J ournal rifClaciology, fiot. 43, No . 145, 1997
Snow accunlulation and ice flow at Dome du Gouter (4300 nl), Mont Blanc, French Alps
1 C. VINCENT, I M. VALLON, I J. F. PINGLOT,' M . F U NK/ L. REYNAUD ILaboraloire de Claciologie el de GeojJ/zysiqlle de l'Environnemenl dll CNRS, BP 96; 38402 Sainl -Martin -d'Heres Cedex, France 2 Versllclzsanslalt for rI asserball, Hy drologie llnd CLazio Logie, Eidgeniissische Technisc!ze Hochschule, CH-8092 Zurich, Switzerland
ABSTRACT. Glaciological exp eriments have b een carried out at D ome du GOLlter (4300 m a.s. !.), Mont Blanc, in order to understand the fl ow of Gm/ice in this high-altitude Alpine glac ierized a rea. Acc umulation measurements from stakes show a very strong spa ti a l vari ability and a n unusual feature of mass-bala nce fluctuations for the Alps, i. e. the snow accumulation d oes not show a ny seasonal patterns. IVleasured vertical velocities which should match with long-term m ean mass bala nce a re consistent with obse rved ac c umulations. Ther efore, the measurement of vertical velociti es seenl.S a good way of quickl y obtaining reliabl e mea n accumulati on values for several decades in such a region. A simple flo w model can be used to determine the m ain fl owlines of the glacier and to propose snow/ice age of core samples from th e two boreholes drilled down to the bedrock inJune 199 +. These res ults coincide with radioactivity m easurements m ade to identify the well-know n radioactive snow layers of 1963 and 1986. \Ve can hope to obtain ice samples 55- 60 years old abo ut 20 or 30 m above the bedrock (110 m dee p). Below, the deformation of the ice layers is too great to be dated accurately.
1. INTRODUCTION
Very few studies have bee n carried out on hi gh Alpi ne gla cieri zed areas (above 4000 m a.s. !.), for obvious reasons: access difficulties, cold temperatures a nd problems with a lti tude. Nowadays, these glaciers elicit an increased interest because they are seen to represent precious atmospheric archives and they seem to be suitable for elimate a nd geo chemical studies. Nevertheless, this kind of research requires knowledge of the fi rn/ice fl ow process, a nd at prese nt this is limited by lack of observation and understanding of the fol lowing unusual conditions of the very high Alpine area: The firn is ver y thick: it can reach m ore than 50 % of the total thickn ess a nd, of co urse, inl1uences the behaviour of the glacier fl ow. The glacier is cold.
Surface conditions are unknown: melting rarely occurs o 2000 4000 6000 8000 at this altitude, but \'e ry little information about accu Fig. 1. Localion of Dome dll COlllel; N[onl Blanc area. mulati on has been coll ec ted. }o r example, nothing IS know n about the seasonal pattern of mass balance. thickness data from radar measurem ents; and Glaciological ex periments h ave been performed at snow/ice age for ice core sa mples, from artificial radio Dome du Gouter, located at 4300 m a .s.1. on th e way to the acti vity methods. summit of Mont Blanc (Fig. I), in order to better understand Secti ons 8 and 9 preselll a simple fi rn/ice now model for the fl ow of firn/ice in this area. The a i m of this study is to determining the snow/ice age of core samples down to the establi sh the main fl owlincs and to compare the chronology bedrock. obtained from a fl ow model with the res ults of radioacti\'e measurements made in two deep boreholes. Secti ons 3- 7 deal with the res ults of glac iological m easurements required 2. PREVIOUS STUDIES for the interpretation of ice cores, namely, The first studies of snow a nd glac iers in the vicinity of the accumulation d ata from stakes; Dome du G OLlter summit were carried o ut by J. Vallot at vel ocity data from stake surveys; the cnd o f the 19th century (Vall ot, 1913). In 1973 and 1974,
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experiments were carried out by the Laboratoire de Glacio logie of Grenoble (Lliboutry a nd others, 1976) and showed 600 the temperature pattern in the snow from the top of Mont Bl anc dow n to Aiguille du M idi. In 1980, snow was cored .+ + 20 m deep at Col du Dom e, and the chron ology of core ••• samples was established from beta radioactivity measure .....- 400 ments, deuterium and tritium content Go uzel and others, E + Measurements () • +. 1984). In 1986, a deep ice core was drilled (70 m deep ) near dates: --..c Col du D ome fo r geochemieal purposes (D e Angelis and .... 30.07.93 0- + • Gaudichet, 1991). In 1990, a surface snow geochemical study m 12.08.93 ° was performed at Col du D om e and compared to others at o 200 ~ ~+ + 29.09.93 <> ~ 6 15.03.94 very high-altitude sites (M a upetit, 1992). These studies pro " vided some accumulati on d ata; we have used only those for it ·6 27.05.94 + « °t"+ 28.09.94 wh ich the geographic positions of the observations are well ~,~ • .,-; 24.03. 95 )( known, because of the ver y strong spati al accumulation o .. variability. 0 .2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Density 3. ACCUMULATION MEASUREMENTS Fig. 2. SUlface density measurements from plls and dri LLing Twenty-six stakes (4 or 5 m long) were set up between 6June core. 1993 and 22 June 1995 in the sn ow on Dome du G outer (sce Fig. 4a), in order to measure both snow accumulation and (2-4 m w.c. a 1). Therefore, spatial variability is ver y impor surface velocity. Abl ati on is negligible at this a ltitude, and tant; accumulation can easily be multiplied by two or three, the annual m ass balance can be assimil ated to the accumu 100 m away. Another importa nt result of these 2 years of lation. Because of large accumulati on values, the stakes observati on is that mass balance does not show any seasonal were replaced several times; m oreover, this site is difficult p attern: summer and winter accumulations are ver y similar to access without a helicopter, es peciall y during winter, (like the precipitation data for Cha monix). and a lot of stakes were lost under the snow cover. At each The obse rved accumulations have been compared with visit, a drilling core or a pit was dug (at stake 4, between the precipitati on at Chamonix for the same period (Fig. 3). Dome and the Col du D om e) in order to d etermine the Stake measurem ents fr om areas exposed to strong winds snow density near the surface (Fig. 2). For accumulati on de are not taken into account, because they are not representa termination, we suppose tha t the bottom tip of the stake is tive of local precipitation. Proportional functions between attached to the snow; therefore, the accumulation is cal each stake measurement and the Chamonix precipitation cul ated as the difference in distance between the lower tip a re determined (1.3, 1.7 or 2.3; cf. Fig. 3) in order to estimate of the stake and the surface of the snow for two dates (in missing values in Table 1 and to calculate mass balance from water equivalent). The accumulation measurements are 1Jun e to 31 M ay for 1993-94 a nd 1994-95 (Fig. 4·b a nd c). summarised inTabl e I, together with the precipitati on meas ured in C ham onix. The D ome du Gouter summit is exposed to very strong 4. VERTICAL VELOCITIES AND LONG-TERM winds, and observed accum ulation (stake 1) is very low M ASS BALANCES (about 45 cm w.e. a \ Because or strong winds in the so uth of this area (in the vicinity of the pass ), accumulati on values Vertical velocities have been determined (i'om topographic there (stakes 3 and 12) are low and erratic. In the northeast surveys (Table 2) and slope corrections. Vertical velocities part, by contrast, one can obser ve ve ry hi gh accumulati ons were calculated from ws = w - 'U t an a, where 'U and w
Tab le 1. Observed accu mulations at Dome dl{ Couter (cm w.e) and estimated annual mass balance (1 June- 31 M ay; cm water)
Observed accumu/atiolls Estimated mass balallce
Slakes 6} ull e- 29}uly 29 Se/)I. 15 March 31 May 28 Sepl. 24 March 22 } une 1993 94 1994-95 1993 1993 1994 1994 1994 1995 1995
I (Dome) 31 25 7 0 0 0 27 27 2, 14 31 17 5 30 5 0 > 40 54 45 3 25 25 5 20 4 27 32 76 63 12 II 20 3 17 3 51
4 46 60 75 25 67 > 160 49 213 266 5, 22, 23,24 52 42 71 > 140 211 245 6. 7, 8, 20, 21 40 48 65 > 160 242 269 II 30 37 50 50 134 147 183 325 10, 15, 16, 17 39 >68 120 > 150 > 150 315 392 26 (Col) 74 92 181 200 9 29 24 84 34 175 224 19 11 2 314 371 Precip. C hamoni x 21. 7 27.7 55.4 31.6 53.6 91.9 32.2 135.4 177.7
514 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Vincent and others: Sno w accumulation and iceflow at Dome du GOlller
arc thc measured horizontal and vcrtical components of thc 250 0 Stake 4 surface ve loc it y and tan Q is the surface slope (Paterson, '2 Stake 5 Q) + 1981). These \·a lucs as an independent res ult from direct ac l!. Stake 6 ~ 200 cumulation measurem cnts, expressed in m w.e., should :; • Stake 11 E • Stake 10 match the long-term average mass bala nccs if we supposc .s. 150 o Stake 9 the D ome glacier is in stcady state (Fig. 4d ). The spati a l dis c o Stake 19 • 1.3 tribution of th e vertical velocities data sccms to be in good 0 x Stake 26 x ~ 100 agrccment with observed accumulations during 1993- 94· ::l a nd 1994- 95 (Fig. 4 b a nd c). Annual m ean Chamonix pre E ::l cipitati on is 1.25 m w.c. between 1959 a nd 1995. In 1993- 94, () 50 «() we can see that Chamonix precipitation (1.36 m w.c. a I) is o very close to this mcan value, and thc D ome's accumulations a rc a lso close to the vertical \"C lo citics (except for stake 26 at o 20 40 60 80 1 00 Col du Dome and stakc 5). By thc way, although vcrtical Chamonix precipitation (cm water) vel ocities requ ire positioning measurements and slope dc tcrminati on, they seem to prm·ide the bcst way o[ easil y ob Fig. 3. Observed accumulation ( cm water) at Dome du GOlI taining reliable mean accumulation values [or scvcral ter with Chamonix precipitation (for different tim e lapse). dccades.
1 0400Or--~----~------L-----~----~--, 1 040 ~------~------~----~------, a b
1.75 10390 1039 ..
1038
1037
1036
Dome Scale (m)
o 50 100 150 20 0 1033~--'------r----~----~r-----~~ 949900 950000 950 100 950200 950300 949900 950000 950100 950200 950300
1~0~r-~----~------~----~------~-' 1040~--~----~------~----~------~-. c d
1039
1038 ~
1037
1036
1035 Coldu Cotdu Dome Dome
Scale (m) Scale (m)
o 50 100 150 200 o 50 100 150 200 1 0 33 ~---r----~------~-----r------~~ 1 033~--~----~------~-----r------r-~ 949900 950000 950 100 950200 950300 949900 950000 950100 950200 950300
Fig. 4. (a) Slnjace topography, stakes, and allnual lz orizontal velocities (m a ') in italics. ( b) Observed accumulatiol1, 1993- 94 ( Ill w.e. a j. ( c) Observed accumulatiol1, 1994 95 (m w. e. a'). ( d) JV1easured vertical velocities (m w. e. a j. 515 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. JournalofClaciology
Table 2. Horiz:.ontal and vertical velocities; stakes were MAA was 1.09 ± 0.23 m w.e. a- I (1970- 79). In the neigh observed with topographic means on 6 J une 1993, 29 Septem bourhood of Col du D ome, a M A A of 1.75 m w.e. a I for ber 1993 and 31 May 1994. (Two aT three values are some 1988- 90 was determined (Maupetit a nd others, 1995). In times given for different periods observed, ill order to show Ihe 1993, shallow ice cOl-es we re also taken for Chernobyl deter scattering of the values) minati on: at the summit of Dome d u Gouter (P20), the M AA is 0.61 m w.e. a I (1986- 93), as compared with 0.45 m w.e. a I (1993 - 95) meas ured with stakes. Stake Anl/ual horizontal ve/ocities Anl/lIal vertical velocities
III year m waler year 6.2. Effect of wind on 137 Cs r edis tribution
I 0.06, 0.2, 0.4 Strong winds scour the Dome summit and remove snow 2 1.7,2.4, 1.7 0.9, 1.0, 0.9 continuall y. The 137 Cs from Chernobyl deposits clearly con 3 3.0,2.0,3.+ 1. 1, 0.65, 1.0 firms this fact. An intermcdi ate ice core (PIS, at the saddle 4 6.2,5.7 2.3, 2.2, 3.2 Ion 6 7.0 2.7 of Col du Dome; 4250 m; December 1986) showed a . Cs 2 8 6.1 1.9 deposit of 538 Bq m (Pourchet a nd others, 1988) from 9 -l.8 1.4 C hernobyl. At the D ome summit the remaining deposit is 11 4.3, ·kO 1.8, 1.8 as low as 10 Bq m - 2, while at drill ing site 2 it is 3000 BC] m- 2 12 2.00, 1.50,2.4 0.7, 0.6,0.7 13 0.8 H owever, for d rilling site I (30 m away), the Chernobyl de 14 0.4 posit is only 25 BC] m 2, demonstrating the efTect of wind 15, 16 8.7, 8.9 3.3,3.3 scouring on short-duration events like Chernobyl. The 17. 18 4.8 3.9, 4.4 137 Cs from thermonuclear-test fall out (at ti me of deposi ti on, 19 9. 1 3.5 20 5.8 2.2 in 1963) is 3000 Bq m 2 [or both ice cores. As can be seen, the 21 7.4 2.8 137 Cs fa ll out from C hernobyl can be as la rge as from the nu 22 7.7 3.5 clear tes ts (ice co re 2). 23, 24 6.9 3.2 26 3.4 2.9 6.3. D eep ice core s
I n 1986, a deep ice core was drilled (70 m; P14) but without 5. HORIZONTAL VELOCITIES (Fig. 4a) a n accurate geographic position: its locati on is at least 100 m away fro m Col du D ome, not ve ry fa r from the 1994 deep Hori zontal vel ocities have been estimated from the positi on drilling cores. The 1963 thermonuclear-tests deposit was de of the bottom tip of these stakes, conside ring tilt a nd Ql'ien tected at 55.7 m depth. As pre\'iously determined in this 1986 tati on of the stakes (two points have been measured along ice core (Pinglot a nd Pourchet, 1995), the thermonuclear each stake at each observation ). Because of the slope and tes ts layer presents two distinct maxima, in 1962 a nd 1963 the strong creep of snow, sta kes til t with time, a nd obse rved (Table 3). In 1994, the 137 Cs radi oactive layers (1962- 63 a nd tilt can reach a deviati on of 20° from the vertical in steep 1986 (Chernobyl)) and 2lO Pb content were determined in slopes. Figure 4a shows that horizontal velocities a re more bo th dee p ice cores I a nd 2 (Table 3). As will be seen later, or less perpendicul ar to contour lines. Furthermore, the it is impossible to neglect the thinning efTect (duc to vertical observed tilts of the stakes after a few months suggest that a strain rate) and the deposit surface ori gin of deep layers. In large part of horizo ntal velocities is attributable to firn terpretati on of these ice co res' dating res ults requires fl ow deformation (about 80 m thick a t the drillhole site shown m odel computatio ns. in Figure 4a). 6.4. 210Pb profiles in deep ice cores
6. RADIOACTIVE DATING O F ICE CORES 210 Pb (a natu ral isotope with 22.3 years half-peri od fr om 38 -') U to 226R a an d 22?-R n ) was J.OI. nt Idy etermll1' e d wll. Il 1';7C S The radioactive fallout from atmospheric thermonuclear tests by gamma spectrometry (Fig. 5). Both profiles (ice cores I (Picciotto and Wilgain, 1963), conducted mainly in 1954· and 1961- 62, and from the Chernobyl accident in 1986 (Pourchet Table 3. Depths d layers resulting from atmospheric nuclear and Olh ers, 1988) provide well-known radi oactive levels in tests (1954- 55 and 1962- 63) and Chernobyl (1986) in deep glaciers, a nd enable an abso lute dating. Ice cores have bee n lce cores drilled in the Dome du Goute r a rea since 1973 (see l able 4). After density measurements, the snow samples were melted D rillil/g Drillil/g Deposition Del)th 137 Cs del)ositiolZ and fi ltered (Dclmas and Pourchet, 1977), then analyzed in site date dat e the laboratory for global-beta (Pi nglot and Pourchet, 1979) l\Jillimum Jla <;IIll/1Il J\ i/ciear tests Cltemob),1 and gamma radioactivity (Pinglot and Pourchet, 1994). m III Eqm 2 Bq III ~ 6.1. Spatial accumulation variation PI '~ 1986 1955 69.07 69.39 2014 1962 57.39 57.54 Analysis of samples from ice cores drill ed lll. 19 76, about 1963 55.67 55.83 200 m so utheast of stake 26 at Col du Dome (P 2), showed a mean annual accumulation (MAA) of about 0.34 m w.e. a- I Core I 1994 1963 85.95 87.67 3000 1986 40.09 41.02 25 (1970- 76), with a large annual variability by a factor of 2 (persona l communication fr om M. Pourchet, 1995). A 20 m Core 2 1994 1954 103.63 104.51 3005 1963 90.28 91. 16 ice core (Pll) was taken out in 1980 precisely at the saddle of 1986 38.61 39.60 3000 Col du Dome Uouzel and others, 1984), close to sta ke 26. The 516 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Vincent and others: Snow accumulation and iceflow at D ome du COllter Table M ean annual accumulation and 137 Cs fallout from 4. of' crevasses near the surface-deposit origin p oint. As much Chernobyl. (Since the drilling holes are shallow, the thinning as 28 Bq kg I o [ ~ , o Pb concentrati on was measured on an ice iffect due to vertical strain rate is neglected) core (P 7, near the summit) expose cl to in-depth crevasses.
Slake drilling Budget years Anl/uat )jJC s So"ree site accumulation deposition 7. RADAR MEASUREMENTS m w.e. Bq m 2 Radi o-echo soundings were m ade from 1 to 5 June 1993, Col rh l Dome along eight profiles. Four additional profil es were measured P2 1970- 76 0.34 M . Pourchet (persona l inJune 1994 where determinati on of the glacier bed was not communication, 1995) possible with thc measurem ents of the fi rst campaign. ' I\Te PII 1970- 79 1.09 J ouzcl and others (1984) 1'1 5 J Ull c- Dcc. 0.96 538 Po u rchet and others used rada r devices, which were built following the des igns 1986 (1988) ofJones and others (1989) a nd Wright and others (1990), i.e. Near to 1988-90 1.75 Maupetit and others with two output stages which generate inverse pulses. PI I P15 (1995) Changes were made in the layout of the free-running pulse DOllle sUln nlit generator a nd in choosing the power devices (Funk and P7 1970 76 0.33 M. Pourchet (personal others, 1995). The speed of electromagnetic wave propaga c0l11lll unication) 1'20 1986- 93 0.61 10 tion in the ice (in our case, cold ice) has been assumed to be identical to the value fo und at Colle Gnifetti (Monte D ome 1'21 1986- 93 1.62 Rosa, Valais, Switzerl and), 175 m /1S- 1 (Wagner, 1994). In the case ofD6me du G Oltter, the determinati on o[ the PlO M ont 1970-73 2.80 J o uzcl and others (1977) Bla nc summit bed topography frol11 the radio-echo tr avcl time is a problem which is much m ore delicate than [or a plane ice shield, because the glacier bed is ve ry rough in the inves ti gated area, with relati vely deep, short and na rrow valleys. and 2 in 1994) exhibit three different sta tes. From the surface The field measurements were performed in such a way as down to about 85 m, 210 Pb decreases, as expec ted. But there to obtain refl ecti ons from the glacier bed situated 111 0re or is a strong 210 Pb deposi tion increase roug h ly by a factor of 6 less in a vel-tical plane with the meas urement points at the for ice layers under 85 m , in both ice cores. glacier surf'ace, all owing the determination of the glacier These increases are definitely not due to thermonuclear bed in two dimensions. The surface of the g lacier bed was tes ts. The disturbed 210Pb signal may be due to the presence co nstructed as an envelope o f' all ell ipse functions, which give all the poss ible refl ection positions to a certain travel 137C s (mBqkg-' ) 210Pb (mBqkg") time between sending and receiving antennae. Interpreta ti on of th e data obtained was difficu lt because o[ 5 oor------n~O'1~ 5 00 137 1963 multiple refl ections from the botto m, characteristic of a rough - Cs I glac ier bed (Fabri, unpublished ). The radio-echo so und ing 400 ...... -210Pb ~ 400 profiles intersect at severa l points, all owing results to be 300 300 chec ked. The resulting bed geometry is shown in Figure 6.
200 1986 200
100 ...... - ..: ....~ !... ,.. :... ; ,.-~ .. 100 ~ .... .,;' .':. ."!...... 103 lr OL-~~~--=-~=-~~~~~~~--·· ·~;~~~~ 0 o 50 100 150 Depth (m)
IJ7C s (mBqkg" ) 210Pb (mBqkg-l)
500 ~------__. 5 0 0 137 Cs 1986 1963 400 210 400 •••• Pb ! ! 300 4174 300 mBq/kg -+
200 200
100 100
LL~~~~--~~~~~~~~~ O 50 100 15 0 103 3 0()J-9-4-9,-9-00-----9-50~1-O-O ----9-5-0,-3 0-0-'- Depth (m) Fig. 5. 137 Cs and 210 Ph activities at Col du Dome du Couter (ice COTeS 1 and 2; 1994), vs dejJth . Fig. 6. B ed tOjJograjJlryfmm radar measumnents. 517 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Journal qfClaciology
The accuracy of the calculated ice thickncss is deter
mined, in part, by the accuracy of the measurement of the 4 ~ ____~ __~ __-L __ ~ __~ ____L- __~ __-r- time delays and the antenna spacing. Additional errors may ari se due to neglect of the passage of the bottom return 3
through a firn layer. If the firn layer is 20 m thick this may 2 give rise to 3-4 m error in the depth estimate. Other errors may arise because the smooth envelope of the reflection el lipses is only a minimal profile for a narrow, deep vall ey o --~--~---,---.----.----r---,----,---1-- shape bed topography, with the result that the ellipse equa tion will be governed by an arrival from a reflector situated 0 1 00 200 300 400 toward the side, and thus not directly beneath the point of Distance from the Dome Cm) observation. One can easily imagine a glacier bed geometry 430 for which no density of observation will yield the correct depth near the centre of a valley-shape bed topography. 425 Further errors may be introduced by assuming that all re I ID f1 ection points li e in the plane of the profile rather than an u 420 ~ ellipsoid. These errors may be important in our case, 8. FLOW MODEL AND AGE OF ICE AS FUNCTION zontal velocity is equal to 80% of the surface horizontal OF DEPTH velocity. The vertical velocity w(x, z) is calculated using mass continuity for the local element: Artificial radioactivity measurements allow us to identify OU ow with confidence the 1986 and 1963 snow layers. Nevertheless, ~+~=O. uX u z it is difficult to determine the age of the lower part of the core a nd to estimate the thickness of annual layers. For this This gives (Ritz, 1987): purpose and for the determi nation of the mean thickness of each annual layer down to the bedrock, a flow model can w[x, H(x)] = b(x) 1 - H(x)I J H4'5 [1 H (x)4z4 ] dz } provide useful information about the age of the firn/ice of { the lower part of the ice core. Gagliardini (1995) developed +u(x,z)_z_oH(x) _ oE(x) a two-dimensional flow model based on mechanical con H ( x ) OJ; ox cepts. H ere, a simple two-dimensional fl ow model was de veloped assuming that the glacier thickness has not where the last term, from u(x, z) to the end of the equation, changed significantly since the beginning of the 20th cen is called kinematic vertical velocity, b(x) is mass balance tury. This assumption is supported by the dynamic beha (m water a I), z is depth (m ), H(x) is thickness (m ), u(x, z) viour of the glacier (vertical velocity measurements) which is horizontal velocity, oH(x) / ox is thickness variation, has been shown to be elose to steady state. In the model, the oE(x)/ox is altitude surface variation, and w[x, H(x)] = mass conservation is considered, in order to obtain the b( x) at surface and 0 at bed rock. balance horizontal velocity. The mass continuity equation Horizontal and vertical velocities expressed in 111 water is solved: a- I are then converted by the following relations: 'Uw ww o[umH(x)] = b(x) _ o[H(x)] U s = -- , W s = - ox ot p p where H (x) is thickness, b(x) is mass balance (m water a \ where 'Uw is horizontal velocity in 111 water a- I, U s is horizon x is distance from the D ome (m ), Urn is mean velocity, and tal velocity in m snow or ice a I, Ww is vertical velocity in o[H(x)]jot is the thickness variation with time assumed to III water a- I, Ws is verlical vclocit y in III snow or ice a I, and be O. ~ From this equation, the mean balance velocity can be .@ 15 ---I1--~--L--'---' __L--L~ __L-L-~--L---l __J....--+- computed for each section. The depth profile of horizontal ";., velocity is derived from the analytical model given by Lliboutry (1981): U(z, H) = ~:~ Um [1 - (~r+l] where u(z, H) is the horizontal velocity at depth z, H is the glacier thickness and n is the Glen flow-law exponent o 50 100 1 50 200 250 300 350 400 (n = 3). The ice temperature is - 11 QC near the bedrock Distance from the Dome Cm) (personal communication from C. Rado, 1995) and the slid Fig. 8. Surface horizontal velocities from /he model results ing velocity is assumed to be O. As a result, the mean hori- (divelgence qfO% and 25%) and measurements. 518 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Vincenl and olhers: Sn ow accu lll ulation (l nd i[eflow at Dome du Gouler 120 140 100 120 100 80 Ii) ~ ~ '" 80 Q) .,a ~ 60 -b Q) Q) «Cl «bJl 60 40 40 /. / 1963 20 20 o 20 40 60 80 1 00 1 20 140 o 20 40 60 80 100 120 140 Depth (m) Depth Cm) Fig. 9. Snow age vs deJlthJi'olll model results and radioactivity Fig. 11. Snow age vs depthfom model results alld radioactil' itv measurements (1986 and 1963). Sen silivil)' to thickness varia measurem ents (1986 and 1963). Sensitivil)' 10 di vergence lion ( ±10 m). (50 % and 25% ). b een studied for som e pa rameters. Fig ure 9 shows the sensi ti vit y to thickness \'a ria ti on; a va ri ation ofbcdrock ele\'atio n 100 ( ± 10 m ), applied o n the profile from the Dome to the dril ling core, in\'oh es a n uncerta inty of ±6years a t II0m 80 depth. Figure 10 shows the sensiti\'iL Y to the m ass-ba lance ~ \'a riation; for this purpose, the standa rd cb 'iati on (20 cm '"til Q) w. e.) of the Cha m o ni x precipitatio n is multiplied by 3 to -b 60 (a = Q) obta in a n estima ti on of the standa rd de\'iati on 60 cm «bIl w.e.) of the m ass bala nce at D om e du G Otlter (according to 40 the res ults of accull1ul ati on measurem ents)" Therdo re, un certainiies equa l to 3a/ jii, \,"here n is the number of years from now, were introduced in the m od el, a nd the age o f the ice core has been o bta ined from these calculati ons (Fig. 10). Sensitivit y lo the horizonta l divergence of the flO\.dines is shown in Fig ure 11. A di vergence \'alue of 50% (dis ch a rge/2) gi,"es results simila r to the res ults without diver o 20 40 60 80 1 00 120 140 gence. That m eans that the model is not very sensitive to Depth (m) horizontal \'elocity m odifications. On the oLh er hand, Fig Fig. 10. SI10 W age vs deplhfolll lII odel results and mdio(lctiu UITS 12- 14 confirm the se nsiti\'it y o f the model to the vertical i£v lII eaSUrell1ents (1986 and 1963). SfIIsi l i v i ~v 10 mass balance varialion ( ±3 standa rd de vialion ). 120 p is local d ensity. Dcnsity m easured in the boreholc is assumcdto be fcprescntati" e fo r tht' wholt' fim. Such a m odel does not ta ke into account the m ass 100 ba la nce cha nge with time; it considers the m ean mass ba la nce obta ined from \'ertica l \'elocitics (Fig. 4d ). 80 (j) This m odel ta kes into account hori zonta l fl owline dive r (;j Q) gencc by correcti ons on flu x a long the m ain fl owline. Never ob 60 theless, measured horizonta l velocity directio ns a rc almost Q) Ol pa ra ll el (Fig. 4a) and horizonta l fl owline divergence is « 40 neglected a t first. Fina ll y, calculated \'C locity \'ectors all ow us to d etermine fl owlines (Fig. 7) a nd the ice age from D ome du G OLIler to 20 the drill site. H o ri zontal velocity va llles a re shown in Figure 8 a nd ha\'C been compared with surface measurem ents. o 20 40 60 80 1 00 120 1 40 Depth (m) 9. RESULTS OF FLOW MODEL Fig. 12. Sno w age vs dePlhjro/ll mo del results. Sensitivil)' to The se nsitivity of the ice age proposed for Ice core 2 has the dep th of drilLing hole ( ±10 m). 519 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Journal qfGlaciolog;y velocity pattern. First, the se nsitivity of the model was 120 studied according to glacier thickness at the si le o[ the dril ling core (Fig. 12). Since the model forces the bottom fl ow 100 lines to foll ow the bedrock whatever the profile of the bedrock, the thickness at the drilling site directly influences the vertical velocity at this sit e. This effect shows the limits 80 of such models. ~ The glaciological surveys carried out on Dome du Gother 7 \ show a n important spatial distribution of the accumulati on: \ \ the mean accumulation varies from 0.3 m w. e. a- I at the top \ 6 \ \ of the Dome to 3.0 m w.e. a- I in the vicinity o[ the drilling \ m snow/ice cores. In addition, an unusual feature of mass-balance fluc \ .... 5 \ \ tuations in the Alps h as been pointed out: the snow accumu " \ 3 \ V> lation in this high-altitude Alpine glacierized area does not V> \ 4 \ ..Q" \ , show any seasonal pattern; summer and winter mass bal <.) , :s , , ances are very sim.ilar, which has not often been observed 3 ---4... ;;l ,-- mass balance (m w.e.) in the Alps. Furthermore, the observed spatial distribution " ",- -...... ~t :r1gm pomt ~ m w.c. " of the accumulation seem s to be very similar to the vertical 2 "- \. velocities obtained from topographic measurements of the \. \ stakes. These values, as a n independent result (i-o m di re et accumulation measurements, match the long-term average mass balances for steadY-Slate conditions. There[ore, the measurement or vertical velocities is a good way o[ quickly o 20 40 60 80 100 120 140 obtaining the reliable mean accumulation values [or several Depth (m) decades in such a region. Fig. 15. AnnuaL thickness /a)l er vs depthJrom the model results The fl ow model described in this paper provides useful in the driLLlwle, and mass balance at the origin poinl qf the information about the urn/ice cores made down to the bed La)ler. rock. It can be shown that, with a simple fl ow model and 520 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use. Vincenl and others: Snow accllmulalion and i[e.flow at Dome dl! COLlier somc precautions (for example, taking into account the j ouzcl, J., I\/. R . Legrand,J. F. Pi nglot. i\1. Pourchet and L. Reyna ud. 198+. kinematic vertical ve locity conn ected with the bedrock Chronologic cl 'u n earollagc de 20 m au Col du Domc ( i\ lassif"du i\Iol11- Blancl. HOllilie 13lollrile, 1984 (G-7), +9 1 497. shape), a reliabl e age/depth relati on can be obtained, a Llibout ry, L. 198 1. i\ critical rC\'iew o f a na lytical ap proxima tc soluti ons for res ult which is supported by radi oacti\'ity measurements stead\' stale \"c1 ocitics and temperatures in cold ice-sheets. ~ (;/et.frhrrkd. (1963 and 1986 events). Gla<.i;tLgeol .. 15 (2), 1979, 135- 1+8. Llibout rv, L. . M. Briat, )\/. Crescvcu r a nd i\I. Pourchet. 1976. IS m deep te mp ~rat u res in thc glaciers of" i\lo nt Bla nc (French Alps). ]. G/aciol., ACKNOWLEDGEMENTS 16 7+), 197 203. ?ll allpetil. F. 1992. C himie de la ncigc de tres haUle altit ud e d a ns les Alpes This study was supported by the Region Rhone-Alpes and rrlllll;aises. tT'hest' ut' doctorat, C ni,"e rs it e Paris \ '11 and Laboratoire de the Ministcre de l'Envi ra n nement, France. Glaciologie et de Gcophys iq ue de I" E Il\'iron ncmclll , G reno bl c. \ i\ i;, upctit, F.. D. 'I'agcnbach, p., I'ecid cking a nd R . .J. Dc/mas. 1995. Seasonal \Ve wo uld like to th ank our co ll eagues who took part in f1 uxes ol' m aj or ions to a high a ltitude cold a lpine g la cier. AlmoJ. Du·irau .. fi eldwork, and especially those \\'h o made m easurements by 291 1, I 9. going on foot: 1. Seljha l, E. LemeLlr, M . T. Vince nt, O. PatCfson, \I'. S. B. 198 1. TI,,' pl!)"JI"rs ifglarifl"s. Snollri eriilioll. O x fo rd, ctr., PlT Gagli ardini and P Mansuy. ga mOll Press. Picc iotto. E. a nd S. 'Vilgain. 1963. Fissio n p roducts in Alllarnic snow, a refiT cnce level fo r m easu ri ng accumulati on.]' Cco})I!J's. Res., 68 (21), .')96:; ~972. REFERENCES Pi nglot, j. 10. and i\ /. Pourchel. 1979. L ow-level bcta counting w it h an auto mati c samplc changcr. "1;1d. IlIslrum . .lIelhods, 166 (3), +83- -+90. Pinl( lot, .J. F. and ?ll. Pourchet. 199-'- SpectromCt rie gamllla it trios bas De Ang·e li s. i\l. and A. Gaudichel. 199 1. Sa haran dust de pos ition O\'er ;, i\"Ca u 'l\"CC a Illi-Com pton :\'"al (TI), pour l'etude des g laciers e t dcs sed i i\Io lll-Bla nc (French Al ps \ dur ing the last 30 years. Yellw, 43B, 61 75. ments. CEe\ . l ale 2756, 29 1- 296. (journccs de Spectrom ct r ie Gamma Cl Dcl m as, R. a nd i\I. Pourc hcl. 1977. Utilisation de filtres cchangeurs d'ions X 93, C EA-DAM.RI, 12-1+ O ctober 1 99:~. Pari s. France.) po ur rc, tude de l"aCl i\'itc;3 g lo ba le d'un carottage g laciologiquc. IlIlmlfi Pinglot, j. F. a nd ?I r. Pourchel. 1995. R adioacti\'ity mcasuremellls a p plied liollal ./ssorialioll if H)"Ilrological Sriellces Publiralioll 11 8 (Symposium a t to glaciers a nd la ke sedimcnts. Sei. Tolal EII1'il"OlI ., 173-174. 21/ 221 . G rcll ohle 1975 IsolojJes alld !/lijJlIrilies ill Suow alld Ire), 159 163. Pflu rchct, ]\I. , J. F Ping lOl, L. Rcyna ud a nd G. Hold s,,·orth. 1988. fdcnrdi Fabri\ K. -U np ublished. Eisd ic ke nnlC'sslI ngf' 1l im A a rcgktschergebi et. eine cati on ofChe rl1!)byl f;tll-ul1 t as a new reference IC\TI in Northe rn Hcmi . \nwend u ng \'on R adio-Echo -Sounding. Zurich, ETH, Pra kti kumsar sphere glaciers.]. (;Iario!., 34 (117). 183- 187. beit an d("J" VA'I' ulller !\nl eitung \'0 11 i\l. Funk und G. i\ leyer. Ritz. C. 1987. Ti me d c pendeIll bound ary conditions for ealculario n of"telll Fun k. i\l.. G. H. Gudmundsson a nd f l-jermann. 199.1. G com cl ry of" the g la pcrat urc fi eld s in ice sheets. IlIlemoliollal .-/ssorialioll of 1-I)"drologiml,S"'ieIlCfJ cier bed o f' the Cllleraa rg lacier. Bernese A lps, S,,·itzcrl a nd . .c P"biiralioll 170 (Symposium at Va ncouvcr 1987 The PI!l'siral 13asisiflte Glelsrilerkd. Gla::.ialgeol .. 30. 1994, 187 19+. Sheel .linddlillg ), :207 :216. Gao' li ardini, O . 1995. COlllribulioll (I la sill/lIlaliou rie Ierolllell1l'11 I rill DOllle riu GUI' \ 'a ll ot, J. 19 13. Va !eur ct \'ariarioll de la tem p(T"ture profande d u g lacier, au ~er (.\lasslfrill .l/olll -Blallr). G renoblc. Cni \"Crs itcj oscph Fouri er. Labora l\Iont- Blanc. c: R. HeM SeauCfs Amd. Sei. Parisl, 156 120 ), 157.1 - 1578. laire d e G lacinlngie et dc Gi'ophys ique de I'EIl\·iro nncm cnl. li-liCm o ire "'agner. S. 199+. Drec/ im cnsionaic lIIod cllier ung zweir G lctscher und Dcfor de 0.£..\ .) matia",,,nalys," \'on cisrcichem Pcrm a fi·osl. (Ph.D. thesis, ETH, ZUrich. .lones, F. 1-1 . i\/.. B. B. Narod a nd G . K. C. C larke. 1989. D esig n a nd opera Dissertation 10659.1 ti on ofa po rtable. d igit a l i1ll p ulse racla r. ]. C;lario!', 35 (1 191, lel:l- Iel-8. \I'right, D. I,., S. i\ 1. Hodge. .J. ,\. Bradlcy. T. P. CrO\"tJ" and R . \\'. j ambe!. J ouzcl. J.. L. i\fe rl i\'at a nd :\1. Pou T" che l. 1977. Deuterium, tritium, and {3ae 1990. A d ig itallow-f"reql1cncy, surface-profili ng ice-radar system . .J (;111 - ti \· itv in a snow corc ra ken Oil til e sum mil of ;\I Olll Bl a nc (H"Cnc h .\ Ips ). rio!. .36 1221, 11 :2 1:2 1. Det,:nninatio n of the accumulatioll rate.]' CIf/rio!.. 18 801. +65- .[70. M S received 7 Febr l1 01~V 1.9.97 alld accejJted III rel"ised/o/"III 28 AfJril 19.97 52 1 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 06:43:33, subject to the Cambridge Core terms of use.