Title Ice Flow Line Modeling and Ice Core Data Interpretation : Vostok Station (East Antarctica)
Author(s) Salamatin, Andrey N.; Tsyganova, Elena A.; Popov, Sergey V.; Lipenkov, Vladimir Ya.
低温科学, 68(Supplement), 167-194 Citation Physics of Ice Core Records II : Papers collected after the 2nd International Workshop on Physics of Ice Core Records, held in Sapporo, Japan, 2-6 February 2007. Edited by Takeo Hondoh
Issue Date 2009-12
Doc URL http://hdl.handle.net/2115/45448
Type bulletin (article)
Note II. Ice-sheet flow model
File Information LTS68suppl_015.pdf
Instructions for use
Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP Ice Flow Line Modeling and Ice Core Data Interpretation: Vostok Station (East Antarctica)
Andrey N. Salamatin*. Elena A. Tsyganova*, Scrgey V. Popov*"'. Vladimir Va. Lipcnkov***
* Kazan Slale Ul1iversily. Kazan 420008. Russia. [email protected] ** Polar Marine Geosurvey Expedition, Sf. Petersburg 1885/2. Russia *"Arctic and Al1Iarclic Research Insfifllle, Sf. Pelersburg 199397, Russia
Abstract: This work, originally based on a series of the isotopic record, determine [101 , 104, 106, 113] the authors' publications [101 , 102, 104, 1[2, 130, 131] , depth-age sequence of the major climatic events considers general questions of ice-sheet now modeling (temperature maximums and minimums), i.e. as related to ice core records interpretation. It reviews geophysical metronome time scale (GMTS). the previous results and, using new geographical, Furthermore, theoretical investigations and geophysical and glaciological data, continues the study computational experiments show that ice flow line aimed at solving the twofold problem of ice core age modeling in two-dimensional (2-D) approximation dating and paleoclimatic reconstmctions from the becomes a useful tool for ice age predictions in central isotopic content measurements in the deep ice cores parts of an ice sheet if the model parameters are from Vostok Station located in central East Antarctica, constrained by a priori chronological information [74, above the vast subglacial lake. The principal idea of the 75, 137]. From this point of view, GMTS can be paper is to develop a general approach to past climate considered [3 , 34, 35, 112] as an important and investigation by means of an improved themlO statistically significant set of the so-called orbitally mechanical ice fl ow line model, involving a wide tuned age markers (control points). Another spectra of supplementary data such as borehole independent source of age markers may be provided for temperature, radio-echo-sounding reflection layers, and future studies by the local insolation proxy properties of air-bubble measurements. atmospheric air trapped in ice [6, 90]. Once the ice age depth relationship is introduced, fitting the 2-D therrno Key words: ice sheet, ice core records, ice flow line mechanical simulations to the borehole temperature modeling, ice age dating, past climate change measurements reliably constrains the transfonnatioll of the ice core isotope time series into the history of ice sheet surface temperature (Ts) variations [10 I, 104, 113, I. Introduction 130). However, the above general strategy of Numerous evidences confirm a correlation between paleoreconstructions is not complete. The borehole hydrogen 00 (and oxygen 0 180) stable isotope content thennometry does not directly constrain the inversion in solid precipitation and local temperature Ti of (condensation) temperature Ti which detennines the atmospheric moisture condensation [II, 12, 18,27,50, waler- vapor equilibrium pressure III clouds 133] which, in central Antarctica, is considered to be the conventionall y correlated [97] in the central Antarctica cloud temperature at the top of the inversion layer. to solid (snow) precipitation. Hence, past temporal However, theoretical predictions of the variations of the ice accumulation rate b, the principal deuterium/inversion temperature transfer function are climatic input of the ice-sheet dynamics, remain highly rather un certain, and the estimates of its temporal slope uncertain. The use only of a local set of the ice age Cr generally do not agree with the observed present-day depth correlation points for tuning a multi-parameter spatial gradients [2 1, 39, 45 , 131]. Obviously, additional ice-flow line model does not account for geographic independent information on past climate changes is peculiarities of environmental conditions and does not needed to further elaborate and constrain the procedure pemlit simulation of a realistic spatial flow pattern. This of processing the unique isotopic signals. This question is especially important when, as in the case of the is closely linked to that of ice core age dating. Actually, Vostok ice core, the drilling site is not a dome summit, simultaneous solution of both problems penn its but is located relatively far from the ice divide above the supplementary paleoclimatic analysis of borehole vast subglacia l Inke [46]. The situation can be temperature profiles. The non-stationary temperature substantially improved if the ice core data on field in the central part of the Antarctic ice sheet with geometrical properties of air inclusions are involved in extremely low accumulation rates remembers [I, 94, the paleoclimatic studies. Based on n self-similarity of 107] recent Milankovich cycles of the past surface dry fim structures at pore closure [30] , a new constraint temperature variations (geophysical metronome) which , on the past accumulation rates was proposed in [55] and being periodically extended and correlated to the has been later discussed in (124]. The original conclusion is that the total bubble number density is
-167 - inversely proportional to the mean ice-grain volume at present the re-examined glaciological time scale ~or t~e the close-off and. thus, due to normal groin growth in Vostok ice core and resultant paleochmatlc snow and fim , must be related to the local climati c reconstructi ons. conditions (b and Ts) of ice fonna tion. Recent studies [103, 105] of the snow/tim densitication process result 2. Paleoclimate in the Antarctic ice memory. [561 in developing an explicit semi-empirical equation Previous studies which links relative past accumulation rates along the flow line to the bubble number measurements and the 2.1 Isotope content of iee ice-sheet surface temperatures. Furthennore, extensive Although we conventionally refer to the correlation radio-echo sounding (RES) observations were carri ed between stable isotopes in so lid precipitation in central out from the ice-sheet surface by the Polar Marine Antarctica and local inversion (condensation)
Geosurvey Expedition (PMG E) in the vicinities of tempcrature TI• it should be noted that the isotopic Vostok Subgltl cial Lu ke (VS L) in 2004-2006. In content of deep ice cores can differ from that of the particular, the bedrock relief and distinct isochronous fresh snow due to the surface snow metamorphism and (reflect ion) layers with the ice tlge up to - 220 kyr were mass exchange with the atmospheric moisturc. The detected in RES profiling over the 106-km trtlverse sublimation and recrystallizat ion effects in snow and along the ice flow line upstream of Vostok Station. The fim (e.g. [28,49, 115)) are primari ly controlled by the described complex of experimental and theoretical near-surface glacier tcmpemture T. which, in centml wo rks for the first time has provided various Antarctica, is significantly lower than T; due to the paleoclimatic, glaciological, and geophysical data from developed inversion strength. As a result, the stable Vostok area to attempt a joint self-consistent analysis isotope content in ice cores corresponds to a certain bllsed on the ice fl ow line modeling and aimed at apparent temperature, which, in geneml, may not simultaneous solving the twofold problem of ice-core coincide with any of the instrumentall y measured values. age dllting lind paleoclimat ic reconstruct ions from ice Nevertheless, it is still assumed that the tempemture core isotopic records. fl uct ulilions thcmselves deduced from the isotopic Aside fro m ice-sheet dynamics and formation of content variations do not differ much from those of the paleoclimat ic signals, the study of heat transfer along effective temperature of the atmospheric moisture ice fl ow lines starting from Ridge Blind pllssing lIcross condensation. The detailed analysis of the present-day the lake and Vostok Stlltion is of primary importance for isotope-temperature correl;llions based on our understanding the gas (air) and wa ter exchange meteorological observations, measurements in pits, and between the ice cover and the subglacial water basi n, as borehole thermometry for the recent 50 years [2 1, 23, well as for investigation of biological processes and 24, 59} confinns this conclusion. Importance of the 18 possible origins of microbial life in the lllke (e.g. [77, deuterium excess du = 00 - 80 0. as a deri ved 11 7]). No n-stationary temperature field s determine the paleosignal. and its relation to th ermodyna~i c ice accretion and melting mtes at the ice - water conditions of moisture fonnalion in the evaporatIOn interface {76. 77, 109, 125, 130] and, as a consequence, zone, e.g.. sourcc temperature T.... , have been lake salinity and the rates of air accumul lLtion in the lake demonstratcd in [38. 42, 43, 79]. A complete set of the in the forms of dissolved air and air hydrates [54, 681· ice core isotopic data from the deep borehole at Vostok Temperature conditions along ice particle trajectori es in Station to a depth of 33 10 m and its detai led analysis are the glacier directly control the air hydrate crystal growth presented in [135]. Fig. I depicts results of these [108, 1321 and the state of micro-organisms transported measurements together with the parabol ic mean-square through the glacier from its surface towards the lake. spline ap proximation of the ice isotope content With this in mind, we, firs t, review and compare after flu ctuations versus dept h. Substantially more detailcd [13 1] different approaches to paleoclimatic experimental studies on the Vostok ice core deuterium interpretation of ice core isotopic records, borehole content to 3350 m were performed and summarized temperature profiles and discuss existing uncertainties earlier in [78]. in ice age datings of different ori gins at Vostok. Then, The advantage to employ simultaneously both in a continuation of [100, 130], an improved isotopic signals, 00 and den in paleoclimatic sophisticated ice flow line the rmo-mechanical model is reconstructions and the necessity to deduce past elabomted fo r simulating the ice sheet dynamics and tempemture va ri ations at a site of solid (snow) tempemture field along the Vostok fl ow line with precipitation together with those in the moisture account of the ice defonnation within the bedrock · eV;lpomtion zone was shown in [14, 134]. Linear subglacial lake tra nsition zone and the ice accretion at relationships were proposed to determine the relatively the glacier bottom over the lake. Recent RES small tempemture perturbations: observations, updated geogruphic, gco physical and glaciological data are summarized. Supplementary 600 = y;aTI - r.. ilT ", + r..,60180 .. , informati on about past lIccumulation r'd tes deduced from (I) the bubble density measurements [56] is also described. 6d~x:: - P/lT + /1,.ilT .. - p",6.0180", . Finall y, the general stmtegy and results of the newly I perfonned computational experiments are discussed to
-168- I Depth, km [21] f}b =: 0.112°C . Close estimates of 'lb - 0.10- 0 2 3 O. 14°C·1 fo llow from Ihe geographical dependence of -400 the accumulation ru tes on the isotope content of the surface snow layer in East Antarctica along the traverses -420 "Mimy Observatory - Vostok Slation" [21, 22, 53] and "Syowa Station - Dome Fuji" [114J. '" -440 The IlIrge inversion strength, Ts - T;, over the -460 ~- Antarctic Plateau generally implies Ihe necessit y to -480 develop special approaches for reconstruction of the surface temperature variations tJ.Ts in the past. Based on the present-day splltial distributions of the surface and 20 inversion tempermures, Jouzel and Merlivat [42] ,; 16 proposed a linear proportionality between tJ.T~ and tJ.T/: u ~'" 12 6T, = tJ.TIC; . (4) 8 0 1110 200 300 4110 Eqs. ( 1)-(4) form a theoretical basis foc Age, kyr paleoreconstructions from the ice core isotopic datl! stored in the Antllrctic ice sheet memory. The principal Figllre I.' DellferiulII CQnfelll and deuterium excess problem of their practical employment is in rel iable measurements ill Vostok ice core vs. depth [/35} (dors) constraining of the coefficients in th is paleoclimmic alld !heir splille approximatiolls (solid lilies). model. In particular, the reviews [14. 48, 102, 134. 135] are devoted to the validation of Eqs. ( I). A summary of Here 0'80 .. is the ocean water oxygen isotope content,!J. results obtained in these publications is presented in means the deviation of the characteristics from their Table I. The simplified Rayleigh-type model for the contemporary values; }j, Y.. , 1... , p" p..., fJ,., are the atmospheric moisture condensation and isotopic regression coefficients. which are introduced as positi ve fractionation in air masses moving along a single values and describe the climatic links of the site under trajectory [10, 18,26,38, 42,69] was used in [ 14, 134} consideration with the processes of atmospheric to calculate the isotopic composition of precipitation in circulation. Central Antarctica. Al though this model omits the At
-169- Table I. Coefficients of the isotope-paleoclimate models ( 1)-(4) and (6) ·
Isotope fractionation Illodels Meteorol. Geographic Ice now Thermo-mechan ica I I'arameter V-I 1141 V-2 1H}2 ] V-3 ]48] data [21 1 data models models n, %ocC ' 10.6 10.3 7.5-9.5 9-13 r... , %o°C' 3.7 2.8-3.6 2.5-2,8 r. 4.8 4.5-4.7 4.5-4.6 A %"CC-' 0.75 1.72- 1.38 0.79-1.1 /3.. , %o 0C-' L3 1.66- 1.76 1.3-1.6 (J. 2.8 3.0-2.9 3.0 Cr, %o0c-' 5.0-7.5 6.2±1.1 13±1[21] 7.7± 1.1 [3] 3.6-7.3 [101 ,104,113] 9 [41 ,78] 6.7[34] 6.1-6.5 ( 130.131] 6.0-6.3 [112] 6.1 c, 0.7-0.8 0.45-0.52 [21] 0,7-0.79 [130. 13 I] 0.67 142] 0.79 6.4±0.2 [15,22] 2.9-5.1 (3.101.104.113] -6 [62) 3.6±1.0 [59} 4.2-4.8 [130,131 ] 4.' a, 0.14-0.31 [3,101 ,104,113] 0.11·0.12 [130.l31} 0.06-0.12 • The most reliable recommended estimates arc given in bold to study the general sensitivity of the isotope content of temporal variations of fl,sD - y",f..,s, gOm and flT; for ice deposits in the Vostok Station area to the global r /w - 0.5-1 in Eqs. (2) will be 15-35% lower. temperature changes did not result in unique estimates Available meteorological observations and special for the coefficients }';, Y.. ~ and Cr in Eqs. (I) and (2) measurements in pits in vicinities of Vostok Station (variant V-3, Table I) and demonstrated a strong were analyzed and summarized in [21]. The deduced dependence on possible moisture exchange regimes. statistically valid regressIOn coefficients of the Systematically lower estimates of }'; and YK' at correlation between the seasonal condensation intermediate values of [J; were obtained in this case in temperature oscillations and the isotopic composition of comparison with the variants V-I and V-2, while, as precipitation (Cr) during the year 2000, as well as emphasized in [14,48], the coefficients r", and AI! were between long-ternl (over 50 years) annual inversion reliably determined. It should be noted after [45 ] that, in temperature variations and the air temperature near the accordance with this work, Ym in Eqs. (I) and (2) is ice sheet surface (CI) are presented in Table I. Let us equal to 4.6 instead of 8 traditionally assumed earlier. note that seasonal changes in the inversion temperature The difference in the estimates of the principal and the surface air temperature give almost a two times coefficients YI, y.... and fJ;, jJ.., is rather significant and, as lower value of C; which agrees with the earlier estimate shown in [102] , can lead to the substantial uncertainty in [80]. This difference is explained by the seasonal paleoreconstmctions. Fig.2a evidently illustrates this character of the inversion strength [21]. conclusion and demonstrates how different the deduced Geographic daw on the present-day distribution of the isotopic content in surface snow over Antarctica and the fluc tuations of flT/ and flT.... can be, depending on a chosen combination of the coefficients in Eqs. (I). correlation between the isotopes and the surface Unfortunately, numerous attempts to use GeMs were temperature, including measurements [15, 62] , were focused [21 , 45] mainly on Eq. (2) describing temporal analyzed in [21, 22). For East Antarctica, the ratio variations of the condensation temperature in order to between the de uterium content variations and the near surface air temperature was deternlined to be investigate the difference of the combined coefficient Cr from the corresponding spatial (geographic) CiCr "" 6.4±0.2%o°e ' and is in close agreement with the isotope/inversion temperature slope. In particular, for value of 6.04%a"e ' from [62] and with the estimate the Vostok area conditions, a 30% reduction of C in [114] obtained for the oxygen isotopes corresponding to r l comparison with its geographic analogues can not be CiCr "" 6.8 %a°e for deuterium. According to [42] , the excluded [39, 45]. Such dev iations are also in agreement spatial relationship (4) between the inversion and with the general relations (I). For example, if the surface temperatures in Antarctica is characterized by contemporary latitudinal distributions of isotopes are the coefficient CI = 0.67. Consequently, the traditionally D i formed by air masses coming from one source, at used estimate of Cr "" 9%o e [78] directly follows [41] flT.... = 0, the spatial Cr slope in Eq. (2) should be from [62]. However, as shown in [21], the inversion identified with }';. On the other hand, in accordance with temperature is close to that of the atmospheric moisture the predictions of isotopic fractionation models (see condensation in clouds only in the central regions, and variants V-I, 2, 3, Table I), the ratio Cr between the spatial variations of the condensation temperature are described by noticeably lower values of Ci "" 0.45-0.52 ,
-170- and temperature in Antarctica can not be directly used in paleoreconstnlctions of climatic time series even in the simplified procedure (2)-(4). Totally, the geographic l estimates of the slope Cr ",,-9-13%o°e lire not in contradiction with the theoretical predictions of the coefficient 1; ""- 7· 11 %noe l in Table L However the observationlll data do not specify the calculated values. At the Slime time, as can be seen from Table I , the meteorological observations of the short-term changes III the inversion temperature and the isotopic composition in precipitation at Vostok Station [21], in spite of their high uncertllinty, give the estimates of the temporal slope in Eq. (2) close to the model results I Cr "" 5-7.5%o°C [48]. Furthermore, it follows from [21] that the difference between the temporal variations of 2 -- 3 the lllversion temperature (apparent condensation temperature) and the surface temperature at Vostok 100 200 300 400 Station (see Table 1) is substantially less (C; ""- 0.7-0.8) T ime BP, kyr in comparison with their spatial distributions (C1 ",,- 0.67 or even 0.45-0.52). b 2.2 Ice sheet tempera ture fi eld The reviewed studies support very high infonllativeness of the ice core isotopic records form deep boreholes drilled in central parts of Antarctic ice sheet. However, it becomes clear that additional independent data on the past climate changes should be involved III the interpretation of these unique paleoclimatic signals to further validate and clllibmte the transfer functions (1)-(4). This task does not exhaust o the whole problem of paleoreconslructions as II procedure of deriving the past temperatures and ,3 precipitation. Another closely related question is the ice planet contain the information about past Figure Uncertainty of paleotemperature 2: temperature fluctuations at the glacier surface. Further reconstructions. (II) Variations of fhe inversion studies [\3,17, 37] of the heat transfer processes in the temperalllre 6T; alld moislllre-sollrce temperatllre 6.T... central regions of Greenland ice sheet with relatively deduced from £qs (I) al the mean vallies of the high accumulation rates and moderate ice thickness coefficients for l'ariallfS v-/ - V-3 ill Table I (cures 1-3, allowed directly to infer the detailed surface respectively). the shaded area is tlte /II/certainty of tlte temperature variations over the recent 25-30 kyr from inversion femperatllre recolIS/me/iolls ill V-3 [48]. the temperature surveys in deep boreholes and made it (b) Variatiolls a/the im'ersioll alld stllface femperatures possible to analyze the relationship between the tJ.Ti and tJ.Ts /rOI11 £qs(2) Gild (4) al the meall values temperature and the isotope content of ice. The far past CT ", 62 %o'C', C; = 0.75 for meteorological history WllS "forgollen". observations [11] and ice flow modeling f/J2l As shown in [101 , 104 , 106, 107], in contrast to (clIIlleS I), for geographic estimates Cr = 9 %0 '\::7"/, Greenland, the non-stationary temperature ficld in the Cj = 0.67 {41.42} (CIII1IeS 2) alld from Eqs (2) alld (6) centre of Antarctic ice sheet wi th extremely low after [3] at Cr = 7.7 %0 "('"/. C;Cr = 3.8 %0 "('"1 with accumulation rates and maximum ice thickness ap = 0.18 (CII/lIeS 3) (lnd ap = 0 (curve 4). remembers distinguishable local temperature perturbations, induced by the recent astronomic resulting in substantially higher estimates of Milankovich cycles with the eccentricity, obliquity, and
CT ",,- \3 ± I ~&/e l for the condensation temperature. precession periods of t l = 100, 12 = 41, and tj = 23, Thus, the correlations between contemporary spatial t ~ = 19 kyr dominating in the Pleistocene climate in distributions of the isotope composition of surface snow central Antarctica [4, 36, 141]. However, more or less
-171- reliable infonnation about the details of short-tenn high-precision temperature profile measured by temperature fluctuations in the past on time scales of 3- Yu. Rydvan [106] at Vostok Stat ion in 1988 to a depth 5 kyr is lost. This restricts substantially the applicabi lity of 1900 m showed [104] that. at least, the recent of direct inverse methods for paleoclimatic climatic fluctuations IlT. contained a selecti vely reconstructi ons on the basis of borehole temperature amplified (supplementary) precession signal q, which measurements alone [72, 10 I]. Yet, representing, in could not be reproduced simply by scaling of the accordance with the Milankovich climate theory. the inversion temperature variations IlT; in Eq. (4). To surface temperature fluctuations as a superposition of account for this, although small, correction, a hannonic oscillations of the fixed frequencies Of ;; 2mtj generalized fonn of Eq. (4) was proposed (j : 1•...• 4).
(6) T,(I) : T•• + t [A I (,o,(wl') - 1)- BI ,;n(w/)J. (5)
I·' 8p(/) = u pi:[A)cos(Wl) - 1) - BJ sin(o)/)] , I~ it becomes possible to find [3,101,104,106,107, 1l3] the contemporary ice sheet surface temperature T.o and where up is the scaling factor of the precession the cosine lmd sine amplitudes Aj and Bj of the four components of the local geophysical metronome (5) [3, Milankovich cycles by minimizing the standard 101 , 104. 11 3]. deviat ion (SD) between simu lated and measured The best-fit values of the product CjCT and the up temperature profiles. Here r is the time counted from the coefficient we re first inferred [104] from Rydvan's far past (I < O. and 1 "'" 0 is the present moment). temperature profi le [106] and in two limiting cases were Va rious borehole themlOmetry data of different I found to be CI CT ~ 4.8±0.3 and 4.2±O.3%o°C . up"" 0.29 quality and observational depths were used in the above and 0.14, respectively. Less accurate stacked cited papers. Despite noticeable deviations of inferred temperature profile down to a depth of 3590 m was used amplitudes. the geophysical metronome (5) reliably in [101. 113] and lead to lower estimates of CjCr "" 3.3 reproduced (with accuracy of - 1-2 kyr) the ages of the and 2.9%o°C 1 at Up "" 0.24 and 0.31. Preliminary results major climatic events (temperature maximums and of the new continuotls temperature survey perfomled by minimums) at the glacier surface. From this point of R. Vostretsov at the end of 1999 to a depth of 3620 m in view, it is of principal importance that the same the record borehole at Vostok Station (almost two years paleoclimatic extrema are clearly distinguished in the aner the drilling operations had been stopped) were smoothed variations of the deuterium content in ice analyzed in [3]. They gave intemlediate values of cores versus depth (Fig. I). Consequent ly, although the C;C ",,3.8±0.I%o°C I and u ",,0.18. In all the above absolute temperature transitions between different r p cited papers, an approx imate quasi-one-dimensional climatic stages ure not precisely detennined, the ice age heat transfer model [10 I, 106, 107] was used for dating seems to be rat her reliable. The resulting simulating the ice-sheet temperature field in central sequence of the depth-age correlation points was called Antarctica. In addition. it becomes clear that the inferred [104] the geophysical metronome time scale (GMTS). values of the tuning coefficients are substantially The
-172- These results agree wi th the calcu lations of IlT; fro m Milankovich components of the local surface Eqs. ( I) in Fig.2a, although they also demonstra te a temperature variations in the past inferred fro m the signi ficant di versit y. In particular. the decrease in the borehole temperature profil e. Possible errors and in vers ion temperature (effecti ve condensat ion uncertllinties of GMTS were di scussed in [ 101, 104], temperature) determined by meteorological observat ions lL nd its overall ave ra ge accuracy was estimated as ±3.5- and the change in the ice sheet surface temperature 4.5 kyr. OrbitlLl ice lIge control points used in (74,75] liS inferred from the borehole tempemture profile fo r the model constraints coincide (to within ±2 kyr) wi th the LGM at Vostok Station are 30·50% larger than the corresponding GMTS ages. corresponding estimates based on the geographic data. Another paleotemperature-proxy signal spanning over The impact of the precession signal 4 in Eqs. (6) is more than 500,000 years is avai lable from the calcite re vealed (see doted curve in Fig. 2b) in more core in Devils Hole (DH), 'evada [139, 140]. The pronounced (by 2·2.5°q cl imat ic maximums in the principal advantage of this S180 record is that the dense surf,lce temperature. vein calcite provides a material for direct umnium-series dating [63] with the relati ve standard errors of about 3. Age of the Vostok ice core. Uncertainties 1.5·2%. In addition , the signal may be influenced by and problems different hydrological factors. In particular, a systematic underestimation of the determined ages on the order of 3.1 Ice age datings of diffe rent origins several (two) thousands of yellrs may take place due to There is no universa l and/or standard procedure to the ground-water travel time through the aquifer [51, detennine depth-age relationships in polar ice sheets at 139]. Nevertheless, the correlation of the Vostok ice sites of deep dri lling. The latter question is of primary core deuterium-depth signal with the Devils-Hole record importance for the deep ice core retrieved from the (see U.S. Geological Survey Open-File Report 97-792 Antarctic ice sheet at Vostok Station [7S]. Possible at http://pubs.water.usgs.gov/ofr97-792) can also be applicability of sophisti cated 2-D and 3-D considered as an independent approach to dating long thermomechanical ice flow models [95 , 96] for solvi ng paleoc limate archives from cent ra l Antarctica [5 1]. th is problem significantly su ffers from inevitable Note, that we do not di scuss here a possibility (e.g. [7. unce rtainties in initial and in put du tu, mainly in glacier 123]) 10 employ vario us glls studi es of Vostok ice cores bottom conditi ons and past accumu lation rates. This was for reilltive dating (correlation) wi th other Antarc ti c, the principal obstacle limit ing the accuracy of eurl ier Greenland or deep-sea core climatic records, because of simulations and ice age predicti ons by - 15-20 kyr. inevitable additional errors which arise in this case from Nevertheless, theoretical studies and computational the uncertllinly in the gas·ice age difference preventing experiments [74, 75, 137] show that the modeling of ice better constraints on the ice agc. sheet dynamics becomes a useful tool for the ice age prediction in cent ra l areas of lurge ice sheets if a priori 3.2 Glacio logical and ave rage tim e scales chronological informati on is used to tune the model The best-guess glaciological time scale si mulated in parameters. Not being free from their own specific [75] was mainly based on the RES dllta by Siegert and errors, different sources of age markers and dated time Kwok [I IS] and is designated as GTS-I aner [13 I]. series can, yet, be considered as re liable constraints if The principal goal of [ 11 2] wns ( I) to combine the all together they deliver statistica lly val id and GMTS and DH sources of chronological information independent estimates of ice age at various depth levels. (70 age markers of climatic events totally) in order to The inverse Monte Carlo sampling method (e.g. [70, 71, constrain ice fl ow model pammeters, reducing to 12S]) is especially helpful in this case [74] to fit the ice· minimum systematic errors in the glac iological time sheet model on aver'dgc, uniformly versus depth, scale based on simulations of ice sheet dynamics in the although wi thout pUlling much weight on local (high. vicinities of Vostok Station and (2) to deduce an frequency) l1uctuations of the simu lated depth-age curve average age-depth relationship consistent with different caused by uncertainties in environmental cond itions, approaches to ice core dllting within the upper 3350 reconstructed ice accumu lation and other paleoclimntic meters. For the grounded part of the ice sheet, the characteristics. From this point of view, as a first reference flow line passing through Vostok Station was approximation, even simplified ice 110w models (e.g. [3, drawn perpendicu lar to the surflLc e elevation contours 34, 35, 110, 112}) may be qui te appropriate to [1 19]. and the ice fl ow tube configuration was incorporate the principal laws of ice-sheet dynamics approx imately determined after [ 11 7, I IS, 127]. Over into the ice core dating procedure. the lake, the 110w line was continued in accord ance with Among different depth-age relationships deve loped the observations [5, 125]. A monotonically increasing for Vostok, the geophysical metronome ti me scale spatial distribution of the normal ized mass balance (GMTS) [104, 106] extended in [3. 101, 113] to the 5(5) in Eq. (3) was schematica ll y taken as similar to maximum depth 3350 m of the Vostok ice core isotope the smoothed accumulation rate profile along the record covering four interglaciatiolls represents the so tr.IVerse to Vostok [53] wi th account of the mass· ca lled orbitally tuned chronologies. As explained in balance enhancement factor 1.65 estimated [40] for secti on 2, it is based on the correlation of the isotopic Ridge B at the locat ion of the Dome B ice core. The temperature signal with the geophysical metronome, i.e, present-day ice-sheet thickness at Vostok was assumed
-173- to be 3755 m afler [64]. The bounds for the mean recent 20 accumulation rate at Vostok were detemlined on the basis of [2,22, 24]. 0 0 TaranlOla's theory [128] and the Monte Carlo »" 10 0 (random walk) sampling procedure [70, 71] were ~ employed in [1 12] to solve the inverse problem and to .2 find the optimal model parameters among which the .§" > principal ones were the present-day accumulation rate " 0 bo and the deuterium/inversion temperature slope Cr in "" • Eqs. (2) and (3). The modelled best-guess ice age-depth '" distribution is called GTS-ll. lis standard deviations '" -10 from GMTS and OH age markers were estimated as -4.5 and 7 kyr, respectively. In general, GTS-ll can be considered as anothe r source of ice age estimates with o 100 200 300 400 minimum systematic error, though containing its own Age, kyr independent short-tenn distortions which are the attributes of the model imperfectness and uncertainties Figure 3: Comparison of the average lime ~'cale for of the geographic input. This finally suggested Vmtok ice core [112] (zero line) with the best-guess construction of an average time scale for the Vostok ice glaciologicaltimc scales GTS-/ [75J GTS-II [1/2] alld core down to a deptn of 3350 m based on GTS-II and GT-4 [78] (curves /-3. respectively). The shaded area is linear interpolations of GMTS and OH age-depth the confidence interval of the runllillg averaged ages. correlation points. The averaging procedure was Filled and open circles are the GArTS and DH age performed iteratively with the weights taken inversely markers. triangles are the co1ll1"o1 points used ill [75]. proportional to standard deviations of the basic chronologies from the resulting smoothed average curve. The average time scale (zero reference li ne) is The highest weighting coefficient (accuracy) of 44% compared 111 Fig. 3 with the previously used was detennined for the best-fit glaciological time scale glaciological time scale GT -4 [78] and the best-guess GTS-II ; the weights of 38 and 18% were fou nd for age~depth relationships GTS-l and II developed through GMTS and 01-1 age markers, respecti vely, in accordance the ice sheet model constraining in [75] and (112]. The with their statistical validity. The average time scale is GMTS and OH control points are shown by empty and consistent wit h all three basic age-depth relationships solid circles, respectively. The shadowed area in the within the standard deviation bounds of ±3 .6 kyr wh ich figure represents the confidential interval for the correspond to the upper estimate of the age uncertainty. average time scale with the boundaries determined as Actually, the weighted mean standard deviation of the the standard deviations of the three basic chronologies averaged chronologies (i.e., ±2.2 kyr) is thought to be a from the mean ages. As can be seen, an obvious more reliable measure of the accuracy of the resulting progress has recently been achieved in ice core age mean ages. Al though one may argue that the simplified dating at Vostok. It is also important that the above ice flow model, high uncertainties in the environmental cited papers [75. I l2l used similar modeling approaches conditions and the use of OH isotope time series do not and inverse methods. The standard deviation between give any advantage to the avemge time scale. the latter GTS-l and II is about 3.3 kyr on average and is age-depth relationship, still , can be regarded as a comparable with the estimated errors of the average common reference basis for intercomparison of different time scale. However, local discrepancies between GTS-I datings for the Vostok ice core. and GTS- U ages still reach 7-8 kyr and are mainly The tuning of t.he ice sheet flow model was caused by differences in the initial geographic and perfonned in [112] for the climatic input described by paleoclimatic data. New studies and special sensiti vity Eqs. (2) and (3), and, at the correction factor of 1m = 8 tests [130, 131] additionally confinn that the reliability for the sea-water isotopic composition. the best-fit of ice core age dating and paleoreconstructions depend values of the temporal isotope/inversion temperature substantially on accuracy of thenno-mechanical slope were inferred as Cr ,," 6.0-6.3%o°C ' with the modeling and quality of input (environmental) 1 standard deviation of about 0.6%o°C • The use of the re infonnation. examined value of 1m"" 4.6 in Eq. (2) instead of 8 1 reduces the estimate of CT by _0.4%o°C- without any 4. Vostok flow line modeling influence on the ice dating. The obtained result agrees with the other data presented in Table I. The best-fit 4.1 Ice now tube geography and RES data present-day accumul~lIion mte was found at its lower As mentioned above, environmental ice sheet flow bound 2.15 cm y( l and matches with the mean value conditions previollsly used in [75, 112, 130, 131] were 2.23 ± 0.03 em y(1 calculated for the recent 190 years rather uncertain and in some cases even schematic. from the depths of the Tambora eruption layer measured In this study, the Antarctic ice sheet surface elevation at Vostok in 9 shallow boreholes and deep pits [24]. map of the Lake Vostok vicinities (Fig. 4) is based on the ERS+1 satellite altimetric data [60, 92] adapted afler
-174- _____ -1
4" -2 ,,-
Figllre 4: Surface elevaliolllllop of Lake Vostok vicinities [60. 92J adapred after [J 29]. J- Vostok ice flow line (VFL): 2- ice flow lube: 3- SPRJ/NSF RES rOlile [19.98]: 4- Lake Vostok waler table [83]; 5- eleva/ioll COI/lOllrs Willi 10-111 spacing.
Figure 5: Bedrock topography map of Lake Vostok vicinilies after ABR1S project [82]. 1- Vostok icefloll' line (VFL); 2- SPRlINSF RES rOllles [20. 98J: 3- Lake Vostok wafer /able [83}: 4- elevatioll co/Uours wilh 200-111 spacing.
-175- Distance from Ridge S, km
-Water Water Ice surface I
Jt~~ ====~~~======::==~~~~::~~~~ l2~:--====~--jJ, , "--______- ,3-----;1 , '-______-- l4------,i, , '-----'--______------l6------1l5------: '---______---l7-----1 ,i , AA.C\".------Sea level ------1, Island t
Dista nce from Vostok Station, km
Figwe 6: Ground-based radio-echo lime sec/ion (a) alld /he illlemaf s/rucfllre, sill/ace and base topography (b) of the ice sheet over rhe I06-km dis/alice along /he ice flow /ille lips/ream of Vas/ok across Vostok subglacial/ake (VSL). Reflecrion layers marked by open circles alld lIumbered jiWl1 LO /0 L7 are /lsed in 'his s//ldy for model calls/raining.
[129]. It has been combined with the detailed measured from Ridge B along VFL with Vostok Station geophysical observat ions around the lake provided by located at So "" 370 km. PMG E [67, 83, 84]. The re-examined Vostok flow line Since the international BEDMAP project [65] , many (V FL) and the flow tube confined between two radio-echo sounding and seismic studies have been neighboring flow lines are drawn in Fig. 4 perpendicular perfonned in Antarctica, in particular in the Lake to the elevation contours for the grounded part of the ice Vostok area (e.g. [67,83,84, 125 , 127]). The revised sheet and follow the ice velocity field over the lake as fragment of the general bedrock elevation map de termi ned in [5,129] and recently con finned by [138]. presented in Fig. 5 is a result of the newly launched We introduce the longitudinal coordinate s as a distance AB RJ S (Antarcti c Bed Relief and Ice Sheet) project
-176- [S2]. The map is created by the Inverse Distance nonnalized width H(s) and current ice4equivalent Algorithm with the 5x5 km grid at the SO-km averaging radius. The estimated llccuracy (- 200 m) is still limited Table 2. VFL model parameters substantill[[y due to non-uniform distribution of the availllble RES profiles. The basic SPRIINSF routes [20, Parameter Denotation Value 9S] are shown in Fig. 5 by dOlled lines. Some of these Snow-fim del1sijicaliol1 airborne radar transects were analyzed in [52, 117, liS]. Density of pure icc, kg m') AI 920 Importantly, one of the flights, starting from Vostok SurfaCC4snow porosity c, 0.69 Station (see Figs. 4 and 5), past closely to VFL in its Exponential densification 1. 0.021 factor, m· 1 middle part, [004200 km upstream of Vostok. Ice flow m()(/el The airborne and ground4based radar observations Prescnt-dayaccumulation bo 2.15 also provide valuable infonnation on internal ice sheet rate at Vostok, cm y(1 structure (layering) controlled by the bedrock Mass-balance exponcntial 0. 11 topography and environmental ice4flow conditions. A factor. oC I ". 1064km RES traverse was undertaken during the two Flow line length, km 370 field seasons of the 50 and 51 4th Russian Antarctic Open lake area, km '"'r 331 Expeditions (200442006) on snow tractors by PMGE Ridge48 highland '. 310 explorers over the subglacial lake area directly along boundar/, km Glcn flow41aw cxponent VFL. The stacked radio4echo time section is depicted in a 3.0 Modified Glen flow41aw 6 Fig. 6a. Together with the underlying rock relief and the p exponentf ice4water interface, eight isochronous reflection layers Shcar4flow-rate factor o 1,0 -177- thickness .6(s. t). It is also relevant to define the vertical intermediate transition zone Sh < S < Sf covering the coordinate S as the relative distance from the glacier vicinity of the western shoreline before the grounding base expressed in te rms of the equivalent thickness of line, the inlet, and the island (see Fig. 6). We assume pure ice and nonnalized by d. that the a parameter cosine-like monotonically The snowlfim and bubbly ice density p versus depth decreases from I to 0 with distance S increasing from Sh II can be presented [103, 107] as to sf where the ice sheet gets anoal. 80th values pand Sh are considered as tuning parameters (see Table 2). The ice sheet thickness is presented as 6(',1) = 6,(,) + &\(1), (10) where Po is the densi ty of pure ice (constant value). Cs is the porosity of the surface snow and r. is the where 6.o(s) is the present-day glacier thickness (in ice densification exponent factor. This directly yields a equivalent) along the now line. Temporal ice sheet relat ionship between sand II thickness nuctuations &let) are reconstructed after [101, 110]. This simplified multi-scale model for &l was s=I--" + - c, (I -e_"' j . (7) verified, and its tuning parameters Yb and YI given in 6. y. 6. Table 2 were constrained on the basis of the 2-D thermo-mechanically coupled model of Antarctic ice The exponential approx imation of the density-depth sheet dynamics [95]. Eq. (IO) was later supported by 3- profile (cs and Ys in Eq. (7» was deduced from the D simulations [96]. Another model parameter eh in Vostok ice core measurements [57] and additionally Table 2 is the relative ice-mass balance excess averaged confirmed in [24]. Ice properties and other model over the area of the now tube. It is directly calculated on parameters used in our study are gathered in Table 2. the basis of the spatial distribution of ice accumulation In terms of the above denotations, ice particle rate. trajectories are the solutions of the following ordinary differential equations 0 2 H(I) d.. d; w(s,;,t) '.6 - = II(S,,",t), (8) 0 dl dt 6(s,t) E 2000 ~ 1.2 """0 0 c ~• where II is the longitudinal velocity and IV is the , .~ apparent vertical velocity in the (s, Q-coordinate system. .".;; , 0.8 E 0 3000 , " The velocity field is given explicitly in [100] , , z0 " "".] OA 4000 0 (9) 0 '00 200 300 Distance from Ridge B, km I (I ()'" 8 ",=-b+(l - ; b + I\'O+ ~n - ) (HAa)1 . \jJ + IH 8s Figure 7: The I/ormalized ice flow l/Ibe width H(s} vs. 1 distance from Ridge B alld the stacked presem-day Here A(s, t) is the total ice now rate along the profile of the ice lhicklle~'s 6.o(s) along VFL (Fig. 4) ill reference now line through the now tube ofa unit width eqlfivalel1l of pure ice willi tirO possible vers;ollS of the illfermediate pal"! (see text). The boundary between the glacial and refrozen ice A = --] Rb + 1VO - -86)Nds H(s) 0 81 (accreted icc thickness 6..:,) along the reference now line over the lake is simultaneously determined from Ihe and I\'O(S, t) is the ice accretion (melting) rate at the ice accreted ice mass balance equation: water (rock) interface. By definition, a is the proportion of the total ice now rate through the now tube due to a6 I 8 ( ' . " ) (II) plastic (shear) defonnation of the glacier body --~ + -- 116. fUd; = 11'0 ' 8t ,., as 0 (0 :S: cr:S: I), and p is the modified Glen flow law exponent, which additionally takes into account the vertical temperature gradient [61]. Three regions are The present-day geometry of the ice now tube is needed distinguished along the Vostok now line: highland area to employ the model (7}-(1 1). The relative now tube 0 < s < Sh of the grounded ice sheet without sliding width /1(s) versus distance S to Ridge 8 directly taken (cr = [) at the bed (Sh < Sf), open lake area Sf< S < So with from Fig. 4 and available infonnation on the ice sheet the zero shear (a= 0) at the glacier bottom, and the thickness 6.0(5) (bedrock depth) in equivalent ofpUTe ice -178- along VFL are ploned in Fig. 7. Based on the wide given in Table 2 is fined to the observed increase in the angle reflection technique, the iee thickness at Vostok ice sheet surface elevation upstream from Lake Vostok has been slightly re-estimated as 3775±15 m in [85], to Ridge B (- 290 m, see Fig. 4); the zero slope (Q = 0 ) being also in agreement with other observational data. is assumed over the deep water area s/< s < so. This is not far (within the 20-metcr uncertainty of RES measurements) from the previously deduced value of 4.4 80undnry conditions 3755 III [64, 66J which is still used here for consistency To complete the icc flow and heat transfer with our earlier studies and trnnsfonns to 3722 m of the problem (7)-(12), boundary conditions should be ice equi valent thickness under Vostok Station in Fig. 7. imposed on the free ice-sheet surface and at the glacier The most accurate 106-km prolile of the glacier bottom bouom. Originally, Eq . ( 12) does not account for upstream of Vostok (solid red line) is the 5-km running enhanced thennal resistance of snow and fim deposits in average of the RES data from Fig.6b. The rcst dashed a relatively thin ncar-surface stratum of the ice sheet. As (black and red) part of the bedrock relief corresponds to discussed in [107], a special heat balance equation the residual cartographic data from Figs.4 and 5 should be fo nnulated at the surface in this case to smoothed in 30-km scale. The intermediate red-dotted preserve the heat fl ow and to link it with the surface line rragment overlapping the dnshed black profile is the temperature T, detailed IO-km running average of the bedrock relief from the airborne radar transect [117, 118] along the lOO-km part of the SPRUN SF RES route [19, 98] = T -T' (13) Il ac , ( , I , passing closely to VFL (see Fig. 4). The red (solid, - , , dotted and dashed) stack presented in Fig. 7 is used furth er as the most reliable available description of the where X is the effecti ve heat transfer coefficient ice sheet base relief over VFL expressed via relati ve densi ty and thennal conductivi ty of snow and fim. Parameter X was estimated for Vostok 4.3 l'leat transfer equation area in [10 1] on the basis of observational data [126, A general equation of convectivc heat transfer in an 136). [ts value, given in Table 2, was later validated on icc sheet in the shallow-icc approximation [3 1, 87] the new field measurements [II I] confinned in [29]. combined with the ice flow line description [86, 91] in Long-tenn paleoc limatic temperature va ri atI ons the (s, (I-coordinate system takes the form [100, 107]: penetrate through the ice sheet thickness into the underl ying rocks, and a conjugated boundary va lue problem should be fonnulated to describe the thennal ( 12) Poc6:,(a ..T +11 -aT + wor ) = a ( A. aT)+Q' state of the glacier at the ice-rock interface [93]. iJ, as Il a( a( a( Preliminary computational experiments [ 130] show that, - '0« <0, O Q=gp- 'l,Iala,(P+2l ) A(I - S) ", , where the ice-sheet surface slope along the flow line !-I ere ab, Ab are the thernlal diffusivity and conductivity of the rocks [73 , 95]. Linear vert ical temperature I l over the grounded pan of the glacier is [130] alias distribution, consistent with the gcothennal flux qo and surface temperature r., is set as an initial temperature fi eld at a time 1 = - to far in the past. a~ I (VA ): 1&1 = gPoll Il ~ Over the lake, SI < S < So, the glacier base is at the melting point, and g is the gravity acceleration, a is the original Glen ( 15) creep exponent in the ice now law. A scaling parameter v is proportional to no n-linear ice viscosit y. Its value -179- wi th the ice fusion temperature Tf linearly related to (borehole temperature measurements, accumulation pressure p rates deduced fonn air bubble properties, ice age markers, isochronous reflection layers. and other sources of glaciological infomtation) to come to the most consistent (best-fi t) model predictions and. The fus ion temperature at zero pressure TfJ and pressure consequently. to more reliable paleoclimatic depression coefficient Kp depend on the lake wa ter reconstruction and ice core age dating. The follow ing salinity and the concentration of dissolved air (gases) general guide tines were used in our complex [54]. Their values resull ing in Tf most consistent with optimization procedure. the borehole temperature measurements at Vostok are 1. A sufficient set of age markers stat istically given in Table 2. independent and unifonnly distributed versus depth at a The accret ion ice at the contact of the ice sheet wi th certain site under consideration (s = Sa) reliably the lake water is generally fonned of the local water constrains the icc-volume flow rate A(s = Sa, r) through frozen due to the upward heat flux (cooling) though the the prescribed reference fl ow tube in Eqs. (9). For a glaci er body but, in principle, we do not exclude a given present-day accumulation bo at Vostok, the flow possibitity that a certain amount of fra zil ice [76, 77] rate determines the isotope/temperature slope Cr in the can be brought by ascend ing fres h water flo w from the precipitati on model (2) and (3) and al10ws tun ing the colder northern icc-melting area [ 117. 125]: shape of the spatial profile 6 (s) to deduce the best-fit icc age-depth relationship. (16) 2. Although limited in distance, the isochronous reflection layers (see Fig. 6), especiall y in the upper, near-surface part of the ice sheet. also deliver unique infonnation on the b(s) -distribution along the now line. where 111' is the rate of fraz il fonnation and Lf is the latent heat of icc fusion. The accretion rate 11'0 is The local configuration and the IOtal descent of assumed to be zero over the island. isochrones in the deeper part of the glacier within the transition zone s ~ < s < sfat the western side of the lake 4.5 General algo rith III and straleg.y of computations are mainly control1 ed by the modified Glen exponent p The age IJ of an ice part icle at a depth of lid related to and the boundary coordinate s~. the '" level by Eq. (7) under Vostok Station at S "'" So, 3. The temperature gradielll in the deeper part of the that is the ice core time scale. is detennined from ice sheet above the lake remembers the thennal state of equation ,;{ - Id) '" I, where the ice particle trajectory the bedrock and the geothenllal flux qo over the (,;{/) , 5(1» is the backward-in-time solut ion of Eqs. (8) highland area in Eq. (14) and determines the ice ( 10) at the init ial conditions 5(0) =50. ,;{O) '" "'. accretion ra te \\'0, Through Eq. (II), the ice flow rate Correspondingly. the deposition site of the particle is (the travel time ac ross the lake) and the accret ion rate :'d '" 5(- 111)' control the lake-icc thickness ~ which, being measured Implicit fi nitc-difTerence schemes were used to solve at Vostok l44], deli vers the information on qo. As the difTerential equations (11 ) and (12) at the boundary discussed in secti on 2, the borehole themlOmetry conditions ( 13)-( 16). "Left-angle" firs t-order constrains the Cr-cocfficient (the product CiCT), the approximations along the s-axis provide stability of the scaling factor a pt and the present-day surface computational algori thm based on the sweep method temperature T.o in Eqs. (6) after substit ution of Eq. (2). along the '-axis. The observed temperature profile extrapolated to the ice The cl imat ic input of the model over the recent 420- sheet bottom provides an estimate for the fusion kyr history covered by the Vostok deuterium record [78] temperature Tf and the Kp-coefficient in Eq. ( 15). is represented by Eqs. (2), (3), and (6) and the 4. Fina ll y. the reconstructed past temperatures on the iterati vely calculated glaciological time scale. For ice sheet surface and the air bubble number density earli er times, the scaled geophysical metronome (5) is measured in the upper part of the Vostok ice core can be employed to extrapolate the inversion temperature recalculated [55, 56, 58] into local LGM-Holocene variations in Eqs. (3) and (6) into the past. variations of the accumulation rate to detennine (andlor An interactive comp uter system was developed to validate) directly the temporal slope CT in Eqs. (2) and perfonn necessary numerical experiments in order to (3). The rest (deeper part) of the available bubble constrai n the im proved thenno-mechanical ice fl ow line number concentra ti on profile represents the spatial model and its climatic input by available geophysical distribution of the accumulation rate b(s) upstream of and glaciological data. Our previous studies [10 1, 11 2, Vostok. 130, 13 1] show that the si mulated fea tures of the ice Numerous se ri es of hundreds of computational fl ow and temperature fie lds in the ice sheet are experimen ts took tota ll y about two years of systemat ic selecti vely sensitive to difTerent model uncertainties. iterative tests and data analyses. The inferred model Thus, the general strategy of the ice core data parameters arc presented in Tables I and 2, and the interpretation was in seq ucntial and iterative fitting the obtained result s arc di scussed below, in the final section. model to various independent sets of observational data -180- 5. Results of model constraining and ice balance given by Eqs. (2) and (3). Available data are core data interpretation gathered in Fig. 8. The present-day ice accumulation rale al Vostok is assumed to be bo = 2.15 ern y(1 which is close to the [90-year mean value [24] and provided 5.1 Revised glaciological time scale Ihe best-guess time scale GTS·II for Vostok ice core Tbe studies of ice sheet dynamics along the Vostok [1 [2). The air bubble number density profile measured ice flow line and ice age predictions reviewed in at Vostok confinned [56] the best-fit isotope/inversion section 3 were based on simplified models and suffered I from the lack of accurate geographic data. Furthermore, temperature slope Cr = 6.1 %o"C deduced at Ym;::: 4.6 in invariable spatial distribution of the accreted ice [130,131] with the use of the GM TS age markers and thickness was implicitly assumed at the glacier bottom allowed reconstruction of the accumulation rate profile over the lake in [112]. However, the total amount of b(s) over - 50 km across the lake (Fig. 8, curve 1). The refrozen ice is directly linked to the local velocity of the latter result is in agreement with the field studies by ice sheet motion and both characteristics undergo Popov and others [81 , 84]. On average, the 30-35% paleoclimatic fluctuations. These perturb strain rates in increase in the accumulation rate at the western side of the glacier body floating across the lake and, as a the lake is also supported by the isotopic and consequence, affect the ice age-depth relat ionship. stratigraphic studies in pits (personal communication by Preliminary series of computational experiments A.A. Ekaykin). These estimates give at least 30% higher perf0n11ed in [130, 13[] showed that imperfectness of present-day b-values at 35 and 59-km distance and a the model and existing uncertainties in its 40% increase at 96 km from Vostok (Fig. 8, squares). environmental input can lead to high local errors in ice The mean accumulation rate over the recent 190 years age predictions wi thi n the eSlimaled standard deviations (2.25±0.04 em y(l) has been directly calculated from of ±3.6 ky r [112]. Here we use the improved 2-D ice the depth of the Tambora eruption layer observed in the flow line model (7)-(16) with the general description of pit at the end of the VFL radar route, 106 km upstream the velocity field transition from the grounded to of Vostok (Fig. 8, diamond), and practically coincides floating ice sheet flow pattern, ice accretion at the with that at Vostok. The ice mass balance enhancement glaci er bottom over the lake, and the re-examined factor of 1.65 estimated in [40] for Ridge B at the geographic data (Figs.4 and 5) based on the recent location of the Dome B ice core (DB site in Figs. 4 and cartographic materials lind RES profiling (Fig. 6) along 5) corresponds to the triangle in Fig. 8. The normalized VF L. spatial di stribution of the accumulation rate deduced in Special attention is paid to better constrain the spatial [52] fonn the air-borne radar observations along the distribution and temporal variations of the ice mass flight route approximately parallel to VFL and passing 40-50 km northward is also shown as curve 2. All these 2,------, data considerably reduce the 5(s) -profile uncertainty. To find the best-guess environmental conditions and tune the ice sheet flow model , we used eight RES reflection (isochronous) layers LO-L7 depicted in Fig. 6b and a selected set of the most reliable age markers. In accordance with our previous analysis [ 112] illustrated by Fig. 3, the less accurate OH control points were excluded from consideration. It is also clear that Ihe 39 GMTS age-depth correlation points practically cover most of the 8 age markers from [74, 75] except for the universal lOse peak [88, 142] observed in the Vostok ice core around the 601-meter depth and rel iab ly dated as 41 ±2 kyr. Thus, the employed set of age 0. 8 +-~___r-~-r_---r-_,_~,J control points was composed of the latter beryllium o 100 200 300 event and 34 GMTS ice age markers older 50 kyr fro m Di stance from Ri dge B, km [3]. The first series of computations were performed with Figure 8: The normalized accumulation rate b(s) vs. the detailed 106-km RES profile of the ice-sheet base dislancefrom Ridge B along VFL (Fig. 4) dedlfcedfi"Ofll (Fig. 6b) continued by the large-scale smoothed bedrock air bubble lIumber dellsity [56J (curve I) alld RES data relief (Fig. 7, black and red dashed line) from the [52] (CIll1'€ 2): the best-jit spatial profiles (curves 3 alld topographic map III Fig. 5. The simple spatial 4) correspond to dijJerem versions oftlte bedrock relief distribution of the normali zed accumulation rate b(s) ill Fig. 7. Available field obsel"l'Gtions {Ire shown by drawn by the black dashed line in Fig. 8 in accordance symbols: sqllares - isotopic {lnd stratigraphic studies in with the presented observational data was found to be in pits (pers. com. by £kaykin). diamond - the depth of the agreement with the near-surface RES re fl ection layers Tambora emption fayer, triangle - tlte estimate [40] for LO-L2 in Fig. 6b and delivered the best-fit ice age-depth the DB site ill Figs. 4 alld 5. relationship. However, the standard deviation (SO) of -181- o LO - Ll L2 - 1000 - L3 L4 : E '" . 2000 - LS- -=0.. -- L6" Cl" = L7 3000 ...- Ice I Bedrock, I I 4000 - a= I I Lake, G=O I 1>a>O- "\ , I , I , 280 320 360 Distance /Tom Ridge B, km Figure 9; Comparison of the besl-flr simulared isochrolles (red linel) dated /1 .2, 23, 37.5, 73. 94.7. 126. 150. alld 210 kyr lI'i(h the respective reflectioll/ayers LO 10 L7 (black /ines)jrolll Fig. 6b. Accreted ice layer is shaded. Ihc simu lated deeper isochrones from the RES reflection part of the 5(s) -profile was adj usted to reduce SO layers L3-L7 (Fig. 6b) reached 6-8 kyr. The calculated between the modelled (glaciologica l) time scale and the timescale deviated from the selected age markers byS.O- ice-age mnrkers at Vostok. For the de tailed stacked 5.5 kyr, exceeding considerably Ihe GMTS bedrock relief (Fig. 7, red line), we succeeded to reach approx imation level of -4.5 kyr by GTS- II ac hieved in the expectt.' -182 - remains within the ±3-3 .5-kyr deviation limits related, 0 )350 as discussed In [131], to uncertamtles in the 14 a paleoclimatic and geographic conditions and differences in the employed thenno-mechanical models. GTS-I 3400 deviates from the 35 age markers used in our study by I. 1000 o 17 5.0 kyr on average (comp. with the 4.4-kyr SO of GTS 0 Ill). At the same time, GTS- I and GTS- UJ have E comparable statisti cal validity characterized by the mean variances of 2.3 and 2.8 kyr with respect to the t eight age markers used in [75]. From this point of view, 82000 GTS- lll based on a substantiall y improved modeling 400 600 800 1000 approach wi th more accurate and broader data scope may be considered as a furt her step towards developing a glaciologica l time scale for the Vostok ice core with 3000 the age errors on the order of 2 ky r or less on average down to a depth of 3310 Ill. The new ice age-depth relat ionship is presented in Tabl e 3 together with the ice particle deposition sites given as di stances from Vostok. o 100 200 300 400 500 Necessit y of the sophisticated modeling and Age, ky r importance of our knowledge about the environmental (paleoc limatic and geographic) conditions of the ice b sheet now for correct ice age predictions were discussed 10 and demonstrated earlier in computational experiments " [1 31 ]. Here to emphasize and illustrate this point, the ~" preliminary best-fit time scale si mulated for the roughly smoothed part of the bedrock (Fig. 7, black dasbed line) .2 ;; 0 and the simplified spatial distribution of the " 0 accumu lation rate (Fig. 8, black dashed line) is also ." 0 shown in Fig. lOb by the black dashed line. <: • Correspondi ng changes in the ice age estimates around '" -10 120- 170 ky r (- 1600-2200 m depth interval) reach 10 kyr. Numerical tests show that th is discrepancy is caused by the substantially lesser ice th ickness around 170- I 90 and 230-250 km from the ice divide in the case o 100 200 300 400 of the smoothed bedrock profile. Thc systematic shifts Agc, kyr between GTS- l, II and [J] timcscales within 70-170 kyr period are also main ly due to differences in the bedrock Figllre 10: Ice (Ige da/illg (/I Vos/ok. (a) Best-jit topography and spatial distribution of Ihe accumulation glaciological time scclle GTS-III (red line) compared to rate. GMTS (filled ci,.c/e~) (llId be/)'lIiulII-IO (/rial/gle) age In spite of the ice now disturbances observed in markers ji"om f3, 88) used for cOl/sfraillillg the ice flow 33 10-3330 m depth interval [78], recent studies of the model. The ill.~el sholl"s Ihe ex/elision of GTS-III to the deepest part of the Vostok glacier ice [120] showed that 3530 m depth le\·e/. 10 m above the bOlllldary lI"ilh Ihe the glacial stages 14 and 16 are still discerned in the accreted lake ice. R£''C({IIIgles alld mill/bers are the dust concentration record within the depth intervals climatic sfllges discem ed il/ the Voslok dust 3380-3405 III and 3435-3450 m, respectively, and most COllcellfmtioll record. (b) Deviations of Ihe likely the interglacial stage 17 covers the depth range glaciological rillle scales GTS-I {75}. GTS-II {Ill} alld from 3460 to 3470 m. This suggests that the ice, at least GTS-II/ (ct/rves 1-3, respectively) ji"om the average lillie to a depth of 3470 m, has undergone onl y local scale for Vostok ice core [ Ill} (zero lille); Cllnlf! 4 perturbations [89]. Hence, an extension of the best-fit corresponds to the dashed fragll/ellt of the bedrock time scale GTS-1[J toward the boundary with the reliefill Fig. 7. age markers are rakel/ from (a). accreted lake ice, to a depth level of 3540 m [44], can provide a new better estimation of possible maximum (120] and their respective durations (505-550, 625-650. variations of ice ages. The statistically expected age 665-700 kyr) estimated after [4} are marked by depth distribution is given in Table 3 and plotted in the rectangles in the inset and indicate that the deeper part inset in Fig. lOa. For example, thc ice age at the 3530 m ofGTS-f[1 ma y underestimate ice ages by -20-40 kyr. It depth, 10 m above the contact with accreted ice, could shou ld be emp hasizcd here that the real basal ice reach - 1000 kyr, provided that the basal ice now had deformation history is much more complicated than that not been disturbed. The depth ranges of the stages 14, modelled in our simulations and the time sca le 16, and 17 suppositionally observed in the dust record extension is given just to illustrate a possible tendency of the ice age growth wit h depth. -183- Table 3. Glaciological time scale GTS-1I1 for Vostok icc core and icc particle deposition sites (distance from Vostok) Depth Ag' Dep.site Depth Age Dep.site Depth Ag' Dep.site m ky, km m ky' km m k}'r km o o o 2198.0 164 222.1 3090.1 328 297.5 113.5 • 7.3 2229.6 168 224.9 3113.3 332 298.6 200.1 8 12.5 2261.7 172 227.7 3136.1 336 299.6 286.8 12 16.0 2294.1 176 230.5 3147.1 340 300.7 343.6 16 20.5 2325.0 ISO 233.3 3155.2 344 301.6 383.6 20 25.0 2353.5 IS' 236,2 3163.9 348 302.5 420.9 2. 29.5 2380.7 1S8 239.2 3172.3 352 303.5 458.9 2. 34.2 2407.9 192 242.4 3180,2 356 304,6 498.3 32 38.9 2436.7 196 245.6 3188.0 360 305.6 541.0 36 44.2 2468.6 200 248.6 3195.9 364 306.7 588.6 40 50.2 2506.0 204 251,3 3203.8 368 307.9 640.9 •• 57.0 2540.6 208 254.1 3211.9 J72 309.1 698.0 48 64.9 2571.7 212 256.7 3220.2 376 310,3 754.7 52 72.4 2607.5 216 258.7 3228.8 380 311.5 808.7 56 78.9 2645.4 220 260,5 3237.5 384 312,7 860.5 60 85.5 2673.9 224 262.3 3245.4 388 314.0 906.0 64 92.3 2694.6 228 264.0 3252.7 392 315.5 949.1 68 99.5 27 12.7 232 265.8 3260.1 396 317.1 992.2 72 106.9 2730.9 236 267.7 3268.8 400 318.3 1037.5 76 114.2 2753.2 240 269.1 3279,3 404 320.4 1088.7 80 120.7 2782.7 244 270.3 3290.8 408 321.8 1140.4 84 126.9 2805,3 248 271.6 3301,8 412 323,0 1182.1 88 133.2 2820.1 252 272.8 33 10.9 416 321.8 1226.2 92 139.4 2833.9 256 273.9 3318.1 420 324.2 1280.2 96 145.7 2849.1 260 274.9 3324.2 424 325.3 1334.0 100 152.1 2863.4 264 276.0 3330.8 428 326.4 1386.3 104 159.5 2875.4 268 277.1 3338.1 412 327.3 1444.7 108 168.3 2886.5 272 278.3 3344.2 436 327.3 1508,8 112 176.9 2898,0 276 279,6 3348.6 440 329.5 1575.8 116 184.0 2911.5 280 280.8 1651.5 120 189,6 2927,2 284 282,0 Extrapol ated time scale 1743.6 124 193.8 2943.1 288 283.2 3360 448 330 1839.6 128 197.0 2957.3 292 284.4 3370 459 331 1918.1 132 200.1 2970.2 296 285.6 3390 485 336 1961.7 136 202.9 2982.8 300 286.9 3410 502 338 1995.0 140 205.7 2996.0 304 288,3 3430 532 342 2027.2 144 208.5 3010.5 308 289.6 3450 570 344 2061.0 148 211.3 3026.6 JI2 291.1 3470 61S 34S 2095.9 152 214.0 3041.9 316 292.6 3490 686 J5J 2130.9 156 216.6 3056.2 320 294,2 3510 776 358 2165.2 160 219.4 3071.7 324 295.9 3530 925 362 5.2 Palco reconstructions considerable temperature contrast between the "cold" A simplified quasi-one-dimensional heat transfer grounded and "warm" floating parts of the glacier along model was used for temperature simulations in the VFL result, as shown below, in large horizontal vicinities of Vostok Station discussed in section 2. In temperature gradients in the near-bottom ice stratum. particu lar, lo ngitudinal heat convection was neglected in The new series of computational experiments were pa leocl imatic borehole-temperature interpretations [3, started in [130,131 ] on the basis of the 2-D fl ow li ne 101 , 104, 113]. However, significant geographic description of heat transfer processes in ice sheets to changes in ice accumulation rate, almost twofold additionally constrain and/or validate the principal increase III ice thickness (see Figs. 6-8), and parameters T.o, Cr, C;, up of the climatic sub-model (2) -184- and (6). Here we continue these studies, using the Temperature deviation, OC improved thenno-mechanical model presented in -0.08 -0.04 0 0.04 0.08 section 4. Following [130], paleotemperatures were deduced from the continuous temperature profile measured by R. Vostretsov in the record 3620 m deep borehole at 1000 Vostok. The preliminarily processed data [3] were E shifted by 0.6°C to minimize the systematic error and to make the measurements consistent with the upper part 15.. 2000 .",' . of high-precision Rydvan's thermometry survey [106]. "' .;'; ..... 2l •<:';. In accordance with [77, 122], the spatial temperature " .. . . "',: .~ drop of 2.rC from Ridge B to Vostok Station was 3000 ";. " ~ : " :;" .. , ~ introduced into Eq. (6) in TsO after [131]. The present -_ ... ;. I;. day borehole temperature profile and mismatch between the measured and fitted temperatures are shown in 40001----.---,----r---,---.----1 Fig. 11 a. SO is about _O.03°C and compares to the -60 -40 -20 o Temperature, OC accuracy of the data. 4,------~----~--~ All constrained climatic pllTameters are given in Table [. The present-day ice surface temperature o T,Q = - 58.5°C at Vostok is similar to that found in [10 I]. The deduced ice fusion temperature at the ice-sheet ~-4 bottom, 3755 m below the surface, Tj = _2.7°C is in "' -8 agreement with [54]. At the same time, the inferred 1 estimates of Ci = 0.79 (the product C;Cr = 4.8 %o0C- ) and a" = 0.06, being close to those of [130, 131], differ 5 considerably from the previous studies [3, 10[ , 104, 113] based on the simplified models and less accurate or "' 0 limited-in-depth borehole temperature measurements. ~ -5 Another temperature profile was measured at Vostok -10 --- I by C. Rado (persona[ communication by J. R. Petit) at --2 the end of 1997 down to 3420 m after 8-month break in -15 1-~~___,~-_,_~--,--~-,____---j drilling operations. Being in agreement with Rydvan's o 100 200 300 400 measurements in its upper part, this survey reveals 0.2- Time BP, kyr O.3°C colder ice with respect to the corrected 3___,------.----, Vostretsov's data in the deeper part of the borehole. As c shown in [130], the best-fit fusion temperature in this case decreases accordingly with only minimum changes 2 in scaling factors C; and ex" at the same SO level. Thus, the isotope/temperature transfer function and the past accumulation rates given by Eqs. (2), (3) and (6) with the recommended parameters from Tables I and 2 can be considered as well established and reliably constrained. The recovered surface and inversion temperature fluctuations are plotted in Fig. l i b. [n agreement with [130, 131 ], the amplitudes of tlTs are noticeably less than before in case of the spatially one-dimensional heat transfer models [3, 101, 104, 113]. In particular, the o 100 200 300 400 Last Glacial Maximum (LGM) surface temperature at Time BP, kyr Vostok is found to be -67.8"C for the non-zero surface temperature spatial gradient, that is only II.4°C lower Figure II: Paleoclimatic //Iodel constraining. (a) The than the Holocene-optimum temperature -56. 5°C. It was borehole temperallIre profile at Vostok and mislllatch 12.5-14.O"C lower in [130, 131 ] for the simplified ice (dOl:;) befll'eell the measured lIlId calel/kued (.low description at the grounding line, while the lempel'otllres. (b) Past inversion and surftlce transitions of I 5-20"C were deduced previously. Special temperature mriatiolls from £qs. (2) alld (6) al the besl computational tests confinn that the latter difference is fit plll'Wllelers Cr "' 6.I%o'C', C; = 0.79, ap = O.06 caused by the considerable decrease in the ratio 11'/ tl in (curves /) alld from Eqs. (2) alld (4) at geographic 1 Eq. (12) along VF L neglected in the simplified estimales Cr = 9 960'C and C1 = 0.67 [41.42J descriptions as well as by the use of the more reliable (curves 2). (e) The reconstructed ice accl/l11/1lal;ol1 rate alld ice thickness variations 01 Vostok -185- and complete thennometry data instead of the -20~------r3 temperature slack [10[, [[3]. Earlier, the best fit a between borehole temperature measurements and -, , -16 ,, simulations was generally found at a higher ',I ,, accumulation rate bo - 2.4 cm y(1 which corresponds to ~. -t2 ,, a 50-year mean value at Vostok [2, 24]. This, most ,, likely, partly counterbalanced in one-dimensional ,, iE -, , approximation a considerable increase in accumulation , rate upstream towards Ridge B. ~ ,, The new estimate of the LGM-Holocene temperature -4 increase is now substantially closer to the conventional predictions (- 9"C) based on geographic data, although remains about 25% higher, as might be expected from 0 tOO 200 ]00 well understandable rlifference between the spatial and Distance from Ridge B, km temporal isotope/temperature slopes [45]. Another 1.4 interesting peculiarity is that the inferred b inversion/surface temperature slope C, "" 0.79 is closer to unity than its geographic analogue C1 =: 0.67 in [42] g and predicts more commensurable amplitudes of '" temporal fluctuations of inversion and surface > "." temperatures than the difference between their spatial .,• variations (see Fig. lib). These results are also consistent with the independent meteorological "E 0 .• 0 observations [21] (see Table l, compo Figs. 2b and lib). Accumulation rate variations determined by Eqs. (2) " 1 and (3) at the best-fit value of Cr = 6.1 %o"e with 0.2 Ym = 4.6 and the corresponding changes in the ice-sheet thickness at Vostok rlescribed by the simplified model 0 ]00 200 300 400 [110] are presented in Fig. [I c. Time BP, kyr 250 ~-~~-----'--'------r6.5 Special computational experiments showed that the c use of the more general equations ([) instead of Eq. (2) I did not noticeably change the discussed above 100 ~ paleoclimatic reconstmclions. The performed analysis E confinns the inferred tuning parameters of the climatic ~~ t50 sub-model (2), (3) and (6) (bold values in Table I) as -- most reliable. :g tOO 3 ,:' / 5.3 Simulated ice fl ow characteristics >0 The simulated contemporary distribution of the surface ice velocity along VFL is presented in Fig. 12a o , by sol id line. Its spatial variation follows the changes in ]20 340 ]60 configuration of the ice flow tube, while the absolute Distance rrom Ridge B, km values are detennined by the current accumulation rates. For the 190-year averaged present-day accumulation Figure 12: lee slleel dynamics and basal cOlldilions rate (bo = 2.15 cm y(l) the calculated ice velocity at along VFL. (a) The preselll.day slIrface vefocily Vostok in Fig. 12a is about 2.03 m yr"1 and approaches (clInle 1) and temperalure distriblllion a/ tlte glaCier 2.3 mye'l for the recent 50-year mean value base (clIrve 2). (b) Normalized slIIface velocily (bo = 2.4 cm yr"I). Both estimates are in perfect I'(IrialiOl1S in cenlral AnlarClica. (c) The presel/l+day agreement with the direct observations 2.00±0.01 mye'l refrozen ice lhickness (clIrve I), a minimal accreled ice [138] and 3±0.8 m y(1 (5). The nonnalized spatial layer (curve 2) after ill/erglacial period~· alld the profile of the surface velocity remains practically distriblltion of the ice accretioll rale over the lake (within 5%) constant in time [130]. Relative temporal (curve 3). variations of the surface velocity are shown in Fig. 12b. They are practically identical for different sites along time needed for ice to float across the lake. The transit the flow line and reveal two times lower velocities time varies from its minimum of about 28 kyr to around 10 kyr BP after the LGM period. maximum of 41 ky r during interglacial and glacial Prediction of spatially non-unifonn and variable-in periods, respectively. For example, due to essentially time ice flow rates upstream of Vostok Station (see reduced velocities in the recent glacial period, it took Figs. 12a, b) is an important result of the computations about 10 kyr for the present-day Vostok ice to cross the which allows a more accurate estimation of the travel II km-wide embayment near the western side of the -186- lake and, totall y, 40 kyr 10 approach Vostok Station. 0,------, This differs considerably fro m preliminary predictions a discussed in [ 11 7] and from the respective values of 4 and 20 kyr found in [5] under the assumption of the 1000 constant ice velocity over the lake. The above estimates E 100 characterize the motion of the surface ice. Due to the ~ 2000 " basal drag in the embayment-island area (see Fig.6b), "- ---200- the bottom ice journey is even longer and takes from 38 8 300 to 57 kyr. 3000 400 Ice core studies at Vostok [441 revealed 215 m of refrozen lake ice at the glacier bottom provided that the total icc sheet thickness is 3755 m [64, 66]. At zero 4000 frazi l fonnat ion rates (111"= 0 in Eq. ( 16», this constrains the geothermal heat flux as C/o"" 0.054 W m-l with o 100 ZOO 300 accuracy not worse than ±5% in agreement with the Distance from Ridge B, km 0 general estimates of [116] for central Antarctica. As b before ( 130], the simulated present-day basal -50 temperatures along the major part of the grounded ice ... 1000 "- , ,' " -," ,..-- , flow line (see Fig. 12a) do no t reach the melting point ._---.---- 0 -40 and remain systematica ll y below -4 c. Consequently, E -, ---_.---- only two fac tors control the ice accretio n: (I ) the 2000 -30 thennal interaction of the cold glac ier (overcooled with "'"- " "- respect to the melting point) with the lake water and 8 3000 (2) the convective drift of the total geothennal heating -10 , , from the lake floor to the northern half of the lake due to the water circulation (e.g. [11 7, 125]). Wi thout direct 4000 geothennal heating from the lake, the heat losses through the ice thickness in the southern pari arc fully coun terbalanced by the water freez ing. Contemporary o 100 200 300 Distance from Ridge B, km distribution of the accreted ice l1a and freezing rates W(l along the VFL are shown in Fig. 12c by solid curves I and 3, respectively. In accordance with these Figure I J: Presem-day ice age distriblllion (aJ lind computations, about 75 meters of the accreted ice are temperature field (b) in the ice sheet alollg VFL. fonned over the embayment near the western side of the Numbers {/I isochrolles and isotherms are ages in J.yr lake at the maximum accrel ion rates of - 6-6.5 mm ye' l. lIlId temperatures ill 'C, respectillely. Accreted ice layer No water freezing is assumed on the island surface, and oller the lake ill (aJ is shaded. the mean accretion rates over the lake are estimated as 5.5 nun ye' l. Because the ice sheet approached the lake icc mass balance b and its paleoc limatic variations (see in the past at noticeably lesser veloci ties than it has now Eqs. (2), (3), and (9». The present-day 215-meter thick at Vostok, the latter accretion rates, although essentially lay~r of the accreted ice, being fomled during - 57 kyr, lower than those predicted in [5, 76, 77}, were suffic ient mam ly, under glacial cond itions, has prac ti cal1y to resu lt in 215 meters of the refrozen icc. However, it ma xilllum thickness which does not exceed 220-225 m. should be noted that, in accordance wi th [85], the ice A minimal accreted ice layer shown in Fig. 12c by the dashed curve 2 is substantial1y thinner after wann sheet thickness at Vostok ma y reach 3775 III and then the accreted ice layer is 235-m thick. This will in~reas~ interglacial periods, decreasing at Vostok to 135-140 m the deduced ice fusion temperature by -oAoC and due to much shorter time - 38 kyr of the basal ice travel 2 ac ross the lake. reduce th e geothennal nux to Qo",, 0.05 \V m· • The present-day ice-age distribution (isochrones) and Altematively, a frazil fonnation rate of 11'/ "" OA mm yr-I temperature field simulated in the ice sheet body along or a smaller non-freezi ng area on the island can result in VFL arc presented in Figs. 13a and b. the same thickness of the refrozen ice. Another im portan l peculiarity of the ice sheet - subglacial lake thernlOd ynamic interaction is that the 6. Conclusion heat flux at the glacier bottom is not noticeably influenced by paleoc limatic surface temperature This re view based on the authors' publications [10 1, variations and remains practically conslant with time 102, 104, 112, 130, 131] demonstrates that the joint [130]. As a consequence, the freezi ng ra tes and the problem of icc age dat ing and paleoc limat ic accreted ice now rate along the flow line do not vary interpretation of icc core isotopic records can not be much. Thus, the accreted icc thickness is sensitive and successfull y solved wi thout involving supplementary inversely proporti onal to the icc velocity which is geographical, geophysical and glaciological infonnation. directly related (through the total ice flow rate A) to the A sophisticated thenno-mechanical ice now line - 187 - model (7)-( I 6) and the computer system are developed in Vostok station area through four climatic cycles and employed as a tool to infer the ice core history at during recent 420 kycars]", Arktika i Antarktika Vostok through fitting the model to various data, which [Arctic and Antarctica], 1/35, 2002, pp. 82-97. include the agc-depth markers, borehole tempcrature [4] F.C. Bassinot, L.D. Labeyrie, E. Vincent, profile, flow-line RES survey, air bubble measurements X. Quidelleur, N.J . Shackleton and Y. Lancelot, "The and additional available field observations. Thc astronomic theory of climate and age of the Bnmhes principal issues of the paper arc thc constrained Matuyama magnetic reversal", Earth Planet. Sci. isotope/temperature and accumulation transfer Lett. , 126(1-3), 1994, pp. 91-108. functions (2), (3), (6) and the best-fit glaciological time scale GTS-III for the Vostok ice core (see Tables I and [5] R. E. Bell, M. Stud inger, A.A. Tikku, GXC. Clarke, 3) simultaneously consistent with a wide spectra of all M.M. Gutner and Ch. Meertens, "Origin and fate of the considered experimental materials. The substantially Lake Vostok water frozen to the base of the East improved modeling approaches with the more accurate Antarctic ice sheet", Nature, 416(6878), 2002, and broader infonnat.ional scope are believed to provide pp. 307-310. a higher reliability of the obtained results. [6] M.L. Bender, "Orbital tuning chronology for the Vostok climate record supported by trapped gas Acknowledgements composition", Earth Planet. Sci. Lett. , 204, 2002, pp.275-289. The authors would like to thank V.M. Kotlyakov for his encouraging and unceasing attention to our work. [7] M.L.Bender, G. Floch, J Chappellaz, M. Suwa, J We thank F. Vemeux and M.J. Siegert for useful M. Bamola, T. Blunier, G. Dreyfus, J. Jouzel and comments and also for providing the original F. Parrenin, "Gas age - ice age differences and the (deuterium and deuterium excess) data from the Vostok chronology of the Vostok ice core, 0 - 100 ka", J. ice core and the digitized RES record in the VFL Geophys. Res., 111 (D211115), 2006, doi: vicinity, respectively. We are grateful to K. Cuffey, 10.102912005JD006488. A.A. Ekaykin, F. Parrenin, JR. Petit for numerous [8] W.F.Budd, The dynamics of ice masses, ANARE fruitful and stimulating discussions in the course of our Scientific Reports. Ser A(lV) Glaciology. 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