Previously, 9 years ago, I produced two posts on Open Water Formation Efficiency, here and here. Now, as a bed rock to a series of posts I am going to revisit that issue. First, in this post, I outline a theoretical model to demonstrate the process involved.
Take a situation in which you have a grid box of sea ice, the sea ice is all one thickness in April, and the loss of thickness from April to September (the melt season) is always 2m. So if the ice is 1m thick then the grid box will be ice free by September, whereas if the grid box is 3m thick then the loss of 2m thickness in the melt season will always leave 1 meter of ice by September and the grid box will not be ice free.
So we can say that in this spherical cow situation the open water formation is 100% for April thickness of <2m and 0% for >2m thick.
However in reality the situation is that the ice will not all be one thickness. So let's presume a distribution of thicknesses. The Normal Distribution is an outcome of the Central Limit Theorem and emerges as a result of the combined probability distributions of contributory factors, which results in a 'bell curve' of probability distribution. Using the Normal Distribution is also backed up by PIOMAS data for thermodynamically grown ice, but I don't want to digress into that right now.
So a normal distribution is defined by an average and a standard deviation, the average is the peak of the distribution, the standard deviation governs the width of the distribution. In the graph below I show three thicknesses of ice, with different average thickness.