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Time–Scale for Adjustment of Glaciers to Changes in Mass Balance

  • Tómas Jóhannesson (a1), Charles Raymond (a1) and Ed Waddington (a1)

Abstract

The length of time TM over which a glacier responds to a prior change in climate is investigated with reference to the linearized theory of kinematic waves and to results from numerical models. We show the following: TM may in general be estimated by a volume time-scale describing the time required for a step change in mass balance to supply the volume difference between the initial and final steady states. The factor f in the classical estimate of τM = ƒl/u, where I is glacier length and u is terminus velocity, has a simple geometrical interpretation. Ft is the ratio of thickness change averaged over the full length I to the change at the terminus. Although both u and f relate to dynamic processes local to the terminus zone, the ratio f/u and, therefore, Tm are insensitive to details of the terminus dynamics, in contrast to conclusions derived from some simplified kinematic wave models. A more robust estimate of Tm independent of terminus dynamics is given by TM= h/(–b) where h is a thickness scale for the glacier and –b is the mass-balance rate (negative) at the terminus. We suggest that Tm for mountain glaciers can be substantially less than the 1O2–103 years commonly considered to be theoretically expected.

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References

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Bindschadler, R. 1980 The predicted behavior of Gries–gletscher, Wallis, Switzerland, and its possible threat to a nearby dam. Z. Gletscherkd. GIaziaIgeol., 16(1), 4559.
Bindschadler, R. 1982 A numerical model of temperate glacier flow applied to the quiescent phase of a surge–type glacier. J. GIacioI., 28(99), 239265.
Björnsson, H. 1974 Explanation of jökulhlaups from Grimsvötn, Vatnajökull, Iceland. Jökull, 24, 126.
Bodvarsson, G. 1955 On the flow of ice sheets and glaciers. Jökull, 5, 18.
Braithwaite, R.J. 1980 Regional modelling of ablation in West Greenland. Grenl. Geol. Undersogelse. Rapp. 98.
Budd, W.F. Jenssen, D.. 1975 Numerical modelling of glacier systems. International Association of HydroIogical Sciences Publication 104 (General Assembly of Moscow 1971 - Snow and Ice) , 257291.
Cole, J.D. 1968 Perturbation methods in applied mathematics. Waltham, MA, Blaisdell Publishing Company.
Echelmeyer, K.A. Unpublished. Response of Blue Glacier to a perturbation in ice thickness: theory and observation. (Ph.D. thesis , California Institute of Technology, 1983)
Fisher, D. Jones, S.J.. 1971 The possible future behaviour of Berendon Glacier, Canada — a further study. J. Glcciol., 10(58), 8592.
Flint, R.F. 1971 Glacial and Quaternary geology. New York, etc., John Wiley and Sons.
Fowler, A.C. Larson, D.A.. 1980 On the flow of polythermal glaciers. 2. Surface wave analysis. Proc. R. Soc London. Ser. A, 370(1741), 155171.
Hutter, K. 1983 Theoretical glaciology Material science of ice and the mechanics of glaciers and ice sheets. Dordrecht, etc., D.Reidel Publishing Company; Tokyo, Terra Scientific Publishing Company.
Jȯhannesson, T. 1986 The response time of glaciers in Iceland to changes in climate. Ann. Glacial., 8, 100101.
Jȯhannesson, T. Unpublished. Dynamics of ice shelves covering subglacial lakes formed by geothermal heat flux. (M.S.thesis , University of Washington, Seattle, 1984)
Jȯhannesson, T. Raymond, F. Waddington, E.D.. 1989 A simple method for determining the response time of glaciers. Glacier Fluctuations and Climate Change.S ymposium proceedings. Amsterdam, Institute for Meteorology and Oceanography, 343352.
Kamb, B. Echelmeyer, K.A.. 1986 Stress–gradient coupling in glacier flow: I. Longitudinal averaging of the influence of ice thickness and surface slope. J. Glaciol. 32(111), 267284.
Kevorkian, J. Cole, J.D.. 1981 Perturbation methods in applied mathematics. New York, etc., Springer–Verlag.
Lamb, H.H. 1972 1977 Climate: present, past and future Vols. 1 and 2. London, Methuen and Co.
Langdon, J. Raymond, C. 1978 Numerical calculation of adjustment of a glacier surface to perturbations of ice thickness. Maler. Glvatsiol. Issled. Khron. Ohsuzhdeniva 233239.
Lliboutry, L.A. 1971 The glacier theory. Adv. Hvdrosci., 7, 81167.
Mahaffy, M.W. 1976 A three–dimensional numerical model of ice sheets: test on the Barnes Ice Cap, Northwest Territories. J. Geophys. Res., 81(6), 10591066.
Meier, M.F. 1984 Contribution of small glaciers to global sea level. Science, 226(4681), 14181421.
Nye, J.F. 1951 The flow of glaciers and ice–sheets as a problem in plasticity. Proc R. Soc London. Ser. A, 207, 554572.
Nye, J.F. 1960 The response of glaciers and ice–sheets to seasonal and climatic changes. Proc. R. Soc London Ser A, 256(1287), 559584.
Nye, J.F. 1963a. On the theory of the advance and retreat of glaciers. Geophys. J. R. Aslron. Soc., 7(4), 431456.
Nye, J.F. 1963b. The response of a glacier to changes in the rate of nourishment and wastage. Proc. R. Soc. London. ser.A 275(1360), 87112.
Nye, J.F. 1965a. A numerical method of inferring the budget history of a glacier from its advance and retreat. J. Glacial., 5(41), 589607.
Nye, J.F. 1965b. The flow of a glacier in a channel of rectangular, elliptic or parabolic cross–section. J. Glaciol.,5(41), 661690.
Nye, J.F. 1965c. The frequency response of glaciers. J. Glacial., 5(41), 567587.
Patankar, S.V. 1980 Numerical heal transfer and fluid flow. Washington, DC. Hemisphere Publishing Coporation.
Paterson, W.S.B. 1972 Laurentide ice sheet: estimated volumes during late Wisconsin. Rev, Geophys. Space Phys., 10(4), 885917.
Paterson, W.S.B. 1980 Ice sheets and ice shelves. In Colbeck, S.C., ed. Dynamics of snow and ice masses. New York, Academic Press, 178.
Paterson, W.S.B. 1981. The physics of glaciers. Second edition. Oxford, etc., Pergamon Press.
Porter, S.C. 1986 Pattern and forcing of northern hemisphere glacier variations during the last millennium. Qual, RES., 26(1), 2748.
Porter, S.C. Denton, G.H.. 1967 Chronology of neoglaciation in the North American Cordillera. Am. J. sci., 265(3), 177210.
Reeh, N. 1983 Ikke–stationasr beregningsmodel for inlandsisens randzone. Gronl. Geol. Undersegelse. Gletscher-Hydrol. Medd. 83/7.
Reynaud, L. 1978 Glacier fluctuations in the Mont Blanc area (French Alps). Z. Gletscherkd. Glazialgeol., 13(1/2), 1977 155166.
Reynaud, L. 1983 Recent fluctuations of Alpine glaciers and their meteorological causes: 1880–1980. In Street-Perrott, F.A.,Beran, M.,Ratcliffe, R.A.S., eds. Variations in the global water budget. Dordrecht, etc., D.Reidel Publishing Co., 197-205
Untersteiner, N. Nye, J.F.. 1968 Computations of the possible future behaviour of Berendon Glacier, Canada. J. Glaciol., 7(50), 205-213.
Waddington, E.D. Unpublished. Accurate modelling of glacier flow. (Ph.D. thesis, University of British Columbia, 1981)
Weertman, J. 1961 Equilibrium profile of ice caps. J. Glaciol., 3(30), 953964.
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Journal of Glaciology
  • ISSN: 0022-1430
  • EISSN: 1727-5652
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