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.
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Bill Illis
Very nice comment! Worthy of a guest post!!!
http://wattsupwiththat.com/2012/08/26/lies-damn-lies-and-anoma-lies/#comment-1065802
What I meant, of course, was that the S-B equation has nothing to do with the extra surface level warming – of about 30C (global average) – that is caused by the greenhouse effect.
What I meant, of course, was that the S-B equation has nothing to do with the extra surface level warming – of about 30C (global average) – that is caused by the greenhouse effect.
>>>>>>>>>>>>>>>>>>>>>>
I see. Everything in the universe obeys SB Law except the greenhouse effect. Got it.
That 33K for the “greenhouse effect comes from the same kind of mis-application of the SB equation.
A blackbody lit on one side by 1000 W/m^2 and dark on the other has temperatures of 364 K and 0 K which gives an average of 182 K.
A blackbody lit on both sides by 500 W/m^2 has a temperature of 306 K on each side and an average of 153 K.
QED.
Sleepalot says:
August 27, 2012 at 8:25 pm:
“A blackbody lit on both sides by 500 W/m^2 has a temperature of 306 K on each side and an average of 153 K.”
============================================
(306 + 306)/2 = …
The following chart shows the calculated effect of increasing the CO2 content from 300 to 600 PPM on energy flowing out of the troposphere in a static environment without feedback effects. This was calculated by MODTRAN a program developed by the Air Force to test their equipment.
File:ModtranRadiativeForcingDoubleCO2.png
From Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/File:ModtranRadiativeForcingDoubleCO2.png
As can be seen, this huge increase in CO2 just produces a slight widening of the CO2 ‘hole,’ which is like a one-foot diameter tree in the middle of a ten-foot wide stream. It can be seen that the CO2 band is almost fully saturated and masks most of the effect of the CO2. This shows the raw effect without feedbacks. The IPCC has postulated that the atmosphere has a dangerously high positive feedback factor that doubles or triples the raw effect. Others, (Dr. John Christy,) have argued that feedbacks, if any, are more likely to be negative.
Some economists are predicting that high extraction costs for increasingly more difficult to obtain carbon fuels will begin to curtail their use after a generation or two, so we can expect at most, one full anthropogenic doubling of CO2 in the atmosphere.
The Fate of All Carbon
by David Archibald
http://wattsupwiththat.com/2011/11/13/the-fate-of-all-carbon/
In the past, the climate has gone through wide temperature shifts without human intervention and there is every reason to expect that it will continue to do this in the future.
@Greg yep, well spotted. So it’s 306 K The point is that it’s different from 182K so it hows the method is invalid.
Dr. Eric Grimsrud wrote:
“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.”
It was demonstrated to you that the average “temperature” can go up while energy balance went down. The idea of this construction does not change if you are using only two areas, or “large number of surface” areas (unless you invoke additional unproven assumptions about statistics of temperature field). It is easier to construct a case when the “global average temperature” goes up which energy balance also goes up. Upon little thinking it must be obvious that there could be cases when the energy balance stays unchanged, but the “global average temperature” can go either up or down. It also be that the energy content does change, but the “global average temperature” stays constant. As one can see, the “global temperature change” is not a “proxy” for change in planetary energy balance. Then how it can be possibly useful, Dr. Grimsrud?
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.
This is of course absolute bogus statement because a global average doesn’t reflect anything such.
Even worse, like AlTekhasski rightly says above, variations in a global temperature average do not even reflect correctly the SIGN
This is mathematically so trivial that one should not even have to mention it.
Here is why the global temperature average is irrelevant to ANY energy and flow consideration.
The dynamics for the surface temperatures are defined by the heat equation with imposed flows on the free surface.
Solving this equation gives a unique temperature and a unique energy flow for every point of the surface.
The key concept to understand that there is a one to one correspondence between the temperature surface field and the energy flow field.
Now what happens if one looks only on the temperature average?
There is no more a one to one correspondence between this one temperature average number and the energy flow.
It has been destroyed by the averaging.
What we have instead is a one to many correspondence, actually a one to infinitely many.
That means for a given global temperature average there is an infinity of possible flows so that it is not possible to even know the sign of internal energy variation knowing the sign of average temperature variation.
That is why looking at temperature averages is not only useless but misleading because people might be lead to believe that average increasing implies internal energy increasing (or flows increasing) what is an absolutely wrong inference.
Besides that is what the data shows too. The “global” warming is anything but global. Actually about one third of the sites sees decreasing temperatures while two thirds see increasing temperatures. The average trivially increases but it still doesn’t say anything about energy or flows unless one looks locally at every single point of the globe where the one to one correspondence is restored again.
Is Boltzmann’s Law the correct law to use?
I do not think so because the important bit is the statement ”at equilibrium” we get a black body response but the planet is never at equilibrium, one reason we get weather.
The effect of CO2 in atmospheric heating, as proposed by the GHG theory, is understandable but wrong since the laws of thermodynamics must not be violated. It is also an observed fact that the mid troposphere heat anomaly, proposed by the GHG theory, has never been found despite daily checks with radiosonde. The radiation ”window” should close with rising atmospheric CO2, another GHG bit of theory, to raise temperatures at the surface. satellite observation shows no such change.
The planet has no temperature average so anomalies are of no real use. Also temperature is a poor metric for climate since no account of heat content is made and that is due to water content of the air mass under study. It is heat that drives atmospheric systems and processes.
Off this topic but always relevant to websites such as this.- Any warming due to industrialisation, and there may have been none, has to be shown to have made the world less habitable to people now living in it – and living lives dependent upon industrialisation – if said warming is to be a justification for alarm and for moves to shackle growth by banning low-cost energy production. Since idustrialisation has led to more people living healthier and longer lives plainly the world has not become a more difficult place for humans equipped as we now are to live in. Habitability is not somthing Nature given but somthing won by Mankind.
Make that ‘something’.
@ur momisugly Stephen Rasey
I said: “The equilibrium response to a forcing is only achieved if the forcing is maintained until the system is no longer changing in response.”
You replied: “That’s not right. If it is a true step function, the “forcing” is applied at t >= t(a); forever!”
That’s not right? My statement is self-defining! Anyone else agree with Stephen?
Anyway, yes, to consider the equilibrium response the forcing is applied forever – or at least as long as it takes for the system to reach equilibrium. That is the only way the true equilibrium response of the climate system could be reached. Now, in real life, the climate is always undergoing a transient response to a whole bunch of forcings. In your volcano example, you only see the transient response to a forcing that is itself a function time, peaking a few weeks after the eruption and becoming negligible a few years later.
“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.”
Yep but I never specified whether/when the original forcing would stop. It’s irrelevant once equilibrium has been reached anyway because you’ve got the value you’re seeking – the equilibrium response.
Reblogged this on The GOLDEN RULE and commented:
Reblogging, as I have said before, is a form of laziness, from an editorial point of view. Yet, when another blog/person publishes a post that I agree with and says basically what I would like to say myself, it makes sense to do it the easy way and simply promote the said post by reblogging.
An attempt will be made to come back to this post with, comment and links to posts and comments I have made in the past. Much of what David says is in tune with previous comments on this blog. It is nice to get some supporting, scientific input.
To TomVonk,
In response to my comment:
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.
You then said:
“This is of course absolute bogus statement because a global average doesn’t reflect anything such”
I don’t get your point. Can we assume that a true global average surface temperature would be the average of temperatures measured at every square inch of the planet? Would that not be the very definition of an average global temperature?
Now of course, we can’t do that continuously every second around the clock at every square inch of our planet’s surface, can we? So we do the next best thing – we make such measurements at as many points on the planet’s surface as we can – and hope that those measurements provide a valid measurement of the “true” global average.
Now, if our current measurement system does not provide a measurement of that true value, it would be simply because we do not have enough measurement sites in place, right?. So the question is simply, do we have enough measurement stations in place such that we are getting a useful measure of the global average.
Thus, I do not see the point of your remarks that followed in your comment of 1:43 am.
Can we assume that a true global average surface temperature would be the average of temperatures measured at every square inch of the planet?
>>>>>>>>>>>>>>>>>>>>>>>>>>
For the purposes of understanding energy balance, no we cannot. Different temperature distributions could result in exactly the same “average temperature” while delivering very different power fluxes. To understand what is happening from an energy balance perspective, one would have to first convert each point in time temperature reading to w/m2, then average and trend that. Attempting to trend either temperature or temperature anomalies as a proxy for energy balance is not mathematically sound.
ericgrimsrud says:
August 28, 2012 at 7:25 am:
“Now of course, we can’t do that continuously every second around the clock at every square inch of our planet’s surface, can we? So we do the next best thing – we make such measurements at as many points on the planet’s surface as we can – and hope that those measurements provide a valid measurement of the “true” global average.
Now, if our current measurement system does not provide a measurement of that true value, it would be simply because we do not have enough measurement sites in place, right?”
===============================================
No, it is not right. You need to have a representative sample. There is a sample, but there is no proof that this sample is representative for the whole world.
Sorry, but I still do have the impression that a measurement of the average global temperature and changes in it over time is of considerable value and even of primary importance.
For example, the fact that the average global surface temperature of Venus is near 400C and that of Earth is near 15C tells me a great deal about existing conditions on these two planetary surfaces. I understand that Venus once had Earth-like temperatures. If scientists existed there at that time and had monitorred the average surface temperatures of their planet, I suspect that those measurments would have been useful to them for seeing what has happening to their planet – even though those measurements might not have directly revealed the “energy balance” of Venus.
I am getting the feeling that a purpose of this threat is to diminish the perceived importance of simple, credible and easily understood surface temperature measurements – in favor of more obtuse measurements along with heavy doses of theory. Sorry, but when I think I might be running a fever, I will get out my theromometer first – before heading for the journals of medicine.
ericgrimsrud says:
“Again an explanation to the contrary would be welcomed by those of us who do not see a legitimate point in this post.”
Sir, the temperature of a location says only a portion about the actual energy content in the volume of air at that location. Please look up enthalpy. Once you understand that then you will grasp why many persons think findinf the average temperature of the earth is a fools errand.
ericgrimsrud says:
August 28, 2012 at 8:41 am:
“Sorry, but I still do have the impression that a measurement of the average global temperature and changes in it over time is of considerable value and even of primary importance.”
===============================================
But look what you wrote 1 posting ago: “So we do the next best thing – we make such measurements at as many points on the planet’s surface as we can – and hope that those measurements provide a valid measurement of the “true” global average.”
HOPE! You can hope whatever you wish, but selling a hope as a scientific fact is a scientific/political fraud.
Greg, Good to hear from you again. Am glad that you think there is more that mere “hope” associated with our AGW problem. I am not so optimistic but don’t let me weigh you down. Please do continue to look for absolute certainty and I sincerely “hope” you find it before its too late (which it might already be). Eric
ericgrimsrud says:
August 28, 2012 at 8:41 am
Sorry, but I still do have the impression that a measurement of the average global temperature and changes in it over time is of considerable value and even of primary importance.
In physics, I find it is often easy to take an extreme case and see the truth there. Then apply that truth generally. So let us assume we have two thermometers, one of which is 100 m down in the Pacific ocean and the other is 100 m up in the air at any location. Now let us assume the two thermometers read 24 C at a certain time. So the average is 24 C. Now let us assume that exactly one year later, the same thermometers were read and the one in the Pacific read 22 C and the one in air read 28 C. The average would now be 25 C. Now considering that the heat capacity of all the water on Earth is about 1000 times that of air, can you really say the thermal energy of the Earth went up and we need to take drastic steps to reduce it? Or is it more appropriate to take a weighted average of 22 in water and 28 in air to arrive at a weighted average of 22.03 or whatever it turns out to be?
Werner,
That would depend on what you were trying to measure – temperature or heat content.
If one was interested in knowing what the average global surface temperature was, one would try to measure the surface temperatures of all places on the Earth’s surface (including the oceans) and take the average of all of those measurements, of course.
And, of course, if one was interested in knowing where the heat of the Earth is stored, one would take the temperature of all matter on the Earth, and multipy that number by the heat capacity and total mass of that form of matter.
And further, if one also wanted to know something about energy flow between all of these places as well as flow out into the universe, one would have to consider all of the know methods of energy flow including conduction, convection, and radiation.
But what’s the point of all of this? Sure heat content and energy transport are important and interesting subjects, but I thought we were talking merely about temperature.
ericgrimsrud says:
August 28, 2012 at 10:19 am:
“Greg, Good to hear from you again. Am glad that you think there is more that mere “hope” associated with our AGW problem.”
=============================================
What “AGW problem”, Eric? You have just devalued the “measurements” of “GW”, in your own words: “So we do the next best thing – we make such measurements at as many points on the planet’s surface as we can – and hope that those measurements provide a valid measurement of the “true” global average.”
And it is not the “best” thing, Eric, in science it is the worst thing.
but I thought we were talking merely about temperature.
>>>>>>>>>>>>>>>>
We are talking about temperature as a proxy for energy balance.
Two points each at 300K have an average temperature of 300K and an equilibrium energy flux of 459.27 w.m2. Points with temps of:
300 and 300 => average temp = 300K, average w/m2 = 459.27
295 and 305 => average temp = 300K, average w/m2 = 460.04
290 and 310 => average temp = 300K, average w/m2 = 462.33
Three different scenarios that are the exact same average temperature yet have three different average power fluxes. It is not possible to rely on temperature averages alone and come up with a meaningful number that helps us understand energy balance. The only way this can be done is to convert ACTUAL temperatures (not anomalies) into w/m2, and average and trend that result.