Simulating glacial retreat and consequent debris flows on Mt. Rainier, WA

I recently worked on a short project for Oregon State University in which I did some data analysis and modeling intended to predict the onset of water and debris flows down the side of Mt. Rainier in Washington state, as a consequence of the the retreat of the semi-permanent glaciers on that mountain. My part of the project was fairly small (3 months out of 3 total years), but it was interesting and informative (and I hope somewhat useful!), and I got to work with a high resolution (10 m) Digital Elevation Model of the mountain and surrounding National Park, and with some Landsat images of the glaciers from 2000 to 2009. The Landsat images and field data of known debris flow sites were prepared by graduate students, but I wrote all the software in C and Python for doing the image processing and display in 2d and 3d, for detecting the glacier outlines over the years, mapping the outlines to the DEM using a Universal Transverse Mercator projection, calculating area and volume loss from the glaciers each year, simulating multiple branched fluid flows down the mountain from the periphery of the glaciers due to the volume loss, and for multi-dimensional data modeling of the flow, surface slope, and other parameters to predict the probable locations of other debris flow initiation sites and to compare them to the field data of actual debris flow sites.

Mt. Rainier is a 14,000 foot high stratovolcano (a tall, conical volcano consisting of many strata, or layers) near Seattle in Washington State. It contains at least 25 semi-permanent glaciers (depending on how you count them) consisting of ice, snow, and frozen rock, soil, and other debris. As are many of the other glaciers, ice packs, and snow fields of the world today, Mt. Rainier's glaciers are currently in retreat, which means that their volumes, surface areas, and perimeters are decreasing from year to year, possibly due to global warming. One consequence of this retreat is that periodically, during the summer and fall, catastrophic debris flows consisting of water, soil, rock, and other materials are initiated near the perimeter of the glaciers and go cascading down the slope of the mountain. The mass and volume of these flows is not well known, but may be in excess of hundreds or thousands of tons per event, which can have significant effects on vegetation, erosion, human structures, and the local geomorphology of the mountain. Although these events may be initiated by several sources (rainfall, accumulated meltwater, failure of underlying strata, etc...) this part of the study concentrated on correlating debris flow initiation only with the yearly retreat of the glaciers.

Here is an elevation map of Mt. Rainier National Park at 30 m/px. Blue = 489 m, red = 4392 m:

Field studies of the mountain (i.e. by researchers hiking up and down the valleys) yielded the locations of a small number of sites where debris flows were thought to begin. There were 18 known debris flow initiation sites, occurring during 2000 - 2009, used in this study. Here are the sites plotted on a shaded view of the park (brightness is surface orientation, with white at 315 degrees azimuth):

The vertical surface slope of the park (min = 0 degrees, max = 86 degrees, mean = 26 degrees, standard deviation = 13 degrees):

The mountain in 3d, showing the debris flow sites with respect to the glaciers:

Landsat images of the park from 2000 - 2009 were prepared by graduate students:

I processed these to extract contours and project them onto the park map:

The next image shows a comparison between the 2000 and 2006 contours. Green pixels are only within the 2000 contour. Red pixels are only within the 2006 contour. Yellow are within both the 2000 and 2006 contours. If the contours are interpreted as glacial outlines (they aren't), then green areas are those from which the glaciers have retreated between 2000 and 2006:

Using a true glacier outline prepared by the USGS, the contours of the Landsat images can be compared to the glaciers. In the images below, red pixels are within the outline, but not within the Landsat contour. Blue pixels are within the contour, but not within the outline. Yellow pixels are within both. This is easier to see if the pixels are filled rather than transparent, and the background is omitted. It is clear that a significant fraction of the glacier area is dark, and does not appear within part of the bright Landsat contours (which are mostly surface snow and high albedo ice):

An adaptive, iterative, technique can be used to find the contour value which maximizes the glacier area inside of it (yellow), while minimizing the area outside of it (blue). This technique can then be used to estimate the glacier outlines from all other Landsat images:

These estimated outlines can then be combined, for successive years, to plot the overall retreat of the glaciers. The following sequence of images show the original glacier outline (blue), and then overlaid with the Landsat outlines for 9 subsequent years. At each step, the new yearly outline (latest outline in red, previous years in other colors) is masked to the previous masked outline to form a nested set. The glacial recession between years is the difference between two outlines at the end of the process. At right, the initial mask and the final mask have been removed to show the sequence of differences for each intervening year.

Additional data provided by graduate students and other researchers allowed us to augment the Landsat glacier outlines with known bounds for the first and last years of the dark regions which were outside of the bright contours:

Using the yearly outline differences (converted to volume) as potential sources of melted water and other material, many Monte Carlo branched flow simulations were created for each year. For each simulation, discrete flow sources could be distributed across the surface of the glaciers, or at the perimeter where volume loss occurred during the year. The following image shows a typical yearly average of 25 such simulations, each of which contained 1000 flow sources distributed randomly in locations where glacier retreat occurred:

Detail of the simulation:

Another of the simulations in 3d:

Detail of the south side of the mountain:

Clearly, many of the known debris flow sites are associated with high levels of runoff from the retreating glaciers. But that's not the entire story, as some of the sites also appear in areas of lower flow. To investigate the involvement and relationship of other parameters in addition to flow, several data models were prepared which mapped properties of the debris sites in several (non-spatial) dimensions, and looked for other points close to this cluster. The following image shows such a model for the variables {flow, the standard deviation of the flow, the slope of the surface, and the distance from the nearest perimeter of retreat}. At left are 3d sub-sections of the 4d model, and at right are the locations of points which are close to the known debris sites in the model. The result is a probability map of where debris sites are likely to form, given the conditions at those locations (points inside the glacier outline have been excluded):

Detail of the resulting probability map:

In 3d, also showing the interior of the glaciers:

Detail of the south side of the mountain:

Note that this model predicts many areas of high probability (red) for debris flow initiation which are away from the known sites. Many of these areas are downslope of and in the same basin of accumulation as the sites themselves, but many potential danger areas are upslope and well away from the known sites. It is natural to conjecture that some of these areas might also contain several undiscovered debris flow sites. Additional field studies to locate these other sites, or more involved processing of satellite or aerial images to automatically detect these sites, is indicated. In addition, other data models using parameters such as temperature or the composition of the underlying surface material, should be created and tested to see if they generate different debris flow initiation maps.

Here is a link to the weekly project work log with lots of additional information, and more images.

© Sky Coyote 2010