Chaotic dynamics of a glaciohydraulic model

A model subglacial drainage system, coupled to an ice-dammed reservoir that receives a
time-varying meltwater input, is described and analysed. In numerical experiments an ice-marginal lake
drains through a subglacial channel, producing periodic floods, and fills with meltwater at a rate
dependent on air temperature, which varies seasonally with a peak value of Tm. The analysis reveals
regions of Tm parameter space corresponding to ‘mode locking’, where flood repeat time is independent
of Tm; resonance, where decreasing Tm counter-intuitively increases flood size; and chaotic dynamics,
where flood cycles are sensitive to initial conditions, never repeat and exhibit phase-space mixing.
Bifurcations associated with abrupt changes in flood size and timing within the year separate these
regions. This is the first time these complex dynamics have been displayed by a glaciohydraulic model
and these findings have implications for our understanding of ice-marginal lakes, moulins and
subglacial lakes.