Having read this http://wattsupwiththat.com/2012/01/29/hansens-sea-shell-game/
I thought I'd do some fag packet calculations. Anyone kind enough to run their eye over the following to make sure I've done nowt overly stupid?

Latent heat of fusion of water is 334 kJkg-1
Greenland ice sheet is approximately 2.85M km3 (or 2.85 x 10^15 m3)
Density of ice is approximately 0.92 gcm-3 or 920kgm-3

It requires approx. 920 x 334 = 307 280 kJ to melt 1 cubic metre of ice, giving
307 280 x (2.85 x 10^15) = 8.76 x 10^20 kJ to melt the Greenland ice cap entirely, although assuming that the Antarctic would have to melt at a similar rate, it may be prudent to double this figure.

Radius of the Earth is 6400 km
Surface area, A = 4πr2
A = 4 x 3.1416 x 6400000^2
A = 5.1 x 10^14m2
Exposed area = 2.6 x 10^14m2

Energy imbalance = 0.65 Wm-2
1W = 1 Js-1 = 60J/minute = 3.6kJ/hr = 86.4kJ/day = 31 536 kJ/year
31 536 x 2.6 x 10^14m2 = 8.2 x 10^16 kJ/year
Energy to melt GIC 8.76 x 10^20kJ

As near as makes no odds, with Hansen’s value for energy imbalance it would take 10 000 years to melt, assuming no warming and no other effects of energy imbalance.

Thanks in advance and apologies for the ugly formatting of the exponents, C&P from Word left me with some remedial work to do.

1. Didn't follow 'exposed area'
2.Where's Hansen's number come from?

Hansen's number is my average from this statement "Argo era observed planetary energy imbalances are 0.70 Wm-2 in 2003-2008 and 0.59 Wm-2 in 2005-2010." at the bottom of page 31 of this paper http://www.columbia.edu/~jeh1/mailings/2011/20110415_EnergyImbalancePaper.pdf
I've seen various figures quoted in this sort of range and it seemed apt to use Hansen's own figures rather than someone else's.

'Exposed area' is my ignorance as to whether one needs to account for the fact that only half of the Earth's surface is exposed to solar insolation at any time is taken into account.

I almost left that bit out, but to be honest, being out by a factor of two in either direction is something of an irrelevance when Hansen's (not a) prediction is looking at the end of this century and me being out by a factor of 2 would still be five millennia beyond that.

Thanks for reading.

You have the latent heat, but it looks like you may have not warmed the ice from ambient to melting point.

I get about 383 kJ/kg more heat is needed to heat the ice from -20 to 0 deg C.

drat....383 kJ/kg total heat. Or about 50 kJ/kg MORE.

SteveW -
Do that last bit again. First of all, the value for global energy imbalance (for all fluxes, in fact) are conventionally figured as a hypothetical average over the entire surface of the earth, hence one should use an area of 5.1E14 m^2. [where E14 is shorthand for *10^14.]

An imbalance of 0.65 W/m^2 comes to
0.65 W/m^2 * (5.1E14 m^2) * (60*60*24*365.25 seconds/yr) = 1.05E22 J/yr.

At that rate, the energy of 8.8E23 J (enough to melt GIS) would accumulate in about 84 years.

This is not to say that I expect that the GIS is in any danger of completely disappearing in 100 years; merely that it is not energetically forbidden, given the assumed energy imbalance. There's also warming the ice to 0 degC, and warming the meltwater to the average ocean surface temperature, but those don't change the order-of-magnitude value you're seeking.

Good spot Harold - my 8.2 x 10^16 near the end should have been 8.2 x 10^18 which makes all of the difference.

That's exactly why I put it out there.

@HaroldW @Steve
Harold is right in final computations
31 536 x 2.6 x 10^14m2 = 8.2 x 10^16 kJ/year
is an error (exponent 18)

BUT
Both of you agree that the bak-of-envelope model is OK: all energy imbalance goes to the "poor Greenland". Assuming so, you agree on a model of "thermal lenses", focusing all excess energy on a selected area of the Earth. In this manner your model can be used to demonstrate that melting of a South Pole area can de done in a few years.

The excess energy spread all over the Earth. How much is transferred to North? How much will affect Greenland? What are possible processes of the heat transfer from the atmosphere to the ice cap of Greenland (radiation from warmer atmosphere into ice - 2-3km above the sea level???,conduction from air???, heat transfer by conduction between rainwater and the ice?) ? All this may change your estimates :)

What processes were involved when last Ice Age was turning into Holocene? Suggest reading of prof. Marcel Leroux.

I feel that if we simplify too much then we start to play instead of doing something resembling science.

WAM, I accept what yuo're saying, but don't entirely agree.

I was looking to see whether it was 'feasible' that the Greenland Ice Sheet could be melted completely inside a century, and I'd hacve to say it's not (under current conditions) since, as you say, it would require the entire energy imbalance to be focussed onto the Greenland Ice Sheet, with no concurrent warmng/melting anywhere else in the system.

I guess that, in keeping with the best traditiona of climate science I should have hidden my working and then claimed the supremacy of my 'model' over reality when anyone asked about it ;-)

@Steve
You have a true making of a Climate Scientist ;). Scare a good dr Hansen, give him an unpalpalable number (10k years), and let him worry :). As for peer review - you gave too much SI. But we can rubber stamp, no?

But I stand by my opinion - too simplified model has given you the lower limit - 100 years, which is rather unrealistically short.
All this rain/snow/2-3km of the icecap height....

@ WAM

Crossed wires a bit, I agree entirely with this

But I stand by my opinion - too simplified model has given you the lower limit - 100 years, which is rather unrealistically short.

It was this bit

I feel that if we simplify too much then we start to play instead of doing something resembling science

that rankled slightly, as, despite the fact that I'd happily describe what I was doing as playing, I'd suggest it's not simplified 'too much' rather, simplified just about enough to demonstrate how unrealistic Hansen's 'scenario' is.

This came up on Greenie Watch a few years ago:

THE GREENLAND-ANTARCTICA MELTING PROBLEM DOES NOT EXIST

An interesting read, but has this story been demolished in the meantime?

:"I guess that, in keeping with the best traditiona of climate science I should have hidden my working and then claimed the supremacy of my 'model' over reality when anyone asked about it ;-)" --SteveW

Why should you reveal your working when all they want to do is find something wrong with it? And don't bother calculating p values. Phil Jones says, "There is no need to calculate a p value for a statement that is based on the laws of physics." Be sure to use "robust" several times in the write-up.

At the height of the Eemian (GAT ~1 - 2C higher than present) mean sea level was ~5m higher than present. It is now thought that the GIS contributed about 1m to this, and the West Atlantic Ice Sheet made up the other 4m.

Perhaps you are asking the wrong questions?

I think the other point missing here is that glaciologists do not argue that ice sheets melt in situ. Rather, in the case of the GIS, surface meltwater drains through the ice sheet (moulin formation), lubricates the base and gravity does the rest. The rate of glacial outflow and calving increases dramatically, and an unstoppable, gravity-driven process of breakup gains momentum.

The sea ice so produced is transported away by ocean currents and melted in open water.

The collapse of the WAIS is likely to be accelerated by warming sub-surface currents in the coastal Southern Ocean. Antarctic surface temperatures do not have to rise above freezing - this is a common misconception. Once the unstable sea ice shelves that block glacial outflow from the ice sheet proper break up, gravity does the rest.

This is why glaciologists are concerned that the GIS and WAIS may well exhibit a non-linear response to rising temperatures.

How do the glaciologists know this? I mean, the non-linear response etc.

How do the glaciologists know this? I mean, the non-linear response etc.

Feb 3, 2012 at 12:27 PM | Shub

It's good for one's ego to know things nobody else does.

Shub

Sorry for the delay. Technical problems.

Well, the uncomfortable suspicion arises from a growing understanding of ice shelf and ice sheet dynamics. A pertinent case study would be the collapse of Larsen B ice shelf and its effects on glacier flow rates:

Rignot E, Casassa G, Gogineni P, Krabill W, Rivera A and
Thomas R 2004 Accelerated discharge from the Antarctic
Peninsula following collapse of Larsen B ice shelf Geophys.
Res. Lett. 31 L18401

Rignot E and Jacobs S S 2002 Rapid bottom melting widespread near
Antarctic ice sheet grounding lines Science 296 2020–3

Scambos T A, Bohlander J A, Shuman C A and Skvarca P 2004
Glacier acceleration and thinning after ice shelf collapse in the
Larsen B embayment, Antarctica Geophys. Res. Lett.
31 L18402

Shepherd A, Wingham D, Payne T and Skvarca P 2003 Larsen ice
shelf has progressively thinned Science 302 856–9

Shepherd A, Wingham D and Rignot E 2004 Warm ocean is eroding
West Antarctic ice sheet Geophys. Res. Lett. 31 L23402