JOllTllalofGlaciology, Vol. 43, No. 145, 1997

Measurements of ice deforrrlation at the confluence area of , Bernese ,

G. HILMAR G UDMUNDSS ON,I ALMUT IKEN,2 MARTIN F UNK 1 I VersllchsanslaltJiir I Vasserball, Hydrologie Zlnd Glaziologie, ETH ;(enI 1'llm. Gloriastrasse 37(39, CH-8092 ;(iirich, Switzerland 2Rockwinkelslmsse 35 A, D-28355 Bremen, Germany

ABSTRACT. An experimenta l study of ice deformati on a t the co nfluence a rea of Unteraargle tscher, , Switzerland, h as been carried o ut. Surface velocities we re meas ured by repeatedl y surveying stakes a nd with the use of rem ote-sensing method s. The \'ariation of the ve rtica l strain rates with depth was measured in boreholes. The confluence center line is subj ected to longitudinal hori zontal ex tension, which is exceeded in m agn i­ tude by a concomitant transverse compress ion. Vertical stra in rates change from positive (ex tension ) a t the surface to negati ve (compression) in the lowes t layers of the glacier.

INTRODUCTION zerl and , are described. The fieldwo rk consisted m ainly of re­ peated sUJ'\ 'Cy ings of stakes and boreholc measurements of The confl uence of two glaciers is an ideal place to study the the \'ari ati on of the vertical velocity component with depth. mechani cs of ice deformatio n, as th e glaciers must adjust Surface ve locities of the co nfluence a rea of hi gh (50111 ) spa­ themselves to a completely new bed geometry O\'e r a short tia l resolution a re presented a nd discussed. The properties di stance of oft en onl y a few m ean ice thicknesses. However, o f the fl ow are inves tigated with two-dimensiona l models rel ati\'ely fe w studies have been conducted o n the ice me­ in a separate paper (Gudmundsson, 1997c). chani cs of glacier confluences, the reason p resumabl y being that the complex ity of the fl ow field makcs interpretati ons Setting offieldmeasurements diffic ult. The most detail ed experimental work done so far on the Finsteraar- and L a uteraargletscher are the two tributa ri es conve rgence of two glaciers seem s to be that on K as kaw ul sh of Unteraargletscher (Fi g. I). They a re both about I km wide Glacier, Yukon Territo ry, Canada, as part of the Iceficld a nd their surface \'ei ociti cs arc simila r in magnitude. ''\Th ere Ranges ResearchProj ec t. Among other things, the bedrock they fl ow together they form a n angle of roughly 100°. topography, surface velocity, crevasses and m orphological U nteraargletscher extend about 6 km eastwards from the features were studied (Brecher, 1969; Clarke, 1969; Holds­ confluence of L a uleraar- and Finsteraargletscher a nd has a worth, 1969a, b; Wagner, 1969a, b; Anderton, 1970; Dewart, mean width of I km and a mean slope of approximately 4°. 1970; Dozier, 1970; Ewing, 1970). The fl ow pattern of the co n­ The confluence itself; which li es within the abl ati on area, flu ence of Tyndall Glacier, southern Patagonia, has also has an area o f abo ut 2 kn1 2 a nd is 2400111 a.s. l. A ll three been analyzed (Casassa, 1992; Kadota and others, 1992), g laciers are temperate. and the formati on and evolution of media l m oraines has been in vestigated in papers by Anderton (1970), Eyles and Rogerson (1978), Gomez a nd Sma ll (1985) a nd Vere and Benn (1989) . Theoretical wo rk on the d eformati on a nd the stress field at the junction of two glaciers has been perfo rmed by Col­ lins (1970). H e used the techniques of slip-line theory and assumed a rigid/perfectly plastic materi al beh avior of ice. Further assumptions inel uded rigid "plug fl ow " mm'ement of the ice above and below the confluence zone and pl ane strain deformation. Collins suggested that the dynamics of a confluence wo uld introduce some surface modifications co unteracted by the onset of "secondary fl ow", i.e. a small amount of ci reul ating fl ow superimposed on the main fl ow. For a V- shape juncti on this wo uld be expressed in a down­ ward fl ow component at the central part of the conflu ence area a nd in a n upward-now component elose to th e outer walls of the confluence a rea. n this paper, the res ults o f a n ex perimenta l study of the Fig. 1. ,Hap of Strahfegg -, Lalltemar-, Finsteraar- alld confluence area of Unteraarglctsc hr r, Bernese Alps, Swit- Ullteraalgfetscil er and their locations within Switzerland. 548 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 14:12:42, subject to the Cambridge Core terms of use. Gudl7l11ndsson and others: Ice dtjOrmaLiofl a/ cOlljlllence area of Un/emCllglelsc!ler

A conspicuous feature of U nte raargletscher is the large drilled \I-ith a ho t-waterjet at a location close to the medial ice-cored m edi al moraine. It is ove rl ain by a surficial rock m oraine about 500 m down-glacie r from the junc tioll point detritus o f typicall y 5- 15 c m thickness. Within the area of (Fig. 2). The holes were only 10 20111 apart a nd ha d depths the confluence, the media l m oraine is 10- 18 m hi gh and of 100-281 m_ The total ice thic kness at the d rilling site is 150 m wide. It becomes high e r a nd \I·ider in the down-fiow a bout 340 m . A ir temperatures were above the freezing directi on, reaching a maximum height of a bo ut 25 m and a p oint, and considerabl e surface melting occurred during width of approx im ately 300 m . Further down-glacier the the day_ l11 edia lmo raine gradua ll y spreads out latera ll y a nd merges with the m a rgin al mora inic debris. \Vithin the confluence area, decp-rcaching c rn'asses are found only close to its southeast edge. About 300 m from the \ = 2'50 junc ti on p oint, th e media l m ora ine is cut by a sm all number I ~ --~~------_/~ ~ of wide crevasses lying p erpendicul ar to the d irection of / ------.---...-- ~ fl ow. I

Previous studies on Unteraargletseher

Unteraal-gletsc her is o ne of the mos t comprehensi\'e ly studied glacier in the Alps. The beginning of quantitati\'e glaciological measurements call be traced back to the work of Hugi in 1827 a nd Agassiz in 184146 (Hug i, 1830, 1842; Agassiz, 1847). Since 1924, systematic measurements of sur­ face cha nges a nd \'C locities have bee n made each yea r (Fl o­ tron a nd Flotron, 1924-97). A comprehe nsi\'e li st of rderences to glaciological work relating to Unteraar­ gletsc her can be (o und in Zumblihl and H o lz ha use r (1988, 1990). Fig. 2. .llal) qf the confluence area, showing bOlh surface (dashed line.l) and bedrock (solid Lines) /0f!0gral} /~) I . The so ­ Flow beftavio r lid cross SIIOWS lit e loea /ion qf/lt e 1991 drilling sile. The fl ow behavior of Unteraargletsc her from 184-5 to date is known in some detai l (H aefe l i, 1970). In 1845- 46, \-e locities a long two p rofil es we re m easured e\-e ry m o nth by Agassiz Vertical strain rates (1847) a nd hi s co-work ers_ One of the profi les was close to the confluence. Both pro fil es showed large seasonal \'elocit y To gain info rma ti on on \-c rtical stra in rates, three of th e flu ctu ati o ns, with their m aximum \'clociti es occurring in boreholes were equipped \I-jth m agnetic rings, a nchored on the r eri od from mid-April until the cnd of June, a nd their 1. 5 m long a lull1inum tubes, at depths of 100, 150 a nd 200 m. minimum from the cnd of O ctober until mid-Ja nuar y. The The \-e rtica l 1l1 0vemr nts of the m agneti c rings we re meas­ m ax imum velociti es (averaged o\u' a few d ays) were about ured se \'C ra l ti m es a day with res pect to rcference sta kes at 1.6 times la rger th an the m ean a nnual \·elocities. the surfaee_ The a bsolute pos iti o ns of th e reference stakes From 1969 until 1980, ice m o ti on \I-as studied by mea ns of were also measured with a theod olite situated on bedroc k a n autom a tic camera positio ned about 2 km below the con­ to the side of the g lacier_ flu ence (Flo tron, 1973). Again, la rge seasona l velocit y vari a­ Yertical ice displacements were rath er stead y a nd sur­ ti ons were fo uncl, with hi g he r velocities during the summer. prisingly la rge: 1. 39 ± 0.07, 1.97 ± 0.27 a nd 2_1 9 ± The summer \'elociti es va r ied from yea r to yea r, but the 0.07 cm d 1 fo r the rings at 100, 150 a nd 200 m depths, respec­ winter velocities remained sta ble. InJune 1975 the ca mera ti\'e ly (pos iti\-e va lu es indicate extension). The displ acc­ records we re compl emented by theodolite m easurements at ments of the ri ngs a t depths of 100 a nd 200 III a rc shown in fo ur transverse prolll es. A number of uplift events inter­ Fig ure 3. ?\[easurements of' the ring at 150 m could not be preted as being due to increased water sto rage at th e bed continued fo r as long as th ose o f the oth er two rings. The \\'ere obse n 'ed (Iken a nd o thers, 1983). R ecent mcasure­ installation a nd the measurem ents of th e magne ti c rings ments showed simila r uplift e\'e nts on Untc ra arglctsc her, a rc desc ribed in m ore detail in Gudmundsso n (1994-b)_ accompa nied by strong la te ra l compress ion a nd \'Cr ti cal ex­ The mean vertical stra in rate o ver the di sta nce between tension (Gudlllundsso n, 1996). A detailed a na lys is is neces­ the magneti c ri ng a nd th e reference m ark at the surface is a sary to de termine whethe r the uplift is caused by strain combinati on of\'ertical strctching a nd hori zonta l shear. On ('vents, wate r storage or both. the bas is of finite deforma ti o n theory, H a rrison (1975) c1 eri\'C d the fo rmula Bed /of!ogmj} /~v Pa rts of Finsteraar- a nd L aute raarglctsc her- a nd th e whole of Unteraargletse her ha\'e b een im'Cs ti gated by se ismi c re­ fo r the stra in ra te e res ult ing bo th from the strain rate per­ fl ecti on m e thods (Kneeht a nd SLi sst runk, 1952) a nd radi o­ pendicul a r to t he surface and from shearing. The ti m e inter­ echo soundings (Funk a nd others, 1994). The bedrock val betwee n m easurements was a pproximately 0.003 a, a ncl geometry o f Unteraa rgletsc he r is therefore known in detail. sin Cl' ~ 0.05. A reasonabl e value fo r the shear st ra in rates is E_,-: ~ 0_05 a 1_ (This estimate fo ll ows fr om an unpublished RESULTS three-dimensio na l 0 0\1- model of the conflu ence' a rea; Gud­ mundsso n, 1994b.) The co ntributio n of shea ring to borehole During the second wee k of September 1991, fo ur holes were stretching is the refore less th a n 0.005 a 1_ i\l easurccl values

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101 .80 ,,------,....-, 196.00 what uncertain as the curve is based on only five data points. ... However, it is beyond d o ubt th at the vertical ve locity 101 .70 195.90 increases with depth and then decreases again, ca using a shift in stra in rates ri'om pos itive (ex tension ) to negative 101.60 195.80 I (compression) so mewhere between 195 a nd 340 m. Vertical 101.50 .HA' 195.70 stra in ra tes obtained by differentiating the interpolation ,'" ,.,.- '" curve a re a lso give n in Fi gure 4. This essentially monotonic, 101 .40 .... 195.60 but quadrati c, va ri ati on of the "crtica l st ra in rates with depth ... ' 101.30 195.50 should be contrasted wi th the ass umption of a constant or lin­ 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 September ea r vari ati on of thc strain rares with depth so oft en made in 1991 th e glaciologicallitcrature (Paterso n, 1994, p. 276- 279). Fig. 3. fertieal displacements qf magnetic rings at depths rif Horizontal strain rates 100 m (sol id line) and 200 m (dashed line) with resjJeet to the glacier sll1Jace, asfullctions riftime. The sy mbols represent The horizontal strain rate at the drilling site was deter­ l17 easured values. The errors associated with each measure­ mined b y measuring the m ovements of fi ve sta kes se t up as ment are estimated to be less tha n ± 1. 5 mm , creeptJo r the last a squa re with one stake a t the (enter. The distance fr om the measurement on I Octobe1;for which the errors are cif the order (' enter sta ke to the others was approximately 50 m. The rif ± 2cm. stakes were survcyed [our times during the winter of 1991 for e are considerabl y larger, so that e ~ Eoo. Hence, the 92, on 17 September and 10 O ctober 1991, a nd I J anuary and contribution of shearing to the changes in distance between 4 April 1992. Strain rates for each interva l ""ere calculated the surface reference ma rk and the magneti c ring can be by finding the best fit of the velocity of each stake to the ex­ ignored. presslOn The movements of the reference m a rks at the surface Vi = (30i + (31iX + (32iY for i = 1,2 relative to a fi xed point outside the g lacier were also m eas­ ured, and they corres ponded to an average thickening rate where Vi a re the hori zontal " elocity ('o mponents,.c and y are of 1.0 ± 0.5 cm d 1. This relati,"C ly high error estimate as the coordinates of the sta ke at whi ch the velocity was meas­ compared to the res ults obtained with the magnetic rings is ured, a nd the (3ji'S are regression coeffi cients. caused by the fact that the measured vertical di splacement From 17 Septcmber to 30 October 1991 the rate 0 [" defor­ is in part due to "ertical stretching/compression and in pa rt mati on was considerabl y la rger th an during the t,,·o subse­ to the overa ll downward fl ow of the glacier. These two com­ quent time peri ods. This seasonal strain-rate vari ati on may ponents ca n be separated only by estimating th e aVC'r age have b een caused by changes in geom etry or a sudden surface slope, which introduces some errors. change in boundary conditions related to cha nges in basal The measured ve rtical velocity profile is depicted in sliding distribution, the latter poss ibility being the preferred Fig ure 4. Measured values were interpolated by using a cause. The ori entati on of the principa l compress ive strain third-degree polynomial with weighting factors that a re in­ rates is approx im ately no rth- so Llth (Fig. 5), a nd th cy exceed versely proportional to the measu rement errors. The most the concomitant cast- 'wes t extension. conspicuous feature is the maximum of V o at approximately 220 m depth. The exact location of this m aximum is some-

0.05 extension 2.0

158.0 :"'" 1.5 ...... - -- "'-'-'- ...... -______..... ,. _ - _ _ - 0.00 . ~ !i " compression ;: : .. 1.0 , , .. , , ~ 0.5 , , , ,, -4.05 M ' ~~~50~~~100~~~15~0 ~~200~~72S~O~~300~'--7$~0 depth [mJ

Fig. 4. Nleasu red vertiral ice veloci£y relative to the sll1Jace as ajiwetioll rif depLh (solid line), and th e corresjJondi llg va ria­ Lion qf vertical stra in rates Ezz with depth ( dashed line). The 157.0 :-::--'----'-'--'---'..-=~-'----'---'---"'_!!~-'---'---'..--'--.J 656.5 657.0 657.5 658.0 solid curve is based Oil an inLerpolation cif the measured velocities cifmagnetic rings in bore/zo les with respect to th e Sll r­ face ( Fig. 3), and the total vertical movement cif the swiace Fig. 5. Velocities and principal strain rates calwlated fro m with respect to aJ iud riference point. Velocities are relative to marker movemen ts du ring the winters rif 1991- 92 and 1.9.92- the glacier swJace, with positive values indica ting downward .93. Vee Lors denote horizontal velocities; conLO llT lines give the movements. The vertieal strain mte ( da shed fine) is the slope speed. The straill -mte cross is at the loca tion rif the drilling rif the solid curve. site. COllto ll r illterva l is 2.5 m a l Coordinates are ill kill .

550 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 14:12:42, subject to the Cambridge Core terms of use. Gudmundsson all d oL lters: lee deforma lion al confluence area of Ull lemclIglelsr/ze r

Considerabl e surface melting took place during Septem­ maximum being reachecl close to the center of the conflu­ ber 1991 and possibl y the first week of O ctober. On 30 ence a rea where the ice thickness is greates t (Fig. 2). Surface O ctober no melting occurred a nd the glacier was covered velocities on Finsteraargletse her are so mewhat large r tha n with fres h snow. This pres umably led to a drop in water pres­ those of Laut eraargletscher, in genera l agrecmr nt with sure and a consequent dec rease in sliding \·eloeity. Changes thickness diflcrences. It is, howe\·e r, ques tion abl e how mllch in sliding velocity will, for such a complicated geometry as emphasis should be pl aced on the interpretati on or annua l that of a confluence area, almos t inevitabl y lead to changes velocities ("or a glacier which is known to exhibit large tem­ in the ice-deformati on pattern. pora l vari ati ons in sliding \·elocity a nd hencc in surface No tempora l stra in-rate variati ons were observed during velocity. Since the boundary conditions ch ange througho ut the winter, and the velociti es of the ma rkers did not change the year (and the surfacc velocity with them ) the a\"C rage with time over this period. Hence, throughout the winter of annua l \·e!ocity fi eld m ay never be reali zed for any particu­ 1991- 92, sliding velocities did not change and we re possibl y la r p eriod of time. The annual \"C locity distribution there­ even zero. No m a rginal sliding was obse rved during the forc renects the sum of different phys ical processes reali zed winter, whi ch suggests that if basal sliding ta kes place, it at different times, but the sum itself m ay not corres pond to must be confi ned to the lower secti ons of thc glacier bed. a ny physical rea lity. On the oth er hand there are indicati ons of some m arginal 10 obta in a bettcr idea about annua l surface \"C loc it y sliding taking place during the summer. varia tions, an additiona l pair of aeri al photograph s, ta ken on 23 July 1991 by the Federal Cadastra l Directorate, was Surface velocities extracted from aerial photographs used together with the aerial photographs from 22 Aug ust for surfacc vel ocity determinati on. The aerial photographs A eri al photographs a rc taken of the Aaregletsc her (the col­ were evaluatcd by\\'. Sehmid at \ 'AW-ETHZ, and the result­ lective name la r Finsteraar- , L a uteraar- , Unteraar- and in g surface \·clociti es can be seen in Fig ure 7. ~o t e that ) during late summer every year. By com­ a lthough \·elocities ofUnteraargleLsc her a rc known to \·al-y paring two different stereo models generated at different on ti mc-scales 0 (" days a nd weeks during sp r ing and summer ti mes, the surface velocit y li eld can be constructed (Flotron, (Flotron, 1973; Iken a nd others, 1983; Gudmundsso n, 1996), 1979; Kaab, 1996). the averaged \·clocities O\'er th e time p eriod 23 jllly- 22 Fi gure 6 shows the surface vel ocity li elcl 0 (" the conflu­ Aug ust 1991 will be referrcd to as Slln1.mer veloc iti es here­ ence area, as extracted from a compa ri son of multi temporal aft er. stereo models from aeri al photographs taken on 15 August The m aximulll sUlllmer \"C locities of the connucnce area 1989 and 20 Aug ust 199 0. The velocit y pl ot \\ as generated arc approx im atel y 55 111 a 1 In the up-g lacier directi on by Baud er (1996) at VAW-ETHZ, ZUrich, and di gital terrain towa rds Laut eraargletscher, the \·elocities dec rease a nd models from both years we re m ade a\·a il abl e by the cngi­ increase again further upstream, whereas in the up-glacier neering firm Fl otron AG. directi on toward s Finstcraargletsc her a continuing increase The vectors in Figure 6 represent the raw data. The con­ with dista nce is observed. On the west side 01" th e conllu­ LO ur lines of the horizont al speecl were calcul ated from fil­ ence, close to the juncti on point, an extencled arra of large tered \"C locities. The filtering of the \"C loeities is ex pla ined \·elocit), gradients can be seen (Fig. 7). Along the north a nd below. l\Iaximull1 annual ve loci tics arc about 45 m a I, the so uth m argins marginal sliding seems to Lake place.

656500 657000 657500 658000 658500 [m]

Fig. 6. Annual horizonla! sw/ace velocilies derivedJmm aerial J)holograjJhs la ken Oil 22 Augusl 1990 and 20 AugllsL 1991. The (on lour inlerval is 5117 a l Coordina les are ill III ele r:r.

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Fig. 7. Horizontal summer swjace l'e/ocil ies extracledfi"Oll1 aerial photogmJ)!Z sJor th ep eTio d 23 J u(y 22 August 1991. The cO lltou r illterval is 5 111 a-I. C:ooTdinat es are il1 l11eters.

In situ velocity Illeasure:rnents but not in the summer velocities. This is a good example of seasonal variation of the deforma ti on profile across a nd a long a glacier surface and shows, together with the tempor­ During winter the snow cover renders the surface more or a l change in surface strain rates, how temporal basal sliding less featureless, and ice \"C locities cannot be extracted from ya ri ati ons can affect the internal deformation pattern of the aeri al photogrammetry. \ Vinter \'eloc iti es were therefore ice. ll' mporal cha nges in deformati on rates may be es pe­ calculated from repeated surveying of sta kes. Altogether, cia ll y marked for a confluence, because a relati\'ely la rge 78 stakes were drilled into the ice, of whi ch 25 were installed contact area between the ice a nd the bedrock over which in autumn 1991. These were repetitivel y surveyed on 30 basal sliding can occ ur transforms a t the junction point into O ctober 1991, 16 January 19 92 a nd 17 19 April 1992. Addi­ a n ice ice contact a rea. Al ong the ice- ice contact area, no ti onal markers were installed during th e radio-echo sound­ or negli gibl e relative slip moti on takes pl ace. Tt is al. ·o cl ear ing survey of April 1992 and meas ured for about 3 d. that the three-dimensional geometry of the con11uence J\[arkers were reinstalled in a utumn 1992 and m easured on m akes a simple plug-11ow ve locity field impossibl e. I December 1992 and 19 J a nua ry 1993. The r es ults of a ll these measurements arc tabula ted in Gudmundsson (1 994). Surface strain-rate pattern extracted from aerial Surface velocities did not change during the period photography O ctober 1991 April 1992. Vel ociti es during the winter of 1992 93 were, within obsen 'ati onal errors, the same as Optima/filtering ojmeasured surface velocities those of winter 1991- 92. Fig ure 5 depi cts marker velociti es Possibl y the most straightforwa rd m ethod of es timating hor­ during the winters of 1991 - 92 a nd 1992- 93. Several addi­ izontal strain rates (Eij ) from measured surface velocities ti onal markers, outside the confluence area, a re not shown. (Vi ) would be to interpolate the velocities to the nodes of a Tnt erpolation of the rather I i m i ted number of veloci ty meas­ sq uare grid, and then to approx i m ate the expression (oij = urements was done with the Akima interpolation algorithm ~ (Vi.) + Vj.i) through unite differences. This method will (Akima, 1978). not work without some adjustment, however, if I-andom There is no indication of m argin al sliding during the data errors introduce apparent spati al velocity va riati on winter months. This observa tio n wa, used in the interpola­ of comparable m agnitude to the actua l (noise-free) \'elocity ti on of the surface speed (Fig. 5) by se tting the \'elociti es \'ari ati ons of the glacier. along the boundary to zero. Extrapolati on of marker Because the spatia l di stance between measurements was \'el ocities to\,'ard the glacier bo undary may depend to so me about 50 m, and the veloeit y error is estimated to be about extent on this assumption. The veloc iti es within the conflu­ 0.3 m a I, the error in the strain-ra te estimate over this di s­ ence area are, on the other hand, not affected by this ta nce will be approximatel y J2 x 0.3/50 = 0.008 a t, which ass umption. is comparable in magnitude to the expected surface-strain Because of large ly reduced or e\"C n totally absent basal rates. Strain rates calcul ated over la rger di stances can be es­ sliding, winter velociti es a re approx im ately 75% of summer timatedmore accurately, but these long-wavel ength stra in­ \·a lu es. H owever, a qualitative difk rence also can be seen by rate \'ari ati ons will not be detectabl e in the noise associated comparing figures 5 and 7. A clear "elocit y m aximum ap­ with the short-wavelength strain-rate variations unless so me pears in the winter \"C locities close to the confluence ce nter, filtering is done. If vertical stra in rates along the surface arc

552 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 14:12:42, subject to the Cambridge Core terms of use. Gudmundsson and others: lee deformation at confluence area qf Unteraargletsclzer to be calculated with the help of the incompress ibi lit y con­ Aug ust 1991 are shown in Figures 8 a nd 9, res pectively. dition, an effective a nd reliable method of error reducti on is These surface strain rates were calculated along a 50111 es pecia ll y importa nt, as the two hori zontal strain-rate com­ squa re grid fr om the vel ocities shown in Figures 6 and 7. ponents tend to be of similar but oppos ite magnitude. Vertical strain rates were calcul ated from the incompl-essi­ Because the errors depend strongly on the waveleng th of bility condition at all g ridpoints \\·here at least eight \'clocity the spati al stra i n-rate \'ari ati on - dec reasing il1\ "C rsely with measurements we re avail able within a radius of 95 m. distanee - a wavelength-dependent filter ean be used to ef­ Although so me differences are detecta bl e, the main fea­ fecti vel y eliminate the high-frequency errors. To this end the tures of Figures 8 a nd 9 are the same. Fricti on along the two-dimcnsiona l Fourier transforms of the ve locit y distri­ ma rg ins gi\'es ri se to zon es of hi gh horizontal shea r but neg­ butions v.r(.r, y) a nd vy (x. y) were caleul ated, a nd a n opti­ lig ibl e \'ertica l strain rates. Close to the juncti on po int, mal \\'iener filter, where Lauteraar- a nd Finsteraargletscher cO Il\'erge, the

2 center line is s ul~ j ec t e d to transverse compression and long­ W (k) = 15( 1.: )1 itudinal ex tension. This is es peciall y prominent over a 2 15(k)12 + IN(k)1 ' roughly circul ar a rea, situated about 500 m down-flow o f

/') .) the juncti on point, \Nhere the tra nS\'erse compressio n constructed, where k = Vk .r - + k y -, and k". and ky a re the greatl y exceeds the longitudinal extension in magnitude, horizontal wavenumbers. N(k) a nd 5(k) are the er ror and res ulting in a considerable ve rtical extension at the surface. the noise models determined from the power spec trum of In Fig ure 9, two points with local maxima in vCTli cal sur­ the measured velocities (Rabiner a nd Gold, 1975; Press a nd face strain rates can be identified, whereas in Figure 8, due others, 1996). The filter W(k) was applied to the Fourier­ to the lack of data, only one such point can be di scovered . In transformed vel ocities. The stra in rates fij(k · . ky) were cal­ 1 aO" reemcnt with the res ults from borchole measurem ents cul ated directly in fr equency space by forming the corres­ mellli oned abO\"C, the transverse compression outweig hs ponding products of the transformed veloc iti es with the the longitudinal ex tension, causing a considerable vertical wa\·e numbers. Calculati on o[hori zontal strain rates is faster stretching along the surface. with this method than with either locall y adaptive linear-re­ In the down-fl ow direc ti on, [he strain-rate regime gression models (Bauder, 1996) o r thc method of Nye (1952) a long the ce nter I i ne cha nges progressively LO wards a pre­ (whi ch has oft en been used in the glaciological liter ature), domina ntly long itudina l compress io n, whi ch is the a nd the res ults a re less prone to errors in the data . It should exp ected state or fl ow fo r a n abl ation a rea (Nye, 1952). A s be stressed that filtering of the velocity data was absolutely a res ult, vertical stra in ra tes are mos tly p os iti ve, with two imperative for extracting informa ti on on the stra in-rate va r­ nota ble exceptions, bo th of wh ich resu I t from surface to po ­ iati on across the g lacier surface from the surface \"(~ l oc iti es . graphic undulati ons. On Unleraargietscher a narrow east- wes l- extendi ng Characteristics qfslllfllce strain -rate pal/ ems zone o f vcrtical compression can be seen in Fi gure 9. This The surface stra i n rates of the confluence area fo r the time zonc coincid es with the medi al mora ine, and this vertical peri ods 23 July 22 August 1991 a nd 22 August 1990- 20 compression and tra nsverse extension is pres umabl y a n ex-

15800~~,.-r

Fig. 8. Horizontal sll1Jace strain rates qftlL e confluence area q/ Cll teraargletsciLel: calClllatedJroll7 jiltered l'elocitiesJor the ti //l e period 23 J u[y- 22 August 1991 ( Fig. 7). COlltour lines represellt l'ertical strain rate,s cal{lllated QJ' lI sillg the ill coll7jJTesJ ibility condilion, fii = O. Yega tive [O l7 tours are dra wn with dolled lines, alld positi1'f ones with solid lilies. The contollr in tm 'alls O. OJ a l Coordina tes m'e in ll7 eters.

553 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 14:12:42, subject to the Cambridge Core terms of use. Journal qfGlaciology

1580011H-~-

157500

1 15700 0.1 a· +

656500 658000 658500

Fig. 9. Sll1jace strain rates, derivedJromJilteml sll1jace velocitiesjor the time jJeriod 22 August 1.9.90 20 August 1.9.9/ ( Fig. 6). Contour lines rejJresent vertical straill rates. The COlltOllT interval is 0.01 a 1 Coordinates are in meters.

pression of the lateral di sintegrati on of the ITlora ine itself. taken in interpreting some of the strain-rate patterns of the This tranS\'erse diffusion of surface features cannot be m arginal zo nes where onl y a limited number of data points obsrr\'ed close to the junction point, because it is masked were a\·a il able. by th e strong ice deformation caused by the flow d ynami cs of the confluence. Not only the ice velocities but also the SUMMARY AND CONCLUSIONS internal ice-deformati onal pattern changes over the co urse of a year (cC Figs 8 and 9). It is i mponam to realize that it is The main features of the surface strain-rate regime a re easy the differential abl ati on, caused by th e supraglacia l debris to explain. Al ong the ce nter lin e (which is considered to co­ cover, which is responsibl e for the build-up o f the medial incide with the medial moraine), the \·clocity increases as moraine, and not the convergent flow of the conflu ence the ice moves from the juncti on point toward the center of area, as can be seen from the fact that (I) the m edial mor­ the confluence. The medi al moraine is, th erefore, subj ected ain e is limited to the debris-covered glacier surface, and (2) to longitudina l extension. The transverse compression fol ­ the zone of transverse co mpression has a much larger trans­ lows from the long itudinal extension, and the cha nge in verse extent than the medial moraine. m ean now directi o n of the two converging arms within the Directly south of th e narrow east- west-extending zone conflu ence area. Practicall y identical results with respect to of \'ertical compression, a para llel running zone of \'e rtical surface strain-ra te pattern were found on K askavvu lsh extension and tranS\'erse compress ion can be identified (Fi g. Glacier, which shows that this kind of strain-rate regime is 9), which coincides with a surface depress ion. This zo ne is not exc!usi\'e to the connuence of Unteraargletsc her. the only debris-free section of U nteraargletscher so uth of Vertical strain rates integrated over depth must be posi­ the medial moraine, and the surface depression results from tive below the m edial morain e as long as ice thickness a combinati on of differential ablation and the erosive effec ts increases in the flow directi on. This will in general be the of supraglacia l streams, which form there ever y spring and case for the distance from the junction point to the conflu­ exist throughout the summer. This zo ne is therefore in so me ence eenter. Because surface longitudinal and a\'C rage verti­ res pec ts an "inverse" medial m oraine, with the corres pond­ cal strain rates must be positive, it (allows from the ing il1\ 'erted deformational pattern with res pect to the med­ incompressibility assumption that the surface-tra nsverse ial moraine. Although it is an interes ting fact that diffusion compression will in general be la rger than the surface-long­ of these sma ll surface undula ti ons, having transverse di­ itudinal extension. mensions of onl y about 150 Ill, can be retrieved and demon­ Summarizing, it is sugges ted that the overall strai Il-rate strated with the help of aeria l photographs, a n accurate regime in a confluence can be understood in terms of three estim ate of the rate of deformation \""ill pres umably only be different mechanisms: (I) the effective ice-thickening in the possible thro ug h direc t field m easurements. flow direc tion along the medi al moraine from the junction Some of the features seen in Fi gures 8 a nd 9, such as the point toward the center; (2) the change in the mean flow di­ sma ll zones of vertica l compress ion found a long the center rection orthe two converging arms as the confluence area is lines of La ut era ar- and Finsteraargletscher, where hori zon­ approached; and (3) a ve locity increase along the medial tal strain rates a rc almos t zero, m ay not be real a nd are most moralllC from the junction point toward the connuence likely caused by measurement errors. Care must also be center. 554 Downloaded from https://www.cambridge.org/core. 27 Sep 2021 at 14:12:42, subject to the Cambridge Core terms of use. Glldmul1dsson and olhers: lee difonnation al confluence area 0/ Unlemarglelsclzer

The vertical strain-rate variation with depth is surpris­ K askawulsh Glacie r. I II Bushncll , \ '. C. and R . H. Ragle, l'd5. ledidd ingl y complicated. The observed reversal from extensive to Rallge5 Resear(h Prqjecl; Scienlific Re.wll.l. 101. 2. i\Iontrcal, Que., Arctic Instit ute of:\"orth Amc rica; "'ewl a rk. Amcrican Geographical Society, compressive flow with increasing depth is, at first sight, 59 76. somewhat surprising and requires an ex planation. A lthough Baudn. A 1996. \lasscn bi la nz lll odcllierungen mir phOlogra mme trisch c n the characteristics of basal flow can be quite complicated i\lcssungen und e ism cchanischcn Be r(" chnungcn am Beispiel des Ut1ler­ (Gudmundsson, 1997a, b), it must be expected, in general aargktschcrs. (Diplo ma rbcir, Eidgenossische ' Iechnisc he Hochschule, terms, that going from the glacier surface towards the 7:Lirich. Vcrsuehsanstalt fur Wasscrbau, H ydrologic und Glaziologic.l Breche r, H. H. 1969. Surface \ "C locit y mcasurc m (" nts on the Kaskawulsh glacier bed, the dip of the vclocity vector wi ll change slowly Glacier. I II Bu shne ll. V C. a nd R. H. Rag le, ed5. Ire/ldd Rallges R esearch towards the dip of the bed- rock interface. If the dip of the Projed; Sciellliflc Reslllls. / "o/. I. i\ lontrea l, Que., Arctic Institute 0 1" No rth velocity vector a long the surface is less than that along the America: .\'ewYork. American Geographical Society. 127 1+3. basal ice-rock interface, the result will be a vertical flow di­ Casassa, G. 1992. Fo li a tion o n'1ynda ll Glacie r, southern Patagonia. BIIII. Glacier Rn. 10,75 77. \'e rgence and a \'ertical extension. The vertical component Clarkc, G. K. C. 1969. Geophysical measurements o n the K as kawul sh and of the velocity vector will, hence, at fi rst increase with Hubbard Glaciers. III Bushne ll, V C. and R. H. R aglc. eds. Ice/ie/d Ranges depth. If no or negligible basal sliding takes place, the basal Research Projecl; Sciflllijic R esulls. 1'01.1. \ lontrb l. Que. Arctic Institute oC velocity, and in particular the vertical component of the 1\o nh Ameri ca: 'iew York, American Geographical Sori,·ty, 89 106. Collins, I. F. 1970. A slip-line field anah-sis o flh e deformation a t the connu­ basal \'e loeity, must be zero. It follows that the down-flow c ncc of"tll'O glacier stream s.] (;I([ciol., 9 (.')6). 169 191 ve locity component must e\'entually start to decrease from Dc\\"a rr, G. 1970. Seislllic ill\"Cst igation of ire properties and bedrock lOpO­ a finite valu(' towarcl zero as the bed is approached, leading g ra phy at the conlluell("C of the nonh a nd centra l arms 0/' the Kaska­ to a vertical compress ion. This could explain the obsen 'ed w ulsh Glacier. 111 Bushne ll, V C. a nd R. H . R aglc, eds. jce/ield Ranges Research Projecl; Scielllific R w!lls. /01. 2. \Iontrb l. Que., Arctic I nstitute \'ertical compression, but the problem with this explanation o f North America; .\'("w Yo rk, America n G eographical Society. 77 102. is the fact that during the time period over which measure­ Dozier, J. 1970. Channel acljustments in supragb c ia l streams. III L oomis, ments of the vertical strain-rate variation were taken, con­ S. R., j. Dozier and K. L. Ewing, eds. SludiesqfllloljJlwlogl'lI lId .l/ream {(rlioll siderable sliding took place. It is not clear what effect basal 011 ablalill,~ iCI'. i\lontri:a L Que., .\relic Institut(, of.\'orth .\mcriea, 67- 11 7. sliding will in general have on the vertical velocity profile, (AINA Resea rch Pape r 57.) E wing. K. 1970. Supraglacial s tr ('am~ 011 lhe K askawul sh Glacier, Yuko n For the special case of sliding without friction, it can be Te rritory. III Loomis, S. R., J. D ozier a nd K . .J. E\\'ing. ,ds. Sludil's cifll/or­ shown (Gudl11undsson, 1997c ) that the \'ertical \'clocity IJlwlogrllllrl .l/rfOlII arlion 011 ablalillg ire. i\ lontrca l. Que., Arctic Instilut(' 01" component increases all the way down to the bed- rock in­ North :\mcri ea, 11 9 167. (AINA Research Paper 57.) terface, and that as a resu lt, no zone of vertical compression E y lcs. N. and R.j. Rogcrson. 1978. A framework f'o r the im'c,ti gation of nlcdia l moraine (ornlation: Austrrdalsbrec n, Norway, ilnd Bc rc ndon develops. H ence, it is clear that the \'Crtical strain-rate \'ar­ Glacier. British Columbia, Canada . .7 Glaciol., 20 (82).99- 11 3. iation must be expected to depend on the exact form of the FIOlron, A. 1973. Phorogramme trische 1\ lessung \on Glctse herbe\\'egungen basal sliding law, and it must be concluded that, with respect lllil <1ulOmati sch cr 1"-aITlc ra. rerll1e.\,lllng, Ph ologrammetrie, Ilidllfrlerhnik, to the observed vCTt ical strain-rate \'a riation, a no-sli p 1973 (1 1, 15 17 Florro n, .\. 1979. Verschiebungsnl<'ssungen aus Luf"tbilckrn. Eidg. Teek boundary condition is more appropriate than a free-sli p J-jOt/l.Ifhllll', :j"irirl!. Ihwrh.flllIsl. IlilSSerb/{lI, f-I J'dlOl. GI{(::.iol ..\/i ll., 4l. 39 +1·. boundarycondiGon. Flotrnn, A , SI' a nd ,\. F IOlron, Jr. 192+ 97. Jiihrlirhe /J erirhie librr die Elgeb ­ Abrasion depends, among other th ings, on the rate of lIisse clPI' Clelsrherlllf5slIlI,!!,1'1I illl . JllJirag der f.-rqflwerke Oberhalli. Krait wcrke fl ow towards the bed (Gilbert, 1906; H all et, 1981). T he \'ert i­ Oberhasli. Funk, i\ I. . G. H. Cudmundsson and F. H ermann. 1995. Geometry of the g la­ eal cOl1\'ergenee of the basal ice of the confluence area ren­ cier bed of [he l 'nreraargla cie r. Be rnese Alps, Swit zerla nd. ~ ders erosion of the glacier bed through abrasion possible. Glel5chnkd. Gla::.ialgeol .. 30 , 199+, 187 19+. T his could, in principle, lead to enhanced erosion w ith re­ Gilbert. G. 1\.. 1906. Cresccntic gouges on g laciated surfaces. Geol. SOl". Alii. spect to the surrounding areas, but there is no indication of BIIII., 17. 303 :316. Gomez, B. and R.J. Sma ll. 1985. "\lcdia l m o raines oC the Ha ut G lac ier this occurring over the confluence of Lauteraar- and Fin­ c1Arnlla. \',tl a is. Switzerland: debris supph- a nd implications for moraine steraargletsch er, and the glacier bed shows no indications formation . .7 (;Iariol., 31 (109), 303 307. of overdeepened areas (Funk and others, 1994). Guclmundsslln. G. H. 199+ COIl\'Crging glacier floll" a case study: the Unteraarglacier. Eidg. 7erl!. f-Iol"il.l"chllle. ;::iirir/i. / ew((lwlII.f/. // ((Jserhrlll. r{J'f/m/. (;Io::.iol ..\I ill. I:j l. ACKNOWLEDGEMENTS Gudmuncisson, G. H. 1996. Ne\\" obsen 'm ions o f" uplif"t ("\Tllls on Unteraar­ g lc tschcr. [Ahst ra.!.J F()S, 77 (+6), F"II i\lcc ting Supplement, 10 213. Researc h funding was prO\'ided by thc Swiss National Gudlllundsson, G. H. 1997a. Basal flo\\" chara n e rislics ora linea r m edium sliding /'rictionlcss 0\"(,1' sm a ll bedrock undulations. J (:Iariol., 43 (1+31. Scienc e Foundation, grant No. 20-29619.90. A number of 71 79. people assisted in gathering the data prese nted here. Special Gudmunclsson, G. H. 1997b. Basal flo\\" characteristics or a non-linca r fl ow thanks are given to A. Abe-Ouchi, H. Bosc h, K. Fabri, M . sliding frictionless O\'er strong ly undulating b edrock. J Glal"iol., 43 (1+31, L Lit hi, B. Nedela and the late ' V. Schmid. Careful reviews 80- 89. by K . H utter, U. Fisc her and two anonymous reyiewers GudmundssO I1 , G. H. 1997(". Ice delormatio n at the confluence a rea oC t,,'n g lacie rs inn'stigatccl \Vith cOllceptualmap-planc and nowlinc Jlloclcl s . .7 stimu lated many impro\'Cl11ents in the presentation of th e (;Ia riol. 43 11 +51, ,,)37 5-f7. paper. H acfeli, R. 1970. Ch;lIlges in the beh,,\'iour of" the Untnaarglnschcr ill the last 12 .~ )T;m.] GI([ciol. , 9 (561, 195 212. Ha llct, B. 1981. Glacial a brasio n a nd

HlIgi. EJ. 18+2. ('ber dos Jl esell der Cletscher. Stuttgart a ncl Tubingen. J. G. R abiner, 1. R. and B. Gold. 1975. Th eol), alld a/J/Jlicalioll of'digilal signal /)/'OCfS ­ COlla'schcr Verlag. sillg. Englc\\'ood C li ffs, NJ, Prelll ice-Ha l!. Iken. A. , H. Rothlisberger. A. FlOlron a nd 11'. Haeberli. 1983. The uplift of Vere. D. ~1. and 0.1. Be nn. 1989. Structure and debris characteristics of Unteraarg1ctscher at the beginning of the melt season a consequence 1l1cclial l110raines in Jotunheimc1\ Norway: im pli o uions for 1l10rainc of wa tcr slOrage at the beeI> J. Glaciol.. 29(101 ),28-+7. classification . .J Glacial., 35(120).276-280. K aab, A. 1996. Photogrammetrische Analyse zur FrLlherkennung g!ctscher­ lI'agncr. \I'. P. 19G9a. D escription ane! evoluti on of snow a ne! ice fea tures a nd unci perma{j'ostbedingter Na turgefa hren im Hochgebirge. Eidg. Tech. snow surface fo rms o n the KaskaIVu lsh G lacier. III Bushncll. v: C. ane! Hocizschlll,'.

l\I/S received 18 April 1997 and accepted in re visedform 16 June 1997

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