150cm/month seems reasonable to me...
And more re-reading, Rob's own estimate is 8 cm/day 240 per month. Which may be the case for the more isolated (though huge) floes as the Big Block.
Big Block is as large as a small country.
It creates its own micro-climate, specifically below the ice.
On top of that, as pointed out by A-team, Big Block did not move around much over the past month.
So it is much less exposed to bottom-melt than the smaller, broken up, pieces of MYI floating in the Beaufort, even while the FYI and other rubble melts out very quickly in the Beaufort right now.
As I stated before, Big Block will be the last to go in the Beaufort, simply because of its size. It may take another month, but it will go.
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Hi Rob!
I would think the same about the micro-climate under the big floes if it wasn't because of the strong turbulent motion of the open water surrounding it.
Secondly, the block has not moved because it is (or was) very thick and its inertia causes to acquire its terminal speed in a time twice or three times longer than other floes with twice or three time less thickness. F = m*a. In April/May this floe acquired high speed because the winds and currents were sustained for days. But now that winds are currents are more erratic, the block just does not move.
PS. Also, the average wind friction per unit area is smaller in a bigger floe (but not so much as could be thought given the difference of size): Overall friction coefficient in a flat plate parallel to a turbulent flow goes as:
CF ~ 0.06 / (Re_x)^0.2
The Reynolds number is Re_x = wind velocity free current W x characteristic length of floe L / kinematic viscosity of air N. This is for a rectangular plate but assume similar friction dependency with typical diameter or length of the floe.
- For a floe with L = 1 Km, Re_x = 4*10^8, CF ~ 0.001
- For a floe with L = 10 Km, Re_x = 4*10^9, CF ~ 0.0007
- For a floe with L = 100 Km, Re_x = 4*10^10, CF ~ 0.0004
Multiply that by (1/2 * density air * wind speed ^2 * floe surface) to get the total pull.
So the average wind pull per unit area in the Big Block is 1/2 of that of a 1 Km size floe. Similar applies for the water drag under the floe (kinematic viscosity being 10 times smaller, but floe relative speed to ocean being 10 times smaller or more than wind velocity); the terminal condition varies, but not much, the reason why a storm separates thick ice with big floes similarly to thinner ice with smaller floes. Coriolis force is stronger for the thicker floe too.
Thanks seaicesailer, that is brilliant !
Indeed the skin drag equations have a factor 1/(SQRT(L)) in them which indeed means that large floes respond slower to wind and current drag than smaller floes.
This explains why "Big Block" does not move around much if the winds are erratic and there is no consistent current one way or the other.
And I like very much that in a separate comment you showed that there is a theoretical basis for the observed (constant, about 1/30) relation between wind speed and floe speed (noted by several posters here, specifically from obuoy 14) since the kinetic viscosity and density of water and air does not change much at these low speeds.
Conclusion: the fact that the floe does not move does not imply much difference of bottom melting w.r.t. smaller floes given the agitation of Beaufort sea.
After all that work, I still do not think you can draw this conclusion.
There are two factors that still need clarification before you can claim that "Big Block" suffers the same bottom melt torture as smaller flows :
1) Big Block did not move around much, which means that the currents and winds were erratic. This means that whatever water flowed below Big Block flowed out quickly again. So it is unclear how far that heat travelled under the ice, and thus there may be large areas underneath Big Block that received no heat at all. Which means that during 'erratic' winds and currents, big floes would receive less bottom heat per unit of area than smaller floes.
2) Even if there was a consistent current underneath the entire Big Block area, it is doubtful that the bottom-melt is uniform. Imagine a floe in a current : There is warm water flowing in from one side, which causes bottom-melt, which cools the water, which flows out on the other side.
Now, as the water flows under the ice, it looses heat (to bottom-melt) so the further it travels under the ice the less bottom-melt it will cause. I don't know how large a floe has to be for this effect (of deminishing bottom-melt) to seriously show up, but the mixed layer is only 20 meters or so, which is puny compared to the 100,000+ meters that water would need to travel underneath Big Block.
The top-layer of water is loosing heat when it travels underneath the ice, and for an ice "field" like Big Block, that effect will reduce bottom melt.
So, based on these two effects, I still claim that Big Block suffered much less bottom-melt than the smaller floes around it, and thus will be "the last floe standing" in the Beaufort.
But it WILL go in the end.
