Temporal dynamics of a jökulhlaup system

Abstract

ABSTRACT. Recurring jö kulhlaups 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 jö kulhlaup lakes.

Chaotic dynamics of a glaciohydraulic model

“…4). Gradual timing shifts have been observed at Merzbacher Lake, Kyrgyzstan (Ng and Liu, 2009), and Gornersee, Switzerland (Huss and others, 2007), with annual floods occurring progressively earlier in the year. These shifts in flood timing are consistent with long-term increases in meltwater production and our results suggest that jökulhlaup systems are also capable of undergoing more abrupt changes in both the timing and the peak discharge of floods.…”

“…Combined with chaotic variations in weather forcing, these dynamics may compound the difficulties of flood prediction associated with uncertain flood-triggering mechanisms and meteorological inputs (Ng and Liu, 2009;Kingslake and Ng, 2013b) and make long-term prediction of flood timing difficult. Due to their sensitive dependence on initial conditions, chaotic systems are practically unpredictable beyond a certain time in the future (e.g.…”

“…Fowler (1999) also showed that modelled floods are larger when the constant input to the lake is larger. This is due to the dynamics of a subglacial hydraulic divide that forms during lake-filling periods and could explain observed variability in the size of floods (Ng and others, 2007;Ng and Liu, 2009;Kingslake, 2013;Kingslake and Ng, 2013b).…”

“…Real ice-dammed reservoirs receive water inputs that vary on diurnal, seasonal and interannual timescales (e.g. Bartholomaus and others 2008;Ng and Liu, 2009;Kingslake and Ng, 2013b;Schoof and others, 2014;Siegfried and others, 2014). Here we investigate the behaviour of Nye's (1976) model when it is forced with a meltwater input that depends on a seasonally varying synthetic air temperature time series.…”

“…It has been used to investigate various aspects of jökulhlaup dynamics (e.g. Spring and Hutter, 1981;Clarke, 1982Clarke, , 2003Björnsson, 1992Björnsson, , 1998Ng, 1998;Fowler, 1999Fowler, , 2009Jóhannesson, 2002;Ng and Björnsson, 2003;Kessler and Anderson, 2004;Evatt, 2006;Ng and Liu, 2009;Pimentel and Flowers, 2011;Kingslake and Ng, 2013a;Schoof and others, 2014). In particular, Fowler (1999) showed that a modified version of Nye's (1976) model can simulate stable, periodic flood cycles when a constant water input is supplied to the lake and the subglacial channel along its length (Evatt, 2006;Kingslake and Ng, 2013a).…”