Journal of Glaciology, Vol. 32, No. 112, 19 MASS-BALANCE MEASUREMENTS: PROBLEMS AND TWO NEW METHODS OF DETERMNNG VARATONS By LOUS R EYNAUD, MCHEL VALLON, and ANN E L ETREGU LL Y (Laboratoire de Glaciologie et Geophysique de 'Environneent, Centre Na tion al de la Recherche Scientifique, 2 Saint-Martin-d'Heres Cedex, France) ABSTRACT. The optiu continuation of series of ass- balance easureents and their extension to unonitored glaciers are iportant probles in conteporary glaciology. For this purpose, two new practical survey ethods are proposed, based on the linear-balance variations odel of Lliboutry (19). The first ethod is a siplified application of the linear odel that uses only a data set liited to selected fixed-easureent sites. t was developed to obtain the ass-balance variation in cases where data are too scarce to obtain the global ass balance or to apply the Lliboutry algorith. This siplified linear odel is used with the years' of surveys on glacier d'argentiere. The second ethod uses the continuity equation to derive the ass balance of a glacier sector deliited by two cross-profiles where the surface velocities, surface altitudes, and depths are known. By using this continuity ethod, the entire ass-balance series is established for a sector of glacier de Gebroulaz (Vanoise area, France) fro 190 to 190, as well as for two sectors of Unteraargletscher (Oberland, Switzerland) fro 192 to 191. RESUME. Mesures du bilan de asse: probli!es et deux nouvelles ethodes pour deteriner les variations. De nos jours, les problees des esures des bilans de asse se situent principaleent, soit dans le developpeent des systees de esures, soit plus sipleent dans la survie des series de esures en cours. Dans cette optique, nous proposons deux nouvelles ethodes d'analyse des esures de bilans effectuees sur les glaciers. Elles sont basees sur le ode le lineaire de variation des bilans propose par Lliboutry (19). La preiere ethode est une application siplifiee du odi!le lineaire de variation, qui n'utilise qu'un systee de esures liitees {t quelques sites fixes du glacier. Elle a ete developpee pour obtenir la variation du bilan dans le cas oil les donnees ne sont pas suffisaent nobreuses pour obtenir le bilan de asse global ou pour appiquer l'algorithe de Lliboutry. Ce odi!le lineaire siplifie est NTRODUCTON As the ass balance of a glacier is indicative of cliatic input to the glacier syste, it should be carefully onitored by glaciologists. Unfortunately, direct easureents were begun only recently: in 19 for Storglaciliren and in 19 for glacier de Sarennes. Practical ethods have been used as an alternative to the direct glaciological ethod, allowing extension, by cartographical or hydrological eans, of ass-balance studies over a longer span of tie (Paterson, 191). The l.h.d. saw an increase in glacier surveying and consequently a survey network is now available. However, now that this enthusiastic.h.d. period has ended, the continuation of these annual surveys, with the large aount of work necessary, has becoe a heavy burden. Not only ust the series in progress be continued but also ore characteristic points are required to coplete our data to iprove tie consistency and area representivity. applique au glacier d' Argentiere pour annees de esures. La seconde ethode, basee sur /'equation de continuite, per et d'obtenir le bilan de asse d'un secteur de glacier liite par deux profils transversaux de sections droites connues, oil ont ete esurees les altitudes et vitesses oyennes en surface. On a de cette fa~on etabli la serie entiere des bilans pour le glacier de Gebroulaz (Massif de la Vanoise, France) de 190 {t 190, ainsi que ceux de 2 secteurs du Unteraargletscher (Massif de 1'0berland, Suisse) de 192 (t 191. ZUSAMMENFASSUNG. Massenbilanzessungell: Problee und zwei neue Methoden zur Bestiung von Schwankulgen. Die beste Fortsetzung von Messreihen der Massenbilanz und ihre Ausdehnung auf nicht uberwachte Gletscher sind wichtige Problee in der Glaziologie der Gegenwart. Zu ihrer LOsung werden auf der Grundlage des Modells der linearen Bilanzschwankungen von Lliboutry (19) zwei neue praktische Veressungsethoden vorgeschlagen. Die erste ist eine vereinfachte Anwendung des!inearen Modells, die nur einen Datensatz, der auf ausgewl1hlte Stellen it festgelegten zur Messungen beschrl1nkt ist, benutzt. Sie wurde Gewinnung von Schwankungen der Massenbilanz in solchen Hlen entwickelt, wo Daten zu sp!\rlich sind, urn die globale Massenbilanz zu eritteln oder den LliboutryAgorithus anzuwenden. Dieses vereinfachte lineare Modell wird auf die achtjl1hrigen Beobachtungen a Glacier d'argentiere angewandt. Die zweite Methode benutzt die Kontinuittitsgleichung zur Herleitung der Massenbilanz eines Gletscherabschnittes, der von zwei Querprofilen begrenzt ist, in denen die Oberfllichengeschwindigkeit, die HOhe der Oberf111che und die Dicke bekannt sind. Mit dieser Kontinuittitsethode wird die gesate Reihe der Massenbilanzen fur einen Abschnitt des Glacier de Gebroulaz (Gebiet von Vanoise, Frankreich) zwischen 190 und 190 bestit, ebenso fur zwei Abschnitte des Unteraargletschers (Berner Oberland, Schweiz) zwischen 192 und 191. Under these circustances, we ust adjust the ethodology in the light of the results already obtained and extend analysis to seek possible rules for wider application, especially in the potential use of reote sensing or satellite iagery of glaciers. One of the ajor points which eerges fro the analysis of glacier balances, in order to deterine their cliatic significance (reconstruction of past balances using eteorological paraeters), their spatio-teporal distribution, or their dynaic response (changes in surface area, length, and levels), is that we use only the coponent varying with tie. The ean ass balance depends too closely on the orphological characteristics of each individual glacier to be used easily. This is the reason why we are investigating new ethods that allow a sipler coputation of the balance variations without having to ake all the de terinations necessary for a global budget. The two ethods presented in this paper have been derived by the application of the linear odel of ass-balance variations given by Lliboutry
Reynaud and others: Mass-balance easureents (19). The first ethod, "the siplified linear odel", gives the balance fluctuations fro a liited stake array. t is applied to glacier d'argentiere (Mont Blanc area, France) using data collected at five cross-profiles for the period 19-3. The second ethod, "the continuity ethod", uses historical topographical surveys of two cross-profiles of a glacier to calculate the ean balance of that sector by eans of the continuity equation. t has been applied to glacier de Gebroulaz (Vanoise area, France) for the period 190-0 and to Unteraargletscher (Oberland, Switzerland) for the period 192-1. The linear-balance varialions odel Lliboutry (19) proposed that the easured in year t at location j, ay be three ters: b jl - aj + t + Ejl balance ~jl' separated to where aj is a geographical ter depending only on location j, 1 is the balance variation with tie, independent of the location for a given glacier (r t DO), and E jt is a centred rando residual, which givd the difference between the odel and the field truth. This approach is supported by the physical behaviour of annual ass-balance distributions of several glaciers, a property already suggested by various authors (Meier and Tangborn, 19; Hoinkes, 190). t appears that the balance varies by ore or less the sae aount along a glacier between two consecutive years. This is, in fact, a wellknown hydrological concept used by glaciologists since definition of the average net budget, which represents a linear distribution of the ass balance over the whole glacier. With the linear odel, the balance coputation no longer needs the always delicate and subjective distribution of the surface area since the variation of the balance is reached directly by a least-squares optiization of the network data. More details on this coputation ay be found in the coplete statistical study by Lliboutry (19). To assess its reliability, it would be necessary to copare it with another ethod, such as the voluetric ethod, which appears to be the ost convenient reference. This has been done by Vallon and Leiva (192) for years of data, by direct easureents and by the photograetric ethod. Application of the linear odel to the glacier d'argentiere data Glacier d'argentiere is one of the large valley glaciers on the north side of Mont Blanc. t has been surveyed since for length variations and since 1903 for levels and velocities at two cross-profiles on the lowest part of its tongue (Martin, 19; Reynaud, 19). However, balance easureents were only begun recently, in 19, with an extension of the other surveys to four cross-profiles on the upper part of the glacier (Fig. ), at the request of E.D.F., the French electrical utility copany, in order to follow the variations of the glacier and acquire a better knowledge of the water captured at the bed beneath the Lognan ice fall. Although ten stakes are located on each cross-profile, only four or five give a coparable data set for the period 19-S3. Furtherore, cross-profiles and disappeared beneath the firn durins the 19 and 19 period of heavy accuulation. Finally, only three cross-profiles are left to provide hoogeneous data for the period 19-3 (Table ). The altitudinal ass-balance distribution shows an alost regular variation with an activity coefficient of +0.0 of ice for 0 of altitude (Fig. 2). This graph also exhibits the ass-balance variation characteristic which is the basis of the linear-balance variation odel: the annual variation of the balance is ore or less of the sae agnitude over the whole glacier. To obtain this ean annual variation, t, we use the linear odel in a siple way, which is in fact the first step of the coplete coputation suggested by Lliboutry (19). This involves a coparison of the individual bjt with the ean value for the location j, giving it Then the final t is the ean of the different values given by the three cross-profiles (2,, and ). This set of ass-balance variations can be copared with those obtained at the sae tie on glacier de Saint Sorlin, loo k to the south, in the Grandes Rousses area (Vallon and Leiva, 192). The years of easureents are ARGENTERE o 0 2K 11. -~'==;.._-=== \ Argentlere J 900 Fig. 1. Map 0/ glacier d 'Argentiere showing locations 0/ cross-sections.
Journal of Glaciology TABLE. MASS-BALANCE DATA FOR GLACER D'ARGENTERE FOR 19-3 N METRES OF CE. THE FRST NUMBER N EACH BOX S THE SPECFC MASS BALANCE FOR THAT LOCATON. THE SECOND NUMBER S THE DEVATON FROM THE AVERAGE BALANCE AT THE STE FOR THE WHOLE PEROD Year Cross- profile nuber (altitude in ) of ice (20) (20) (20) (20) 2 () St r.s t 19-2. -3. -3.3-1.31 -.11-1. -9.0-1. -1.3-1.3 19-1.3 +0.9-2.90 +0. -1>. +1.0 +0. --0.9 19-1. +0.9-2. +1.1-1>. +0.1 +0.9 +0.3 199-2.39 +0. -3.0 +0.0 -.0 --0.29 --0.03 +0.32 190-0. -1.3-1.2 +0.0-2.2 +1.0-1>.3 +1.0 +0.9 +1.29 191-0.9-2.0-2.3 +0.09 --.21-0. -. --0.33 -{).2 +1.03 192-1.3 - -3. -0. --.22 --0. -1>. +1.01 --0.0 +0.9 193-1.3-2.33 - --0. --.1 --0.9-9.20 - --0.9 0 (-1.1) (-2.3) -2.2-3. -.1 2 Y / 'il X <0 x x ~ x. / ~ Cl... Cl,aj(J9-193J x VAW.ETHdoto(MoytoOct J1 0 19 ' 'il 19 G 19 19 9 <> 19 0. 191.192 ''--'---'---'--'---'----'----''--L---'--..L..-'---'----'----'_L---'---'--'--L--.J 0 1900 2000 20 2200 20 20 0 20 0 200 200 200 Al titude ( J Fig. 2. Distribution of the average annual balance over glacier d'argentiere at different cross-sections versus the altitude for the period 19-3. very close to the first line, with a correlation coefficient of 0.93 (Fig. 3) (Letreguilly, unpublished). To exaine the influence of the differences between the series on the standard variations of the ice ass, the accuulated values are plotted in Figure, together with those given by Aletschgletscher (Aellen and Kasser, 19). The curves obtained show a very siilar tie variation, 2 o -!\ Argentiere ( of ice) / 9;0 ; -oj~-- 2 01 3 / (1=0.93!)t st Sorlin ( of ice) -2~------~------~--------~------~ -2-0 2 Fig. 3. Coparison of the balallce variatiolls St given by glacier d'argentiere and glacier de Saint Sorlin for the period 19-3. covering practically the sae agnitude range, in spite of the different ethods used: the linear odel for glacier de Saint-Sorlin and the hydrological ethod for Aletschgletscher. n order to analyse globally the statistical significance of this data set, in view of its use with the linear odel, one can copare the variance of the different ters. For each site we obtained a Sjt each year which is E jt fro the ean S' The standard deviation of S;t is 0.93 of
Reynaud and others: Mass-balance easureents 2 o -!St ( of ice) o A rgentiere Sf Sorlin ~ Aletsch Tie (A. D) MASS BALANCE BASED ON THE CONTNUTY EQUATON Monitoring the state of health of glaciers has always been a point of interest to glaciologists. n the beginning, variations in glacier length were thought to be ost indicative of glacier health. Later, around the end of the last century, when boring techniques were less welldeveloped, topography was largely applied to the onitoring of glaciers. Glaciers were surveyed at different crossprofiles and painted rocks were placed to easure oveent. n France, Vallot (1900) adopted this ethod and odified it in 1, when he becae aware that to assess annual variations in velocity on Mer de Glace, the painted rocks had to be replaced each year along the sae profile. This ethod was applied on glacier de Gebroulaz by the,.- 9~ o 0 0 200 1"--1-1 -... 1 ---< -2 19 Fig.. Accuulated variations 0/ at with tie for glacier d'argentii!re, glacier de Sarennes, and Aletschgletscher for the period 19-3. ice and that of the deviation jt is 0.3 of ice. The aount of the total variance accounted for by the linear odel, T, is given by the Quotient of the at variance by the total variance of the saple 3 x ~ a~ T = = 0., -- t=1 j=1 while the residual variance t=1 j=1 contains the reaining 1% of the total variance not taken into account by the linear odel. Although this field-data analysis does not give the ass balance of the whole glacier, it does allow us to estiate the fluctuations of the ass balance in a very siple way, with a data saple liited to a few locations on the glacier, where variations of both level and velocity have been surveyed. Such a ethod sees well suited to the onitoring of balance fluctuations, in order to include new glaciers in the surve~ syste or siply to continue surveys already begun, especally under present circustances where the aount of work has to be reduced. t would clearly be of value to test the application of this linear odel with the results of other usual ethods applied to the sae glacier. This could be done on soe large glaciers presently surveyed by the hydrological ethod where both accuulation and ablation have been easured at several stakes. Even if such stake data are too scarce to define the ass balances, they ight be sufficiently nuerous to obtain their fluctuations. Fro this kind of coparison, the efficiency of the new ethod can be evaluated in order to deterine the degree to which survey work can reasonably be reduced. Fig.. Map 0/ the tongue 0/ glacier de Gebroulaz showing different terinal positions and locations 0/ two cross-profiles. French Water and Forest Resources Bureau (Eaux et Forets) fro 190 to 19 (Fig. )(Reynaud and others, 193). Annual ean altitudes of cross-sections together with ean velocities are given by to S painted rocks (Figs and ). Since the topography is known (Fourno, 19), the ass balance of the section between the two cross-profiles ay be obtained by the continuity equation applied in a discrete anner to this sector (Fig. ). and 9
Journal of Glaciology 20r-----r----,---,--,--r--.---,-.----,----,----,-- --,-,2EO 2 20 220 J20 2:0 2 200 GLAC ER de GEBROULAZ MEAN ALT T UDE S OF THE PROFLES 290 2 Fig.. Mean altitude variation of two cross-sections. where ql and q2 are the annual ice fluxes through the two cross-sections, A is the surface area of the glacier between the two profiles, <b> is the ean annual ass balance of this sector, and <dh/dt> is the ean annual altitude variation of the surface at the two cross-profiles. Unfortunately, the velocity distribution over the whole cross-section of the surface area Si is not known, and yet it is required in order to copute the discharge of ice q. - J Uds - S <U> 1 Si 1 1" However, Nye (19) suggested that the ean section velocity is given by the ean surface velocity <U>S.. Thus 1 qi - Si<u>s 1 The only test available at present for this very siple assuption lies in the data for Athabasca Glacier (Canada), 3 2 20 1 Mean velocity at cross profi les ( / on) ~ 1\... " /.. : :, ~---i, : '...1, ('\J' { / ~,_,,. '0.., GLACER. de GEBROULAZ ANNUAL V ELOCTES FR OM EAUX ET FORETS DATA_ OL- ~ L L- L L- L L- L ~ ~ 190 19 1920 19 190 190 19 T i e. (A.D) Fig.. Mean velocity variation at two cross-sections for 190-. <b> where Rayond (191) actually easured the whole velocity distribution at three cross-sections. He found a ean surface velocity 12% higher than the ean cross-section velocity (Rayond, 193). A siple translation gives then k <b> = -«u>s,s2 - <u>s,s) + <dh/ dt >. A 2 Fig.. Geoefrical sketch of the continuity equation applied to part of a valley glacier between two cross-profiles. The general lack of data on this factor k, found to be around 0.9 for Athabasca Glacier, is a proble since it affects <b> directly. Therefore, the Nye assuption concerning flux coputation presently reains an adequate approxiation, especially in view of errors of at least siilar agnitude in this kind of application within the areas of the cross-sections because they were deterined by 0
Reynaud and others: Mass-balance easureents seisic soundings. For this reason, for want of a general rule, we will adopt the Nye assuption for flux coputation. Although the surface area between the two crosssections did not vary appreciably over the period 190-0, reaining at about ha, the ean altitude of the sector varied by approxiately 0. n order to aintain hoogeneity of the ass-balance data, they are copared at the sae altitude, that of 190, with a gradient of 0. of water for each 0 of altitude. The coplete data set necessary for the coputations is given in Table 11. They show a ean ass balance siilar to_ that recently observed with ablation stakes: <b> = -0 of ice, i.e. -1.0 of water equivalent. The deviation fro the ean is given each year by These data are plotted in Figure 9 together with the accuulated values in order to show the trends for the period. The expected sequences of balances favourable to TABLE n. GLACER DE GEBROULAZ DATA FOR THE PEROD 190-0. SUBSCRPTS AND 2 NDCA TE RESPECTVELY THE UPPER AND LOWER PROFLES A ha dh dt a- 190 190 1909 19 223.0 220.0 219. 219.2 239. 23.9 23.0 23.3 1. 1. 1. 33.0 32.9 32.9-3.3 -{).0 0.00 -{).1 -{).1 -{).1-3. -1.22 -{).1-0.9 1. 1911 1912 19 191 191 219.0 22. 222.1 223.0 22.0 11 23 22 22 3.1 3.3 3.3 3. 3. 23. 23. 23. 23.9 23. 11 1. 1. 1. 1. 1. 32.9 33.1 33.1 3 33. 0.00 1.0 -{).O 0.0 0. -{).1 -{).1 -{).1 -{).1 -{).1 -{). 0.9-1. -0 -{).9 1. 2.29 -{).1 0.1 0.3 191 191 191 1919 1920 22.9 22. 22. 22. 22.3 21 19 23 2 2 3. 3. 3. 3. 3. 23.9 23. 23. 239. 239.0 12 1 1 1 1. 1. 1. 1. 1. 33. 33. 33. 3.0 3.0 0.0 1.1 -{).0 1. -{). -{).19 -{).20 -{).20 -{).21 -{).21-1.00 -{).9-1.1 -{).1-2.3 0.1 1.22 -{).Ol 1.19 -{). 1921 1922 1923 192 192 22.0 22. 22.0 22.1 22. 3 31 2 3. 3. 3. 3. 3. 23. 21. 22. 21.0 21. 1 2 21 1 1 1. 1. 33.9 3.3 3. 3.3 -{).0 1.0 0.20 -{).0 0.0 -{).20 -{).21-2.2 -{).9-1 -2. -1. -{).92 0. -{).20 -{). 0.0 192 192 192 1929 19 229.1 22. 22. 22.0 22.0 32 32 31 23 3. 3. 3. 3. 3. 2.0 23. 22.9 22. 23.0 3 29 23 1 2.1 2.0 3.9 3. 3. 3. 3. 2.0-0. -{). 0. -{).2 -{).23 0. -3.11-1.2-2. -1.3 2.1-1.0 0. -{). 0.33 1931 1932 1933 193 193 22.0 22. 22.2 223.0 222. 20 20 1 3. 3. 3. 3. 3. 21. 21. 239. 23. 2 1. 1. 1. 3.3 3.3 33.9 33. 33.3 -{). 0.2-2.1-2. -{).0 -{).21 -{).20 -{).1 -{).1-2.1-1.2-2. -2.0-1. -{).3 0. -1.1-1.00 0.2 193 193 193 1939 190 222. 221. 221.0 220.2 219. 9 3. 3.3 3.3 23.0 23. 23. 23.0 231.1 1. 1. 1. 1. 1.3 33.1 33.1 32.9 32. 32.3 -{).0 -{).2 -{).0 -{).0-1. -{).1 -{).1 -{).1 -{).1 -{).1-1.32 -{). -1.1-1.29-2.39 0.39 0. 0. 0.2 -{). 191 192 193 19 19 21. 21.0 21.0 21. 21. 3.1 3.1 3.0 3.0 2.9 229.3 22. 22.0 223. 220.0 1.2 1.1 1.1 0.9 0. 32.0 31. 31. 31.0. -1. -\.0 -{). -1. -0 -{).l3 -{).12 -{). -{).O -{).0-1.9-2.2-1.2-2. -2. -{).19 -{).1 0.19 -{). -{).3 19 19 19 199 190 21.0 212.0 2.0 20.0 20.0 9 2.9 2. 2. 2. 2. 222.0 21. 21.2 2.0 209.0 0.9 0. 0. 0. 0.3. 29. 29.3 29.0 2.3 0.2 -.2-1. -1.0-3.00 -{).0 -{).0 -{).0 -{).02 0.00 -{).9 -.3-2.0-2.00-0 1.12-2.3 -{).3 -{).29 - Z, ean cross-profile altitude; V, ean annual velocity; S, area of the sector; dh / dt, ean annual elevation change of the sector surface; Ch' altitude correction as a function of the 190 level with db/dz = 0.00; b t, specific annual ass balance of the sector ( of water); 3 t, annual balance deviation fro the ean for the period ( of water). 1
Journal of Glaciology ~--~---.---'----.----r---.----r---.----.---.---' 0 L [ ( of waler) 192-1. The three cross-profiles: Misselenegg, Dollfus, and Brandla, give two coputation sectors (Fig. ). The basic data are presented in the annual reports of the Swiss Glacier Coission for the survey ade by the K.W.O and in the papers of Jost (193) and Haefeli (190) for the topography of the bed. The data for Unteraargletscher are given in Table ll. The deviations fro the ean balance derived fro the continuity equation are plotted in Figure 11, as well as their cuulated values to be copared with those for glacier de Sarennes and Aletschgletscher. The Unteraargletscher values are located within the range deliited by the two known series. The fluctuations are coonly very siilar but occasionally, notably around 190, they ay be distinct. Nevertheless, one can find in these two sectors of Unteraargletscher all ajor features that arked the changes in ass balance, especially around 190-0 and in the recent favourable period for glacier -2 1900 19 1920 19 190 Tie 190(A.D) 0 0 Sk ~ ~t UNTERAAR 0 - -2 Fig. 9. B t balance series fro the continuity equation (190-0) applied to glacier de Gebroulaz ( of water equivalent), and a coparison of cuulative variations with two long series available in the Alps for glacier de Sarennes and Aletschgletscher. 1 1 glacier growth (190-1) are observed as well as those which are unfavourable (190-0). n the sae way, the B t reconstructions for glacier de Sarennes (Martin, 19; Valla, 19) and the hydrological values for Aletschgletscher (Aellen and Kasser, 19) are plotted. The usual patterns are ainly the sae sequences of variation, glvg a very siilar axiu range. Nevertheless, note that field data or reconstructed values present ore detailed variations with tie while, on the contrary, the curve for glacier de Gebroulaz is soother. This is probably due to soothing of the field data when soe values are issing. We ust, however, note that the inforation given by a whole sector is different fro that obtained at individual stakes. A global balance includes the variations of elting in the central part of the glacier, generally clean and regular, where stakes are usually placed, as well as in the arginal areas, where there are ore crevasses and debris covering. But the error sources are nuerous; in addition to the Nye assuption, there are those errors related to velocities and surface areas. As opposed to altitudes which vary in a regular anner, velocities exhibit unexpected vanatjons, so that issing easureents can hardly be replaced by interpolation. On the other hand, the lateral argins of the glacier were not surveyed regularly. Such surveys are iprecise in any case, since in any years the liits are hidden by orainic cover on the right argin or by firn on the left. Nevertheless, these series are consistent. This further suggests that this new series of ass balances is representative, and that it constitutes a unique test of the reconstruction of the glacier de Sarennes balances of Martin (19). There are several glaciers which have been surveyed in the sae way as glacier de Gebroulaz, with recent deterination of the glacier-bed topography, that are prie candidates for further application of this new ethod. Unteraargletscher in Switzerland provides this opportunity with a continuous set of data for the period Fig.. Map of Unteraargletscher showing the location of cross-profiles (Aellen and Kasser, 19)., Misselenegg;, Dollfus; 2, Brandla. r.fl ( ofwaler) t - o -2 - - - 0SARENNES - - o ALETSCH 1920 19 _1- nl~~ fji'nnd v 0 JJLi n--cj-~ ~ L { - F-==U= W= _ MESElENEGG-OOllFUS E 1 - o Fig. 11. Coparison of two ass-balance series derived fro the continuity equation applied to two sectors of Unteraargletscher (Misselenegg-Dollfus and Dollfus Bralldla) with the series of Aletschgletscher alld glacier de Sarelllles for the period 192-1. 1990 2
ReYllaud and others: Mass-balance easureents TABLE. UNTERAARGLETSCHER DATA FOR THE PEROD 1923-1. SUBSCRPTS, 2, AND 3 NDCATE RESPECTVELY THE MSSELENEGG, DOLLFUS, AND BRANDLAMM CROSS-PROFLES FOR ALTTUDE (Z), VELOCTY (V), AND CROSS-SECTON AREA (S). S12 AND A 23 ARE THE TWO SECTOR AREAS LMTED BY DFFERENT CROSS-PROFLES. THE CONTNUTY EQUATON APPLED TO EACH SECTOR GVES A SERES OF SPECFC MASS BALANCES (bti) AND THE DEVATONS (Bti) FROM THE MEAN Year Z S V Z2 S2 V 2 Zs S3 Vs S12 S23 b a Bll b a Ba ha a- ha a- ha a- ha ha 1923 220.9 3. 22. 2.9 21. 1. 2. 21. 192 220. 3. 0.0 22.1 2. 33. 21. 1. 22.0 2.3 21.3-3.0 0. -2.3 0.0 192 219. 3. 3. 22.9 2.9 3.3 2129. 1. 21. 2.3 21.2-2. 0. -2.9 0.3 192 21. 3. 3. 22. 2.9 3.3 2129. 1. 20.2 2.1 21.1-3. 0.0-3.0 0.3 192 22 3.9 0.0 22.2 2..3 212. 1. 2.0 2.3 21. --0.9 2. -.29-1. 192 220.2 3. 3. 22. 2. 33. 212.3 1. 1.0 2. 21.1 -.09 -{).9-3. -{).3 1929 2 3. 222. 2.3 3.0 212.0 1.3 1. 2.2 21.1 -.03 -{).9 -.0-1.1 19 21. 3.3 3. 222.3 2.3 33.0 212.0 1.2 1.2 2.0 21.0-3.09 0.0-3. -{).03 1931 21.3 3. 221.3 2.2 33. 2122. 1.0 1.1 2. 21.3-3.39 -{).2-3.99 -{). 1932 21.0 3.1 3. 221.0 2.2 32.9 2122.9 1.1 1. 2. 21.3-2. 0.1-2.9 0. 1933 21. 3.9 3.9 220.2 2.1 3.1 2122.1 1.0 1.1 2.3 21.0-3.3 -{).20-3. -{).2 193 212. 3. 33. 22.3 2.9 31. 2121.2 1.1 23. 2. -3. -{).3-3.9 -{).2 193 211. 3. 31. 22. 2. 29.9 2120. 1. 23. 2.1-2.9 0.3-3 0.20 193 211. 3. 3 22.9 2.. 211. 1. 23. 212. -2.3 0. -3. -{).31 193 2. 3. 31.0 22. 2. 2. 211. 1. 1.2 23.0 212.0-3.1 0.01-3. -{).0 193 2. 3. 33. 22. 2. 29. 211. 1. 1.2 22.9 211. -2. 0. -3.33 0. 1939 209.2 3.3 3 223. 2. 2.3 21 1. 1.0 22. 211.2-3.1 0.00-3.3 0.0 190 209.1 3.3 32.2 222. 2.3 29.0 211.1 1.3 22. 2.9-2.0 0. - 3.1 0.2 191 209.0 3.3 3.0 22 2.2 29.3 211.3 1.3 1.2 22.2 2. -2.0 0. -3 0.20 192 20.3 3.0 3. 220. 2.1 31.3 2112. 1.1 1.2 21. 209.9-3. -{).2-3.9 -{). 193 20.2 3. 3.0 229.3 23.9. 2 1.0 1.0 21.3 209.2-3.92 -{). -.09 -{). 19 202.3 3. 33.9 22.2 23. 29. 29. 1. 1. 20. 20. -.1-1.2 -. -{).1 19 202.0 3. 33. 22.9 23. 29.2 2.9 1. 1.1 20.3 20.9-2. 0.2-3. -{).3 19 201. 3.3 33.1 22. 23. 2. 2.2 1.. 20.1 20.2-2.99 0.1-3.9 -{). 19 239.0 3.9 31.2 221. 23.1 2.9 2 1.3 12.9 29.1 20.9 -.09 - -. -1.3 19 239. 3. 31.2 220. 23.0 2.3 21. 1.2 11. 2. 20.3-3.1 0.01-3.3 0.09 199 239 3.3. 22.2 22. 2.9 2099. 1.0 11. 2. 20.2 -.12 - -. -1.11 190 2390. 3.0 29. 22. 22. 23.2 209. 1. 11.0 2.0 203.0 -. -1.33 -.3-1.20 191 2390.0 3.9 2.0 223. 22.3 22.0 209. 1. 9. 2. 202. -2.3 0.2-2.9 0. 192 23.3 3. 31.0 220. 22.0 22. 2093. 1..0 2.1 201. -.2-1.12 -.19 -{). 193 23. 3. 2.3 22. 21. 22. 2090.0 1.2 9.2 2. 200.3-3. -{).9 -.9-1.0 19 23.2 3.3 29.1 22. 21. 22. 209. 1.1. 2.1 200.0-2.2 0.3-2.3 0.0 19 2 2. 22. 21. 21.1 209.0 1.1. 2. 199. -2.0 0.3-2. 0. 19 233. 3.1 2. 22. 21. 20. 20. 1.0.9 2. 199.1-2.2 0.3-2. 0. 19 23. 3.3 2.9 22. 21. 20. 20.1 1.0. 2. 19.3-1. 1. -3. -{).03 19 23. 2. 222.1 21.1 19.3 2092. 1.. 2.1 19.3-3.0 -{).2-3.1 -{).3 199 232.2 33.9 2. 2239. 20.9 19.2 200. 1.. 23. 19.3 -.0 -{).90-3. -{).2 190 231.0 33. 2. 223.1 20. 1.1 20. 1.2. 23.0 19. -3.02 0. -3.31 0.12 191 239. 33. 2.1 223. 20. 19.0 20. 1.0. 22. 19. - -{). -3 0.19 192 23. 33. 2. 223.9 20. 20.2.9.0 22.1 193. - -{). -3.1 -{).0 193 23.0 33.3 2.1 2233.3 20.2 1. 202... 21. 193.1-3. -{).31-3.1 0.2 19 23. 33.0 2. 22.9 20.0 1.0 209...1 21.0 19 -.1-1.00 -.02 -{).9 19 23.1 33.0 29.2 2229. 19.9 1. 20.2..9 20. 191.3-2.1 0. -2.9 0. 19 23. 33.1 29.2 2229. 19.9 1.9 20..3. 20.9 190.9-3 1.22-2.3 1.0 19 23.3 32.9 2.3 222. 19. 203..0. 20. 190.0-3.01 0. -3.39 0.0 19 2. 32..2 222. 19. 19.9 201. 12.9. 20.0 19.3 -.11 -{).9-3.0 0.3 199 239. 32.3 32. 222. 19. 19.0 20. 12..3 29. 1.0-3. -{).1 -.09 -{). 190 23.9 32.2 31.1 222.2 19. 1. 20. 12. 3. 29.2 1.3-3. -{).1-3.11 0.32 191 23. 32.0 3. 2223.3 19.3 21.0 20. 12..9 2. 1. -3.9 -{).3-3.0 0.39 192 23.9 3 3. 222. 19. 19. 201.9 12.1. 2. 1.1-2.32 0.3-2.39 1.0 193 2 31. 3. 2223.0 19.2 19. 202. 12.2 3.9 2. 1.1-3.0 -{). -2.0 1.3 19 23. 31. 3 2220. 19.0 20.3 20. 1 3. 2.0 1. -3. -{).2 -.3-1. 19 23. 31. 31. 2221. 19.1 20. 20. 11..2 2.1 1.2-2 1.23-2.1 1.02 19 232. 31. 29.9 2219. 20.1 20.3 11..2 2..3-3.1 -{).3-3.3 -{).OO 19 233.0 31. 2.3 2219.3 1.1 202. 11. 3.3 2. 12.0-1. 1.3-2.3 0.90 19 233.1 31. 2.0 2219. 1. 201.0 11.3. 2. 12. -1.3 1.2-1 1.2 199 233.3 31. 2. 2219.2 1. 2039. 11.2 2. 2. 1-1. 1. -2.2 1.1 190 233. 31.. 221. 1. 19. 203. 11.1 3. 2. 11.3-2. 0. -2. 0.9 191 232. 31. 32.0 221.0 1. 20. 20.9 3. 2.1. -3.3 -{).20-3. -{).01 3
Journal of Glaciology TABLE V. STATSTCAL CHARACTERSTCS OF THE TWO MASS-BALANCE SERES FOR UNTERAARGLETSCHER COMPARED WTH THOSE FOR ALETSCHGLETSCHER AND GLACER DE SARENNES Mass-balance series of water Mieselenegg-Dollfus Dollfus-Brandla Glacier de Sarennes Aletschgletscher Mean -3.1-3.3 -{l. -{l.l Standard deviation 0. 0. 0.9 0.9 growth. The characteristic values of the four series are given in Table V. Despite their different nuerical values, the standard deviations do not show statistically significant deviations over the years, and the correlation coefficient for the two series for Unteraargletscher is about 0.3. However, we ust note that the ean values of the balances for the two sectors are very close, giving an activity coefficient of only 0.2 of water for each loo of altitude. Adopting this coefficient in the altitude correction for the lower sector, we obtain a new curve very siilar (but not identical) to those for the upper sector and those for glacier de Sarennes (Letreguilly, unpublished). That is probably caused by the orainic debris covering the lower sector acting as an insulator and reducing the ablation as is usually observed on ost glacier tongues of the sae type. Finally, a very decisive test for these series would be a coparison with soe direct easureents of ass balance based on a set of ablation stakes. That would be a very good opportunity to assess the representivity of the longest series of direct ass-balance data in the Alpine region. CONCLUSON These two new ethods ay be regarded as adequate alternatives to the usual ethods, either as an extension of easureents on new glaciers or siply as a continuation of ongoing surveys in the event of difficulties. While the first ethod, the linear-variation ethod, using a stake array placed in the central and regular parts of glaciers gives soe inforation on the balance variation siilar to that obtained by the usual ethod, the second, the continuity ethod, takes account of the global balance of the sector in between the cross-sections, that is to say, with the influence of the debris cover and the crevasses near the edges. Furtherore, the large variations of the glacier tongues with tie can present surfaces changing fro very "clean" to totally debris-covered. This can cause non-hoogeneous coparison series. The second ethod also requires deterination of the validity of the Nye assuption and the definition of several ore general relationships on the flux coputation for various cross-sectional shapes. Nevertheless, this global ethod is ore adapted to giving the actual balance variation and it is the only way to assess the representativeness of ass-balance reconstruction in the past by the use of historical survey data. On the other hand, such cross-profile surveys are frequently abandoned, largely because of the aount of survey work. Nevertheless, the new possibility offered by distanceeters has reduced the work load by a factor of about two, aking the topographical ethod increasingly attractive. A further advantage is that it also gives altitude and velocity variations with tie. nforation of this type is extreely useful, since it describes the etabolis of a glacier's variation with unexpected changes in velocities. These ethods should, nevertheless, be tested where data present such an opportunity or have been against different types of easureents on the sae glacier. ACKNOWLEDGEMENTS This work was ade possible by the extensive data available on glacier d' Argentiere, glacier de Gebroulaz, and Unteraargletscher. We thank all those involved in providing these data, at E.D.F., CEMAGREF (Eaux et Forets), and the Swiss Glaciers Coission. Field surveys on glacier d'argentiere were ade under contract No. 99 112 with Electricite d'eosson S.A. and on glacier de Gebroulaz under contract No. X-19 with the Parc de la Vanoise. Finally, the two anonyous referees offered any interesting suggestions, ost of which have been adopted. REFERENCES Aellen, M., and Kasser, P. 19. Rapport preliinaire annuel de la Coission Suisse des Glaciers. Paris, Societe Hydrotechnique de France. Section de Glaciologie. Fourno, J.-P. 19. Deterination de 'epaisseur du Glacier de Gebroulaz par prospection sisique. Travaux Scientifiques du Parc National de la Valloise,, p. 9-0. Haefeli, R. 190. Changes in the behaviour of the Unteraargletscher in the last 12 years. Journal of Glaciology, Vo!. 9, No., p. 19-212. Hoinkes, H. 190. Methoden und MOglichkeiten Massenhaushaltsstudien auf Gletschern. Zeitschrift Glaziologie und Glazialgeologie, Bd., Ht. 1-2, 3-90. von filr p. Jost, W. 193. Das Griselgebiet und die Gletscherkunde. Die Alpen, Jahrg. 29, Ht., p. 203-1. Letreguilly, A. Unpublished. Bilans de asse des glaciers alpins: ethodes de esure et repartition spatiale-teporelle. [Third cycle thesis, Universite de Grenoble, 19.) Lliboutry, L. 19. Multivariate statistical analysis of glacier annual balances. Journal of Glaciology, Vo!., No. 9, p. 31-92. Martin, S. 19. Analyse et reconstitution de la serie des bilans annuels du Glacier de Sarennes, sa relation avec les fluctuations du niveau de trois glaciers du Massif du Mont-Blanc (Bossons, Argentiere, Mer de Glace). Zeitschrift fur Glaziologie und Glazialgeologie, Bd., Ht. 1/ 2, 19, p. 12-3. Meier, M.F., and Tangborn, W.V. 19. Net budget and flow of South Cascade Glacier, Washington. Journal of Glaciology, Vo!., No. 1, p. -. Nye, J.F. 19. The flow of a glacier in a channel of rectangular elliptic or parabolic cross-section. Journal of Glaciology, Vo!., No. 1, p. 1-90. Paterson, W.S.B. 191. The physics of glaciers. Second edition. Oxford, etc., Pergaon Press. (Pergaon nternational Library.) Rayond, C.F. 191. Flow in a transverse section of the Athabasca Glacier, Alberta, Canada. Journal of Glaciology, Vo!., No., p. -. Reynaud, L. 193. Flow of a valley glacier with a solid friction law. Journal of Glaciology, Vo!. 12, No., p. 21-. Reynaud, L. 19. Glacier fluctuations in the Mont Blanc area (French Alps). Zeitschrift filr Glaziologie und Glazialgeologie, Bd., Ht. 1/2, 19, p. 1-. Reynaud, L., alld others. 193. Analyse et synthese des esures glaciologiques effectuees sur le Glacier de Gebroulaz, Massif de la Vanoise, France, by L. Reynaud, M. Vallon, and C. Carle. Travaux Scielllijiques du Parc National de la Vanoise,, p. 9-23. Valla, F. 19. Bilans du Glacier de Sarennes. Houille Blanche, /, p. 2-2. Vallon, M., and Leiva, J.C. 192. Bilan de asse et fluctuations recentes du Glacier de Saint-Sorlin (Alpes Franltaises). Zeitschrift filr Glaziologie und Glazialgeologie, Bd. 1, Ht. 2, 191, p. -. Vallot, J. 1900. Annales de 'Observatoire Meteorologique du Mont Blanc. Toes, et. Paris, Stenhai!. MS. received 1 February 19 and in revised for 1 May 19