J ournal rifClaciology, fiot. 43, No. 145, 1997

Snow accunlulation and ice flow at Dome du Gouter (4300 nl), Mont Blanc, French Alps

C. VINCENT, I M. VALLON, I J. F. PINGLOT,' M . F UNK/ L. REYNAUD1

ILaboraloire de Claciologie el de GeojJ/zysiqlle de l'Environnemenl dll CNRS, BP 96; 38402 Sainl -Martin-d'Heres Cedex, France 2 Versllclzsanslalt for r I asserball, Hy drologie llnd CLazioLogie, 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. Accumulation measurements from stakes show a very strong spa­ti a l va ri ability and a n unusual feature of mass-bala nce fluctuations for the Alps, i. e. the snow acc umula tion d oes not show a ny seasona l p a tterns. IVleasured verti cal velocities which should match with long-term m ean mass bala nce a re consistent with observed ac­c umulations. Ther efore, the measurement of vertical ve loc iti es seenl.S a good way of quickl y obtaining reliabl e mea n acc umulation values for seve ral decades in such a region.

A simple flow model can be used to determine the m a in fl owlines o f the glacier and to propose snow/ice age of co re sampl es from the two boreholes drill ed down to the bedrock inJune 199+. These results coincide with radioactivity m easurements m ade to identify the well-known radioac tive snow laye rs of 1963 and 1986. \Ve can hope to obtain ice samples 55- 60 yea rs old abo ut 20 or 30 m ab ove the bedrock (110 m deep). Below, the deformation of the ice layers is too g reat to be dated acc urately.

1. INTRODUCTION

Very few studies have been carri ed out on high Alpi ne gla­cieri zed areas (above 4000 m a.s. !.), for obvious reasons: access difficulti es, cold temperat ures a nd problems with a lti­tude. 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 geo­chemical studi es. Nevertheless, thi s kind of research requires knowledge of the fi rn/ice fl ow process, a nd at present this is limi ted by lack of observation and understanding of the fol­lowing unusua l conditions of the ve ry high Alpine a rea:

The firn is ver y thick: it can reach m ore than 50 % of the tota l thickness a nd , of course, inl1uences the behaviour of the glacier fl ow.

The glacier is cold.

Surface conditions a re unknown: melting rarely occ urs a t this a ltitude, but \'ery little information about acc u­mulation has been coll ec ted. }o r example, nothing IS

know n about the seasonal patte rn of mass balance.

o 2000 4000 6000 8000

Fig. 1. Localion of Dome dll COlllel; N[onl Blanc area.

thickness data from rada r measurem ents; and

Glaciologica l ex periments h ave been performed at D ome du Gou ter, located at 4300 m a .s.1. on the way to the summit of Mont Blanc (Fig. I), in order to better unde rstand the fl ow of firn /ice in this a rea . The a i m of thi s stud y is to establi sh the main fl owlincs and to compare the chronology obtained from a fl ow model with the results of radi oacti\'e measurements made in two deep boreholes. Sections 3- 7 deal with the res ults of glac iological m easurements required fo r the interpreta tion of ice cores, namely,

snow/ice age for ice core samples, from a rtificial radio­ac ti v ity methods.

acc umulation d a ta from stakes;

veloc ity data from stake surveys;

Sections 8 and 9 prese lll a simple fi rn /ice now model for determining the snow/ice age of core samples down to th e bedrock.

2. PREVIOUS STUDIES

The first studi es of snow a nd glac iers in the vicinity of the Dome du G OLlter summit were carri ed o ut by J. Vallot a t the cnd o f the 19th century (Vallot, 1913). In 1973 and 1974,

513

J ournal rifClaciology

experiments were ca rried out by the Laboratoire de Glacio­logie of Grenoble (Lliboutry a nd others, 1976) and showed the temperature pattern in th e snow from the top of Mont Blanc dow n to Aiguille du M idi . In 1980, snow was cored 20 m deep at Col du D om e, and the chron ology of core samples was established from b eta radioactivity measure­ments, deuterium and tritium content Go uzel and others, 1984). In 1986, a deep ice core was drill ed (70 m deep ) near Col du D ome fo r geochemieal purposes (D e Angelis and Gaudichet, 1991). In 1990, a surface snow geoch emical study was performed at Col du D om e and compared to others at very high-a ltitude sites (M a upetit, 1992). These stud ies pro­vided some accumulation d a ta; we have used only those for wh ich the geographic positi on s of the observations are well known, because of the ver y strong spati a l accumu lation variability.

3. ACCUMULATION MEASUREMENTS

Twenty-six stakes (4 or 5 m long) were set up between 6June 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 surface velocity. Ablati on is n egligible at thi s a ltitude, and the annua l m ass balance can be assimil ated to the accumu­lation. Because of large accumulation values, the stakes were replaced several times; m oreover, thi s site is difficult to access without a helicopter, especially during winter, and a lot of stakes were lost under the snow cover. At each visit, a drilling core or a pit was dug (at stake 4, b etween the Dome and the Col du D om e) in order to d etermine the snow density near the surface (Fig. 2). For accumul ati on de­termination, we suppose tha t the bottom tip of the stake is attached to the snow; therefore, the acc umula tion is cal­cul ated as the difference in distance between the lower tip of the stake and the surface of the snow fo r two dates (in water equivalent ). The accumulation measurements are summari sed inTable I, together with the prec ipitati on meas­ured in C ham onix.

The D ome du Gouter summi t is exposed to very strong winds, and observed acc um ulation (stake 1) is very low (about 45 cm w.e. a \ Because or strong winds in the south of this area (in the vicini ty of the pass ), accumulation values there (stakes 3 and 12) are low and erratic. In the northeast part, by contrast, one can obser ve very high accumul ati ons

.....-E () --..c .... 0-m o

600

400

200

o

.+ + • ••

• + Measurements +. dates:

+ 30.07.93 • ~ ~+ +

12.08.93 ° 29.09.93 <> ~ 6 15.03.94 " it ·6 27.05.94 +

« °t"+ 28.09.94 • ~,~ .,-; .. 24.03. 95 )(

0 .2 0.3 0.4 0.5 0 .6 0.7 0.8 0.9 Density

Fig. 2. SUlface density measurements from plls and driLLing core.

(2-4 m w.c. a 1). Therefore, spa tial variability is ver y impor­tant; accumulation can easily b e mu ltiplied by two or three, 100 m away. Another importa nt result of these 2 years of observation is that mass balance does not show a ny seasonal p attern: summer and winter accumulations are ver y similar (like the precipita tion data for Cha monix).

The observed accumu lations have been compared with precipitati on a t Chamonix for the same period (Fig. 3). Stake measurem ents from areas ex posed to strong winds a re not taken into acco unt, becau se they are not representa­tive of local precipitation. Proportional functions between each stake measurement and the Chamonix precipitation a re determined (1.3, 1.7 or 2.3; cf. Fig. 3) in order to estimate missing values in Table 1 and to calcu late mass balance from 1 June to 31 M ay for 1993-94 a nd 1994-95 (Fig. 4·b a nd c).

4. VERTICAL VELOCITIES AND LONG-TERM M ASS BALANCES

Vertical velocities have been determined (i'om topographic surveys (Table 2) and slope corrections. Vertical velocities were calculated from ws = w - 'U t an a, where 'U and w

Table 1. Observed accumulations 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} ulle- 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 I I 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 hamonix 21.7 27.7 55.4 31.6 53.6 91.9 32.2 135.4 177.7

514

250

'2 Q)

~ 200 :; E .s. 150 c 0

~ 100 ::l E ::l 50 () ()

« o

0 Stake 4 + Stake 5 l!. Stake 6

• Stake 11 • Stake 10 o Stake 9 o Stake 19 • 1.3 x Stake 26 x

o 20 40 60 80 1 00 Chamonix precipitation (cm water)

Fig. 3. Observed accumulation ( cm water) at Dome du GOlI­ter with Chamonix precipitation (for different time lapse).

1 0400Or--~----~------L-----~----~--,

a

10390

949900 950000 950 100 950200 950300

1~0~r-~----~------~----~------~-'

Scale (m)

Cotdu Dome

c

o 50 100 150 200 1 033~---r----~------~-----r------~~

949900 950000 950 100 950200 950300

Vincent and others: Snow accumulation and iceflow at Dome du GOlller

a rc thc measured horizonta l and vcrtical components of thc surface veloc it y and tan Q is the surface slope (Paterson, 1981). These \·a lucs as an independent result from direct ac­cumulation measurem cnts, expressed in m w.e., should ma tch the long-term average mass bala nccs if we supposc the D ome glacier is in stcady state (Fig. 4d ). The spati a l di s­tribution of the vertica l velocities data sccms to be in good agrccment with observed acc umulations during 1993- 94· a nd 1994- 95 (Fig. 4 b a nd c). Annual m ean Chamonix pre­cipita tion is 1.25 m w.c. between 1959 a nd 1995. In 1993- 94, we can see that Chamonix precipitation (1.36 m w.c. a I) is very close to this mcan value, and thc D ome's accumula tions a rc a lso close to the vertical \"C locitics (except for stake 26 a t Col du Dome and stakc 5). By thc way, although vcrtica l vel ocities requ ire positioning measurements and slope dc­tcrmination, they seem to prm·ide the bcst way o[ easily ob­ta ining reliable mean acc umulation va lues [or scvcra l dccades.

1 040~--------~------~----~---------,

1039

1038

1037

1036

Scale (m)

1.75 ..

o 50 100 150 200

b

Dome

1033~--'------r----~----~r-----~~ 949900 950000 950100 950200 950300

1040~--~----~------~----~------~-.

~ 1039

1038

1037

1036

1035

Scale (m)

d

Coldu Dome

o 50 100 150 200 1 033~--~----~------~-----r------r-~

949900 950000 950100 950200 950300

Fig. 4. (a) Slnjace topography, stakes, and allnual lzorizontal 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

JournalofClaciology

Table 2. Horiz:.ontal and vertical velocities; stakes were observed with topographic means on 6 J une 1993, 29 Septem­ber 1993 and 31 May 1994. (Two aT three values are some­times given for different periods observed, ill order to show Ihe scattering of the values)

Stake

I 2 3 4 6 8 9 11 12 13 14 15, 16 17. 18 19 20 21 22 23, 24 26

Anl/ual horizontal ve/ocities

III year

1.7,2.4, 1.7 3.0,2.0,3.+ 6.2,5.7 7.0 6.1 -l.8

4.3, ·kO 2.00, 1.50,2.4

8.7, 8.9 4.8 9.1 5.8 7.4 7.7 6.9 3.4

Anl/lIal vertical velocities

m wa ler year

0.06, 0.2, 0.4 0.9, 1.0, 0.9 1.1, 0.65, 1.0 2.3, 2.2, 3.2 2.7 1.9 1.4 1.8, 1.8 0.7, 0.6,0.7 0.8 0.4 3.3,3.3 3.9, 4.4 3.5 2.2 2.8 3.5 3.2 2.9

5. HORIZONTAL VELOCITIES (Fig. 4a)

Hori zontal velocities have been estimated from the position of the bottom tip of these stakes, considering tilt a nd Ql'ien­tation of th e stakes (two points have been measured a long each stake at each observation ). Because of the slope and the strong creep of snow, sta kes til t with time, a nd observed tilt can reach a deviation of 20° from the vertical in steep slopes. Figure 4a shows that hori zontal velocities a re more or less perpendicul ar to contour lines. Furthermore, the observed tilts of the stakes after a few months suggest that a large part of horizontal velocities is attributable to firn deformation (about 80 m thick a t the drillhole site shown in Figure 4a ).

6. RADIOACTIVE DATING O F ICE CORES

The radioactive fallout from atmospheric thermonuclear tests (Picciotto and Wilgain, 1963), conducted main ly in 1954· and 1961- 62, and from the Chernobyl accident in 1986 (Pourchet and Olhers, 1988) provide well-k nown radioactive levels in glaciers, a nd enable an abso lute dating. Ice cores have been drilled in the Dome du Goute r a rea since 1973 (see l able 4). After density measurements, the snow samples were melted and fi ltered (Dclmas and Pourchet, 1977), then analyzed in the laboratory for global-beta (Pi nglot and Pourchet, 1979) and gamma radioactivity (Pinglo t and Pourchet, 1994).

6.1. Spatial accumulation variation

Analysis of samples from ice cores drill ed lll. 1976, about 200 m southeast of stake 26 at Col du Dome (P 2), showed a mean annual accumulation (MAA) of about 0.34 m w.e. a- I (1970- 76), with a large annual variability by a factor of 2 (persona l communication from M. Pourchet, 1995). A 20 m ice core (Pll) was taken out in 1980 precisely a t the sadd le of Col du Dome Uouzel and others, 1984), close to sta ke 26. The

516

MAA was 1.09 ± 0.23 m w.e. a- I (1970- 79). In the neigh­bou rhood of Col du D ome, a M A A of 1.75 m w.e. a I for 1988- 90 was de termined (Maupetit a nd others, 1995). In 1993, shallow ice cOl-es were also taken for Chernobyl deter­mination: at the summi t of Dom e 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) measured with stakes.

6.2. Effect of wind on 137 Cs r edis tribution

Strong winds scour the Dome summit and remove snow continually. Th e 137 Cs from Chernobyl deposits clear ly con­firms this fact. An intermcdiate ice co re (PIS, at the saddle

Ion of Col du Dome; 4250 m; December 1986) showed a . Cs

2 deposit of 538 Bq m (Pourchet a nd others, 1988) from C hernobyl. At the D ome summit the remaining depos it is as low as 10 Bq m - 2, whi le at dri ll ing site 2 it is 3000 BC] m- 2

H owever, for d rilling site I (30 m away), the Chernobyl de­posit is only 25 BC] m 2, demonstra ting the efTect of wind sco uring on shor t-duration events like Chernobyl. The 137 Cs from thermonuclear-test fa llou t (a t ti me of depos i ti on, in 1963) is 3000 Bq m 2 [or both ice cores. As can be seen, the 137 Cs fa llout from C hernobyl can be as la rge as from the nu­clear tests (ice co re 2).

6.3. D eep ice core s

I n 1986, a deep ice co re was dri lled (70 m; P14) but without a n acc urate geogr aphic position: its location is at least 100 m away from Col du D ome, not very fa r from the 1994 deep drill ing cores. The 1963 thermonuclear-tests deposit was de­tected at 55.7 m depth . As pre\'iously de termined in thi s 1986 ice core (Pinglot a nd Pourchet, 1995), the thermon uc lear­tes ts layer presents two distinct maxima, in 1962 a nd 1963 (Table 3). In 1994, the 137 Cs radioactive layers (1962- 63 a nd 1986 (Chernobyl)) and 2lOPb content were determined in bo th deep ice cores I a nd 2 (Table 3). As will be seen la ter, it is impossible to neglect the thinning efTect (duc to vertical stra in rate) and the deposit surface origin of deep layers. In­terpretati on of these ice co res' dating res ults requires fl ow­m odel computa tio ns.

6.4. 210Pb profiles in deep ice cores

210 Pb (a natu ra l iso tope with 22.3 years half-period from ')38U 226R d 22?R ) . . Id ' d . I 1';7C - to a an - n was JOI nt y e termll1e wll l ' S

by gamma spectrometry (Fig. 5). Both profi les (ice cores I

Table 3. Depths d layers resulting from atmospheric nuclear tests (1954- 55 and 1962- 63) and Chernobyl (1986) in deep lce cores

D rillil/g Drillil/g Deposition Del)th 137 Cs del)ositiolZ site date date

l\Jillimum Jla <;IIll/1Il J\ i/ciear tests Cltemob),1

m III Eqm 2 Bq III ~

PI '~ 1986 1955 69.07 69.39 2014 1962 57.39 57.54 1963 55.67 55.83

Core I 1994 1963 85.95 87.67 3000 1986 40.09 41.02 25

Core 2 1994 1954 103.63 104.51 3005 1963 90.28 91. 16 1986 38.61 39.60 3000

137 Table 4. Mean annual accumulation and Cs fallout from Chernobyl. (Since the drilling holes are shallow, the thinning iffect due to vertical strain rate is neglected)

Slake drilling Budget years Anl/uat )jJ Cs So"ree site accumulation deposition

m w.e. Bq m 2

Col rh l Dome P2 1970- 76 0.34

PII 1970- 79 1.09

M . Pourchet (persona l comm unicat ion, 1995) J ouzcl and others (1984)

1'15 J Ullc- Dcc. 1986

0.96 538 Po u rchet and others (1988)

Nea r to PI I P15

DOllle sUln nlit

P7

1'20

D ome 1'21

PlO M ont Bla nc summit

1988-90 1.75

1970 76 0.33

1986- 93 0.61

1986- 93 1.62

1970-73 2.80

10

Maupetit and others (1995)

M. Pourchet (personal c0l11lll unication )

J o uzcl and others (1977)

and 2 in 1994) exh ibit three different sta tes. From the surface down to about 85 m, 210Pb decreases, as exp ec ted. But there is a strong 210Pb deposi tion increase roug h ly by a factor of 6 for ice laye rs under 85 m , in both ice co res.

These increases a re definitely not due to thermonuclear tes ts. The disturbed 210Pb signal may be due to the presence

137C s (mBqkg-' ) 210Pb (mBqkg")

5oor------------------------n~O'1~ 500 137 1963

- Cs I 210 ~ 400 .. .... - Pb 400

300 300

200 1986 200

.. : .... ~ ! ... , .. : ... ; ,.-~ .. ~ .... .,;' .': .. "!. ....... .

lr 100 ...... - 100

OL-~~~--=-~=-~~~~~~~--·· ·~;~~~~ 0

500

400

300

200

100

o 50 100 150 Depth (m)

IJ7C s (mBqkg" ) 210Pb (mBqkg-l)

~------------------------__. 5 00 137

Cs 1986

210 •••• Pb !

1963

! 400

4174 mBq/kg

-+ 300

200

100

LL~~~~--~~~~~~~~~ O

50 100 150 Depth (m)

Fig. 5. 137 Cs and 210 Ph activities at Col du Dome du Couter

(ice COTeS 1 and 2; 1994), vs dejJth.

Vincent and others: Snow accumulation and iceflow at D ome du COllter

of' crevasses near the surface-deposit origin p oint. As much as 28 Bq kg I o[ ~ , oPb concentration was measured on an ice core (P 7, near the summit ) exp osecl to in-depth crevasses.

7. RADAR MEASUREMENTS

Radio-echo soundings were m ade from 1 to 5 June 1993, along eight profiles. Four additional profil es were measured inJune 1994 where determination of the glac ie r bed was not possible with thc measurem ents of the fi rs t campaign. ' I\Te used rada r devices, which were built following the designs ofJones and others (1989) a nd Wright and o thers (1990), i.e. with two output stages which generate inverse pulses. Changes were made in the layo ut of the free-running pu lse generato r a nd in choosing the power devices (Funk and others, 1995). The speed of electromagnetic wave propaga­tion in the ice (in our case, cold ice) has been assumed to

be identical to the value fo und at Colle Gnifetti (Monte Rosa, Va la is, Switzerl and ), 175 m /1S- 1 (Wagner, 1994).

In the case ofD6me du G Oltter, the determina tion o[ the bed topography frol11 the radio-echo tr avcl time is a problem which is much m ore delicate than [o r a plane ice shield, because the glacier bed is very rough in the investi­gated a rea, with relatively deep, short and na rrow valleys. The field measurements were performed in such a way as to obtain re fl ec tions from the glacier bed situ ated 111 0re or less in a ve l-tical plane with the measurement p oints at the glacier surf'ace, allowing the determination of the glacier bed in two dimensions. The surface of the g lacier bed was constructed as an envelop e o f' a ll ell ipse functions, which give all th e p oss ible refl ection positions to a certain travel time between sending and receiving antennae.

Interpre ta ti on of the data obta ined was difficu lt because o[ multiple refl ections from the bo ttom, characteristic of a rough glacier bed (Fabri, unpublished ). The radio-echo sound ing profiles intersect at severa l points, allowing results to be checked. The resulting bed geometry is shown in Figure 6.

103

10330()J-9-4-9,-9-00-----9-50~1-O-O----9-5-0,-30-0-'-

Fig. 6. B ed tOjJograjJlryfmm radar measumnents.

517

Journal qfClaciology

The accuracy of the calculated ice thickncss is deter­mined , in part, by the accu racy of the measurement of the time delays and the antenna spacing. Additional errors may a ri se due to neglect of the passage of the bottom return through a firn layer. If the firn layer is 20 m thick this may give rise to 3-4 m error in the depth estim ate. Other errors may arise because the smooth envelope of the reflection el­lipses is only a minimal profile for a narrow, deep valley­shape bed topography, with the result that the ellipse equa­tion will be governed by an arrival from a reflector situated toward the side, and thus not directly beneath the point of observation. One can easily imagine a glacier bed geometry for which no density of observation will yield the correct depth near the centre of a valley-shape bed topography. Further errors may be introduced by assuming that all re­f1ection points lie in the plane of the profile rather than an ellipsoid. These errors may be important in our case, because the bed topograp hy changes rapidly in all direc­tions. The two boreholes reached the glacier bed at 126 and 140 m. The ice thickness as derived from the radio-echo soundings at the same si tes is 122 and 130 m, respectively. The agreement is seen to be excellent, 4 and 10 m difference between the radio-echo a nd borehole depths.

8. FLOW MODEL AND AGE OF ICE AS FUNCTION OF DEPTH

Artificial radioactivity measurements allow us to identify with confidence the 1986 and 1963 snow layers. Nevertheless, 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 purpose and for the determi nation of the mean thickness of each annual layer down to the bedrock, a flow model can provide useful information about the age of the firn /ice of the lower part of the ice core. Gagliardini (1995) developed a two-dimensional flow model based on mechanical con­cepts. H ere, a simple two-dimensional fl ow model was de­veloped assuming that the glacier thickness has not changed significantly since the beginning of the 20th cen­tury. This assumption is supported by the dynamic beha­viour of the glacier (vertical velocity measurements) which has been shown to be elose to steady state. In the model, the mass conservation is considered, in order to obtain the balance horizontal velocity. The mass continuity equation is solved:

o[umH(x)] = b(x) _ o[H(x)] ox ot

where H (x) is thickness, b(x) is mass balance (m water a \ x is distance from the D ome (m ), Urn is mean velocity, and o[H(x)]jot is the thickness variation with time assumed to be O.

From this equation, the mean balance velocity can be 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 (n = 3). The ice temperature is - 11 QC near the bedrock (personal communication from C. R ado, 1995) and the slid­ing velocity is assumed to be O. As a result, the mean hori-

518

4 ~ ____ ~ __ ~ __ -L __ ~ __ ~ ____ L-__ ~ __ -r-

3

2

o --~--~---,---.----.----r---,----,---1--

0 1 00 200 300 400 Distance from the Dome Cm)

430

I 425

ID 420 u

~ <i:

415

410 50 100 1 50 200 250 300 350 400

Distance from the Dome (m)

Fig. 7. Vertical transectJrom Dome du Cou/er 10 drilling site 2 withflowlines ( dash) and isochrones.

zontal velocity is equal to 80% of the surface horizontal velocity. The vertical veloci ty w(x, z) is calculated using mass continuity for the local element:

OU ow ~+~=O. uX u z

This gives (Ritz, 1987):

{ I J H 5 [1 z4 ] } w[x, H(x)] = b(x) 1 - H(x) 4' H (x)4 dz

+u(x,z)_z_oH(x) _ oE(x) H ( x ) OJ; ox

where the last term, from u(x, z) to the end of the equation, is called kinematic vertical veloc ity, b(x) is mass balance (m water a I), z is depth (m ), H(x) is thickness (m ), u(x, z) is horizontal velocity, oH(x) / ox is thickness variation, oE(x)/ox is a ltitude surface variation, and w[x, H(x )] = b( x) at surface and 0 at bed rock.

Horizontal and vertical velocities expressed in 111 water a- I are then converted by the following relations:

'Uw U s = -- ,

p

ww W s = -

p

where 'Uw is horizontal velocity in 111 water a- I, U s is horizon­tal velocity in m snow or ice a I, Ww is vertical velocity in III water a- I, Ws is verlical vclocit y in III snow or ice a I, and

~

.@ 15 ---I1--~--L--'---' __ L--L~ __ L-L-~--L---l __ J....--+-" ;.,

o 50 100 1 50 200 250 300 350 400 Distance from the Dome Cm)

Fig. 8. Surface horizontal velocities from /he model results (divelgence qfO% and 25%) and measurements.

Ii) ~ Q)

~ Q)

Cl «

~

'" til Q)

-b Q)

bIl «

120

100

80

60

40

20

o 20 40 60 80 1 00 1 20 140 Depth (m)

Fig. 9. Snow age vs deJlthJi'olll model results and radioactivity measurements (1986 and 1963). Sensilivil)' to thickness varia­lion ( ±10 m).

100

80

60

40

o 20 40 60 80 1 00 120 1 40 Depth (m)

Fig. 10. SI10W age vs deplhfolll lIIodel results and mdio(lctiu­i£v lIIeaSUrell1ents (1986 and 1963). SfIIsil iv i~v 10 mass­balance varialion ( ±3 standard devialion ).

p is local d ensit y. Dcnsity m easured in the boreholc is

ass um cdto be fcpresc nta ti" e fo r th t' wholt' fim.

Such a m odel does no t ta ke into acco unt the m ass­ba la nce cha nge with time; it considers the m ean mass

ba la nce obta ined from \'e rtica l \'elocitics (Fig. 4d ).

This m odel ta kes into account hori zonta l fl owline di ver­gencc by co rrecti ons on flu x a long the m ain fl owline. Never­

theless, measured hori zonta l velocity directi o ns a rc almost

pa ra ll el (Fig. 4a) and hori zonta l fl owline dive rge nce is neglected a t first.

Fina ll y, calcul a ted \ 'Clocit y \ 'ec to rs a llow us to d e termine

fl owlines (Fig. 7) a nd the ice age from D ome du G OLIler to the drill site. H o ri zont a l veloc it y va llles a re shown in Figure

8 a nd ha\ 'C been compared with surface measurem ents.

9. RESULTS OF FLOW MODEL

The se nsitivity o f th e ice age proposed fo r Ice co re 2 has

Vincenl and olhers: Sn ow acculllulation (l nd i[eflow at Dome du Gouler

140

120

100

~

'" 80 a ., -b

Q)

60 bJl «

40 /.

/ 1963

20

o 20 40 60 80 100 120 140 Depth Cm)

Fig. 11. Snow age vs depthfom model results alld radioactil' itv measurements (1986 and 1963). Sensitivil)' 10 divergence (50 % and 25% ).

b ee n studied fo r som e pa rameters. Fig ure 9 shows the se nsi­ti v it y to thickness \ 'a ria ti on; a va ri a ti on ofb cdrock e le\ 'a ti o n

( ± 10 m ), applied o n the profil e from the Dome to the dril­ling co re, in\'oh es a n uncerta inty of ±6years a t II0m

depth. Figure 10 shows the sensiti\'iLY to the m ass-ba lance

\'a riation; for thi s purpose, th e standa rd cb 'ia ti on (20 cm w. e.) of the Ch a m o ni x precipita ti o n is multipli ed by 3 to

obta in a n estim a ti on of the standa rd de\'iati on (a = 60 cm

w.e.) of the m ass bal a nce a t D om e du G Otlter (acco rding to

the res ults of acc ull1ul a ti on meas urem ents)" Therdo re, un­ce rta inii es equ a l to 3a/ jii, \,"here n is the number of years

from now, were introduced in th e m od el, a nd th e age o f the

ice co re has bee n o bta ined from these calcul ati ons (Fig. 10). Sensitivit y lo the ho ri zonta l di ve rgence of th e flO\.dines

is shown in Fig ure 11. A di vergence \'a lue o f 50% (di s­

ch a rge/2) gi,"es res ults simila r to th e res ults without di ve r­

gence. That m eans th a t the mode l is not very se nsiti ve to hori zo ntal \ 'elocity m odifications. On the oLher hand , Fig­

UITS 12- 14 confirm the se nsiti\'it y o f the model to the ve rtical

120

100

80 (j) (;j Q)

ob 60 Q) Ol «

40

20

o 20 40 60 80 1 00 120 1 40 Depth (m)

Fig. 12. Snow age vs dePlhjro/ll model results. Sensitivil)' to the depth of drilLing hole ( ±10 m).

519

Journal qfGlaciolog;y

~ <n .... '" Q)

-b Q) OJ)

-<

120

100

80

60

40

20

o 20

963

constant strain-rate

40 60 80 100 120 140 Depth (m)

Fig. 13. Snow age vs depthJrom model results and radioactiv­ity measurements (1986 and 1963). SensitivifY to vertical strain rate ( constant and non-constant strain rate ).

1963 20

o 20 40 60 80 100 120 140 Depth (m)

Fig. 14. Snow age vs depthfrom model results and radioactiv­it)! measurements (1986 and 1963). The dashed line does not take into account the kinematic vertical ve/ocifY.

7

6

.... 5 " 3 V>

4 V>

" ..Q <.)

:s 3

" ;;l

~ 2

\

o

\ \

\ \

\

\ m snow/ice \

\ \

\ \

\ \

\ , , , , ---4... mass balance (m w.e.)

-...... ....... ~t :r1gm pomt ,--",-

m w.c. " "-

\. \.

\

20 40 60 80 100 120 140 Depth (m)

Fig. 15. AnnuaL thickness /a)ler vs depthJrom the model results in the driLLlwle, and mass balance at the origin poinl qf the La)ler.

520

velocity pattern . First, the sensitivity of the model was studied according to glacier thickness at the si le o[ the dril­ling core (Fig. 12). Since the model forces the bottom flow­lines to foll ow the bedrock whatever the profile of the bedrock, the thickness at the drilling site directly influences the vertical velocity a t this sit e. This effect shows the limits of such models.

Furthermore, it can be seen that the model is very sensi­tive to the vert ical strain rate. A constant vertical strain rate, [or which vertical velocity is b(l - z) / H , where b is the mass balance, z is the depth, and H is the thickness, gives very different res ults (Fig. 13).

Finally, the effect of the kinematic vertical velocity (see section 8)was analyzed (this term allows the bottom flowlines to follow the bedrock). \Vhen this parameter is deleted , the model indicates an age o[ the ice core which is older than inferred from radioactivity measurements (Fig. 14). Thus, it seems that the calculated age is not very sensitive to uncer­tainties on surface conditions (mass-balance variation) and bottom conditions (bedrock topography uncerta inty) between Dome du Gouter and the drilling site (that does not mean a good knowledge of absolute va lues of these parameters is not required ). However, the parameters linked to the verti­cal velocity at the drilling site are predominant: vertical strain rate, thickness and mass ba lance at the drilling site.

Figure 8 a llows us to compare the horizontal velocities obta ined from the model and the measured velocities. A lthough the uncer ta inti es about measured velocities are large, it can be seen that the ca lculated velocities are too high. These differences can be explained by horizonta l di­vergence of the flowlines (about 20- 30% ) without changing the ice age (Fig. 11). In Figure 15, the mean thickness o[ annu a l layers in the drillhole is calc ulated according to depth. Below 110 m , layers are very thin. In the same fi gure, the m ass ba lance at the beginning of the flowline is shown. This ofTers the possibi lit y of distingui shing the parameters which lead to thinning of layers: the deformation of ice layers due to the strain rate, and the sp a ti al distribution of mass ba lance between the Dome and the drilling site.

10. CONCLUSIONS

The g laciological surveys carried out on D ome du Gother show a n important spatial distribution of the acc umula tion: the mean accumulation varies from 0.3 m w. e. a- I at the top of the D ome to 3.0 m w.e. a- I in the vicinity o[ the drilling co res. In additi on, an unusual featu re of mass-balance flu c­tua tions in the Alps h as been pointed out: the snow accumu­lation in this high-altitude Alpine glacieri zed area does not show any seasona l pattern; summer and winter mass bal­ances are very sim.ilar, which has not often been observed in the Alps. Furthermore, the observed spatial distribution of the accumulation seem s to be very simila r to the vertical velociti es obtained from topographic measurements of the stakes. These values, as a n independent res ult (i-om di re et accumulation measurements, match the long-term average mass balances for steadY-Slate conditi ons. There[ore, the measurement or vertical velocities is a good way o[ quickly obtaining the reliable mean accumul ation values [or several decades in such a region.

The fl ow model described in thi s paper provides usefu l information abo ut the urn/ice cores made down to the bed­rock. It can be shown that, with a simple fl ow model and

somc precautions (for example, taking into acco unt the kinema tic vertical ve loc ity connected with the bedrock shape), a reliable age/depth relation can be obtained, a res ult which is supported by radioacti\'it y measurements (1963 and 1986 events).

ACKNOWLEDGEMENTS

This stud y was supported by the Region Rhone-Alpes and the Ministcre de l'Envi ra n nement, France.

\Ve wo uld like to th ank our coll eagues who took pa rt in fi eldwork, and especia lly those \\'ho made m easurements by going on foot: 1. Seljha l, E. LemeLlr, M . T. Vincent, O. Gaglia rdini and P Mansuy.

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521