Outburst floods from glacier-dammed lakes: The effect of mode of lake drainage on flood magnitude

Abstract

Published accounts of outburst floods from glacier‐dammed lakes show that a significant number of such floods are associated not with drainage through a tunnel incised into the basal ice—the process generally assumed—but rather with ice‐marginal drainage, mechanical failure of part of the ice dam, or both. Non‐tunnel floods are strongly correlated with formation of an ice dam by a glacier advancing from a tributary drainage into either a main river valley or a pre‐existing body of water (lake or fiord). For a given lake volume, non‐tunnel floods tend to have significantly higher peak discharges than tunnel‐drainage floods. Statistical analysis of data for floods associated with subglacial tunnels yields the following empirical relation between lake volume V and peak discharge Q p : Q p = 46 V 0.66 ( r 2 = 0.70), when Q p is expressed in metres per second and V in millions of cubic metres. This updates the so‐called Clague–Mathews relation. For non‐tunnel floods, the analogous relation is Q p = 1100 V 0.44 ( r 2 = 0.58). The latter relation is close to one found by Costa (1988) for failure of constructed earthen dams. This closeness is probably not coincidental but rather reflects similarities in modes of dam failure and lake drainage. We develop a simple physical model of the breach‐widening process for non‐tunnel floods, assuming that (1) the rate of breach widening is controlled by melting of the ice, (2) outflow from the lake is regulated by the hydraulic condition of critical flow where water enters the breach, and (3) the effect of lake temperature may be dealt with as done by Clarke (1982). Calculations based on the model simulate quite well outbursts from Lake George, Alaska. Dimensional analysis leads to two approximations of the form Q p ∝ V q f ( h i , θ 0 ), where q = 0.5 to 0.6, h i is initial lake depth, θ 0 is lake temperature, and the form of f ( h i , θ 0 ) depends on the relative importance of viscous dissipation and the lake's thermal energy in determining the rate of breach opening. These expressions, along with the regression relations, should prove useful for assessing the probable magnitude of breach‐type outburst floods.