Annal ' ofGl ac iology 2 1 1995 © International G laciologica l Society

Application of inventory data for estirn.ating characteris­tics of and regional clirn.ate-change effects on rn.ountain

glaciers: a pilot study with the European Alps

WILFRI EO HAEBERLl A:,\O M ARTl:\ HO ELZ LE

Laboml01), oJ i-{J,drau/irs, J-{JIdrolog)1 and Glaci%g)', Federal Institute qf T echnology ( ETH) , CH-8092 <linch, Switzerland. and World Glacier ",Iollitoring Service (CEJIS/ U. \'EP, IHP/ [;SESCO . FAGS/ ICSu'. ICSl /IAHS)

ABSTRACT, A parameteri z<ttion sc heme using simple algorithms for unmeasured glaciers is being app li ed to glacier invcnto ry d a ta to es tim ate th e basic glac iolog ica l characteristics o[ the inventori ed ice bodies and simulate potentia l climate-change effects on mountain glaciers, For past a nd potential climate scena rios, glacier cha nges for assumed mass-balance changes a re ca lculated as step functions between steady­state conditions (or lime inlen'a ls that approx im ately correspo nd to the characte ri stic d ynamic res ponse time (a fell' decades) of the g lac iers. In order to test the procedure, a pilot stud y was car ried out in the European Alps w here detai led glac ier im'ento ri es had been compiled aro un,d the mid-1970s, Total g lacier vo lume in the Alps is es ti ma ted at abo u t 130 km .l [or the mid-1970s; strongl y nega til'C mass ba lances are likely to have ca used a loss of about 10- 20% of thi s total I'o lume during the decad e 1980 90. Bac kward calcu lat ion of glac ier-length changes using a mean a nnu a l mass balance 0 1' 0,25 m I\'.e, a I since the end of the " Little Ice Age" around 1850AD gives cons iderab le sca tter but sa tisfacto ry ove ra ll results as compared Il'ith long-term observations, The total loss of Alpine surface ice mass since 1850 can be es tim a ted a t about ha lf th e origina l va lu e, An acceleration of this del 'e lopment, with ann ua l mass losses of around I m a I or more as anti cipated from IPee scenario A for the coming century, co uld eliminate major parts of the presentl y ex isti ng Alpine ice I'olume within decades.

INTRODUCTION

An extens il 'C data base on topographic glacie r para­meters has been built up in regional glac ier in ven tori es (H aebe rli and others, 1989 ). R epe titi on of such glacier im'en to ry wor k is planned a t time interva ls comparable to the cha racteris ti c dynamic response times of mountain

g lacie rs (a fel" decades) , This should help with ana lyz ing changes at a regional sca le and with assess ing th e represe n tat i l 'Cness of con li n uous measu remen ts which can onl y be ca rried out on a few se lected glaciers. In addi tion, g lacier inventory data serve as a statistica l basis for extrapolat ing th e res ult of obsen'at ions o r

mod e l calc ul ations co nce rning indi vidu a l g lac ie rs (O erlemans, 1993, 1994) and to simulate regiona l aspects of past and potential cl im ate-cha nge effect s. T hi s latte r app lication requires the introduction of a

parameteriza tion sc heme using si m pie a lgori th ms for

unmeasured glaciers. A co rresponding sc heme is ex­p la in ed and illustrated with the exam pl e of the European Alps. The procedure described a lso enables p la usibility checks to be ca rri ed ou t on the la rge sampl e of il1\ 'entory d a ta a nd is presentl y being systematica ll y applied whil e loading available d etailed inventori es into the new data ba nk of the W orld G lacier M on ito ring

Sen' ice (W Gl\ IS) (paper in preparation by M. H oelz le and M. Trindler) .

206

PARAMETERIZATION SCHEME

The basis for the parameterization scheme (cr. H oelzle ( 1994) for more detailed disc ussion ) cons ists or measured ilwentory data on the total length (La ) , maximum / minimum a ltitud e (H l1Iax , H lllin ) and to ta l surface area (F ) of the investigated glac ie rs, From th ese basic

para meters, m ean a ltitude (Hm = [Hmax - Hmin]/ 2), vert ical extent (i1H = H lJJax - H min ) a nd average sur­(ace slope (a=aretan[L1H/ Lall arc derived as a first step, The leng th of the central Oowline in the ab latio n area (La) is empiri cally set as 0.5Lo (MLiller, 1988 ) for g lac iers :::;2 km , and as O,75Lo for g laciers > 2 km. The

mean slope of th e ab lat ion area (aa ) is then computed from a rcta n (H l1I - H min ) / La' Average ice depth a long the cent ra l Oowline (hr) is es tim ated from a and a mean basa l shear stress along the centra l f1 0wline (Tt' = jpghrsina, where p is density and 9 is acceleration due to grav ity) which depends in a non -linear way on i1H as a function

of mass tu rnol 'e r (Fig, I ; cr. H aebe rli , 1985; Dri edger and K en nard , 1986) . The shape factor j is chosen as 0.8 for a ll glac iers, I ce thi ckness in th e ab lat ion area (hr.,, ) is derived from Tf and aa and maximum thickness (hlllax ) is I'ery roughly determined a t 2.5h£.a, as estim ated from known ice thickness measurem ents on va ri ous Alpine glac iers (:dull er a nd others, 1976; unpu bli shed ra dio-ec ho sou ndings /hot-water drillings by VA W /ETH ZLirich)

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Haeberli alld Hoel.::/e : :J/J/)/iralioll (if IIll'eIl tOI)' data 10 mOlll1taill glariers

1.8 ,--------------------------,

1.6

1.4

1.2

o

Marilime glaciers in the Alps (dbldh large)

Cb 0 0

o

o o

~ l.0 .. 0.8

06

0.4 o

0.2 0.4 0.6

o o

o

Continental glaciers in the Alps (dbldh small)

0.8 1.0 L2 1.4 1.6

IJH [km]

Fig. 1 . . eJw·age basal shear stress a/oug Ihe cmtra! ./701c/ille I'S altitudilla/ eltmt oJ ( recollstructed la/e­Pleistorelle : ll/JilZf) glaciers ( modified Jrom Haeberli ( 1985)) . T he jJo[l'lIomial./il gil'fS Ihe ./illlrlioll lIsed ill the /Jrfsenl Stll({J' . . J I//(I\il//IIIII mllle of 1.5 bar ( 150 kPa) was aHlIIlwl[or the largest glaciers.

t.s

a nd in ord cr to acco unt 10 1' som e lo ngitudina l \'a ria ti ons in n. A\'eragc thi ckn ess o f th e entire (three-dim cnsiona l) g lac ie r is ass umed to be hF = (7r/4)hr in acco rdan ee with

a scmi- elli p ti c cross-sec ti ona l geo m etry. T o ta l g lac ier

yo lume th en beco m es V = FhF .

:\I ean a ltitud e (Hm) is ta ken as a n a pproxima ti on fo r

equilibrium-lin e a ltitud e ( ELA; cr. Bra ith wa it e a nd ?\Hill e r, 1980 ), a nd th e m ass ba la nce (a nnu a l a bla ti on ) a t th e g lac ie r to n g ue is co mputed as bt = db/ dH (Hm - Hmili ) \\·hcre th e m ass-ba lan ce g radi ent db/ dH recei\'es a \ 'a lue o f O. 75 m\\'.e . per lOOm a nd yea r fo r th e

a blat ion a rea, as a ppea rs quite cha rac te ri stic for the Alps (O e rl em a ns a nd H oogend o rn , 1989; O erl em a ns a nd FOrluin. 1992 ) . D epth- iwe raged m ea n llo \\' \ 'e loc it y a lo ng th e ce ntra l Oo\\' lin e in th e a bl a ti o n a rea is

calcul a ted as ba la nce \·e loc it\· fo r th e lower ha lf of th e

a bla ti on a rea as 'Um.a = [(3bt/4)(La/2)J/hra . For simpli­

ci ty, th e co rres pond ing surface fl o\\' \ 'c1 oc i t y Us." is ass um cd no t to diffe r sig nifi ca ntl y fr o m 'U m .a ; it s co mpo n e nt of ice d e fo rm a ti o n is ca lcul a ted fro m Ud .a = 2ATf li hr/(n + 1) wh ere A is unifo rml y chose n as 0.1 6 a I ba r 3 a nd 11 = 3 to g i\ 'C rea li sti c \'a lu es l Cr.

P a te rso n , 198 1). The co m bined co nside ra ti on of m ass

co nsc l'\ 'a ti on a nd th e ice-flow la \\' would. in principl e, a II O\ \' th e , Iiding \'C locity in th e a bl a ti o n a rea to be es t im a ted as ILb." = U s.a - 1I d.a. Th e \'e loc it y ra ti o in th e a blat ion a rea \\-o ul d th en be d efin ed as Ub.a/U,.a. j n \·iew

of th e limited d a ta basc a nd th e un ce rta inti es il1\'ok ed

with th e [] o \\'-I a \\, pa ra m e ters, ho\\,e\'er , firm conclusions

ca nn o t be ex pec ted fi-o m such d yna mi c cons id era ti ons. G lac ier- leng th cha nges (8L = Lo8b/bt ; c r. P a terso n,

198 1; H aebe rli , 1994) fo r g i\ 'e n di sturba nccs in m ass ba la nce (bb ) a re ca lcula ted \\'ith res pec t to th e cha rac ter­

isti c d yna mi c res ponse time t resp = h max/b l (c f. J 6 ha nn es­

so n a nd o th ers, 1989 ) in th e se nse o f step fun c ti ons

be tween s tead y-s ta te co nditi o ns. Th e reac ti o n tim e be t \\ 'ee n th e onse l o f 8b a nd th e first reac ti o n a t the g lac ier te rminus is es tima ted as t reaC' t = L,Jc. \\'he re c is th e kin em a ti c \\'a \'c \ 'eloc it y (N ye , 1965 ). The a ppl ica ti on

of kin em a ti c wa \'(' th eo ry is es pec ia ll y d eli ca te (L1ibo u tn'

a nd R ey na ud , 198 1) , but th e reac ti on times ca lcul a ted

\\'ith c = ..t u,_" seem to compa re q uite \\ 'C II \\ 'ith o bse l'\ 'Cd ach'a nce pa tt e rn s (i\1OlI er , 1988 ). Th e tim e inten 'a l

bet\\'('( n th e firs t reac ti on a t th e g lac ier terminus a nd

full r es ponse to Db is ca ll ed relaxa ti on tim c (pa per III

pre pa ra ti on b y T.J. H . C hinn ): f re!;" = f r,.,,, - f react .

:'\ea r-surbce th e rm a l regim e ( 10 m tempera ture is d efin cd ri-o m empiri ca l re la ti ons be tw ee n m ean a nnual air . firn a nd ice tempera tures (H ae berli a nd :\lca n, 1985 ) in

th e fo ll O\\' ing \\'a)' : co ld firn is beli e\-ed to exi s t e\'e rY\\'he re

a bo\'e th e 12 C mean a nnua l a ir-tempera turc iso th erm. a nd a blati on a reas a re ex pec ted to be pa rti a ll y co ld \\ 'he re mcan a nnual a ir tempera ture a l th e ELA (H tll ) is below ­+ c. This fir l-o rd er a pproac h co uld be im pro \'ed b>' using

a rela ti o n be t\\' ee n 10 m ice a nd m ca n summ er a ll'

iempera tures (Hooke a nd o th ers, 1983 ).

PRESENT -DA Y GLACIERIZA TION

Th e d a ta for th e Euro pea n !\I ps as used in th e present

stud y a nd cont a ining a total o f 5050 perenni a l surface ice

bodi es \\,(, I'C compil ed fo r th e mid-1 97 0s ,Austri a 1969. Fra nce 196 7 7 1. G erm a ny 1979, Ita ly 1975 84 , Switze r­la nd 1973 ). On\\- 1763 o r th ese ice bodi es 35°/., ) a re g lac ie rs la rge r th'an 0 .2 km 2 with co mpl e tc info rm a tion

anl ila ble a bo ut surface a rea, to ta l length a nd m a ximum

a nd minimum a ltitud e. Th e a bo\'e-ex pla ined pa ra m e ter­

iza ti o n sc hem e is ap pli ed to thi s pa n of th e sample. Th e

rem a ining 3287 ice bodi es (65'10) a re pe renni a l ice pa tches and g lac icre ts slllall rr th a n 0 .2 knl~ and a rc trea ted se pa ra tely.

The to ta l surface a rea of a ll 5050 ill\'C nto ri ed surfacc

ice bod ies is 2909 km~ (H ae bcrli and o th e rs. 1989 ). The

surface a rea of th e 1763 glac ie rs> 0 .2 km 2 is 2533 km 2. o r

88% 0 [' th e to tal surface a rea . The to ta l \ 'o lum e 0 [' th ese g lac iers > 0. 2 km 2 is ca lc ul a ted as 126 km :! . tha t 0 [' th e

3287 g lac iere ts ::;0 .2 km 2 as 2.6 km 3 Th e la tte r \ 'a lue is

g loba ll y es tim a ted b\' taking ha lf (7.5 m ) th e m ea n \'a lue

o f hF \ 15 ± + m J fo r g lacie rs \\ 'ith 0.2 < F < 0.4 km 2. The

o\'e ra ll \ 'o lum e of perenni a l surfil ce ice in th e Alps aro und 1970 is thus a bout 130 km 3 Complete m elting of this ice \'o lume wo uld cause a sea-l e\'C1 ri se 0 [' a bo ut 0 .35 mm. Such a sm a ll va lu e is no t o f g rea t import a nce 10 1' sca -Ic\'C1

rise but sugges ts th e n dn e ra bility to c lim a te cfTects o f

g lac ie rs in co mpa ra bl e hi g h m o unta in a reas \\'ith

prcd omin a ntl y sm all g laciers. Th e d ecad e 1980 90 \\'ith it m ea n a nnua l m ass ba la nce 0[' - 0. 65 m \\·.c . as m eas ured on eight regularl y o bse n 'ed g lac iers in th e A lps (C a rcse r , G ri es . Hinte reis, K esse h\'a nd, Sa int So rlin . Sa renn es,

S ikrc lt a, Sonnbli ck; H ae be rli a nd ;\li.iller , 1988; H ae be rli

a nd H oclz le . 1993 ; c f. H ae berli. 1994) m ay It a \'e broug ht

abo ut a loss in surface ice \ 'o lum e of nea rl y 20 km :; o r

abo ut 10 20% of the to tal \ 'o lume exi sting a ro und 1970. I t is reaso na ble to ass um e th a t th e to ta l \ 'o lum e of pe renni a l Al pi ne su rface ice is nO\\' ( 1994 ) no t mu ch

hi g he r th a n 100 km :;. C ompa ra b ly lo\\' to ta l g lac ier

\'o lum cs m ay ha \'C ex isted a ro und 1950. \0 . a ro und

+000 BP a nd a round 5000 BP; e\'en sm a ll e r ice \'o lum es ca n poss ibl y be a ttributed to th e ea rl>' H o locene, i.e. the tim e pe ri od a ro und 7000 6000 BP \ H ae be rli. 199+ .

Anum bel' o f int erestin g g lacio logical cha racte ri s ti cs

ca n a lso be d eri\ cd \\'ith res pec t to th e ill\ 'es tiga ted

sa mple of Alpin e g lac iers (Fi g. 2 ) . Only 54 13% ) of th e

207 Downloaded from https://www.cambridge.org/core, subject to the Cambridge Core terms of use.

ffaeberfi and Hoelde: AjJjJ/iwlioll I!/ illl'fIIlol)' dala 10 mOlllllaill glaciers

208

300 r---------~~----------_.

a)

200

100

o J.......--=<;:LJ.....L.....r.J..-Ll.-L.j...L.W..k,l....l....D;~ 2000 2500 3000 3500 4000 4500 5000

Hma1.[ma.s,1. 1

350..----------------------------, c)

250

150

A Ih 50

()

300

200

100

o 2000

1600

1200

BOO

400

0 to.

j 2400 2800

Hmlma.s.l .J

b)

k 3200 3600

d)

1000 1500 2000 2500 3000 3500 0 10 20 30 40 50 60 70 BO 90

350

250

150

50

o o

1200

800

400

J IQ 20

Hmin[mll.S.J.)

R 30 40 50

al·,

Urn,a lm/a]

e)

60 70 BO

g)

800 ~--~----~--~----~--~--~----~

j)

o 20 40 60 80 100 120 140

'react lal

I)

o 10 20 30 40 50 60 70 80 90 100 I 10

Lrc lax Lu)

F[1un2)

.------ j) 400 -

300

I-- .------200

L--

.------lOO

L-- J----,

o r-1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

1'[barl

11)

600

400

200

I k 0

0 50 75 lOO 125 150 175 200 225 250 25

700

o

IresplaJ

k)

I ~ o 25 50 15 100 12 5 ISO 175 200 225 250

tresplal

Fig . 2. Frequellc} dislribulioll of ( a) highest glacier elevation H lllax , ( b) meall glarier elevatioll fi" I> (c) Lou'esl glacier elevalioll H ll1in , ( d) gLacier area F, (e)

average s1I1Jace slope Cl' , U) average basal shear slress along Ihe celllral flo w/ille rf, (g) balance veloci{JI in the ablalioll area lL IlI .a alld ( h ) resjJollse lime t,.psp for l/ie glaciers> 0.2 km2 as defilled ill l/ie 1nl.

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Haeber/i alld Hoel::.le: . JjJfJ/i(([tion 0/ ill1'flltOl) ' data to mOllntain glacier.1

1763 g laciers > 0.2 km 2 begin abo"e +000 m a .s. !. a nd. he n ce, delinit e ly h ave p a rt s o f co ld firn in th e ir accumu la ti o n areas. On th e o th er hand , 1323 (75% ) of a ll g lac iers> 0.2 km 2 hal 'e ELAs (m ea n a ltitudes ) ahon"

2800 m a .s. !. , Il" here mean an nual air temperature is

around -+ C. This means that for the most part the

Alpin e g lac iers a re no t s tri c ti , · tempera te but rather po lyt henn a l \V i th more or less extended co ld parts (surface layers) in th eir a b la ti o n areas. \I os t g lac iers (88'10 I ha\ 'e m ea n an nu a l a ir tempe ra tures at the

equilibrium lin e between 2° a nd - 6 C (2500:S Hili :S 3200 ) , indicating tra nsiti o nal climatic conditions as

o pposed to maritime ( > 2 C, 2% ) and contin enta l « Gce, 10% ) types or g lac iers (er. H aeberli , 1983 ). \] o re th a n rour o ut of fil T g lacie rs (83'10) e nd a bolT 2400 m a.s. I. , i.e. ill th e a ltit ud in a l belt where di scontin­

uo us perm afros t reg u larly occ urs. :-l ore th a n 90% o f th e

g laciers> 0.2 km2

h a"e tota l surface a reas sma ller th a n 'J _

10 km- , lengths sho rter than :J km and o,'e ra ll slopes stee per than 10 . This mea ns th a t the sa mple or pn:se ntl y ex is tin g Alpine g lac iers is d o mina ted by sm a ll a nd steep mo u 11 tain g lac ie rs wi th a I'erage th ic kn esses or a fcw tens or

metrcs . About 70% of th ese small mountain g lac ie rs h a,'e

a , 'cragc basal shea r stresses a lo ng th e central nOIl·line

which remain below 1 bar ( 100 kPa ) . Such rath er stat ic ice bodi es, call ed "gl([riers risen'oirs" bl' L1iboutry (un­publi shed ) , rea c t throug h (IT rli ca l) surrace a ltitud e c hanges rath er th a n pronounced (horizo nta l) advance!

re trea t as ca n be typ icall y obsen'ed [o r the m o re d ynami c.

rapidl\' llo\\'ing "glaciers I'OclIalellrs" with hi g he r basa l

shea r stresses ( > I bar, or > 100kP a ) . Calcu lated sur[ace \T loc iti es in the ab lati on a reas oL the small m o untain g lac icrs are typ icall y a LelV tens oC metres. R cs ponse tim es centre around a fel\' decad es and a re Cl strong ly no n- lincar

fun c ti o n o[ s urf~lce slope (Fig. 3 ). This result is m a inl y

rel a ted to th e para m e teriz a tion a ppli ed ill th e present

stud y but cou ld a lso be physica ll y reaso na bl e: wi th slope dccreasing tol\'ards the ho ri ;'.on ta l, th c dille rencc bCtllTc n equi librium-lin e an d terminu s a lti tuclcs ( h e r e : H ili - H min ) and , hence, a bla ti o n a t th e terminus tends

to becom e ze ro a nd the respo nse tim e tend s to beco m e

45

0

40

35

30

;;-

" 25

20

15

10

5 0 20 40 60

o

ind e finit e ly lo ng beca use a non-fl oll' comli tion is being ap proached . On th e o ther ha nd . s lopes increas in g tOIl'a rd s the I'e!'l ica l redu ce maximum thickness to ;'.cra

a nd asy mptoti ca ll y sho rt en respo nse tim es tOIl'ards zero.

I n such cases, mass transler on Sleep to ,'Cnical lI'a lls is b,'

il1'll abilit ies and fa lling of snoll and ice rather than by

steady icc nOli' . R eac ti o n tim e "aries lj'om a fcl\' yea rs to a [ell' d ecades and te nds to be onc-third to t\l'o-thirds oL the responsc tim c, th e hi g he r rracti o n being mo re characte r­is ti c Ja r th e sm a ll er g laciers. De ril'ed relaxation time has a

peak fj'equ e ncy a round 10 years with decreasing prob­

abi liti es for lo nger tim c intel'l'als.

SIMULA TION OF CLIMATE-CHANGE EFFECTS

. \ firs t experiment lI'as run to simula te maximum glac ie r

extent a round 1850.-\]) , th e end o f th e "Little lee Age" in

centra l Euro pe , in o rder to c hec k hOIl' rea list ic the pro posed sc heme is as compa red to obse J'\ 'Cd lo ng- term c h a nges a nd th e n to simul a te c h anges th a t h alT happe ned sin ce . The co nsidered tim e in ten'a l is 120

130 yea rs. I n , ·iell· or th e f'ac t that ,\lpin e glaciers

re m a in ed quit e un changed bC:'tll'ec n 1890 a nd 192 -

(Pa tz elt and A ell en, 1990 ). th e time intcJ'\ 'al since the middl e of th e pas t ce nturl ' spa ns a ho ut tll·ice th e c ha racteri sti c mean respollSe tim e or th e illl 'es ti ga ted sa mplc o[ Alpin e glaciers . Instead or ca lculating t\l'O

subseque nt s teps with increas ing un ce rt a inti es a bo ut the

pa ram eters inl'oh'ed (for insta nce, a blati o n at th e g la c ier

tongue in tim es lac king measurements ) .. one sing le s tep I\'ith a positil'e mass-ba lance (s tep ) change or I m a I wm assumed [o r the entire tim c int c l'\·a l. This procedure corresponds to a calculation \I'ith t\l 'O steps ass ul1ling tll'O

rul l dynami c respo nses fo r in stance . 18.')0 1900 a nd

1930-80 ) to a step c hange in m ass ba lance or 0.3 111 a I

a nd a n al'erage ba la nce oC 0.23111 a I for both pal'lial inte l'l·a ls. The comparison be tween ca lculat ed and m cas ured icngth c ha nges f() r selec ted g lac iers Table I )

shO\I's th a t the difTe re nt se nsiti\ 'iti es o r lo ng-tcrm g lac ier

leng th as a response to uniform m ass-balance (a rci ng ca n

o o o

80

lrcsp raj

100 120 140 160

Fig . 3. Res/Jollse limes t rcsp as OfllllClioll 0/ m'froge .Iurfaa slo/)(' cv /or glacierj IOllger t/tall 2 kill.

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Haeberli and Hoel::./e: AjJjJ/i{(Ltion of im'entol)' data to mOlllltal1l glaciers

Table 1. Jl f easured alld calculated (lllllllla tive leugth challges al/d average mass balances of selected Alpine glaciers sillce 1850 .1D. bLm, measured cumulalille length change, 1850 1970 .1D; bLc, ({Lleulated total length change , /850- 90 alld 1925- 70 with a meall mass balallce of 0.25 m w.e. a I

fo r both jJartial time illlervals : b * . average lIIass balallCf, /850- 90 and 1925 70 as corrected b)' bLm/ bLc for the measured lellgth change

Glacier DLm DLc bL III/bLc km km

AJetsc h 2.5 2.5 1. 00 A rgenti c re 0. 8 0. 9 0.89 Gepa tsch 1.7 1. 6 1. 06 G urg le I' 2.3 1. 9 1. 2 1

Hintereis 2.2 1. 6 1. 38

HLifi 2.6 1. 3 2.00 La ng ta ler 1. 2 1.4 0.86 ~lo rte ra tsch 1.9 1.0 2. 00 O ed en\\'inkel 1.4 0. 9 1. 56

Rhone 2.2 1. 8 1. 22

T o ur l.1 l.l 1.00 Tri ent 1. 2 0.8 1. 50 U pper G rindcl wald 0 .8 0.6 1.33

;-'lea n 1.3 1 S.d . 0.38

be quite \\ 'C' II reprodu ced (c r. , fo r insta nce, U pper G rind elwa ld a nd Aletsch ) a nd that th e chosen mass­ba la nce fo rcing a ppea rs to underes tim a te sli ghtly th e real

e\·olutio n . DiOe rences be tween measured a nd calcul a ted

Q\'era llleng th cha nge for indi yidua l g lac iers, on th e o ther ha nd . ca n be co nsid era bl e a nd a rc ex pl a in ed b y un ce rta inti es in th e simpl e p a ra meteriza ti o n sc heme a pplied. by th e limited d a ta base a\'<lil a bl e for each glacier in in ve ntori es, a nd by \'<lri a ble clim a te/mass­

ba la nce conditi ons a t eac h glac ier. Correc ting th e mass­ba la nce fo rc ing for each g lac ier to fit th e measured leng th cha nge g i\ 'C's a n a \ 'e rage mass ba la nce of 0.33 ± 0. 09 m a 1

<l \ 'e rage (sec ul a r) mass loss for th e sampl e of g lac ie rs considered in T a bl e I. H th e tim e peri od 1850 19 70 is trea ted as one single retreat peri od witho ut consideration

of th e 35 yea rs of sta ti ona ry glaciers. th e a bove ca lcula ted

\'alue reduces to a n ave rage mass loss of 0.2 0. 3 m \\·.e.

a I . The energy required for melting thi s a mo unt or ice during th e tim e inte rn. 1 1850- 19 70 ,\1) is 2- 3 \\' m 2 S uch \'a lu es ro ug hl y co rres po nd to th e obsen 'ed long-term trend of a tmosph eri c \\'a rming a nd could be quite

representa ti ve of (non-pola r?) mo unta in g lac ie rs a ll ove r th e wo rld (O erl ema ns. 1994).

T he ca lculated le ng th c ha nge di v id ed b y tw o relaxa ti on times for th e twO peri ods consid ered g in's charac te ri st ic a \'C rage ra tes o r leng th cha nge during ma rked adva nce/ retrea t peri ods o f a rew tens of meters

per yea r with steep /high-stress glaciers such as Bionn as­sey. T aco nnaz, Bosson , Brel1\'a , Mi age, Lower Grind el­wald a nd Bchoed ere being a mo ng th e mos t ac ti\ 'C ones a nd re la ti\ 'C ly na !.. pl a tea u-like glacie rs such as Care:se r and Sa rsu ra belo nging to the most inert ones. The rotal glacier a rea fo r 1850. \D was ca lcul a ted fo r th e glac icrs

> 0. 2 k m ~ fr 0 m F1 S,iO = 0 .002 + 0.285 L 1850 + 0.219

2 10

b* SO l/ rce fo r bLm m \\·.e . a

0. 25 Aell en ( 198 1) - 0 .22 Blcss ( I 984)

0. 27 H ae berli a nd ~li.ill e r ( 1988 ) - 0. 30 H ae berli a nd ~li.ill e r ( 1988 )

- 0 .35 H ae berli ( 1985) 0 .50 Ae llen (198 1) 0 .22 H ae berli a nd MLill e r ( 1988 )

- 0 .50 \tI a isch ( 1992 ) 0 .39 H ae berli a nd H oelzle ( 1993 )

- 0. 3 1 Aell en ( 198 1)

- 0. 25 Bless (1984) 0. 38 Bless ( 1984) 0 .33 Aellen ( 198 1)

- 0.33 0 .09

( L I8:'0)2 - 0 .004 ( L 1800 )3 , wh ere L l850 is the in fe rred leng th a t th e end or the " Littl e I ce Age" . Th e third­d egree polynomial fit to th e d a ta was chosen in ord er to

avoid nega ti ve a rea values for th e sm a ll es t glacie rs a nd to

optim a ll y reproduce the length /a rea re la ti on for Alctsch , by ra r th e la rges t Alpin e glacier. The so-calcula ted F I13.;o is a t leas t 1. 5 tim es th e a rea ca lcul a ted for th e mid - 1970s but neg lec ts not onl y th e area cha nges lor ice bodi es < 0. 2 km 2 in th e presentl y exi sting in ve ntori es but a lso a ll

ice bodi es th a t complete ly vanished befo re th e mid-1 970s. It is th erefore reasona ble to ass ume th a t a t leas t 35 % of th e glac ieri zed surface a rea ex isting a round 1850 has di sa ppea red. Th e co rrespo nding \'o lum e c ha nge a s es tim a ted by multipl yin g th e m ass -balan ce fo rc ing (0. 25 m a lover the entire tim e inten 'a l of 125 years, as

expl a ined a bQ\'e ) with th e aYerage a rea (F + F 1830 l/2

yields a \'o lum e cha nge o f a t leas t 45- 50 % . After th e m ass losses o r th e d eca de 1980 90, so mewh a t more than ha lf th e vo lume or ice ori g ina ll y existing a round 1850 has pro ba bl y di sa ppea red by now ( 1994).

In a seco nd step, ca lcula tions were mad e wi th a mass­

ba la nce forcing of 0.9 m a 1 during a time inten 'a l o f

50 yea rs a nd sta rtin g from th e conditions or th e mid-1970s . This could m ore o r less co rres pond to th e consequences of IPCC scenario A (business as usua l) till 2025 ;\0 with a n accele ra ti on by a fac tor or 3 4 with

respec t to th e e\'o lutio n since a bo ut 1920 (Kuhn , 1989,

1990). In such a scena ri o, 44 1 sma ll g laciers representing

25% o r th e glaciers > 0 .2 km2 ex istin g in the d e ta il ed Al p in e il1\ 'entori es from the mid-1 9 70s would di sa ppea r because th eir leng th wo uld be reduced to ze ro , th e equilibrium line would ri se a bove th eir hig hes t point a nd ! or th eir maximum thi ckness wo uld be exceed ed by

cumul a ti ve mass losses . In compa ri son with co nditi ons

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Haeberli and Hoel::.le: . .J.jJJJ/ication of illl'enlol), dala 10 lIIolll/lain glaciers

In th e" mid - 1970s, a bout onc-third o r the s urf~l ee a rea and more" th a n hair th e ice yolum e \\'o uld be los t. This m eans that less than ha ir-the surface a rea a nd abou l onc-q uarter

o f' the ice \ 'o lum e co uld be left in the \'ear 2025 from the

Alpin e ice cO\'Cr existing a t th e end of th e "Little Ice Age" . Beca use surface area in the initia l decaci e"s of th e cons idered tim e inten'al is s tili relatively extended , roughl y one"-third of the simul ated \'olume loss hetwee n

th e mid-1970s and the yea r 2025 may a lrea d~' ha\ 'C

occurred since about 1980,

Due to in creas ing un ce rtainti es a nd pron o un ced non ­lin ea riti es such as changing response times with cha nging g lac ier size, e"tc., calcu lations for scenarios o r continued accelerat ion tend encies of the climate and mass-ba lance fo rcing beyond th e ea rl y d ecad es of th e 21 st century ca n

be o rd er-o(~magnitud e estimates on ly, Annual m ass losscs

of 1- 2m a I as must be expected [i-om IPCC: scenari o A

would reduce the surface a rea and \'olull1 e or Alpine g laciers to a fCl\' pe r cent or th e \'a lu es estimated for the "Littl e Ice .\ ge" m ax imum by th e second ha lf ofthe 21 st

century, \\, it h such a de\ 'c\opment, only the larges t and

hi g hes t-reaching Alpine g lac iers co uld p ersist into the

22nd centu ry, a nd these g lac iers would be affected bv

dras ti c cha nges in geometry, DO\\'n-\\'ast ing rath er than aCl i\ 'C re trea t \\ 'ould thereb y proba bl y be the predom i­na nt process ill\·oh 'Cd.

DISCUSSIONS AND CONCLUSIONS

The calcu lat ions and es tim a tions prese" nted In thi s slUd\' build on [our simple geomet ri c paramete rs conta ined in

d e tai led invento ri es, This justifi es the simplicity of the

appl ied a lgo rithms but a lso mea ns [ha t un ce rtainties

i Iwoked ,,·i th t h C' proposed proced ure arC' co nsidera blc,

I n fa ct , th e la rge sca tte r in deri\ 'ed param ete rs such as now \'Clocities, response times, etc .. poinrs to th e" fact that the app li ed param eterization sc heme is more use fu l fo r re lat i\'Cly large g laciers than for sm a ll ice bodies, The large

g lac ie rs, on th e other hand , ha\'(' a predominant inOuen ce

o n O\'Cra llm ass changes a nd , hence, m a ke th e es timates of co rres ponding cha nges pro babl y quite reali stic. TPee scen a ri o A ma y g i\ 'e upper-bound \'a lues co ncerning po tential future e\'o lutions, a nd less dramatic scenarios

a rc possible as \\'e ll , In any case, hO\\'e\ 'er, th e striking

scnsi ti\·i ty or g lacie riza tion in cold mou n [ai n areas ,,·i th

res pect ro atmospheric warming trends clea rl y appea rs. The proposed sc heme needs f'urther im'Cst iga lion and

app li cation. As a next s te p, detailed di sc uss ion and se nsitivity ana lysis \\·ill be ca rri ed out \\'ith respect to

the nlrious assump ti ons and simplificat ions introduced,

es pec ia ll y concern ing ice depth and \'olume ca lcul a tions

as \\ell as es timates of [l 0\\' velocities a nd response cha racteri stics. I n add iti on , adaptation poss ibiliti es of empirica l/ regional a pproach es im'oh-ed (e,g, character­isti c balance g radients, ab lation area leng th ) must be

chec ked to see ,,'he lher th ey ca n be app li ed ro o th er

mountain ranges , It is planned to make similar analyses

for all <wailable detailed g lacier im'entor ies while load ing th em into the new data ba nk and to check the data base in coo pe ration with th e res ponsibl e national correspon­dents o[\\'G ~lS, Th e possibilities are also prese nth' being

in\'estigated of' re trie\'ing add ition a l informat ion on

g lacier dynamics (do\\,n-\\'as ting!retreat, rock /sediment bed s. etc. ) o r h yd ro logy (seasonal run-off \·a riati o ns. e tc .) .

Perhaps the most important possibility is orquantitati\'Cly

inferring a\'erage decadal mass bala nces fo r unmeasurcd

g laciers b\· a nalyzing cUlllul a ti\ 'e leng th cha nge from fi e ld e\'idence (mora ine mapping, sa tellite im agen', aer ia l photography, long-term observa ti ons) . The repetition o f' d e tailed regiona l g lac ier il1\ 'Cntories \\'ou ld th e re by not

onlY rurni sh important info rm a tion on local to regional

ell\'ironmen ta l changes bu t also pro\'ide th e basis for

e\'a luat ing sce na rios of g loba l warllllng .

ACKNOWLEDGEMENTS

The prese nt study ,,'as carried out as part of the data

ana lysis " 'ork for \\'C7\IS , \\'ith spec ia l grants from

l):\TEP /GE.\lS through Project :'-010, FP /9 101-8 7-62 (2896 ) Rn'. 7 a nd FAGS/ leSt...: , and as pan of th e S\\iss :\ ationa l R esearch Programme on Clim a te Change

and i\"alUral Catastrophes through Project ~o, +03 1-

3+232 with fund s frolll the S"'iss National Scien ce

Foundation, Special thank s arc du e to Professor

\ ' ischer, Direc tor 0[' the Laboratories of H\'drauli cs, H ydrolog\' and Glacio logy \ ':\ \\' ) at ETH Zurich , lo r his continucd intere"st and encourage m ent. :-'1. :\e ll en, H. Gudmundsson, Andreas K aab and D, \ 'o ncl er !'IHihll at

\ 'f\ \\. a nd ~l. Kuhn , !\I. !\leier, C, O strem and V. Popo\'llin as co nsultants to \\'G\lS c riti ca ll \' rea d th e

manuscript.

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