By Graham Cogley
When the weather is warm enough, meltwater is produced at the surface of the glacier. Some runs off directly. Some finds its way into the glacier interior and, although much of this englacial meltwater flows out again, some of it is left over at the end of summer.
The Phillips paper focusses on the thermodynamics of the leftover englacial meltwater. If the ice is at the melting point, or is temperate in glaciological jargon, it can’t get any hotter without melting. But what if the ice is cold, which in the glaciological jargon means “below its melting point”? The meltwater can be no colder than the melting point, so we have a difference of temperature and therefore a flow of heat from the water to the cold ice.
If, or rather once, the meltwater is at the melting point, it freezes as the winter advances. The freezing releases about 335,000 Joules of heat for each kilogram of water that turns to ice, roughly equivalent to one 60-watt light bulb burning for an hour and a half (but of course we are talking about lots and lots of kilograms, not just one). This latent heat of fusion adds to the thermal contrast between the cold ice and the gradually freezing meltwater.
Phillips and his co-authors show that, far from being just an interesting curiosity, the whole phenomenon of cryohydrologic warming, heat transfer from meltwater to cold ice, might be highly significant.
Internal accumulation, by refreezing of meltwater, implies warming of the glacier interior. It explains why, in glaciers that are mostly cold, the ice at high altitude in the accumulation zone is usually warmer than the ice at lower altitude in the ablation zone. But Phillips and his co-authors are more interested in cryohydrologic warming of the ablation zone. In particular, they point out that when the equilibrium line rises in a warmer climate, the part of the glacier that was formerly above the equilibrium line switches from net gain of mass (more snowfall than melting) to net loss (more melting than snowfall). The warming climate produces more meltwater, and any of the meltwater that fails to get out of the glacier drainage system will add fast cryohydrologic warming to the slow climatic warming.
It is a matter of simple physics to work out what “slow” and “fast” mean. The warming proceeds by conduction, so divide the heat content per unit volume by the thermal conductivity, both of which can be looked up in a book. The resulting number is about 212,000 seconds per square metre. Then imagine that the ice is divided into a grid of square columns, every one of which has a meltwater conduit in the middle. Now multiply 212,000 by the cross-sectional area of each column. If the conduits are 20 m apart, the cross-sectional area is 400 square metres and the cryohydrologic warming happens on a time scale of 2.7 years. (There are 31,536,000 seconds in a year.)
The same kind of back-of-the-envelope calculation works for the slow climatic warming, but now all of the heat has to be conducted downwards from the surface. An appropriate number to substitute for the conduit spacing is the ice thickness, say 100 to 1000 m. The resulting time scale for the climatic warming is about 70 to 7,000 years.
Bringing cold ice to its melting point in a few years, instead of a few centuries, implies that the ice suddenly becomes able to move a lot faster. Temperate ice is ten times less viscous (less stiff; runnier) than ice at —10°C.
Cryohydrologic warming has further implications for the response of cold glaciers to climatic change, but for the present there are loads of questions to be answered, starting with geometrical ones. What about the varying size and spacing of the meltwater conduits? Is 20 m a good representative number for the spacing? How thoroughly does the system of conduits permeate the bulk of the cold ice? What if no englacial meltwater remains at the end of summer? What if there is some, but not all of it freezes in the winter? Does the ice really speed up as expected, and if so does that mean more cracks for the meltwater to penetrate, and thus still faster cryohydrologic warming?
All this reminds me of the undergraduate essay I had to write on the subject ‘Clever ideas, whether right or wrong, stimulate research.’ Discuss.