Wednesday, February 17, 2010

Sea Level Rise - Part 2

Ice Melt

In the previous post on Sea Level Rise, I argued there is a clear association between the Red Sea sea level reconstruction from Siddall et al. (2003) and the Vostok temperature reconstruction from Petit et al. (2000), with sea level lagging temperatures by about 4,700 years, at least for the last 50,000 years. This is corroborated by other reconstructions, such as the SL reconstruction from Arz et al. (2007) for the time span 83,000 years to 13,000 years before present.

The magnitude of SLR since the last glacial maximum 20,000 years ago is about 130 meters (427 feet), which again, is non-trivial. If we had similar SLR today, essentially all coastal cities around the world would be under water.

Much of that SLR has to be the result of ice melt. The rest, if any, would have to be the result of thermal expansion. Ice that is floating in the ocean should not cause SLR when it melts. What matters in this sense is ice over land.

In this post I'd like to estimate the magnitude of sea level rise due to ice melt alone.

NOAA provides a reconstruction contributed by Peltier (1993), along with applets that let you visualize ice coverage and ice topography in a world map. The resolution is 1,000 years, and the data goes all the way back to the last glacial maximum.



Fortunately, most of the ice coverage is over land, as you can see. So I took the 21K-year-old ice coverage data, and used it as a baseline for the calculation of changes in ice volume. The topography data includes land topography, evidently, but we're interested in ice volume change (not so much absolute ice volume) so it will do for now. In a footnote I will provide the processed data, along with an explanation of how it is obtained. The following graph shows the ice volume data along with the Vostok temperature reconstruction.



So we're talking about a change in ice volume in the order of 3.9·107 km3 in the last 21K years. The density of glacial ice is about 90% that of ocean water. (The tip of an iceberg is about 10% of the iceberg.) So the change in ice volume translates to 3.5·107 km3 of additional ocean water.

Now, the surface area of the ocean is 3.61·108 km2. If sea level rises, this surface area will change in a manner that is negligible, even if some areas are flooded. Does that make sense? Therefore, a good approximation for the change in ocean volume (ΔV) that results from a rise (ΔL) in sea level, is:

ΔV = 3.61·108·ΔL

Solving for ΔL, we have that:

ΔL = 0.097 km

That is 97 meters. It follows that thermal expansion must be responsible for the remaining 33 meters of SLR since the LGM.

[Correction 2/28/2010: As it turns out, SLR due to thermal expansion can't be anywhere near 33 meters. See Part 3 of the series.]

What if we lost all ice?

Let's assume, conservatively, that only 2.5·107 km3 of ice remain over land. If we managed to melt all of it, the ocean would get an extra 2.24·107 km3 of water. Dividing this volume by the surface area of the ocean, we get 62 meters of SLR.

That scenario is, of course, not something we'll see in our lifetimes, by a long shot. Even if we raised the temperature of Earth enough, it would take thousands of years to be realized, no doubt.

It's not an impossible scenario, however. About 50 million years ago, during the Paleocene-Eocene Thermal Maximum, global sea level was about 200 meters higher than today.

Data
  • Summarized Ice Coverage and Ice Volume from Peltier (1993)
    This is obtained by processing all ice*.asc and top*.asc files in "ASCII special" format. The area of a grid cell is calculated by dividing the area of a spherical ring 1-degree wide (corresponding to each latitude in the data) by 360. Only grid cells with ice coverage in the 21K-year-old data are considered when calculating land+ice volume.

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