Temperature Index Modelling in Mountainous Terrain – Reducing Complexity at What Cost?

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Wapta Icefield (and Peyto Glacier) from nearby Cirque Peak

Peyto Glacier is located about 30km north of Lake Louise in the Canadian Rockies. It’s pretty famous in scientific circles as far as glaciers go. Not only does it offer fantastic ski touring, it was also the first (and one of only a few) glaciers to be consistently monitored since the late 60s. Since the International Hydrological Decade, all kinds of studies have taken place on the glacier, most notably bi-annual/annual trips to monitor glacier mass balance.

The first studies done with the first decade of Peyto Glacier results involved relating it to air temperatures and precipitation from a weather station in Lake Louise. Initial results were promising, showing fairly strong statistical relationships between temperature and glacier health. Naturally, the next step was to install a weather station right at the glacier, because if air temperature really explains glacier melt, we should expect the weather station at Peyto to predict changes better than one 30km away in a valley at Lake Louise. Monitoring continued, and in 1988, Anne Letréguilly published some surprising results. As expected, the weather station at the glacier produced statistically significant relationships with glacier changes, but what was unexpected was that Peyto Glacier’s mass balance was better predicted by weather stations in Lake Louise and Jasper, much further from the glacier.

The reason for this surprise lies in the fact that a statistical relationship between temperature and melt doesn’t explain the physical processes that are melting the glacier. If you’ve ever stood outside on a sunny day, you feel all the heat you can get from sunlight, even when the air temperature isn’t all that warm. Air temperature is certainly a measurable part of glacier melt, but in many cases, sunlight is the primary supplier of melt energy.

With Letréguilly’s study in mind, folks went back out to the glacier and measured all the things we would need to predict glacier mass balance using an energy balance. Armed with hourly measurements of air temperature, wind speeds, net radiation, humidity, among other things, studies set out to compute the mass balance. But here’s where it gets interesting – for the most part, these studies weren’t measurably better than using Lake Louise air temperatures, precipitation, and calling it a day.

This anecdote is fundamental to a lot of the problems faced in Geography/Earth Sciences (and other disciplines, I’m sure…). Every time we add more sophistication to our models of the natural world, we end up having to deal with more and more natural complexity. Although the energy balance properly accounts for energy transfers at a point on the glacier, we have to make assumptions about the uniformity of the landscape and the representativeness of that point. Is this spot as reflective as 100m over? Does that area get more shading?  Is the snow deeper over there? We can’t know it all.

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Inconsistent shading, confined walls, unequal winds, and much more makes trying to fully account for where and how much energy is being transferred next to impossible.

So where does this leave us? I don’t mean for this to turn into an Anti-Energy Balance rant, in fact, quite the opposite. Quantifying energy exchanges is an incredibly important tool, and in reality, actually helps reinforce our usage of Temperature Index Modelling.  But it comes down to purpose. Most of the time, we are interested in glacier mass balance because we want to know something about stream flow, or want to relate it to climatic shifts. If that’s the case, we don’t need to quantify every nook and cranny; we just need the big picture. Temperature Index Modelling gives us that.

There’s a bunch of ways that Temperature Index Modelling can work, but the most straightforward is Degree Day factors. Essentially, melt is the sum of positive air temperatures over a time period, multiplied by a ‘degree day factor’. This ‘degree day factor’ is statistically derived for each glacier, and differs for ice and snow, meaning you calculate how long until the snow is gone, and then after that for how much ice you can melt.

Energy balance studies have helped our understanding, and to a certain extent, validated the use of Temperature Index Modelling.  Energy balance studies have shown that while sunlight is the main energy input, it’s highly correlated with air temperatures (hot days are usually sunny!). Air temperature, it turns out, is well correlated with most of the energy inputs on the glacier, meaning that air temperature can explain a lot more melt than originally thought. Simplifying the procedure means we can eliminate a lot of complexity, and still get reasonable results. This is good news because it means fewer inputs are required and costly weather stations and weather station maintenance is limited, since valley stations work about as well. Unfortunately, it probably means fewer trips in to Peyto glacier.

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There are probably worse places to work…

Further Reading:

Regine Hock wrote a very helpful paper on Temperature Index Modelling that I highly recommend if you can get through the paywall:

Hock, Regine. “Temperature index melt modelling in mountain areas.” Journal of Hydrology 282.1 (2003): 104-115. (link)

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