Annals of Glaciology 35 2002 # InternationalGlaciological Society

Cold firn in theMont Blanc and MonteRosa areas,European : spatial distribution and statisticalmodels

Stephan SUTER,* Martin HOELZLEÀ Versuchsanstalt fu  rWasserbau,Hydrologie und Glaziologie,Eidgeno ssischeTechnische Hochschule,ETH-Zentrum,CH-8092 Zu rich, E-mail: [email protected]

ABSTRACT.Near-surface firntemperatures weremeasured in22steam-drilled bore- holesin the summit regionof (F ranceand I taly)at 3800^4800 m a.s.l.in June 1998and in 3 1boreholesin the Monte Rosaarea ( and Switzerland )at3900 ^ 4500m a.s.l.in May^July1 999.Borehole temperatures werelogged to 22 m depth.The temperatures at1 8mdepthranged between temperate conditionsand approximately ^15³C. In a small altitudeband, the observeddistribution pattern suggests astronginflu- ence ofshortwaveradiation and turbulent heatexchange (being generally more effective atwind-exposed sites) .Thesetwo energy fluxes mainly determine the melt-energy input intothe snowand firn during summer and,thereby ,the measured near-surfacetempera- tures. Astatistical analysisof the measured firntemperatures revealedaltitude-dependent firntemperature gradientsof ^1.48and of ^2.36³ C (100m) ^1 forthe Mont Blancand Monte Rosaareas, respectively .Thehigh lapse rates, ascomparedto the air-temperature lapserate, arethe result ofenglaciallatent-heat contribution.The parameters elevation, potentialdirect solarradiation, slope and accumulation explain 480%of the variation ofthe meanannual firn temperatures. Aspect-dependent lowerboundaries for the cold- firnoccurrence inthe twoareas ranged between 3500 and 4 100ma.s.l.

INTRODUCTION observedsurface and air temperatures dueto release oflatent heatwithin the uppersnow and firn layers from penetrating Coldglaciers are a uniquearchive for climate andenviron- andrefreezing surface meltwater . mentalstudies. Near-absence ofmelt guaranteesa continuous The MAFT is mainlya result ofthe energyand mass recordof the climate andenvironmental history in the firn balanceat the glaciersurface. Important parameters affect- andice. Incontrast tothe polarregions of Greenland and ing the MAFT aremean annual air temperature (MAAT), ,relatively little is knownabout the spatialdistri- radiationflux, volume and seasonality of accumulation/ butionof negative firn temperatures inthe EuropeanAlps ablation,volume of penetrating and refreezing meltwater , andmany other mountain ranges. Knowledge of the relevant topographiclocation (hollow or ridge) and wind effects atmosphericand englacial processes leadingto the formation (Aleanand others, 1984;Suter andothers, 2001).Someof ofcoldfirn is crucialfor finding representative Alpinecore- these parameters areclosely linked to each other (e.g .topog- drillingsites andfor assessing possiblethermal consequences raphy,windeffects andvolume of snow deposition) .Other forthese sites inview of a potentialclimate change. parameters thatmay influence the near-surfacethermal Inorder to quantify firn and ice temperatures amean regime areglacier flow velocity ,extensionand characteris- annualfirn temperature (MAFT)can be defined. Seasonal tics ofthe catchment basin(e.g. snow avalanches) ,firnand surfacetemperature fluctuationsare normally reflected ice deformation,ground heat flux and occurrence of withinthe uppermost10^20m ofthe firn.The MAFT is found crevassed zones(Suter andothers, 2001). ata depthwhere seasonal temperature fluctuationsvanish or , Fora longtime it wasassumed thatglaciers in the Alps inpractice, where they are within the accuracyrange of the weregenerally temperate, althoughV allot( 1893,1913) measurement. Inthe recrystallizationzone (Shumskii, 1 964), reported coldfirn in the MontBlanc asearlyas the the MAFT is veryclose to the observedsurface or air tem- turn ofthe 20thcentury .Discussion ofcold firn and ice in perature.In the recrystallization-infiltrationand cold-firn the Alpswas reanimated by investigations in the MonteR osa zones(Shumskii, 1 964),the MAFT isnormallyhigher than area(Fisher ,1953,1954,1 955,1963)andin the Jungfrauarea (Haeberli andBrentani, 1955).Haeberli( 1976)andLliboutry andothers (1976)wereamong the first tosystematically assess the distributionof cold firn and ice inthe Alps.Inthe past,

* extensivefirn- andice-temperature measurements werepre- Present address: MeteoSwiss, P.O.Box5 14,CH-8044 dominantlycarried out at locations of specific practicalor Zu« rich,Switzerland. scientific interest inconnection with construction work (e.g . À Present address: GeographischesInstitut, Universita « t Haefeliand Brentani, 1955;Haeberliand others, 1979), Zu« rich-Irchel, Winterthurerstrasse 190,CH-805 7Zu « rich, risk prevention(Lu « thi andF unk,1 997)andhigh-alpine core Switzerland. drillings(e.g .Oeschger andothers, 1978;Alean and others, 9 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suterand Hoelzle:Coldfirn in Mont Blanc and Monte Rosa areas

inthe Mont Blancarea, W estern Alps(F ranceand I taly), andin the Monte Rosaarea, Southern Alps (I talyand Switzerland).Englacialtemperature measurements were therefore madeso as to 1.measure ameanannual firn temperature; 2.coveran altitudeband as largeas possible; 3.choosesites withvarying climatic andtopographic con- ditions; 4.detect analtitude-dependent boundary between cold andtemperate firn,and 5.comparethe present-dayfirn temperatures andcold-firn occurrence withearlier observationsand models.

FIELDOBSERVATIONS

Fig.1.Locationof the Mont Blancand Monte Rosa studyareas. Study areas

TheM ontBlanc study area ( 45³50 ’30’’ N, 6³51’00’’ E; Figs 1 1984;Haeberli and F unk,1 991;Vincent andothers, 1997).A and2 )coversabout 3 km 2 andis locatedto the northof the scheme forthe spatialdistribution of cold firn and ice wasout- MontBlanc summit. Itextendsfrom about 3800 to 4800 m linedby Hooke and others (1983)includingnear -surface tem- a.s.l.and comprises the accumulationareas of de peratures ofalpine and polar regions, and by Haeberli and Bionnassay,deTaconnazand des Bossons,as wellas the sum- Alean( 1985)focusingon firn and ice temperatures fromthe mits ofM ontBlanc ( 4807m a.s.l.)andDo ªme duGou ªter Alps.Alean and others (1984)investigatedinteractions (4304m a.s.l.).Theclimate ofthe investigatedarea is charac- betweensnow deposition, firn temperature andsolar radi- terized byalmost constantly negative air temperatures and ationin the ColleGnifetti (MonteR osa)area. An altitude- veryhigh wind speeds since the massif isfullyexposed to the andaspect-dependent statistical modelof the distributionof (north)westerlies and,therefore, highprecipitation rates. coldfirn and ice inaccumulation areas of the Alpswas devel- Due togenerally high wind speeds, accumulationshows a opedby Suter andothers (2001). largespatial variability from 0. 2ma ^1 w.e.at very wind- Thegoal of the present studywas to systematically exposedsites (personalcommunication from S. Preunkert, investigatethe present-dayspatial distribution of coldfirn 2001) to 4 m a^1 w.e.at wind-protected sites (Vincent and andits dependenceon climatic andtopographic variables others, 1997).Observed firnand ice depths rangefrom a few

Fig.2.Boreholelocationsandobserved18mtemperatures (³C) in the Mont Blancarea,1998,showinggrid-interpolated values using aspline interpolation algorithm. ** denotes alocation with avalue measured at 8m,and *** with avalue measured at 12mdepth. 10 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suter and Hoelzle:Coldfirn in Mont Blanc andMonte Rosa areas

metres toabout 40 matexposed crests anddomes, and from thermistor chaintogether with the loggingunit was carefully 120 to 4200m atsaddles and basins (Vincent andothers, calibratedat several temperatures between0³ and ^1 8³C 1997;unpublisheddata) . usinga coldbath and a temperature-measuring devicecali- TheMonte Rosastudy area ( 45³55 ’20’’ N, 7³52’00’’ E; bratedat the Swiss FederalOffice ofMetrology .Theaccuracy Figs1 and3 )is about4 km 2 andcovers the accumulation ofthe calibrationis givenby the stabilityof the coldbath, the areasof the eastern partof Ghiacciaiodel L ysand of Grenz- resolutionand accuracy of the data-loggingunit, the charac- gletscher aboveapproximately 3900 m a.s.l.The climate in teristics ofthe thermistors andthe cableand the absolute the studyarea is characterizedby high-altitude conditions, accuracyof the temperature-measuring device.The absolute i.e.practically persistent sub-zero airtemperatures through- accuracyof a thermistor measurement is 0.03³C at0³ to § outthe year,relativelyhigh precipitation rates andhigh ^10³C and 0.04³C at^1 2.5³to ^20³ C. Therelative accuracy § windspeeds. Snowaccumulation is stronglyvariable, betweenthe thermistors orof one and the same thermistor rangingfrom 0. 3ma ^1 w.e.at wind-exposed saddles and usingthe same measuringbridge is evenbetter , 0.02³ and ^1 § ridgesto 2^3 ma w.e.at wind-protected sites (Ga « ggeler 0.01³C, respectively . § andothers, 1983;Haeberli and others, 1983;Alean and After the steam-drillingoperation, which lasted typically others, 1984;Eichler andothers, 2000).Observed ice depths 60^90min toa depthof 22 m ,the thermistor chainwas inthe studyarea range from 40 to 1 20m atwind-exposed installedfrom 12hoursto several days after drilling.Normally, crests andsaddles and from 80 to 4200m inthe centralpart noliquid water was found in the boreholes,and if it occurred, ofthe firnbasins (Haeberli andothers, 1988;personal com- nomeasurements weremade within the watercolumn. After municationfrom D.S.VonderMu « hll,1995;personal commu- the thermistor chainwas installed, the boreholewas carefully nicationfrom G .C.R ossi, 2001). sealedwith isolating material at the surfaceto protect against snowdriftor immediate near-surfaceair movement in the Methodology boreholedue to air -pressure fluctuationsat high wind speeds. Thisprocedure could not completely prevent rare in-borehole Firntemperatures weremeasured insteam-drilled andair- temperature fluctuationsdue to wind pumping .Aconvection filledboreholes to a maximumdepth of 22m toensure the effect inthe air-filledboreholes with a maximumdiameter of detection ofa MAFT.Atborehole 0 (Fig.3) ,firntempera- 6cm canbe excluded (Zotikov ,1986).Measurements were tures wererecorded at a permanentlyinstalled thermistor madefor 1 2^24hours at a 10^15min samplingrate. chainto 30 m depth.In all other boreholes, thermistor Measured resistances wereconverted into temperatures chainswere removed after eachmeasurement. usingthe Steinhart^Hartequation NTCthermistors incorporatedin three different 30m 1 longthermistor chainswith a 2msensor intervalwere used a b ln R c ln3 R ; 1 T ˆ ‡ T ‡ T … † tomeasure acomplete temperature profile.Data were recordedon three externaldata-logging systems applyinga where T is the temperature (K), RT isthe resistance ( «) four-wirefull bridge measurement onthe thermistors. Each and a, b and c arecalibration coefficients. Duringthe cali-

Fig.3.Borehole locations and observed 18mtemperatures (³C) in the Monte Rosa area,1996 and 1999,showing grid-inter- polated values using aspline interpolation algorithm.The two values from 1996 (boreholes 95-1and 95-2)are taken from Lu«thi (1999). *denotes alocation with avalue measured at 16 mdepth. 11 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suterand Hoelzle:Coldfirn in Mont Blanc and Monte Rosa areas

brationprocedure, resistances weremeasured atthree or fivedatasets wherethe first 5,6, 7,8or9 hourswere omitted, more reference temperatures, andcoefficients determined respectively.Thefinal temperature wastakenfrom the best foreach thermistor ,individually. linearrelation (highest correlationcoefficient) of these five Steam drillinginto cold firn or ice disturbs the tempera- sets. Below1 0mdepth,differences betweenthe fivesets were ture distributionaround the borehole.Therefore, a certain generallysmall andtypically 50.01³C. When temperatures amountof time must elapseuntil temperatures haveadjusted weremeasured inthermally undisturbed boreholes, the first tothe previouslyundisturbed conditions. The time forcom- 3^5hoursof data were omitted anda meanvalue obtained plete adjustment withina measuringaccuracy of 0 .1³C is on fromstable conditions. Repeated measurements inthe same the orderof afewdays up to about 2 weeks(Laternser ,1992). boreholeunder disturbed andundisturbed conditions were Thus,extrapolation of continuous readings right after drill- madefor one borehole in the Mont Blancarea (borehole 6; ingis aneasier andquicker way to obtain final (undis- Fig.2)andfor two in the Monte Rosaarea (boreholes 2 1 turbed) temperatures. Thisprocedure was applied to all and24; Fig .3).Measurements wererepeated after 1.5and temperature measurements insteam-drilled boreholeswith 6weeks,respectively .Below1 0mdepth(where a short-term nopermanent installationof a thermistor chain.T empera- variationdue to seasonal temperature changescan be ture T, at time t after drilling,is excludedfor the periodunder consideration) ,maximum Q 1 differences foundbetween extrapolated and undisturbed T t T 2 … † ˆ 4ºK t ‡ f … † valueswere 0. 12³(Monte Rosa) to0 .15³C (Mont Blanc). Sincequite astrongwind pumping occurred during the (Lachenbruchand Brewer ,1959),where Q is the energy ``undisturbed’’measurement inthe Mont Blancregion, inputper unitlength, K isthe thermal conductivityof firn extrapolatedtemperatures mayrepresent the undisturbed and T isthe undisturbedtemperature orfinaltemperature. f conditionswith an accuracybetter than 0.1³C. Thus, T t isproportionalto 1 =t and T isthe shift onthe § … † f Inthis study,firntemperatures measured at1 8mdepth temperature axisfound at 1 =t 0 for t .Nodifferences º ! 1 (18mtemperature) weretaken as MAFTs. Numericalcalcu- withinthe accuracyof the measurements couldbe foundfor lationsshowed that underhigh accumulation rates aseasonal the extrapolatedfinal temperatures whenusing more signalcan penetrate downto 18mdepth.Thetime horizon sophisticatedextrapolation formulae (Lachenbruch and ¹ whichis resolvedat 1 8mdepthis onthe orderof 2^3 years, Brewer,1959)includingthe durationof the thermal disturb- practicallyindependent of the accumulationrate (unpub- ance(cf. Laternser,1992;Suter ,1995).After insertion ofthe lisheddata) . thermistor chaininto the borehole,two effects ofadjustment canbe observed: Firntemperatures 1.thermal inertiaof the thermistor whenadjusting to the ambienttemperature, and Theresult ofthe observed1 8mtemperatures inthe 22steam - 2.recording of the decrease inthermal perturbation drilledboreholes of the MontBlanc area from J une1 998is causedby steam drilling. shownin Figure 2 .Temperatures wereobtained using the lin- earextrapolation (boreholes 4^22 ;Equation( 2)),anexponen- Atthe beginningof the measurement these twoeffects can- tialextrapolation by plotting exp( T) vs 1=tformeasurements notbe separated. Thermal inertia of the thermistor when whichcould only be made for a fewhours right after drilling adjustingto the ambienttemperature canbe expressed by (boreholes1 and2 )orno extrapolation at all in thermally the followingexponential relation: undisturbedconditions (borehole 3 ).Thetemperature meas- t=½ urements fromboreholes 2 and3 represent temperatures at12 T t Tf Tb Tf e¡ ; 3 … † ˆ ‡ … ¡ † … † and8 mdepth,respectively .Due torefrozen meltwater inthe where T t isthe temperature attime t, T isthe finaltem- boreholesafter drillinginto more orless massive ice,no tem - … † f perature, Tb isthe starting temperature and ½ is the time perature measurement waspossible below these depths. constant.The time constant ½ is ameasure forthe thermal Althoughtemperatures werenot measured at1 8mdepthin inertiaof asensor anddefined as the time untilthe sensor these twoboreholes, they were considered for further analysis hasadjusted to the finaltemperature towithin 1 /eofthe asthe observedtemperature profilesin J unewere generally totaltemperature change.In the case ofthermistors, ½ is veryclose to a uniformtemperature below8 mdepth.The mainlya functionof the thermal insulationof the thermis- 18mtemperature fromborehole 6 is the meanbetween an tor fromsurrounding conditions and the medium inwhich extrapolatedand a thermallyundisturbed value. The meas- temperature is measured. ½ wasdetermined experimentally urements showa generaltrend tohigher values with decreas- inthe fieldby measuring in thermally undisturbed bore- ingaltitude. The ` `hot’’spot foundat 4 100ma.s.l.on Glacier holesand typically found to be 11^31min. Measurements des Bossonsis the result ofthe highvalue (^1 .35³C) observed undernearly ideal conditions (practically no wind) showed atborehole 1 6.N oerrors weredetected duringthe measure- that thermal adjustment tothe ambientconditions was ment anddata analysis, so the valueis consideredrobust. The reachedafter 4^5hoursat the latest after inserting the ther- influenceof a cannotbe completely excluded, how- mistor chain.Therelatively large thermal inertiaof the sen- ever.Therelatively high value at the MontBlanc summit is sors isdueto their wrappingin thermally isolating material remarkableas compared to the observedfirn temperatures at andthe lowthermal conductivity( 0.025W m ^1 K^1) of the lowerelevations and to earlier observations of ^1 6.5³C by surrounding(still) air.Thus,for the linearextrapolation Vallot( 1893)andof ^20 .2³C byLliboutry and others (1976), procedure,the first 5hoursof dataafter inserting the ther- althoughthe latter measurement is verylikely to be influ- mistor chaininto the boreholewere generally omitted to encedby a crevasse. Comparedto earlier measurements, a avoidany effect ofthermal sensor inertia.Since in extreme warmingcould be observed at Col du Do ª me (^12.8³C in1 911 cases aperfect thermal adjustment ofthe thermistors was (Vallot( 1913);^10.3³C in1 998),whereasthe valuemeasured at onlyreached after 9hours,extrapolation was made using GrandPlateau (^8. 6³C in1 998)wassimilar tothat in1 974 12 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suter and Hoelzle:Coldfirn in Mont Blanc andMonte Rosa areas

(^7.3³C; Lliboutry and others (1976)).Thedeep values at the Table1.Statisticalresults of the simple linear regression of the footof the MontBlanc north face could be the result ofcold- MAFTsvs elevation ( ELEV)for the Mont Blanc (MB) snowdeposition due to avalanche activity .Temperate firnwas and Monte Rosa (MR)areas foundbelow about 3800 m a.s.l.on Glacier deT aconnaz, whereasthe firnwas still coldon the upperreaches ofGlacier r r2 des Bossonsat 3920 m a.s.l. Area Ftest pvalueEquation The1 8mtemperatures measured inthe 31steam-drilled MB^0.800. 6435.9 50.001 MAFT 52.7^0.0148 ELEV boreholesof the Monte Rosaarea in May^J uly1 999were ˆ MR^0.770. 6047 .6 50.001 MAFT 92.4^ 0.0236 ELEV generallyobtained using the linearextrapolation procedure ˆ (Equation( 2)).Noextrapolationwas made for boreholes wherere-logging was done in J uly1 999due to absent or erro- neousmeasurements (boreholes1 3,1 6and1 8^24).Atbore- duringJ une1 999^May2000 .Asinthe Mont Blancarea, an hole8, a valuecould only be measured at1 6mdepthdue to accumulationindex was derived for each borehole site. refrozenmeltwater inthe borehole.The value from the per- manentlyinstalled thermistor chainat borehole 0 isadaily meanvalue from 3 1May1 999and accumulation-corrected. STATISTICALANAL YSISAND MODELS Theobserved firn temperatures areshown in Figure 3 .The 18mtemperatures followa strongtopographic pattern on Methodology Grenzgletscher,withdeep values on shadedslopes, exposed firnsaddles and crests. Surprisinglyhigh values were found Thefollowing simple andmultiple linearregression calcula- onthe steep southslope beneath Colle Gnifetti, reaching tionsare based on the assumptionthat observationsare inde- almost^1³ C andleading to extreme firn-temperature gradi- pendentand normally distributed andthat residualshave ents withina short distance.A more altitude-dependentfirn- uniformvariances. Several statistical methods andtests were temperature distributionoccurs onthe gentlesouth slope of used toquantify the qualityof the statistical validity: correla- 2 Ghiacciaiodel L ys.Thetransition between cold and temper- tion coefficient r, coefficient of determination r , F test and p value. atefirn occurred between approximately 3950 (Grenz- Acausalrelation between the dependentvariable MAFT gletscher) and4050 m a.s.l.(Ghiacciaio del L ys).Compared andthe independentvariables elevation ( ELEV), aspect toobservations in the early1 990s(Suter andothers, 2001), (ASP), slope (SL),potentialdirect solarradiation ( RAD), stronglyincreased MAFTswereobserved on the steep south accumulationindex ( ACCI)andaccumulation ( ACC) was slopebelow Colle Gnifetti at4250 m a.s.l.(+1 .7³C) andat 4300m a.s.l.(+4. 9³C) ,whereassimilar MAFTsweredetected onGrenzgletscher below4250 m a.s.l.in 1 999.

Accumulation

Verybad weather conditions during the remainderof 1 998 preventedthe stakes set inthe MontBlanc area in J unefrom beingrevisited, sono direct accumulationmeasurements weremade. An accumulationindex was used forthe following statistical analysisdistinguishing between weak ( 1),medium (2),heavy( 3)andvery heavy ( 4)accumulationas estimated fromtopography and (estimated) meanwind velocities. Inthe Monte Rosaarea, accumulation at borehole sites 1^24was estimated usingstake observations from May^J uly 1999and snow-height measurements froman energy- balancestation at the Seserjoch(Fig .3).Forthe extrapola- tionto an annualaccumulation rate, weassumed that accu- mulationfollows a regularspatial pattern overthe year. Thus,the valuesobserved from May to July 1 999at the above-mentionedsites wereextrapolated taking a conver- sionfactor derived as the ratioof the Seserjochaccumula- tionsbetween 1 June1 999and 3 1May2000 ( 2.1mtotal accumulation)and between 1Juneand 15July1 999.Nostake observationscould be made for boreholes 1 1and1 9.The valuesfor boreholes 4 and95-2 were taken from Lu « thi (1999)andfor borehole 1 7froma meteorologicalstation at Colledel L ys(personal communication from G .C.R ossi, 2000;Fig .3).Nostakeobservations could be madefor bore- holes25^3 1onGhiacciaiodel L ysin1 999.Instead,annual accumulationrates fromnearest stakepoints based on obser- vationsfrom September 1997to August 1998were considered Fig.4.Observed MAFTsfrom the Mont Blanc (a)and the (personalcommunication from G .C.R ossi, 2001)assuming Monte Rosa (b)ar easas afunction ofelevation and calculated precipitationconditions during this periodsimilar tothose regression lines. 13 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suterand Hoelzle:Coldfirn in Mont Blanc and Monte Rosa areas

Table 2.Statisticalresults of the multiple linear regression of the MAFTsvs elevation ( ELEV), aspect (ASP),slope (SL), potential direct solar radiation ( RAD),accumulation index ( ACCI)and accumulation ( ACC)for the Mont Blanc (MB) andMonte Rosa (MR)areas

Area r r2 F test pvalueEquation

MAFT vs ELEV and ASP MB 0.85 0.73 22.5 50.001 MAFT 54.8^ 0.0158 ELEV + 0.6337ASP ˆ MR 0.90 0.81 50.7 50.001 MAFT 80.1^0.0218 ELEV + 1.0081ASP ˆ MAFT vs ELEV and RAD MB 0.81 0.65 17.6 50.001 MAFT 53.8^ 0.0155 ELEV + 0.0080RAD ˆ MR 0.90 0.82 47.6 50.001 MAFT 94.8^ 0.0269 ELEV + 0.0419RAD ˆ MAFT vs ELEV and ACCI MB 0.86 0.73 26.3 50.001 MAFT 17.5^ 0.0074 ELEV + 1.5822ACCI ˆ MR 0.78 0.61 24.0 50.001 MAFT 77.6^ 0.0205 ELEV + 0.6447ACCI ˆ MAFT vs ELEV and ACC MR 0.78 0.60 21.1 50.001 MAFT 81.5^ 0.0212 ELEV + 0.4067 ACC ˆ MAFT vs ELEV, ASP and SL MB 0.85 0.73 14.5 50.001 MAFT 52.3^0.0154 ELEV + 0.6213ASP + 0.0488SL ˆ MR 0.94 0.88 57.7 50.001 MAFT 84.5^ 0.0219 ELEV + 1.0781ASP ^ 0.2680SL ˆ MAFT vs ELEV, ASP and ACCI MB 0.89 0.79 20.3 50.001 MAFT 23.4^ 0.0091 ELEV + 0.5480ASP + 1.4322ACCI ˆ MR 0.90 0.81 32.4 50.001 MAFT 82.4^ 0.0223 ELEV + 1.0148ASP ^ 0.0992ACCI ˆ MAFT vs ELEV, RAD and ACCI MB 0.88 0.77 20.6 50.001 MAFT 12.3^ 0.0074 ELEV + 0.0187RAD + 1.9391ACCI ˆ MR 0.91 0.82 46.8 50.001 MAFT 81.7^0.0242 ELEV + 0.0418RAD + 0.5673ACCI ˆ MAFT vs ELEV, RAD and ACC MR 0.91 0.84 45.6 50.001 MAFT 94.7^0.0271 ELEV + 0.0460RAD ^ 0.0415ACC ˆ MAFT vs ELEV, ASP, SL and ACCI MB 0.89 0.79 14.4 50.001 MAFT 22.8^ 0.0091 ELEV + 0.5439ASP + 0.0230SL + 1.4031ACCI ˆ MR 0.94 0.89 43.3 50.001 MAFT 70.8^ 0.0190 ELEV + 1.0432ASP ^ 0.2879SL + 0.5940ACCI ˆ MAFT vs ELEV, RAD, SL and ACCI MB 0.90 0.81 18.0 50.001 MAFT 9.2 ^ 0.0079ELEV + 0.0320RAD + 0.1390SL + 1.8093ACCI ˆ MR 0.91 0.82 34.1 50.001 MAFT 78.4^ 0.0234 ELEV + 0.0410RAD ^ 0.0291SL + 0.7249ACCI ˆ MAFT vs ELEV, RAD, SL and ACC MR 0.91 0.84 33.1 50.001 MAFT 94.8^ 0.0271 ELEV + 0.0459RAD ^ 0.0181SL ^ 0.0088 ACC ˆ

presumed. Thestatistical modelsare considered to be valid in tainarea, as canbe seen below.Aspect andslope informa- the parameterspace of the observations.Theyha vea restricted tionwere derived from the correspondingDEMs foreach validityfor aspects inthe rangewest-southw est^south^east- boreholeor estimated fromthe map(aspect) .Acoding southeast (WSW-S-ESE) andpotential direct solarradia tion system wasused forthe aspect wherenorth receives the exceeding350 W m ^2 inthe MontBlanc study area, due to a smallest (1)andsouth the highestvalue ( 9).Theaspects limited number ofmeasurements inthese aspects. northwest andnortheast (value 3) ,west andeast (value5) andsouthwest andsoutheast (value7) were considered sym- Furtherinput data metrical. Noaspect wasattributed tosites witha slope 4³. µ Theregression analysisrequires additionalinput data: Potential direct solar radiation Digital elevation models (DEMs) Potentialdirect solarradiation is agoodapproximation of TheDEM ofthe Mont Blancstudy area is basedon digitally the shortwaveincoming radiation, making an important analyzedaerial photographs of the Mont Blancregion from contributionto the surface energybalance and its spatial 1993obtained from the Institut Ge¨ographiqueN ationalin andtemporal variation (e.g. F unk,1 985).Usingpotential Franceand on manualcorrection based on the Swiss topo- direct solarradiation as a proxyparameter forshortwave graphicmap 1: 50000. incomingradiation neglects the effect ofspatialand tempor- TheDEM ofthe Monte Rosastudy area was compiled alvariationsof cloudcover on the MAFTs. Due toa lackof usingdigitized contour lines fromthe 1977land registry plan observations,no statement canbe made on the impactof 1:10000for the Swiss partand merged witha DEM ofthe cloudcover .Itcan,however ,beassumed that its spatial ItalianGhiacciaio del L ysbased on aerialphotographs from variationis small withinthe studyareas given their small 1994(personal communication from G .C.Rossi, 1999). extent. Potentialdirect solarradiation was calculated for eachborehole site usingthe grid-basedcomputer program Aspect andslope SRAD (Mooreand others, 1993a,b) andthe DEM data. Thetopographic aspect andslope can be considereda good Theprogram calculates the radiationtotal on adailybasis proxyparameter forincoming solar radiation in a moun- andconsiders, besides aspect andslope angle, topographic 14 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suter and Hoelzle:Coldfirn in Mont Blanc andMonte Rosa areas

shading.Additionally,atmosphericscattering, reflection Table 3.Lower boundary (ma.s.l.)of cold-firn occurrence as andabsorption are taken into account. F orthe regression afunction of aspect ( ASP)for the Mont Blanc andMonte calculationsa dailymean value averaged over 1 yearwas Rosa areas calculated.V aluesranged between 1 75and 405 W m ^2 at the drillsites. ASP Mont Blanc Monte Rosa Simple linearregression N 3510 3720 Theregression ofthe observed1 8mtemperatures or NW/NE 3590 3820 W/E 3670 3910 MAFTsagainstelevation ( ELEV)canbe written as SW/SE 3750 4000 MAFT a bELEV ° ; 4 S 3830 4090 ˆ ‡ ‡ … † where a is the intercept, b is the slopeand ° is the residual. Statisticalresults aregiven in T able1 .Figure4 showsthe observed MAFTsplottedagainst elevation. F orthe Mont effectivein flatter terrain thanon steep slopes.Elevation Blancarea, 64% of the variationof the MAFTs can be andaccumulation alone do not sufficiently explain the 18m explainedby the elevationalone; 60% in the case ofthe temperature variationexcept for the Mont Blancregion MonteR osaarea. An altitude-dependen tfirn-temperature where deep MAFTscoincidewith a lowaccumulation gradientof ^1 .48³C (100m) ^1 andof ^2. 36³C (100m) ^1 was index (r2 0.73).However,satisfyingresults areobtained calculatedfor the MontBlanc and M onteR osaareas, respect- ˆ whencombining radiation or radiation proxy-parameters ively.Thecalculated boundary between cold and temperate aspect andslope with accumulation. F orthe Mont Blanc firnlies at35 70m a.s.l.in the Mont Blancand at 3920 m a.s.l. area,the parameters elevation,aspect andaccumulation inthe MonteR osaarea. The large discrepancy in gradients index,or elevation,aspect, slopeand accumulation index, andlower boundary of cold-firn occurrence is dueto the areable to explain 79% of the MAFT variation.F orthe under-representationof southerly aspects inthe MontBlanc Monte Rosaarea, the parameters elevation,aspect, slope sampleand the relativelyhigh MAFTatthe MontBlanc sum- andaccumulation index explain 89%. When combining mit andshould not be interpreted climatologically.If the high altitude,radiative, heat-exchange (slope) andaccumulation MAFT atthe MontBlanc summit isomitted andonly values information,coefficients ofdetermination of 0.8 1(Mont in` `cold’’aspects (WNW-N-ENE) areregressed inboth Blanc)and 0 .82^0.84(Monte Rosa) arefound. samples, gradientsare ^1 .90³C (100m) ^1 forthe MontBlanc ^1 and^2 .14³C (100m) forthe Monte Rosaarea. Compared to Lowerboundaries of cold-firnoccurrence anearlier investigation (Suter andothers, 2001),altitude- dependentfirn-temperature gradientsare higher in the Usingthe abovestatistical relationships,it is possibleto current datasets. derivespatial distribution models forcold firn based on the topographicand climatic parameters ELEV, ASP, SL, Multiple linearregression RAD and ACCI whichare relatively easy to measure, esti- mate orcalculate.The lower boundary of cold-firnoccur- Therelation between the dependentvariable MAFT and the rence is foundwhere the MAFT becomes 0³C andcan independentvariables elevation ( ELEV), aspect (ASP), then bewritten as(cf. Equation( 5)) slope (SL),potentialdirect solarradiation ( RAD), accumu- a cASP dSL eRAD fACCI lationindex ( ACCI)andaccumulation ( ACC) is given as ELEV ‡ ‡ ‡ ‡ ; bound ˆ ¡ b MAFT a bELEV cASP dSL eRAD ˆ ‡ ‡ ‡ ‡ 5 6 fACCI gACC ° ; … † … † ‡ ‡ ‡ where ELEVbound isthe lowerboundary of the cold-firndis- where a isthe intercept, b, c, d, e, f and g arecoefficients and ° tribution, a is the intercept, c, d, e and f arecoefficients and isthe residual.Thestatistical results forseveral combinations b isthe slopeof the parameter elevation. ofparameters aresummarized inTable2 .Allmultiple linear

regression modelsshow high correlation coefficients, coeffi- ELEVbound vs ASP cients ofdetermination and F-test values.All models are very Theaspect-dependent lowerboundaries of the twoareas stronglysignificant. Care must betaken for the MontBlanc (Table3) are quite similar anddiffer on the orderof 230m. area,as southerly aspects areunder-represented, whichis Thediscrepancy increases towardssoutherly aspects, per- critical whenlooking at aspect andradiation. This fact leads hapsdue to a lackof observationsin the Mont Blancarea. togenerally better statistical results forthe MonteR osaarea. Theeasily determined parameters elevationand aspect areable to explain 73% and 8 1%ofthe MAFT variationin Table 4.Lower boundary (ma.s.l.)of cold-firn occurrence as the Mont Blancand Monte Rosaareas, respectively .Forthe afunction of potential direct solar radiation ( RAD) for the Monte Rosaarea an even better result is achievedwhen Mont Blanc and Monte Rosa areas aspect isreplacedby potential direct solarradiation ( r2 ˆ 0.82).Thisis notthe case forthe Mont Blancarea due to the RAD Mont Blanc Monte Rosa radiation-exposedlocation of some verycold sites (Fig.2). W m^2 Anequal(Mont Blanc)or improved(Monte Rosa)result is foundwhen the regression is madewith elevation, aspect 200 3570 3840 andslope. Thecombination of aspect andslope gives a better 300 3630 3990 proxyfor radiation. In addition, slope can be considereda 400 3680 4150 proxyfor turbulent heatexchange which is generallymore 15 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suterand Hoelzle:Coldfirn in Mont Blanc and Monte Rosa areas

Table 5.Lower boundary (ma.s.l.)of cold-firn occurrence as Table 6.Lower boundary (ma.s.l.)ofcold-firn occurrence as a afunction of aspect ( ASP) and slope (SL)for the Mont function of aspect ( ASP)and accumulation index ( ACCI) Blanc and Monte Rosa areas for the Mont Blanc and Monte Rosa areas

Mont Blanc Monte Rosa Mont Blanc Monte Rosa ASP SL SL ASP ACCI ACCI 10³ 20³ 30³ 10³ 20³ 30³ 1 2 3 4 1 2 3 4

N 348035 1035403790 3660 3540 N 27702930 3090 3250 37 403740 3730 3730 NW/NE35603590 3620 3880 3760 3640 NW/NE2890 3050 32 1033603830 3830 3830 3820 W/E36403670 3700 3980 3860 3740 W/E301031703330 3480 3930 3920 3920 39 10 SW/SE 37203750 3780 4080 3960 3840 SW/SE 31303290 3450 3600 4020 40 1040104000 S 38003830 3860 4 1804060 3940 S 325034 1035703720 4 11041004 1004090

ELEVbound vs RAD decrease inelevation of the 0³C firn-temperature linefor Theradiation-dependent lower boundaries of the twoareas the Mont Blancarea, whereas practically no influence can showa slightlynarrower range than the aspect-dependent beseen forthe Monte Rosaarea (T able6) . values(T able4) .However,rangesare very similar . ELEVbound vs RAD and ACCI ELEVbound vs ASP and SL When aspect is replacedby calculated potential direct solar When aspect andslope information are combined, lower radiation,an even larger lowering of the lowerboundary boundariesrise forsteeper terrain inMont Blanc,whereas canbe observedfor the Mont Blancarea. A rangeof lower the oppositeis observedfor Monte Rosa(T able5 ).Thiscan boundariessimilar tothat inT able6 is foundfor Monte beexplained by some relativelydeep values on steep and Rosa,showing elevated lower boundaries with increasing shadyslopes inMonte Rosa.The ranges obtained are radiationand accumulation index (T able7) . similar tothe aspect-dependent lowerboundaries, showing that the influenceof slope alone is weak.Thescatter is some- Cold-firndistribution in theZermatt region whatlarger in the Monte Rosathan in the Mont Blancarea. Basedon the relationbetween the observed MAFTs in the ELEVbound vs ASP and ACCI Monte Rosastudy area and the parameters elevationand Incorporationof an accumulation index leads to a strong aspect, afirn-temperature distributionfor a largerarea in

Fig.5.Statistically simulated distribution of cold firn in the region based on the parameters elevation and aspect. MAFTsare given in ³C.Lightgrey ,white dotted areas represent glacier extent. (Topographic data: DHM25 # Swiss Federal Office ofTopography.) 16 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use. Suter and Hoelzle:Coldfirn in Mont Blanc andMonte Rosa areas

Table 7.Lower boundary (ma.s.l.)ofcold-firn occurrence as a showeda coolingeffect inthe Monte Rosaand a warming function of potential direct solar radiation ( RAD) and accu- effect inthe MontBlanc area. The distribution of cold firn mulation index ( ACCI)for the Mont Blancand Monte Rosa wasmodelled for the Zermatt regionbased on the statistical areas relationshipbetween 1 8mtemperature fromthe MonteR osa studyarea, elevation and aspect. Comparedto an earlier dis- tributionmodel based on elevation and aspect usinga dataset Mont Blanc Monte Rosa RAD ACCI ACCI ofthe Alpsfrom 1 950to 1 994(Suter andothers, 2001),cold 1 2 3 4 1 2 3 4 firnnow occurs atlower elevations on slopes withsoutherly aspects inM ontBlanc and at higher elevations on slopes with W m^2 northerlyaspects inthe Monte Rosaarea. Theaspect-depen- dent rangeof the lowerboundaries is less pronouncedin the 2002420 2680 2940 3200 37 503770 3790 3820 3002670 2930 3 1903450 3920 3940 3970 3990 present studyand is foundat 300^400 m comparedto 7 50m 4002920 3 1803440 3700 4090 4 1204 1404 160 inthe earlierinvestigation. Some single sites inthe Mont Blancand M onteR osaareas show a significantincrease in MAFT since earlierinvestigations. Thepresent-day distribu- tionpattern ofcold firn lies wellwithin the boundariesof the the Zermatt regionwas computed (Figs 1and5) .Sucha dis- previousdistribution model based on elevation and aspect tributionmodel should be ableto explain 8 1%ofthe firn- (Suter andothers, 2001).Althoughlower boundaries of cold- temperature variation(T able2) .Thecalculation was per- firnoccurrence are higher in northerly aspects andlower in formedwithin AR C/INFO andArc View basedon adigital southerlyaspects thanin the previousmodel, a majorchange elevationmodel with a 25m resolution(DHM25 # Swiss incold-firn occurrence cannot be inferred forthe Alpsover FederalOffice ofTopography).Ascomparedto an earlier the last 50years. distributionmodel for the region(Suter andothers, 2001), the present occurrence ofcold firn is restricted tohigh- elevationsites aboveapproximately 3 700m a.s.l. ACKNOWLEDGEMENTS Thisresearch wassupported by the EuropeanU nion Environmentand Climate Programme under contract N o. CONCLUSIONS ENV4-CT97-0639and the Swiss Government underBBW Nr.97.0349-1.Wegratefullyacknowledge many students and Inthe MontBlanc as wellas in the Monte Rosaarea, MAFTs colleaguesat the Sectionof Glaciologyof the Laboratoryof generallydecrease withelevation. Wind-exposedsaddles and Hydraulics,Hydrology and Glaciology (V AW)atETH crests showlow temperatures, whereasrelatively steep slopes Zu« rich,the Laboratoirede Glaciologie et Ge ¨ ophysiquede withsoutherly aspects oftenhave near-temperate conditions, l’Environnement,Grenoble, F rance,and the Institute of whichresults inhigh to extreme firn-temperature variations Geographyat the Universityof Zu « rich fortheir helpwith withinvery short distances.Observationsin the Monte Rosa the strenuous fieldworkat high altitude. W eareespecially areashow a clearer dependenceon aspect andpotential dir- indebtedto G .C.R ossi forproviding many useful data and ect solarradiation than those inthe Mont Blancarea. 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18 Downloaded from https://www.cambridge.org/core. 03 Oct 2021 at 03:19:01, subject to the Cambridge Core terms of use.