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Sunday, November 25, 2012

Greenland Melting

I suspect that the  melt rate of Greenland in the years to come and hence it's effect on sea level will prove to be another little surprise from Gaia.  Having said that, I am only applying simple high school physics to a horribly complex phenomenon (the weather patterns in the Arctic) so add as many pinches of salt as you see fit as you read on.

Just to the north of Greenland we have the Arctic Ocean and as anyone who is following the situation will tell you, the floating ice is melting 'rather quickly'.  This summer  caught almost all the predictors of ice melt by surprise once again.  The ice was already melting at a rate equal to the previous most extreme year when on Aug6, 2012 a hurricane formed and sent the ice extent graph plummeting.  Climate change deniers site this hurricane as a once off, freak event.  Boy! are they in for some surprises.

Ice extent reaches its minimum each year around September 15.  Some scientists who are prepared to say it as they see it instead of hedging their bets, predict that  September 15, 2016  will see a virtually ice free Arctic Ocean.  Following 2016, with various up and down fluctuations, it is predicted that an open Arctic ocean will occur earlier and earlier each year.

Since open water absorbs most of the solar radiation falling on it instead of reflecting it back into space, the Arctic Ocean is becoming a giant solar collector.  The question is what mechanism might transfer this heat to the Greenland ice sheet and cause vastly increased melting.  There are a few bits and pieces we have to look at first.  Let's have a look at Katabatic winds for a start.

For the sake of illustration, let's assume that the whole Greenland Ice block is at 00C.  An air mass moves over Greenland which is also at 00.  Nothing happens.  The ice neither warms or cools the air and the situation is stable.  Then an air mass of 100C moves over Greenland.  The air in contact with the ice is cooled, shrinks, becoming more dense than the surrounding air and starts to flow down slope.  We have a Katabatic wind and since air is flowing down the flanks of Greenland, it sucks more air from it's surroundings to, in turn, be cooled and  flow down slope.  Now an interesting phenomenon kicks in.  If you have ever pumped up a bicycle tire with a hand pump, you will have noticed that the pump heats up where the flexible tube connects to the pump.  For the physics purists, work has been done on the air as it is compressed and this work shows up as warmed air.  The same thing happens when you compress air by taking it to lower altitudes.  This is called the Adiabatic Lapse rate and it is 9.80C per vertical kilometre*.  The  very top of the Greenland Ice sheet is 3.7km above sea level so a body of air falling from the peak to sea level without gaining or loosing heat to it's surroundings, would heat up by 360, Of course this doesn't happen and if it did, it would stop the Katabatic wind as the air warmed and became equal in temperature to the surrounding air.  What actually happens is that this heat is given up to its surroundings; namely to the ice !!!  Next, let's have a look at hurricanes.

* Note - the dry lapse rate is applicable when talking about descending air.

In the open oceans of the tropics, the sea surface must be above 250C  in order for a hurricane to form.  Storms are caused by rising air reaching the dew point (temperature at which the water vapour in the air begins to condense into water).  Each gram of water uses 540cal* of heat to evaporate.  It  gives out exactly the same amount of heat when it condenses.  Just to put the whole thing into context, to heat a gram of water by one degree requires one calorie so you need 100 calories to raise a gram of 00 water to boiling.  While we are at it, the heat needed to melt one gram of ice is 80 calories.  We will need these figures a little later.  So back to the formation of a tropical hurricane.

*Any physics purist will tell you I should be using SI units.  I chose to use calories because they are defined in terms of the heat needed to raise the temperature of a gram of water by one degree C and so are easier to get your head around in this context.

With minor perturbations, the whole extent of the open tropical ocean is at more or less the same temperature.  Say the water is a little warmer at one point and this causes the air above it to rise.  If this air reaches the dew point, heat will start to be given out as the water vapour condenses into liquid water,  accelerating the air upward.  Air then rushes in along the surface of the sea to replace this air and is given a counter clockwise spin (in the Northern Hemisphere) by the Coriolis effect.  It depends on how much water vapour is in the air whether this will simply develop into a thunder storm or a hurricane and apparently, 25 degree  water is the border between thunder storms and hurricanes because of the amount of water vapour that the warmer water can put into the air.  As air flows into the centre of the weather system, it picks up water vapour from the ocean and this continues to power the hurricane.  What is important here from our point of view is that all the power of the Hurricane comes from the "suck" at the middle of the hurricane.  Incidentally, the effect of Coriolis is relatively weak near the equator.  A body of air travelling a kilometer is only coming a few tens of meters nearer to the axis of the earth (the spinning skater is only pulling in her arms a little)

The situation in temperate and arctic zones is quite different.  The pressure in the centre of the hurricane that occurred this summer (Aug6,2012) in the Arctic was 964mb which puts it right on the border between a category 2 and a category 3 hurricane.  The surface water temperature was under 10 degrees.  So what was happening.

What actually causes a hurricane is the pressure gradient from areas adjacent to the developing weather pattern  to centre of the storm.  In a tropical hurricane in a big open ocean, all the gradient is due to the suck at the middle of the storm.  In the Arctic, if you have a high pressure system, say, on adjacent land, the gradient can be strong enough to cause a hurricane.* So why are hurricanes important.

*There may be another factor at work here.  The Coriolis effect increases, the closer you are to the poles.  This could give an extra spin to a cyclonic system.

Hurricanes pump heat up into the atmosphere.  They pump this heat at a couple of orders of magnitude greater than, say, thunder storms and even thunder storms are pretty narly tranmitters of energy.  Remember that 540cal that is needed to evaporate a gram of water, which is released when the water vapour condenses back into water.  Here you have  the heat in the ocean evaporating water which is sucked upwards until it starts to condense and gives out its heat into the atmosphere.  Water falls out of the sky leaving much of its heat behind in the air*.  Here we are talking, not about radiation or conduction which are pretty gentle methods of heat transfer, but rather mass transfer (convection process) which  can move much greater amounts of heat.  Two more factor and we can tie all this together.

* heat left in the water goes back to the ocean

When a low pressure system (storm) sidles up to the coast of Greenland, it induces katabatic winds *  down the slopes of Greenland.  This is not so surprising when you think about it.  You have a weather system which is pushing heat up into the atmosphere, probably resulting in air over the adjacent slopes of Greenland which is warmer than the ice.  As mentioned, it is necessary that the air body over the ice is warmer than the ice, for Katabatic winds to form.  In addition, this low pressure system just off the coast is sucking on the air that is flowing down the slope. And finally:

* See the section on "Impacts"in this link.

Hurricanes in the Atlantic apparently tend to follow along the temperature difference between the Gulf Stream and the surrounding cooler water.  I haven't quite got my head around how this works but for now I'll just accept it as fact.  In the Arctic, a hurricane will apparently follow along the edge of the ice pack.  In other words, the ice pack which is still quite solid off the Northern coast of Greenland will hold Arctic Hurricanes off at arms length.  What happens when this ice pack is finally gone a few years hence.

Hurricanes are more and more likely to form in the Arctic as the ocean becomes ice free earlier and earlier and hence absorb more energy.  Add to this that there is less and less ice to keep the water cool as it melts.  (Once the ice cube in  your drink is all melted, you drink warms up rather rapidly).

  With no ice pack protecting the north coast of Greenland, the hurricane can get  up close and personal to the coast of  Greenland.  We have a whole new order of magnitude of heat being pumped up into the atmosphere right beside the ice sheet and this upward flow of warmed air, potentially coupling with katabatic winds flowing down the slopes of Greenland melting the ice.  One additional little wrinkle in this story; a tight little Walker Cell.

You remember we said that to melt a gram of ice takes 80cal and that when a gram of water vapour condenses, it gives out 540g of heat.  In other words, if all the heat from the condensation of one gram of water vapour was applied to ice, it could melt just under 7 grams of ice.  I suspect we are going to have another little surprise regarding our estimates of how fast the Greenland ice sheet will melt.


John McCormick said...

William, thanks for that easy to follow lesson.

One observation: last paragraph;

"You remember we said that to melt a gram of ice takes 80cal and that when a gram of water vapour condenses, it gives out 540g of heat."

I believe you meant 50 cal.

John McCormick

William Hughes-Games said...

Hi John
I think I have it right. Have a look at this site

jimvj said...

Very good explanations. One small request: Please specify F or C when indicating temperature. The word 'degrees' is entirely superfluous. And by itself is ambiguous.

William Hughes-Games said...

Hi Jim
At the start of paragraph 5, I mention 0 degrees C and just mentioned degrees following this. I had almost forgotten that some people still use F in scientific discussion. Wasn't this the reason one of your rockets crashed. Some of the designers were using SI units and some the antiduluvian system you use in America. It really is time for America to come up into the modern world.