Estimation of Alpine glacier water resources and their change since the 1870s

Transcription

1 INTRODUCTION Hydrology in Mountainous Regions. I Uydrological Measurements; the Water Cycle (Proceedings of two Lausanne Symposia, August 990). IAHS Publ. no. 9, 990. Estimation of Alpine glacier water resources and their change since the 870s Jiyang Chen & Atsumu Ohmura Department of Geography, Swiss Federal Institute of Technology, Winterthurerstrasse 90, CH807 Zurich, Switzerland ABSTRACT An empirical formula relating volume of an Alpine glacier to the surface area is improved based on the data measured by radioecho sounding and seismic method. The formula is used for calculating the present volume of the Alpine glaciers based on the surfacearea data registered in the World Glacier Monitoring Service. The past volumes at several stages are estimated from the surface area and its change. The icecovered area of the Alpine glaciers was 8± km in the 870s, ± km in the 90s, and 909 km in the 970s. For the period 870s970s, the volume of Alpine glaciers decreased by 7.±0. km with the volume in the 970s being 0±0 km. The mean rate of changes over this period is about km /a for the icecovered area, 0.7 km /a for the volume and 0.6 m/a for the mean thickness. The massturnover time of an Alpine glacier, which is important in investigating the water cycle of a basin with glaciers, is estimated to be in the order of 0!0 a It is of both scientific and practical importance to know the present amount of and historical changes in the water stored in the Alpine glaciers. The significant decrease in the volume of small glaciers and ice caps may contribute to sea level rise (Meier, 98). In addition, the Alpine glaciers are of special significance as water resources. As an example, almost 6% of the electricity consumed in Switzerland is from the hydropower plants and % is produced through the reservoirs which collect glacier meltwater (Mûller et al., 976). The present icecovered area of the Alpine glaciers is rather accurately known through the glacier inventory (Haeberli et al., 989). The volume given through the glacier inventory is. km for the Swiss glaciers (Mûller et al., 976) and km for the Austrian glaciers according to Patzelt (980) whereby various estimation methods were used. A literature survey suggests that the present ice volume and the changes in the icecovered area is known only for local regions and not for the whole Alps (Vivian, 97; Miiller et al., 976; Kasser, 98; Gross, 987). In comparison with changes in icecovered area, the changes in thickness and volume are much poorly understood. In this work, the volume of the Alpine glaciers in the 970s are estimated according to an improved empirical volumearea relationship and the data base of the Alpine glacier inventory registered in the World Glacier Monitoring Service. The changes in area and volume of the Alpine glaciers for the period 870s970s are examined. Finally, the mass turnover time of an Alpine glacier is briefly discussed. THE EMPIRICAL VOLUMEAREA RELATIONSHIP The volume V of a glacier is well related with its surface area S and a power relationship is commonly applied: 7

2 Jiyang Chen &Atsumu Ohmura 8 V = c 0 S Cl () with Co and c\ being the empirical constants which are often deduced from the measured V and S. The common method for finding y of a glacier is to measure its thickness after the grid points or along profiles. A chart of the thicknessisoline is compiled and V can then be calculated. The accuracy of V is therefore strongly influenced by that of thickness soundings. The volume estimation of the Swiss glaciers by Miiller et al. (976) is based on Briickl's (970) thicknessarea relationship: <h> =. +. S () where <h> [m] denotes the mean thickness over the entire glacier and S [km ] is the surface area. Equation was then the best available formula and used for the Swiss glacier inventory. Equation was based on the depth measurements by seismic soundings for 6 Alpine glaciers. Recently, a number of mountain glaciers have been measured through radioecho soundings (Driedger & Kennard, 986; Zhuravlev, 988). The experiments on Swiss glaciers show that rather reliable results can be obtained through radioecho soundings (Wachter, 98 ; Haeberli et al, 98). As the measured V data of more glaciers become available, it is possible to improve equation. From the data of 6 mountain glaciers (Table ), it is found that: V = 8. S 7 () with the squared correlation coefficient r = 0.96 (Fig. ). The unit of V is in 0^ m and that of S is 0^ m. The standard deviation of the residuals s e of equation increases with S. s e [06 m] is 0. for S [06 m ] < 0.,.9 for 0. < S <.0, 6 for.0 < S <.0, for.0 < S < 0.0 and 0 for 0< S < 0.0. From equation, the mean thickness <h> is <h> = 8. S 7 () and the change in the volume AV of a mountain glacier can be approximated from the change in the surface area AS: AV = 8.76 S 7 AS. () DISCUSSION ON THE VOLUMEAREA RELATIONSHIP Equation just concerns the mountain glaciers (except for icecaps). It is deduced from the measured data of different accuracy and from the glaciers in different regions. The selected glaciers include from the Alps (Briickl, 970), from the Cascade Ranges, from the Rocky Mts., from Wind River Range, from Sierra Nevada, from Mt. Shasta, from the Kebnekaise Massif (Driedger & Kennard, 986) and 7 from Svalbard (Zhuravlev, 988). The <h> m or V of some Svalbard glaciers may be underestimated (Dowdeswell & Drewry, 98). It is therefore necessary to give some discussions on equation before it is used for the Alpine glaciers. Firstly, the magnitudes of the coefficients Co and c\ in equation remain within a certain range (Table ). Except for the VS relationship for 7 Svalbard glaciers, CQ is between 70 and c\ is between.. whereby the difference is due to the fact that various types of glaciers are involved and due to accuracy of V determinations. Furthermore, two parameters which are physically related to the mean thickness are not considered in the VS relationship: the surface slope and the basal shear stress (Paterson, 970). The main difficulty in involving them is due to the data availability.

3 9 Estimation of Alpine g;lacier water resources TABLE The measured volume V [ÎO'W] and area S [km^] used in this work. <h> [m]: the mean thickness. <h> m = VIS. <h>j: this work (eq. ). <h>? by eq. after Millier et al. (976). Data sources: Brûckl (970), Driedger & Kennard (986), Zhuravlev (988), cited from, Kappenberger (976), and 6 Wâchter (98) and Haeberli et al. (98). * Not considered in eq.. **V is underestimated (Dowdeswell & Drewry, 98) Name (Sr NJ A.[' ] S V <h> m <h>] <k> Sources Athabasca* Brandner Carbon Cascade S. Coalman Coe Collier Diller Dinwoody Eliot Emmons Findelen Gefrorenewand* Gepatsch GosauGr. Grinnell Gurgler Guslar Gr. Halls taetter Hayden Hintereis Mails Kesselwand Ladd Langille Lost Creek Maclure NewtonClaric Nisqually Palmer Pasterzen Prouty Rabots Reid Russell Sandy Schladminger Schiedinger Storgl. Sulztal Tahoma N.L. Vernagt White River Whitney Wilson Winthrop Zigzag Zmutt Aldegonda Antonia Bertill Boger Bruegger Bost Braegger Zap. Vôring Dalfonna Lein Loven Srednii Meryal Penk** Revtan Suess Finsterwalder** Gess Enlman Laika* Rhône* IKtec^temW Z(<h>c<k>ri/N E E 8 E 0 E 9 W 0 9 E W SOW E 7 W 0W 0W W E 0E E 6 E 0W 9 E 9 E 7 E E E 8 E 0W W E E 8 E W E

4 Jfyang Chen &Atsumu Ohmura 0 00 o N = r= s*= S o B P O o > 0^rw ^ _ r t t Area (km ) FIG. Relationship between the volume [km*] and the surface area [km ] of a mountain glacier. Based on the data from 6 glaciers in Table (Briickl, 970; Driedger and Kennard, 986; Zhuravlev, 988). r: the correlation coefficient. s e : the standard deviation of the residuals. Secondly, the accuracy of different VS relationships can be evaluated by comparing the residual for the calculation of the mean thickness e = <h> c <h> m. It can be shown that the residual is e = S 0.7 [ m ] f or equation of this work and e= 9 0. S for equation (Briickl, 970). It follows that equation does give better results than the <h>s relationship applied in the Swiss glacier inventory by Miilleretal. (976). Thirdly, the measured change in the mean thickness <Ah> or volume AV of a glacier, which is revealed by comparing the large scale topographic maps over relatively long period, are compared with the values calculated from equation based on the known area of the glacier and the measured area change AS. From the data of 6 observations for Alpine glaciers (Finsterwalder,9; Finsterwalder & Rentsch, 97; Long & Patzelt, 97; Chen & Funk, submitted), it is found that the standard deviation of the residuals of the linear relationship between the measured and the calculated values is xl06m for AV and.6 m for <Ah>. The calculated and measured values agree fairly well, especially when the considered period is longer. TABLE Comparison of the values of coefficients Co and c\ of equation. The coefficients for No. 9 are recalculated. N: number of the glaciers; r : the squared correlation coefficient; s e [lo^m^]: the standard deviation of the residuals; : the area range; Method: Sei.seismic soundings, Rec.reconstructed from geomorhpological evidence, Rad. radioecho sounding, Mix.seismic or radioecho sounding, and Est.: estimated. Data source: Erasov (968) and cited from 6; Briickl (970); Maisch (98); & Driedger and Kennard (986); 6 from & ; 7 Shi et al. (98); 8 Zhuravlev (988); 9 from, and 8. No N _ Co Ci r Se S [km ] Method. Sei. Rec. Mix. Rad. Mix. Est. Rad. Mix. Mountain glaciers in Central Asia Alps Graubiinden, Alps Cascade & other areas Cascade, small glaciers Alps, Cascade and other areas Qilian Mountains, China Mountain glaciers in Svalbard Alps, Cascade and Svalbard etc. Data source

5 Estimation of Alpine g;lacier water resources ESTIMATION OF THE AREA CHANGE The measured areas of Swiss glaciers are selected and compared for the period of 870s90s970s whereby the data are from Jegerlehner (90), Rindlisbacher (9) and Miiller et al. (976). It shows that the area of an Alpine glacier at different times is related with each other in the following manner for 8 glaciers larger than 0. km : (870s) = S(970s) (r* = 0.98 &s e = 0.9) (6a) S(90s) = S(970s) (r* = 0.99 & s e =0.98) (6b) and in the forms below for 06 glaciers smaller or equal to 0. km : S(870s) =.0 S(970s) 0 89 (r = 0.6 & s e = 0.0) (6c) S(90s) =.006 S(970s)0800 < r i = Q.9 & s e = 0.8) (6d) with the decade in the bracket being the reference time. A rough estimation of the change in the Alpine icecovered area since the 870s can be made under the following assumptions: () The area of Alpine glaciers has not changed much after the inventory time (970s). This seems to be reasonable (Wood, 988); () Equations 6 ad are representative of the Alpine glaciers; and () No glaciers have disappeared since the 870s. This is not the case (Gross, 987), but there is not an easy way to estimate. The changes in the icecovered area in the Alps are estimated by using equations 6 ad for single glaciers registered in the data base of the WGMS, that is, using equations 6a and 6b for glaciers with S > 0. km and equations 6c and 6d for glaciers with S < 0. km. The results are summarized in Table for three stages: the 870s, 90s and 970s. The calculated Swiss icecovered area is 80± km in the 90s and 88±8 km in the 870s which agrees well with the measured values given by Rindlisbacher (9). According to Gross (987), the measured icecovered area in Austria in 870/87 is 99 km which is based on Richter's (888) work plus the small glaciers not considered by Richter. The area in 90 calculated by Gross (987) is 808 km and the method for his calculation was not declared. The icecovered area in the 90s can thus be interpolated as 77 km with a mean rate of. km /a for the period These values are considerably larger than those estimated from equations 6 ad, which are 78±7 km in the 870s and 6+ km in the 90s. In fact, Richter apparently overestimated the glacier area since the rock area above the snow line was partly counted as glacier area. Moreover, the disappeared glaciers can not be considered in the present work which make a significant portion (6.%). It may also suggests that the area loss of glaciers is much larger in the eastern Alps than in the Swiss Alps. TABLE Icecovered area [km ] for the period 870s90s970s in the Alps. Data sources: Alpine glacier inventory (Haeberli et al., 989); Rindlisbacher (9), Miiller et al. (976), Gross (987); This work; and 6 Estimated from Gross (987). Reference period France Switzerland Austria & Germany Italy Alps 870s 90s 970s 60+ () 68 () 7() 88() 6 () () 99 () 77 (6) () 99 () 7 () 607 () 8 909

6 Jiyang Chen &Atsumu Ohmura ESTIMATION OF THE VOLUME AND ITS CHANGE Equation is applied for the single glaciers registered in the glacierinventory data base of the World Glacier Monitoring Service to calculate the present icevolume. For finding the volume change during the 870s970s, equations 6a and 6c are used to estimate the area change AS and then the volume change is approximated by using equation. The results for the entire Alps are presented in Table. The uncertainty intervals are determined at the confidence level of 9%. The results given in Table are considered to be a rough estimation. However, it covers the entire Alps and it has improved the result of previous studies. Through the inventory, Millier et al. (976) showed that the ice volume of the Swiss glaciers in 97 is. km^, which is obtained by applying equation for the glaciers with 0.<< km. A constant of <h> = m was assumed for those with <0. km and individual estimation was made for those with S> km. It is clear that equation underestimate the mean thickness of a glacier in most cases (Table ). The present work shows that the total volume of Austrian glaciers is km^. This can be compared with the km^ which is given by Patzelt (980) through glacier inventory and which is obtained by assuming a mean thickness of 0 m for all the Austrian glaciers. The data in Table suggests that the icecovered area of the Alpine glaciers has decreased by 9+ km or % for the period 870s970s. The area loss during the 870s90s (9%) is slightly larger than that during the 90s970s (8%). It is shown that the volume of the Alpine glaciers has decreased by about 9% or 7±0 kmy for the period 870s970s. The mean rate of changes in the total area, the total volume and area weighted mean thickness of Alpine glaciers for the period 870s970s is km /a, and 0.7 kmtya and 0.6 m/a, respectively. TABLE Change in area AS and volume ÂV of the Alpine glaciers for the period 870s 970s S: the present area; V: the volume in the 970s; V/(V+lVI): the relative volume change; and <Ah>/At: the mean rate of change in the mean thickness. Region S [km ] AS [km ] V Don ] AV [km ] AV/(V+\AV\) [%] <Ah>lAf. [m a" ] France Switzerland Austria & Germany Italy ± ± ± Sum Mean 909 9± TURNOVER TIME OF AN ALPINE GLACIERS' MASS The turnover time of an Alpine glacier's mass x g is important in investigating the water cycle of a basin with glaciers. % can be defined as the ratio of the volume to the rate of mass output and it can be expressed as: <Tg> = <h>i<ma> (7) with <h> being the mean thickness of the glacier and <md> the annual mass turnover. A bar specifies the mean over time. <md> is

7 Estimation of Alpine g;lacier water resources <ma> = (<b a c> + l<*aa>0 / (8) where <b^c> and <baa> are the annual balance in the accumulation area and ablation area. Both are averaged over the entire glacier. The specific annual mass turnover <md> of Alpine glaciers is calculated from the available data (Kasser, 9, 97; Mtiller, 977; Haeberli, 986; Haeberli et al, 988). The mean <ma> of Alpine glaciers is 0 mm w. e./a (mm water equivalent per year) with the standard deviation being 78 mm w. e.. The turnover time of an Alpine glaciers' mass is estimated from equation 7 whereby a reference value of <md> of 0 mm w. e./a is used. The mean time needed for an Alpine glacier to renew its mass totally is estimated to be 060a for a glacier with the surface area S = 0..0 km, 000a for one with S =.00.0 km, and 000a for one with = km. CONCLUSIONS AND PERSPECTIVES The general changes of the Alpine glaciers can be approximately summarized as follows for the period 870s970s: The icecovered area of the Alpine glaciers was 8+ km in the 870s, ± km in the 90s, and 909 km in the 970s. For the period 870s970s, the volume of Alpine glaciers decreased by 7+0 km^ while the volume in the 970s is 0.±0. kna The mean rate of changes in the total area, the total volume and the mean thickness of Alpine glaciers for the period 870s970s are approximately km /a, 0.7 km^/a and 0.6 m/a, respectively. The estimated mass turnover time of an Alpine glacier is in the order of 0l0 a. At present, the volume area relationship is widely applied in glacier inventory and water resources estimation due to its simplicity. However, such volume area relationship should be improved as more accurately measured volume data become available. It is necessary to establish different volume area relationships according to the type of mountain glaciers (cirque glacier, hanging glacier, valley glacier etc.). In addition, the surface slope of a glacier should be involved in future investigations for estimating the thickness and volume. Because the absolute error of volume estimation increases with the size of the glacier, the volume of larger glaciers (>0 km ) should be individually estimated. ACKNOWLEDGEMENT Dr. W. Haeberli of the World Glacier Monitoring Service has given kind permission for the access to the data base of the Alpine glacier inventory. Dr. P. Miiller helped with the transfer of the glacier inventory data. We would also like to express thanks to Mr. M. Aellen and the colleagues of the Department of Geography, Swiss Federal Institute of Technology in Zurich for the discussions and assistance. REFERENCES Briickl, E. (970) Eine Méthode zur Volumenbestimung von Gletschern auf Grand der Plastizitâtstheorie. Archiv fiir Météorologie. Geophysik und Bioklimatologie. Ser.A. 9, 78. Chen J. and M. Funk, (submitted) Mass balance of the Rhône Glacier during 88/8 986/87. J. Glaciol. Dowdeswell, J. A. and D. J. Drewry. (98) Radioecho sounding of Spitzbergen glaciers: problems in the interpretation of layer and bottom returns. J. Glaciol Driedger, C. and P. Kennard. (986) Glacier volume estimation on Cascade volcanoes an analysis and comparison with other methods. Annals of Glaciology. S, 96.

8 Jiyang Chen &Atsumu Ohmura Erasov, N.V. (968) Method to determine the volume of mountain glaciers. Materialy Glyatsiol. Issled. Khronika. Obsuzhdeniya. no.. Moscow. Gross, G. (987) Der Flâchenverlust der Gletschern in Ôsterreich Z, Gletscherkd. Glazialgeol.... Finsterwalder.R. (9) Die Zahlenmâsige Erfassung des Gletscherriickgans an Ostalpengletschern. Z. Gletscherkd. Glazialgeol..,899. Finsterwalder,R., and H. Rentsch. (980) Zur Hôhenânderung von Ostalpengletschern imzeitraum Z. Gletscherkd. Glazialgeol Haeberli, W. (986) Fluctuations of Glaciers 98098,, IAHS (ICSI) AJNEPAJNESCO, Paris. Haeberli, W., H. P. Wàchter, W. Schmid, and G. Sidler. (98) Erste Erfahrungen mit dem U. S.GeologicalSurveymonopulsradioecholot im Firn, Eis und Permafrost der Schweizer Alpen. Z. Gletscherkd. Glazialgeol. 9.. Haeberli, W. and P. Millier. (988) Fluctuations of Glaciers 98098,, IAHS (ICSI) AJNEPAJNESCO, Paris. Haeberli, W., H. Bosch, G. Scherler, G. 0strem and C. C. Wallèn. (989) World glacier inventory status 988. A contribution to the International Hydrological Programme and the Global Environment Monitoring System. IAHS(ICSI)UNEP UESCO. Jegerlehner, J. (90) Die Schneegrenze in den Gletschergebieten der Schweiz. Gerlands Betrage zur Geophvsik. _, Kappenberger, G. (976) Massenhaushalt und Bewegung des Laika Gletschers, Coburg Island N. W. T. 97/7. Diplomarbeit am Geographischen Institut der ETH Zurich. Kasser, P. (9) Fluctuations of Glaciers 9996,, IAHSAJNESCO, Paris. Kasser, P. (97) Fluctuations of Glaciers 96970,, IAHS(ICSI)AJNESCO, Paris. Kasser, P. (98). Rezente Gletscherveranderungen in den Schweizer Alpen. In: Gletscher und Klima. Jahrbuch der Schweizerischen Naturforschenden Gessellschaft. 978, Wissenschaftliche Teil, 068. Lang, H. and G. Patzelt. (97) Die Volumenânderung des Hintereisferners (Oetztaler Alpen) im Vergleich zur Massenânderung im Zeitraum 996. Z. Gletscherkd. Glazialgeol Maisch, M. (98) Glaziologische und Gletschergeschichtliche Untersuchungen im Gebiet Zwischen Landwasser und Albulatal (Kt. Graubiinden, Schweiz). Physische Géographie. _, Geographisches Institut, Univ. Zurich. Meier, M. F. (98) The contribution of small glaciers to global sealevel. Science Miiller, F. (977) Fluctuations of Glaciers 97097,, IAHS(ICSI)AJNESCO, Paris. Mûller, F., T. Caflish and G. Mûller. (976) Firn und Eis der Schweizer Alpen. Publ. no. 7. Geographisches Institut der ETH Zurich. Paterson, W. S. B. (970) The application of ice physics to glacier studies. In: Glaciers. Proc. Workshop Seminar. Canadian National Committee for the International Hydrological Decade. Ottawa,. Patzelt, G. (980) The Austrian glacier inventory: status and first results. IAHS Publ. no. 6, 88. Richter, E. (888) Die Gletscher der Ostalpen. Handbiicher zur Deutschen Landes und Volkskunde.. Bd. J. Engelhorn, Stuttgart. Rindlisbacher, J. (9) Flachenstatistik, Planimetrierung der Gletscher (Schweiz u. ausland. Terriotorium). Bearbeitet auf Landeskarte by Eidg. Amt fiir Wasserwirtschaft Vol. &. Shi Yafeng, Wang Zongtai and Liu Chaohai. (98) Note on the glacier inventory in Qilian Shan Mountains. In: Glacier Inventory of China., Qilian Mountains, Lanzhou Inst, of Glaciology and Geocryology, 9. Vivian, R. (97) Les Glaciers des Alpes Occidentales. Imprimerie Allier, Grenoble. Wachter, H. P. (98) Eisdickenmessungen auf dem Rhonegletscher Ein Versuch mit RadioEcho Sounding. Diplomarbeit am Geographischen Institut der ETH Zurich.

9 Estimation of Alpine g;lacier water resources Wood, F. B. (988) Global alpine glacier trends, 960s to 980s. Arctic and Alpine R&s Zhuravlev, A. V. (988) The relation between glacier area and volume. In: G.A. Avsyuk (eel.) Data of Glaciolopical Studies, no. 0. Russian Translations Series, no.. A. A. Balkema, Rotterdam..

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