Temporal dynamics of a jökulhlaup system

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.