The Subglacial Siphon
Vatnajökull and the Runaway Physics of Ice-Dammed Floods
Glaciologist Helgi Björnsson watched radar altimeters and seismic sensors across the Vatnajökull ice cap in southeastern Iceland drop rapidly on the evening of November 4, 1996. More than 3.2 cubic kilometers of subglacial meltwater were vanishing from the Grímsvötn caldera into the dark beneath the glacier. Five weeks earlier, on September 30, a volcanic fissure at Gjálp had erupted directly underneath six hundred meters of glacial ice. Instead of blasting ash into the sky, the erupting basaltic magma melted a vast subterranean cavern. A river of warm meltwater drained fifteen kilometers south into Grímsvötn, a subglacial volcanic lake sealed off from the southern coastal plain by a 500-meter-thick ice dam.
For thirty-five days, Björnsson and Iceland's civil defense authorities tracked the rising ice dome over the lake as the trapped water reservoir swelled. Every glaciologist in Iceland knew that the water would eventually break through the fifty-kilometer path beneath the Skeiðarárjökull outlet glacier to reach the Atlantic coast. What made the 1996 jökulhlaup—the Icelandic word for a glacial outburst flood—so destructive was the runaway thermodynamic siphon that governs water flowing through pressurized ice conduits. Describing the feedback mechanism that turns a tiny basal leak into an inland sea, Björnsson explained that once pressurized water lifts the ice off its bedrock sill, the escaping flood carves its own highway by melting the tunnel walls with the heat of its own friction.
Unlike an earthen or concrete dam that fails by eroding from the top down, a subglacial ice dam fails from the bottom up through a four-stage physical cascade established by Swiss glaciologist Hans Röthlisberger:
- * Hydrostatic Flotation Threshold ($\rho_{\text{ice}} \approx 0.917 \rho_{\text{water}}$): Because glacial ice has a density of 917 kilograms per cubic meter compared to 1,000 kilograms per cubic meter for liquid water, an ice barrier floats off its bedrock seal as soon as the subglacial water level rises to roughly 91.7 percent of the overlying ice thickness—at Grímsvötn, warm volcanic water lifted the 500-meter ice dam even slightly earlier by melting its basal seal.
- * Potential-to-Frictional Heat Conversion: Once water forces a thin film beneath the lifted ice sill and flows down a 1,400-meter vertical drop toward the sea, every cubic meter of descending water converts gravitational potential energy ($\rho_w g \Delta h$) into viscous frictional turbulence against the ice roof and walls.
- * Röthlisberger Conduit Runaway: The size of a subglacial tunnel reflects a competition between inward plastic creep of the overlying ice under overburden pressure (Glen's Flow Law) and outward melting of the ice walls by frictional water heat; because frictional heating scales with water discharge as $Q^{3/2}$, a rising flood melts the tunnel wider far faster than ice creep can squeeze it shut.
- * Exponential Discharge Spike ($50,000\text{ m}^3/\text{s}$): Each meter of tunnel enlargement lowers hydraulic resistance and draws a larger volume of lake water into the conduit, which in turn generates more frictional heat and melts the tunnel even wider until the entire subglacial reservoir empties in hours.
At 7:30 a.m. on November 5, 1996, sediment-blackened water burst from the snout of Skeiðarárjökull across a twenty-kilometer front. It carried icebergs the size of three-story houses weighing up to two thousand tons. Within fourteen hours, discharge peaked at 50,000 cubic meters per second. That flow temporarily exceeded the Congo and Mississippi rivers, making the flood the second largest river on Earth after the Amazon. The torrent swept away the Skeiðará Bridge and twisted nine-ton steel girders like wire. Icelandic highway engineers now build the Ring Road across the Skeiðarársandur plain with sacrificial earthen embankments designed to wash away cleanly during a jökulhlaup so the expensive steel bridges survive.