JOllrnal qfGlaciolog)" Vo!. 46, No. 152, 2000

Sensitivity of m.ass balance of five Swiss glaciers to tem.perature changes assessed by tuning a degree-day m.odel

ROGER]' BRAITHWAITE, Yu ZI-IANG

School qfGeogmjJh)i, UniveTsil» q/iIlanchester, iIlallchester jlIl3 9PL, Ellgland

ABSTRACT. A degree-day model is used to assess the sensitivity of the mass balance of fiv e Swi ss g laciers to tem p erature changes. The model uses temperat ure data ex­trapolated from nearby climate stations, and is tuned by varyi ng precipitation to make Ih(' model fit the observed distribution of mass balance with a ltitude. Once the model is tuned, the effec t of temperature change is simulated by recalculating the mass balance with the same parameters as before, but with a temperature increase of 1°C thro ughout the year. The largest mass-ba la nce changes, im'olYing increased abla ti on of > Im w.e. a 1oC I, occur a t the snout, lVith a progressi\ 'c1 y smaller increase lVi th a ltitude. T he area-aver­aged sensiti\' ities for the fi ve glaciers are - 0.7 to - 0.9 m w.e. ale I. If annua l prec ipitation a lso increased by 20% it would panly offset the effect of' the I QC hig her temperatures but cou ld not compensate [or it.

INTRODUCTION

In thi s paper wc est imate the senSItI\'lt y of g lac ier mass balance to te mperature changes using a deg ree-day mode\. The model is appli ed to five Swiss glaciers (Fig. I) for IVhich detailed mass-ba lance data arc ava il able. Wc did this wo rk as a pilol stud y for a new assess ment of world sea-level ri se from increased melting of g lac iers, following up earlier 1V0rk by ~Ieier (1984), Oerlemans and .Fortuin (1992) and Kuhn (1993). Alpine g lac iers are LOO small to have any direct effect on wo rld sea Icvel, but in the present paper wc desc ri be a simple me th odology and tes t it o n some lVell-documented glac iers; we will apply it late r to larger but less known ice masses.

The prese11l study uses the mass balances of five Swiss glaciers tha t ha\'e been measured over a se ries of years by sc ient ists [rom th e Swiss rcderal Institute of 1cchnology (ETH ) in ZLlrich, i.e. Griesglelscher (1961- 95), Limmern­glet scher (194-7 85), Platta lvagletscher (194-7- 85), Rhone­gletscher (1979- 83) a nd Sil\Tettagletscher (1959 92). These da ta refer to the direct glac iologica l method whereby the mass

Fig. 1. Loea/ions q/ Swiss glacieTS with long mass-balance records, together with nearb)1 high-elevation weather stations.

balance is meas ured as a fu nct ion ofa ltilude by a combina ti on of ablati on Sla kes a nd accumulat ion pits. Mass-balance data rrom two other Swiss glaciers arc not used because they do not g ive the mass-ba lance \'s alti tude rela ti on: Alerschgletscher where the hydrological and "index" stake met hods are used , and Clar idenfirn where the "index" sta ke method is used . Da ta ror the fi ve g lac iers a rc summarized in the publications of the Permanent Sel'\· ice on the Fluctuations of Glaciers (K asser, 1967, 1973; ~li.iller, 1977) and the World Glacier ~,Ioni ­

toring Sen'ice ( Haeberl i, 1985; H aeberli and Mi.i ller, 1988; H aeberli and Hoe lzlc, 1993). The most rece lll balance a ltitude data for Griesgletscher a rc gi\ 'Cn by Funk and others (1997). The most deta iled mass-balance study, including separate measurements of winter a nd summer balances, is for Rhone­g le tscher (Funk, 1985), while only a nnua l balances are a\'ail­able for the other g lac iers.

For glaciologiea l purposes, the best climate stat ions are a t relat ively high elevat ions, where essenti a ll y the same climatic condi tions a rc sam pled as those at the glaciers. tor present pu rposes, the stations at G iHsch ob Andermall and WeissO uh­joch (Table I; Fig. I) a rc relati\'ely close to the o\ 'e glaciers, and theirdata arc used in the present slud y. The data for these a nd other Swiss stations arc gi\'en in annual publications (Annalell der Sc/iwei;;:erisc/zeIl JIe/eorologisc/ien <en/m/al1Stal!) from the Swiss l-.leteoro logica l OOicc in Zurich. Clim ate obscr-

]{,ble I. Lo[([/ions q/Iive Swiss glaciers with mass-balance records. together with locations oItwo high-£yillg clima/e stations

C/arifl Lal. Long. (.'fill/alr .llalioll Lal. LOllp._ . lIl illlrir

\ .\1 ) (E ) 1:"\ ) (E ) 111 a.s. 1.

Gries Hi 26' 8 20' Giil srh ob Andcrm all lti 39' B 37' 2287 Lillllllcrn 16 ·f9' 8 59' Giil srh ob .\ ndermall ·I(i 39' B 37' 2287 Plallah-a 16 .jO' 859' GllIsrh ob .\ndermall Hi 39' 8 37' 2287 Rhone 16 37' 824' GllI sch ob .\ ndermall I(i 39' 8 37' 2287 SikrcI la +6 51' 1005' \ \ 'ci,s llul~nch ·I(i 50' 949' 2690

7

J ournal qfGlaciology

\'ations have also been made for more than a cenLury a t Santis at 2500 m a.s.l. j LIst to the northeast of the study a rea (Fig. I).

The simplest, and possibly most obyiou , way to link mass­balance data to climate is by correlation of m ass-balance measurements with climate data. For example, Liestol (1967), Martin (1975), Braithwaite (1977), Laumann and Tvede (1989), Chen and Funk (1990) and Mliller-Lemans and others (1995) have all ca lcul ated multiplr rrgrrssion models for m ean spe­cific mass-ba lance data in terms of summer mean tempera­ture and annua l precipitation a t some suitable nearby climate stati on. According to this approach, the sensitivity of the mass balance to temperature change would be represented by the temperature coefli cient in the regression equati on. Although we prefer to calculate the mass-balance sensitivit y with the degree-day model, we first calculate multiple regres­sion models so that we can compa re the two approaches.

REGRESSION MODELS

The first problem o[ the regression approach is tha t it is di f­fi cult to presc ribe the length o[ summer [or tempera ture averages, or the choice of hydrological year fo r the annual precipita tion. This point is illustrated by correla ting the mean specific m ass balance of each glacier with m ean tem­peratures fo r differenL periods, i.c. T7 fOl'july temperatures only, T7- 8 fo r the july- August average, n - 8 [or june­August, T6- 9 forjune- September, T5- 9 for May- September a nd T5- 1O fo r M ay- O ctober.

There a re onl y 3 years of da ta fo r Rhonegletschcr, so no regression models a re calculated [or that glacieL The high­est mrrrlations [or the other four glaciers (Table 2) appea r [or T6- 8, suggesting thatthejune-August period (92 d ays) is the best choice for the summer p eriod for the whole glacier. This seems a little too short, however. l;or example, the equilibrium-line a ltitude (ELA) is genera ll y r egarded as the most representati\'e altitude on the glacier (Ohmura a nd others, 1992), a nd extrapola tion of climate-sta tion tem­peratures to the ELAs of the [o ur glaciers sugges ts a longer melting season a t this altitude: from 11 2 days at Gri esglet­scher to lLP d ays at Si lvrettagle tscher. There is a lso a hint in Table 2 of a secondary maximum correlation coelIicient for mass balance and temperature for May- September (153 days ), but thi s seems much too long a period to repre­sent the melting season at the ELA.

The mean pecific mass ba lances were also correlated with annual precipitat ion for different choices of hydrological year: PS- 7 for the total precipita tion from August in one cal­endar year tojuly in the following year, P9- 8 for September­August, PlO- 9 for O ctober-September and P ll - lO for Novem­ber-O ctober. The correlations between mass balance and annual precipita tion (l able 3) a rc genera ll y weaker than

8

Table 2. Correlations belween mean sjJecijic mass balance and SlImlller mean temperatllre, assuming variolls /eugths ojsllmmer

Glacier . \ . T, T, ~ T6 - h TG- 9 T5 - 9 To- Ill

C ri es 33 -0.-1 3 0.58 0.70 - 0.66 0.70 - 059 Lilnmcrn 32 -0.52 - 0.60 - 0.72 - 0.57 0.64 - 0.47 Plattah-a 32 - 0.42 - 0.51 0.67 - U.51 - 0.61 O . .J.5 Rhone 4 Sih-rclla 34 -0.62 - 0.65 0.71 - 0.55 0.58 0.51

Mean -0.50 059 -0.70 0.57 0.63 - 0.51

Table 3. ConeLalions belween mean sjJecific mass balance and annuaijmcijJitationjor varioZls choices qf "ydroLogicaiyear

Glacier \~ P~-, [h- o PIO- 9 P11 - 1O

Cries 33 0.45 0.49 0.52 0.51 LinlJ11Crn 31 0.59 0.63 0.58 0.52 Platla lvag 31 0.62 0.65 0.61 055 Rhone 4 Silnclla 34 0.37 0.40 0.39 0.35

1\1can 0.51 0.5 ~ 0.53 0.48

those for temperature. There is a very slight max imum for correlati ons between mass balance and P9- 8, but other choices of hydrological year cannot be precluded.

The patterns o[ correlati ons inTables 2 and 3 sugges t the following multiple r egression model:

Q = a + {3T 6- 8 + , P 9- 8 , (1)

where Q is the mean sp ecific balance of the glacier, Cl' is the inte rcept in the multiple regression equ ation and (3 a nd , are regression coeffi cients for summer temperature Uune­August) and annua l precipitation (September- August), re­spect ively. The intercept and regress ion coefficients in Equa­tion (I) are readily de termined for a m a trix of mass-ba la nce, temperature and precipitation data using a commercia l p er­sonal computer data package.

MASS BALANCE AND DEGREE-DAY MODEL

The model used here is based on that developed by Braithwaite (1977, 1980, 1985) and used by Braithwaite and Thomsen (1989). The earli er model a ttempted to ta ke ac­count of the refreezing of meltwater a nd rainfall in subpola r glaciers, which is assumed to be neglig ible for the tempera te glac iers considered in thi s paper.

The mass bala nce of the glacier is characteri zed by observed mass-balance values at regul a r altitude interva ls on the glacier, i. e. 100 m intervals. The observed bala nce a t the jth altitude is bj , a nd the co rresponding mean specific ba la nce for the whole g lacier is Q defined by:

j=J

!z = (1/ 5) I>.h, (2) j= !

where Sj is the area of the jth altitude band and 5 is the' to tal a rea o[ the glacier. The co rresponding modelled balances a re b/ and Il, respec ti vely. The modelled balance at jth a lti­tude is given by:

b/ = c/ - a/, (3)

where c/ and a/ a re the annual accumulation and a nnual ablation at the .ith a ltitude in the model.

The annual ablation a* is generall y m ade up of a sum of ice ablati on ai* and snow abl ation as *, a nd is calcula ted by the deg ree-day model (Braithwaite a nd Olcsen, 1989):

a/ = kiPDD j + ksPDDs, (4)

where PDD j and PDDs a re the annua l pos itive degree-day sums (sum of positive a ir temperatures measured a t screen height above the g lacier ) at the altitude in question [or the periods of ice melt a nd snowmelt, respectively. The par­a meters kj and ks a re the degree-day factors for ice m elt a nd snowmelt. (To avoid a cluttered no tation, the subsc ript .i is implicit for PDD variables.)

Brailhwaite al/d -<:/wng: Sensitivity qfglacier mass balance 10 tem/Jeralllre changes

The degree-day model has alread y been used to ca l­cul a te the sea-l evel rise from the increased melting of the Greenland ice shee t (Huybrecht s and o thers, 1991) and can be a pplied to other glacie r a reas if the appropriate k values are known. There is a mple evidence from both fieldwork and m odelling studies that snowmelt gene ra ll y has a lower degree-day fac tor than ice melt, but there is otherwise no evidence of a ny sing le se t of universa l factors that can be applied to all situati ons. A summary of positive degree-day factors from the lit erature is gi\'en in Ta ble 4, together with values fo r ice ablation on Griesgle tscher (at 2510 a nd 2560 m a .s. l.) meas ured by the authors inJuly- August 1996 and Aug ust 1997.

The reasons fo r the different deg ree-d ay fac tors in Table 4- a rc not immediately obvious. The three highest values in Table 4- fo r Spitsbergen a nd Green land refl ec t rather cold low-abla ti o n situati ons where higher degree-day factors may be expected from energy-ba la nce consideratio ns (Braithwaite, 1995b). The g reater a ltitude of Griesgletscher compa red with the Norvvegian and Greenl a nd glaciers in Table 4 wou ld sugges t that Griesgle tscher o ught to have lower turbulelll Duxes, a nd therefore a lower degree-day factor fo r ice (Bra ithwaite, 1995a ), in agreement with, for exampl e, K asser (1959), but thi s is contradic ted by the field data.

Table 4. Posilil'e degree -dcl)'filclors at variolls localiolls. ['lIits are 111111 d / c(,. I

Irr SIlOll.:

+ .. 1 5.0 7.0 18.6 13.8 6.3

5.5 .J . .J ±23

4.5 6.3 ± 1.0 :20.1 22.:2 6.0 :i.O

7.7 3.7

6.~ ++

7.3 2.8

6.0 1 .. 1

.J.5 +.0

.J.5 :~ .. 'i

8. 1 2.9 8.3 3.7

6.9 7. 1

5.9 9.8

62 3R

8.3 lH

6.3 +.1

Loca/ion SOl/rre

\\c i ssnlll~och . Swilzerland Z ingg 1951 \ 'a rioLls Swiss g lac iers Kasscr 1959 1 [(; IC ' Camp IV, GnTnland Amhach \1963, 1988) Spitshcrgcn Schytt 196+ Sl. SlIpphcllebrccn. :\nrll"ay Orhcim 1970 (;r. .\ IClschglctscher. S"'itzcrland Lang and ot hcrs 1977 \ 'a ri ous g lac iers, 7\or\\"ay BrC1 ith\\"ail(, 1977) \\'ciss flllhj och, Switzerland De Qucn 'a in (1979) .\ relic Canada Bra ith\l'aitc 1981 G I:\I Ex t prori le. \\'cst Green lancl Van de \\'a l 1992 i'j·<1 nz.JoscfGlacicr. :\c\\' Zea land \ \ '00 and Fitzha rri s

(1992) Sit llUiikllll, lu land J 6 han ll l'sson and

others 1993 :"Jigarcisbrcc Il , ~onray j hhannessoll and

others (1993) Qalllal1~irsSllp scnnia, \ , res t .J6ha nn rsson and Green la nd o thers 1993

AII'llbn'cll. '101'\1''''' L a UI11ann Cllld Rcch (1993)

~igilrdsbrl'('n. :'\Jor\vay I .aumann and Reeh 1993

Hell"lugubn'C'tl. :\or\\'ay La lllll ann and Rcch (1993)

.\Iordboglctscher, \\'e<t Green land Bra ithwaitc (1995 b ) QamamirssLlp scrmia. \\ '(':-.t Brailh\\'aitl' 199.'i b ) Greenland Patagoni<l, Ar~(, lltin a 'Ia kclIch i and others

(1996) :\onh G reenl a nd Bra ithwait(, and o ti1ns

1998 Glacier de Sarennes. France \ ' inccn t a nd \ '"l lon

(1997) Gr icsglc tschcr, Swit zerland This study SlUrglar i IT n. Sweden Hock 1999

• Exped ition g;laciologiquc inlcrll ll lionale i-HI G rol' llia nci.

t Green la nd k e :-Ia rgin [xperiml'nt Lni\Trsities or l 't rccht a ncl Amstcrdam .

The m odelled balance is then given by:

b/ = c/ - kjPDDj - ksPDDj - k,PDDs' (5)

The deg ree-da y sum for the snowmelt per iod PDDs IS

c/ / k" so the degree-day sum for the ice-melt period IS

gi\'Cn by:

PDDj = PDD - c/ j ks PDD > c*jk ) s (6a)

and

PDDj = 0 (6b)

where PDD is the annua l positive degree-day tota l equal to PDDj + PDDs. Equation (6a ) appli es to the a bla ti o n area, and Equation (6b) to the accumul ati on area.

Snow acc umulation a t any particul a r a ltitude is est i­mated fo r each momh from monthly mean temperature and m011lhly precipitati on by ass uming that precipitat ion is split be tween rain and snow according to the probability that air temperatures within the month li e above or below O°e. This probability is estima ted from monthl y m ean tem­perature (Fi g. 2) by assuming th at temperatures within the month a re di stributed according to the norm a l di stribution with sta nd a t'd deviation (J = 4°e (Brailhwaite, 1985). The estimation of acc umula ti on here implicitl y ass umes that (I) precipitati o n fall s as snow if a i I' temperature is below O°C, a nd (2) the probability of precipita tion occ urring is inde­pendent of temperature, Neither of these ass umptio ns is ex­ac tl y correc t, but they may compensate (e.g. snow often falls when surface temperat ures are above the freez ing point, but precipita ti o n in the Alps also generall y occurs in the colder part of a summer month ).

Cl c 'N Q)

~ '0 .~ .D co .D 0

ci::

1.0

0,8

0.6

0.4

0.2

0 -10 -5 0 5

Monthly mean temperature (DC)

Fig. 2. Probabili[J' qf Jree;::. ing vs mOll lh0' mean leill/Jeralllre assuming tizal lellljJeralllTes are 1l0nllaL£)' dislributed withill Ihe month, wilh (J = 4 C

10

Rain in the model is ass umed to run off the g lacirr a nd not to contribut e to the mass ba la nce, and the a nnua l sno\\' accumula ti o n c/ in the model is found by summing the ca l­cul ated acc umul ati on for each m onth.

The degree-day to tal is ca lcul a ted for each month from the monthl y mean temperature according to the Braithwaite (1985) model which assumes that temperat ures arc norm a ll y di stribut ed within the month. Annual degree­day total is th en fo und by summing the monthl y tota ls, a nd the mass balance is obta ined from Equations (5), (6a) and (6b) using the a ppropria te deg ree-day factors. For cxample, degree-day factors of8 a nd 4.5 mm d I cC t a re used for ice a nd snow a bla ti on, respec tivel y, in Figure 3. The former is

9

J ournal rifGlaciology

3

Ice Cl> ~ 2 E c: o ~ .0 ctI

.r::; -c: o

::E

1

o~------~~~------------------

-12~------,------,-------,------~

-10 -5 o 5 Monthly mean temperature (QC)

Fig. 3. J\Jonthly ablationJor snow and ice vs monthly mean temperatllres assuming that temperatures are normally dis­tributed l1 ,ithin tize monliz, witiz (J" = 4°C. Degree-da),filcton fo r ice alld snow are taken to be 8.0 and 4.5111111 d ' oC " re­sjJective0'·

10

close to that found [or ice in Greenland (Braithwaite a nd Olesen, 1989) and on Griesgletscher, whil e the latter is re­ported [or seasona l snow in Switze rla nd (Zingg, 1951; D e Q uervain, 1979). Vlhenever other va lues o[ the degree-day [ac to r for ice were used in the present study, the same ra tio of snow to iee fac tors, i.e. 4.5/8.0 = 0.6, was maintained .

The month ly mean a ir temperatures for the acc umu­lati on and ablation calculations a re estimated at each a lti­tude by extrapola ting fi·om a suitable weather sta tion below the glac ier using a standa rd lapse rate (e.g. 0.006-0.008°e m I).

MODEL TUNING

As the annual precipita ti on for each glacier is not well known, precipitatio n is treated as a tuning va ri able in the model and vari ed to m ake the model fit the observed da ta . T he time di stribution of precipita ti on over the glac ier is ass umed to be the same as at the cl ima te stati on, although pa r ti tion bet ween ra i n a nd snow var ies accordi ng to tem­pera ture. For Gri esgletscher it is sufficient to use the same precipitati on for all a ltitudes, although the vertical lapse o[ temperature ensures a n increase of accumu lati on with a lti­tude.

At the beginning of the study, which sta rted with Gries­gle tsch e l~ the tempera ture lapse rate a nd degree-day factor [or ice melt were also rega rded as uncertain, and model cal­cul a tions were made fo r a range of values. In all , 96 different runs of the model were made [or threc values of lapse rate (0.006- 0.008°e m \ two values of degree-day facto r (8 or 9 mm d 1oC I) and 16 values of precipitation (1.0-2.5 m w.e. a I in intervals of 0.1 m w.e. a- I). The accuracy o[ any model run is expressed by the erro r f bet ween mean spe­ci fi c values of modelled balance 1;/ a nd obse rved balance Q.

j=J

e = b' - b = (l / S )"'"' 8 (b * - b ). (7) - - - ~ J.7 J ) = 1

For m any o[ the m odel runs, there is little resembla nce be tween the modelled a nd observed m ass ba lance, but a

10

1.0 Gries~letschler

«J 0.5 . :> Q)

~ .

E-.... 0 g Cl)

Qi -g -0.5 ::E •

-1.0 I I I

0 20 40 60 80 100 Model-run number

Degree-day factor (mm d·' ·C·' ) 8.0 l 9.0 .

. ., Lapse rate ( Cm)

1--0 . 006"':'-0 .007rO.008tO. 006T,O . 007~ :.....0 .008 ...

Precipitation (m w.e. a ) 1.0-2.5 1.0 - 2 .5 1.0-2.5 1.0-2.5 1.0-2.5 1.0 - 2.5

o 20 40 60 80 100 Model-run number

Fig. 4. " l odel errors alld asslllllptiollsJor 96 nllls if the degree­da)1 modelJor GriesgletscizeJ:

number o[ runs appear to give a reasonable fi t between model and d ata. For example, the model error in Figure 4-is small [or a number o[ d ifferent combi nations of the model variables. This shows tha t tuned models are not unique. In the present a pproach, increased precipitati on can usually be offset by increasing the d egree-day [ac to r to mel t more snow, or by reducing the lapse rate to give higher tempera­ture (and ablation) at the altitude in question. Presumabl y, more sophisticated models like the energy-ba la nce model o[ Oerl emans and FOI'w in (1992) will also suffer rrom this problem of non-uniqueness.

From a visual examina ti on o[ the ba la nce- a ltitude rela­tions for the different model runs, the res ults o[ model run 26 appear to g ive the best ove ra ll agreemcnt be twee n model and data [o r Griesglc tscher. The parameters fo r thi s model are annual precipitati on = 1.9 m w.c. a I, temperatu re lapse rate = 0.007°e m I a nd degrec-day fac LOr [or ire = 8.0 mm d 1oC- I, which a re a ll plausible values. H owever, it is clear from Figure 5 that the model cannot exactly repro­duce the observcd da ta, which show a distinct "kink" between about 2950 and 3150 m a.s.l. Presumably thi s is caused by a local precipita tion anomaly. The results o[ model 92 a re also sholV n in Fig ure 5, to illustrate the fact that some m odels can fit the d a ta ve ry we ll in one altitude range (near the snout in the present case) whi lst deviating greatly elsewhere (in the accumulati on a rea).

The tuning is repeated in a simil ar way [or the other rour Swiss g laciers: Limmerngletscher, Pla ttalvagletscher, Rhonegletscher and Si lvrettaglctscher. \ Ve became confi­dent eno ugh to presc ribe the lapse rate and degree-day [ac­tor for ice, with values of 0.007°e m I and 8.0 mm d 1oC I, respectively, rathcr than treat them as pa ra m eters. For the first three g lac iers it was a lso found necessar y to va ry pre-

Brailhwaile and <hang: Sensilivit)1 qfglacier mass balance 10 lem/Jeralure changes

2

Griesgletscher

CD ~ 0 E ~

~ -1 c 1\1 1\1 .0 -2 <Jl <Jl 1\1

~ -3

-- Observed . ... . .. Model (run 26)

--- Model (run 92)

-4~------.------.------'-------'------'

2400 2600 2800 3000 3200 3400 Altitude (m a.s.l.)

Fig. 5. Observed and modelled mass balances vs aftill/dejar Griesgfelscllfl:

cipita ti o n with altitude to fit the bala nce- a ltitude models to da ta . to r Limmerng letscher the modelling indicated pa r­ticula rl y heavy acc umul a tion U II the sno ut, whil e Rhonegle­tscher needs a strong precip it a ti on increase with altitude to re produce its \'er tical m ass-balance cun'e. In the case o f Rhonegletscher, th e m odelled acc umul a ti on of 2.09 m w.e. a 1 can be compared with the measured winte r bala nce of 1.89 m \N.e . a 1 for the 4 yea rs of reco rd. In the nature of things, a nnual acc umu la tion (whole year ) must be some­wha t hig her than winter balance (net ba la nce for pa rt o f the yea r), so the modell ed a nd obsen 'ed d a ta a re in reason­able agreemen t.

Th e m odel led a nd observed averages fo r mea n specific bala nce a re give n inTl bl e 5 for the fi ve glaciers. The per iods of record a rc incomple te in a couple o f cases because ba la nce- a ltit ude da ta could not be fo und fo r a ll yea rs. In a ll cases, however, the m odel uses tempel-a ture data for the sa me peri od as covered by the mass-bala nce d ata.) The tun­ing process natura ll y involves reducing the error betwcen model a nd data, but over-t uning was avoided . Fo r example, model run 26 was judged to give the bes t m'erall agreement with obse rved altitude distri buti on o f m ass ba lance for C ri esgle tscher, a lthoug h it did not give the lowest error fo r mean sp ec i fi c balance.

EFFECT OF TEMPERATURE CHANGE

Once thc mass-ba lance m odel has been sati sfaetor ily tuned, the effec t of temperature cha nge is simul a ted by recalc ul a t­ing the m ass bala nce w ith the same pa ra meters as before,

Table .5. (;olll/JarisOIl o/modelled and obsenw/ mean s/Jecijir bala/lce/or/h'e Swiss glaciers. Figures ([re ([vemgesjarlhe gi1'et7 /Jeriods

(;Ia ripr Period . \ /od"I/,,1 Ob.>l' I"I'('(1 Error

111W. (' . a IllW.C . a III \\.C. a

(;ries 1961 90 OJ I 0.38 +0.07 i j lll1l1lTI1 1976 8:; O.Of 0.02 -om Plallalva 197(j fl5 +O.2B +0.28 0.00 Rholll' 1980 82 +0.20 +0.28 D.OO Sil \T('l la 1960 90 +0.07 +0.08 (1.01

1\1

CD

~ E Q) () c 1\1 (ij .0 <Jl <Jl 1\1 ~

2

Griesgletscher

0

-1

-2

-3

--- Observed .... ... Model (run 26)

--- Model (+ PC)

-4~~----.------.-------.------.-----~

2400 2600 2800 3000 3200 3400 Altitude (m a.s.l.)

Fig. 6. M odeLLed lIlass baLanceJor Griesglelscherfor jJreselZ1 climale andjor a + I C tem/Jemtllre rise.

but with a cha nged tempera ture. In the present paper we a rc onl y conce rned with a un ifo rm cha nge of I QC through­out the yea r. Th is is purely a n ill ustration, a nd different tem­perature cha nges can easil y be a pplied to different months when plausibl e climate-cha nge scenarios becom e available for the Swiss A lps.

T he effec t o f a I QC tempera ture cha nge o n the mass ba lance ofCri esglctsc her is illustra ted in Figure 6 fo r model run 26. It is no tewo rthy that the la rgest change, involv ing a n increased a b la ti on of > I m w.e. a 1, occ urs a t the snout, with a progress ively sma ll er increase with g reater a ltitude on C ri esgle tsche r, in agreem ent with Oerlem a ns a nd H oo­gendoorn (1989), j 6hannesso n a nd others (1993) a nd Lau­mann a nd R eeh (1993). There a rc probably two reasons for this: (I) \"a ri a t io ns in ablati o n increase with the m ag nitude of the abl a ti o n itse lf, a nd (2) snow ablati on, with a lower de­g ree-day fac tor tha n ice abla ti o n, becomes mo re common with increas ing a ltitude. The first point is ill ustra ted by the abla ti on cunTS in Figure 3 whe re the ablati on temperature gradients increase as abla tion increases.

The ove ra ll cha nge in the m ass ba la nce ofCr iesg le tseher as a result o f the increased tempe rature, i.e. the sensiti vit y of the mean spec ific mass ba la nce to temperature c ha nge, is - 0.69 m w.e. a 1 C 1 for model run 26. Thi s represents a n a rea a\Trage o f" th e ba la nce cha nges at different a lt itudes. The same procedure ca n a lso be a ppl ir cl to the o ther model ru ns that g ive a reasonable fi t to the data (e.g. the II cases in Figure 4 whe re the model er ror is less than ± O.lm w.e. a 1,

a nd a range o f sensiti viti es results. The sensiti vity is strongly correlated w ith the a nnua l prec ipitati on (Fig. 7), in agree­ment with Oerlem a ns and Fo rtuin (1992) who proposed a n explicit fun cti o nal rclation be tvveen mass-ba la nce sensit iv­it y and precipita t io n. A more obvious expla na tio n is that where there is high prec ipita ti o n there is also high a bla ti on a nd therefo re g reater negative sensiti\·it y.

The range o f sensiti\'iti es in Fig ure 7 casts a new I ight on the problem o f uniqueness fo r tuned models. [n this case, wc have a numbe r o f"m odel runs w ith a similarl y sm a ll error, as shown in Fig ure 4, a nd it may seem un importa nt which onc we choose, but t hey do have differelll se nsiti vit ies.

The m ass-ba la nce sensiti vit ies calcula trd fo r the fi ve glac iers by the deg ree-day m odel a re considera bly la rge r tha n those [o r the regress ion m odel (Table 6). This m ay be pa rt ly a sta ti sti ca l a rtefact, i. e. regression models "sm ooth"

11

Journal qfGlaciolog)1

-0 .5

-"0 -0 .6

°

Q) -0 .7 ~ E

~ -0 .8 '> :E <Jl C

~ -0.9

Grlesgletscher

-1.0 +---,---r-- ,---,-----r---,

1.4 1.6 1.8 2.0 2 .2 2.4 2.6 Assumed annual precipitation (m w.e. a·1

)

Fig. 7 Sensitivity vs assllmed annual fmcipitationfor Gries­gl etsc/m:

the processes that they purport to descr ibe, but it m ay a lso be because the degree-day model is phys ica lly more realis­tic. For example, in the degree-d ay model, higher tempe ra­ture will ex plicitly reduce the model acc umul a tio n (by reducing the proportion of precipita ti on falling as snow ) even if the prec ipitati on remains the same, while thi s e ffect can only be implicit, a t best, in the temperature coeffi c ient in the mu ltiple regression model. Also, the regression m odel cannot distinguish b etween ice- a nd snowmelting (Vincent a nd Va llon, 1997).

Tclble 6. Changes in mass balance iffive Swiss glaciers due to (l

rc rise in temperature, estimated by two different models

Gtarin

Gries Lil11111ern Pl atlaka Rhone Silvretta

Mean

::\ot enough data.

Regressioll lIlodel

111 wc. a I C I

- 0.4+ ± 0.09 - 0.53 ± 0.09 - 0.50±0.10

- 0.6+±0.1 0

0.53

Degrre-da), modPi

Jl1\\'.C.a I C 1

- 0.69 - 0.79 - 0.82

0.68 - 0.89

- 0.77

iVlore fund a m enta ll y, the regression model explieitly ass umes a linear relation between m ean specific balance a nd temperature, while the degree-day model implies no such relat ion . The m ass-ba lance sensitivity quoted here refers to the mass-ba lance change for the first increase of 1°C because this is the convention in discussions of glac iers a nd sea level (e.g. M eier, 1984; Oerlemans a nd Fortuin, 1992; Kuhn, 1993), although most workers agree that th e re la tion between mass balance and mean temperature mu t be somewhat non-I i nea r.

DISCUSSION

The temperature-cha nge ex periments (above) were carried o ut holding preeipita ti on constant, but it was found that model acc umula tio n fel1 by 5- 8% with a temperature rise of 1°C. This reOects the red uced proporti on of snowfa ll at higher temperatures in the model. As future c lim a te

12

changes cou ld invoh-e ch a nges in precipitation as well as temperature, a furth er experiment was m ade for Griesglet­scher (model run 26) where precipitation was increased or decreased by 20% to compa re with the effect of raising or lowering temperatures by 1°C. The results (Table 7) show that increased precipitat ion would partly offset the effect of higher temperatures, but even a 20% increase in precipita­ti on canno t compensate for the increased abla tion due to a I QC temperature ri se. By contrast, decreased precipitation would substa ntia l1 y reinforce the effec ts of increased tem­perature.

Table 7 CalClllaled changes ill mass balance qf Griesgletscher due to temperatllre and/ oT /necipilatiol1 changes. Units if balance change are 111 w.e. a- I

Precipitation change 7em/Jemtllre change -/ C PreJenl + / C

+ 20% +0.91 +0.37 - 0.30 Present + 0 . .5:; 0.00 - 0.69

20% + 0. 18 -0.39 - 1.13

A small experiment was performed by r erunning the model for Griesgletscher (m odel run 26) a nd varying th e ratio of degree-day factors ks / ki from the standard value o f 0.6 for this study to a value of 1.0. The result is generally to increase ablation by > 0.5 m w.e. a 1 at th e glacier snout, a nd to stra ig hten the bala nce- a ltitude curve somewhat. Insofar as it would be more diffic ult to fit these stra ig hter curves to the observed data, the use o f differing degree-day factors for ice and snow in this a nd o ther studies (Huybrechts and others, 1991; J 6hannesson a nd others, 1993; L a umann a nd Reeh, 1993; Vincent and Vallon, 1997) seem s justifi ed . This means that the degree-day approach is more realistic than the power-law model of Krenke and Khod a kov (1966), re­centl y resurrected by D avidovich and Ananicheva (1996) and PfeITer and others (1997), because it di stingui shes between ice a nd snow. The latter model is obviously based upon a ve r y extensive dataset from the former Soviet Union, and we urge our Russia n coll eagues to re-analyze their data in terms of th e differing a blat ion properties of ice and snow.

The rel a ti on between temperature sensitivit y and a lti­tude is shown [or a ll five g laciers in Figure 8, supporting the earlier finding for Griesgletscher. It is interesting that the fi ve glaciers have roughly simil a r sensitivities for the same a ltitudes. The strong relation between sensitivity a nd altitude suggests that climate-change experi m ents should be performed for individu a l a ltitude bands ra ther than for whole g laciers. For example, as the tongue of a glacier, with the high es t sensitivity, is m elted away, th e average sensitiv­ity of the remaining part o f the glacier must be reduced .

The sens itiviti es found for the fi ve glac iers, i.e. -0.7 to - 0.9 m w.e. a 1 QC 1 in round fi gures, probably represent an intermediate range in g lobal terms, with lower va lues for subpolar a nd high-a ltitude g laciers a nd higher values for very maritime glaciers. From an ene rgy-ba la nce study of 12 glaciers from different regions, Oerlemans and rortuin (1992) suggested a global sensitivity of - 0.4 m w.e. a 1 QC \ which would give a world sea-I e\'el rise of 0.6 mm a - I QC I.

As the latter figure is only ha lf that given in the 1990 Inter­governmenta l Pa nel on Climate Change report (\Varrick and Oerlemans, 1990), it is important to confirm or refute this lower fi gure by furth e r work.

BmilhwaiLe and Z hang: Sensilivil)! cfglacier mass balance la temperature changes

~ -0.2 U o

Grtesgletscher y .... . ... .

/.~~:::~:~~---- ..

Q)

~ -0 .6

E

~ :E -1 .0 Ul c: Q) Ul

~ :J -1.4 ~ Q)

a. E

Plattalvagletscher

Rhonegletscher 6&tI'-4"t' : .... ~ ,','''' SlIvrettagletscher

,',' ........... .... ...

:./:/i.. Limmerngletscher

~ -1.8 +---.--.---r--.--.---.----r-----. 2000 2400 2800 3200 3600

Altitude (m a .s .L)

Fig. 8. Tem/JeraLure sensiLivil)1 vs aLLiludeforJive Swiss gla­Ciers.

CONCLUSIONS AND OUTLOOK

T he degree-d ay model can be tuned LO fit th e mass ba lance or five Swiss g la ciers by va rying prec ipita ti on in t he model a nd ass um ing a temperature la pse ra te orO.007 °C m I and a degree-day rac tor ror melting ice or 8.0 mm d I °C I. A 1°C tempera ture r ise in the model g ives a n increased a blat ion or > I m w. e. a I at the glacier snouts, with a p rog ress i\'C' ly sma ller increase wi th greater a lt itucle. A 20% precipi ta tion increase cou lcl part ly oITsetthc increased abl ation caused by the 1°C tempe ra ture ri se but co uld not compensate [or it.

The area-averaged sensiti v iti es ro r the fi ve Swiss g laciers a re - 0.7 to - 0.9 m w. e. a I °C I, proba bly represent ing a n in­lrrmed iate ra nge in globa l terms, i.e. hi gher tha n sensitiv­it ies ror subpo lar glaciers a nd lowrr than [o r m a ritime g laciers.

ACKNOWLEDGEMENTS

The study is ru nded part ly by the C.K. :\iatura l Em'iron­ment Resea rch C o uncil (gra nt No. G R 9j01777 LO the Uni ver­sity or ~ lanches t e r ) and pa rt ly by the C li m a te and Environment P rogramme, European Union (g ra nt No. El\'\'+-CT95-0l 2'~, co-ordin a tecl by the Clim ate Research Uni t, University orEas t Angli a, u.K.). ~ I. Fu nk orETH pro­vided im'a lua ble advice. R. E\ 'ans ( ~ la nrhes t e r M etropoli­ta n Un iversity), R. Bassrord ( University or M a nches ter), J. H a ncack ( ~ Ia nr h es t e r Gra mma r School) and th e Na nzer fa mil y (Hotel Furka in Oberwa lcl , K a nton Wall is) helped us with fi eldwork on Griesgletschcr in summers 1996 a nd 1997.

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