Wednesday, November 20, 2013

Predicting Madison Lake Ice 2013

I made a model to predict when the lakes in Madison, WI would freeze this year. This could be an interesting calculation, particularly if you like ice fishing or ice skating:)

Given current temperatures and weather forecasts I predict Lake Wingra to freeze sometime next week, between Saturday, November 23rd and Thanksgiving (Nov 28th). My range of uncertainty is much greater for Monona (Dec 8- Dec 25th) and for lake Mendota (Dec 15-Jan 11th). My best guess for the three lakes are 11/24, 12/13, and 12/23 respectively.

You can see surface temps of lakes here:

I built the model quickly so my level of confidence is therefore low but it I am pretty confident we can be out fishing about 20 days sooner than last year - freeze dates last year were 12/21, 12/31. and 1/14. I think this years dates will be closer to long term averages.

Figure 1: Red Line - surface water temp, 2013, Blue Line - surface water temp, 2012. Approximations done with calculations based on air temps, not observations.

Lakes act as a thermal mass, and the larger (primarily deeper) the lake the more cold it will require to freeze. Actually it is probably more accurate to think of the lake as heating the air, then the air cooling the lake - but I guess that's more of a philosophical point. In one extreme, a body of water will freeze almost immediately (think of a puddle or a film of water on a cold surface) so a few hours with air temperatures marginally below freezing will suffice. On the other extreme, a large enough body of water in a region where the average annual temperature is above zero would never freeze. Lake Michigan and Lake Superior are examples although even these large bodies of water will freeze on cold years.

The freezing process can be thought of in three phases - the whole lake cooling to 39 degrees, the surface cooling to 32 degrees, and the surface fusion. Cooling only takes about 1.2 % of the energy of fusion (1:80) but the cooling process down to 39 degrees cools the entire lake while the fusion process just freezes the surface. This is because water is most dense at around 39 degrees and so water from the surface of the lake will displace deeper water until the whole lake is at 39 degrees. Thereafter, it is a quick trip down to 32 degrees, and then takes a relatively long time to freeze (fusion).

For deep lakes therefore, the warmth of the summer is an important consideration since it will take longer to get down to 39 degrees. The three Madison lakes are relatively shallow (9 feet, 27 feet, and 41 feet) so the consideration is not great.