Subglacial Lake Outburst: Channel Drainage Dynamics

Ice & Basin

Ice thickness 450 m

Channel slope (β) 2.0°

Hydrology

Meltwater recharge 0.8 m³/s

Time acceleration 20 hr/s

Live Readout

Discharge Q

0.0 m³/s

Lake remaining

100%

Channel diameter

0.16 m

Effective pressure N

0 kPa

Elapsed time

0.0 h

Peak discharge

0.0 m³/s

How it works

A subglacial lake sits in a basin at the bed of an ice sheet, held in by the weight of the ice above it. Drainage happens through a Röthlisberger channel (R-channel) — a conduit melted into the ice-bed interface — whose cross-sectional area S evolves from two competing processes (Röthlisberger 1972; Nye 1976):

Effective pressure:   N = ρ_i g H_ice − ρ_w g h_lake
Melt-opening:         dS/dt|open  = Q·(dΦ/dx) / (ρ_i L)
Creep closure:        dS/dt|close = 2 A S (N / n)^n,  n = 3 (Glen's flow law)
Net:                  dS/dt = dS/dt|open − dS/dt|close
Discharge:            Q ≈ k · S^(4/3)   (turbulent conduit flow)

This is a genuine positive feedback: a larger channel carries more discharge Q, which dissipates more frictional heat and melts the channel walls faster, carrying still more Q — a runaway that only stops when the lake empties enough for Q (and hence melt-opening) to collapse, letting slow ice creep pinch the channel shut again. That asymmetric rise-then-shutoff is exactly the shape of a real jökulhlaup hydrograph.

Ice thickness sets the overburden pressure ρ_i g H_ice — thicker ice resists channel opening more strongly and raises the flotation threshold.
Channel slope sets the hydraulic potential gradient dΦ/dx that drives viscous-dissipation melting.
Meltwater recharge is the steady inflow refilling the lake between outbursts.
Trigger Outburst seeds a small basal fracture (S ≈ 0.05 m²) connecting the lake to the drainage network, the way a crevasse or flotation event does in nature — the feedback then runs on its own.

The ice surface directly above the lake sags into a shallow subsidence bowl as the void drains and ice flows to fill it — the same signature glaciologists track by satellite altimetry to detect real subglacial outburst floods (e.g. beneath Antarctica and Vatnajökull, Iceland) from orbit.

Subglacial lake Drainage channel Ice sheet

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