AGW Mathematics : -30 + 5 = 0

By Steven Goddard,

From The Vancouver Sun, a survey of leading climate scientists.

“More than half the experts think there is a more than 10 per chance we’ll get five degrees C warming under that scenario,” he says. “And five degrees C is gigantic,” says Keith, noting it is enough to “knock out” the Greenland and Antarctic ice sheets. The meltwater would eventually raise sea level by as much as 100 metres.

The experts seem to be having a little difficulty with their maths. Temperatures have risen a whopping 0.7C over the last 120 ppm CO2 – but just for fun, let’s pretend that the next 150 ppm increase really did raise temperatures by 5C. What would that do to Antarctica? As you can see below, it would move the summer 0°C line inwards maybe 50 miles. At least 95% of the ice sheet would remain below freezing all year round. Ice does not melt below freezing. Warmer winter temperatures would mean more snow.

http://en.wikipedia.org/wiki/File:Antarctic_surface_temperature.png

The video below shows in green the areas of Antarctica which would move above 0C in summer with 5C warming.

Ah – but what about Polar Amplification? While the earth has warmed 0.7C, Antarctica has warmed about 0.0c. That gives us an amplifcation factor of zero.

Must be the Ozone? I’m curious how one gets to be a “climate expert.”

“Science is the belief in the ignorance of the experts”

– Richard Feynman

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July 2, 2010 9:17 am

T ~ log2(N) or N ~ 2^T
What does this mean… what is N (CO2 concentration?), what is ~ (“approximates?”) and what is your argument? Temperature increases as the common log of CO2 concentration?
The formulae used are:
Δ T(s) = λ RF
where T(s) is surface air temp, λ is climate sensitivity and RF is radiative forcing.
λ is currently estimated at 3°K ± 1.5°, RF for CO2 alone is 5.35 ln(C/C0)
Note that looking at this forcing alone doesn’t take into account forcings for other GHGs, solar cooling, volcanic emissions, ocean heat uptake etc. etc. etc. Yes, it’s complex. We live on a planet.

jcrabb
July 2, 2010 9:21 am

S Goddard,
Indeed it does sound daft, but considering just how quickly, on a Geological scale, the Arctic is collapsing, one wonders if the system is more sensitive to rising temperatures than previously thought.
Also, CO2 levels have only been around 400 ppm for a very short time, so it could be pre-emptive to consider Global temperature rise thus far to be the total result.
To hazard a guess I would say that over time, a long time, once heat sinks have been exausted, ie ice melted, seas warmed etc, perhaps ‘low’ CO2 levels can drive up temperatures to that proposed in the paper.

Alan D McIntire
July 2, 2010 9:21 am

Common sense would indicate that the logarithmic effect of CO2 is only an APPROXIMATION, and cannot be accurate for all values. Consider the drop in CO2 from 1 molecule to zero molecules. Plug in the logarithm difference and you get something like minus infinity. For a small number of molecules the effect must be roughly linear. As the quantity of molecules increases gradually, the forcing APPROXIMATES a logarithmic effect once a certain density is reached. Incidentally, even that approximation refers to WATTS rather than temperature. Since temperature is proportional to the 4th root of the wattage flux, temperatures will increase even slower than that logarithmic approximation.

July 2, 2010 9:21 am

Paul Daniel Ash
The inverse of a log function is an exponential function. Now try again “genius”
http://wattsupwiththat.com/2010/07/02/agw-mathematics-30-5-0/#comment-421804

July 2, 2010 9:25 am

Peter Czerna
Apparently you either didn’t read the entire article or didn’t understand the part about polar amplification. Antarctica is the slowest warming place on the planet. Satellite data shows it cooling.
Try reading the entire article before writing long-winded criticisms.

Enneagram
July 2, 2010 9:27 am

I have just read the following, about MODELS (non-fashion related, just in case):
ectoplasm generated by a previous excursion into computer models and equations….
……..The most important issue separating the Electric Universe from conventional views is that evidence based in laboratory experiments can be used to support EU theories of cosmogony. The mainstream sinks its foundations in ground where computer models and complex equations are used for support. It is this philosophical divergence that inhibits the general acceptance of plasma and electricity as active agents in space.
By Stephen Smith

http://www.thunderbolts.info/tpod/2010/arch10/100702truth.htm

July 2, 2010 9:30 am

Paul Daniel Ash
BTW – I wrote this half an hour before your post.
http://wattsupwiththat.com/2010/07/02/agw-mathematics-30-5-0/#comment-421804
Seems like your nastiness is running at least a half hour ahead of your reading.

July 2, 2010 9:30 am

stevengoddard says:
July 2, 2010 at 8:52 am
Phil – this satellite image might help out
http://climateinsiders.files.wordpress.com/2010/07/barrowcloseup1.jpg

Yeah it proves you don’t know where NARL is!
Try this one: http://seaice.alaska.edu/gi/observatories/barrow_breakup/bathymetry.png
stevengoddard says:
July 2, 2010 at 8:48 am
Phil.
That was one of your worst posts.
As discussed yesterday, long range weather forecasts change constantly. The WRF cloud forecast has changed over the last week – you surprised?

No, but you saw fit to rely on it to make a post predicting a record late breakup of the Barrow fast ice! I didn’t notice any lack of confidence in the WRF cloud forecast when you wrote a post that relied on it.
And yes, the ice did break away from the city of Barrow, after I wrote the article.
I don’t know when you wrote it but the post was dated June 26, 2010 whereas the fast ice off Barrow broke up early morning June 25th according to the radar.
Here’s a webcam view for the morning of the 26th:
http://ak.aoos.org/data/webcam/2010/06/26/18/ABCam_20100626_1835.jpg
Are you one of those people who bets on the outcome of games after they are played?
No I don’t bet. However to continue the betting analogy you appeared to bet on the loser after the game was over!

sod
July 2, 2010 9:36 am

How about daily mean!
daily mean also is irrelevant. melting will be caused by daily max temperature above 0°C.

July 2, 2010 9:42 am

stevengoddard replied, “UAH shows cooling in Antarctica.”
My comment was not about UAH TLT anomalies. It was about the GISTEMP trend map you posted that showed a warming of Antarctica, not a cooling.

July 2, 2010 9:45 am

stevengoddard replied, “Quick question for you. If GISS shows 1.7 global and 1.3 for Antarctica, just how much polar amplification is that? ;^)”
I already answered that question in my earlier comment. But here it is again:
Also Polar Amplification does not apply to the high latitudes of the Southern Hemisphere. Refer to the Wikipedia discussion on Polar Ampilification. They write in the opening paragraph, “Polar amplification is defined by International Arctic Science Committee on page 23 of the Arctic Climate Impact Assessment ‘Polar amplification (greater temperature increases in the Arctic compared to the earth as a whole) is a result of the collective effect of these feedbacks and other processes.’[1] It does not apply to the Antarctic, because the Southern Ocean acts as a heat sink.”

July 2, 2010 9:51 am

stevengoddard says:
July 2, 2010 at 7:44 am
Bob Tisdale
UAH shows cooling in Antarctica.

Interesting considering UAH can’t make TLT measurements there.

Buffoon
July 2, 2010 10:02 am

Steve,
You keep referring to this 0°C number, which of course is a magical number, but I’m curious what the actual melting temperature is for ice (by zone) in the antarctic? Can’t sit in the middle of all that salt for zillions of centuries and not pick a little bit up, can it?

July 2, 2010 10:06 am

[snip]
I’m still waiting for a response to my post from almost anhour ago asking what your argument is. What are you trying to express with all these exponential functions and common logs?

July 2, 2010 10:08 am

Buffoon
Glacial ice comes from snow. Snow comes from freshwater evaporated (distilled) out of the ocean. The freezing point of fresh water is 0C. That is how 0C is defined.

James Sexton
July 2, 2010 10:11 am

lol, dang Steve, you sure bring out the critics. Uhmm, definition —-the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce that number. ——nice circular discussion, ladies. I’m not sure if it is even pertinent to the discussion. What I took from the article is there is really a great bit of uncertainty about our climate, and specifically the polar caps. Of course, the uncertainty is expressed in alarmist terms. I also believe the thrust of Mr. Goddard’s posting is there really shouldn’t be too much concern about the melting of the caps……not that I was worried to begin with. As it has been pointed out, H2O freezes at the temperature of 0 degrees C. It doesn’t really matter what the anomaly is, as long as the actual temp stays under 0 in most of the area. I think we’re safe so far. Or, we could panic and run out and buy life jackets if that would make people sleep better. I don’t know why you guys don’t just go ahead and get to the base of the argument and start talking about chickens and eggs.

July 2, 2010 10:14 am

Bob Tisdale
Read Hansen’s 1988 paper about polar amplification, instead of Wikipedia.
Plate 4
http://pubs.giss.nasa.gov/docs/1988/1988_Hansen_etal.pdf
He forecast symmetrical warming at both poles.

July 2, 2010 10:17 am

sod
Over huge bodies of ice which are close to the melting point, the daily mean temperature in the summer only varies by a degree or two maximum. The heat absorbed by the melting process doesn’t allow the temperature to ever get more than a degree or so above freezing. This is clearly evident at the north pole.
http://ocean.dmi.dk/arctic/meant80n.uk.php

July 2, 2010 10:18 am

Phil,
The mass balance site is located 8 miles away from the web cam. The ice has not broken up there yet. Is that difficult to understand?

Foley
July 2, 2010 10:34 am

Wikipedia, ouch. Now there is an authoritatively legitimate peer reviewed consensus source of real science periodically corrected 10% of the time by 50% of users. Not…

Enneagram
July 2, 2010 10:37 am

Paul Daniel Ash says:
July 2, 2010 at 9:17 am
….simply that no matter how much CO2 you add to the atmosphere, temperatures WOULD increase just very, very little.
But that’s taking that factor ALONE. But if you consider that:
The atmosphere, the air you know, does not have the capacity to “hold” enough heat, it only “saves” 0.001297 joules per cubic centimeter, while water , the sea you know, has 3227 times that capacity (4.186 joules).
Would you warm your feet with a bottle filled with air or filled with hot water?

You will arrive at the conclusion that: No matter how beautiful models are, they couldn’t get what they expected: A HOT SPOT of saved heat in the tropical atmosphere. Sorry, the earth has no CEILING, so warm goes up, up and away!
If we had no seas we were not talking about these things but frozen under miles of ice.
So, the next time you go to the sea shore, thank Mare Nostrum, our sea, our Holy Mary. See?

July 2, 2010 10:41 am

Phil,
AMSU covers almost all of Antarctica

July 2, 2010 10:46 am

Paul Daniel Ash
I have responded numerous times, you just don’t seem to be up to speed with the science.
As Gavin clearly states at RealClimate, temperature should increase by a fixed amount with each doubling of CO2. That is a logarithmic function. Each additional 100 ppm has less temperature effect that the previous 100 ppm. The first 100 ppm has by far the most effect.
If you want confirmation from Gavin, go ask him at realclimate.com

DB
July 2, 2010 10:50 am

Bob T. quoted: “It does not apply to the Antarctic, because the Southern Ocean acts as a heat sink.”
Bob, on your website (post dated July 28, 2008) you show a profile of projected warming from a doubling of CO2:
http://i33.tinypic.com/10fu8p2.jpg
While smaller than the Arctic, the southern polar region shows a warming as great as at the north pole or up at 300mb.

July 2, 2010 10:50 am

snip one part of the argument or both, moderator: [snip]

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