Archive for the ‘ice shelf’ Category


Rahmstorf (2009): Off the mark again (part 5), Variation of gamma

April 14, 2010

Another post on Vermeer’s and Rahmstorf’s 2009 PNAS paper, “Global sea level linked to global temperature.”   This time we consider the variation of gamma (γ) in equation 4 of part two.  The curious result will be that for γ>1 the temperature will continuously increase, while the sea level rise rate will continuously drop.

In Part 1, I laid out the basic problem.

In Part 2, I went into a little more detail on the math.

In Part 3, I gave a few examples that show some bizarre consequences that would result if equation were correct.

In Part 4, improbable parallel universes.

This is very simple. 

The plots below will show hypothetical temperatures that satisfy equation 4 of part 2, with all parameters equal, except γ.  But the fact that the temperature is derived from this equation is not really important.  The important thing is that the version with a faster increasing temperature has a decreasing sea level rise rate, and vice versa.

How can this be?

As before, these bizarre results are not my invention – they follow directly from Vermeer’s and Rahmstorf’s equation relating sea level rise rate to temperature.  The answer to the question is very simple:  Vermeer’s and Rahmstorf’s model does not make sense.  Their model causes realistic temperature scenarios to yield unrealistic sea level rise rates.

A future post will discuss Vermeer’s and Rahmstorf’s misguided concept of a “positive, but time-lagged, sea level response.”


Rahmstorf (2009): Off the mark again (part 4): Parallel Universes

April 12, 2010

Let’s consider Vermeer and Rahmstorf’s equation that relates sea level rise rate to temperature again.

You can read Vermeer and Rahmstorf’s PNAS paper (referred to as VR2009 for the rest of this post), Global Sea Level Linked to Global Temperature,  here.

In Part 1, I laid out the basic problem.
In Part 2, I went into a little more detail on the math.
In Part 3, I gave a few examples that show some bizarre consequences that would result if equation were correct.

As a reminder, here is their equation


  • H is the sea level, and dH/dt is the change in sea level per unit time (the sea level rise rate)
  • T is the temperature, and dT/dt is the change in temperature per unit time
  • a = 05.6+- 0.5 mm*a-1K-1
  • b = -49 +- 10 mm*K-1
  • To = -0.41 +- 0.03 K

Parallel Universes

Let’s think in terms of parallel universes, just for the fun of it.  Both Universes will be the same as the one we live in up to this point.  Starting in 2010 they will continue as the same universe with a hypothetical increasing temperature scenario for the planet earth.  I will choose a temperature scenario that satisfies equation 4, from part 2.

The advantage of this temperature scenario is that the increasing temperature yields a perfectly constant sea level rise rate when applied to VR2009’s equation (equation 1, above).  Other than that, there is nothing special about this scenario, but it is convenient to work with for illustrative purposes, and in and of itself uncovers some of the bizarre nature of VR2009’s model.

After another 30 years, our universe will bifurcate into two parallel universes.  One will continue to have an increasing temperature due to all the nasty undertakings of the human scum that occupies the planet.  The other will experience a divine halt to the temperature rise, probably due to the mercy of Gaia after receiving years or prayers of intercession from faithful environmentalists.  In this second universe, the temperature will become constant.

How will the sea level rises in these two universes compare?

Universe #1

Universe 1 Excel file link

Universe #2

Universe #2 Excel file link


Look closely at what happens in 2040, when the two universes split.  In Universe #1, where the temperature keeps increasing, the sea level rise rate remains constant.  But in Universe #2, where the temperature becomes constant, there is a sudden rise in the sea level rise rate.

Remember, this is a consequence of VR2009’s model, not my imagination.  How can this be possible?  It all comes down to VR2009’s model and the fact that they find the constant b in equation 1 to be negative.  They recognized the strangeness of this conclusion and attempted to explain away the counter-intuitive sign of b by saying that it points to a …

positive, but time-lagged, sea level response. That a negative b corresponds to a lag is easily seen… Several mechanisms could be envisaged for a delayed onset of sea-level rise after warming. For example, mass loss of ice can be caused by warm water penetrating underneath shelves, triggering their collapse and subsequent speed-up of outlet glaciers banked up behind the ice shelf. We cannot explore the causes of delay in more detail here, but note the statistical result is robust irrespective of causes.

So, in both universes, water was penetrating underneath the ice shelves.  Drop for drop, molecule for molecule, the water penetration was identical.  The condition of the ice shelves in the two universes were identical at the moment of bifurcation.  In the universe where the temperature continues to rise the ice shelves do not collapse, as evidenced by the fact that the sea level rise rate does not increase.  This is despite the fact that the increasing warmth would cause even more water to “penetrate underneath shelves.”   But in the universe where the temperature becomes constant, the ice shelf immediately starts to collapse, increasing the sea level rise rate.  OK, sure.

Conclusion (for now)

It’s too bad that VR2009 “cannot explore the causes of delay in more detail,” because I would love to hear how they explain the bizarre results that follow from their model.  My conclusion is that their model is bogus.  As such, it has no predictive power for sea level rise rates for the 21st century.


The Thermohaline Circulation Only Stops for Extreme, Unrealistic Models

June 4, 2009

Return to Criticisms of Al Gore’s “An Inconvenient Truth”

Gore gives a cartoon description of the ocean circulation system when he explains what has become known as the thermohaline circulation, or the meridional overturning circulation.  In his simplistic scenario the surface ocean current that flows north in the Atlantic, bringing warmth to northern Europe will be halted by melting ice from Greenland, subsequently throwing Europe into an ice age. 

Here is Gore’s explanation in his own words from the Inconvenient Truth movie:

The Earth’s climate is like a big engine for redistributing heat from the equator to the poles.  And it does that by means of ocean currents and wind currents.  They tell us, the scientists do, that the Earth’s climate is an non-linear system – just a fancy way they have of saying that the changes are not all just gradual, some of them come suddenly, in big jumps… And so, all those wind and ocean currents that have formed since the last ice age and have been relatively stable – they’re all up in the air – they change. 

And one of the ones they’re most worried about, where they’ve spent a lot of time studying the problem is in the the North Atlantic where the gulf stream comes up and meets the cold winds coming off the Arctic over Greenland and that evaporates the heat out of the gulf stream and the steam is carried over to western Europe by the prevailing winds and the Earth’s rotation.  But isn’t it interesting that the whole ocean current system is all linked together in this loop, they call it the ocean conveyor.

vlcsnap-324533And the red are the warm surface currents, the Gulf Stream is the best known of them.  But the blue represent the cold currents running in the opposite direction…

vlcsnap-32114Up in the North Atlantic, after that heat is pulled out, what’s left behind is colder water, and saltier water, because the salt doesn’t go anywhere. And so, that makes it denser and heavier.  And so that cold heavy dense water sinks at the rate of 5 billion gallons per second.  And then that pulls that current back south.ani-21

At the end of the last ice age as the last glacier was receding from North America the ice melted and a giant pool of fresh water formed in North America, and the Great Lakes are the remnants of that huge lake.  An ice dam on the eastern border formed, and one day it broke, and all that fresh water came rushing out, ripping open the St. Lawrence there, and it diluted the salty dense cold water, made it fresher and lighter so it stopped sinking, and that pump shut off.

 vlcsnap-549956-smallAnd the heat transfer stopped.  And Europe went back into an ice age for another 900 to 1000 years.  And the change from conditions like we have here today to an ice age took place in perhaps as little as ten years time.  So that’s a sudden jump.  Now, of course, that’s not going to happen again because the glaciers of North America are not there… Is there any other big chunk of ice anywhere near there…?  Oh, yeah [Gore says ominously, as the image pans to ice covered Greenland] we’ll come back to that one…

Later in the movie Gore tells us that Greenland is rapidly melting.  The point being that it will provide a massive amount of fresh water that will stop the the thermohaline conveyor and  “would raise sea level almost 20 feet if it ‘went,'” Gore tells us.  He tells us about water seeping to the bottom of the ice sheets where it “lubricates where the ice meets the bedrock” causing the ice to slide toward the ocean.

Then he shows a series of pictures purporting to show the amount of melting in Greenland.  Gore says…


“In 1992 they measured this amount of melting in Greenland … Ten years later this is what happened…And here’s the melting from 2005”


Hosing Experiments

But what if…?  What if there were a huge amount of low density fresh water dumped into the North Atlantic where the high density water is supposed to be sinking, just like the giant Canadian lake crashing through the barrier of ice the Gore told us about?  This possibility is explored with computer models known as  “hosing experiments.”  In a hosing experiment a model that simulates the ocean and atmosphere circulation patterns is modified to artificially dump huge amounts of extra fresh water, as if from a giant hose, into some location in the ocean.   It has been found that when enough fresh water is forced in, the circulation can be slowed, but rarely stopped

How much fresh water do the hosing experiments use to nearly stop the thermohaline circulation?  Typically (or here), they use one million cubic meters of fresh water per second, for 100 years!!!  (One million cubic meters per second has its own unit name: One Sverdrup or 1 Sv).  How does 1 Sv compare to, say, the rate of water flowing over Niagara Falls?

Niagara falls168,000 cubic  meters of water fall over Niagara Falls every minute.  That is about 2,800 cubic meters of water per second.  So one Sverdrup of water is the same as about 350 Niagara Falls!  (1,000,000 / 2,800  = 357).  So, roughly speaking, if 350 Niagara Falls were dumped into the oceans around Greenland continuously for 100 years, then we could expect to see a significant slow down of the thermohaline circulation.

River systems discharging into the Arctic Ocean.

River systems discharging into the Arctic Ocean.

How does one Sverdrup compare to the freshwater discharge of ALL the rivers emptying into the arctic ocean?  One Sverdrup of fresh water amounts to nearly 32,000 km3 of water per year  (1 Sv  x 106 m3 s-1/sv x (86,400 s/day) x (365 day/year) = 31,536 km3/year).  The total fresh water discharge from all rivers into the arctic is only about 4,300 km3 per year.  So, typical hosing experiments that nearly stop the overturning circulation add a water volume about 7 times the amount of water from all rivers discharing into the Arctic Ocean combined.

What about Greenland?

Hosing copyGore ominously implies that the amount of fresh water needed to turn off the overturning circulation is just waiting to pour off of  Greenland, due of course (drum roll), to CO2 induced anthropogenic global warming.   His pictures of Greenland, shown above, imply that about half of Greenland’s 2.8 million cubic kilometers of ice have melted in the 13 years between 1992 and 2005.  This is wildly misleading.  Only a miniscule fraction of the area shown in Gore’s Greenland images actually melts every year.   This is evidenced by mass balance studies, which show Greenland loses on the order of hundred cubic kilometers of ice every year,  which translates into a measly 0.003 Sverdrups.

100 km3 /year= 1011 m3/year

(1011 m3/year) / (365 days/year) / (86,400 seconds/day)
             = 3 x 103 m3/second
             = 0.003 Sv

Put another way, one Sverdrup of fresh water is 86.4 km3/day.  So the hosing experiments pouring in one Sverdrup put about as much fresh water into the ocean each day (86.4 km3) as Greenland provides in a year (100 km3).

But if Greenland actually started melting, by some extraordinary circumstance,  300 times faster, then it would yield 1 Sverdrup, or 1,000,000 cubic meters, of fresh water every second.  What would happen after 100 years of melting at that rate?  Well, that’s a trick question, because at a melting rate that gives 1 Sverdrup of freshwater Greenland would run out of ice in about 90 years.  This is because Greenland has only 2.85 million cubic kilometers of ice, and one Sverdrup of water is the same as about 31,500 cubic kilometers of water per year.  Ignoring the difference in density between ice and water, then 2.85 million cubic kilometers divided by 31,500 cubic kilometers per year gives 90 years.


You don’t hear as much about the threat of the collapse to the thermohaline circulation today as you did a few years ago.  This is because it has become recognized as being a very far fetched possibility, even by most alarmists who want to maintain a shred of dignity.  But I have a feeling we will not see this wildly exaggerated threat removed from new editions of Gore’s “An Inconvenient Truth” anytime soon.

Return to Criticisms of Al Gore’s “An Inconvenient Truth”