The main advantage of the alsorithrn as compared to a pure Eulerianipproach is thafit is diffusion free, which makes it much more accurate in ttte lower part of the ice iheet. Application of PIC immediately yields the trajectories of the-particles, which is important for reconstruition of the flow peculiarities and the distribution of transported properties on isochronous surfaces.
To irnplement it in the most effective way it is necessary to follow accurate balance between computational overhead and designed accuracy.
Ice sheet, ice chronolog, isotopic composition, mathematical model, Antarctba
BBBAEHI,IE
Peruenue Bal.asv aABeKIIT{I4 B MareMaruqecnoM MOAeJrr{poBaHAV reilIluKoBblx IqrlTOB CBfl 3aHO, Irpe)K- Ae Bcefo, c BoccraHoBJIeHr{eM xpoHoJIorI4I{ JIbAa }r efo
@ O.O. Prr6ar, tD. X66pextc,2007
r43OrOrrHOfO COCTasa, a raK)Ke c Heo6xoAnMocrblo pac- rrera a,qBeKrlur4 TelJIa npl4 pacqere noJl.fl TeMneparypbl ar4a. TpagnqlroHHo ypaBHeHI4e a,4BeKIILlI4 pelraercs B
]IATPAHiITEB METON PACqETA BO3PACTA U NSOTONHOTO COCTABA Nb,4A paMKax sHnepoBa MeToAa, T. e. perreHl,Ie HaxoAr{rcfl B
y3nax npocrpaHcrBeHHofi cerKu. 3ro, o4Harco, ue e.4r,rHcrBeHHo Bo3MoxcHblit noAxoA. B nocleAnue ue- cKoJrbKo ner B paSrI4qHbIX r,TgIII4OnOfUrreCKUX npUJIO- I}CceHr4fl X CT A.Jil4 I-dCfiOrrb3OBaTbC.s naIpaHXeBbI MeTOAbI.
.Ilarpanxeou MeroAbI He .f, BJI.aIorcs coBeprueHHo HOBbIMI4 B MATEMATHI{CCKOM MOACNI4POBA]F-]I1IIL. OHI4 npr4MeHqroTcs B pa3n[qHblx HaJnIHbIX U npaKTr'tqec- Kr4X rlpr{JIOXeHrrqX, Har{rtHarl c Tofo BpeMeHl4, KaIt AJrfl.
3TI4X UeJIIefi C"ra]|rl,Zr U1rroJrb3oBaTbc.tr caMll KoMnbIoTe- pu. llo-qu4lrMoMy, oAHI4Mrr rr3 nepBblx o6lacrefi rrpI4JIOXeHH.fl JrafpaH)KeBblx MeroAoB cranr4 rnEpoAI.4- HaMrrKa n $uzuxa IrrIa3MbI fHarlou, 19641. Yxe Ha paHHeri cralvv 6u,'Io yraaaHo Ha ocHoBHyIo rpyA- Hocrb npr{MeHeilus qucro nafpaH)KeBa MeroAa. fL Be- naHAep fWelander, 19551 noxazar, rrro MHo)KecrBo xrlAKrlx q acrurl u3 Harr a,'IbHo peryJlgpHo pacnpeAe - J'reHHbrx, BnocJreAcTBrrr,I AeoopMupyercfl HacronbKo' qTo efo cTaHoBuTcfl HeBoSMOXHO TTI4CIeHHO nHTelpZ- poBaTb. B cesau c STrrM Ha npaKTI{Ke rlarle ucnoJlb- SyroT aJrropI4TMbI, coqeTaloull4e B ceoe ooa MeToAa - afi "repoe rr JrarpaHxeB.
B Ha.{are 1950-x rr. rpaQrlvecKrfi narpanxeB aJrropr4rM 6lu npe4lo)KeH AJIfl pellreHrr"f, 6aporpon- HO|O ypaBHeHVs. BvIxps. B 3aAaqe [pofHo3a noroAbl [Fjortoft, 1952]. 3napa6oracrarla Irr{oHepHofi B pflAy TaK HaSbI BaeMbIX nOJIyJIaf paH)KeBbIX (I'IJII,I KBa3I4nar-
panxenHx) MeroAoB (Semi-Lagrangian Technique,
SLT). Cauo rloHflrr{e noJIyJIarpaH)KeBa MeroAa 6bIJIo BBeAeHo HecKoJIbKo rlo3xe n pa6ore fWiin-Nielsen,1959).8 ocHoBe ero JIe)IcI4r nAe.fl o6HoBnenufl.Ha6o- pa JrarpaH)KeBbrx qacrr,Iq (rpaccepon) Ha Kax,qoM Bpe- MeHHoM ruare rrHrerpr{poBaH}rs fSt anif orth, C 6t e, 19911. Paz6op aroro aJlroprrrMa, no cyqecrBy "sBn"fl- Ioil{erocs [epeoopMyJlrrpoBaHHblM BapI4aHrOM pa3Ho- crHofi cxeMbr Jlarca-BeH.upo00a, B Koropoft ql4cro KypaHra Moxer 6rtrr 6olrrue I fBermeio, 1990f, nw- xoAr.rr 3a paMKr4 Hacroslqefi pa6oJbl. Yraxena roJIbKo, rrro flocJre cyqecrBeHHblx ,qopaooroK r{ ycoBeplxeH- crsosauufi s 1960-1980-x rr. fKrishnamurti, 1962;
Sauger, 1963; Bates, McDonald, 19821 on craJl Ixnpo-
KO rlpr,IMeHgTbcg Ha npaKTI{Ke, B r{acTHOCTI4, rlpl,I qUC- JreHHbrx npofHo3ax nofoAbl. B rrgq[olorl4qecKrrx npHnoxeHl,If x rlonyJlarpaHxeBbl MeToAbI Harlanu r4c- rroJrb3oBarbc.s HecKoJIbKo JIer Ha3aA Anfl MOAenI4pO- BaHvfl SBOJIIOqT{OHLTpyIOIUI4X CrparI{rpaQI'IqecKux crpyKryp fpeHJIaHACKOTO r{ aHrapKrurrecKoro JIeAHrr- KOBbIX IqUTOB, AJI.f, BOCCTAHOBJICHII"fl I{X IT3OTOIIHOTO 6ar'auca, Ant nocrpoeHrr{ BeprtrKaJ'IbHblx KpHBbIx reMneparypbl Ir Ll3ororlHofo cocTaBa JrbAa B BI4pryaJIb- Hbrx KepHax lClarhe, Marshall,2002; Tarasoo, Peltier, 2003; Clarke et a\'2005; Lhomme et a1.,2005a, bl.
A.ns ue,reft HacroflIrero zccneAoBaHn.s SLT ne noAxoArrr no psAy nputlr{H. Bo-nepaux, oco6eHHocrl4 anropr.rrMa SLT rarosH, qro B [poqecce pacqeroB Tepsercs vrnp.r4Bu4y aJrbH ocrb KaxcAoIT rI a crI4IIbI, ro - cKoJrbKy, KaK yKa3aHO BbIIrIe, Ha KDKAOM BpeMeHHOM rrrafe rrporr3B ol.r4'rcx. o6Hoereuue Ha6opa rpaccepoB.
Bo-eropr'rx, cBoficrBa fiepeHocr{Mblx KoHcepBarrrB- Hbrx [onefi r{HTepnonEpylorc.s Ha Ka-)KAOM BpeMeH- HOM llrare, qTo, Iro cyTI4, o3Har{aeT I4x npocTpaHcT- BeHHOe CUraxr,rBaHI{e. BMecro sLT ulr ucIIoJIb3yeM Apyryrc KOM6I4HaUI4IO Sfi"uepona u JIarpaHXeBa MeT0- AoB, rroJl)ryuBlxylo HasBaHI4e Particle-in- Cell (PIC) fHarloa, 1964; HochneA, Eastu)ood, 1992l.Tar )Ke KaK z SLT, aJrropl4rM PIC npe4noJlaraer I4cIroJIb3oBaHne pery.napuofi npocrpaHcrBeHHofi CerKI{, Ha KOTOpOI;
paccquTblBaloTcs MOAeJIbHbIe rIoJIfl cKopocTI'I rloroKa JrbAa. Tpaccep, KoTopblfi [epeHocrlr HeKoropoe cBofi- crBo rro,,rf, nepeMelrlaeTc.f, BHyrpr{ flqeftKr4, o6paao- BaHHOfi y3JIaMIr CerKI4 (OTCIOAa npOlIcxo/nr HasBa- Hr4e MeroAa). Konruouenrbl cKopocrll rIoToKa vHTep- floJrrlpyloTc.fi B ToqKy c TeKyIunMr{ KoopAl4HaraMrr rpaccepa. flocrcoarry B Haluefi pa6ore vccne[yrorcfl KOHCepBaTI{BHbIe rIoJIg r{, cJIeAOBaTeJIbHO, Tpaccepbl He B3alIMoAeftcreyror MelKAy co6oit vr c noJIeM cKopo- cTvr, sanaqa locTpoeHl{t TpaeKTopr{u qacTuubl cBo- n.Vljt Cfl, K [OCJIeAOBaTeJIbHoMy trHTelpI4poBaHHIO KOM - rroHeHT cKopocTl4.
B pa6ore fRgbak, Hugbrechts,2003l n rpocrofi
AByMepHofi cxeMaTl4qecKofi MoAerI.l Hcc"'IeAoBaHbI Ao- cror{HcrBa r{ HeAocrarKn o6ovx MeroAoB - 3firepoBa 14 JrarpaHxeBa (PIC-ueroAa). B 3rofi xe pa6ore o6o- r4Mr{ MeroAaMu r{3JAIeHO rlone BoSpacra JIbAa B cralllll- onapHoir Bepcrrl4 rpexMepHofi aHrapKrurlecKofi MoAe- Jrn, ortrtcaHHofi B fHuybrechts, de Wolde, 1999;Hug bre chts, 2 0 0 21. Ycrauos,'Ieno, qro ofi nepoB MeroA Aaer 6cirnruyro oruu6xy B oIIeHKe Bospacra JIbAa no cpaBHeHr4ro c narpaHxeBblM MeroAoM. ornoclrrell- Hiur paSHr{ua B Aarl{poBKax BeJIrrKa y 6oronlrx rpa- Hr{rI n oco6eHHo y HI4XHefi fpaHrrllbl LuIrTa, rAe afilepon MeroA nporHo3r{pyer Bo3pacr c ourra6Kofi nop.flAKa HecKo,rlbKr{x npoIIeHTOB OTHOCUTeJIbHO aHa-
II,ITUIIECKO|O PEIXCHI4.'I (B ilPOTHO3C JIAIPAHXPBbIM
MeroAoM oHa cocraBJls.er ilonn npoqenra). 3rb o6- cro.rrrenbcTBo Aenaer JIarpaHXeB noAXoA IIepcneKTr{B- HbrM MeTOAOM B rI;UIeOKJII'IMaTUrrecKux peKoHcTpyK- ullsx, nocKoJlbKy Bo3pacT JIbAa SKCTIOHeHUITZUIbHO pa- cret c rny6uHoir, vr MaKcr{MaJIbHo roqHa-f, AarI4poBKa B Hr4)KHrlX CJTO'X neAHpIKOBbIX IqI'ITOB npeAcraBJlf er co- 6ofi naxHylo 3aAar{y, Koropa;I BoaHI{Kaer, Hanpr{Mep, B xoAe o6pa6orKl4 AaHHbIX uy6ororo 6lpeuux.
fIoreHIInarlHble oruu6Kl4 JIarpaH)KeBa MeroAa cBfl3aHbr, npexAe Bcefo, c oluu6KaMl'I IrHTepnOJI.f,IIrlu KOMTTOHeHT nOJIfl CKOpOCTV B TOTIKy TeKynlero noJlo- )Ke:f.;nfl rpaccepa. 3ra ourn6ra aKKyMynupyercs rlo Mepe ABrr)rceHr{g Tpaccepa v lponopqr{oHaJlbHa ero B03pacry.
Cyuecrnenublfi HeAocraroK JIarpaHXeBa MeroAa cB.fl3aH c uoreperz I4HoOpMaIIHrr c rJry6vrBofi no uepe TO|O, KaK TpaCCepbI paccel4BaloTcs B npocTpaHcTBe I'I noKr{Aaror JIeAHI{KOBbIfi IqUT rrepe3 6orosrre rpaHl,I- qrr. 3ro o6ycaonnunaer rIo.aBJIeHue "
o6tactefi 'renLr", r. e. o6nacrefr., xyga rpaccepbl He nonaAalor I.r rAe r.rnQopuaqn.s o noJle Bo3pacra (n.nu uHoro KoHcepBa- TT4BHOTO CBOfi CrBa) OrCJrTCrByer.
t l
O.O. PbIEAK, @. XEEPEXTC
H acros uree u ccJreAoBaH r4e fl.v Jrfl er cs npoAon - )KeHZeM pa6oru lRgbak, Hugbrechts, 20031. 3Aecr
npuMeHflroTc.f, JrafpamrceB lI 3llnepoB MeToAbI l,Jrfl vrc- cleAoBaHu.s AByx KoHcepBaTI4BHbIX nOJIeft - IIOJIS BO3paCTa rr rroJrfl r43oTolrHofo cocTaBa JIbAa B 3BoJ'IIo- rlr.r oHrlpyrouefi aHrapKruqecKofi Mo,4eJrr{. B uoAelz BOCnpOr,r3BOA.STCfl KTHMaTUqeCKUe y CnOBng Ha no- BepxHocrpt rqr{Ta, efo Tonofpaor4t r{ fIoJIe cropocrefi Ha [poTg)KeHuu qerblpex [ocJIeAHr{x JIeAHrlKoBblx rlrrKrroB (420 ruc. aet).
?lHrepec K MoAeJrr{poBaHulo rl3oronHoro cocra- Ba JrbAa He cryiraeH. J[eA e roHruHeHT:LIIbHbIX ileLl1'Zl- KOBbrx rqr,rrax, IIo cyrrr, [peAcraBJrser co6ofi [p]rpoA- Hbrfi apxr.rB KocBeHHbIx AaHHbIX o KJII,IMaTe IZ UlIpKy-
nflrlrlu aruocseprr B npou,'roM. zeoronHHfi cocraB JrbAa, Koropbrfi npaKTu.recKvr JrvHeilrHo 3aBACI'IT OT reMneparypbr Bo3Ayxa y eepxnefi fpaHr{IIbI repMrr- qecKoft vr]HF'Bepc]|.'u, sBJrs.ercs BDKHeftIUI4M Anfl naJleo- peKoHcrpyKrlnfi KocBeHHbrM rzHAuKaropolt eapuaqufi
reMneparypbr Bo3Ayxa lRobin, I 974. EctecrneuHo,
IICM TIY6xtC SAJICIACT JICA, TEM AAJIbIIIE B TIPOI]IJIOE OT- CTO?TT vr BpeMs QOpMI4pOBaHI4.f, eIO LI3OTOIIHoTo co-
craBa. OAHaKo nprr aHaJIH3e ero Heo6xoArlMo )nIIarbI- earl Sarrop aABeKIII{u: ecJII'I cKBaftuHa npo6ypeHa He Ha JreAopa3AeJre, To JreA B HI,I)KHefi qaCTU KepHa Mor 6brrb orJloxeH Ha noBepxHocrr'I qI4Ta B corHtx KLrJrOMerpoB BBepx IIo noroKy or cKBaiKI4Hu. K sa- croglrleMy BpeMeHr,r n Auraprrr.IvecKoM neAHI4KOBOM rrlr4re npo6ypeHo rrerbrpe cKBaxvHbI, Bospacr JIbAa B ury6unHbrx rracrsx ux npeBbllrlaer 400 u,rc. rer. 3ro cKBa)Kr4Hbr Ha craHqlr.flx Bocror, Kyno.n (DyAxIa, Ky- ilon KoHKopAvrs. n Koneu. Izlurepnperalllls l43orolr- nux (6180 u 6D) pagoe rr3 KepHoB 3rt4x craHIIIaft no-
3BOJII4JIa BOCCTaHOBTITb XOA KTUMaTI4TI eCKUX Bapl4a-
qzfi reuneparypbr BoBAyxa Ha,4 AHrapKrugoftlPetit et al., 1999; Watanabe et al., 2003; EPICA community members, 2004, 2006) vr ux cBflsb c Kore6aHr'ItMI,I
reMnepaTypu n cenepnoM rloJlylllapl4yl B reqeHlre rocJreAHero JreAHr{KoBoro qr{KJra IEP I CA community memb ers, 2 0 061. CoruracHo MoAeJIbHbIM oIIeHKaM, Bo3- pacr HaLr6onee ApeBHero JIbAa B IleHTpaJlbHoirsacru Bocro.r Ho -AHrapKTI{qecKoro JIeAHI4KoB oro IqI'ITa
Mo)Ker [peBbrruarb 1,2 v.nn ner fHuybre chts, LAb ak,
2 0 0 n, u [peABapureJlbHble MoAeJIbHbIe pe3yJlbrarbl OTHOCVTeJIbHO BepOflTHOTO rr3OTOrIHOfO COCTaBa JIbAa MoryT 6rrrr oqeHr rIoJIe3HbI AJIfl nocJleAyloruux rIoJIe- B brx rr ccJre.4o F,a:j]'uir.
9fr IEPOB O I{ JIATPAH}KEBO O [I,I CAHI,IE A.4B EKIII,I}I
O6oaHa.ruM uepes 1 HeKoropoe KoHcepBarr'IBHoe csoficreo cpeAbl. Ssorloqus IroJIs KoHcepBarl4BHofi lpr,rMecn onl4cblBaeTcs ypaBHeHI4eM
4 = 0 .
dt
Paccnorpuu B npocrpaHcrBe cr{creMy KoopAI,I- Har c foprrsoHTaJlbHblMr4 OCflMU r, A Vr Bep'rr4KALIIbHOfi
ocbro z u ror{Ky, qbI,I KoopAnHarbl B ua'{aJlHnfi N4o- MeHr BpeMeHu (xs, Ao, zs). flycrn B MoMeHr BpeMeHrI / era ro.{ra nepeMecr}rJlacb B roqKy
\xt, At, zt.). Ecttu lepeMerqeHr4e qacrl{ubl ctll4Taercs QyHKIIT'IeL{ ee Ha-
qanbHblx KOOpAT{Har, TO TaKOfi CIOCO6 On]j1lCAH]1^'-
Ha3brBaercs nafpau)KeBbr fLlibouhy, 1 9 87):
rt - x0 =Ut(xo, !g, zs, t), a t - U o = V t ( r o , !s , z s , t) , z, - zg =Wt(xg, !g, zs, t).
Ias (2) cJle4yer, qro rIoJIo)KeHLIe qacrnllbl (paln- yc-BeKrop )Q onzcrraaercs ypaBHeHueM
(2)
(3)
r4e U - BeKTop cKopocrrr noroKa JIbAa c KoM[oHeHra- MVr 11, O, U. Ha'raJ:tr.nnte ycJloBt{g ycraHaBJII{BaIOT, YTO Tpaccep e Ha.raftHHfi MoMeHT BpeMeHI{ tgnaXogUncn Ha [oBepxHocruuuraH * h:
X { / o ) = l ) c 1 1 , ! / s , z = ( H + h \ - .. . l, ( 4 )
- - \ v / | t " t \ l J o , y l , t o I
r[e H -ftorrt"rru*t" m; h -a6corrornaq u-t.ot" noo- crr4Jrarouer? noBepxHocrrl.
Ec-nu nepeuetueHlze qacrlrllbl JIbAa paccMarpl,I- Baerc.rr KaK oyHKrlt4.f, KOHeqHbIX KOOpAuHar, ro rarofi cnoco6 ofiucaHr4s HasblBaerc"fl 3{Teponrrn'r. B clyvae efi "nepona onucaHvfl aABeKurr u Ha6rloAarerb orcJle-
?{cr4BaeT vSMeI:IeIlvs B OKpy)KaIOqeM ero SBOJIIOqVO- Hr.rpyroilIeM rroJre, HaxoAacr n surcr.rponaHHofi rovre npocrpaHcrBa. Sror cnoco6 lao6en rlrfl. peatrnla\uv Ha peryJrrpHblx npocTpaHcrBeHHblx cerKax. B c.nyrae, ecnrr aABeKrILrfl. olrr4cbrBaeTcg B JIarpaHXeBbIx TepMI'I- Hax, Ha6nIoAareJIb HaxoAurcs. B 4uaxyqeftcs roqKe lpocrpaHcTB a v onucbrBaeT SBOJITOUUIO CpeAbI, Ilepe- Merrlzurcb BMecre c ueir lStanif orth, C6te, I 9 9 1). Ar'u' xyuefica roqKe [pocrpaHcrBa MoxHo rlocraBurb B coorBercrBr{e qacruuy (rpaccep), Koropuu flepeMe- rrlaerc.g BMecre c ABl4xytqvMcfl rloroKoM. B AanHofi pa6ore MbI orpaHLIlI uBaeMcs. paccMorpeH[eM roJIbKo rrepeMerlleHr.I.fl rIaccIrBHbIX TpaccepoB, T. e. qacTuIL Ko- ropbre He B3ar{MoAeftcrnylor Apyr c ApyroM I{ c oKpy- xarolllefi cpe4ofi. Taxofi rpaccep Moxer rlepeHocrlrb lpro6oe KoHcepBarrrBHoe ceofi creo (no reprr,ru Ho JTIrlIl,r' fC larhe, M arshall, 2 0 0 21, 6nrr n uaprcep o u no na). 3r o Moxer 6urr uaprep Bo3pacra JIbAa (BpeMeHrr orJlo-
X C H I , I f l I I A C T I I I b I H A I O B C P X H O C T b J I C A H I 4 K O B O I O rqura), r.r3ororlHoro cocraBa,rl4a (QarrzqecKu reM- nepaTypbl Bo3Ayxa B MoMeHT BblrlaAeHrlfl ocaAKoB, rrocKoJrbKy nocJleAHss QyurqzoHaabHo cB.fl 3aHa c Hr4M), KoopAI4HarbI nponcxox4enr4s. Ha rloBepxHocrll uIilTA U r. A. o6ecueql4B AOCTarOrrHOe KorHsecrBo rpaccepoB BHyrpI4 o6tenaa JIeAHr.lKoBOrO ql{ra, MOX- HO nocTporrrb IIOJIS pacnpeAeJleHvrs rro6ofi I{3 rlepe-
#=ur*, a, z,t),
( 1 )
]IATPAMKEB METON PACqETA BOSPACTA N ASOTONHOTO COCTABA JIb,AA rrucreHHbrx Bbrrxe xapaKTepr{cTr.rK. Eoree Toro, yKa-
sauul,rft cnoco6 cpa3y .qaer Kaprr.rHy aznzfi rora BHyrprr ur.rra.
B nerropHofi Soprue efi.uepono ypaBHeHr{e aA- BeKIIT{I4 3arrnrxeTcfl KaK
AA
* + W A = O . ( 5 )
fpauravnoe ycnoBr,re Ha noBepxHocrr.r ufiTa A(t, A, zn*h, t)=,46. lpaHuvHoe yc,rroBr4e y noAcrr{- .raroulefr floBepxHocrr{ npHHHMaer Br{A
aA ^aA [ , aA1 [, aAl
E= oE-Ll'* a, l-lq'* a,I'
rAe B - cKopocrb 6asamHoro r,asHws (u/ro4 n "rre- AOBOM SKBLrBaJreHTe); Ul_ ,-, d_ ,- - KOMrrOHeHTbr
u"*ropu cKop ocrr4 6L= ^Tfr", o' tlorro*"n" s.. E c nn
6azatnnas. reMneparypa (reuneparypa Ha pa3Aene .ue4nzxonrrfi ruur-noAcrlrJraroqarr nopo4a) Huxe rov- Krr [JraBJreHr{ff, To B = 0 v 4r=t, v 4r=n TaKXe paBHbr HyJrro I1 rpaHr4qHoe ycJroBr.re cTaHoBr{rcfl HeonpeAe- JreHHbrM. r{ro6u r436exarb Dr oro, n fHug bre chts, 1 9 9 4l 6uro npe4roxeHo Ao6ar.u'tb B rpaByro vacrl (5) AolroJrHr.rreJrlnufi 4zQQyazonHufi .rreH. B pa6ore lCaloo et al., 19981rroKa3aHo, rrro rrpr{ MaJrbrx 3Harre- nuax 4ra$$yst4oHHoro qreHa r{cKaxeHufl s noae A He3Haqr,rTerbHbr 14 npo.rrBJr.rrroTc.f, ToJrbKo npu npu6.nu- )KeHVrI1l K HUxtHeft rpaHr4Ue rqr{Ta.
METO.4 I4 CCJIEAO B AIIVrfl .
Anraprruvecrar MoAenb. B Hacrosrueit pa6ore Anrfl. onvcaHrra AuraprruqecKoro JreAHr,rKoBoro rrrr4Ta r,rcnoJrb3yeTc.fl TpexMepHarr TepMoMexaHfirrecKarr Mo- AeJrb, noApo6uo onucaHnarr B crarb.f,x fHuybrechts, de Wolde, 1 9 9 9 ; Huu bre chts, 2 0 021. Mo.(ear Bocrporr3Bo- Arrr 3BoJrroquro ronorpaSun noBepxHocru Iur{Ta tr ro- norpa$uz noAcrvJraroruero Jro)Ka, 6atartc Maccbr rrlu - 'r a, vrzo cr rr nrrecKo e npncnoco6aeHn e, TpexMepHbr e nor.fi reMnepaTypbr JIbAa v cKopocTrr pacreKaHrr.fl .
Pacreranr,re KoHTrrHeHTaJrbHoro JrbAa orrrzcbr- Baerc.fl B TepMr4Hax npn6auxeurrfl MeJrKoro JrbAa (Shallow Ice Approximation, SIA fHutter, 1983)).
B paurax SIA c.ruraerc.rr, qro AeQopMarlr414 Jrbila o6yc.nonlunarorc.g roJrbKo raHreHrII4:uIbHbIMI,I Hanp.f, - xleHr4flMu B f opr{3 oHTaJr bHo ft rrJro cKo cTt4. II oarouy MoAyJrb BeKTopa roprr3onrzlrrbHofi cropocru onpeAe- Jrfl.ercfl. JroKaJrbHbrMrl rpaAHeHTaM u a6corrorRofi sH- corbr rroBepxHocrr.r. fieQopnaaunr4 rrreJrb$oBblx JIeA- HLTKOB OlpeAengroTcs HopM;L/rbHbrMr{ Harrp.f, xeHnflMu I{ TaHreHUr,rzurbHbrMr,r HanpsxeHr,rrMl4 B rop}l3oHTzulb- HOfi ilrocKocru. fi,nao6ecne.renras rrJraBHoro nepexo- Aa or KoHrr.rHeHrzlrrbHofi o6tacrv r nelnQonofi uex- .4y,rreAHr4KoBbrM rIIr,rToM u xrerbooBbrM nbAoM BBo-
Iurcfl. rrepexoAHa.fl soHa rrruprlHoft 20 rcMI, Koropaq pacrr oJroxeHa B o KpecrH o cr flx Jrvr:jj^vrrr sa.neraHz.s. fI o - TOK JrbAa BHyTpr,r 3OHbr paccMaTpr,rBaercr KaK [epe- xoAnufi or KoHTr{HeHTaJrbHoro n ure.nrQonoMy, I4 n neri npucyrcrByer rroJrHbrft na6op HanpxxeHrafi.
Kar n s 6oar'ruraHcrse fJlaurloJloruqecKrlx npr{Jloxe- nr,rfi, cropocru 4e$opir,raru4tr cBsganbr c HanptxeHl4- .sMH 3aKoHou flena c rloKagarenew crenenu n:3
fPaterson, 1 9941.
O 6lacrr r,rHrerpr.rpoB aHr{s, Koropat 3aBe4o- MO npeBblrllaer MaKcr4MaJIbHO BO3MO)KHOe paclpo- crpaHeHr4e KoHTI{HeHTaJI bHblx n urealQonblx ne4- HutKoB, npeAcraBJr.f,er co6oir KBa,{par 5600x5600 rcru (28tx28| ysnon), IOxur,tfi ro,IIIoc pacnoJloxen B rleHrpe o6tacrn B roqKe c KoopAl4Haravu (74I, I4I).
Beprr.rra-nrHoe pa3pelxeHlre Mo.qeJII{ 30 croee, ro- ropbre pacrroJroxeHbl HepaBHoMepHo rlo r ny 6une, yurorHrflcb no HanpaB,rreHulo K ocHoBaHrrlo Iur{Ta.
B eprr.r rar n uas Ko opA r{H ar a ((r, g ) 6ezpazrtepuax, 0 (uonepxnocrr qura) <((x,D < 1 (auo).
Ssorroulrs Mo4e,rru Bo BpeMeHv ocyuecrBJlter- c.fl BHerrrHr{M Bo3.4eficrBr{eM Ha 6aranc Maccbl Iuura qepe3 r,r3MeHeHrre cKopocTl4 aKKyMyJIsuuu pI TeM[epa- Typbr ero rroBepxHocTI4, a TaK)Ke nocpeAcTBoM KoHT- poJr g Ml,IrparJvrr4 Jrr4Er4r4 H aJlelaHl{"f, q epe3 u3MeHeHIlIt ypoBHfl Muponoro oKeaHa (rar na^aunaeMblfi KJII{Ma- ru.{ecxufi Sopczur). B ra.recrse $opcr,rnra lIcIroJIb- BoBaJrucb psAbl aHoMarufi relrreparypbl Bo3Ayxa I4 ypoBns Muponoro oKeaHa, BoccraHoBJreHHbIe no u3o- TOrrHbrM PflAa"na. .{.na noccranoBJleHl4.fl aHoMzulrlfi TeM- leparypbr r4cnoJrb3oBaHbr pflA 6D ras Kepna JIbAa craHrlr{u Bocror [Petit et al., 1999] u pxg anov.wrnir ypoBH.s Muponoro oKeaHa, BoccraHoBJIeHHbIft no AaHHbrM 6180 pa4a SPECMAP flmbrie et al., 19841.
B ocnony napaMerpr43al\4l4 cpeAHeroAoBoro KoruqecrBa ocaAKoB na4 Aurapkr uloir. ( Qalcrnvec- xu6arauca Maccbl Ha rloBepxHocrl,I, TaK KaK TaiIHue orcyrcrByer) noroxeu a saBvcvlMocrl erofi neaz- ql4Hbr oT I\aBJreIlI.s. HaCbruIeHHOrO BOA.SHOTO napa ilp?I reMneparype KoH.{eHcar\vr4 Ha nepxHeft rpaHuIIe cJror rrHBepcuu florius et al., 19851. Oco6ensocru rocrpoeHr{.rr prAoB Sopcunra o6cyxgatorca n
fHugbrechts, 20021.
flpo4o"nxureJrbHocrb rrr{cJreHHoro grcfieplaMeH- TA COCTABLTJIA 420 TNTC. MO,IICJIbHbIX JICT.
(Dopua:rusaqnff aABeKrIr{[ rroJrefi Boapacra lr r{BororrHoro cocraBa JIbAa. Irlsyraeurre HaMI4 KoHcep- Barr{BHbre xapaKTepr{cTr{Kr,r - Bospacr JrbAa r{ r{3oro[- Hlrir cocras Jrb4a (6180). Irlaorolurrfi cocras cBr3aH c TeMneparypoft eos4lxa y noBepxHocrr{ rqr{ra cooT- HorrreHr.reM 6180: 0,755Tr- 7,6. flpocras ilunetrHar 3aBr4crrMocrb MexAy reMneparypofi noaepxH ocrn Ts n 6180 o3Hayaer, r{To B KarrecrBe MapKepa Mo)rcHo r4c- rroJrb3oBaTb HenocpeAcTBeHHo TeMrleparypy, KoTopail flBlrfler cfl cocTaBJIfl lolqefi K,'ruMarH.recKoro Qopcunra MOAeJrr{, a pe3yJrbTrapyrcuee ee pac[peAeJreHr4e B Mac- ce rrlr4Ta nepecqurbrBarl s 618O rocJre oKoHyaHr4t 3KCrrepLIMeHTa.
llepeuennofr A sa noBepxHocru rrpucaafiBa- e T c . f l 3 H a r r e H u e , \ = t 4 r o , e c n u A - B o 3 p a c T , u
4 =T,(ta"p), ecnu A - reMrreparypaaosryxa; t6o - MoMeHr BpeMeHr4, Kor.4a qacrurla JrbAa (rpaccep) or- noxeHa Ha [oBeDxHoc"tu ilrura.
73
O.O. PbIBAR, @. XEEPEXTC 9 zcaeHHo r{Hrerprrpy.s (5 ), uaxo4Izrr,r afi repoao
note A Ha Ka.iKAoM BpeMeHHoM rxare MoAenz B y3Jlax perynapHorlr npocrpaHcrBeHHofi cerKr4.
.IIarpaHxeno noJre A onwcunaercx na6oportr rpaccepoB, pac[peAeJreHHbrx B Macce rqura. Tpaccepu crapryror c noBepxHocrrl r,r3 KaxAofo y3Jra cerKrr, Ha- xofl.4grueroct B o6Jracru KoHTuHeHTaJrbHofo lIInTa I,IJIIT ruear$oaoro JrbAa, Kax.qbre 100 nroAenrHux rer. flo- cTerreHHo Tpaccepbr 3arroJrHflroT Bcro Maccy JIbEa, kr nx
KOJIUqeCTBO CTaHOBTTTCfl npOIIOpIII4OHaJIbHbIM ero
o6rerr,ry. KoopAznaru rpaccepoB Ha BpeMeHHoM Ilrare f + 1 HaxoAqrcfl nz coorHorueHIzfi
J C * I = X t + l t \ t '
yr*, = y, I rLLt, (6) Z t + t = Z t + U L t ,
Koropoe cJreAyer r,ra $opva-nrHoro olpe.{eJreHvfl Me- roaa (2). flostnrytu rpaccepoB orcJrexr{Balorcfl Ka}c- Alre 10 .ner (A/: 10 aer). 9ro6u l,r36elKarb HaKonJIe- Hr,rs rpaccepoe y Hr,rxHefi rpaurrllbl turrra B o6nacrax, rAe orcyrcreyer 6aeamHoe rzulHr.Ie, cqlzraercs, qro rpaccep, nepecexrurzfi rpanuuy 99%-fi ornocure.nlHofi my6unu, noKuAaer JreAuurcoslrfi qI4T qepffi HI4)I(HIoIo fpaHzuy. Ilepecranr orcJ're)KrrBaTl'cs I,I rpaccepbl, KOTOpbr e noKr.rAalor o6lacrr, cooTBeTcrByloqylo KoHTr{HeHTzL/rbHoMy u rue,rrQonoMy JIbAy. Hecuorpx Ha Kaxyqyrcct npocToTy rIocTaHoBKI4 3KcrIepI{MeHra c JralpaH)KeBb-rMr4 TpaccepaMu, ero [paKTutlecKail pea-
Jfi43a\Vs. Tpeoyer 3Har{urerbHblx 3arpar l\{allr{HHoro BpeMeHrr, nocKoJrbKy oAHoBpeMeHHoe oorlee llzcro orcJrexvBaeMbrx rpaccepon roae6nerct B npeAe,lax 2,5-5,5 MJrH B 3aBI,IcLIMocrI{ or Sasrr uo4enupyeMoro
JICAHI4KOBOTO UIIKJIA.
Ha puc. 1 norasana roppl3oHraJlbHztt rrpoeKur{.f, coBpeMeHHofo noJr.fl pacTeKaHrrtr aHTapKTuqecKoro
.rr4a. MaprclrpoBKa rpaHuU o6racru I4HrefpI4poBaHI,Is AaHa B COOrBercrBLlr{ c HyMepaunefi ye,ron [pocrpaH- crBeHHoft cerKr,r c ruaroM 20 rrr,r. Oxnrrft nonloc pac- noJroxeH B rorrKe c KoopAl{Harauu (I41, l4I). Ha- HeceHbI f oprr3oHTaJIbHbIe KOOpA14HarbI TpaCCepO B,
KOTOpbIe IIA){OATIJI?ICL B MaCCe UIITa B TerleHue IIO-
cJreAHr4x 10 ruc. rer. Onu Aalor KaprlrHy Jrr4nr4fi.rona rIoJI.fl pacreKankrr. JbEa. o.renr.r4Ho, rrro 3Tu JrutrrfiKa- xyTc.g He[pepbIBHbIMI4 B O0JIaCTI4 KOHTI{HeHTaJIbHO| O
Jrblia u npeAcraBJrtror co6oft nocJleAoBareJlbHocTb ro- qeK B o6racrz ruean$onoro JIbAa, KoHIIeHTpI{pytcb BAOnb BbrBOAHbrx rroToKon. Xopouro BrlAHbI JIeAopa3- AeJrbr, Ha Koropblx ropI43oHTaJIbHoe [epeMel]IeHue Jrb4a orcyrcrByer r{nv rcpafiue He3Harlnrerbuo. lopr- soHraJrbHbre npoeKlllru KoopAr'IHar rpaccepoB $arcru- qecKr,r [peBpaqarcTc.s 3Aecb B ToqKv. fopnsoHrall- Hbre JrLrHr{u a,6,6 na puc. 1 uoxasblBalor rIoJIoxeHI4e BeprrrK:urbHbrx pa3peaoB (rpancerroe). (Drarcrapya KOOpAT{Harbr Bcex rpaccepoB, Koropble norlaAalor B noJrocy +10 rrra or rpaHceKTa, non]nlaeM KaprLIHy nu- Hr4fi roKa B BeprlrrzL/IbHofi nrocxocrr'L
4 M
3000 2000 1000 0 - 1 0 0 0
M
3000 2000 1000 0 -'t000
M
3000 2000 1000 0 -1000
20 60 100 14O 180 220 260 xu Puc. 2. Ilpoexqun KoopAlrHar rpaccepoB Ha rlJroc- KOCTb BeprrrKaJrbHbrx paSpesoB a,6, 8.
1 8 0 140 1 0 0
60
20 2201 8 0 220 260ru
Puc. I. O6racrl KoHTuHeHraJrbHoro u ruentQororo nbAa B Anraprruuecrofi MoAenI{:
a, 6, e - Beprr{raJrbHble pa3pe3br (rpancercrrr).
* )i3
",%*^,
140 1 0 0 60 20
]IATPAHN{EB METON PACIIETA BOSPACTA N U3OTOIIHOIO COCTABA JIbNA Ha prc. 2 nora.aaHnr JruHu\r roxa, 6epyruue Harra-
Jro Ha noBepxHocrr4 B arerHbrx y3Jrax cerrn. Ha TpaHceKTax BrrAHo, qro B rleHTparbHbrx o6Jracr.sx AH- rapKrrrAbr Tpaccepbr rrepeMe[Iaorcq B Macce qnTa npaKTr4r{ecKr{ BeprI,IKa,rIbHo, BJrlrgHr,Ie foprl3oHTZL/Ib- Hoft cocranrt.sroulefi cKopocrr4 npoflBn.flercs ro./rbKo lrpvr npu6r'uxeHrar4 K noAcrvnarcqeit nonepxnocrrt vr rro Mepe npu6nuxenus K oKparrHaM Marepr.rKa. Hapy- rueHrr.fl B floroKe rpaccepoB 3aMerHbr B oKpecTHocTflx npenxrcreufi. Ouenu4uo, qro BAecb ropzeoHra.nrHrrfi rroroK ou{6aer HepoBHocrr4 noAcrr.rJrarorueft nonepx- Hocrr4. Ha puc. 2, aSro coaAaer Kaprr{Hy, Koropzur Ka- qecrBeHHo HarroMr4Haer ryp6ynenrHoe rerreHue B )Kr{AKocrrl. O6,nacru pacxoxAeHr4 s. nnnnfi roxa e6rr.r- zv no [c'rv Jraroqeri noBepxHocrr4, xoporuo B;rMerHbre
Pnc. 3. Boepacr nr4a rro efinepouy (a, a) u;Iarpanxeny (6, z) uero4an:
a, 6 - na 50 %, a, z - ua90 % ornocn"rennuoit ray6uurr. Boepacrurre rrrKaJrbr AaHbI B rbrc. Jrer
Ha pr4c. 2,6 u genrpa.rrbHoil qacrl.t Bocro-{Hofi Au- TapKTr{AbI, co3Aalor cBoero poAa "TeHeBbIe 3oHbI", B KOTOpbrx Tpaccepl'r orcyTcTByIoT, cJIeAoBaTeJIbHo, oT- cyrcrByer nHSoprr,raqlra o6 usyvaeuoM noJle.
CPABHEHI,TE PESYJIbTATOB SIZJIEPOBA I,T JIATPAH}KEBA METO,ITOB
Henocpe4crBeHHoe cpaBHeHve afinepoBblx I4 ,TarpaHxeBbrx pe3ynbraroB HeBo3MoxHo.,{na aroro neo6xoA r,rno BbIIToJIHT{TI, npeABapI,ITen bHylo rrHTep - noJrflrll{rc ,ru6o .uarpauxeBblx AaHHbIx B y3JIbI npo- crpaHcrBeHHofi cerrr, nn6o afitepoBblx AaHHbIx Ha rcarcyro-ru6o rr3oxpoHHylo noBepxHocrb. B ilocne- .4HeM CrJrqae JrarpaHlceBbl AaHHbIe MoryT oblTb rIoJIy- rreHr,I HenocpeAcTBeHHo Ha lr3oxpoHHofi nonepxnocrn a
0 -20 -40 / -80 -120 - 1 6 0
0 -50 - 1 0 0 -200 -300 -400
F"
.;do
.fo
@I J
O.O. PbIEAK, @. XEEPEXTC
Puc. 4.Ilaoronulrfi cocraB nbAa rro efiaepony (a, o) n narpaHxeBy (6, z) ll'erogalr:
a,6 - taa50 %, e, z - sa90 76 ornocutenatoftr.:ly6ur.m. Zaoronnas urxatra Aa:uaB rlpoMr{JrJre.
oo
oo2
0 -30 -40 -50 -60 -70
I
Io
.i'o
@F"
o
oo
@npocrbrM or6opou rpaccepoB oAHoro Bo3pacra. 3fiae- poBbr xe non.fl Bo3pacra (ntru u3ororrHofo cocraoa) Heo6xoAuMo r{HrepnonupoBarb r.r3 yBJroB cerKlr Ha nu6paHHyro n3oxpoHHyro noBepxHocrn. Tarnu o6pa-
3OM, fOBOpr{Tb O TOTTHOM CpaBHeHI4rr MeTOAOB HeKOp-
peKrHo. Cnoco6 cpaBHeHHs (ua ornocureJlbHblx rny- 6uuax wrv Ha r{3oxpoHHbrx noBepxnocrax) 6yaer coAep)Karb o [rlr6xy r,rHTepnoJrfl rlr4r4 p$ynbraToB, no- Iyr{eHHbrx oAHr{M r.r3 AByx cpaBHI4BaeMbIx MeTOAOB.
Teu ne MeHee Mo)KHo BoccraHoBr{Tb KaqecrBeHHylo Kaprr.rHy pacxoxAeHr{rl uex4y AByMfl Mero4aMu.
3a$nrcnpyeM no3r{II?IU Bcex rpaccepoB, rlonaB- Ixzx B cttoit up=(n*uLt, t1e a - BepruKa,lbHa.s cKopocrb; (p - vu6panHair orHocrrreJ'IbHail rty6uua.
Ocpe4uran 3HarreHr.rfl MapKepoB y Bcex rpaccepoB B
paArryce npocrpaHcrBeHHoro rrara cerKl{ (20 ru) or y3na cerKr{ (i, j) u B yKa3aHHoM clroe- upt npI{cBoIrM noJrro B ysne (i, j) noJryqeHHoe cpeAHee sHa.{eHue. Ha puc. 3 npe4craBJreHbl efi"neponu I4 JIarpaHXeBbI no,'I.f, Bo3pacra rrb/.a Ha orHocr,IreJlbHlrx uy6uuax 50 n 90 % (k: 0,5 u fr : 0,9). flo,rg Ha ropl{3oHre h: 0,5 (cu. prc. 3, a,6) oyeHb cxolcu. Pasnnvus. npo.aBJls- IOTCfl JIlrrXb B AeTaJLflX, B .raCrUOCrn, 6O,rrUrUfi noa- pacT uMeeT neA B Br'rBoAHbIX TIOTOKaX Ha Urenn$OnltX JreAHHKax (DrarlxHepa u Pocca. B ,rarpaHxeeoM rIoJIe B nonoce 80-82' w.n., t20-150" e.t. BrrAHa noJloca orHocr4TeJrbHo 6o-nee MonoAoro JIbAa, Koropail orcyr- crByer n ertreponou rore. CyurecrBeHHble paanrrrufl MexAy er?repoerru rr JrarpaHXeBbIM Bo3pacroM Br{A- Hbr Ha roprr3oHre h: 0,9 (crvr. puc. 3, e, z). Kponre
JIATPAHiKEB METON PACIIETA BO3PACTA N NSOTONHOTO COCTABA Nb.4A
Puc. 5. Pacnpe4eneuue rpaccepon na 50 % (a) nsag0 % (6) oruocnremuofi ury6nnu.
a o
o
.|o @
,""
oo
6onee craporo JrbAa B BbrBoAHr,rx [oroKax (rar ra na k :0,5), orlrerrzu $parueHrapHuit xapaKrep Jra- rpaHxeBa noJr.rr Bo BHyrpeHHr.rx pafioHax Bocro.rHofi Auraprru4lr.
AHaaorH.{HrIe BbIBoAbI MoxHo cAeJlarb orHo- cr4Te"rrbHo efi-neponux r{ narpaHx{eBrrx no,refi u3oron- Horo cocrana (puc. 4). Cnetyer orMerr{rb 6oaee
"xono4Hnfi"
re4 B BbrBoAHbIx rloroKax Ha IUeJIb- Qoelrr:r ae4 lr $parrvreHTapHocTb rro.rrfl Ha ropr4soHTe h: 0,9 Bo BHyrpeHHux parTrouax Bocro.rHofi AHrapx- u.r4rr. KavecrBeHHbre paznu-r'vs. MexAy efi"uepoau-
Mrr Lr JrarpaHXeBbrMH rroJr.f,Mr.r Bo3pacTa rr Ir3oToF- HOIO COCTaBa 3aMerHbr Ha ropr,r3oHre k :0,9: uola BO3paCTa HaMHO|O 6Olee UaAXr{e, rIeM IIOJI.II I{3OTOIr- Horo cocraBa. "Xoro4Hr,rft"
Jre[, n afi"uepooou role nak:0,9 (cu. pLrc.4, a) cocpe4oroqeH B oAHoM rsr- He B ceKrope 76-80" rc.u.,60-120' s.a. B rlarpaHrKe- BoM none (cru. puc. 4,z) utrua "xoro4Horo" rb4a He orpaHurreHbr yKa3aHHbrM cexTopoM. lIo-an4lrtnroruy, BcneAcrBr.re auQ$yslttz n efirepoeou ro,'Ie B npr{AoH-
ttofr. sacru crrzparorc.s MeJIKI,Ie 4eraJflr rIoJIt I43orolr-
HO|O COCTaBa.
m t ' o
l# o,e ltti'1;1 ^ ^
w"o
f f i u . +
ry 0,2
I - 0
Puc. 6. Oruocuremnue rury6unbr rraoxpoHHbrx rroBepxHocrefi 15 rrrc. rer (a) r rrbre JrarpaHxeBbrM MeToAoM.
llkalrr.uaurr B orHocr4rerlbHnrxr.nv6uuax 0 < ( < 1.
1 , 0 0 0,95 0,90 0,70 0,50 0
.lo
o,""
.5s @ F"
120 "rrtc. rcr (6'l, rroJr) reH-
7 7
O.O. PbIEAK, @. XEEPEXTC Brrrue ynoMnHzl/rocb o pacceflHrrr{ TpaccepoB c
rny6vruofr. BcJreAcrBrre roro, r{To rpaccepbr noKr4Aa- ror o6"rracru qepe3 6orosHe rpaHr4rlbr. Ha pnc. 5 npr{BeAeHbr rpaccepbr, nola"qaroqueB cJrofr ap (eru Tpaccepbr 6rr"rrr.r ucn oJrb3o BaHbr AJrrr n ocrpoe Hrrs puc. 3, 6, z u 4,6, z). OuenvrAHo, qro pacnpeAeneHr4e rpaccepoB HepaBHoMepHo, oHrl KoHueHTpr4pyrorc.fl 6nuxe r 6eperonrrM KoHrIaM BbrBoAHbrx noroKoB IbAa, ilpfir{eM 3Ta KoHrleHTparlkt.fl 3aMeTHee Ha foppr- sonre fr : 0,9 (crra. pvrc.5,6).
Kar yxa:unzl/rocb paHee, JrarpaHxeB MeroA Aaer HenocpeAcrBeHHoe pacupeAeneHrre xapaKTeprrcr[K rroJrr Ha r43oxpoHHbrx [oBepxHocr.sx. Moxno no- cTaBr{Tb 3a,4arry uHar{e - paccvvTaTb oTHocr4TeJrbHyro rny6nny zsoxpouuofi rroBepxHocrlr, coorBercrByro- rrlyro 3aAaHHbrM MoMeHTaM BpeMeHu B rrporxJroM.
3a$urcrapoBaB rroJroxeHrre rpaccepoB, Bo3pacr Ko- Topblx, HanpLIMep, tl: l5 rblc. JIer u t2: 120 rmc.
JIer, nocrpor4M rroJre rny6nn coorBercrByrourrx r43o- xpoHHbrx noBepxuocrefi (puc. 6, a,6). Conocras- Jrfl.fl. ?TU KapTbr c KapTaMH Tonrqr,rHbr JrbAa, Mo)KHo IroJIJArurb Kaprr4Hy paclpeAeJreHr.,rs B [pocrpaHcTBe JrbAa o[peAeJreHHoro Bo3pacra. B paurcax efirepona loAXoAa aHarou{rrHbre pacqerbr norpe6onaru 6u r{HTepn oJrrrl ur{ n oJroxeHprr rroBepxHocTrr Me)KAy y3JraMr{ ceTKI4.
ocHoBHbrEBbrBoAbr
B panaxax ofirepoBa Merola paccqnraHHbre rroJr.fl BO3paCTa r,I rl3OTOrIHOfO COCTaBa OOJIee rJIaAKr{e IIO cpaBHeHuro c [oryrreHHbrMra IIo JrarpaHxeBy MeToAy.
flocromry afi aepoarr pacr{erbr 6onee aronoMr,rqHbr, 9ror MeroA MoxHo peKoMeH,4oBurb Lrrfl. npeABapr,r- TeJrbHofo aHaJvF,a, AJrs [oJrrrenus. o6ryefi Kaprr4Hbr rlpocrpaHcrBeHHoro pacnpeAeJreHvrfl. I1lsyrtaeMoir xa- paKTepkrcrr4Kn rrb!.a. Heua-nona:rHoe c [paKTktyecKofi TorrKr4 3penr{g nper,rMyuecrno afi.nepoBa MeroAa cocTorrT B ToM, qTo orIeHKu noryqaroTcr B y3nax
cer Ku Lr rpa@u.recxoe npeAcraBJreHlre pesyJrbraro B He rpe6yer AorroJrHr4TeJrbHbrx r4HTepnoJrfl UrroHHbrx nporleAyp.
"Ilarpanxenbr orleHKH paccqurbrBarorcs Heno-
CpeACTBOHHO Ha I{3OXpOHIIbIX nOBepxHOCT.[X BHyTpIUI
JreAHr4KoBoro rr{r4Ta. ,{ra roro .{To6br cpaBHrrrb pe- 3yJrbrarbr c afi.neponrrna n, Ax Heo6xo4ral,ro rpanc$op- MVpOBarb B y3Jrbr perynapnofi ceTKr{, rrTo Her{36e)(Ho Brer{er r{x crJra)Kr'rBanue. B o6tacrsx pacxoA.rlqr{xcg noroKoB Korr4rrecTBo rpaccepoB MoxeT 6rrtr c"nuru- KOM MZL/rO AIg n0JlyqeHu.f, a,4eKBaTHbrX OTIeHOK B pe- ryJr.spHbrx y3Jrax. oAHaro B ycJroBr,rx AocraroqHoro Kor[qecrBa rpaccepoB (xor4a, ycJroBHo roBops, rlx KOJrr,rqecTBo Ha eAnHt4 rly nJroqalv [peBbr rrraeT rrJroT- Hocrb ysJroB cerru) JrarpaH)KeB MeroA eQQexrzneH AJrf Bbr.flBJreHr,r.fl ToHKr,rx cTpyKTyp B Iro.Ilflx Bo3pacTa, rr3oTorrHofo cocTaBa n llpoqux, KoTopbre He MoryT 6urr noryveHbr B paMKax sfilepona MeroAa. Taxuv
o5pasou, JrafpaHxeB noAXoA, orreBuAHo, 6oree uoA- xo4r4T LnflAeraJrbnoro o\ucaHwfl no"refi B orpaHuqeH- nrrx o 6racr flx, r,Jrfl perl4onaJlb HbIX r{ccJleAo n aunir, IAe Ba)KH bI Ae'ratwI v CcneAyeMr,IX nOJIeft .
Jlnreparypa
Bates J.R., McDonald A. Multiply-upstrearn, Semi- t agrangian advective schemes: Analysis and application to a multi-level primitive equation model // Mon. Weather Rev., 1982, vol. 110, p. l83l-1842.
Bermejo R. On the equivalence of Semi-Lagrangian schemes and Particle-in-Cell finite element methods // Mon. Weather Rev, 1990, vol. 1 18, p. 979-987.
Calov R., Sawin A., Greve R. et al. Simulation of the An- tarctic ice sheet with a three-dimensional polythermal ice-sheet model in support of the EPICA prcject / / Ann. Glaciol., 1998, vol. 27 , p. 201-206.
Clarke G.K.C., Marshall SJ. Isotopic balance of the Green- land ice sheet: modelled concentrations of water isotopes from 30,000 BP to present // Qratern. Sci. Rev., 2002, vol.2l, p.419-430.
Clarke G.K.C., Lhomme N., Marshall SJ. Tracertralsportin the Greenland ice sheet: three-dimensional isotopic strati- graphy // Quatern. Sci. Rev., 2005, vol. 21,p.419-430.
EPICA community members. Eight glacial cycles from an Antarctic ice core / / Nattre,2004, vol. a29, p.623-628.
EPICA community members. One-to-one interhemispheric coupling of polar climate variability during the last glacial / / Nature, 2006, vol. 444, p. 195-198.
Fjdrtoft R. On a numerical method of integrating the baro- tropic vorticity equation / / Telhn, 1952, vol. 4, p. 179-194.
Harlow F.H. The Particle-in-Cell computing method for fluid dynamics // Methods of Comput. Phys., 1964, vol.3, p.319-343.
Hockney R.W., EastwoodJ.W. Computer simulations using particles. Bristol and Philadelphia, Inst. Phys. Publ., 1992, 540 p.
Hutter K. Theoretical$laciology: material science of ice and the mechanics of glaciers and ice sheets. Dordrecht etc., D. Reidel, 1983, 510 p.
Huybrechts P. The present evolution of the Greenland ice sheet: an assessment by modelling // GlobaI and Planetary Change, 1994, vol.9, p.39-51.
Huybrechts P. Sealevel changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles // Qratern. Sci. Rev., 2002,vo1.21, p.203-231.
Huybrechts P., de WoldeJ. The dynamic response of the Greenland and Antarctic ice sheets to Multiple-Century Climatic Warmins // J. Climate, 1999, vol. 12,p.2169-2188.
Huybrechts P., Rybak O. A 3D model reconstruction of the Antarctic ice sheet during the last 8 glacial cycles // Polar Regions and Quaternary 'Climate: Abstr. ESF Conf.
Acquafredda di Maratea, Italy, 2005, p.24-27.
ImbrieJ.Z., HaysJ.D., Martinson D.G. et al. The orbital theory of Pleistocene climate: support from a revised chronology of the marine 6180 record // Milankovich and Climate / Ed. A. Berger et al. Dordrecht, D. Reidel, 1984, p.269-305.
Krishnamurti T.N. Numerical integration of primitive equa- tions by a Quasi-Lagrangian advective scheme // J.AppI.
Meteorology, 1962, vol. I, p. 508-521.
IIA1PAmKEBMET1IPACIIETAB}SPACTAaUsoTonHofoCjCTABAIbIA Lhomme N., Clarke G.K.C., Marshall SJ. Tracer tralsport in
the Greenland ice sheet: constraints on ice cores and glacial history / / Quatern. Res., 2005a, voI. 24' p. 173-194'
Lhomme N., Clarke G.K.C., Ritz C. Global budget of water isotopes inferred from polar ice sheets // Geoy\1s.Res' Lett', 2005b, vol. 32, L29502, doi: 10-1029 /2005GL02377 4'
Lliboutry L. Very Slow Flow of Solids. Basics of Modeling ir-r- Geodynamics and Glaciology. Dordrecht, Martinius Nijhoff Publ., 1987,510 p.
Lorius C., Jotzel!., Ritz C' et al. A 150,000-year climatic record from-AntarCtic ice //Nature, 1985, vol. 316' p.591-596' Paterson W.S.B. The physics of glaciers:3rd ed' Oxford, N'Y', Tokyo, Elsevier, 1994,480 P.
PetitJ.R., JouzelJ., Raynaud D. et al. Climate and atmo- spheric hist-orv of ihe pasi 420,000 -ve-ry9 froalhe. Vostok ice cbre, Antarctiia // Na[ure, 1999, vol 399, p. 429-436' Robin G. de Q. Ice cores and climatic change // Philos' Trans' Roy. Soc. London, B, 1977,vol. 280, p. 143-168.
Rvbak O.. Huvbrechts P. A comparison of Eulerian and La- er""tei"" rnethods for dating in numerical ice-sheet models / / Ann. Glaciol., 2003, vol.37, p. 150-158'
Sawver I.S. A Semi-Lagrangian method of solving the vorticicy adueition equation / / tellui,1 963, vol. 15, p.336 -342' Staniforth A., 6teJ. Semi-Lagrangian integration schemes for atmosoheric models-- A review // Mon. Weather Rev', 1991' vol1i9, p.2206-2223.
Tarasov L., Peltier W.R. Greenland glacial listory borehole
"onrttui"tt, and Eemian exterfi / / J. Geophys' Res', 2003' vol. 108 (83), 2143, doi: 1029 /2001J8001731'
Watanabe 0., JouzelJ., Johnsen SJ. et a[' Homogenous ctirnat" vatiaUility u..oi. Eust Antarctica over the past three glacial cycles // Nature, 2003, vol. 422, p' 509-512'
Welander P. Studies on the general development of motion in a twoldimentional, ideal fluid-// Tellus, 1955, vol'7,p' 141-156' Wiin-Nielsen A. On the application of trajectory methods in numerical forccastin1// Tellus, 1959,vol' 11,p' 180-196'
Ilocmgnuna e Pe)ax4uro 11 0era6w 2006 z.
