JournaL oJ G'laciolog)', /"01. 42, . '\ '0. 142, 1996
Mass balance of White Glacier, Axel Heiberg Island, N.W.T., Canada, 1960-91
J. GRAHAi\l COGLEY, ' IV. P. ADA~lS, NI. A. E CCLESTOKE D ejJarlmmt oJ Geograph)l, Trent Ul1il'crsity, Peterborough, Ontario Jl9J 7BB , Canada
F. J UNG-ROTHEl\H.A.US LER Aljred- II'egener-1nslitllt fir Polar- lInd Aleeresforscllllllg . CollllllbusstrajJe Postfac/i /20161. D -2B50 Bremerhal'en, Gemwl~) '
C. S. L. Oi\I \IAXl\EY International G'laciological Sociel)', Lenifield Road, Cambridge CB2 1ER , England
2 ABSTRACT. While Glacier is a ya lley glacier a t 79.5° N with an area of 38.7 km . Its m ass bala nce has been measured , oyer 32 years with a 3 yea r gap, b y standard techniques using th e slra ti graphic sy ·tem wi th a stake densi l)' of th e order of onc slake 2 pCI' km . Errors in stake mass bala nce are about ± (200- 250) mm , due largely to the local un represe n ta ti\'el1ess of measuremen ts. Errors in the whole-glacier mass balance B arc of the same order as sin gle-slake errors. However, the lag-I autocorrelation in th e time seri es of B is efTec tiyely zero, so it consists of independent ra ndom samples, a nd the error in the lo ng-term "bala nce normal" (B ) is noticeably less. (B ) is - lOO ± 48 mm. The equilibrium-line altitude (ELA) averages 970m, with a range of 470- 1400 m. M ass bala nce is well correlated with ELA, but detail ed modelling shows th a t the equilibrium line is undetecta ble on \'isible-ba nd satellite images. A reduced network of a fe\\' sta kes could gi\'e accepta bl e but less accurate es tima tes of th e mass ba lance, as cou ld estimates based on data from a \\'eather station 120 km away. There is no evidence of a trend in the m ass balance of \ \'hite Glacier. To detect a c1im atologi call y plausible trend will require a ten-fold reduc tion of measurement error, a conclusion which m ay well a pply to most es timates of mass bala nce based on similar sta ke d ensities .
INTRODUCTION accumulation, probably not regiona ll y representa ti\'e, of about 370 mm for a 41 year record of annual laye rs The m ass-bala nce record of \\,hi le Glacier, Axel H ei berg studied in a n ice sha ft near the hi ghes t poinl on th e Isla nd, ;'\Jorthwes t Terri tories, Canada (Fig. I), now :\ltiller I ce Cap, 40 km no rth of \\'hite Glacier. In short, ex tends over 32 yea rs, with onc 3 year gap. H ere we th e neigh bourhood of Whi le Glacier appears to recei\'e documenl the record , assess its accuracy, conside r more precipitation than d oes the neares t weather station alterna ti\'Cs to a sta ke-based measurement progra mme a t Eureka. The mean ann ua l temperature near sea Ie\'el a nd assess th e \'alue of W hite Glacier as a n index of a t Eureka is -19.7 C. clima tic cha nge. All of the ra\\' data for this srud y, a nd The ice cO\u or Axel H eiberg Isla nd is d escribed in further a nalytical material, will be found in Cogley a nd detail in Ommanney (1969) . White Glacier is a compound others (1995 ). \'alley glacier, about 15 km long and 38 .7 km2 in a rea (Fig. I). The surface ele va tion abm'e sea level ranges frol11 1782111 down to 75111 , with moraine-cm'ered ice to 53m. SETTING AND HISTORY OF MEASUREMENTS The tongue is about I km wide. Thicknesses, typically 200 11l a nd up to 400 m, are reported by Bee ker (1963 ), The mean a nnua l precipitation at Eureka, 120 km Red pa th (1965) a nd Bl a tter ( 1985, 1987 ). Whi te Glacier is northeast of White Glacier, is 58 mm. At Isachsen , poly therm a l, lI'ith a cold upper shell and, beneath most of 280km to th e so uthwes t, it is 11 7 mm. K oerner's ( 1979) th e tongue, a temperate sole (Blatter, 1985, 1987). Surface measurements on the eastern and northern sectors of the velocities measured a few kil ometres up-glacier from th e ~ I tiller Ice Cap indicate accumulation of a bout 160 mm snout (F . :\1i.iller, 1963e) are a bout 20- 30 m a I. The snout a I. Ohmura a nd :'Itiller (1977) report a 3 year mean for is retreating at frol11 3 m a 1 (1959- 62; F . :\ILiller and slimm er precipitation of more th a n 60 mm , a nd an increase others, 1963) to 5111 a 1 (1960- 70 ; Arnold , 1981 ). I nforma with c1 eyati on at a rate of 72 mmkm I, for th e \ \'hite tion in :\IIoisan and Pollard ( 1992) for 1960-88 is consistent 2 Glacier area. F. t-.1till er (1963d ) reports a mean a nnua l \\'ith th ese estima tes. Thompson Gl acier (area ",280 km ) ,
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N
79.5N
2500- m • Stakes
Fig , I, [, 'hile (; lacia, Longilude, lalilude mark:, al leJi art' each 0,02" 101/g : tOnlollr ill terval 100 m, Slakes showll are Ihose 0/ 1987, huel: loealion oj [Ulile Glacier and oliter I}laces mel/l ioned il/ tnl: SIPB: SI Palrich- B (~) I ice cajJs ,
contiguous with the snout or\\,hite Glacier, is ad yancing a t During 1963 79, a nnual measure mcnts \\'elT m ad e on 20m a I , few er sta kes (varying fr om 23 to 80), These we re i\lass-ba la nce measurem e nts hal'e been m ad e on d ocumented , \I'irh a nnua l comme nta ri es, in \\'e iss Whitc Glacie r since 1959, R elcya nt processes h a ye bee n ( 198-1- ), Spec ia l proj ects produced additional m easure studied by, a mong oth ers, H a vens a nd oth t" rs (1965: m e nts in so me years (e,g, Arnold , 198 1), meteorology, clima tology), Ike n ( 1974: surface \'C lociri es ), There is a gap in th e record fo ll owing th e d ea th of Bla tter (19H5, 1987: th erma l regim e) a nd Ada ms a nd F , i\IOller, th e principal il1\'es ti ga to r, The mi ss ing yea rs, others (1995 : eq uilibrium-zone processes), Omma nney 1980, 198 1 a nd 198 2, a re addressed below, (1987a, b) g ives a bibliogra phy of glaciological research in In 1983, measure m ents were resumed by groups fr om the a rea, Trent UnilTrsity, C a nada, a nd these halT continued , In 1960, a n extensil'e pa ttern of stakes was es ta blished, The balance for the first year of res umed measurem e nts is i\li.iller (1962, 1963c), Ada ms (1966), i\fLill e r a nd K eeler pro ba bl y more uncertain th a n la te r es tim a tes, The (1969), Young (1972) a nd Arnold (1981 ) ha \'C exploit ed n um ber of sta kes (Fig, 2) has been a bout 30 per year or the deta il ed kno wl edge of the m ass bala nce fo r the earl y 0. 6- 0.9 per km 2 ~ to be cO lnparccl \vjlh 2- 3 per kn,2 in yea rs 1960- 62, som e earlier years,
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3.0 supe ri m posed-ice zon e, in the lo wes t pa rt o f the percola ti on zo ne, ne t accumula tion is often a combina N 2.5 ti on of snow (measured in pits) and, beneath the snow, 'E '·concealed superimposed ice" (measured as a ri se of the ~ 2.0 .iij~ ice surface against ta kes loca ted close to th e pits). An c:: 1.5 Q) added complicati on is th at spa ti al vari a ti ons in tota l
Q) accumulati on, tota l melt and forma tio n of superimposed ".¥ 1.0 m icc produce outli ers o f accumula ti on and inliers of U; 0.5 a blation. Above th e superimposed-i ce zone, pits are dug to 0.0 1960 1964 1968 1972 1976 1980 1984 1988 1992 id entify mass added between th e end of one summer a nd the end of the nex t. The density o f the accumula ted Fig . 2. Density oJ stakes in each sLratigraJ)/Zic-balall ce volume is determined by id entifying distinct layers in the jlea/". walls of the pit a nd m easuring th e d ensity of each layer. The average density is the layer-depth weighted sum of the m easured densities . (Before 1983, a complete column METHODS OF MEASUREMENT of accumulated snow was we ighed.)
Definitions Calculations
·We use b to d enote th e net mass balance at a nyone stake The net mass bala nce B for the w hole glacier IS, b y for anyone year. The symbol b(h), on th e other hand , d efinition, d eno tes a I yea r mass-ba la n ce es tima te m a d e by fA bdx dy averaging all the stake measurements in the sm all range B = "-7--:---:-- (1) of elevati ons between h - ! dh a nd h + 4dh. The a nnual fAdx dy ' mass bala nce for th e whole glacier is denoted b y B . The long-term average of B is represented by (B) a nd is call ed wh ere A is th e a rea covered by the glacier and the mass-ba la nce norm al. These quantities a re quo ted as b == b(x. y, 6.t ) represents th e mass ba la nce at each point spec ific bala nces, in units of m ass per uni t a rea per unit (x , y ) on th e glacier over th e tim e-spa n 6.t. The a rea is 2 time (kg m a I, or mm water a I ) . We refer to strati ass umed not to cha nge during 6 t . We ass ume tha t gra phic yea rs b y the calenda r year ill which th!!)1 end. Thus, elevati on h is the d ominant influence over b, a nd 1960 refers to the mass-balance year 1959- 60. extra polate from the sta kes only in the \·e rtical direc ti on. M easure ments of b are grouped into 100 m hig h Field methods el evation bands, a nd a fun cti on, fJ( h) say, is fitted to b(h), the se t of el e\'a ti on-ba nd averages of the meas ured b. This T he standard approach to m ass-balance work, ad opted reduces bi as fr om the uneven di stribution of stakes a nd is here, is described in Paterso n ( 1981 ) and 0 strem and consistent with the weighting of elevati on-band es tima tes Brugman (199 1). Wc have reli ed on th e stra tig raphic by their areas a( h): sys tem, but with a modifi cation . R eso urces allow onl y a sin gle fi el d visit each year, a nd it is not possible to B = =L~"H.,-a...:....(h...:....) fJ--,- (--"h )_d_h (2) estimate se pa ra te winter a nd summer ba la nces. The L "H. a( h) dh, a nnual visit is therefore mad e in spring (la te ?\1ay or earl y June). This allows us to dete rmine with good accuracy where the range of summa ti on 7-i is from the glacier's the winter accumula ti on of the CllTre11 / (September-to minimum el evati on to its maximum elevati on. September) stra ti graphic ba la nce year, while in the As shown below (see also appendix B of Cogley a nd a bl a ti on zone we measure the loss of ice during the o thers, 1995 ), the structure of th e rel a ti onship between b previous balance year. The lowering of th e ice su rface is a nd h is relatively simple. fJ( h) is evalu ated a t the d etermined wi th reference to a mark on a sta ke (or a midpoint of every 25 m eb ·a ti on ba nd, a rela ti\·ely fin e thermistor cable) inse rted yerticall y into the glacier. T o resol ution which takes ach- an tage of h ypso metric es ti m obtain the stake mass balance b we assume th a t the lost ice a tes of the area a(h) deri\"Cd from a digital elevation had a density of 900 kg m 3 model (DEM) by a simple binning routine. The DEM On pola r glaciers, there m ay be a m o re-or-Iess (C ogley, 199 2a; National Research Council of Can ad a, ex tensi\·e superimposed-ice zone abO\"C th e equilibrium 1962a, b, 1965) has a hori zo nta l resolution of 50 m . lin e (Ad ams a nd oth ers, 1995). Especiall y in hollows, th e Equa ti on (2) is a pplied to obtain B. initial melt refreezes to form superimposed ice at the base The polynomia l fJ( h) always fits the data very well of th e wi n ter snowpack. At lower eleva ti ons the super (Cogley and others, 1995). Because polynomi als diverge, imposed ice even tuall y melts, but higher up some of it it is risky to ex tra pola te them. Beyond th e eleva ti on ra nge persists and contributes to net accumula ti on. vVh ere there or the data, therefo re, fJ( h) is se t to its valu e at the highes t is superimposed ice, net accumula ti on is measured as the or lowes t h at which there is a measurement. The effect of rise of the glacier-ice surface with reference to a m a rk on a this assumption can be seen in the vertical lin e segm en ts sta ke (times 0.9 to obtain wa ter-equivalent ITlass, which with which graphs of fJ( h) (shown below) begin a nd end. introduces a n error sin ce the d ensity of th e superimposed The ELA ho a nd accumulation a rea rati o (AAR) a re Ice IS usua ll y less th an 900 kg m \ Just a bove the computed by locating the first zero-cross in g o f the
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polyno mia l (3( h), which is accepted as a n es tima te of ha. ha\'e a lso tried to measure year-oyer- year c ha nges of AAR is simply the ra tio of th e area a bo \'e the zero d ensity in the sno\\' beneath tha t of th e current year, but crossi ng to to tal area. The risk of there b ei ng more tha n sampling erro rs tend to be very la rge. Tra ba nt a nd ~I ayo onc zero-c ross ing, a nd m ore genera ll y o f the polynomia l ( 1985) d educed interna l accumula ti on by m easuring th e predic ting n egati ve m ass ba lance a t hig h ele\'a ti ons, has a noma lo us h eating a t d e pth due to the refreezing to be c hecked visua ll y. N o ne of th e mass-ba la nce years in m eltwa te r, but appropri a te m easurem e nts a r e not the current record exhibits this quirk. ava il a ble fo r White Glacier. In the accumula ti on zone we obtain two es timates o f" R ea sse sstnent d epth, one fro m the year-ta-year differe nce in stake readings a nd the other from identification of the IJre\'ious Wc ha \ "C d eta iled sta ke diagrams and calcula ti ons for a ll year's surface in a nearby snow pit. The t\\·o d epths may years since 1983. All of these have been checked carefully be ass umed to sample ra ndo mly th e local varia bility. three times, with special attention pa id to o utliers. Som e which genera tes uncerta inty. Fo r ten such pa irs in 1990 but no t a ll of the outliers were found to be in error a nd a nd 199 I the sta ndard erro r was 68 mm o f sno\\-, or on were corrected or rej ected ; not all of the d e tected errors awrage abou t 10 % of the aye rage of th e two d epths. \\' e were o utJiers. \\'e a lso correc ted a few errors in earli er cannot repeat this exercise fo r the densities m easured in ta bula tions and transcriptions, including a number o f the pit wall s, but it seems reason a bl e to ass ume a n error of in compa tible es tima tes of sta ke ele\'ati o n , which we the same o rde r; the spring ba la nces used in the fi e ld he\\T a ltered ta m a ke the ye rtical sta ke traj ecto ri es from year been checked against a la bo ra tory ba la nce a nd fo und to to year pla usible. be accura te to better th a n ± 2%, but the error in th e All sta ke mass ba la nces b a re presented by Cogley a nd sa mpled \'o lume remain s undetermined. Simila r errors o th ers ( 1995), as are elevatiolJ-ba nd averages a nd probabl y a ffect the who le-column weig hts m easured sta nda rd d e\·ia ti ons. Informa ti on befo re 1983 com es before 1983. A ± 10% erro r in positi\'e va lues of b \\·i11 from W eiss ( 1984), fo r 1963- 79; fro m diagrams a nd typicall y be a bo ut ± (20 30 ) I11m wa ter equiya lent. ta bl es in F. MUll er ( 1963a, b) for 1962; a nd fro m Since 1987 the ele\' a ti o ns o f sta kes h a ye been diagra m s in Adams ( 1966 ) for 1960-61, inc luding som e measured b y a ltimeter (a po rta ble a neroid ba ro meter, averages for sta ke cross-profil es . calibra ted b y m easuring atmospheri c press ure at th e known e1 e\'a ti o n of the base cam p). These eleva ti o ns a rc considered accura te to \\'ithin ±5 m. For 1960- 62, eb' ERRORS a ti ons were es tima ted fro m recent ma ps, a nd simila r es tima tes seem to han" been m a d e up to 1967, fro m \\-hi ch ~ eas uretn ent errors d a te th e ele\'ations were based on occasion a l a ccurate triangul a ti o n. Earlier elevati o ns a re rega rded as accurate Sta ke m ass ba la nces a re built up from simple meas ure to no be Ll er tha n ± 20 m. The impact of this uncertain ty ments o f leng ths and weights, which in themse h'es a re is proba bl y negligible. since the sta ke readings a re ra ther accura te. Ada ms ( 1966) sho\\'s tha t sta ke readings grouped into 100 m ele\'ati o n-ba nd a\'eragcs before the a re accura te to ±5 mm, in the se nse tha t th ey a re balance calcula ti ons proceed. reproducible within this ra nge a nd a re representa ti ve for a n a rea of severa l sq uar e metres. ~f easure m en ts of sno\\' Satnpling erro rs d ensity a re less accura te (sce be lo w ) , while so m e uncerta inty must a ri se from th e ass umption th at the The grea tes t uncertaint), in B is pro ba bly due to d e nsity of g lacier ice is 900 kg m 3. If this is a n undersampling , i.e. to th e unre prese nta ti\'eness o f meas overes timate, as is possible in th e superimposed-ice zone, urements o f b as a sample o f the glac ier surface. At the the ensuing calcul a ti o ns will be bi ased. \\'e cannot assess local scale (te ns to hundred s o f metres) g lacie r surfaces this possibility, a nd a bias in b of up to a fe\\" tens o f ha \"C no ti ceable microto pography. Promine nces must millime tres is quite possible for some sta kes. have mo re negati ve mass ba la nces than d epressions, Differences between stake readings a re less accura te o th erwise the irreg ul a r surface, whic h is steadil y th a n sing lc readings, esp ecia ll y if th e sta ke tilts or se ttles regenera ted b y the interna l d ynami cs of the g lacier. between the two measure m ent epochs, or w as not \'ertical would becom e steadily more irregul ar. The microclima ti c to sta n w ith. Specia l pro blems a rise in the superimposed effec ts of local va ria ti ons of slo pe and as pec t a lso a mplify ice zone, where th e glacier gains mass in the form o f the spa ti a l \'ari a bility of m ass ba la nce. On the g lacier refrozen m eltwa ter . H e re differences b e tween sta ke wide scale, it is imposs ibl e to sample a reas which a re readings m ay be misinterpreted because th e sta ke in accessible o r d a ngerous, a nd undersampling is likely as a ppears to ha\'e sunk into the glacie r. In the lower \\-e1I , due fo r example to uneven coverage o f" a reas exposed percola tion zone (Ada m s a nd others, 1995), next a bove, to a nd shelte red from \\-ind o r sun. a n unknown fraction of the added mass is lost to interna l L1iboutry ( 1974) mod ell ed a bl ati on-zone sta ke time accumula tion when it m elts and percola tes, often \·ia se ri es as the sum of a consta nt sta ke-dependent te rm, a pipes of res tricted extent, to depths be low th e current time-\'a rying stake-independent term and a G a ussian error year's snow. This effee t is \'ery diffi cult to qua ntify, but it term. The erro r term (i. e., the sta ndard error o f a n yone b) must lead to a n underes tima te of accumula ti o n. We have was about ± 200 mm. Young ( 198 1) cl aims "consen 'a ti w" tri ed to es tima te the losses by in serting pa ns into the sta nda rd erro rs o f 20 mm in the a bl a ti on zone a nd 50 mm snowpack, but a bandoned the method because it was in th e accumula ti on zone of Peyto Gl acier, Alberta, time-consuming a nd ga\'e poor a nd doubtful res ults. 'I'V e Canad a, a lthoug h a ppa rentl y on a subjective basis.
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R ogerso n (1986) es tima tes an error in B of ± 100 mm for is large the uncertainty o ug ht lo dec rease; this po int IS glaciers in Labrad or, again subjec ti vely. Pelto (1988) co m plica ted by correla tion betwee n s takes, a nd is es tima ted erro rs of ± (150- 200) mm for densely sampled disc ussed below. Secondly, there ,,·ill be a " miss ing-sta ke sm a ll glaciers in the north"'es tern en i ted S ta tes. bi as" if a sta ke cannot be read because of melt-out or Braithwai te and Olesen ( 1989) give errors of ± 23 0 mm, buria l. T ypi cal accumula ti on is less th an the length of a which is th e standard de\'ia ti on o[ three sta kes a few metres typi cal stake (3.5 m), so burial is not a problem on White apart, a nd ± 280 mm from Lliboutry's ( 197 4) mod el, for G lacier. Sta kes in the a bla ti on zone d o melt out a n a bl a ti on zone in southwes t Greenland. occasiona ll y; we do no t h a \'e complete records, but [or Adams (1966 ) d escribes White Glacier cross-profil es a t 1983 9 1 only three readings out of " 'ell over 100 ha\'e \'ario us eb 'ations, which sa mple the (roughly) horizonta l bee n los t in this \l' a)'. (The mos t co mmon explana tion for \'aria bility at hec tometre-to-kilometre scales which is n o t losin g a reading is th a t the stake is in accessible for sa fety sampled by th e stake networks of most la ter years (T a b le rel ated or other reasons; this does not introduce a bi as. ) I). Sta ndard devia ti ons in th c ta ble average 196 mm. The a reas of e! e\'ati o n ba nds, and of the glacier as a Ridges Profil e was d eliberately es ta blished to pro be wh ole, ha ve been assumed constant at values based on vari a bility in an area of rough microreli ef and diffi cult sun'eys d a ting [rom 1959- 60. The glacier has shrunk access, a nd its standard devia tion o[ 3 14 mm may be sin ce then. The snout is retreating at 3- 5 m a- I and has a accepted as an extreme valu e. The large sta nda rd mass ba la nce of about 2 111 a I (T able 2) . Thus, in any devi a ti on at M ora ine Profil e in 196 I is due to slush cross-sec ti on through th e snout a (tri ang ular) area of ava la nches " 'hi ch introduced superimposed ice into pa rts a bout ~ x 4 x (-2) m 2 is los t each year but is no t of the profil e. accounted [or in calcula ti ons. Volumetrically, with the snout width taken as 1000 m, this is equivalent to a spurious trend of - 0. I mm a 2 in th e calcula ted balance Table I. Enor measlIres ji"01l1 cross-/J1"ojifes, reanaLyzed se ri es, or to a balance in 199 I whi ch is 3.2 mill a I too low, from .-l dGllls (1966) . n , !lulllber oj stakes ill /JlojiLe : O"b, and is negli gible e\'e n if we double or treble it to all ow standard de via tion oj cross-/JlojiLe baLances crudely fo r shrinkage a long the sid es of the glacier to ngue. We also neglec t the additio na l error due to the decrease in total glacier area, whi ch is perhaps 0. 3 km 2 or 0. 8% over ProfiLe r ear n E Le vatio!l O"b th e 1960- 9 I peri od. range Fina ll y, the in co rrec t recording and processing of fi eld m m m measurements is an importa nt so urce of error. As noted by Bra ithwaitc (1986), m ass-balance measurements are M ora ine 1960 13 18 149 usua ll y made by tired obsen 'ers working in harsh and ~1 0 r a in e 1961 13 18 292 so meti mes d angerous condi ti ons, and so errors are to be Anniversa ry 1960 I I 52 68 expec ted in fi eld notebooks. There is less excuse for errors Annive rsa ry 196 1 11 52 157 made in the offi ce, bu t they seem to occur ne\·ertheless . Ridges 1961 20 70 3 14 These erro rs are very difficult to find , let alone quantify, A\'erage 196 but their impact can be reduced greatly by careful double-checkin g. Althoug h this disc u. sion is not a ri gorous analysis of errors, the conclusion we d raw from it is tha t measure The stake network on \\'hite Glacier is uneven bo th in ments o f b should be considered to have a standard error space a nd in time. Sta ke density is g reater on the lower o[ about ± (200- 25 0) mm. In the acc umula tion zone the tongu e th an else where, exceeding two (and in so me years errors a re greater, by a t least a few tens of millimetres, 2 ten) stakes per km , while stake densiti es are usuall y 0.5 than in the abla ti on zone, because the measurements are sta kes per km 2 or less a bove abou t 1000 m. Therefore, more sp a rse, and because in places th e actual accumul uncerta inty in the ba nd-a \'eraged ba la nce b(h) is a ti on is either o\'eres tima ted due to overes tima ted proba bly greater at higher ele\·ations. In recent years densities assumecl [or superimposed ice, or uncl eres ti gaps have developed in th e coverage, s Ll ch that there a re ma ted due to losses b y p ercola ti on (i.e., in tem a l no stakes at all between 400 and 600 m or between 800 accum ula tion). and 900 m. The stake network does not cover the entire vertical Errors in whole-glacier mass balance ra nge orthe glacier. Until 1983 th e upperm os t 10-15% of the glacier had never bee n sa mpled, the hi ghes t long-li ved M easurem ents at different stakes are in general hi ghly sta ke being at a bout 1420m. Since 1983 the hi ghes t sta ke correla ted , so an increase in the number of stakes does not has been a t nearl y 1600 m, so tha t extrapola ti on is necessarily increase sig nificantly oLlr confidence in the required over only a bout I % of the glacier. However, es tima te o[ B. rf a ll pairs o[ sta kes give perfectly ex tending th e stake network upwards has had minima l co rrela ted sequences of res ults, th en our confidence in B effect: [or 1983- 91 , when B is reca lculated, the m ean is no better than our confidence in each b, while at the differ ence (bala n ce with new stakes minus ba la nce other extreme perfec tly uncorrelated stakes will reduce witho ut) is 2 mm, a nd the root-mean-square (rms) differ the uncertainty towa rds zero as th eir number grows large. ence is 8 mm. In fact, the White Glacier network exhibits very high V a ri a ti on in sta ke d ensity from year to year introduces correla ti o n betwee n sta kes (Fig. 3), such tha t it is prudent two kinds of uncertainty. First, when the number o[stakes to take the uncertainty in single-sta ke b as a good es tim a te
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TabLe 2. ,I/ass baLance /3(h) ( mill ) ~) ' elevalioll band an(J'ear. ELevalions are balld !/lid/loillls, 1750 alld 50 111 bands each occujJj' LeH Ihan 0.2% oJ area, alld are omilled; tit!,)' cOlllaill 110 slakes , alld their eslimales are el/ra/loLaled ~) ' selling them equal 10 Ihe highest /lowesl band wilh stakes. The righlll70sl COllllllll is affected by rOilnd-off error
Elevation (m) 1650 1550 145 0 1350 1250 11 50 1050 950 850 750 650 550 450 350 250 150 :/rea 2 (km ) 0.4 1,6 +.0 6.1 5.7 5.1 3.7 2.6 2.0 1. 3 1.4 0.9 0.7 1. 0 1. 2 0.8 38.7
1.1 4. 110.4 15.8 14.8 13. 1 9.5 6.7 5. 1 3.4 3.7 2.3 1. 9 2.7 3. 1 2.0 99.7
1960 480 480 470 252 - 29 - 287 526 - 750 - 961 11 64 - 1362 - 1559 - 1758 - 1964 - 2179 - 2408 -404 196 1 208 208 245 300 298 246 153 26 - 127 298 480 -665 - 846 - 10 13 - 1161 1247 23 1962 407 407 267 68 -376 662 929 - 11 8 1 1420 1651 - 1876 - 2100 - 2325 - 2556 - 2796 3047 -781 1963 407 407 402 269 107 - 26 - 140 - 249 - 362 494 - 654 -855 - 110 - 1428 - 1823 2307 -154 1964 606 606 604 53 1 452 402 368 34 1 310 266 197 95 52 - 253 -520 - 837 350 1965 200 200 200 216 218 194 143 64 -43 179 - 345 - 542 - 77 1 - 1032-1326 1593 -9 1966 349 349 349 334 282 193 74 - 71 - 239 424 62 1 - 826 - 1035 - 1243 - 1445 - 16 15 -22 1967 342 342 343 360 357 3 19 249 152 29 I 16 282 --463 - 659 - 866 - 1081 1265 121 1968 178 178 178 140 33 129 - 335 - 574 835 - 11 05 - 1375 163 1 18642061 - 22 11 2298 -406 1969 419 4 19 420 43+ 412 341 225 73 - 11 2 - 321 55 1 - 793 - 1042 - 1292 - 1538 - 1749 74 1970 245 245 246 274 27 1 219 124 5 - 160 334 520 - 709 894 - 1067 - 1220 1336 -4 197 1 352 352 352 320 225 77 - 11 4 -336 - 576 83 1 - 1082 - 132 1 - 1538 - 1720 - 1858 19 37 -184 1972 287 287 287 270 256 248 237 215 171 98 14 - 173 - 389 670 - 1025 - 1463 115 1973 348 348 350 391 418 404 352 266 149 5 162 350 - 555 - 772 - 1000 - 11 5 1 190 1974 225 225 226 223 195 137 54 - 54 - 182 328 - 489 - 664 - 848 - 1040 - 1236 1399 -46 1975 588 588 588 586 554 485 383 250 89 - 96 304 - 532 776 - 1034 - 1304 1538 247 1976 29 1 291 292 339 364 339 270 164 27 135 3 15 - 506 - 702 - 896 - 1082 1246 112 1977 78 78 81 20 I 238 12 1 I 19 - 48 - 833 1242 - 1642 - 2000 2283 - 2458 - 2493 2365 -372 1978 209 209 210 285 310 229 64 - 164 - 435 7:29 1025 1302 - 1539 - 1716 - 1813 182 1 -134 1979 196 196 197 226 213 136 9 - 156 - 349 556 766 - 966 - 11 44 - 1289 - 1387 1428 -109 1983 160 160 193 3 15 344 279 136 - 67 314 588 872 11 50 - 1404 - 1629 1777 186 1 -83 1984 338 349 354 326 265 174 56 - 89 - 258 ++9 660 - 889 - 11 34 - 1393 - 1664 1945 -55 1985 34 1 324 286 253 219 177 123 49 - 51 - 182 350 - 563 825 - 11 44 - 1524 - 1972 -12 1986 125 212 355 386 319 167 56 - 336 - 659 10 11 1380 1750 - 2108 - 2440 - 2734 2974 -259 1987 47 38 2 62 - 156 282 --44 1 - 635 - 867 11 38 - 1449 1804 - 2203 - 2649 - 3143 3688 -617 1988 427 357 227 163 149 171 210 253 282 283 239 135 --47 - 320 - 70 I 1203 128 1989 393 309 ISO 63 32 42 76 118 152 163 134· 49 - 107 - 35 1 - 698 - 11 65 28 1990 134 11 2 44 41 - 143 - 263 398 - 54·9 - 716 - 897 - 1092 1300 1522 - 1756 - 200 1 - 2259 -448 199 1 333 294 206 130 59 - 13 - 9 1 - 183 - 293 - 429 - 596 - 800 1048 - 1346 - 17 00 - 2 11 5 -179 Average 300 296 280 266 203 119 5 -134 -296 -479 -679 -894 -1122 -1358 -1601 -1836 -100
of the uncertainty in I\'hole-glacier E. There must be RESULTS so me recluction in uncertainty as th e number of'sta kes in creases, but the red uction is un lik ely to be la rge a nd is Revis ed series not im'esti gated furt her h ere; it is the subject 0 (' work in progress. N o r d o we try to infer errors from the reduction Figure 4 sho \o\'s b as a function of elevation for a ll years, of vari ance achie\'Cd by (illing th e curve /3( h). The with simple linear interpola ti on be tween sta kes , These a re \'a ri a ti on we a re trying to infer is nol adequale£JI sa lll/lled by not graphs of b(h) or (3( h); the ta ngle of lines illustra tes the obse rvations, so that the good fit of the curves (3( h) to the obm"ved lo ng-term \'ari ability 0 (' stake mass balance. the data b(h) is not rele\'ant here. The larges t measured net accumula ti ons a re about 500- The time series of a nnua l mass bala nces of White 600 mm and the la rges t ne t losses arc as g reat as Glacier has a lag-I autocorrelation of O. Fo r estim ating -5000 mm, a ltho ug h typically a bla ti on c10es not exceed th e balance norma l (E ) this means that we can assu me - 3000 mm. This o bsen 'ed range is consid erably small er th a t each B is a n indepe ndent, random sample of (E). tha n th a t found o n ma ny mid-la titude glaciers, especia ll y Thus the standa rd error of this long-term average will be in maritime climates. in versely proportional to the sq ua re root of N", the Figure 5 illustrates the polynomial /3( 17,) for a sm a ll sampl e number o f years of record. With Nv =29 the e rror in (E ) of balance years, a nd Table 2 ta bu la tes (3( h) fo r all years, is less, by a factor of fi ve or mo re, th an the e rro r in E , i. e. togeth er with Da nking da ta on a(h) a nd th e time average about ± (40- 50) mm ra ther tha n ± (200- 250) mm. of /3( h). Table 3 summa ri zes E, ha a nd AAR fo r each
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1.0 Table 3. "lass balance and related jJro/Jalies. n, /lumber
0.8 0/ stakes; B , allllllal whole-glacier mass balance : ho, equilibrium-line allitude; AAR: accumulation area ratio 0.6 (area of afCImllllation ZOll e divided b)1 area oJ glacier) 0.4 c: 0.2 .2 ...... ; ', ' ~" :.. : 1ii Tear n B AAR 0.0 ". ha e!.. ,'. '" 0 -0.2 () mm m -0.4
-0.6 1960 71 -404 126 1 0.40
-0.8 196 1 85 23 93 1 0.74
-1.0 1962 11 5 - 781 1371 0.20 400 800 1200 1600 1963 80 - 154 1171 0.50 Vertical separation (m) 1964 31 350 480 0.91 1965 28 - 9 886 0.77 Fig. 3. Balance time-series correlations oJ2676 slake jJa irs 1966 5 1 - 22 996 0.69 vs heighl dijJerence. Each dot rejJresents il.l 'O slakes with al 1967 29 121 828 0.80 least 5 ),ears oJ co mmon record. Triangles : average 1968 50 -406 1225 0.43 correlatiolls within 100111 wide bins on horizolllal axis. 1969 76 74 908 0.76 Three-quarlers oJ slake /Jairs differ ill heighl by less than 1970 68 - 4 953 0.73 610 m; Jour-fifths have conelations exceedillg + 0.6. 1971 5 1 - 184 110 7 0.59 19 72 91 11 5 659 0.86 1973 49 190 746 0.82 1974 48 - 46 997 0.69 1975 63 247 800 0.81 1976 65 11 2 832 0.80 1977 76 - 372 1093 0.59 1978 23 - 134 1018 0.67 19 79 63 - 109 1043 0.65 1983 26 - 83 980 0.71 1984 27 - 55 1009 0.69 1985 28 - 12 897 0.76 1986 33 - 259 10 72 0.62 1987 31 - 6 17 1444 0.09 1988 25 128 470 0.9 1 Stake mass balance (m) 1989 3 1 28 5 1\ 0.90 1990 27 - 448 1395 0.1 6 199 1 27 - 179 11 68 0.50 Fig. 4. Slake mass balances Jor all jlears, 1960- 91, with Average 5 1 - 100 974 0.65 linear inler/Jolation belween slakes. All slakes thal survived Oll r reassessment are showlI. These gra/Jhs show all o/Ihe raw measurements 011 which Ih e mass-balance calculations Qf Ihis /Jap er are based. Previously published eSlimates Mass-ba lance data for vVhite Glacier were first desc ribed in B.S.Mi.ill er (196 1) for 1960 and 196 1, a nd F.l\full er and year. The ba la nce norm al (B l, i.e_ the a\'erage of the 29 others (1963 ) for 1960- 62, with furth er reports by Adams values of B in T ables 2 and 3, is - IOOmma I , while the (1966), Young (1972 ), Arnolcl (1981 ) a nd Weiss (1984). average ha is 974m and the a \'erage AAR is 0.65. The The record is published in Fluctuations oJ Glaciers (F. estimate of ha is representa ti ve of values es timated by Mull er, 1977; Haeberli, 1985; H aeberli and H oelzle, simpler, visual methods for th e locali ty, and th e AAR is 1993), but with an unfortuna te recording error: one seri es close to what would be ex pected from observatio n of reported from Trenr U ni versi ty was displaced by I year, mountain va ll ey glaciers in many pans of the world. such tha t the published ba lances for 1984--89 are actua ll y those for 1983- 88 (i. e., fo r th e ba lance years 1982- 83 to Alternative estilIlates of lIlass balance 1987-88). The rrn s difference between the publish ed se ries (as corrected: Table 4) and th e new seri es reported The expense and diffi culty of fi eld work make more here is 39 mm , attributable ro th e correction of stake data economi cal methods of mass-ba la nce measurement during reassessment a nd to th e substitution or automated attractive. This subsec tion deals with so me previous for visual curve fitting in th e es timation of {3( h). This is estimates of the mass balance of White Glacier, and well within the sta ndard error for stake measurements b. with the cali bration of so me a lternative methods. The a lternative mass-balance rim e se ries di sc ussed here may Eslimates ]rom ELA be found in Table 4. Many a uthors have no ted rhat glacier mass bala nce IS
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Table 4, Estimates of th e mass balance ( mm ) of Wlzile Glacier b)' differenl methods
l ear This FIGl' Visual Glellday From ho Tongue Work met/w(ft ( 1989) stakes+
1960 -404 - 410 -404 - 347 1961 23 60 50 -53 1962 -781 -780 -745 -392 1963 -154 - 140 - 100 - 269 1964 350 350 4 10 330 1965 -9 - 20 20 -22 1966 -22 - 30 30 - 11 8 1967 121 140 130 28 1968 -406 -430 -360 - 316 1969 74 50 50 - 41 1970 -4 - 10 - 20 129 - 80 197 1 -184 - 200 - 190 - 214 - 213 1972 115 100 110 2 175 1973 190 180 180 152 100 1974 -46 - 70 - 60 - 26 - 11 8 1975 247 240 250 90 53 1976 112 130 130 11 6 25 1977 -372 - 380 - 380 - 288 - 20 1 1978 -134 - 140 - 140 20 - 137 1979 -109 - 90 - 90 - 122 - 158 1980 - 178 198 1 - 175 1982 - 92 1983 -83 - 104 - 120 5 - 103 - 123 1984 -55 - 64 - 70 - 83 - 128 - 92 1985 -12 - 16 - 40 - 100 - 31 - 87 1986 -259 - 304 - 330 - 183 - 372 1987 -617 - 790 - 670 - 506 - 603 1988 128 91 110 339 57 1989 28 10 304 102 1990 -448 - 470 - 463 - 213 199 1 -179 - 190 - 266 - 160 rms c1iOerence§ 39 3 1 90 122 99
Estimates published in Flu ctuatiolls oj(;laciers, r'ols. [If, I V and rI (F. Mi.iller 1977; Haeberli 1985; H aeberli and Hoelzlc 1993 ). (An error in the published datin g of post-1982 reslIlts has heen rorrerted: a ll ha\'e hee n moved onc year earlier.) Estimatf's obtained by \'isual fitting of the fun ction (3 (h) to stake mass-balance data; this method was replaced by a utomated polynomial fittin g during our reassess ment of the record. t Estimates obtained from a regression model relating results from a network of fi\ 'e sta kes on the glacier tongue to resu lts £i'om the whole glacier. § R oot of mean of sq uared difference between column and This Work col umn,
we ll correlated with eleva ti on of the eq uilibrium line (e.g. K oerner, 1970; Ostrem, 1975; Braithwa ite, 1984; H agen B = 771 - 0.894ho , (3) and Liestol, 1990; Kulka rni, 1992 ). The rela ti onship is to be expected from the success of Lliboutry's ( 1974) model, where ha is in m a.s. !. , and n in mm. The standard error whi ch decomposes stake data sets into a stake-dependent of the estimate of B is 126mm, and the expl ained function (i.e. an algebraic representation of the shape \'ariance r 2 is 77 % . Model performance is illustrated in (3 (h) ), a time-dependent function representin g the Fi gure 6 and Table 4. The model is simply a rearrange translation of the shape, a nd an error term. ment of existing inform a ti o n, ha ha\'in g been derived The result of a simple first- ord er regression for White from the same data as were used to estimate B. But Glacier is ind ependen t measuremen ts of ha are possi ble, a nd the
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Area (per cent) Area (per cent) 012345 012345 1962 1964 1.6 ~(h) ~(h)
a(h)
E 1.2 ~ -c: o :; 0.8 > ~ W
0.4
0.0
1987 1.6 ~ (h) a(h)
-E 1.2 ~ -c: .2 al 0.8 -> ~ W
0.4
·5 ·4 ·3 ·2 ·1 o 2 ·5 ·4 ·3 ·2 ·1 o 2 Mass balance (m) Mass balance (m)
rzg. 5. (3( h ) in four different years : least (1978) and grea test (1962) numbers of stakes, and most positive (1964) , most negative ( 1962) and second most negative ( 1987) mass balances. Thick lines : third-order pof:yrLOmial (3( h ). T hin lines : a (h ), the hY/Jsometric cu rve of the glacier. Small ojJen circles : measured slake mass balances. L arge solid circles: b(h )for 100 m elevation bands . Standm'd devia tion of measurements with in each band is shown as an error bar; in bands with 0 or 1 measurement there is no bar, but even with several measurements the error bar is sometimes invisible because it is narrower than the symbolJor b(h ).
rela ti onship suggests tha t they are likely to be useful. For example, there is only a handful of suita bl e end-of Whether such a model is useful in practice depends on season images of White Glacier from th e entire Landsat whether ha can be d etermined economicall y, for example series of satellites . Moreover, much of the surface texture from satellite imagery. Independent es timates of ha a rc whi ch helps the human observer to tell snow apart from likely to have errors unco rrela ted with th ose in B. glacier ice is fine-scaled , and is lost in satellite pi xels Therefore th e error in the regression may be added in having dimensions of 10- 100 m. A detailed inves ti gati on quadra ture (i. e., we add the vari a nces) to the error of of one end-of-season image showed tha t neither the ± (200- 250) mm in th e measured B , in order to es tima te equilibrium line nor the closely related sn owline we re the total error, about ± (235- 280) mm, in the hypo th detec ta ble. After full correcti on for a tmospheri c and eti cal space-based es tima te of B . The ex tra cos t - a n topogra phic effec ts (C ogley, 1992a, b ), the surface added uncertainty of (35-50) mm - seems attracti ve reOec tance was found to be clearly bimod a l, the darker when set against the saving achieved on fieldwork mode representing th e glacier tongue, and the brighter expenses (partly offset by th e cos t of imagery). mode parts of th e accumula ti on zone. However, the J ung-Rothenha usler and others (1992) and J ung transition was gradual, over a vertical sp a n of at leas t R othenha usler (1993) disc uss measurement of ha from 150 m, and much of the accumula ti on zone was in the space, and illustra te some of the reasons wh y early dark, low-refl ectance mode. J ung-Rothenha usler (1993 ) expecta tions (e. g. 0 strem , 1975 ) have not been realized. adduced two fa ctors to explain this incomplete se para-
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800 stakes with records of a t least 6 years which co rrela ted a \\'ith concurrent es tima tes of B a t l' 0.9, or T 0.707 600 2: 2: (1'2 = 0.5) for stakes below 650 m a .s.L \V e then c hose E 400 .s subscts of fi\ 'C to ten sta kes located close to the snout. Cl) 200 0 Linea r regress ions of B on B !',lIc, the \un\\'eig hted ) c: toll <'G (ij average of b at the su bse t stakes, were computed over as .c ·200 many years as possible (up to nine). Standard errors w ere
'"<'G ·400 a lwa ys bet\\'ee n ± 100 a nd ± 120 mm, Figure 7 and :E'" ·600 Tablc 4 shO\\· the predini\'e po\\'er o f a typica l subset.
·800 There are sta ti sti cal objections to this proccd u re: 1960 1964 1968 1972 1976 1980 1984 1988 1992 B tOllgll~ a nd B are no t independ e nt. l\'e\'C rtheless a reduced stake network co uld yield useful estim a tes of m ass balan(,e, but with greater uncerta inty tha n the
800 equilibrium-line re lationship dis(' usscd a bo\'C. Because B b a nd Btongue are so hig hly co rrela ted, the standard erro r of 600 the regress ion should be added linearf), to the sta nda rd E 400 .s error of B. gi\'ing a tota l error of a bo ut ± (300- 370 ) mm . Cl) 200 0 I! I! The extra uncertainty is a serio us penalt\" because the c: -- <'G • o nl y sa \'ing is in the time and diffi c ulty of \'isiting more (ij .c ·200 stakes higher up the g lacier. But we conc lude that a m ass
'"<'G ·400 I! ba lance cs tima te need no t be forfeit ed for lack of timc, o r :E'" B =771 ·0.894 h. because of in ability to mo\'e up-g lacier fo r other reasons. ·600 I! se(B) =126 mm ·800 400 800 1200 1600
Equilibrium-line altitude (m) 800 a 600 E Fig. 6. 11 'lzoLe -glacier balallce series aJ observed (" This §. 400 JI 'ork") alld as predicted from 17 0 ("',liodelled"; Cl) 200 U c: Equatioll (3)). a. T ime series; b. seatter cl; rajJh. <'G 0 (ij .c ·200 III fII <'G ·400 ti on: resid ua l errors, and glazi ng. G lazin g prod uces strong :E ·600 contrasts in reflccta nce between snow surfaces, and slopes __ ThlaWork ·800 --- Modelled \\'hich face the afternoon sun a re m o re likeh- to be g lazed. 1960 1964 1968 1972 1976 1980 1984 1988 1992 A ra pid transitio n from dark ice to brig ht sno\\', \\'hich is a prerequisite for exploiting Equation (3), sim ply was not present on Jung-Rothenhausler's Lanelsa t image. 800 This res ult seems a t odd s \\'ith the spec tacula r images B 324 + 0.255 BlOngu. b 600 = o ften sho\\'n as indicati ons of the po tentia l fo r satellite se(B) = 112 mm E remote se nsing of glacier mass balance. We suspect th a t .s 400 such images have either been e nha nced. using O\'e r Cl) 200 0 si m plifi ed a lgori thms, or sim p ly d o not represen t the c: a nnual snowline; rather, they are images of tra nsient, (ij'" .c ·200 hrig ht hi gh-a ltitude sno\\' eO\'er dating fro l11 shortly I! '"<'G ·400 before the time of the im age. The distributio n of this :E'" tra nsielll snow wi ll not in general be related to th e ·600 - position of the a nnual snowli ne. Jung-Rothenhausler's -800 -4000 ·3000 ·2000 ·1000 image \\'as unusua l in dating from the \-ery end of a n Tongue mass balance (mm) abla ti o n season , sl! o\\'ing a m a ture snow pack \\'ith re fl ec tance o nl y moderately g reate r than that of exposecl Ice. Fig. 7. I1 'h ole-gLacier balal/ce series as obserl'ed (" This Thus space-based es tima tes of ho for White Glacier do II 'ork") alld as jJredicted frOIll .itl'e tOllgue stakeJ with not seem to be practi cable, at least in the visibl e spectrum 9 JIf(US ofmwd (" jllodelled") . a. T ime series : b. sea l/er and until understa nding of g lacier surface reflec tance has gmjJh . ad\'<\nced conside ra bly.
Estimates .from redllced ne/works Estilllates ./1'0111 meteorological data Sa\'ings could be reali zed if we could ex ploit hig h inter Gle nday ( 1989) modell ed the mass balance of Whi te stake correla tions (Fi g. 3) to infer B from measurem ents Glac ier as a function of climalOlogical d a ta. The on a fe\\' stakes near the snout. This id ea is the same as ad van tage of sLl ch models is that th e g lacier need not be tha t underlying advocacy of ho as a n es timator o f B. visited at all ; the cos t is negli gible. " 'e examined the se ri es of b at each sta ke, selecting G le nday's best re la tionship expla ins 71 % of the
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vari ance in the mass-balance record (Fig. 8; T a ble 4): each case), so we can es tim a te B for the 2 year interval 1980- 82 (reca lling tha t measurem en lS in spring refer to B = 223.9 - 73.57T + 5. 758P - 2.751K*, (4) the end of the pre" ious ba la n ce year). By linear regress ion, \\'e find the relationship
B = 443 + 0.287 B tongue (5) 800 a 600 between \\' hole-glacier ba lance B a nd th e (unweig h ted ) E 400 .§. a yerage, BtollgllP' o f the balances [or the three stakes oyer (I) 200 CJ the ni ne years 1983- 9 I; r is 0.95, a nd th e standard error is c:: ttI 0 tV ± 105 mm a I . For the same three sta kes, B tonguc for 1980- .c -200 8 2 is - 1755 mm a I , and hence, [i-o m Equa ti on (5), VI VI ttI -400 B = -6lmm a I . This es tim a te h as an unce rta inlY of :2: I , -600 ± (300- 350) mm a- but it is consistent with meLeorolo __ ThlsWork -800 -- Modelled gical es tim ates from Equa ti on (4 ) (T a bl e 4), vvhi ch 1960 1964 1968 1972 1976 1980 1984 1988 1992 average - 148 mm a I . Apparently the mass ba la nce during the gap was close to norma l.
800 b DISCUSSION 600
E 400 .§. The balance norInal (I) 200 CJ If! c:: • ttI 0 •• The stand ard error in any single B is ± (200- 250) mm. tV .. .c -200 • • • • T o estim ate the uncertainty in the balance norma l (B ), VI VI • ttI -400 • w hich is simply the a,'e rage of all the a nnual bala nces, we :2: m ay take as a sta rting-point either this es tim a te or an -600 B =224 • 74 T + 5.8 P - 2.8 K" se(B) =119 mm independent es tima te based on the vari ability in the lime -800 -4 ·3 -2 -1 series. :-Iainl y because ± (200- 250 ) mm is an informal 1000 mbar temperature (0C) ra ther than a rigoro us es tim ate of the stand ard error of B. we choose th e la n er cu urse. [f wc ass ume (e.g. Lyo ns, 1991 ) tha t th e N y es ti ma tes Fig . 8. vVhole-glacier balance series as observed (" T his o[ B are ra nd om , independ ent samples from a popula ti on II -o rk") and as predicted il1 lerms oJ weather data Jrom with fi nite ya ri a nce, th en th e bes t es timate of th e sta nda rd Eureka ("M odeLLed" : Equa tioll (4)). a. T ime series : b. error, se ((B)), of the norma l is eq ual ta th e sta nda rd scatter gra/J/z, projected onto B- T plalle. T, mean slimmer d eyi a ti on, 258 mm, di"ided by y'I'l; = J29 = 5.4 . (B) for (Julle- August) tempera ture ( DC) at JOOO mbar (about 1960- 9 1 may thus be quoted as - 100 ± 48 mm a 1 112 m abo ve sUlJace); P, annual jJreci/Jitatioll (mm); it, se (( B)) defin es a ± 68% confidence region for (B ); sUlIZmer ave rage global solar radiation ( ~1 -1Il - 2). tw ice se (( B)) d efin es a ± 95% confidence region . The Coifficients ),ield estimate of B il7 IIlI11 a J. n ormal differs from zero by m o re than two sta nda rd errors, so, ifour assumptions are justified , we may be 95% confident th a t itis negati ve . where lempera ture T , preCl pIta tion P and globa l solar T o judge whe th er th e Bs a re independent of each radia ti on J(* are all measured a t Eureka (Fig. I). The o ther, we have computed the lag-I a u tocorrela ti on r (i.e. standa rd error of the es tima Le of B is ± I 19 mm, to be the corre lati on o[ the balanee seri es with a co py of itself add ed in quadratu re to the n ominal error o[ ± (200- o ffi et forwa rds b y one year). H r is not zero, then (Zwiers 25 0) mm for a total error o f ± (230- 280 ) mm. Thus, a nd von Starch , 1995) th e effecti ve sample size mig ht be Equa ti on (4 ) is about a ' power[ul as Equation (3), and less than Ny , and thus the es timated sta ndard error might has considerable appeal. Of a ll the alterna tives disc ussed be too small. H owever, for White Glacier T = 0.02, w hi ch here it is the onl y one tha t requires no contact with th e is indistinguisha ble from zero. glacier, remote or oth erwise. The coe fTi cien t of varia tio n (sta nd ard d evia ti on Equa ti on (4) co uld pro ba b ly be improyed upon. For divided by the m agnitude of the m ean) is 2.6. Thus th e example L efauconnier a nd H agen (1990) fo und hi gher m ass-balance record is rath er n oisy, due to na tural correla ti ons betwee n th e m ass balance of a glacier in vari a bility and m easurement error. Spitsbergen a nd c1 im atological quantiti es from a nearby weather station. The balance trend
M ass balance JOI 1980- 82 D etec ting a trend is more diffi cult than determining th e Stakes were measured on White Glacier in 198 1 by J. sign of B. Whether a n estim ate o[ dB/ dt is co nsisten t with W eiss. W e haye readings from 1983 [or Lhree of "'eiss's the true dB/ dt being zero foll ows fr om inspec ti o n of Lh e 198 1 sta kes, a ll of whi ch ha ve r em ain ed in use. Their tim e sta ndard erro r. \Ve risk wrongly accepting th e h ypothesis se ri es ofb a re well correla ted with the tim e series of B (the tha t there is a trend, but the risk is readily qua ntifiable. correla ti ons being 0. 822, 0.866 a nd 0.882, with N r = 9 in The hard part is avoiding th e error of wrongly concluding
Downloaded from https://www.cambridge.org/core. 01 Oct 2021 at 22:25:43, subject to the Cambridge Core terms of use. 558 Cogle)1and others: 111 ass balal/ce Dj 1·I·hite GLacier th a t d B / d t =0, i. e. th a t there is no tre nd . This ri sk is need thi s informa ti on on residuals if we are to es timate th e enl a rged u pon below. probability tha t dB/clt is no t 0 (i.e., th e risk of a type II T he trend and its sta nda rd error se (dB /dt), in mm error). \\re must not use it tw ice. But \ \T were o bliged to a 2, a re bo th deri ved from a linear regressio n of th e se ries draw on it w hen es tima ting the sta nd ard erro r of th e B on the time t, measured in yea rs since to = 1960: trend , se (d B /dt), because we d o not ha\'e ind ependent es tima tes of the error in each B , only th e nom i na l error of B(t ) = B (to) + (dB/ clt) X t. (6) ± (200- 250) mm deri\'ed earli e r. T o gras p the practi cal impo rta nce of' th ese uncerta in H ow sho uld we ex pect glaciers to res p o nd to cha nges ti es, consider \-\'hite Gl acier's response time T. whi ch we 2 in forci ng? In going fi"o m o nc equilibri um to a noth er, a may es tim a te crudely as '" I 0 a because th e glacier is + .) I glacier must e\'olve fro m (B) = 0 back to (B) = 0 \·ia a n ", 10 m long a nd Oows a t ", IO- m a . J 6ha nnesson and exc ursio n. Figure 9 shows th e mass ba la nce o r a glacier in o thers (1989), w ho rrana lyze the kinema ti c-wave model equili brium \I'ith th e clima te un til time t Q, w hen th ere is a o f' glacier termi nus flu ctua ti on s (HulLcr, 1983; L1iboutry, step cha nge in forcin g. The re is an immedia te change in 1987), suggest calcula ting T as - H / bslIout , where H is a B: the g lacier is no\\' eithe r too long and thi ck or too short typica l thickness, and bSlIout the mass bala nce a t the snout. and thin, so B becomes n egatiw or positive accordingly. Appropri a te \'al ues, H = 200 m a nd bSllOlll = - 2 m a I, (We assume tha t (3( h) vari es so th at a glacier whi ch is too again suggest T c::: 100 yea rs. rc dB/ dt is indeed - 2 mm long \I· ill g ro\\' shorter, and one \\'hi ch is toO short will a 2, and if this trend continued for T yea rs, the ba la nce grow lo nger . Note th a t B is a specifi c qua ntity, cxpressed normal would become 300 mill a I - ~ ur ely a sig nifi cant per unit a rea ovcr th e c ha nging tota l extent of th e response. But is it phys icall y likely or reali sti c? From glacier. ) B remains no n-zero un til th e glacier a ttains the Equation (4 ), the te mpera ture se nsiti\'iry of the bala nce area a nd thickn ess a ppropria te to th e new clima te. but its oB/aT is - 74 mm a I K I, ro ug hl y co nsiste nt with magnitude must approach zero more a nd m o re closely. [n es tima tes by Kuhn ( 1993) based on energy-bala nce oth er words, there ought to be a non-zero trend dB/dt in modelling. \\,ith predi cted wa rming fo r the nex t cenrury the mass ba la nce of' a glacie r not a t equilibrium . oCaT/at ",0.0 1 0.03 K a I ( H o ug hton and o thers, 1990, 1992). a (tra nsient) balance trend cl B/dt of a bo ut - I or - 2 mm a 2 sho ul d thus be expected in th e near future, a nd perh aps no\\'. This is j us t wha t has a lready been t ?> measured, a nd rej ec ted because o f its large uncerta inty. Forcing We cannot meas ure suc h su btle trends, N atura l \'ari a bili ty m ay defea t our bes t efforts, bu t it seems that a way must be fo und to m easure mass ba la nces a nd I ba la nce trends \\'ith about te n-fold greater accuracy. With th e d a ta a\'a il a bl e now, se (dB/clt) = ±5 mm a 2 is B ------~----_= __ ------o f ~lr too la rge, but \\' ith se (d B/dt ) = ±0.5 mm a 2 we m ight alread y ha \'e a firm detection of a clima ti call y pla usibl e tre nd fo r White G lacie r. T o repeat a n earli er conclusion: because its mass ba lance is not zero, there V o ught to be suc h a trend. One line of inquiry \I'hi c h does not d e pe nd on dB/dt im pro\'Cd accuracy is to explore how uncertainties e\'o"'e ~ as th e anlil a blc record gro\\·s . The res ult (Fi g. 10 ) shows a to slow increase, pro portiona l to j"FT:. in our confidence in es tim ates of (B ) a nd dB/clt. G i\'en only th e fi rs t ha lf of Fig. 9. Schematic resjJollse of a gl(lrif)' to a change ill the record , ,ve might draw quite misleading conclusions, jorcillg. T lte dimale ( " Forcing") changes at lime to : the T\\·o of th e m ost negati\'C ba la nces in the series were balance B, and therefore also the trend dB/dt, resjJond measured in its first a nd third years; pres uma bl y this a{{ordillg~J'. T he shajJe dmwlI jor B is arbitrm)'. but ill pl acement is cl ue to chance, bu t, wha te\'er the reason, it general dB/dt is llel'er .:ero while B is 170t .:ero. On(J' in expl ain s \\'h)' the es tim a tes e\'oh'e rapid'" in the first half the limit q/ a ste/J-jilll ctioll res/JOllle (i.e. a rectangular of th e record. Only aft er 25 years can we cla im with 95% shajJe./or B ) l('ill dB / dt be .:ero during adjustlllflltto the confidence tha t (B) is no t zero, a nd a l'el)' Inuch LOl/ger altered ./orcillg. ,\ ote that we are not regardillg the balal/ce record will be needed be fore we can detect with the sa me as 'Jorcil/g" jor chal/ges ill glacier lmgth, as is sOllletimes confidence tha t dB/clt is no t zero. dOl/f , Are trends d etectable in the cl ima ti c fo rcing? Surface tempera tures in the Canadia n Arcti c a ppear, from th e la rge-sca le a na lyses of H a nse n a nd Lebedeff ( 1987 ), J ones For White Glacier, d B /df; is estima ted as - 2 ± 5 mm ( 1988 ) and F o ll a nd and o thers ( 1990 ), to have cooled a 2 T hus the conclusio n tha t dB/cl L = 0 seem s fa irl y safe. m odera tely in recent decad es, but th e trends a re not But it m ay be a tvpe 11 erro r, tha t of' \\'ro ng ly accepting a strong. \\'alsh a nd Chapma n ( 1990) a na lyzed sta ti on fa lse hypothes is, We canno t qua ntify the risk of such a n tempera ture d a ta; none of th e Canadia n Arcti c sta ti ons error, because, of th e [Ot a l stock of info rma ti on in th e showed signifi can t trends. K a hl a nd others ( 1993) show da ta, tha t o n de\'iations of the obsen'ed B fr om th e fitted tha t th e tro pospheri c tempera ture in th e Canadia n Arcti c lin e has a lread y bee n " used up" (cf. L yons, 199 1). We during 1958- 86 ex hibited mod e ra tely signifi cant summer
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1000 200
800 a b
600 120 --'ca I:D III E 400 iii ~ E 0 -a; 200 40 (I) ~ E 0 -(I) ... ~ 0 Q. C Cl) ·200 ·40 (.) -3 C 3 as ·400 a; III m N ·600 ·120 - ·800
·1000 ·200 60 64 68 72 76 80 84 88 9260 64 68 72 76 80 84 88 92
Fig. 10. Evolution of estimates qf the balance norll1al and trend. Il le step through the record one )lear at a time, recalCIIlating the Ilonllal and trend with the record alJailable 10 date. ( E\cejJtlhat the information became available ill this chronological order . there is 110 jJarticular reason for stepping forwa rds through the record, orfor slarting at the beginning.) Thick lines : estimated normal (Cl) and trend ( b). Thin lilies: 95% confidence regiolls (i.e. ± 2 x standard error of estilllate oJ normal or trend. assuming 110 serial correlation ill the time series). 1980- 82 gap Jilled u'ith estimates fro III Equation ( 4) .
cooling, at levcls up to 300 mba r. It would be interes ting measurem ents. For three glaciers we present additional to kno\\" whether this represents a n increase in lapse rate. multi-year balances based on stake readings more th a n
But as it stands, this study is consistent with the surface 2 years a pa rt; in these cases N y is simply the number of stud ies : no evidence for regional warming in recent years sepa ra ting the two se ts of read ings. d ecades. Unfortunately the spatial distribution of the glaciers is For precipita tion, the most recent large-scale com pila unfavourable for mapping. T o es tima te th e regional tion (VinnikO\' and others, 1990) excludes the Canadian balance normal (BR)' it seems more reali stic to se ttl e for a Arctic, so we have used our own data set (Briggs a nd simple regional average. The average of the normals of Cogle)', 1990). Precipi ta tion can be highl y variable th e fi ve longest records (T able 6), weighted by record spa tia ll y, and in parti cular altitudinall y (Ohmura a nd leng th N", is (BR ) = - 82mma I. V a rious weighting l'v'fLill er, 1977 ). Moreover, it is difTi cult to measure because sc hemes sLl ch as not weighting at a ll, including the gauges, es pec ia ll y snow gauges, tend to undercatch (e.g. shorter records, a nd weighting by extent, a ll gi\'e \Voo and others, 1983). Thus the e\'idence (Table 5) is of es tima tes within 30 mm a 1 of - 82 mill al. The error in d o ubtful qua li ty, and is also inconclusive. At three (BR) is no t easy to evaluate, beca Ll se of spatial auto stati ons there appears to be no trend, whi le at two there correla ti o n a nd ex trem e undersampling, but it mu st be of a re ma rgina ll y significant increases. A signifi cant decrease in accumula ti on was observed by F. ~Ii.ill e r (1963d ) at a site not far from "Vhite G lacier. This record derives from Table 5. Anl1ual jJrecipitation al High Arctic weather a n earlier interva l, a nd th e information is described as stations preliminary, but it adds to a strong impression th a t no trend in prec ipita tion can be id entified with confidence. Since clim atic trends are not evident, it is perhaps Slation [nterva( Average Trend unsurprising tha t trends arc no t d etectable in g lacier mm a mm a 2 response to climate. But then (Fig. 9), why is White Glacier's mass balance negative? This paradox illustrates the most important conclusion from the analysis a bove: Alert 1960- 79 153 ± 9 -0.5 ± 1. 6 with the present technology of mass· balance measure· Eureka 1960- 79 58 ± 3 1.0 ± 0.5 Isachse n 1960 79 117 8 2.1 1. 3 m ent, the trends which we should expect now a nd 111 ± ± coming decades wi ll be almost impossible to detect. Mould Bay 1960- 79 94 ± 7 - 0.8 ± 1.2 R esolute A 1960- 79 129 ± 7 - 0.6 ± 1. 3 The regional balance normal White Crown Mountaint 1921 - 6 1 375 ± 17 - 5.2 ± 1. 2 \Ve ha\'e gathered data for other High Arctic glaciers fr om literature sources. For each g lacier, T able 6 includes W eather-station data (Briggs and Cogley, 1990) are for basic geographical information as well as th e ba lance calenda r years. no rma l and, if the record is long enough, th e trend. The t Snow accumula ti on ra te at 1920 m a.s.l. , about 40 km time-span gi\'e n may include one or more years without north of White G lacier (F. :'Ii.iller 1963d ) .
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T able 6. AJass-balance series Jor H igh Arctic glaciers ( Fig. I ) . Source:> : 1, This work; 2, R. M . Koemer (personal communication, 1994); 3, BLallel' and K ap/Jenberger (1988); 4, B rad/~y and Serre<.e (1987); 5, Kassa (1973) : 6, Aleall and NldLler ( 1977); 7, Ommall111!)1 ( ulljJub hshed a); 8, Ommall lley (ulZjlubLished b); 9, SagaI' ( /964) . Amold (1968)
Kame (B) dB/ dt d Area Alill- ma.\ T ime-span N.l Island Source elevation
.) mm a mm a - 2 km km- m
White Glacier - 100 ± 48 - 2 ± 5 0 38.7 53- 1782 1960- 91 29 Axel H eiberg Ba by Glacier - 11 2 ± 9 1 3 ± 11 10 0. 6 715- 11 75 1960- 9 1 19 Axcl H eiberg 6, I M eighen Ice Cap - 129 ± 52 7 ± 5 172 85.0 70- 267 1960-9 1 30 NI eighen 2 Devon Ice Cap NW - 50 ± 23 1± 3 505 1696 0- 1800 196 1- 9 1 30 D e\'on 2 South I ce Cap - 29 ± 57 - 19 ± 15 730 66.0 490- 71 5 1963- 74 10 l\Ieh'ille 7 Sou th I ce Cap. - 73 730 66.0 490- 715 1974-80 7 l\Ieh-i li e 7 Gilma n G lacier - 97 ± 47 454 480 4 10- 1850 1957- 6 1 5 E lI es mere 9 Gilma n G lacier . - 29 454 480 4 10- 1850 1957- 67 11 E ll esmere 9 Per Ard ua Gl ac ier - 320 339 4 .7 300- 1700 1968 ElIes mere 5 Laika I ce Cap -630 484 9 .8 0- 530 1975 1 Coburg 3 SPB NE Tce Cap 20 ± 54 - 8 ± 14 538 7.6 850- 900 1972- 82 6 ElI es mere 4,8 SPB N E Ice Cap. - 130 538 7. 6 8.10- 900 1972 11 E lI es mere 4,8 SPB SW Tce Cap 165 538 3.0 740- 820 1983 I ElI es mere 4
• Multi-year balance. d, Dista nce fr om White G lacier.
N y , Number of years of record (excluding gaps). SPB, S t Pa trick Bay.
th e orde r of th e uncertainty in th e measured normals (B ), mended onl y 1'0 1' sa h- aging a n es tima te 111 difficul t fi eld na mely a bout ±50 mm a I . conditions. H ydrometeorological modelling is a prac ti cal This es timate of (BR), a nd ~r e i e r 's ( 1984) \'alue of solution ifit is im possible e\'en to \'isit th e glacier. R emote 108600 km2 for th e glacierized a rea or the Canadi a n Hig h sensin g or m ass balance is nOl presentl y practical, a nd Arcti c, give a contributio n to sea-I e\'el ri se of 0.024 ± \'isiblc-ba nd imagery may nC\'er become a ro utine tool in 0. 0 15 111m a I . T his es tima te is co mpa tible with Meier's the es tim a ti on of mass ba la nce. 0.0 19 mm a I, but being based on fewer ass umptions it is White G lacier is representa tive of the Canadia n High more robust. Thus th e C a n adia n High Arctic, although it Arcti c, a nd the dispersion of single glaciers a bout a con tains one-fifth or the " 'orld area coyered by sma ll regional bala nce normal or a bo ut - 80 mm a 1 is not ve ry glaciers, supplies onl y o ne-twentieth or the total sma ll great. The e\·idence for trends is weak, a nd in pa rticul a r glacier contribu tion to ri . ing sea le\'el , es tima ted by l\Ieie r \ \'hite Gl acier seems to h ave a consta nt mass bala nce. as 0.46 ± 0.26 mm a 1 consistent w ith a simila r a bse nce of e\'idence 1'0 1' trends in cl im a ti c forcing. Howe\'er , present methods of balance measureme nt a re in adequa te for detec ting tre nds of th e SUMMARY m agni tude to be ex pected from genera li zed c1im a tological reasoning. Errors in stake mass b a la nce b a re a bout ± (200 This is a serious probl em for glaciology. L a rge errors 250) mm , due la rgely to undersa mpling . Errors in a re attached to our es tima tes, errors whi ch we suspec t to whole-g lacier mass bala nce B a re or the same order as be typical of many other m ass-balance eS lima tes. A sin gle-sta ke errors. H owever, th e lag-I a u tocorrela ti on or founda ti on o f measurements, however sparse, is esse nti al th e time seri es or B is zero, so the error in the long-term in moni toring cl im a ti c cha nge. But the measurements ave rage orB is noti ceably less . A number or recording a nd reported here a re ra th er inaccura te, and all of the cheaper processing errors \I'e re d etected during reassessment or the alternatives a re e\'en more inaccura te. Researc h on more record , but wc do not think th a t our work has bee n less accura te \Nays or es tima ting m ass bala nce d eserves hi gh careful th a n th at of other g laciologists. R a ther, th e errors priority. a re a consequence or the complexity a nd lo nge\'it y of the enterprise. The bala nce norma l (B ) is - 100 ± 48 mm ai, deri ved ACKNOWLEDGEMENTS from 29 a nnual measurem ents of B. The reassessed bala nce se ri es agrees closely with previo usly published W e gra teful ly ackn owledge the work of a ll those who have valu es. made or assisted with mass-ba la nce measurem ents on Among less accura te a lterna ti \'Cs to th e present stake White Glacie r. ' Ne thank the following organizations th a t based p rogramme, a red uced stake network is recom- ha \'e su pported mass-bala nce work on \\'hi te Glacier:
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Pola r Continental Shelf Projec t, Energy Mines a nd Axel H eiberg Island , ~.W . T , 1970 80. (I3. A . thesis. Trent R esources Canada; Na ti onal H ydrology R esearch Inst U ni\·ersit),. ) Haeberli , \\'., I'd. 1985. Flllcll/ations oJ glacim 1975- 1980 ( 1'01 . 11 ). Pari s, itute, Environment Ca nada, Sas katoon; Geographisch es I nternationa l Commission o n Sno\\' and rc e uf the International Inslitut, ETH, ZUri ch; Trent U ni\'ersity, Canada; the Associa ti o n of H yd rological Sciences/Unesco. M cGill Sta ti on, Axel H eiberg Isla nd; th e J acobse n Haeberli , W . a nd ~1. Hoclzlc , eds . 1993. Fiuril/alions oJ glarim 1.985-1.990 iVl cGill Arcti c R esearch Expeditions; Science Institute, ( /'01. f'I). \\'all ingford, O xon ., IAHS Press; :"k-o.\ , 39, 31 38. Bl a ller, H . 1985. On the thermal regime of Arcti c glaciers: a st ud y of th e Kahl , .1 . D. W ., J\1. C. Se rreze, R . S. Stone. S. Shi o ta ni , j\1. Kisley and \\'hi te G lacier. Axel Heiberg Island, a nd the La ika Glacier, Coburg R . C. Schnell. 1993. Tropospheric tempera ture trends in the Arc tic: Isla nd, Canadi a n Arcti c Arc hipelago.
Downloaded56 from2 https://www.cambridge.org/core. 01 Oct 2021 at 22:25:43, subject to the Cambridge Core terms of use. Cogley and olh ers: i\lass balance of ll "ltile GLacier
/)J"flilllilla~)' re/Jorl 1961 1962. t.l olllr('a l, Que., :-- lcGill Uni\Trsity. 37 Ollllllanney, C. S. L. 1987b. Axcl Heiberg Island \·isitaLions. 111 ,\ dams, +6. Axe! Heiberg Island R csearch Reports.) 1' ., I'd . Field research 011 .. h el lIeibag "Innd . . \'. fI'. T.. Cfl/rada: t. l ull cr. F. 1963 b . . \ ccumulation studies. III t.l u ll er, F. and 18 others, eds . bibliogra/)hies alld dala reporl .1 1.l' ilh appelldicc; I.!f dala from Ihe .I/c(;i/I ]acohsell ,IIcGill . Irclic Research ""/mlilioll 1.959 1962: /He/illlillal)' re/JOrl Subarelic Resea rch Slalioll. ScheJfen'ille. P. Q \lontJ'CaI, Que .. t.kGi ll 1961 1962. :-'I ontreal, Que., t.IcGill Cnin'rsit y. 7 25. ,\ xei H eiberg Ull i\'ersity. Centrc for :\Torthern Sludies a nd R esearch. 56 66. Island Research Reports. ) ;\IcGill Subaruic Researc h Paper +1. Axel H eiberg Island :--Hiller, F. 1963c. G lacier mass budget a nd climate threc years of Research R eports. ;\ Iiscell aneous Papers 2. ) m easuremcnts on Axel H eiberg Islanel ). III t.Hiller, F. alld 18 olhers, Olllmanney, C. S. L. Unpublished a. Calladioll glacier l'fIriatiolls alld lilt/I> eds. ]aco/rwl ,\lcGil! . Irelic R" .Ierll'ch E\/m/iliol1 1959 1962: /mlimillal)' halallC(' rhallges: 1975 1980 quadrellllial re/)lIrl 10 Ihe Penllallelll Serl'ice lI lI Ihe 1'1'/)01'1 1961- 1962. :--I ontrbl, Que., :--1cGill Cni\Trsit y. 57 64. (Axcl Fluclualiolls o/Glariers. Otta",a. Ont., En vironment Canada. "ational H eiberg Island R esearch R eports. H \'drology Rcsearch Institu te. Snow and Ice Di\·ision. t.lLill er, F. 1963d. 1l1\Tstigations in an ice shaft in the accumulation a rea Ollllllanncy, C . S. L. Unpubli shed b. Qjladrl'llllial 1'1'/)01'1 10 Ihe Perlllall elll of th" t.JcGill Ice Cap. III t.liilier, F. alld 18 olh en, eds. ]acob.lell J lc(;i/I Serl,ice 011 th e Fiut/ualioll of Clarins 011 Calladiall gla cier l'fI rialioll.I alld lIIau . Jrclic Rwardl E,/m/ilioll 1959 1962: /mlilllillal), re/)orl 1961- 1962. balallff rhall,l5fJ. Ottawa, Onl., Fishcries and EI1\'ironment Callada . :--lontr<'al. Quc., :-- IcGill Cni\·crsit\,. 27 36. Axcl Hl'ibcrg Island Inl a nd lI'aters Di rectora te. Glaciology Di\·ision. R esearch Reports. ) Ostrem, G. 1975. ERTS data in g laciologv an effo rt to monilor glacier t.IOller, F. 1963e. SU I'\'c\'ing ofglacin mOlT ll1 e llt anel mass changes. III mass bala nce {i'o lll satelli te imagery. J. Glacial., 15(73 ). 403 +15. :--1 0Ilcr. F. a nd 18 othcrs, cd.l . ]acoblell-. l/cGill. lrclic ReJl'arch E,/)edilioll Ostrcm, G. and ;\1. Ilrugman. 1991. Glarier lIIass-balallre lIIeaSllrelllflllr. .1 1959 1962: /m/illliIlOl)' reporl 1961 1962. :-- Io n treal. Qui'., :--lcGi ll mallllal Ior Iield nnd office uwk. Saskatoon. Sask., EI1\'ironlllcnt Cni\·ersit \·.65 80. (,\ xcl H cibrrg Island R esca rch Reports. ) Canaela. :\Tational Hydro logy R esearch Institutc. (:\T HRI Science t. loller, F .. I'd. 1977. nlltillaliOll .l o/glaciers 1.970 1975 ( I·nl. Ill) . Paris, Report +. ) International COJllmiss ion on Snow and l ec of th e Internationa l Paterson. \ \ '. S. B. 198 I. Th e /)lu'sir.1 a/glaciers. Second edilioll. Oxford, ete .. Association of H)drological Sciences G:\TESCO. Perga mon Press. :-- I Oil er. F. alld 18 olhers. 1963. ]arobwl .IIcGi/1 ..I n lir Rmarch E,/mlilinll Pelt o, :--1 . S. 1988. The annual balall cc of " orth Cascad e gla ciers, 1959 1962: /mlilllillfl/)' reporl 1961 1962 alld lIIap .IIlNlnll l'lIl. ;\lo ntrca l. \V ashing Lo l1 , LT.S.A., mca sured an d predicted Ll sin g an acti\'ity-index Que., :-- lcGill UniH'!'sily. (Axcl Heiberg Island Research Reports.) Il1nhoel.]. Gla riol .. 3411 17), 19+-199. ~"oller , F. and C.:-- 1. K eeler. 1969. F.rrors in short-term ablatio n Redpath . B. B. 1965. SeiJmic ill1'e.l/igaliulI cif glaciers nil . I \d lleiberg Islalld. measurements on melting ice surfaccs. J. Glacial .. 8 (52 ), 9 1- 105. Calladiall , Irrlir .Irrhi/)e/ago . t. lonlrea l, Que .. :--IcGi ll Uni\'Crsit y. Na ti o nal Rcsearch Council of Canada. 1962a. Tholll/).lolI Glacier regioll. Uacobst'll i\ IcGi ll Arctic R esearch Exped ition 1959- 1962. Axel . h el lleiberg hlallrl . . \'. 11 '. T.. Callada. based all 28 ]lILI' alld 13 .1l/gl/sl 1959 H eibe rg- Isla nd Research Repo rts. Geophysics 1.) pholograpl(}'. :--I nntrc-al. Que .. Ph otogrammctric R esearch Section of Rogcrson. R .J . 1986. t. lass balance orfou!' cirquc g laciers in the Tomga t the National Research Council of Canada in conjunction ",ith thl' \Iountains oJ'northcrn Labrador, Canada. J. Glacial., 32 I I I . 208 218. J acobsen :--l cGill .\rcric R esearch Expeditio n to ,\xci He ibcrg SagaI', R . 13 . 196-1. t.letl'orological and glaeiological obscJ'\'alions on the Island, N. II'.T .. t. lcG ill LTnin'!'sity. Gilma n G lacier, northern Ellcsmere Island, 1961. (;l'ogr. 131111.22. 13 56. Na ti onal Research Council of Canada. 1962b. I i'llile Glarier. Tll oll1/).lolI Trabant, D . C. and L. R. t. 1ayo. 1985. Estima tion a nd enects ofintl'rna l Glacier regioll, A \fl lleibfl~!; islalld. Calladiall . Irclir Arrlllj)rlago . based 011 2 accull1ulation on li \'e glaciers in .~I a,ka .. 11111. Glariol., 6 , 11 3 I 17. .·llIglol 1960 phologra/"(l' . t.rontri-a l, Que., Photogrammetric Research YinnikO\', K . Ya .. P. Ya. Groism all and K. :--1. Lugi n a. 1990. Empirica l Sectio n of the National R esearch Council o J' Canada in conj unction data on con tcmporary global clima te changes tempcratulT and with the I\ xc l H ci bcrg bland Expedition or i\IcGill Uni\'('rsit )' . prccipita ti o n !. J. Clilllale. 3 , 662 677. "mional Resea rch Council o f Canada. 1965. I J 'hile Glarier . . he! lIeiberp, \I'"lsh, J . E. and \I'. L. Chapman. 1990. Short-term cl imatic \'ariabilit y Islalld, Calladiall . Ir·clie . Irrhi/Je/ago . /rasl'd 011 2 . 1l/gllsl 1960/)hologra/)I(I'. of the ,\ rc ti c. ]. Clilllall'. 3 (2 , 237 250. t. lo ntrc'a l, Que., Ph otogrammclric Resea rc h Section of the National \I·e iss . ,J . 19 8~. :-'I asse nhaushalt e ines Gletsc hers, Frag-c n a ll glaziolo Resea rch Council of Canada in co njunc ti o n with the .\ xcl H eiberg gisc he LTntc!'suchungcn und die R rsu ltate del' :--Icss rc ih e am II'hite Isla nd Expedition of :--l cG ill LTni\'CJ'sit\. G lacier,in dcr kanadisc hcn Arktis. Diplomarbe it , Geographisc hcs Ohmura, ,\ . a nd F. :--Ioller. 1977. Di e mcsoklimatische \ 'l'rt ei lung \'on Institut, L' ni\·c rsit\· or Zlirich and ETH. Lul'ttemperatur und N iedersc hl ag liber del' hocharktisc hcn Tundra \\'00, t. 1. -k., R . Heron , P. i\ larsh and P. Steer. 1983. Comparison o f \'on " xci HcibC'J','i Island, N. \I'.T .. Kanada. Ceogr. I-leh .. 32 111, 185 19·1. \\ ,(,~ llh e r station sno\\' rall wil h v.- inter snow acclIl11Lti a lion in Hi gh Ommanncy, C.S. L. 1969 . . 1 sllld}' ill glarier illl'fIlIO/)': Ihe ire ma.llf.' ifA \f1 .\ rCl ic basins . . l/lIIo;/)here Oceall. 21 3',312 325. lIeibel/!, 1;lallrl. Calladiall . Irrlir .Irr/ripelago. :--I o ntrt'al. Que .. :-- IcGill Young, G.,J . 19 72. \I'hitc G lacie r mass balance. III :--I olkr. F. a nd 6 UnivCI'si ty. Axcl H eiberg Island Research R eports. Glaciology 3. ) others, edl. IlIlel'llaliollal Ceogra/lhical 1'lIioll . Field 7 0111' Ea 2, .Ir·clir Ollllllannc\,. C. S. L. 1987a. Axcl Hcibcrg Island bibl iograph y. III . Irrhi/)e/ago 1. 2211d IlIlmwliollal Gfogra/)/riwl COllgre.,.\. t.l o nrreal, Que., Adallls. P., I'd. Fidd re.;mrch Oil . h '" HribPl~r; 1,lalld . .I'. JI'. T, Call1lda: t.IcGill Uni\'Crsit)', 25 30. (f\ xl'i Hei berg Island R esearch Reports. bibliographie.1 lIlId dflla 1'1'/)01'11 1l'ilh appelldicf.) of dala frOIll Ihe .I/r(,·ill :-- lisccllancous Papers. S"b(lrclir Hereardl SllIlioll, '<;chel/i'/'/'ille. P.O.o :--I ontr<'a l, Que., ;\IcG il l You ng, G. J . 198 I. The mass balance of Pey to Glacier, A lberta, Canada. UnivCI'sity. Centre fur Northcrn Studics ancl Re,earch, 5 55. 1965 10 1978 . . Irrl . . lip. Re.I ., 1313),307 3 18. t.IcGill SubarClic R esearch Paper 4 1. A xcl Heiberg Island Zwiers, F .. l. a nd H. \'on Storch. 1995. Taking se ri a l correlation into R esearch R eport'. :--l iscelLa ncous Pa pers 2. ) accou lll in tests of th e mea n. J. C/imale, 8,336 35 I .
MS received 30 M arch 1994 and accejJled ill re vised Jorlll 5 June 1996
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