Data Science

The Deadly Power of the 2015 Everest Avalanche

The 18 deaths on Everest are a small fraction of the 5200+ fatalities across Nepal due to last Saturday's earthquake.  The tragedy of the avalanche at Everest Base Camp is dwarfed by the catastrophe facing the residents of Nepal's major cities.  In the next few weeks, when the Western climbers return to the comfort of home, Nepalis will continue to reel from the destruction, recovering bodies of those who perished and beginning to rebuild the vast tracts of the country that lay in ruins.  If you've been moved by the stories of the destruction in Nepal, please consider donating to the relief efforts.  Both the Huffington Post and Charity Navigator have a useful index of charities providing earthquake-related aid in the region.

For the last five weeks I've been checking the International Mountain Guides (IMG) Everest blog with religious devotion.  Until a few days ago, Luke Reilly, my guide for my mountaineering expedition to Ecuador in January, and Nic Dumensil, a fellow climber on that Ecuador trip, were on Everest gearing up for a summit attempt.  Through blogs and Facebook feeds, I followed Luke and Nic as they acquired climbing permits in Kathmandu, trekked across the Khumbu Valley, climbed Lobuche to acclimatize, and settled into base camp.  It was exciting to read the dispatches and cheer them on from afar, but with Saturday's 7.8 magnitude earthquake and the resulting avalanche, my buoyant ritual became a grim vigil.  Nic and Luke are safe, as is the entire IMG expedition, but 18 other climbers are dead and many more are critically injured.  All the Everest climbing expeditions are retreating back towards Kathmandu, which is itself a difficult proposition because much of Nepal's infrastructure has been destroyed. 

Everest 2015 Avalanche Facts
Serac Size1100 ft x 300 ft (330 m x 92 m)
Serac Weight1.4 million tons
Serac Impact Velocity180mph
Energy Released2.0 kilotons of TNT

I have read and re-read every report from the last few days, attempting to make sense of the violence endured by the climbers.  The devastation simply didn't add up to me.  Mountaineers only make camp in locations that are shielded from hazards such as rock fall and avalanches, and the location of Everest Base Camp is a time-tested safe haven amid the chaos of the Khumbu Glacier.  Make Hamill, an IMG guide, verifies this in his account to National Geographic:  "[I]n the middle of the expansive U shaped Khumbu Valley, we feel safe, buffered by lateral moraines and ice ridges a half a mile wide."  So how did an avalanche surmount the ridges with enough energy to create such devastation?  The first clues came for me in this video:

Video from Everest Base Camp of the powder cloud and gust front of the 2015 Everest avalanche

This wasn't your typical avalanche.  Most avalanche fatalities are due to asphyxiation due to burial (source), but most deaths in this avalanche were due to trauma.  Sure the video shows a powder cloud, but photos of the aftermath of the avalanche only show a dusting of snow on broken tents and scattered equipment.  What's different here is that a blast wave, and not a tide of snow, caused the destruction.  You can actually see evidence of this in the video:  Notice how the prayer flags languidly hang from their tethers (before 0:18 in the video) only to be drawn horizontally by the gust front (0:22 and later) as the avalanche approaches.

According to first-hand accounts, this "avalanche" was spawned when a tenuously perched serac broke free from its ridge and plummeted over 2300 ft (700 meters) to the valley floor.  The photos on the the IMG Everest Blog (here and here) show the serac ("ice cliff") that caused all this destruction.  When the serac hit the valley floor, the energy released caused a shockwave, which rocketed 1.9 km (1.2 mi) towards base camp, over the protective walls of rock and ice that normally shield the camp from avalanches and rock falls.

So what is a serac?  Perhaps not surprisingly, "serac" is a just fancy word for a beautiful chunk of ice that will eventually break loose and hurtle downhill.  Seracs are usually seen at the terminus of glaciers or wherever a glacier flows over a ridge or convex feature on a mountain.  Once a section of ice detaches from the main body of the glacier, the ice becomes a serac.  Thereafter, mechanical stress - due to glacier movement, snow loading, or vibrations caused by human or seismic activity - or melting due to solar heating can cause the serac to break loose and hurtle downward.  Below you can see a photo I took on the Nisqually Glacier of Mount Rainier in 2013.  You can see seracs in the top center of the photo which will eventually break loose and join the pile of rubble in the center of the photo.

Seracs on Mount Rainier, 2013 (Patrick Mauro)

Based on a crude analysis of the IMG photos, the serac measures 330m (1100 ft) in length and 92m (300 ft) in height.  Approximating the serac as a triangular prism, the ice in the serac weighs 1.3 billion kilograms or 1.4 million tons.  Using simple conservation of energy equations, released from a height of 700m (2300 ft), the ice fall would impact the ground at 180 mph (80 m/s) with an energy of 9.0 trillion joules, or 2.0 kilotons of TNT.  (In the rarefied atmosphere of the Khumbu Valley, energy lost due to drag is insignificant.)  The energy released is equivalent to 66% of the destructive power of the Halifax Explosion, which killed 2000 people, and 14% of the Little Boy atomic bomb dropped on Hiroshima.  It's no wonder now that the avalanche was so deadly and a miracle that more people weren't killed.

There have been some incisive editorials in the last few days challenging the wisdom of mountaineers to attempt a mountain as dangerous as Everest.  Explaining why climbers challenge themselves in these deadly environs is a complicated task, which I'll leave for a later time.  For now, consider that 18 people died when the equivalent of a tactical nuclear weapon was loosed only a mile away from them.  Imagine the terror of those in areas closer to the epicenter of the earthquake, and the helplessness the survivors must feel as they try to recover from this disaster.  I, for one, have contributed to the relief efforts in Nepal, and if you feel so compelled, check out the links at the top of the article for a list of charities involved in the recovery efforts.

NYC Marathon 2014: The Wind

For the last few months I have been tossing around the idea of analyzing data sets sourced from my hobbies:  endurance sports (triathlons and marathons), sailing, and mountaineering.  Athletic endeavors lend themselves quite well to statistical analysis (see Moneyball and Nate Silver's NCAA tournament predictions), but such careful and thoughtful scientific investigation rarely reaches the realm of less commercial sports.  I've often been frustrated because speculation, anecdotal heuristics, and qualitative arguments dominate most discussions about factors which influence athletic performance in amateur sports.  I hope that in this series of posts I can bring some clarity to these debates.  This is a work in progress, so if these analyses pique your interest or you have comments, please send feedback my way!

In this post I attempt to ascertain how much the wind affected the results of the NYC Marathon earlier this month.  On marathon Sunday runners were battered by a 11-21 mph headwind with gusts of up to 36 mph.  The wind made running tough.  I would know.  I was one of the marathoners.  During the first two miles of the marathon, runners summitted the Verrazano Narrows Bridge.  Racing 150' above NY Harbor, there was no protection from the breeze.  Runners dashing down the bridge at 7:00 min/mile pace were often blown sideways by sudden puffs.  I found a sad humor in the image of my fellow runners stumbling down the course towards Brooklyn looking as if they were all racing the marathon in a drunken stupor.  I probably didn't look much better.

Despite my enthusiasm for my charity (City Harvest) and my teammates, I did worse in this year's marathon:  In 2013's marathon I finished in 3:27:48, but this year, I (quite literally) limped across the line in 3:37:30.  So what happened?  At the conclusion of the race my coach Liz Corkum consoled me saying that the wind probably added 8:00 minutes to my finish time.  Is there any truth in that?  We'll see.

For this analysis I scraped data from the NYC Marathon website for finishers in the men's 20-29 year old age group for the 2013 and 2014 races (3129 finishers in 2013 and 3043 finishers in 2014).   Here's a plot of the distribution of finish times in both marathons:

Over-populations in the distribution just before half-hour boundaries in finish times are immediately obvious (at 3:00, 3:30, 4:00, 4:30, and 5:00).  These half-hour boundaries are very common target finish times for marathoners, so it's not surprising that on race day competitors push themselves to meet their training targets.  Interestingly, there isn't a large spike just before the Boston qualifier time of 3:05, another common goal for marathoners in NY.  I guess that if you're going to run a sub-3:05 marathon, you're most likely fit enough to go for a (much more fashionable) sub-3:00 marathon time.  

Looking at the distribution, we see that the 2014 distribution (blue) often exceeds the 2013 distribution (orange) for finish times slower than the mode (just before 4:00:00).  The opposite is true for times faster than the mode.  This would seem to imply that that people ran the 2014 marathon more slowly than the 2013 marathon.  Let's examine this next.

By comparing the finish time at the boundaries of every 5th-percentile interval (groups of ~150 runners), we see that the percentage difference of finish times across all runners is remarkably consistent:  For all but the top 5% and bottom 5% of runners in the age group, the 2014 marathon times were on average 2.44% slower than 2013 marathon times.  In the top 5th percentile and bottom 5th percentile, the runners are probably running an entirely different race than the rest of the pack.  The runners in the bottom 5th percentile are probably walking and just struggling to finish; while the runners in the top 5th percentile (3:01:52 or faster) are probably fit enough to deal with whatever race day might throw at them.  Thus, I think it's acceptable to throw out both groups when computing this average. 

At this point you might object that if wind resistance is the cause of the slow down, then we'd expect to see a greater decrease for faster runners.  After all, the simple act of running generates its own headwind on a calm day, and wind resistance increases with the square of velocity.  However, for an ultra-competative marathoner running 6:00 minute miles, a 15 mph headwind accounts for 84% of the wind resistance experienced by the runner.  This percentage increases for slower runners, so wind-generated wind resistance is the dominant factor for strong headwinds for most runners in the analysis.  (Fun fact:  For our same 6:00/mile runner, a 4.2 mph headwind is all that's required for the wind-generated headwind to begin to dominate wind resistance.)

Assuming a 2.44% slowdown as a rule, the following table gives the projected slowdown for a range of 2013 marathon times:

2013 Finish Time (hh:mm:ss)
Predicted Amount of Slowdown (m:ss)
3:00:00 4:24
3:10:00 4:39
3:20:00 4:53
3:30:00 5:08
3:40:00 5:23
3:50:00 5:37
4:00:00 5:52
4:10:00 6:07
4:20:00 6:21
4:40:00 6:51
4:50:00 7:05
5:00:00 7:20

For me, a 2.44% slowdown would have meant a 2014 finish time of 3:32:52, indicating that about half of my slowdown (5:04) was due to wind and half (4:38) was due to my lack of training.  (I was a bit light on long runs in my training program this year.  Life got busy.)

This jibes with conventional academic analysis of the effect of wind on runners.  A calculator from renowned running coach Dr. Jack Daniels indicates that a ~5 mph headwind is enough to produce the 2.44% slowdown observed in the results.  Indeed, the headwind experienced by the marathoners might have been closer to 5 mph rather than 11-21 mph because of the wind shadow created by buildings and other structures along the running route.  A paper by C.T.M. Davies in the Journal of Applied Physiology indicates that a world champion runner would experience a 3.9% decrease in their time if they could run a marathon in a vacuum. 

Finally, while I have demonstrated that 2014 marathon times were slower than 2013 marathon times, it's worth noting that I haven't proven why the times were slower.  Besides the wind, other factors could also be to blame: 

  • Weather conditions in the months before the marathon might have been less conducive to training;
  • As the economy strengthened, perhaps people were more busy at work and had less time to train;
  • The course might have been slightly altered; or
  • A timing error might have occurred. 

I've seen no evidence to support the final two possible causes and the first two statements don't seem likely.  Having run both the 2013 and 2014 marathon, I believe the wind was the only significant factor that could induce such a consistent slowdown over the entire population of runners.  Let's hope for a tailwind next year!