# Sea level rise due to floating ice?

It is widely believed that melting of floating sea ice does not contribute to sea level rise. Is this really true?

Let us think of a simple experiment we are all familiar with: imagine an ice cube floating in a glass of water. What happens to the water level in the glass when the ice cube melts? Right, nothing happens. The ice cube displaces its own weight in the underlying water and the water level remains constant when the ice melts, because the melting process replaces the water which has already been displaced by the ice. This effect is known as Archimedes’ principle.

Now let us consider a slightly different experiment. It’s again water with some ice in it, but now the water is salty (like the real ocean). The blue color has no effect on the experiment, but it shows the ice cube in the water more clearly.

It took quite a time to melt all ice but finally it was done and the result is clear: The water level is higher!

According to Noerdlinger and Brower (2007) it doesn’t because the principle refers to weight and not volume.  The salt in sea water raises its density from about 1000 kg/m3 for salt free water to 1026 kg/m3 for normal sea water. The ice however is nearly salt free because of a process called “brine rejection” (the salt from sea water doesn’t enter the crystal structure of ice).

When the ice melts then this is a kind of freshening of the ocean and the overall salinity is lowered. The lower salinity, the lower density  and the larger volume.

The melting of sea ice therefore doesn’t increase the mass but it increases the volume and therefore causes the water level to rise. After Noerdlinger’s and Brower’s calculations the volume of the meltwater is about 2.6% larger than the displaced sea water.

But what is the actual relevance of this effect? Does is contribute significantly to sea level rise? Before answering this questions we should deal with an objection raised by Jenkins and Holland (2007). They are arguing that a huge amount of energy is required to melt the ice. They find that the energy comes from the ocean, as the albedo (reflectivity) of ice is very high, it doesn’t absorb much solar energy. Hence the ocean will cool a bit, causing the density of the briny water to increase (It should be noted that fresh water exhibits the peculiar behavior that its density increases as the temperature falls almost all the way to freezing; but just before freezing, the density is reduced. Briny water does not exhibit that reversal). The cooling  therefore offsets the density decrease at least partially in the words of Jenkins and Holland.

As they put it, Noerdlinger’s and Bower’s result is a good first approximation in cold waters where most floating ice is found. The density of cold water is mainly determined by its salinity while for warmer water temperature is also an important factor. Therefore in warmer water the cooling effect matters.

Back to the question, if this effect contributes to sea level rise in a relevant way. Shepherd et al 2010 examine this. They combine satellite observations for an assessment of the loss of floating ice. According to this 743 km3/yr floating ice was lost in average between 1994 and 2004. They further conclude that 1.6% of current sea level rise (about 3.1 mm per year) is caused by loss of sea ice. This is not very much compared to other sources. However the authors assert that this effect should be considered for future assessments of global sea level rise.

Posted by MartinS on Wednesday, 28 September, 2011