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Temporal dynamics of a jökulhlaup system

  • Felix Ng (a1) and Shiyin Liu (a2)

Abstract

Recurring jökulhlaups from ice-dammed lakes often form irregular time sequences that are seemingly unpredictable. Using the flood dates of Merzbacher Lake, Kyrgyzstan, as an example, we study these sequences through a model of lake filling and drainage where flood events initiate at a threshold water depth. Even with a constant threshold, model simulation can explain key aspects of the Merzbacher flood sequence. General analysis of model dynamics reveals a pacing mechanism that links one flood to the next, and which may be represented mathematically as an iterative map. This theory clarifies how environmental factors govern the long-term pattern of flood timings and their frequency distribution in the year. A reconstruction of the past level of Merzbacher Lake also suggests that its flood-initiation threshold decreases with the rate of lake-level rise. These results may help us understand how to forecast future outbursts from jökulhlaup lakes.

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References

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Aizen, V.B. and Aizen, E.M.. 1998. Estimation of glacial runoff to the Tarim River, central Tien Shan. IAHS Publ. 248 (Symposium at Merano 1998 – Hydrology, Water Resources and Ecology in Headwaters), 191–98.
Aizen, V.B., Aizen, E.M., Dozier, J., Melack, J.M., Sexton, D.D. and Nesterov, V.N.. 1997. Glacial regime of the highest Tien Shan mountain, Pobeda-Khan Tengry massif. J. Glaciol., 43(145), 503512.
Anderson, S.P. and 6 others. 2003. Integrated hydrologic and hydrochemical observations of Hidden Creek Lake jökulhlaups, Kennicott Glacier, Alaska. J. Geophys. Res., 108(F1), 6003. (10.1029/2002JF000004.)
Anderson, R.S., Walder, J.S., Anderson, S.P., Trabant, D.C. and Fountain, A.G.. 2005. The dynamic response of Kennicott Glacier, Alaska, USA, to the Hidden Creek Lake outburst flood. Ann. Glaciol., 40, 237242.
Ayrapet’yants, S.E. and Bakov, E.K.. 1971. Morfologiya lednikovogo Ozera Mertsbakhera i mekhaniizm ego katastroficheskikh proryvov [Morphology of the Merzbacher glacial lake and the mechanism of its catastrophic outbursts]. In Shchukin, I.S. and Zabirov, R.D., eds. Nekotorye zakonomernosti oledeneniya Tyan’-Shanya [Some patterns of glaciation in the Tien Shan]. Frunze, Ilim Press, 7584. [In Russian.]
Björnsson, H. 1988. Hydrology of ice caps in volcanic regions. Vísindafélag Ísl. Rit. 45.
Björnsson, H. 2002. Subglacial lakes and jökulhlaups in Iceland. Global Planet. Change, 35(3–4), 255271.
Clague, J.J. and Mathews, W.H.. 1973. The magnitude of jökulhlaups. J. Glaciol., 12(66), 501504.
Clarke, G.K.C. 1982. Glacier outburst floods from ‘Hazard Lake’, Yukon Territory, and the problem of flood magnitude prediction. J. Glaciol., 28(98), 321.
Clarke, G.K.C. 2003. Hydraulics of subglacial outburst floods: new insights from the Spring–Hutter formulation. J. Glaciol., 49(165), 299313.
D’Innocenzo, A., Paladini, F. and Renna, L.. 2006. Leaky tap behavior described by a simple discrete mapping. Nonlin. Dyn., 43(4), 379390.
Drazin, P.G. 1992. Nonlinear systems. Cambridge, Cambridge University Press.
Flowers, G.E., Björnsson, H., Pálsson, F. and Clarke, G.K.C.. 2004. A coupled sheet–conduit mechanism for jökulhlaup propagation. Geophys. Res. Lett., 31(5), L05401. (10.1029/2003GL019088.)
Fowler, A.C. 1999. Breaking the seal at Grímsvötn, Iceland. J. Glaciol., 45(151), 506516.
Fowler, A.C. and Ng, F.S.L.. 1996. The role of sediment transport in the mechanics of jökulhlaups. Ann. Glaciol., 22, 255259.
Glazyrin, G.E. and Popov, V.I.. 1999. Lednik severnyi Inyl’chek za poslednie poltora veka [North Inyl’chek Glacier in the last 150 years]. Mater. Glyatsiol. Issled. 87, 165168. [In Russian with English summary.]
Guðmundsson, M.T., Björnsson, H. and Pálsson, F.. 1995. Changes in jökulhlaup sizes in Grímsvötn, Vatnajökull, Iceland, 1934–91, deduced from in-situ measurements of subglacial lake volume. J. Glaciol., 41(138), 263272.
Hagg, W., Mayer, C., Lambrecht, A. and Helm, A.. 2008. Sub-debris melt rates on southern Inylchek Glacier, central Tian Shan. Geogr. Ann., Ser. A, 90(1), 5563.
Hock, R. 2003. Temperature index melt modelling in mountain areas. J. Hydrol., 282(1–4), 104115.
Huss, M., Bauder, A., Werder, M., Funk, M. and Hock, R.. 2007. Glacier-dammed lake outburst events of Gornersee, Switzerland. J. Glaciol., 53(181), 189200.
Kalnay, E. and 21 others. 1996. The NCEP/NCAR 40-year reanalysis project. Bull . Am. Meteorol. Soc., 77(3), 437471.
Kistler, R. and 12 others. 2001. The NCEP/NCAR 50-year reanalysis: monthly means CD-ROM and documentation. Bull. Am. Meteorol. Soc., 82(2), 247267.
Konovalov, V.G. 1990. Metody rascheta i prognoza elementov rezhima proryvoopasnogo ozera Mertsbakhera [Methods of computation and prediction of the danger of outburst regime of Lake Mertsbakher]. Mater. Glyatsiol. Issled. 69, 141147. [In Russian with English summary.]
Kuzmichenok, V.A. 1984. K voprosu ob obrabotke materialov topograficheskikh s’emok dna glyatsial’nykh ozer [Questioning the treatment of materials from topographical surveys of glacial lake beds]. In Dikikh, A.N., ed. Gliatsiologicheskie Issledovaniya v Tsentral’nom Tyan-Shane [Glaciological studies in central Tien Shan]. Frunze, Ilim Press, 130137. [In Russian.]
Lai, Z. 1984. Characteristics of glacial flood – example of rivers in Xinjiang. J. Glaciol. Cryopedol., 6(2), 4552. [In Chinese with English summary.]
Liu, J. 1992. Jökulhlaups in the Kunmalike River, southern Tien Shan Mountains, China. Ann. Glaciol., 16, 8588.
Liu, J. and Fukushima, Y.. 1999. Recent change and prediction of glacier-dammed lake outburst floods from Kunmalik River in southern Tien Shan, China. IAHS Publ. 255 (Symposium at Birmingham, UK 1999 – Hydrological Extremes: Understanding, Predicting, Mitigating), 99107.
Liu, S., Cheng, G. and Liu, J.. 1998. Jökulhlaup characteristics of the Lake Mertzbakher in the Tianshan mountains and its relation to climate change. J. Glaciol. Geocryol., 20(1), 3036. [In Chinese with English summary.]
Martien, P., Pope, S.C., Scott, P.L. and Shaw, R.S.. 1985. The chaotic behavior of the leaky faucet. Phys. Lett. A, 110(7–8), 399404.
Mavlyudov, B.R. 1997. Drainage of the ice-dammed Mertzbacher Lake, Tien Shan. Mater. Glyatsiol. Issled. 81, 6165.
Mayer, C., Lambrecht, A., Hagg, W., Helm, A. and Scharrer, K.. 2008. Post-drainage ice dam response at Lake Merzbacher, Inylchek Glacier, Kyrgyzstan. Geogr. Ann., Ser. A, 90(1), 8796.
Merzbacher, G. 1905. The central Tian-Shan Mountains, 1902–1903. London, John Murray.
Ng, F.S.L. 1998. Mathematical modelling of subglacial drainage and erosion. (DPhil thesis, University of Oxford.)
Ng, F. and Björnsson, H.. 2003. On the Clague–Mathews relation for jökulhlaups. J. Glaciol., 49(165), 161172.
Ng, F., Liu, S., Mavlyudov, B. and Wang, Y.. 2007. Climatic control on the peak discharge of glacier outburst floods. Geophys. Res. Lett., 34(21), L21503. (10.1029/2007GL031426.)
Nye, J.F. 1976. Water flow in glaciers: jökulhlaups, tunnels and veins. J. Glaciol., 17(76), 181207.
Shaw, R. 1984. The dripping faucet as a model chaotic system. Santa Cruz, CA, Aerial Press.
Shen, Y., Wang, G., Shao, C., Mao, W. and Wang, S.. 2007. Response of glacier flash flood to climate warming in the Tarim River Basin. Adv. Climate Change Res., 3, Suppl., 5156.
Spring, U. and Hutter, K.. 1981. Numerical studies of jökulhlaups. Cold Reg. Sci. Technol., 4(3), 227244.
Sugiyama, S., Bauder, A., Weiss, P. and Funk, M.. 2007. Reversal of ice motion during the outburst of a glacier-dammed lake on Gornergletscher, Switzerland. J. Glaciol., 53(181), 172180.
Thórarinsson, S. 1939. The ice dammed lakes of Iceland with particular reference to their values as indicators of glacier oscillations. Geogr. Ann., 21(3–4), 216242.
Walder, J.S. and Costa, J.E.. 1996. Outburst floods from glacier-dammed lakes: the effect of mode of lake drainage on flood magnitude. Earth Surf. Process. Landf., 21(8), 701723.
Walder, J.S. and 6 others. 2006. Local response of a glacier to annual filling and drainage of an ice-marginal lake. J. Glaciol., 52(178), 440450.

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