How Much Energy Is Required To Melt All The Ice In Greenland?
Posted by pwl on March 12, 2012
The Wicked Greenland Soothsayers of the West say “I’m Melting”, now “How much energy is required to melt all the ice in Greenland?”
by pwl
How much energy is required to melt all the ice in Greenland?
How much ice is there in Greenland?
“The Greenland ice sheet (Kalaallisut: Sermersuaq) is a vast body of ice covering 1,710,000 square kilometres (660,235 sq mi), roughly 80% of the surface of Greenland. It is the second largest ice body in the world, after the Antarctic Ice Sheet. The ice sheet is almost 2,400 kilometres (1,500 mi) long in a north-south direction, and its greatest width is 1,100 kilometres (680 mi) at a latitude of 77°N, near its northern margin. The mean altitude of the ice is 2,135 metres (7,005 ft).[1] The thickness is generally more than 2 km (1.24 mi) (see picture) and over 3 km (1.86 mi) at its thickest point. It is not the only ice mass of Greenland – isolated glaciers and small ice caps cover between 76,000 and 100,000 square kilometres (29,344 and 38,610 sq mi) around the periphery. Some scientists predict that climate change may be about to push the ice sheet over a threshold where the entire ice sheet will melt in less than a few hundred years. If the entire 2,850,000 cubic kilometres (683,751 cu mi) of ice were to melt, it would lead to a global sea level rise of 7.2 m (23.6 ft).”
Wikipedia on Greenland Ice Sheet.
2,850,000 cubic kilometers of ice in Greenland.
So claim of a 100 years to melt 2,850,000 cubic kilometers of ice. Hmmm… we’ll get back to that.
How much energy to melt ice?
“When ice melts, it absorbs as much heat energy (the heat of fusion) as it would take to heat an equivalent mass of water by 80 °C, while its temperature remains a constant 0 °C.” – wikipedia on ice
Ok, that’s very cool, it takes a lot of energy to melt ice. Pardon the pun.
“The enthalpy of fusion is the change in enthalpy resulting from heating one mole of a substance to change its state from a solid to a liquid. The temperature at which this occurs is the melting point. The enthalpy of fusion is a latent heat, because during melting the introduction of heat cannot be observed as a temperature change, as the temperature remains constant during the process. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion, while the molar heat of fusion refers to the enthalpy change per amount of substance in moles. The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because the molecules in the liquid experience weaker intermolecular forces and have a larger potential energy. When liquid water is cooled, its temperature falls steadily until it drops just below the freezing point at 0 °C. The temperature then remains constant at the freezing point while the water crystallizes. Once the water is completely frozen, its temperature continues to fall.
…
To heat one kilogram (about 1 litre) of water from 283.15 K to 303.15 K (10 °C to 30 °C) requires 83.6 kJ.
However, to melt ice and raise the resulting water temperature by 20 K requires extra energy. To heat ice from 273.15 K to water at 293.15 K (0 °C to 20 °C) requires:
(1) 333.55 J/g (heat of fusion of ice) = 333.55 kJ/kg = 333.55 kJ for 1 kg of ice to melt
PLUS
(2) 4.18 J/(g·K) = 4.18 kJ/(kg·K) = 83.6 kJ for 1kg of water to go up 20 K
= 417.15 kJ
Or to restate it in everyday terms, one part ice at 0 °C will cool almost exactly 4 parts water at 20 °C to 0 °C.”
Wikipedia on Enthalpy of fusion.
Ok, so we need to know the temperature of the ice in Greenland in order to calculate how much energy it takes to melt it. Most likely it’s not all one temperature. It must vary.
We can simplify for starters assuming the ice is 0c.
2,580,000 cubic kilograms of ice is a mass of 2.85×10^18 kilograms (wolframalpha.com/input/?i=2850000+cubic+kilometers+ice+in+kilograms.).
Using equation (1) above we find that 333.55 kJ for 1 kg of ice to melt and we have 2.85×10^18 kg of the darn stuff which means that to melt it we need to input 333.55 kJ * 2.85×10^18 kg which is 9.51×10^20 kg kJ (kilogram kilojoules). That’s a lot of energy required.
9.506×10^20 kg kJ to melt all the ice in Greenland. For those challenged by scientific notion, that is 950,600,000,000,000,000,000 kJ to melt the 2,580,000 cubic kilograms of ice.
Wolfram Alpha reports that that amount of energy, wolframalpha.com/input/?i=%282.85×10%5E18%29+*+%28333.55+kJ%29, is:
3) ~1.9 x estimated energy released by the Chicxulub meteor impact;
4) ~24 x 2003 estimated energy in world’s total fossil fuel reserves;
5) ~37 x 2003 estimated energy in world’s coal reserves.
Ok, that is a huge amount of energy.
Could we intentionally melt all the ice in Greenland if we wanted to?
How?
“Nukes of course! They are the practical answer to every mega engineering problem. Wikipedia informs us that approximately 2,100,000 TJ (2.1 * 10^6 terajoules) of energy has been released by all the nukes ever tested by humans. Converting terajoules to kilojoules is done by multiplying by 10^9, that’s then ~2.1 x 10^15 kJ of energy from all nukes detonated on, above or in the Earth/Ocean.”
How could we melt enough ice for a 20ft rise in sea levels.
So all the nukes every detonated generated ~2.1×10^15 kJ of energy and it would take 9.506×10^20 kJ to melt Greenland. Wow, we couldn’t do it with all the nukes ever detonated!!! We’d need 452,677 (4.527×10^7) times as many nukes!!! That’s a SIX ORDERS of MAGNITUDE larger amount of energy required! We don’t even have enough nukes to do the job.
Does Mother Nature have enough energy in the Earth System to melt that much ice? Over what time period?
Note that the volume of ice in Greenland would drop the temperature of four times the volume of water at 20c to 0c with this melting. What effect would that have?
Is there any physics that would have the ice melt faster? How much more energy is required? What if it’s flowing water over the ice? Does that make it melt faster? It would still need the same amount of energy would it not? Ice causes the air temperature to be cooler thus limiting the rate of melting further.
About the only way that we could melt all the ice in Greenland is to maneuver an asteroid the size of the Chicxulub and get it to drop on Greenland. Baring unpleasant side effects of doing that it would get the job done quickly. No doubt about that.
So how can Mother Nature do this? Where does the Earth Climate System have a spare 9.506×10^20 kJ kicking around?
The Climate Scientists claim that it could do that in 100 years? Really? There’s really 9.506×10^18 kJ of extra energy kicking around in the Earth’s Climate System each year for a 100 years to do that? Really? Please oh where are you energy?
So if the Earth’s atmosphere did warm up and Greenland started melting like crazy, four times the volume of water that melted would drop from 20c to 0c in the process and that would alter the temperature of the oceans on a global scale which would cool the planet and stop or dramatically shift the atmospheric temperatures likely enough to stop the warming. So maybe this is part of the climate negative feed back system?
All this from a desire to do a back of the envelop calculation. Damn us system scientists and engineers, always with our back of the envelop calculations.
Peter
Originally posted as a comment here: wattsupwiththat.com/2012/03/12/gosh-really/#comment-920967.
Truthseeker said
How dare you introduce logic and mathematics into this debate.
You are a bad person … but I like you.
Pete of Perth said
How can these modellers – reviewers get it so wrong? Surely someone amongst the we’re all going to die camp have studied chemistry / physics / etc were the latent heat of fusion of ice is taught at high school and up. Maybe the curriculum has changed since I was in highschool in the 70s.
pwl said
[;)]
pwl said
Excellent questions that need to be answered.
Rosco said
How can these modellers – reviewers get it so wrong?
Easy ! They can’t even get a correct interpretation out of their own model energy balance.
They say at the top of atmosphere there is a “balance” of energy such that incoming solar energy = outgoing longwave IR.
OK
Then they present an equation like solar radiation (w/sqm) x ( 1 – albedo) x area of disk illuminated (pi x r^2)
=
Effective temperature ( sigma x T^4) X area of sphere ( 4 x pi x R^2).
What this really says in a nutshell is that for balance when the energy is illuminating a disk shape the whole sphere only needs to radiate a quarter of the incoming energy to achieve balance – see the 4 x factor is on the outgoing side.
Then they confuse themselves, the poor dears, by assuming the solar energy is one quarter of the solar constant.
But this is backwards – the outgoing longwave IR is numerically one quarter of the incoming solar radiation not the way they claim.
They seem to be too dumb to see their original formulation of an energy balance DEMANDS the solar radiation is 4 times the outgoing longwave IR.
Yet in every “calculation” these people make the first thing they do is reduce the solar radiation by 4 then tell us how clever they are.
I see no justification for using one quarter of the solar radiation in any calculations other than to demonstrate that because of geometry a sphere radiates one quarter of the numerical strength of the illuminating radiation – there is no way anyone who thinks about can justify the one quarter insolation theory.
And don’t tell me it is an average without explaining how the solar radiation knows how to spread all around the globe and sneak in under the cover of darkness.
DavidR said
It takes 3.34 * 10^17 joules to melt 1 cu Km of ice. So it would take 10^24 joules to melt the Greenland ice cap. This is about 3 months total energy from the sun or 0.25% of the total energy over the century.
The decline in the arctic sea ice cap will lower the albedo of the earth sufficiently to add this amount of energy into the global system. On top of this the increase in temperature as a result of AGW will add far more energy into the system. There is no doubt that the required energy will be abundantly available over the next century, the question is where it will have an impact.