Dr. David Bahr

Regis University, Department of Computer Science


Ski Moguls Move Uphill!

Most skiers assume that ski moguls or "bumps" get pushed down the mountain.  Makes sense, right?  Skiers are pushing snow down the mountain.  But actually, bumps move uphill, and there's video to prove it!

What's that really mean?  Well, if you could stand still on a mogul, it would slowly move you uphill as if you were standing on an escalator.  Very slowly.  Ok, reeeeally slowly -- like a few centimeters per day.  Never the less, all the bumps in a mogul field are migrating uphill, and with time-lapse photography it is easy to see them crawling up the mountain.

 

Show me!

This video is constructed from pictures taken at the same time every day from December 2005 through April 2006 at Mary Jane Ski Resort.  Stand back just a bit, and you'll quickly see that the bumps are moving from the bottom right to the top left -- that's uphill.

More videos:

If you are curious, here's an explanation of the video construction.

 

Explain the uphill movement please.

It's simple.  Skiers push snow down the mountain by scraping it off the downhill side of a bump, but simultaneously they pile the snow onto the uphill side of the following bump.  Each mogul, therefore, loses material on the downhill side but gains new material on the uphill side.  The unintuitive net effect is that the bumps migrate uphill.

 

Ummm, I want more details.

Ok, everyone correctly assumes that snow moves downward like rainwater – snow falls from the sky, avalanches move down mountains, glaciers flow downhill, and with every turn, skiers push snow down a ski resort.  What few realize, however, is that processes within snow and ice can move uphill.  The process is analogous to car brake lights on a busy highway.  The cars are all moving in the same direction, but if any car hits their brakes, then a “wave” of red brake lights will move backwards down the highway.  The cars themselves don’t move backwards (just like the snow doesn’t move uphill), but sitting on a hill in twilight above rush hour traffic, these backward propagating brake-light waves are easy to spot.

Snow moguls or “bumps” at ski resorts are like the brake lights, and they move backwards (uphill) to organize themselves into neatly-placed, easily visible rows.  Take a look at the following picture of the Riflesight Notch mogul field at the Winter Park/Mary Jane Ski Resort.  Notice the cool rows indicated by the dashed lines? 

The neatly aligned rows look as if someone placed them there on purpose.  Nope, not the case.  Sometimes I get asked if there are hay bales under there.  Nope, the bumps just spontaneously self-organize with no "traffic directions" or feedback from the ski resort or the skiers.  That was the first clue that the moguls had to move.  How else could they get so neatly aligned?

When the run was first opened at the beginning of the ski season, it started as a smooth field of snow with no bumps.  Then skiers started pushing the snow around with their skis.  However, skiers on one side of the ski trail, did not coordinate with skiers on the opposite side.  Instead, each skier was independently making small piles as they pushed the snow down the mountain with every ski turn. The independent piles (bumps) started out haphazard and uncoordinated, but somehow the field of moguls organized into smooth rows that span the entire ski trail.  Even though skiers made no attempt to create these rows, the moguls still lined up perfectly, implying that the moguls must have moved from their initial positions and merged into the smooth rows.

So then the question is, "How do they move?"

Again, take a look at the picture of the Riflesight Notch mogul field (above).  See how the uphill side of every bump has some loose (rough looking) snow?  The uphill side has loose snow pushed into place by skis that scrape the snow off the downhill side of the previous mogul.  So the uphill side is continually growing, and the downhill side is continually being scraped and eroded away.  That "scrape and pile" process makes the bumps move uphill.

In general, the bumps will migrate uphill until they are aligned with other bumps, and then together the bumps continue to march "hand in hand" up the mountain.  Once a bump gets in line, it never gets out of line.  Why?  Because the skiers would preferentially "scrape and pile" that misaligned bump until it was re-aligned.  So each row of bumps marches in lockstep up the hill. 

Think of the bumps as a marching band.  At first everyone in the band mills about haphazardly, then they organize into rows, and finally each row marches in sync.

 

Yeah, so who cares?

Well, besides the fact that it's just cool to know (and defies our intuition)... 

The bumps are self-organizing.  That places them into a special class with other self-organizing systems that include diverse phenomena like spiral galaxies, sand piles, earthquakes, bird flocks, and even LCD TV crystals.   The science behind these self-organizing processes is relatively recent (requiring modern computational power), but all self-organizing systems share the same mathematical foundation.  Therefore, insights into any one process help elucidate aspects of all the others.  Compared to galaxies and earthquakes, moguls are very easy to study experimentally.  So we study something easy to access (moguls), and as a by-product we learn about the nature of galaxies, earthquakes, and practical applications ranging from pharmaceuticals to LCD TV production.

 

And moguls act like a computer.

Say what?!

Yup, those fields of moguls act just like your desktop computer.  Seriously.  They can do anything your desktop can do.  Think of the moving moguls as electrons.  The ski trail is like a wire.  As multiple "wires" come together, the moguls interact and perform calculations (technically, the junctions of ski trails act as "logic gates" just like the wires, transistors, and chips in your Mac, Lenovo, or Dell PC).  Of course, moguls don't come with keyboards and monitors, but the input (keyboard) and output (monitor) are written in a kind of "bump Braille".  Each mogul is a raised "dot" in the Braille -- just run your hands (or skis) over the bumps to see what the moguls are calculating.

There's a technical math proof that the moguls behave as a computer.  If you are curious see the details in my 2009 article, "On fundamental limits to glacier flow models: computational theory and implications," Journal of Glaciology, vol 55, no. 190, pp. 229-238.  The paper talks about glaciers, but the theory applies equally well to moguls.

Oh, and next time you need a day off from work, go skiing and tell your boss "I'll be spending the day on the computer."

 

Other Research

The mogul study started primarily as a fun (and inexpensive) illustration for the classroom -- it demonstrates self-organizing behavior and unexpected computation in natural/man-made systems.  However, if you are curious, most of my research involves glaciers and their interaction with climate change and sea-level rise.  Many of my studies have also focused on cellular automata and complex global systems that arise from simple local interactions.  A list of my published papers indicates my general research interests. 

 

Who's involved?

This admittedly fun research is a cooperative project between

 

Please contact me directly with any questions, comments, revisions, corrections, rants, or raves.

Contact:  David Bahr at dbahr at regis.edu

 

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