Ice Growth:  Thin to Thick

Summary:

Once the first layer of ice catches on a lake it grows thicker at rate that is dependent, most obviously, on air temperature. Freezing degree days (FDD) are the average number of degrees below freezing over 24 hours. For example is the average temperature over a day is 17 degrees that day had fifteen FDDs.  An ice sheet will, in theory, grow at a rate of roughly one inch per fifteen FDDs starting from ice between 1/2" and3" thick (as the ice gets thicker the growth rate decreases).  This is based on there being a bit of wind, a reasonably clear sky and no snow/frost on the ice.  If there is no wind or there are cloudy skys,  the ice will grow about half as fast. 

For example, starting from 2" ice, if the maximum temperature yesterday was 22 degrees and the minimum overnight was 12 degrees the average is 17 deg giving 15 FDDs for the 24 hour period (assuming a typical, clear sky, day-night temperature profofile).  The ice should be about an inch thicker than yesterday.  As explained below there are a number of reasons why 'your results might vary'.  Even a  thin layer of snow or frost will dramitically slow the growth rate.  As always, check the ice itself to see what the ground truth is.

 

27 mm(1.06") ice: Not quite enough to stay on top. It needs another mm to barely support 175 lb. To have a reasonable safety factor it needs another 20 or 30 freezing-degree-days to make it thick enough.

Details:

For an ice sheet to grow thicker it has to dissipate 80 calories per gram of water that turns to ice. The heat has to get out of the ice sheet either by conduction into overlying air or by radiational cooling from the ice surface.  In general, when the ice is thinner than 3" the cooling rate is limited by the ability of the air over the ice to transmit heat.  This is particularly true at temperatures closer to freezing.  As it gets thicker than three inches the conductivity of the thicker ice becomes the biggest factor. 

The following graphs are based on a formula proposed George Ashton in 1989.  It covers both thin and thick ice.  The 100+ year old Stephan solution works well with an adjustment coefficient of 0.5 to 0.8 for thicker ice or very cold conditions but dramatically overestimates the growth rate of thin ice and less severe temperatures. The Stephan solution does not factor in the heat transfer capacity of the air over the ice sheet but the Ashton formula does.  Neither directly factors in radiational cooling, solar heating, wind, snowcover and other factors that can affect ice growth rates however by using adjustment coefficients they approximate the effect of some of these factors.  The following charts show calculated growth rates for different periods of time.  This can be handy for making a rough guess of growth over time at a constant temperature.  As always, actual measurements of thickness trump estimated numbers.

 

Reality is more complicated.  The temperature is rarely constant for more than a few hours.  Radiational cooling on a clear night with low humidity can be the major part of the cooling effect (thin ice grows at above freezing temperatures in this situation).  Sun angle is a big factor as is the presence or lack of sun, especially later in the season.  Cold wind increases heat removal from the top of the ice.   Snow is a very effective insulator and it dramatically slows growth.   Slush on the surface or as a layer within the ice sheet (layered ice) stops growth on the bottom of the ice sheet until the slush is fully frozen. 

These graphs are of most practical use to determine how much an ice sheet is likely to grow in a day or two of fairly constant temperatures.  For example if you have bare ice that 2" thick and it is going to average 10 degrees for the next two full days, the ice will probably grow to about 5" in that time.  As with everything else about ice, make sure you measure what the ground truth is (and don't use your truck as your testing tool).  There are lots of reasons it could have grown less than expected and not many that it might have allowed it to grow more.  

Related to this, the temperature data for several of the 2013 season fatalities shows they were preceded by several days of temperatures that held near freezing. Many important details about the incidents are not known but it does appear likely that ice in these circumstances may slowly thaw.  

The following graph from Ashton's paper Thin Ice Growth shows reality against the calculated estimate. The upper three lines are the Stephan Solution with adjustment factors of 0.5, 0.7 and 1.0.  The lower three lines are for the Ashton approach with the lines representing different values of the bulk heat transfer coefficient from ice top surface to air well above the ice (Hia).    I used a value of Hia of 20 in making the graphs shown above as that best represents the empirical data. This is based on conditons similar to the St Lawernce River.  If the area you are interested in is less windy, expect slower ice growth. (December-January winds average about 9 mph with average gusts at 22).  

 

Most of the data falls within a factor of 2 the predicted value at Hia=20.  The extreme cases at low thicknesses  (1/4" thick, red arrow) that freeze faster than the average by nearly 10 times.  This may well be a situation where the temperature is slightly below freezing and radiaitonal cooling is the main cooling mechanism. The blue arrows point to growth rates that are slower than typical.  Sunny weather and/or calm winds are possible contributors to this. 

 Click here to see George Ashton's paper: Thin Ice Growth.  It was published in WATER RESOURCES RESEARCH,VOL. 25, No 3, Pages 564-566, March 1989.

For a look at Jan-Erik Gustafsson's forecast method skating ice,  see the January 24, 2012 Blog entry or go directly to his North American Forecast Site.

Click here for more info on bearing strength. 

 Note:  This page was rewritten in May of 2012 and edited last on 9/12/2013

 Bob

PS 12/16/2013: A popular ice growth chart found on FishingVermont.net is within rounding error of the Ashton numbers for everything except temperatures below 10 degrees combined with starting from thin ice where it predicts somewhat higher one day growth than the Ashton formula.