How Ice Melts

There is always lots of excitement at this time of year as people anticipate their first trip out to the islands. To finally get out to the cottage is something we all look forward to, and the ice can seem to take an eternity to melt. Everybody wants to know how thick the ice is and how soon will it melt.
However, how much do most people really understand the physics behind the melting of ice? This page is intended to supply food for thought on how that might happen this year.

For those of you who don't already know, heat is transferred in only three ways.

1. Conduction. The way heat transfers along a metal spoon in a bowl of soup that is on the stove top.
2. Radiation. Examples are a warm fire, a bright sun, or a home radiant heater.
3. Convection. Warm air blowing out of a heating register.

Each of these methods contributes in varying degrees to the melting of ice.

Conduction. This is the least effective method of melting ice. The water temperature at the boundary between ice and air at the surface and ice and water below the surface is always zero degrees. Because of this, warm air and water are not actually in contact with the ice; air and water are only in contact with a boundary layer of zero degree ice/water. Furthermore, air is a terrible conductor of heat. Of course, if the air or water is moving, such as in a channel, then this boundary layer effect would not hold. But that is heat transfer by convection, not conduction.

Radiation. It's a nice sunny mid-March day. That's got to help melt the ice, right? Only sort of. Yes, the radiation is adding energy to the ice. However, part of the energy is transferred right through to the water. Furthermore, heat radiation has little effect on ice thickness. Rather, this form of heat transfer has a greater effect on ice density. It turns solid ice into what is commonly known as rotten ice. Rotten ice is easily broken up by high winds or even a boat, sometimes as small as a kayak.

Convection. This by far is the form of thermal transfer that has the greatest effect on ice thickness. As warm air blows over the surface of the ice, or as water, which is warm compared to ice, flows underneath, it constantly renews the heat source at the boundary layer.
The US Army Corps of Engineers has published a report with some mathematics that are beyond the scope of this web page, but it concludes that ice thickness will be reduced by about 3.7mm per warming (Celsius) degree day. Warming degrees are the number of degrees above zero that a temperature is. For example, 5 degrees C is 5 warming degrees. Therefore, a temperature of 1 degree C for a sustained 24 hour period would melt the ice by 3.7 mm. However, remember that this form of heat transfer is convective. That is, a moderate wind is required for this formula to work. Also, the temperature is unlikely to be same all day. To determine the warming degree days one must integrate the degrees above zero over the whole day.

It doesn't matter if it's day or night. Daylight drives heat transfer radiation and I've already said that radiation does not affect thickness. Also, the ice won't melt from underneath, except where there are water currents. This is why streams and rivers melt earlier in the season.

Unfortunately, the temperature may not be above freezing all day long. The same study by USACE does not contemplate how quickly the ice thickness will increase when the temperatures are sub-zero.

Also, contrary to what many may believe, rain fall has very little effect. The rain at this time of year is far too cold to add any significant amount of heat to the ice.

Now let's make a lot of bold assumptions!
On March 27, 2022, the ice thickness 1.5 km out from Snug Harbour was 45 cm. (Yes, that is a lot of ice for this time of year.)
Following the USACE calculation, and assuming a 5 degree C average daily temperature which never goes below zero, and moderate winds, the ice will melt at a rate of 18.5mm per day. At a thickness of 45 cm, it will take 24 days from March 27 for the ice to melt. If all of these assumptions are correct, and there is no reason to believe that they are, the ice should be melted by April 20. However, remember that there is a current in the South Channel and that aids in melting. That is, when the measurement was taken outside of Sung Harbour, it was likely thicker that the ice in Sans Souci.
If the winds are light, the melt will take longer. If the days are warmer, it will take a shorter time. Unfortunately, if the days are colder, it will take longer. However, it is not unlikely that the Sans Souci waters will navigable by Easter Sunday (April 17th).
Let's all hope for moderately warm, windy days! And forget the sun- let's save that for the summer.