A Primer On Floating Ice And Supraglacial Lakes
By Enrico Uva | May 17th 2012 02:00 AM | 5 comments | Print | E-mail | Track Comments

I majored in chemistry, worked briefly in the food industry and at Fisheries and Oceans. I then obtained a degree in education. Since then I have...

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If enough ice from land slides into the sea, the sea level can measurably increase, in the same way that the water in a glass will rise if an ice cube is dropped into it. Because water's molecules are more closely packed in the liquid state than they are in the solid state, they can support ice's open, hexagonal and  less dense structure. When ice is floating, water's buoyant force has the same magnitude as the ice's weight. And the buoyant force is simply equal to the weight of water displaced by floating ice.

For both of these forces in equilibrium, weight is the product of mass and gravitational acceleration, g,  Since g cancels out the mass of the floating ice is equal to the mass of displaced water.  If we express mass as the product of density and volume, our previous statement becomes equivalent to the expression:
diVi = dwVw
where di and dw are the respective densities of ice and water; Vi = volume of ice; Vw is the volume of displaced water and also the volume of ice below water's surface. The formula can reveal more than the fact that most of floating ice is submerged( Vw/Vi = di/dw).  If it was possible for the entire 2 850 000 km3 Greenland ice sheet to end up in the ocean, by how much would the sea level rise? (This calculation will ignore, among other things, the rebounding effects of the asthenosphere and lithosphere after the pressure of this incredible weight is relieved, and thermal expansion of a sea in a climate mild enough to melt all of Greenland).

hA= Vw = diVi/dw
where h = rise in sea level and A = surface area of the world's oceans.

h (361 419 000 km2) = 0.91 g/cm3(2 859 000 km3)/(1.027g/cm3)
h = 0.007 km or 7 m. This very rough calculation is not far from the 7.2 m equivalent given by the
Intergovernmental Panel on Climate Change.

Of course, once floating ice melts, there is no subsequent rise in water level because melted ice will turn into a smaller volume of water. The latter is exactly equal to the volume of submerged ice. Conceptually this follows from the fact that mass is conserved during melting. One can use the same derivation as above and simply replace the volume of displaced water with that of the water left behind by the melted ice. Since they both equal to diVi /dw the  two volumes  have to be equal. Of course, it can also be demonstrated concretely by marking off a glass' water level while ice floats in it. After the ice has melted, the water level remains the same. For this reason, if existing sea ice in the Arctic or off the coast of Antarctica melts, it will have virtually no impact on sea level.

As the name suggests, supraglacial lakes are  transient bodies of water on top of a glacier. At times deep blue in color, they break up the monotony of Greenland's white snowscape.  As the volume of the lakes increases during the summer, the resulting pressure on the ice underneath can cause them to drain quickly. (In the case of Lake Pointing, the three million cubic meter lake drained within a few hours, which is 50 to 70% of the volume of water flowing over Niagara Falls in that time frame, depending on what the authors mean by a few hours). Then the injected meltwater creeps into the subglacial drainage system and causes changes in the glacier's basal drag and sliding speed.

A recent 10-year investigation by Liang and Colgan found that during more intense melt years, the lakes don't necessarily get bigger, but they drain more frequently and earlier in the summer. When that happens close to the edge of the island, more ice ends up in the sea. In milder years, the lakes also appear at higher elevations, leading to more drainage in inland areas, but the authors could not conclude that this made the inland parts of the ice sheet more sensitive to sliding.

Sources:

Liang and Colgan. A decadal investigation of supraglacial lakes in West Greenland using a fully automatic detection and tracking algorithm
Tedesco. Willis. Measurements of supraglacial lake drainage and surface streams over West Greenland and effects on ice dynamics