Glacial Lake Floods Stop Cutting at a Shallow Angle, Whatever Their Size
In 1950, a lake called Jancarurish, high in Peru's Cordillera Blanca, broke through the ridge of loose rock holding it back and emptied down the valley. An aerial survey photograph kept by the water authority in Huaraz shows the moraine before the flood; a satellite image shows the notch left behind. Between those two pictures sits a quantity three researchers have now measured across the world's largest moraine-dam floods: the slope of the channel the water cut, at the point where it stopped cutting.
Those images open a brief communication published Wednesday in Natural Hazards and Earth System Sciences by Adam Emmer, a geographer at the University of Graz and Charles University in Prague, with Ashim Sattar of the Indian Institute of Technology Bhubaneswar and Jan Hrebrina of NTNU in Norway. Their subject is one of the least examined inputs in flood forecasting: how deep a moraine dam actually breaks.
Breach depth sets how much water leaves the lake, and standard formulas turn it into breach width, failure time, and the peak of the flood wave. Calculating it properly means knowing what the dam is made of (grain sizes, buried ice, boulder content), and at most high-mountain lakes nobody has been out to look. So modelers assume it, and the usual assumption is that the lake empties completely.
Emmer's group worked the problem from the other end. From a global database of past outbursts they pulled every moraine-dam failure that released at least a million cubic meters, left a channel still visible in satellite imagery, and had elevation data covering the aftermath; the final list ran to 26 events. Fourteen are in High Mountain Asia, nine in the Andes, and three in Canada's Coast Mountains, with nothing from the Alps or the Caucasus. For each, they measured the drop from the lake surface to the dam's foot, the channel length between them, and took the angle.
The angles are shallow, and they cluster. The median is 4.9 degrees. The two flattest channels, at South Lhonak in Sikkim and Nostetuko in British Columbia, both come in at 2.3 degrees; the steepest, at Zhangzangbo in Tibet, at 19.5. Floods spanning two orders of magnitude in volume left much the same grade behind, and the authors report no correlation between flood size and slope, a statement the main text makes without a supporting statistic.
What the method does with that is easy to get backwards. The number it feeds into the calculation is not the median but the minimum: 3 degrees, and a more cautious 2 degrees, slightly below anything in the record. The median says where a breach channel typically stops. The minimum bounds the worst it could plausibly do.
The arithmetic is trigonometry a surveyor would recognize. Take the lake's water level before the flood, the elevation of the moraine's toe, and the distance between them; project a line up from the toe at that angle, and the height it reaches is the deepest cut the dam is likely to sustain. Multiply by the lake's surface area for the largest volume that can get out.
Run against published worst-case scenarios, the numbers come out smaller. The reduction is greatest for lakes behind broad, flat dams and close to nil for narrow high ones with steep outflows. That direction matches the historical record: an earlier survey the authors cite found complete emptying in fewer than one case in ten, all of them small, shallow lakes. A deep basin gouged out by the glacier keeps its water below anything the breach can reach.
The 2023 South Lhonak flood in Sikkim shows the other control the paper presses on: where the breach opens. It formed toward one side of the moraine rather than at its lowest point, and roughly half the lake's volume stayed behind. Deeper incision, the authors argue, would have followed a breach at the low point.
The same measurements carry a second implication, and it is the one most easily over-read. A lake whose outflow channel is already flatter than about 3 degrees is unlikely to be breached, while, as the authors write in the same breath, such lakes can still be prone to dam overtopping-induced floods. The finding limits one failure mode. It is not an all-clear for the valley below.
Every slope in the set is, in the authors' words, substantially lower than the 10-degree threshold Koji Fujita and colleagues proposed in 2013, though the two numbers measure different geometry: Fujita's the depression angle of a lakeshore, Emmer's the grade of a breach channel. Fujita is thanked in the acknowledgments for comments on an earlier version.
No uncertainty is reported on any of the slopes, no error bars, no interval on the median, and they come from satellite elevation models with pixels 12.5 to 30 meters across. That matters most at the flat end, where a few meters of drop over a few hundred does all the work, and the flat end is where the method takes its input. The authors mark their own limits too: not for floods bigger than anything in their dataset, not in terrain unlike it, and the depth it returns is an upper bound wherever buried ice, clay or bedrock could stop the erosion early.
The appeal of the approach is what it needs: a lake level, a dam toe, a distance, a map. At the lakes where nobody has ever come out with a drill rig, which is most of them, that is the difference between a scenario and a guess.