# The Greenland ice sheet isn't melting anywhere near as fast as you think.

A repeated assertion I've heard from many people who are worried about climate change is that the greenland ice sheet is going to melt in the near future - 20-30 years and that the whole world will sink. I think people have mistaken the statement that the arctic ocean could be ice free by 2050 with the statement tha the greenland ice cap will melt by 2050.

The greenland ice sheet won't melt by 2050. Here's why.

# NASA says' it's melting really quickly

Lots of people quote this NASA press release, Loss of ice is 220 cubic kilometers per year, or 264 billion gallons of water. The important questions are :-

### How big is the greenland ice sheet.?

Very. Wikipedia and other sources suggest about 2.85million cubic kilometres.

### How long will it take to melt at current rates

So, divide, 2 850 000 by 220 and you get 13000 years.

To put it another way, if the rate of ice melt in Greenland accelerates by a factor of 300 and remains at that level for the next 43 years the icecap will finish melting in 2050.

### Latent heat of ice

To melt greenland you need to provide enough energy for all the ice to melt. You need 334kJ/kg to melt ice. The ice sheet is about 2.85 * 10^6 km^3 = 2.85*10^15m^3 which is 2.85*10^18kg of ice. So that's pretty much 10^21kJ of energy. Let's suppose you paint it black and stick it in the sahara with the sun directly overhead. The surface area is about 1.7*10^12m^2 which nets you about 2x10^12kW. Divide one by the other and you get pretty much 5*10^8s = 16 years.

The more observant among you will notice that the sun doesn't shine at night, integrating out for over the whole day we get 1/4 the energy you do at peak which gives us 64 years.

To put it another way, were we to pick up the greenland ice sheet and relocate it to the sahara, paint it in a perfect absober, replace the atmostphere overhead with something as transparent as a vacuum, assuming the ice sheet temperature is 0C and we can dispose of all the water at 0C without accidently heating it up, and there is not a cloud for the next 64 years and we can distribute the suns energy perfectly evenly over 1700000000000m^2 we could melt the greenland ice sheet in only 50% more time than the scaremongers suggest.

A vague accounting estimate, for greenland being at 72 degrees latitude (30% of the sunshine), ice is reflected (80% reflected energy), you start scaling that estimate up towards 500 years. Fortunately the ice sheet doesn't radiate any energy away to space. Oh, hang on a minute...

### What about the gulf stream.

Wikipedia suggests the gulf stream supplies about 1.4*10^15W of heat. Assuming all that can be delivered to the greenland ice sheet with perfect efficiency we get to recycle the sahara argument but with a source energy flow of 1.4*10^12kW instead of 2*10^12kW. You would get to grow another ice sheet over northern europe though.

### D'uh. It's going to break up and float out to sea.

The distance from the centre of greenland to the sea is 550km. To do it in the 43 years we have remaning, it needs to crack in the centre and travel at a uniform speed of 12.7km/year towards the ocean in all directions.

There is a glacier in Greenland (Jakobshavn Isbrae) which has been measured moving this quickly at it's fastest point (2005), and Kangerdlugssuaq even faster (14.6km/s in the summer of 2005) for a short period.

In order for the ice sheet to disappear in time, the centre of the ice sheet needs to start moving now at the same rate as the fastest ice flow in the world. Since the rest of the ice sheet is in the way and gravity means you can't go over it, the whole ice sheet needs to start moving. This should be pretty obvious - by 2010 there will be a 75km wide ice free hole exactly in the middle of the Greenland ice sheet, by 2020 it will be 330km wide, 2030 584km wide, 2040 838km wide, 2050 1100km wide covering the whole of Greenland.

### How much did the sea level rise ?

220km^3 = 53miles^3. The ocean is about 360000000 square miles, we get 1.5*10^-7 miles = 0.2mm. Scary stuff indeed!

### Isn't that terrifyingly fast?

Maybe. 20000 years ago the sea level was 125m below what it is today, that's an average rise over the last 20000 years of 6mm/year, about twice as fast as the sea level is rising today. That doesn't necessarily mean the current rise isn't concerning though.

Many thanks to Nick Barnes for pointing out some errors, in particular regarding ice sheet flow.