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« Imperial wizard | Main | A Rose on winter »

Melting ice

Reader Steve W has done some rough calculations on how long it will take the Greenland Ice Cap to melt and is asking for the mathematically minded among you to cast an eye over it.

His post is here.

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Reader Comments (46)

That link's a bit recursive Bishop!

Jan 30, 2012 at 10:12 PM | Unregistered CommenterCumbrian Lad

Try instead.

Criticism and correction gratefully accepted.

Jan 30, 2012 at 10:57 PM | Unregistered CommenterSteveW

Considering that the P-38 recovered on July 15, 1992 from a depth of 268 feet of additional Greenland ice accumulated in the 50 years from when it force-landed in 1942, ie the time of 'unprecedented anthropogenic warming', estimates of growth of the Greenland Ice Cap might also be appropriate.

Jan 30, 2012 at 11:18 PM | Unregistered CommenterPharos

There is a model run several years ago (see ref below) suggesting that IF the Greenland ice sheet were to enter a sustained melting until its ice completely dissolves, the process would take about 3000 years. The average addition to sea level would be 2.3 mm per year, with a peak rise of 5.5 mm/yr somewhere along the process. However, that rate of melting would necessitate extreme global warming (i.e. strong fossil fuel burning under elevated (four times pre-industrial) levels of atmospheric CO2) lasting at least for three millennia, which is rather too much and too long in view of the amount of fossil fuels remaining on this planet.
The Ridley et al 2005 study is approvingly cited in AR4 (WG1 report, p. 772).

Ridley, J.K., P. Huybrechts, J.M. Gregory, & J.A. Lowe, 2005. Elimination of the Greenland ice sheet in a high CO2 climate. Journal of Climate, 17: 3409–3427.

Jan 30, 2012 at 11:18 PM | Unregistered CommenterHector M.

Is this right? "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"?
Should it not be 0.0009167kgm-3?

Jan 30, 2012 at 11:36 PM | Unregistered CommenterTim Curtin

Oops - I missed the cm-3 as opposed to kgm-3!

Jan 30, 2012 at 11:39 PM | Unregistered CommenterTim Curtin

Cubic centimetres versus cubic metres.
1 cubic centimetre of water has a mass of 1g and a density of 1g cm-3
1 cubic metre is 100 x 100 x 100 cubic centimetres, i.e. 1M cubic centimetres.
1 m3 of water has a mass of 1 000 000g or 1000kg - density therefore 1000kg m-3

Conversion factors are easier with unit volume and/or unit mass :-)

Jan 30, 2012 at 11:41 PM | Unregistered CommenterSteveW


Oops - I missed the cm-3 as opposed to kgm-3!

That's exactly why I've put it up there for comment - I'm half convinced I've done something similar, but I'm damned if I can see it. Best way to spot it is to have someone else spot it for you.

Jan 30, 2012 at 11:43 PM | Unregistered CommenterSteveW

An objective overview of Greenland ice mass growth/decay, citing various research work is here

As might be expected, the conclusion is that all we really know is that we know f all, viz.

'In summing up the bottom-line take-home message of all of these many studies, perhaps the fairest thing that could be said is that we really do not know if there is any long-term positive or negative mass balance change occurring on either the Greenland or Antarctic Ice Sheets. Hence, it is important that we continue collecting data in these two polar regions, so that someday we will be able to unambiguously discern whatever trends or non-trends are representative of reality. In the mean time, don't believe anything about these ice sheets that sounds either too good or too bad. Neither is likely to be correct'.

Jan 30, 2012 at 11:51 PM | Unregistered CommenterPharos

Here is the text and a working link:

Having read this
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.

Glad to be of some help.

Jan 31, 2012 at 2:10 AM | Unregistered CommentersHx

Your Grace,

News reports claim you've sold out to Big Wind! What, Big Oil not paying you enough?

Buffet's MidAmerican Energy to acquire Illinois wind project

The energy business of Berkshire Hathaway, a conglomerate headed by billionaire Warren Buffett, has agreed to acquire the 81MW Bishop Hill II wind project under construction in Illinois from developer Invenergy Wind.

[Emphasis added. Source: European Wind Energy Association via]

Beg your indulgence for being OT, but couldn't pass it up.

BTW, the above raises the question regarding why governments are subsidizing wind, when private parties seem to be willing to put their own money on the line -- or is Buffett's idea to harvest these subsidies? Regardless, Buffet must hathaway to make money!

Regardless of whether it makes sense for Warren Buffet, it makes little sense for gov't to subsidize such schemes.

Jan 31, 2012 at 3:30 AM | Unregistered CommenterIndur M. Goklany

My apologies for crediting EWEA for the story in my previous "comment". The source is RECHARGE, which bills itself as "the global source for renewable energy news." I got mistook an ad by EWEA for one of its conferences masquerading as a logo for the website.

Jan 31, 2012 at 3:37 AM | Unregistered CommenterIndur M. Goklany

Even by the dismal scientific standards of the BBC this is laughable. The suggestion is that climate change is a primary and noteworthy influence on the mass of the earth.

Jan 31, 2012 at 3:54 AM | Unregistered CommenterCarnwennan

Steve: 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. (and -20 is very conservative).

Jan 31, 2012 at 7:16 AM | Unregistered CommenterLes Johnson

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

Jan 31, 2012 at 7:59 AM | Unregistered CommenterLes Johnson

I think someone has worked this out before (how long it will take for the Greenland Ice sheet to melt at current rates) and iirc the figure was something like 30,000 years. Stephen Sackur (BBC Hardtalk) evidently did some homework on this (he even went to Greenland before interviewing Gerd Leipold, the outgoing leader of Greenpeace) a couple of years ago. Here's the relevant bit of the interview. It is one of the very rare moments the BBC has had some credibility on the global warming issue, and worthy watching again. Kudos to Sackur for not falling for the spin.

Jan 31, 2012 at 8:51 AM | Unregistered Commenterlapogus

John Redwood MP all change climate change

Jan 31, 2012 at 11:07 AM | Unregistered CommenterAnoneumouse

John Redwood MP all change climate change

Jan 31, 2012 at 11:13 AM | Unregistered CommenterAnoneumouse

How long before Trenberth discovers that the "missing heat" is being spent melting the icecaps?

Jan 31, 2012 at 11:17 AM | Unregistered CommenterMaurizio Morabito

forgot the "notify"...

Jan 31, 2012 at 11:17 AM | Unregistered CommenterMaurizio Morabito

How long before Trenberth discovers that the "missing heat" is being spent melting the icecaps?

Jan 31, 2012 at 11:17 AM | Maurizio Morabito
I don't know about that, but it appears that NASA claim that they have found the missing heat; it is going into the oceans, see

No doubt WUWT will post an article on this.

Jan 31, 2012 at 11:53 AM | Unregistered Commentereichard verney

Little Ice Age goes Global.

It would appear that the LIA was initiated by volcanic activity in the tropics and later sustained by changes in solar activity.

This research infers that global temperatures prior to the onset of the LIA where indeed higher. So the MWP was probably not of regional origin and impact, but simply a regional indicator of much higher temperatures globally.

Just as important is that LIA was an 'abrupt' change in temperatures globally, i.e., the planet cooled quickly.

This 'abruptness' falsifies the Hockey Stick arguement of a long slow decline in global temperatures over the millennium followed by an 'unprecedented' rise in 20th century global temperatures.

It may point to a bath-tub type curve over the last millennium regarding global temps, and also that 'abrupt' step changes in global temperatures are both the norm and are natural in origin.

Jan 31, 2012 at 12:22 PM | Unregistered CommenterMac

Re: Mac
From the article:

And it was climate modelling that showed how sea ice exports into the North Atlantic set up this self-sustaining feedback process, and that's how a perturbation of decades can result in a climate shift of centuries.

In other words they wanted a cause for the LIA that would not interfere with the "CO2 is the most dangerous substance in the Universe" meme so they played with some computer models until they managed to get them to say what they wanted. In this case it was a feedback mechanism that extended the impact of a volcanic eruption from years to centuries and with solar radiation only managing to maintain it (not cause it).

Jan 31, 2012 at 12:39 PM | Unregistered CommenterTerryS

A bit too simple, I am afraid. There is a good book on the topic that may be of interest: Mass Balance of the Cryosphere

Temperatures will warm as the surface altitude get lower, there must be a mechanism for the energy transfer from the global system to the ice sheet, it will be affected by albedo, changes in precipitation, timing of precipitation, air masses, wind speed, cloud cover, etc, etc, which gives a very large range of combinations even if the "global energy imbalance" is fixed

Jan 31, 2012 at 12:48 PM | Unregistered CommenterPatagon


This research is important because up to this point both the MWP and the LIA have been effectively eliminated by the acceptance of the Hockey Stick arguement. We now have evidence that the LIA was abrupt and longstanding, a cataclysmic natural event due to volcanic activity that produced a step change in global climate. It is that 'abruptness' and that long term claw-back in global temperatures that undermines the Hockey stick, it is no where to be seen in the consensus-driven paleoclimatic reconstructions.

Jan 31, 2012 at 1:09 PM | Unregistered CommenterMac

Yes Mac but the LIA actually last for a couple of hundred years if you count the start of the drop in temp to the return to the same temp. No volcano has ever been shown to last that long except in their fairytale models.

Jan 31, 2012 at 1:19 PM | Unregistered Commenterstephen richards

It was a telepathic Volcano, just like the telepathic bristlecone that mapped global temps all on its own stuck to a stationary rock (which must have come from the same volcano).

Jan 31, 2012 at 1:54 PM | Unregistered CommenterBreath of Fresh Air

From the press release

As part of the study, Miller and his colleagues radiocarbon-dated roughly 150 samples of dead plant material with roots intact collected from beneath receding ice margins of ice caps on Baffin Island in the Canadian Arctic. There was a large cluster of “kill dates” between 1275 and 1300 A.D., indicating the plants had been frozen and engulfed by ice during a relatively sudden event.

In other words the ice cap has not yet retreated (in those areas) to where it was during the MWP.

Jan 31, 2012 at 2:07 PM | Unregistered CommenterTerryS

This research infers that global temperatures prior to the onset of the LIA where indeed higher.

No, Mac, the research implied it - you inferred it.

Jan 31, 2012 at 2:23 PM | Unregistered Commentersteveta_uk

I was looking at the press release for the paper hoping to find out what volcanoes it was that erupted and caused the LIA. The press release doesn't give any details of the eruptions but it does says this:

The team used NCAR’s Community Climate System model to test the effects of volcanic cooling on Arctic sea ice extent and mass. The model, which simulated various sea ice conditions from about 1150-1700 A.D., showed several large, closely spaced eruptions could have cooled the Northern Hemisphere enough to trigger Arctic sea-ice growth.
The researchers set the solar radiation at a constant level in the simulations, and Miller said the Little Ice Age likely would have occurred without decreased summer solar radiation at the time.

So it looks to me like they haven't tied the LIA to any specific eruption. Instead they have looked at how many short spaced eruptions it would take for their model to enter a LIA.

Jan 31, 2012 at 2:30 PM | Unregistered CommenterTerryS

Before the Greenland ice cap can be persuaded to start melting its temperature will have to be raised to the melting point of ice, which is 0°C. I believe its current temperature is about -31° C, so an awful lot of global warming will have to take place before that happens.

Jan 31, 2012 at 2:40 PM | Unregistered CommenterGordon

The research has indentified two long and sustained periods of intense volcanic activity that caused abrupt changes in global climate. We do see such step-like changes in Loehle, 2007. However we do not see those abrupt changes in the Hockey Stick science. Why is that?

Jan 31, 2012 at 3:09 PM | Unregistered CommenterMac

Re: Mac
Can you tell me which volcanoes erupted and when?
The reason I ask is that I only know of one large volcanic eruption in the time frame and that is Quilotoa in 1280. If their paper is working from real eruptions, that have been detected, in the past then it might have some merit. From what I have read the eruptions have only been in their climate simulations and not the real world.

Jan 31, 2012 at 3:23 PM | Unregistered CommenterTerryS

When I was writing a discussion document about Global Warming for a local group I found this comment somewhere (I did not make a note from where)

It is recorded that the ash and dust cloud from the eruption of Tambora in Indonesia, in 1815, led to a fall in world temperature of 1.1°C. There was a reddish-yellow haze in the sky all over Europe during the months following the eruption. The following year was known as ‘the year without a summer’. Many food crops failed, or produced lower yields in Europe, and heavy unseasonable snowfalls experienced in the USA.

It would need at least one volcano of this magnetude, each year, to cause the LIA.

Jan 31, 2012 at 3:59 PM | Unregistered CommenterJohn de Melle


The reason I ask is that I only know of one large volcanic eruption in the time frame and that is Quilotoa in 1280. If their paper is working from real eruptions, that have been detected, in the past then it might have some merit.

While it is true that there are eruptions virtually every day, truly massive ones, such as Quilotoa are rare and far between -- and very carefully searched for by those interested in them. You raise an excellent point. I doubt that there are that many "undetected" massive volcano blowouts.

I guess we will now be pegged as "volcano skeptics" as well.

Also, I am beginning to wonder if we aren't trapped in a massive computer generated simulation like that portrayed in the movie The Matrix with Agent Smith being played by Mikey Mann?

Jan 31, 2012 at 4:02 PM | Unregistered CommenterDon Pablo de la Sierra

The calculations look reasonable at first glance, but I haven't got the calculator out. The writer may wish to make some suggested additions.
As the ice is mostly quite a long way above sea level then it will also have some geopotential energy that would be released when it melts (just like water in hydroelectric schemes). The ice is, presumably, not at 0 degrees C either. It will also have a different amount of angular momentum from the global average for ocean water.
Some of these may turn out to be trivial amounts, I haven't calculated them. I'm sure readers could make other suggestions.

Jan 31, 2012 at 4:22 PM | Unregistered Commentermichael hart

Re: Don Pablo de la Sierra

I've skimmed the paper (available here courtesy of Leif Svalgaard) and the only eruption they actually identify is one in 1452.
For the start of the LIA they say

The PDF peak defining abrupt LIA cooling 1275–1300 AD coincides with an interval of four large stratospheric sulfur loadings from explosive volcanism following a multi-centennial warm interval, during which complete revegetation of deglaciated sites would have fully reset the radiocarbon clock (Figure 2c)

They do not provide dates, names or locations of these 4 large eruptions.

Jan 31, 2012 at 4:46 PM | Unregistered CommenterTerryS

Interesting factoid If I remember the numbers correct:
If all of Greenlands ice would melt, GLOBAL sealevel would rise about 6m or so.
In the North Sea and similar places, the present sealevel is already 4m higher then it would be without the ice, due to the gravitational pull from the icemass.
So the sealevel rise in the Northsea would be around 2m or so.

Jan 31, 2012 at 4:46 PM | Unregistered CommenterBenAW


First of all, I love how fast this was published

Received 29 November 2011; revised 29 December 2011; accepted 30 December 2011; published 31 January 2012.

It was received, reviewed, revised and accepted in four weeks! I guess nobody had to do any Christmas shopping, go to Christmas parties, take Christmas off, go skiing for the weekend, etc.
My, what dedicated scientists.

I also get a kick out of

1275–1300 AD coincides with an interval of four large stratospheric sulfur loadings from explosive volcanism

Why didn't they show that sulfur levels increased in bands of ice from those periods in Arctic and Antarctic ice? Both sets of ice cores exist along with several others that should show that result. Surely, it would be easy enough to look at them, and probably just the results of countless studies already conducted on these cores.

Jan 31, 2012 at 5:19 PM | Unregistered CommenterDon Pablo de la Sierra

Oh, and one more point --

While the Europeans were all huddled in their huts freezing in the dark, the Chinese were writing down all sorts of information, dated to not only a particular day of a specific year, but down to their hour and minute notation. Surely four large volcanic explosions would have been noticed and recorded by them. There are records about the such happenings going back thousands of years. Bamboo Annals

Jan 31, 2012 at 5:34 PM | Unregistered CommenterDon Pablo de la Sierra

o/t - Three people die of exposure in Serbian snowstorms. Of course, that's chaotic weather caused by CAGW.

Jan 31, 2012 at 7:23 PM | Unregistered CommenterHuhneMustGo

I looked at the Trenberth paper cited

I was reminded of the instruction on how to weigh a fly that I saw on the TV many years ago:

1. Put a 1 kg jelly on a weighing scale
2. Put another 1 kg jelly on another weighing scale.
3. Wait until a fly lands on one of the jellies.
4. Read the weight indicated on each scale
5. Subtract the smaller reading from the larger. This gives the weight of the fly.

Page 44 of the paper states:

The precision achieved by the most advanced generation of radiation budget satellites is indicated by the planetary energy imbalance measured by the ongoing CERES (Clouds and the Earth's Radiant Energy System) instrument (Loeb et al., 2009), which finds a measured 5-year-mean imbalance of 6.5 W/m2 (Loeb et al., 2009). Because this result is implausible, instrumentation calibration factors were introduced to reduce the imbalance to the imbalance suggested by climate models, 0.85 W/m2 (Loeb et al. 2009).

The accuracy of climate models is impressive.

Jan 31, 2012 at 10:12 PM | Unregistered CommenterMartin A

Any Brain Boxes on here try and calculate this

If water expands when it freezes
Thats why you lag your pipes in your loft

And Ice floats mostly under water
As we all know from watching Kate Winslett and Leonardo snogging on the deck of Titanic

So if you melted all the ice in Both the poles how much would the sea level actually rise
Or would it stay the same level

Jan 31, 2012 at 10:45 PM | Unregistered Commenterjamspid


Sea ice melting has no effect on sea level, land ice (Greenland Ice Sheet, Antarctic Ice Sheet etc...) would raise sea levels were it to melt (ignoring for the moment that the Greenland Ice Sheet sits in a rather large natural basin so would be incredibly unlikely to drain completely into the see in the unlikely event that it were to melt in its entirety), as the ice is not currently supported on/floating in the oceans.

Feb 1, 2012 at 12:25 AM | Unregistered CommenterSteveW

Martin A @10:12 PM--
The paper which you've linked is Hansen et al., not Trenberth's. I agree (as does Hansen) that the CERES data can not provide a sufficiently accurate measurement of energy flux, to act as a confirmation (or refutation) of forcing estimates.

SteveW@12:25 AM--
Technically, melting sea ice does produce a slight effect on sea level, because the ice is nearly pure water and the ocean is salty. Noerdlinger and Brower say "if all the extant sea ice and floating shelf ice melted, the global sea level would rise about 4 cm. Shepherd et al. claims that melting of floating ice is currently responsible for about 50 microns (!) per year of sea level increase.

However, note that part of the West Antarctic Ice Sheet is grounded below sea level, so although it can be considered sea ice, it is not floating, and its melt would cause a sea level rise. Its surrounding ice shelves are "normal" floating sea ice.

/end pedantic mode

Feb 1, 2012 at 4:08 AM | Unregistered CommenterHaroldW

Okay so if Global warming is uniform across the planet

What are the ice levels doing in Norway Scotland Siberia the mountains in Africa and Asia and do they have ski resorts in New Zealand( There are snowy bits in Lord of the Rings)

And that isnt what im actually saying
Some one get a calculator and a pen and paper and actually WORKOUT the tonnage of ice etc and heat jules etc

See how much extra heat it actually takes to melt all the ice
and how much extra water that will that create and the added volume to the oceans
There by get the extra sea level

Its either a couple of milimetres or a couple of inches
Considering hoe deep and vast the oceans are its going to be a couple of Milimeters
Then from that you can calculate the land loss

There are some pretty clever people out there im not one of them so who work it out

I bet the mathematical genius brother of the FBI agent in Numbers or Sheldon Howard Raj and Leonard of Bang Bang Theory could work it out

Feb 1, 2012 at 11:13 AM | Unregistered Commenterjamspid

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