Author Climbing in the Queyras, Summer 2013

Thursday, December 12, 2013

Disappearing Acts:
the Life and Death of a Great Alpine Glacier

Using Nineteenth Century Sources to Study the melting of the Glacier Blanc


..... field geographers can speak with authority about the clarifying effects on the mind of direct physical danger in the real world and there exists a terrible antagonism between field geographers and armchair academics. Not only do those in their armchairs think and write junk, obfuscation, obscurantism, and endlessly convoluted self-referral to their literature in windowless libraries, they do not care about the human condition.”

--William Bunge,
Geography is a Field Subject
Area, 1983

This paper is a shorter version of talk given in 2010 and that will be published later this year.
See the session Measuring Environmental Impact at the Institute of Historical Research, University of London School for Advanced Studies, and my paper Disappearing Worlds.

The Glacier Blanc is the largest glacier in the Southern Alps. From the Dome des Ecrins it reaches a height of 4014 meters down to its snout at 2315 meters, the glacier covers an area of 5.34  square km, extends 5.9 km in length and has a mean slope of approximately 30%.  Measurements have been carried out on the Glacier Blanc since the late nineteenth century with the first real quantitative study in 1887.
Glacier Blanc from the Dome de Neige des Ecrins (click on image to enlarge)

Click on Images to Enlarge
Several important studies have summarized the historical variation of the glacier's mass balance, length and thickness. (see Thibert, E., J. Faure and C. Vincent. 2005. "Bilans de masse du Glacier Blanc entre 1952, 1981 et 2002 obtenus par mode`les nume´riques de terrain". Houille Blanche 2, 72–78.)

Approaching the Glacier Blanc from the Village of Alfoid  (click on image to enlarge)

The approach to the Refuge des Ecrins (click on image to enlarge)
In the center section the main stream the Glacier Blanc is about 800 to 1000 metres wide. The greatest depth of ice occurs near the Refuge des Écrins where it is up to 250 metres deep; some 30 metres less than it was in 1985. My visit  to the glacier this summer showed that the glacier had shrunk back significantly from its previous position leaving only exposed rock near the lower Refuge du Glacier Blanc.

The map below, last updated in in 1991, shows the position of the glacier relative to the refuge, and portrays the snout many tens of meters further down the valley than its present location. The glacier flows at a speed of around 40 meters per year in its central section (in the mid-1980s it moved at 50 m/yr) and at about 30 metres per year near its snout. Its reaction time, i.e. the time that elapses before the foot of the glacier advances or retreats due to major changes in conditions in the accumulation zone, is about 6 years. So the melting we are seeing now is a window into the recent past. 

Map of the area around the Glacier Blanc showing the Refuges Ecrins, Blanc, and Cezanne along with the Glacier Blanc's smaller and rock covered partner, the Glacier Noir  (click on map to enlarge)
Glacier Blanc in the Summer of 2012 (click on image to enlarge)

Schematic of the Structure of the Glacier Blanc (click on image to enlarge)
As with almost all alpine glaciers, the foot of the Glacier Blanc has retreated significantly, as should be evident from the graph of its length below. In earlier times, most recently in 1866, it formed a single glacial system with its southern neighbour, the moraine-covered Glacier Noir, whose streams joined one another above the Pré de Madame Carle. The Glacier Noir is much different in morphology than the Glacier Blanc and is covered with rockfall and boulders from its lateral moraines.
Glacier Noir  (click on image to enlarge)
During the Small Ice Age the combined ice system reached its maximum extent in 1815 and ended roughly at the height of the Cezanne Hut (1,874 m), near the village of Alfoid. Today looking at the Refuge de Cezanne and the Pre Madame Carle it is difficult to believe that the two glaciers ever extended that far down the valley.

Map of Historic Extent of the Noir and Blanc

Refuge de Cezanne near the historic confluence of the Glaciers Blanc and Noir (click on image to enlarge)
There are many sources for glacial heating and the thermodynamics of glaciers is quite complex requiring the solution of several different complex differential equations.

For more of the solutions to theses equations and modeiling of glacier energy balances see the notes Thermodynamics of Glaciers from the McCarthy Summer School at the University of Alaska. Characterizing the heat sources is further complicated by the difficulties in making field measurements for some areas on mountain glaciers that have complex or irregular geometries.

As of 2010 the tongue of the Glacier Blanc lies at a height of about 2,400 m. In the 20th century it is estimated that it retreated by about 1 km, accompanied by a reduction in area of some 2 km². Between 1989 and 1999 alone the glacier lost about 210 metres; it retreated a further 300 metres in the years to 2006. The ice thickness in the centre reduced during the period from 1981 to 2002 by 13.5 metres, an estimated loss in volume of 70 million m³ of ice.

Seracs on the Glacier Blanc in 2012  (click on image to enlarge)
Crucial to the survival of a glacier is its mass balance, the difference between accumulation and ablation (melting and sublimation). Climate change may cause variations in both temperature and snowfall, causing changes in mass balance. Changes in mass balance control a glacier's long term behavior and is the most sensitive climate indicator on a glacier.From 1980-2008 the mean cumulative mass loss of glaciers reporting mass balance to the World Glacier Monitoring Service is -12 m. This includes 19 consecutive years of negative mass balances.

A glacier with a sustained negative balance is out of equilibrium and will retreat, while one with a sustained positive balance is out of equilibrium and will advance. Glacier retreat results in the loss of the low elevation region of the glacier. Since higher elevations are cooler than lower ones, the disappearance of the lowest portion of the glacier reduces overall ablation, thereby increasing mass balance and potentially reestablishing equilibrium. However, if the mass balance of a significant portion of the accumulation zone of the glacier is negative, it is in disequilibrium with the local climate. Such a glacier will melt away with a continuation of this local climate.The key symptom of a glacier in disequilibrium is thinning along the entire length of the glacier.bare, melting and has thinned.

In the case of positive mass balance, the glacier will continue to advance expanding its low elevation area, resulting in more melting. If this still does not create an equilibrium balance the glacier will continue to advance. If a glacier is near a large body of water, especially an ocean, the glacier may advance until iceberg calving losses bring about equilibrium.
Melt Zone outlet in the summer 2012  (click on image to enlarge)
For the first time since 2001 the mass balance of the Glacier Blanc became positive. It has gained 21 cm (water equivalent) over the last few years. However the snout remains very thin and is vulnerable to another hot summer, such as the kind we are experiencing here in the northeastern United States this year.

The last few year’s positive figures have not really effected the glaciers disappearance, as the snout of the glacier is still retreating. 

For more on the Glacier Blanc see glaciologist Mauri Pelto's excellent analysis on his website From a Glacier's Perspective,

Author taking a rest at the Refuge du Glacier Blanc  (click on image to enlarge)
Many historical sources that could help us in our efforts to understand the melting of the great Alpine Glaciers remain locked up in small and obscure local journals and travelers accounts. Many of these where published in the things like the annual of the Alpine Club of France, or in traveler's account like James Forbes' Journals of Excursions in the High Alps of the Dauphine. Forbes, pictured below, was one of the first scientist/explorers of the Alps to understand the principles of glacier mechanics and it is through his Travels through the Alps of Savoy that we can get a sense of how difficult to do glacier science was in the mid-nineteenth century.

There are many more obscure sources however like the measurements of Prince Roland Bonaparte who cataloged the sizes of many of the glaciers of the Dauphine in the 1880s and 90s.

Bonaparte took many photographs (click on images to enlarge) of his Alpine travels and a comparison of the landscape that he encountered with what is currently ice covered is quite shocking. One of Bonaparte's publications, Le glacier de l'Aletsch focuses on his journey across the glacier in 1888-89.

The Aletsch Glacier or Great Aletsch Glacier is the largest glacier in the Alps. It has a length of about 23 km (14 mi) and covers more than 120 square kilometres (46 sq mi) in the eastern Bernese Alps in the Swiss canton of Valais. The Aletsch Glacier is composed by three smaller glaciers converging at Concordia, where its thickness is estimated to be near 1 km. It then continues towards the Rhone valley before giving birth to the Massa River.

The Aletsch, because of its size is one of fastest shrinking glaciers in the alpine chain as it apparent from the three images below taken in 1979, 1991 and 2002. (click on images to enlarge)

The Aletsch Glacier has been studied for almost 200 years. This data has been compiled by the Swiss Glacier monitoring network and is shown graphically below.

The entire area around the glacier has been declared a UNESCO world heritage site. The United States Geological Survey has begun a Repeated Photographs Study that seeks to show in dramatic form the extent of glacial melting using historic photos. For example in Glacier National Park they have looked closely at the Grinnell Glacier from various vantage points.

Most alpine glaciers are in trouble and some have become dangerous as their melting has caused the formation of large glacial lakes in places where few had been before. About a decade ago a second lake appeared in front of the Arsine glacier just across the Barre des Ecrins from the Glacier Blanc. I visited this series of glaciers several year ago just after the snow melt, crossing the large moraines that are left behind from its larger bygone days.

The author approaching the calving front of the Arsine Glacier (click on image to enlarge)

Arsine Glacier as mapped in 1979 and in 2008 (click on images to enlarge) Note the creation of a second lake due to the melting glacier

To give the viewer an idea of the scale of these glaciers, note the author in the center of the photograph

Glacial melting not only affects the activities of climbers and geographers but also the daily lives of those who live in villages near mountain environments and those make their livings from them. One of the best recent studies glacial melting from this perspective can be found in the book In the Shadow of Melting Glaciers: Climate Change and Andean Society by Mark Carey. Carey's book has been the subject of much discussion and was the subject of an H-Environment Round table Review in 2011.

For more on the melting of glaciers worldwide and their mapping go to the resources available at Glacier Works and at the Extreme Ice Survey .

For more on glaciology and the effect of climate change on glaciers see:

H. Holzhauser, "Glacier Fluctuations in the western Swiss and French Alps in the 16th Century," Climate Change 43 (1999) : 223-37.

H. Holzhauser, "Glacier and glacial-lake variations in west-central Europe over the last 3500 years," The Holocene 15 (2005): 791-803.

Roger Hooke, Principles of Glacier Mechanics (Prentice Hall, 1998)

A. Nesje and S.O. Dahl, Glaciers and Environmental Change (London: Arnold, 2000)

Ben Orlove, Ellen Wiegandt and Brian Luckmann, Darkening Peaks: Glacier Retreat, Science and Society, (University of California Press, 2008)

W.S.B. Patterson, The Physics of Glaciers (Butterworth-Heinemann, 2001)

Daniel Steiner, "Two Alpine Glaciers over the Past Two Centuries: a scientific view based on pictorial sources," in Darkening Peaks (2008): 83-99

Friday, November 01, 2013

New Three-Dimensional Models of the Melting of the 
Mer De Glace, Chamonix, France

Le Centre de Researches sur les Ecosystemes d' Altitude has published a times series of three-dimensional views of the Mer de Glace....and a new glacier coverage map...dramatic....






Friday, August 23, 2013

Through Pollock's Eyes:

Reflections on the Fractal Nature of Geographic Curves, Abstract Cartographic Spaces and the Last Pool of Darkness

The idea that one gets a better and better approximation of the length of a shoreline by measuring it in finer and finer detail is false; the series of approximations does not converge to an answer, it just gets bigger and bigger, to infinity.... ....................................................................---Tim Robinson, The Connemara Fractal

Many of my best mathematical reflections seem to come to me while wandering around in museums, especially the Museum of Modern Art in New York City. The abstraction of shapes and colors found in the paintings of many of the 20th century's greatest masters, all of which line the walls there, remind me of spatial and geographical forms that have been bled of reference, seemingly residual landscapes and spaces devoid of human action; the proverbial blank on the map or a vast bringing together of spatial silences. Recently, while standing in front of one of Jackson Pollock's great drip paintings, the connection that I have often felt between mathematical and geographic spaces and the planar surfaces created by the abstract expressionists suddenly crystallized in my mind as geometry. Fractal Geometry. I am of course not the first to think of this connection. J.R. Mureika for example, studied perceptual color space, and related it to the fractal forms of Pollack's paintings ("Fractal dimensions in perceptual color space: A comparison study using Jackson Pollack's art," Chaos 15 (2005))
Both geographic spaces and most of Pollack's drip paintings are fractal in nature. In contrast to lines on a map, which are one-dimensional, and are pure generalizations of reality, fractals consist of patterns that recur on finer and finer scales. Because of this 'scaling', fractals can build up natural shapes of immense complexity like coastlines, boundaries and even full landscapes. The Pollock drip paintings are similar and when looked at in finer and finer scales, such as those shown in the detail images below, are much more like geographical curves than cartographic maps actually are. His paintings, strangely enough, unlike maps, can be seen as scaled portions of the whole at larger and larger scales. Several scholars have looked at the fractal dimension of Pollock's paintings using one of the easiest, at least from a mathematical perspective, methods to determine dimension. A method known as box-counting. Mathematically, box-counting is relatively easy to calculate, and to program and its origins go back to at least the 1930s when it was known as Kolmogorov entropy after its Russian inventor. The dimensions calculated for Pollack's paintings show them to be somewhere in the range of 1.3 to 1.7, and unlike those of typical cartographic expressions, are actually closer to that of real world geographic curves.

Real geographical curves are so complex in detail that their lengths are often infinite, or to put it in a more accurate sense, indefinable. Many of these curves, such as those representing a coastline, are statistically 'self-similar', which means that each portion can be considered as a reduced-scale model of the whole, much like we see in a Pollock drip painting. [1] . This peculiar feature of self-similarity, which is an artifact of scaling (something Galileo would have loved), can be described mathematically as a type of dimension, which unlike normal curves, is fractional.
This fractional dimensional property of coastlines was first posited in a formal way by Benoit Mandelbrot in his classic article in Science from 1967, entitled, "How Long is the Coast of Britain ? Statistical Self-Similarity and Fractional Dimension."

Self Similarity of the von Koch Curve. It looks the same no matter what scale we look at it in.

In that article [2] Mandelbrot studied the form of geographic curves, and simpler examples like the von Koch curve shown above, for which the concept of 'length' has no apparent meaning. The von Koch curve is built up by an algorithmic procedure that at every stage in the operation the middle third of each interval or line segment is replaced by the other two sides of an equilateral triangle. These types of curves, to use Mandelbrot's language, can be considered as "superpositions of features of widely scattered characteristic sizes." As he puts it, "as even finer and finer features are taken into account, the total measured length increases, and there is usually no clear cut gap or crossover, between the realm of geography and details with which geography need not be concerned". [3]

Mandelbrot set of a quadratic function in the complex plane. Self-Similarity at every scale

One of the best reflections on this problem of crossover and scaling in cartographic thought comes from the writer and mapmaker Tim Robinson's essay, 'The Connemara Fractal' published in his Setting Foot on the Shores of Connemara and other essays. Robinson, who is one of the great writers on cartography and what for him is the solitary process of map making, writes in that he is "not very interested in maps from a technical point of he will move on to the more interesting questions of what it is like to make a map...insofar as I can untangle my memories of the process." The process of map making that Robinson is speaking is "a long walk," and "an intricate, knotted itinerary that visits every place within its territory." The idea of a long and very detailed walk that Robinson invokes was suggested to him by the extraordinary form of the southern coast of Connemara. Robinson tells us that, "it looks so complicated as to be unmappable; it is a challenge to be unraveled." ...a very Mandelbrotian series of images indeed.

Robinson crosses over to details that according to Mandelbrot "geography need not be concerned", when he starts looking at actual distances along the twisting and knotted coast of Connemara. What he finds are not mappable distances, but rather impossibly infinite curves. Robinson writes that the "distance from Ros a' Mhil to Roundstone is only about 20 miles, but the coastline in between is at least 250 miles long, even as estimated on a small-scale map." He continues, "when I wrote that I was ignorant of the work of Benoit Mandelbrot, who had proved that an outline as complex as a coastline does not have a definable length." Robinson first learned of Mandelbrot's work through a newspaper article sent to him by a reader of his essays on Connemara and he calls Mandelbrot's work "a disturbing doctrine---disturbing to one who fondly imagined he had walked a coastline with due attention to its quiddity....for [Mandelbrots paper] was an annihilating critique of my essay's imagery."

In most respects Mandelbrot's paper was not really a critique of Robinson's essay, but rather a profound theoretical statement that opens up a clearing for us to conceive of a very different, and inherently less positivist conceptual foundation for the cartographic spaces we create. For as Robinson says, the process of map making, like that of discourse must stop somewhere. To be true of the world of fractals is to be infinitely and indefinitely seeking a precise measurement of length or to possess the unexplainable talent of a Jackson Pollock. But to find our way in the real and empirical world it appears that you and I will have to be satisfied with our approximations and our finitude.

[1] For more on Pollack's paintings as fractals see, "The Visual Complexity of Pollack's Dripped Fractals by R.P. Taylor, at

[2] Benoit Mandelbrot, "How long is the coast of Britain? Science 156 (1967) 636-638.

[3] For more on the concept of fractal dimension and measurement see M.C. Shellberg and Harold Moellering's classic paper, "Measuring the Fractal Dimension of Empirical Cartographic Curves."

Tim Robinson is one of the most interesting cartographer's working today. His books on the Aran Islands and Connemara are must reading for anyone interested in the practice of cartography and its relationship to landscape. His short essay called, Interim Reports From Folding Landscapes, imagines the process of cartography in a way that few, if any, other cartographers have ever been able to describe in detail.

Robinson writes that, "A map is a sustained attempt upon an unattainable goal, the complete comprehension by an individual of a tract of space that will be individualized into a place by that attempt."

In Connemara, the last pool of darkness, Robinson reflects on the time Ludwig Wittgenstein spent in the remote parts of Ireland writing and thinking. Wittgenstein, as is well known loved these remote and barren places. These rocky shores seem to have enabled him, in a way not possible in places like Cambridge, to reflect on mathematics, logic and his sins. Landscapes like those of Iceland, western Ireland and the fjords of Norway were the places he worked best and so it seems with Robinson who like Wittgenstein (or not so like him) was a Cambridge trained mathematician.