Anomalies are unsuitable measure of global temperature trends
Guest post by David M. Hoffer
An anomaly is simply a value that is arrived at by comparing the current measurement to some average measurement. So, if the average temperature over the last 30 years is 15 degrees C, and this year’s average is 16 degrees, that gives us an anomaly of one degree. Of what value are anomalies? Are they a suitable method for discussing temperature data as it applies to the climate debate?
On the surface, anomalies seem to have some use. But the answer to the second question is rather simple.
No.
If the whole earth was a single uniform temperature, we’d have no need of anomalies. But the fact is that temperatures don’t vary all that much in the tropics, while variations in the high temperate zones are frequently as much as 80 degrees over the course of a year. How does one compare the temperatures of say Khartoum, which on a monthly basis ranges from an average of 25 degrees to 35 degrees C, to say Winnipeg, which might range from -40 in the winter to +40 in the summer?
Enter anomalies. By establishing a base line average, usually over 30 years, it is possible to see how much temperatures have changed in (for example) winter in Winnipeg Canada versus Khartoum in summer. On the surface, this makes sense. But does the physics itself support this method of comparison?
It absolutely does NOT.
The theory of CO2’s direct effects on earth’s surface temperature is not terribly difficult to understand. For the purposes of this discussion, let us ignore the details of the exact physical mechanisms as well as the order and magnitude of feedback responses. Let us instead assume that the IPCC and other warmist literature is correct on that matter, and then see if it is logical to analyze that theory via anomaly data.
The “consensus” literature proposes that direct effects of CO2 result in a downward energy flux of 3.7 watts/m2 for a doubling of CO2. Let’s accept that. Then they propose that this in turn results in a temperature increase of one degree. That proposal cannot be supported.
Let us start with the one degree calculation itself. How do we convert watts/m2 into degrees?
The answer can be found in any text book that deals with radiative physics. The derivation of the formula requires some in depth understanding of the matter, and for those that are interested, Wikipedia has as good an explanation as we need:
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
For the purposes of this discussion however, all we need to understand is the formula itself, which is:
P=5.67*10^-8*T^4
It took Nobel Prize winning work in physics to come up with that formula, but all we need to use it is a calculator.
For the mathematically inclined, the problem ought to be immediately obvious. There is no direct correlation between w/m2 and temperature. Power varies with T raised to the power of 4. That brings up an obvious question. At what temperature does the doubling of CO2 cause a rise in temperature of one degree? If we use the accepted average temperature of earth surface as +15 degrees C (288 degrees K) simply applying the formula suggests that it is NOT at the average surface temperature of earth:
For T = 288K
P = 5.67*10^-8*288^4 = 390.1
For T = 289K (plus one degree)
P = 5.67*10^-8*289^4 = 395.5
That’s a difference of 5.4 w/m2, not 3.7 w/m2!
So, how does the IPCC justify their claim? As seen from space, the earth’s temperature is not defined at earth surface, nor can it be defined at the TOA (Top of Atmosphere). Photons escaping from earth to space can originate at any altitude, and it is the average of these that defines the “effective black body temperature of earth” which turns out to be about -20 C (253 K), much colder than average temperatures at earth surface. If we plug that value into the equation we get:
253K = 232.3 w/m2
254K = 236.0 w/m2
236.0 – 232.3 = 3.7
There’s the elusive 3.7 w/m2 = 1 degree! It has nothing to do with surface temperatures! But if we take this analysis a step further, it gets even worse. The purpose of temperature anomalies in the first place was supposedly to compare temperature changes at different temperature ranges. As we can see from the analysis above, since w/m2 means very different things at different temperature ranges, this method is completely useless for understanding changes in earth’s energy balance due to doubling of CO2.
To illustrate the point further, at any given time, some parts of earth are actually in cooling trends while others are in warming trends. By averaging temperature anomalies across the globe, the IPCC and “consensus” science has concluded that there is an overall positive warming trend. The following is a simple example of how easily anomaly data can report not only a misleading result, but worse, in some cases it can report a result the OPPOSITE of what is happening from an energy balance perspective. To illustrate, let’s take four different temperatures and consider their value when converted to w/m2 as calculated by Stefan-Boltzmann Law:
-38 C = 235K = 172.9 w/m2
-40 C = 233K = 167.1 w/m2
+35 C = 318K = 579.8 w/m2
+34 C = 317K = 587.1 w/m2
Now let us suppose that we have two equal areas, one of which has an anomaly of +2 due to warming from -40 C to -38 C. The other area at the same time posts an anomaly of -1 due to cooling from +35 to +34.
-38 C anomaly of +2 degrees = +5.8 w.m2
+35 C anomaly of -1 degree = -7.3 w/m2
“averaged” temperature anomaly = +0.5 degrees
“averaged” w/m2 anomaly = -0.75 w.m2
The temperature went up but the energy balance went down? The fact is that because temperature and power do not vary dirfectly with one another, averaging anomaly data from dramaticaly different temperature ranges provides a meaningless result.
Long story short, if the goal of measuring temperature anomalies is to try and quantify the effects of CO2 doubling on earth’s energy balance at surface, anomalies from winter in Winnipeg and summer in Khartoum simply are not comparable. Trying to average them and draw conclusions about CO2’s effects in w/m2 simply makes no sense and produces a global anomaly that is meaningless.
TomVonk says:
August 27, 2012 at 4:06 am
So there is a huge difference between the 4th power of an average and and average of 4th powers.
This is true but NOT very obvious. Even grade 12 physics students may not appreciate the difference and get an answer wrong because of it. I would like to illustrate this fact in a different way by answering the following question: How much does the kinetic energy of a 2 kg mass increase when the speed goes from 1 m/s to 3 m/s? The formula for kinetic energy is E = 1/2mv2. So the correct answer to this question is change in E = 1/2(2)(3)2 – 1/2(2)(1)2 = 9 – 1 = 8 J. The wrong answer is to assume the change in speed was 2 m/s, so the change in energy is E = 1/2(2)(2)2 = 4 J.
stephen richards says:
August 27, 2012 at 1:23 am
How do you know what the “normal” is?
You raise an excellent question. What is to stop any one from deciding that the average of the last 30 years was normal and that all anomalies from 1850 to 1980 were below normal? The facts would not change, but there would be a huge difference as to how things are perceived!
Scarface says: @ur momisugly August 27, 2012 at 9:02 am
…Well, the more I read and learn about it, I would dare to say that the science is septic.
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That is the most precise summing up of the state of climate science I have seen so far. (I am glad I had just finished off my glass of iced tea before reading that given I am still laughing)
Thank you — This will fall on deaf ears again though.
David Ball says:
For the lay people out there, it is impossible to know if something is an anomoly if you have no understanding of what is “normal”.
You misunderstand the concept. The use of anomalies as critiqued by David is not intended to measure ‘man made’ or as an objective measure of ‘unusual’ or as deviation from an ideal. It is just a method of expressing measurements as differences from an arbitrary baseline, so that change can be assessed across sites that have different baseline values. It is not normative.
As David points out, there can be problems with the use of temperature anomalies for various purposes, but there is nothing intrinsically wrong with expressing temperatures as anomalies from an aribtrary baseline.
JJ says that “The use of anomalies … is just a method of expressing measurements as differences from an arbitrary baseline … and … is not normative.”
I disagree. To anyone who speaks English well enough to have met or used the word ‘anomaly’, there is always the connotation in its meaning that something ‘anomalous’ is wrong. If you are talking about ‘differences from an arbitrary baseline’ in any field of normal science, you will use a word like … well, ‘difference’, or ‘variation’ or whatever, a word which does not suggest wrongness, just … variation. Only in climate science is it felt necessary to apply the subliminal brainwashing effect of “blah, blah, man-made greenhouse gases, blah, blah, anomaly blah blah”. The repeated juxtaposition of anything man-made and anomaly is just programming the public to feel that (whatever it is they’re blaming this time out) is causing things to be wrong.
No. They haven’t even shown yet that mankind has had any measurable effect on global climate (inasmuch as that phrase has any meaning), still less that anything is wrong. Thus far, all these “anomalies” with which we are beaten are merely modest differences from an arbitrary baseline – and nowhere near going outside the normal variability of Earth’s climatic parameters. There are NO ‘anomalies’, within the correct linguistic use of that word. Just Newspeak.
Nice post, David. Thanks.
Stephen Rasey says:
August 27, 2012 at 9:23 am
@Monckton: when the climate has finished responding to a given forcing (typically after 1000-3000 years):
Whoa! Where did “1000-3000 years” to equilibrate come from?
When we have a KE=8 volcanic eruption, we get “a YEAR without summer”. A year — not a millennium. On a planet with day-night temperature swings, with seasonal cycles, any instantaneous forcing is quickly blended into the atmosphere. The evidence from volcanos are that the relaxation from the impulse is on the order of a couple of years, not millennia. Speculation that forcings are carried into the deep ocean for 1000 years are just that: speculations of disparate advocates trying to square the circle of their own making.
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A volcano provides an impulse which propogates across the planet in a few weeks and then persists until the material injected into the atmosphere is removed, usually within a year or so.There is not time for a large heat loss from the ocean, so the effect of the eruption shows mainly in air temperatures and damps out quickly.
The forcings under discussion are sustained over decades. Since water has a high heat capacity, only a sustained increase in air and land surface temperature will produce a significant and long-term change in sea temperatures
There is no such thing as a “global temperature”. The entire concept is bogus nonsense.
@Entropic Man
Perhaps we should be clearer about what we call a forcing. In evaluating a system response, you should consider the output from an impulse. A volcano is a clear impuse at a climate scale and the data supports a response and relaxation time of just a couple of years.
The addition of a marginal 10 GT of CO2 into the atmosphere in a summer is another forcing. Since 450 GT are cycled per year through the biosphere, I would argue that the system response is also likely quick.
But I disagree that an extra 10 GT/year of CO2 is ONE Forcing. That is a step change input, not an impuse. It is equivalent to repeated, continuous forcings. If you argue that this step change is one forcing, then you must hold that a volcano is two forcings, one positive, one negative, an absurd concept.
So it seems that “forcings” is a term used for impulses (i.e. volcanos), balances (solar constant, CO2 in atmosphere), rates (x GT CO2/year added to atmosphere), and accelerations (Y GT CO2/year^2, CO2 balance in atmosphere under non-zero rates of addition.) To call all them forcings seems a bit imprecise.
@ur momisugly Stephen Rasey “Perhaps we should be clearer about what we call a forcing. In evaluating a system response, you should consider the output from an impulse”
No, you should consider the output from a step change. That’s a big difference! The equilibrium response to a forcing is only achieved if the forcing is maintained until the system is no longer changing in response. Once again, Wikipedia to the rescue: http://en.wikipedia.org/wiki/Climate_sensitivity#Equilibrium_and_transient_climate_sensitivity
The climate system does not have time to equilibriate to the impulse from a large volcanic eruption because the material causing the reduction in energy absorbed at the surface is mostly gone within a couple of years.
Excellent article. I hope to see more articles from you. I have followed your posts for some years and you have an excellent understanding of the climate debates and of scientific method.
@Stu N: The equilibrium response to a forcing is only achieved if the forcing is maintained until the system is no longer changing in response.
That’s not right. If it is a true step function, the “forcing” is applied at t >= t(a); forever! If you stop the forcing at t = t(b), then you are in fact applying a second negative step function super imposed on the first. That would be a box-car input.
http://en.wikipedia.org/wiki/Impulse_response.
Stephen Rasey says:
August 27, 2012 at 1:07 pm
@Entropic Man
Perhaps we should be clearer about what we call a forcing. In evaluating a system response, you should consider the output from an impulse. A volcano is a clear impuse at a climate scale and the data supports a response and relaxation time of just a couple of years.
The addition of a marginal 10 GT of CO2 into the atmosphere in a summer is another forcing. Since 450 GT are cycled per year through the biosphere, I would argue that the system response is also likely quick.
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We may be playing with semantics here.I attempted to distinguish between a short term change like the release of gas and ash from a volcano and the longer term changes associated with a change such as increased CO2.
The volcano generates a short term decrease in surface insolation, detectable for a year or two as a downward blip in the air and surface temperature record which quickly damps out. The high thermal inertia of the oceans means that they are hardly affected.
A change such as doubling CO2 over 100 years produces a gradual increase in energy flow, with each increment of CO2 producing a small increment of air and land temperature, with little or no lag. In the short term this will be hard to distinguish from the normal short term variation, but becomes apparant over decades.Sea temperature will lag considerably behind,acting to slow the overall rate of change and leading to a delay of up to 100 years before the system reaches equilibrium for the new CO2 concentration.
You do see differences in CO2 in a season. The Hawaian data shows a seasonal minimum in CO2 during the Northern Hemisphere Summer, though its effects on seasonal temperatures in the two hemispheres are hard to pick out of the noise.
TimC says:
August 27, 2012 at 4:40 am:
More fundamentally, I agree that global annual-average surface temperature is not a very good metric by which to measure global warming or cooling – but what is to replace it?
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It is not necessary to replace it with another bad method, it would be enough if “climate scientists” admitted it publicly. And I do not care, if they lost their climate jobs then.
“As I said in the article itself, my point was not to debate the physical processes themselves, but to demonstrate that temperature anomalies as measured at the surface are unsuitable for tracking those processes.”
Well put David. Thanks for the interesting article. It’s nice to see a guest post from you, I always enjoy your comments.
Rich Dommer
Mr. Rasey asks where the value 1000-3000 years to restore equilibrium after a forcing comes from. It is to be found in a 2009 paper by Susan Solomon, the lead author of the IPCC’s 2007 “science” report. Dr. Solomon had not thought through the implications of so long a time to equilibrium: what it means is that the headline equilibrium warming of 3.26 K per CO2 doubling (even if correct) will not be reached for at least 1000 years, with only half of it occurring this century.
Mr. Hoffer says surface temperature anomalies are unsuitable: however, the IPCC’s adjustment of the value of the Planck parameter allows them to be used with little error.
The real problem with the IPCC’s projections lies in its assumption of strongly net-positive temperature feedbacks that are not warranted either by theory or by any empirical method. Warming since the first IPCC report in 1990 has occurred at half of the IPCC’s then central estimate. Though a decade is not a long time in climate politics, it is now appropriate to question the reliability of the IPCC’s central estimates of future global warming.
@Entropic
I remind you the issue was Monckton’s statement: when the climate has finished responding to a given forcing (typically after 1000-3000 years):
That implies to me that the system response to an impulse is 1000-3000 years. Volcano data implies a much faster response. Now, if you want a, 200 year string of gigantic input forcings, well I grant you it might be 1000 years before the system settles down, especially since it is a non-linear biologic system.
But “finished responding to a given forcing”? 1000 years seems to me to be a little long for ‘a given forcing.” That was my point. Making the forcings huge doesn’t invalidate it.
Stephen Rasey says:
August 27, 2012 at 5:01 pm
1000 years seems to me to be a little long for ‘a given forcing.” That was my point. Making the forcings huge doesn’t invalidate it.
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We probably see wont settled this until the data comes in. See you in a hundred years, or a thousand. Loser buys the drinks.
Monckton of Brenchley says:
August 27, 2012 at 4:48 pm:
“The real problem with the IPCC’s projections lies in its assumption of strongly net-positive temperature feedbacks that are not warranted either by theory or by any empirical method.”
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A simple logic requires the supporters of the “greenhouse gases warming” concept to agree with the notion of “net-positive temperature feedbacks”, because it is already a part of the concept.
As a second step they need to see that the “net-positive temperature feedbacks” would lead to a pretty much endless increase in temperatures and are therefore absurd.
Then they have no other choice than to conclude that the premise (greenhouse gases warming) is false. This method is called “reductio ad absurdum”.
And please, Christopher, do not rush to write a reply, take some time and think over it.
[Snip. Not referring to WUWT readers in derogatory terms like “the peanut gallery” would assist in getting your comments approved. ~dbs, mod.]
This sounds like the case of confusing average temperature and average energy. It is similar to confusing average voltage with average energy in a situation where all voltages are positive.
You may have seen a rating that says 110 Vrms. RMS is short for [square]Root of the Mean[average] Square[ed values.] This usage is based on the fact that energy flow (power) is proportional to the square of the voltage if the resistance remains constant. So that the square root of the average value, usually averaged over time, of the squares of the observed voltages gives a single constant voltage that would dissipate the same energy as the actual values did. In this case negative values are allowed for the voltages. This term is often used to specify the direct current (DC) voltage that is equivalent to an alternating current (AC) voltage applied.
Most radiation calculations are based on the local equilibrium requirement that net energy flow coming in must be equal to the net energy flow going out. As energy flowing out is proportional to the fourth power of the temperature, the sum of all energy flows is proportional to the sum of all temperatures raised to the fourth power. If one takes the average of these values over the surface of the Earth, one gets a nominal average energy flow or power per unit surface area required to sustain equilibrium.
An inverse calculation from this energy-flow calculates the equivalent *uniform* absolute surface temperature required for equilibrium, this result is, of course, not an arithmetic mean temperature. It is the fourth-root of the average of all absolute temperatures after each has been raised to the fourth power. This might be called a ‘QRMQ’ (Quad-Root of the Mean Quad power) average. You probably would not want to plan your daily activity on such an average, nor, for that matter, would you want to do this on the basis of an overall simple arithmetic average.
I doubt if you will ever see a published paper that will have numbers like 271 Kqrmq, but that is what is meant by overall absolute temperatures derived from average radiated power.
Monckton of Brenchley,
I don’t see that the manner in which the IPCC adjusts anomaly data excuses the manner in which HadCrut and GISS use it to calculate global average temps, but I am interested to know more as to exactly what they are doing vis a vis Planck’s constant. Have you got a link or other pointer to the details?
As Tim C said,
“I agree that global annual-average surface temperature is not a very good metric by which to measure global warming or cooling – but what is to replace it?”
Our “defined” method of measuring our “global average temperature” is useful because it provides a single number that reflects temperature CHANGES that occur on Earth with time. As long as the defined method (whatever we choose to use) includes a very large number of surface measurements recorded throughout the world and the measurement sites are selected to be distance from obvious local sources of heating or cooling, the so called “temperature change” thereby obtained is very likely to be useful. As long as one sticks to this criteria for the defined method, the observed “temperature change” thereby obtained is very likely to very useful in monitoring climate changes.
By injecting fundamental physical equations, such as the Stephan-Boltzman equation, into this discussion appears to be meaningless and inappropriate to me.
Again, these discussions seem to be designed more to “impress” the lay readers of this website than to clarify. Again an explanation to the contrary would be welcomed by those of us who do not see a legitimate point in this post. l
By injecting fundamental physical equations, such as the Stephan-Boltzman equation, into this discussion appears to be meaningless and inappropriate to me.
>>>>>>>>>>>>>>>>>>>>>>
Fundamental physics is meaningless and inappropriate in the climate debate? Seriously?
LOL
BTW, it is Stefan-Boltzmann.
Michael Lowe
OMG, that Feynman story is so funny!