On Being the Wrong Size

Guest Post by Willis Eschenbach

This topic is a particular peeve of mine, so I hope I will be forgiven if I wax wroth.

There is a most marvelous piece of technology called the GRACE satellites, which stands for the Gravity Recovery and Climate Experiment. It is composed of two satellites flying in formation. Measuring the distance between the two satellites to the nearest micron (a hundredth of the width of a hair) allows us to calculate the weight of things on the earth very accurately.

One of the things that the GRACE satellites have allowed us to calculate is the ice loss from the Greenland Ice Cap. There is a new article about the Greenland results called Weighing Greenland.

Figure 1. The two GRACE satellites flying in tandem, and constantly measuring the distance between them.

So, what’s not to like about the article?

Well, the article opens by saying:

Scott Luthcke weighs Greenland — every 10 days. And the island has been losing weight, an average of 183 gigatons (or 200 cubic kilometers) — in ice — annually during the past six years. That’s one third the volume of water in Lake Erie every year. Greenland’s shrinking ice sheet offers some of the most powerful evidence of global warming.

Now, that sounds pretty scary, it’s losing a third of the volume of Lake Erie every year. Can’t have that.

But what does that volume, a third of Lake Erie, really mean? We could also say that it’s 80 million Olympic swimming pools, or 400 times the volume of Sydney Harbor, or about the same volume as the known world oil reserves. Or we could say the ice loss is 550 times the weight of all humans on the Earth, or the weight of 31,000 Great Pyramids … but we’re getting no closer to understanding what that ice loss means.

To understand what it means, there is only one thing to which we should compare the ice loss, and that is the ice volume of the Greenland Ice Cap itself. So how many cubic kilometres of ice are sitting up there on Greenland?

My favorite reference for these kinds of questions is the Physics Factbook, because rather than give just one number, they give a variety of answers from different authors. In this case I went to the page on Polar Ice Caps. It gives the following answers:

Spaulding & Markowitz, Heath Earth Science. Heath, 1994: 195. says less than 5.1 million cubic kilometres (often written as “km^3”).

“Greenland.” World Book Encyclopedia. Chicago: World Book, 1999: 325 says 2.8 million km^3.

Satellite Image Atlas of Glaciers of the World. US Geological Survey (USGS) says 2.6 million km^3.

Schultz, Gwen. Ice Age Lost. 1974. 232, 75. also says 2.6 million km^3.

Denmark/Greenland. Greenland Tourism. Danish Tourist Board says less than 5.5 million km^3.

Which of these should we choose? Well, the two larger figures both say “less than”, so they are upper limits. The Physics Factbook says “From my research, I have found different values for the volume of the polar ice caps. … For Greenland, it is approximately 3,000,000 km^3.” Of course, we would have to say that there is an error in that figure, likely on the order of ± 0.4 million km^3 or so.

So now we have something to which we can compare our one-third of Lake Erie or 400 Sidney Harbors or 550 times the weight of the global population. And when we do so, we find that the annual loss is around 200 km^3 lost annually out of some 3,000,000 km^3 total. This means that Greenland is losing about 0.007% of its total mass every year … seven thousandths of one percent lost annually, be still, my beating heart …

And if that terrifying rate of loss continues unabated, of course, it will all be gone in a mere 15,000 years.

That’s my pet peeve, that numbers are being presented in the most frightening way possible. The loss of 200 km^3 of ice per year is not “some of the most powerful evidence of global warming”, that’s hyperbole. It is a trivial change in a huge block of ice.

And what about the errors in the measurements? We know that the error in the Greenland Ice Cap is on the order of 0.4 million km^3. How about the error in the GRACE measurements? This reference indicates that there is about a ± 10% error in the GRACE Greenland estimates. How does that affect our numbers?

Well, if we take the small estimate of ice cap volume, and the large estimate of loss, we get 220 km^3 lost annually / 2,600,000 km^3 total. This is an annual loss of 0.008%, and a time to total loss of 12,000 years.

Going the other way, we get 180 km^3 lost annually / 3,400,000 km^3 total. This is an annual loss of 0.005%, and a time to total loss of 19,000 years.

It is always important to include the errors in the calculation, to see if they make a significant difference in the result. In this case they happen to not make much difference, but each case is different.

That’s what angrifies my blood mightily, meaningless numbers with no errors presented for maximum shock value. Looking at the real measure, we find that Greenland is losing around 0.005% — 0.008% of its ice annually, and if that rate continues, since this is May 23rd, 2010, the Greenland Ice Cap will disappear entirely somewhere between the year 14010 and the year 21010 … on May 23rd …

So the next time you read something that breathlessly says …

“If this activity in northwest Greenland continues and really accelerates some of the major glaciers in the area — like the Humboldt Glacier and the Peterman Glacier — Greenland’s total ice loss could easily be increased by an additional 50 to 100 cubic kilometers (12 to 24 cubic miles) within a few years”

… you can say “Well, if it does increase by the larger estimate of 100 cubic km per year, and that’s a big if since the scientists are just guessing, that would increase the loss from 0.007% per year to around 0.010% per year, meaning that the Greenland Ice Cap would only last until May 23rd, 12010.”

Finally, the original article that got my blood boiling finishes as follows:

The good news for Luthcke is that a separate team using an entirely different method has come up with measurements of Greenland’s melting ice that, he says, are almost identical to his GRACE data. The bad news, of course, is that both sets of measurements make it all the more certain that Greenland’s ice is melting faster than anyone expected.

Oh, please, spare me. As the article points out, we’ve only been measuring Greenland ice using the GRACE satellites for six years now. How could anyone have “expected” anything? What, were they expecting a loss of 0.003% or something? And how is a Greenland ice loss of seven thousandths of one percent per year “bad news”? Grrrr …

I’ll stop here, as I can feel my blood pressure rising again. And as this is a family blog, I don’t want to revert to being the un-reformed cowboy I was in my youth, because if I did I’d start needlessly but imaginatively and loudly speculating on the ancestry, personal habits, and sexual malpractices of the author of said article … instead, I’m going to go drink a Corona beer and reflect on the strange vagaries of human beings, who always seem to want to read “bad news”.

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Some time ago I did a graph of the Greenland’s temperature anomalies (ref 1950)
http://www.vukcevic.talktalk.net/LFC10.htm

Geoff Shorten

Willis, the paragraph beginning with ‘That’s my pet peeve’ should have 200 km^3 rather than 200 tonnes I think.

James Allison

Hi Willis. Corona is good or maybe a Stella but either choice needs the little slice of lemon squeezed into the bottle neck.

Julian Braggins

Good to see things put in proper perspective. I think there is a typo in the paragraph opposite “Lukewarmers” in the r/h column, should be 200 km^3, not 200 tonnes ?

Figures don’t lie, but liars do figure…
Make me want to call for a global day of OooooooooOOOooooooo[!]
This article, like many on WUWT, is exceptional educational material for our kids, that they might see through the #AGW #AGWC farce.
Ignorance breeds fear, understanding breeds confidence.
Thanks for writing this article Willis
and for posting it Anthony!
Going to RT with #AGWC hashtag…!

Andrew

Good discussion of the problems that a lack of context often causes in the climate change debate. Most journalists and politicians wouldn’t know an order of magnitude if it hit them in the head.
For correctness though –
“The loss of 200 tonnes of ice per year…” should read “The loss of 200 gigatonnes of ice per year…”

Patrik

Hear, hear, Will!
What you write here actually needs to be repeated time and time again.
A few months ago I asked on RealClimate how come they where worried about ice loss, since all available figures, trends etc. tell us that it will take 10-20 000 years before all ice on earth has melted.
Gavin answered: “…it’s irrelevant.”
Of course it is, if you want to live your life in fear. 🙂

Al Gore's Holy Hologram

What about the garbage going around for the last 15 years that the Amazon is losing a football pitch worth of trees every second? At that rate the jungle would have gone years ago but it’s still there in pretty good shape.

Capn Jack

Willis, I suggest a lemon twist in the neck.
No point getting all ugly and pissed, over a melting ice block.
Now if it was the ice block keeping the corona kool in the esky, that is something worth real emotion. But it’s not, Greenland has melted before, long before Gracie.
(I don’t know if you heard, but Santas homes was gonna be a canoe about now, but it’s not).
Cheers. 😉

Evan Jones

Yeah, they used to tell us in hushed voices that the Amazon rain forest was being destroyed at the rate of the area of Rhode Island every year.

Chris

Human beings always want to read ‘ bad news’. Absolutely. A few years ago a British TV news reporter complained that there was never any ‘good news’ on TV. There was a roar of protest from the media. Apparently ‘good news’ is not news!

vigilantfish

I wish my fits of spleen were as entertaining and informative as yours, Willis. Thanks for doing the number crunching and giving us some perspective on this. Of course, one wonders how long Greenland will continue to lose ice mass, and whether a reversal of trends would be seen as “good.”

spangled drongo

Willis
Thanks for pointing out the GRACE error bars. Always wondered.
If that is the case how accurate is satellite SLR measurement do you think?

toby

Of course it is only six years of evidence, but taken with all the other peices of evidence, it IS bad news. Like this:
http://www.nature.com/nature/journal/v465/n7296/abs/nature09043.html

Ian H

You might want to fix the error before everyone uses it as an excuse to jump all over you.
A cubic kilometre weighs a lot more than a tonne. A cubic metre of water weighs a tonne.
Ice is a little less dense, but a cubic kilometre of ice would weigh just a tad less than a billion tonnes.
Oops.

Temperature record from Greenland:
http://data.giss.nasa.gov/cgi-bin/gistemp/gistemp_station.py?id=431042500000&data_set=1&num_neighbors=5
Station composite from all Greenland stations:
http://climexp.knmi.nl/data/icrutem3_300-340E_55-85N_na.png
There really was 15-year warming (which leveled in the meantime), but there was exactly the same warming in 1910-1945 and present temperatures are on the same level as in 40ties. Typical that such graph is NEVER presented in all those catastrophic visions about Greenland.

tty

In any case that 10% error estimate is wildly optimistic. The problem is that to estimate the ice loss you also have to be able to estimate the vertical movement of the rock bed beneath the ice. Conservatively estimating that the rock is three times denser than ice that error estimate means that the vertical movement of the glacier bed has to be exact to within 3 millimeters/year, and even that only if there are no other sources of error.
Since the isostatic movement of the glacier bed is modelled based on a very few GPS-measured points beyond the edge of the ice cap, mostly in southern Greenland, and that there is also evidence of active tectonics under the ice in northern Greenland that error estimate is completely unrealistic.

David C

Good piece Willis, but I think you have a typo – 200 tons for 200 cubic km.

AC of Adelaide

Dont want to be the first to ask when you are having your seniors moment but …
“That’s my pet peeve, that numbers are being presented in the most frightening way possible. The loss of 200 tonnes of ice per year is not “some of the most powerful evidence of global warming”, that’s hyperbole. It is a trivial change in a huge block of ice.”
Shouldnt that be 200 km^3 ?

Jerry

Willis said

The loss of 200 tonnes of ice per year is not “some of the most powerful evidence of global warming”, that’s hyperbole. It is a trivial change in a huge block of ice.

In the article you talked about 200 cubic kilometres. As far as I recall a cubic km of ice weighs a bit more than a tonne. Perhaps the cubic km or the tonne figure are wrong?

Spector

From my grade-school days, I seem to remember noticing several occasions that first-grade boys who saw water leaking out of the sprinkler system valve-box would be worried that this seeping flow would eventually flood the world.

Ulric Lyons

When can we start farming there again? best to get in quick, as a good thing never lasts forever.

I wonder how much of this is lost by calving of icebergs, which would perhaps then be ‘instantly’ lost from the icecap mass once they are a certain distance from the coast, and how much is from surface and peripheral ‘melt’.
Great stuff Willis. I like reading things that make me think.

DavidB

The most useful way of indicating the importance of the ice melt would be to say what effect it has on sea level. Taking a rough value of 350 million square km for the sea surface of the earth, 200 cubic km would be spread very thin.

Inspiring – a great post Willis. See if I can send you something.

Johan van der Laan

First, thanks, Anthony for the great blog! Here in Holland most people are brainwashed by the AGW-politicians, AGW-journalists’ and AGW-managers. It’s a relief to folllow your blog, and the comments of your readers.
I would like to make some simple comments about the melting of the Greenland Iceshield in ‘presentday’s worldclimate’.
Maybe it’s trivial, but anyway.
I’m always very suprised when the icemelting of Greenland is used as THE argument by the Gore adepts to prove AGW.
I think, on the contrary, that it would be very weird if Greenland didn’t melt. Regions on the SAME latitude, like Finland, Siberia or Alaska have lost their iceshield many thousand years ago because of their continental climate (hot in the summerseason).
Greenland hastens after because of its surrounding seaclimate (cool summers), but will ultimately also lose most of its ice remnants of the glacial iceshield, if we stay in the interglacial era long enough. Its to easy to blame AGW for the melting ,its just postponed melting because of Greenlands cool seaclimate at its shores. Such an icy spot that far from the real pole is doomed to melt away. Nothing special. Only the speed of the melting will vary eventually with cold and warm periods, like the Little Iceage or the Medieval Warm Period. Probably is the melting on the peninsula of West Antarctica of the same order (also about 30 degrees from the real pole and in ‘seaclimate’.
As a consequence sealevel will rise a few inches this century. Again, nothing special.

STEPHEN PARKERuk

i have told them a million times not to exaggerate!

anna v

Some people say we are overdue the onset of the next ice age, some say the slide has already started, looking at something like this :
http://c3headlines.typepad.com/.a/6a010536b58035970c0128766b0364970c-pi
and some think there may be some hundreds of years till the next one.
I have found the animation provided by Anthony very instructive. The only true climate prophecy is that an ice age will come. Certainly before the next ten thousand years.
http://wattsupwiththat.files.wordpress.com/2009/12/noaa_gisp2_icecore_anim3.gif
So not to worry about Greenland, it will “soon” get its ice back with a vengeance on all.

Bruce of Newcastle

Usually the SI unit is the elephant or sometimes the blue whale. So melting roughly 36 billion elephants or 1.2 billion blue whales per year give or take. Or about 350 billion poley bears, fits better with Greenland.
On this topic I was amused when New Scientist reported the icebergs are melting oh no sea level will rise by 0.046mm article a couple of weeks ago. They kept the alarmist flavour but carefully left out the 46 microns figure.

Evelyn

And if that is not enough, we’re told that Greenland is rising because the ice no longer holds it down as it’s melting away.
See: http://news.yahoo.com/s/livescience/20100518/sc_livescience/greenlandrisingrapidlyasicemelts

Willis Eschenbach

Geoff Shorten says:
May 23, 2010 at 12:58 am

Willis, the paragraph beginning with ‘That’s my pet peeve’ should have 200 km^3 rather than 200 tonnes I think.

Thanks, fixed.

wayne

Thanks Willis for highlighting what alarmists and journals are doing with scale and the units. You have extracted the kind of real facts that someone, anyone, can wrap their mind around.
It’s a shame that that type of coercion must be applied to every single article and published data from supposedly scientific journals but it has become a necessity. Get out the calculator and conversion tables and put the figures into something your mind can actually visualize realistically.

Willis Eschenbach

tty says:
May 23, 2010 at 1:45 am

In any case that 10% error estimate is wildly optimistic. The problem is that to estimate the ice loss you also have to be able to estimate the vertical movement of the rock bed beneath the ice. Conservatively estimating that the rock is three times denser than ice that error estimate means that the vertical movement of the glacier bed has to be exact to within 3 millimeters/year, and even that only if there are no other sources of error.
Since the isostatic movement of the glacier bed is modelled based on a very few GPS-measured points beyond the edge of the ice cap, mostly in southern Greenland, and that there is also evidence of active tectonics under the ice in northern Greenland that error estimate is completely unrealistic.

tty, the measurement by the GRACE satellites is not measuring the height of the ice and estimating the ice loss from that. It is measuring the weight of the ice. As such, the isostatic rebound doesn’t affect the answer, because although the underlying rock moves vertically, the weight of it doesn’t change.

dscott

Let’s not forget the underlying premise of the entire article: Extrapolation Fallacy. The author of the article assumes the cause will continue indefinitely by assigning an assumption of the presumed cause – AGW. AGW itself being based on another premise called Correlation Fallacy over an arbitrary period of time cherry picked to give the impression of rising in tandem of temperatures and CO2 ppm . Of course temperature as a measure of heat is also another fallacy since total heat is measured in Btu/# or Joules (for you metric fans) not in degrees F or C which only measures sensible heat. You can add heat to boil water all day long at 14.7 #/in^2 (1 bar or 1000 millibars) but you will never see a temp above 212F (100C).

Slabadang

Can someone please answer??
Conserning ice core data and temperature history. How is years or decades of icemelting readable in the ice core data? My persupmtion is that if the ice surface melts and declines under periods..how is that readable and traceble in the icecoredata?
So far i found no one who seems to be able to answer this question. This can not possible be an neglected aspect??? The years of vanished and melted icecovers? How do the ice cores readings fill in the blancs??

Ah, but what you forget is that they’ll claim that we are about to reach a tipping point and the whole lot will vanish in the blink of an eye.
No one can predict anything about that tipping point though, which is why they are such wonderful things. Nebulous, unprovable and beautifully scary.

wayne

Willis Eschenbach says:
May 23, 2010 at 2:43 am
[…] tty, the measurement by the GRACE satellites is not measuring the height of the ice and estimating the ice loss from that. It is measuring the weight of the ice. As such, the isostatic rebound doesn’t affect the answer, because although the underlying rock moves vertically, the weight of it doesn’t change.
Now Willis, I’m not sure I buy that 100%. The vertical aspect I will agree, but the general statement of mass I have a problem. From what I have gathered it measures the geometric gravitational field variances and from that infers mass changes, but an inference of mass can also impersonate a change in mantle/magma density, tectonic displacements, etc. I don’t read that as a firm mass variance reading unless there is some other supporting data to prove that all of the other factors are actually absent. That is exactly where statements derived from the immediate measurements can be easily distorted.

Vincent

Another way of looking at is is to imagine you have $3,000,000 under the mattress 🙂
You spend $200 each year. How long would your stash last?
A more accurate conclusion would be to say “Ice loss is almost immeasurably small and much less than anyone thought.”

Slabadang

Sorry!
“Assumption” instead of “persumption” of course!! Or maby mt question is persumpted?? : )

kwik

One very typical AGW approach;
When someone says the vikings at Greenland prove that it was a warm-period “back then” , the AGW answer is; NO that was a LOCAL warming!
If the Greenland melts by 0.005% os something TODAY, its GLOBAL warming.
Already at that point, you realise, its a religion.

Slabadang

Its “Much worse than expected!!
“How much worse??”
“0.007% worse than we expected! We all gonna die!!”

DirkH

About the source fo the article, from Jimbo Wales’ Knowledge Trove:
“Grist (originally Grist Magazine; also referred to as Grist.org) is a free American non-profit online magazine that publishes environmental news and opinion articles. Launched in April 1999, Grist is headquartered in Seattle, Washington.”
They are begging for donations on their website.
“Grist employs a full-time staff of 18 ”
Here’s an interview with the CEO of grist:
http://www.bizjournals.com/seattle/stories/2008/01/21/story12.html

Chris Korvin

A common fallacy is the “if present trends continue”. I read that” if present trends continue” by 2030 ( I think it was) 40% of the worlds population will be Elvis impersonaters.

Spaceman

Excellent post, thank you, and I appreciated the nod to Haldane in its title. Just because a number has a lot of zeroes on the end doesn’t mean it is big – it depends on what you are (perhaps implicitly) comparing it to. I think the problem is basically one of using the wrong units – the cubic kilometre is not the ideal unit for measuring volume changes in the Greenland ice sheet, though it is a bit more useful than the ‘Lake Erie’ unit. That one is just stupid and there’s no excuse for using it – after all, the Greenland Ice Sheet isn’t discharging into Lake Erie, is it?
The way I encourage my students to think about figures like this is to try to find something to normalise them to. You have normalised the volume change to the to total volume, so the ratio is the number of Greenland-Ice-Sheet volumes lost per year, which is indeed around 0.00007. Wow – now we have a small number! Oh, wait a minute – the article you are commenting on implies that it’s a big number. Unless there is a theory that says what it ‘should’, it’s just a number, which is more or less interesting. As you say, if it goes on at the same rate, the ice sheet will be gone in a period of time of the order of 10,000 years. If.
You could normalise the rate of change of volume in other ways. One way would be against the total area of the GIS. If we take that as 1.71 x 10^6 km^2, the ratio is equivalent to a mean loss of ice thickness of about 12 cm per year (from a mean thickness of around 1600 metres), which is also a bit easier to visualise than 0.33 Lake Eries per year. Or again, to its contribution to global sea level. My back-of-envelope calculation puts that at 0.5 mm per year. Again, I think that is not so difficult to visualise.
This stuff is important. The inability or unwillingness to do these back-of-envelope calculations is widespread, even in the scientific community. I’ve lost count of the number of papers I have reviewed in which some ridiculous error could have been detected by the authors if only they had taken the trouble to check it. Ho hum.
Hope the Corona did the trick. Cheers!

Sera

Willis, I get the same way sometimes. But then I remember that old adage…
“A sunny disposition won’t solve any of your problems, but it will annoy enough people to make it worthwhile.”
Enjoy your day!

rbateman

12,000 years for Greenland to melt?
Why, that’s only 1/5 the time needed to send a probe to Alpha Centauri with present technology.

Richard111

I remember when the 1 meter sea level rise by 2100 scare came out I calculated that 400,000 km^3 had to melt to get that 1 meter rise in sea level.
Using the figure of 200 km^3 melt per year it would take 2,000 years.
That of course assumes the climate will remain constant. Any bets? 🙂

Willis Eschenbach

toby says:
May 23, 2010 at 1:39 am

Of course it is only six years of evidence, but taken with all the other peices of evidence, it IS bad news. Like this:
http://www.nature.com/nature/journal/v465/n7296/abs/nature09043.html

toby, I’m not willing to spend $18 to read that. My rule of thumb is like the old one which states that “Any country with the word ‘Democratic’ in the name of the country … isn’t”.
The corresponding rule for climate papers is “Any study with the word “Robust” in the title of the study … isn’t”. If you think so little of your results that you have to advertise them as the new, improved, “Robust” version of the truth, you don’t have much faith in your results. If it really is robust, everyone reading it will see that, there’s no need to advertise.
But in any case, you seem to think that a warming ocean actually means something. Remember that at any given instant, the ocean will either be warming or cooling. The question is not which one it is doing. It is whether the warming or cooling is anomalous, whether it is unusual or unprecedented or outside of the normal natural variability.
To this question, I fear we have no answer, as our historical records are very spotty both spatially and temporally. We will know more in twenty years or so, but at present all we can do is observe — we don’t have the historical data necessary to draw any conclusions.
In any case, the abstract says:

Accounting for multiple sources of uncertainty, a composite of several OHCA curves using different XBT bias corrections still yields a statistically significant linear warming trend for 1993–2008 of 0.64 W m-2 (calculated for the Earth’s entire surface area), with a 90-per-cent confidence interval of 0.53–0.75 W m-2.

Now, we’re back into the range of numbers – what does that 0.64 W/m2 actually mean? If we assume (as is usually done) a blackbody, that warming trend is about a tenth of a degree in fifteen years … perhaps you want to breathe hard about that, but I’ll pass.
But they have given us their graphs, hang on, let me check them … OK, there’s another problem. I have digitized their Figure 2 showing the average change in heat content. And I get the same number that they get for the change in W/m2. The problem is that there is only 16 years of data (1993-2008), and as a result, their mean trend is not statistically significant (p = 0.11). It appears that they neglected to adjust for autocorrelation in the data. The trend seems significant if you ignore autocorrelation, but like many climate scientists, they don’t appear to have noticed that you can’t ignore autocorrelation.
So to use your syntax, it IS NOT bad news, it’s not even news at all, there is no statistically significant trend in their results. And even if there were, that would only be NEWS, because we have nothing with which to compare it.
w.

David, UK

Thanks for this, Willis. I have left a comment on the source page (subject to approval, so my hopes are not too high that it will be published) summarising that at this rate the Greenland ice is being lost at a rate of a few thousandths of one percent every year, and that if this rate increases then the ice will be lost even faster than that. I ended the comment with the question : Should I be alarmed?
I urge other rational people to leave a comment. These Government-sponsored charlatans (for that is what they are) must be made to realise we weren’t all born yesterday.

Louis Hissink

Willis,
The real issue is the nature of gravity itself. I touched on it for my MSc., indirectly, two decades ago, but had to confronti it directly last year when a drill hole survey instrument measured negative gravity vectors. Consulting geophysicists were thoughtless.
But the data lie not, and in the best of Popperism, I, as a scientist, question the basics underlying the science I work from.