# Thermodynamics: Growth

When cold air cools the ocean surface to the freezing point, ice begins to form. As the ocean temperature nears the freezing point, the water density increases and the water sinks. Warmer water that replaces it must also be cooled, so more than just the ocean surface needs to reach the freezing point. Once ice begins to grow, it acts as an insulator between the ocean and atmosphere. Heat from the ocean must be conducted, or pass through, the sea ice before being emitted to the atmosphere. Ice growth slows as the ice thickens because it takes longer for the water below the ice to reach the freezing point.

The relationship between thermodynamics and sea ice thickness can be thought of most simply in terms of freezing degree days (FDD), which is essentially a measure of how cold it has been for how long. The cumulative FDD is simply daily degrees below freezing summed over the total number of days the temperature was below freezing.

The freezing temperature of ocean (saline) water is typically -1.8 degrees Celsius (28.7 degrees Fahrenheit). If the average daily temperature was -5.8 degrees Celsius (21.6 degrees Fahrenheit), this would be -4 degrees Celsius (24.8 degrees Fahrenheit) for one day, as the following equation shows:

`(-1.8) - (-5.8) = 4 degrees below freezing`

`4 degrees below freezing, Day 1 = 4 cumulative FDD`
`7 degrees below freezing, Day 2 = 11 cumulative FDD`
`2 degrees above freezing, Day 3 = 9 cumulative FDD`

Scientists have developed different formulas to estimate ice thickness from thermodynamic growth, using the FDD. One such formula (from Lebedev 1938) is:

`Thickness (cm) = 1.33 * FDD (°C)0.58`

The ice thickness increases at a rate roughly proportional to the square root of the cumulative FDD. Formulas such as this are empirical, meaning they are calculated only with observed data, so they really are simplifications of the ice growth processes. The formulas assume that the ice growth occurs in calm water and is reasonably consistent, and they do not take into account sea ice motion, snow cover, and other surface conditions.

Snow cover is one factor that dramatically alters the actual sea ice thickness calculated from the above formula. Snow is an effective insulator, slowing the transfer of heat from the ocean, through the ice, and to the atmosphere. Snow essentially slows the growth of ice.

Last updated: 3 April 2020