More on Ice Growth
Mårten Agne sent the following summary of ice growth that gives insight on the relative contributions to thin ice growth. In particular, he stresses the importance on radiational cooling on long, clear, still winter nights
Ice-growth remark (September 24, 2014):
Here autumn struck this very Sunday, with unsettled weather arriving from north, already producing reports of local night frost and snow. There still will be another month before any decent skating opportunities can arise. This once again raise the question of ice-growth.
Looking at your web site,(http://lakeice.squarespace.com/ice-growth/) I find you referencing an Ashton paper. At the time of writing my little piece of ice-physics, I wasn't aware of that paper. I agree on the formula. But it can be further refined.
In my opinion, it is an astonishing fact that the heat transfer coefficient (denoted by H(ia) by Ashton, me using k(ia), subindex "ia" obviously for ice-to-air ) can be shown to be directly related to the Stephan Boltzmann law, or rather its first derivative with respect to temperature.
This is sufficient in wind-less conditions, being 4,6 Watts per square metre and degree Celsius, at zero degree air temperature. With wind the effect of turbulent heat-flux adds on, adding another ~2 W/m2 C for every m/s wind speed.
The theoretical background is an exercise in calculus, which I try to outline in "Surface heat transfer" pp 58-77. The key (and most beautiful part) is the Taylor series expansion on p 66.
Further, for an accurate estimate, the driving air-temperature needs to be adjusted for heat transfers that are independent of the ice surface temperature. This is mainly radiation, which in my opinion, is the main driver of thin ice-growth. This mathematical maneuver will allow for ice-growth also in super-zero temperatures, so often encountered in reality. Almost one extra mm per hour can be gained in clear-skies compared to cloudy for the same air temperature.
It would be interesting to calibrate formulas with empirical measurements, but to do that also cloudiness, wind-speed and humidity need to be captured.
(end of Mårten's ice growth remark).
Note from Bob:
If you have read this far you really should have Mårten's book: Ice physics for recreational ice-users (page down a couple of entries in the blog) . It goes into considerable detail on heat flow in ice and the role of long wave radiation (infrared), short wave radiation (sunlight), air temperature and wind. I am planning to get a few copies this winter. Email me if you would like to buy one.
11/15/2014 9:30 AM