Posts Tagged ‘arctic’


When was the last time this happened?

August 4, 2013

We are in the middle of the Arctic melt season.  The rate of sea ice melt is at it greatest from about mid-June (day 156) to about mid-August (day 216).  Thirty years ago, according to satellite data, the arctic lost about 5 million square kilometers of ice during this period.  For the last decade the arctic has lost closer to 6 million square kilometers of ice during this period.  That averages out to about 100,000 kilometers per day.  Of course, it recovers all, or most, of that area during the freezing season.  This point is illustrated in the follow image from Cryosphere Today (8/4/13, with my annotation).

Northern Hemisphere sea ice area 5

Now look closer.

Northern Hemisphere sea ice area 4

Notice that for the last 10 days there has been no drop in sea ice area. We would have expected a loss on the order of one million square kilometers!  Either something extraordinary is happening, or there is a problem with the satellite data.

When was the last time this happened this time of year?  This image shows the entire history of the arctic (which everyone knows really means back to 1979).  This is “unprecedented!”


Rahmstorf: Is it OK to call him an “alarmist” now?

May 9, 2012

Some folks never give up.  In the following video Stefan Rahmstorf says…

To me a tipping point in the climate system is like a sweet spot in the climate system, where a small perturbation can have a major, even qualitative effect.  It’s like a small change in temperature moving, for example, the Greenland Ice sheet beyond the point where eventually it will melt down all together…from about 2 degrees global warming there would be a risk of the complete meltdown of the Greenland Ice sheet…I think this two degree limit agreed in Cancun by the politicians may not be enough to prevent a dangerous interference in the climate system.

Now let’s be clear about this: a “complete meltdown” of the Greenland ice sheet would raise the planet’s sea level 7 meters (7000 mm).  The sea level rise rate today is about 3 mm per year and decreasing according to satellite data.  A rational reading the tide gauge data is even less.

I guess in Greenland ice must melt at -25°C.  Here is today’s temperature outlook…

Oh, I know, the scientifically sophomoric sophisticated will tell us all about the rapidly accelerating glaciers.  Well, their favorite journal, Science, throws a little icy cold water on their dreams of catastrophic nirvana.  In 21st-Century Evolution of Greenland Outlet Glacier Velocities ( T. Moon, et. al., Science, 4 May 2012, Vol. 336, pp. 576-578)  Moon et. al. produced “a decade-long (2000 to 2010) record documenting the ongoing velocity evolution of nearly all (200+) of Greenland’s major outlet glaciers.”  They found that in some regions there was a glacier acceleration (SEE! SEE!), but not very consistently over the last 10 years.  Here is their conclusion

Our observations have implications for recent work on sea level rise. Earlier research (33) used a kinematic approach to estimate upper bounds of 0.8 to 2.0 m for 21st-century sea level rise. In Greenland, this work assumed ice-sheet–wide doubling of glacier speeds (low-end scenario) or an order of magnitude increase in speeds (high-end scenario) from 2000 to 2010. Our wide sampling of actual 2000 to 2010 changes shows that glacier acceleration across the ice sheet remains far below these estimates, suggesting that sea level rise associated with Greenland glacier dynamics remains well below the low-end scenario (9.3 cm by 2100) at present. Continued acceleration, however,may cause sea level rise to approach the low-end limit by this century’s end. Our sampling of a large population of glaciers, many of which have sustained considerable thinning and retreat, suggests little potential for the type of widespread extreme (i.e., order of magnitude) acceleration represented in the high-end scenario (46.7 cm by 2100). Our result is consistent with findings from recent numerical flow models (34).

So, Rahmstorf is worried about a “complete meltdown of the Greenland ice sheet” which would lead to 7 meters (7000 mm) of sea level rise, but the data shows “sea level rise associated with Greenland glacier dynamics remains well below the low-end scenario (9.3 cm by 2100)” (93 mm by 2100).  Does being off by a factor of 75 (7000/93) qualify as “alarmist?”

By the way, when Moon says “Earlier research (33) used a kinematic approach to estimate upper bounds of 0.8 to 2.0 m for 21st-century sea level rise” he is talking about Kinematic Constraints on Glacier Contributions to 21st Century Sea-Level Rise (Pfeffer, et. al., Science, 5 September 2008, Vol. 321. no. 5894, pp. 1340 – 1343).  I discussed this paper at length two years ago in my “Reply to John Mashey.” (Still feeling smug, John?) 

And finally,  Moon’s last sentence says “Our result is consistent with findings from recent numerical flow models (34).”  He is talking about Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade (Price, et. al., PNAS, 31 May 2011, vol. 108 no. 22 pp. 8978-8983).    Price, et. al. say

The modeling conducted here and some reasonable assumptions can be used to make approximate upper-bound estimates for future SLR from GIS [Greenland Ice Sheet] dynamics, without accounting for future dynamical changes explicitly. As discussed above, numerous observations indicate that the trigger for the majority of dynamic thinning in Greenland during the last decade was episodic in nature, as the result of incursions of relatively warm ocean waters. By assuming that similar perturbations occur at regular intervals over the next century and that the ice sheet responds in a similar manner, we can repeatedly combine (sum) the cumulative SLR [sea level rise] curve from Fig. 4B to arrive at additional estimates for SLR by 2100. For example, if perturbations like those during the last decade recur every 50, 20, or 10 y during the next 100 y, we estimate a cumulative SLR from GIS dynamics by 2100 of approximately 10, 25, and 45 mm, respectively…Addition of the estimated 40 mm of SLR from changes in SMB [surface mass balance] by 2100 would result in a total SLR from Greenland of 85 mm by 2100.

Holy cow! Rahmstorf is telling us to be worried about 7000 mm of sea level rise due to the “complete meltdown of the Greenland ice sheet,” but Price et. al. say maybe 85 mm due to Greenland by 2100.


The End of the line for Kevin O’Neill

July 28, 2010

When I accepted Mr. O’Neill’s challenge

The North Pole has never been ice-free; not once in the history of the earth.

… and I can prove it. I’ll wager you $100 to be given to the other’s favorite charity.

I said I would give hm “opportunity to address my criticisms” of his proof.  On July 26th I asked Mr. O’Neill the following…

You have submitted a few short comments after my refutation. Shall I take these comments as your response to my refutation? If so, then I am ready to proceed.

Mr. O’Neill responded with…

If for some reason you are waiting for me to tell you to proceed in your rebuttal – then please proceed.

Mr. O’Neill’s opportunity to respond to my refutation of his “proof” is now over.

Readers can consider the aggregate of his comments dated July 22nd to July 27th to be his address of my criticisms.


I will give my conclusion before I rebut Mr. O’Neill’s comments, since most people will not want to read the boring details. 

Mr. O’Neill has not addressed my refutation of his “proof.”  Instead he has engaged in a sophist and sophomoric game centered around his claimed inability to associate a scalar value with a point.  I suspect that he will never concede defeat and pay the required $100 to Save The Children.  I will wait a week in the weak hope that his conscience will get the better of him.   After that, I will pay Save The Children the $100 myself to prevent them from being stiffed by Mr. O’Neill.  I will post a receipt when that time comes.

Mr. O’Neill has posted two other comments that remain in my moderation queue.  One of them is a 1500 word treatise on my supposed moral, mental and/or character deficiencies.  The other is a whiny diatribe about how I treated him unfairly (boo hoo) by pointing out that a journal article he cited actually supported my view.  Both of these comments will receive special treatment and be released in their entirety at some future date.

In the mean time, I do not feel obligated to provide a forum for the unending dribble of sophistry coming from Mr. O’Neill.  New comments from Mr. O’Neill will go to my moderation queue, and unless they end up in my special treatment page for Mr. O’Neill, then in all likelihood will end up being deleted. Mr. O’Neill has overstayed his welcome

I may still have a little bit of  fun with his “proof” in some later posts though.

If you are interested in boring details, have a strong cup of coffee and read on…

Therefore I proceed

I ended my refutation of Mr. O’Neill’s “proof” with the following…

O’Neill needs to do all of the three following things: he must prove my paleontological & geological evidence is wrong; he must show that his “proof” does not lead to bizarre consequences; he must show that Li/Lt is “undefined” (as he claimed in his proof) as opposed to “indeterminate.”

Mr. O’Neill flippantly dismissed my paleontological & geological evidence with the statement “The geology/paleontology stuff is just irrelevant.”  Sorry Mr. O”Neill, your dismissal does not counter my refutation of your proof.  On that basis alone I have already won the wager.

However, I will play along with his clumsy sophistry for the moment

First sophistry (equivocation)

Mr. O’Neill couches his “proof” in the language of math and physics.  He defines the North Pole as a “point” in the mathematical sense.  He also defines two properties of this point when he says “Li is L’s ice covered area and Lt is L’s total area.”  He creates a metric for the ice covered fraction at L by taking the mathematical ratio of Li and Lt when he says “To satisfy the definition of ‘ice-free’ Li/Lt must be < .15.”  He later simply asserts that “for any point L the quotient for Li/Lt is always undefined.”

Why is “the quotient for Li/Lt is always undefined?”  He doesn’t explain this in his “proof.”  In some of his comments which he says can serve as a rebuttal to my refutation, he says that Lt is simply undefined because L has no area.  He explains that area is not a property of a point, and therefore Lt is undefined. 

But wait, didn’t he personally define Lt as an AREA when he said “Lt is L’s total AREA.”  So, he personally defines Lt as an area, uses it in his “proof,”  and then claims Lt is undefined to conclude the validity of his “proof.”  This is an extraordinary case of equivocation (Lt is defined as an AREA early in the “proof” and claimed  to be undefined later in the “proof.”).

The absurdity of his “proof” would be clear to all when the mask of  equivocation is lifted.  Suppose  his “proof” said “Li is L’s  ice-covered area and Lt is undefined”  and “To satisfy the definition of ‘ice-free’ Li/Lt must be < .15.”

O’Neill can’t just deliberately create what he feels is a bogus metric (Li/Lt with Lt undefined) and then claim that since his metric is bogus the thing being quantified must be undefined.

Second sophistry (non-sequitur)

O’Neill claims that since his metric (Li/Lt) cannot quantify the thing he wants to quantify (surface density of ice), then the thing he wants to quantify must be undefined.  Why?  Does the supposed failure of his metric prove that all other approaches will also fail?  This is a non-sequitur.

Third, and most important sophistry

 By calling the North Pole a “point” he thinks that he has removed all scalar properties associated that point.  That is, he deliberately tries to confuse the difference between the properties of a point with the properties associated with a point.

The only properties of a point are the n coordinates that define it in an n-dimensional space.  However, there are an infinite number of properties that can be associated with a point.  So, for example, while temperature is not a property of a point, it can be associated with a point.  When we speak of the temperature at a point, we are not talking about a property of the point, but rather a property associated with the point.  Similarly, and more importantly for this discussion, the surface density of ice is not a property of a point, it is a property associated with a point.  The usefulness of any coordinate system is zero without the ability to associate properties with points.

scalar is a quantity that can be described by a single number (either dimensionless, or in terms of some physical dimension).  A scalar field is an n-dimensional space with a scalar value associated with every point in a that space.  Temperature as a function of position and surface density of ice as a function of position are simple examples of scalar fields.  The concept of a scalar field is intuitive to most people, but is summed up nicely here

In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure.

Note to Mr. O’Neill:  air pressure is force per unit AREA.  By your reasoning, air pressure cannot be defined at a point.  But, in fact  it is always defined at a point.

Mr. O’Neill’s sophistry denies both the intuitive and mathematically rigorous concepts of a scalar field.  Why? Because he denies the possibility of associating a scalar property (such as surface density or temperature) with a point simply because that scalar property is not a property of the point.  He seems to see some clever trap or paradox in his own blind spot of understanding. 

Fourth sophistry

Mr. O’Neill has a choice: he can either say that his proof requires a mathematical foundation, or it does not.   O’Neill couches his “proof” in the language of mathematics, with definitions of variables (albeit equivocating definitions) and mathematical ratios.  Why blow smoke with all the math when he could have simply argued that “the concept of a surface density of ice at a point is simply undefined and therefore cannot have ever been less than 0.15. QED”   He couldn’t make this simple argument because he cannot back it up – the concept of the surface density of ice associated with a point is easily defined.

Mr. O’Neill’s attempts to brush aside the use of L’Hopital’s rule to resolve an indeterminacy of the surface density of ice at a point.   In a statement that stands as a monument to his mathematical ignorance,  Mr. O’Neill says…

Parenthetically, and irrelevant as far as I can see, I suspect that L’Hopital’s rule would not apply since the denominator is a constant zero – I suppose the numerator is as well. So, even if we accepted your 0/0 equation, would L’Hopital’s rule apply since we’re dealing with two constants and not a converging series?

While L’Hopital’s rule can be a useful tool to judge the convergence of a series, it is by no means used exclusively or even mostly for  that purpose.  It is typically used to find the value of f(x)/g(x) at a value of x that yields an indeterminate form (such as 0/0 or infinity divided by infinity).  Mr. O’Neill’s argument against the use of L’Hopital’s rule in this instance can best be summed up as the fallacy of  “invincible ignorance” (seriously, see the Philosophical Society).”  Mr. O’Neill, go back and take a first year calculus class, then re-read my refutation of  your “proof.”

Fifth sophistry (tu quoque)

I am afraid this gets to the heart of the matter for Mr. O’Neill.  As I mentioned in my refutation of his “proof,” Mr. O’Neill seeks to claim some sort of moral victory by saying that in order for me to win the wager I must retract some dishonest or misleading claim that the North Pole is a “point” in the mathematical sense.  Of course, I never made such a claim, Mr. O’Neill’s ramblings about my pictures of submarines at the North Pole notwithstanding.

When another commenter (Charlie A, July 19, 2010 at 2:17 pm) mockingly criticized Mr. O’Neill’s “proof” by saying “Perhaps, just perhaps, there is a logical fallacy in the proof” O’Neill responded (July 19, 2010 at 11:20 pm) with the following …

“There’s no logical fallacy. What there is is a lesson: It’s stupid to define the North Pole as s point when discussing ice-free conditions in the Arctic – otherwise we get this sort of nonsense.”

When I accepted Mr. O’Neill’s wager, I defined the term North Pole as

North Pole. This means the area at which the axis of rotation exits the current Northern Hemisphere. It is not the magnetic pole. The North Pole, for the purposes of this wager, does not change with a magnetic reversal. The North Pole is not required to include the entire Arctic Ocean or the entire Arctic Basin (features that have not even existed through the whole “history of the [E]arth”).

Mr. O’Neill twists himself into a logical pretzel trying to show that this definition implies I have defined the North Pole as a point in the mathematical sense.  He comments (2010/07/22 at 4:58 pm)

Someone said,

…the area at which the axis of rotation exits the current Northern Hemisphere ..

A line intersecting a sphere would be …. a point?

 Get it?  I said “area” in the colloquial sense, and Mr. O’Neill claims I said “point” in the mathematical sense.  Oh well, it doesn’t really make any difference.  Mr. O’Neill’s naive arguments about undefined values and the inapplicability of L’Hopital’s rule fail even if the North Pole is defined as a point the the mathematical sense.

In other words, Mr. O’Neill justifies making what he admits is a “stupid” argument because he claims I had already made the same argument (which, of course, I have not).  A pathetic case of tu quoque.


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