The loss of multi-year sea ice Part 2.

In the previous post I looked at what had been happening to the extent of Multi Year (MY) sea-ice and the nature of it's presence in the Arctic sea-ice. There is more research however that pertains to changes in it's thickness, and the thickness of the Arctic sea ice in general.

Firstly there's a very interesting paper by Cecilia Bitz & Gerald Roe "A Mechanism for the High Rate of Sea Ice Thinning in the Arctic Ocean", Journal of Climate 2004. In it Bitz & Roe note observations of the thinning of Arctic sea-ice from Submarine cruises under the ice. What they find is interesting and at first glance appears puzzling: There is a relationship between the initial thickness of the sea-ice and how much it thins. Between 1958-76 and 1993-97 4 metre thick ice thinned by around 2 metres yet 3 metre thick ice only thinned by around 1 metre, with ice around 1 to 2 metres hardly thinning at all! As Bitz & Roe note, their work is an expansion of earlier work by Thorndike (1992), and by Hansen (1985) - Hansen yet again is ahead of the pack.

Bitz and Roe develop a simple energy flux model and pursue it's implications in light of the above observations. They observe that various models incorporating sea-ice, some of which have a motionless ice pack, still show this increasing loss with thickness relationship. That strongly suggests that what is going on is thermodynamic in nature and not due to other issues like wind forcing (e.g. changes in sea-ice export through the Fram Strait). Which is not to say that sea-ice export isn't a factor in the decline, sea-ice export just doesn't explain the changes in thickness. So arguably it's not the major factor. I'll spare you the worst of the maths (for that the inclined can refer to the paper), it's not my strong point anyway, but what was going on can be explained in light of the processes in play in the ice pack.

First year sea-ice can rapidly grow to around 2 metres thick in one season, once the initial layer of ice has formed (called Nilas) it coheres to form a layer of ice. Further growth is by freezing onto the base of the sea-ice, for the ice to grow this way there has to be a flux of heat throught the ice, the ocean is liquid so is therefore above freezing. This flux of heat (Q) from the warmer ocean to cold atmosphere is given by the following equation.

Q = k(Ts - Tw)/z
where
Q = Heat flux Watt/m^2.
k = Thermal conductivity .
Ts = Surface Temperature.
Tw = Ocean temperature in the vicinity of the sea-ice/ocean boundary.
z = Thickness.
Due to the 1/z relationship Q drops off rapidly.

Using typical values for Arctic sea-ice in the Winter:
Ts = -35
Tw = 0
k = 2.29

z = 0.1 Q = -801
z = 0.5 Q = -160
z = 1 Q = -80
z = 2 Q = -40
z = 3 Q = -27
z = 4 Q = -20

So you can see that as the ice thickens (z increases), the heat flux through the sea-ice rapidly decreases. You may also appreciate that as sea-ice thins it can release more heat into the atmosphere from the ocean. This is a negative feedback, as we see a thinner ice-pack it should release more heat into the atmosphere, which acts against the processes putting heat into melting the ice (e.g. ice albedo feedback).

As mentioned in the previous post, First Year (FY) sea-ice can typically grow to around 2 metres thick in one season. However the thicker, older MY ice mostly grows not thermodynamically, but by mechanical processes: Compression and ridging. So we have 2 types of ice; quick growing FY, and slow growing MY, and it is the very difference in rates (time constants in Bitz & Roe) that accounts for the differences in thinning for different thickness. Amidst an array of processes that are melting or moving the ice, the thin (FY) ice is more rapidly able to grow back each Winter, while it takes years for the thicker ice to grow back. This is why the MY ice has thinned more than the FY.

Kwok & Rothrock 2009 use data from submarine cruises and the ICESat mission. The submarine cruises use upward looking sonar to measure the sea-ice draft, ICESat uses a LIDAR to measure freeboard (the amount the ice sticks up above sea level) and thence using the bouyancy of ice to estimate thickness. The graphic that follows is part of figure 2 of Kwok & Rothrock, it shows the changes that have occurred in the Data Release Area (DRA), an area of the Arctic in which the cruise data was declassified and released for scientific useage.

Figure 2 of Kwok & Rothrock 2009.

The DRA covers the central Arctic ice pack, with the long straighter edge at the bottom of the figures being off the Canadian Arctic Archipelago and north of Greenland. From the graphics it can be appreciated that there has been a substantial thining from 1988 to 2004-2008 and a concomitant reduction in summer ice concentration. Kwok & Rothrock note that between 1980 and 2008 winter peak thickness declined from 3.64m to 1.89m, a decrease of 1.75m with 0.44m of the decline between 2000 and 2008. The summer decline between 1980 and 2007 is from 2.80m down to 1.15m.

In the face of the processes leading to a reduction in ice volume the thick ice hasn't got a chance, it can't grow back unless the current envionmental regime in the Arctic changes to allow it's slow accumulation over periods of years. And it's the thick ice that the ice pack needs to be resistant to weather driven losses such as 2007.

For those wanting to read more but reluctant to read scientific papers, here's an article from Physics Today.
Kwok & Untersteiner, 2011 article, "The thinning of Arctic sea ice." Physics Today. PDF.

Bitz & Roe, 2004, "A Mechanism for the High Rate of Sea Ice Thinning in the Arctic Ocean." Journal of Climate. PDF.
Kwok & Rothrock, 2009, "Decline in Arctic sea ice thickness from submarine and ICESat records: 1958–2008." GRL. PDF.