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.
ericgrimsrud says:
August 29, 2012 at 7:56 am:
“OK, so would those of you who say that average global surface temperatures are meaningless and that the anomalies thereby observed are nothing more than “anoma-lies” please suggest a measure that would replace those simple and readily understood temperature measurements?”
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Eric, there is apparently no reliable scientific method to find out, whether the so called “global temperature” changes or not.
Do you really suggest we should use something unreliable and sell the result as a scientific fact? Don’t you think it would be a fraud?
To ericgrimsrud
Mission accomplished – we then would no longer have any measurement that reliably tells us whether the Earth’s temperature is changing !!!
You apparently decided to stubbornly misunderstand so that one wonders why you even posted here first place.
Nobody needs global temperature averages to know that tempeatures change. They trivially do, do so since 4 billions of years and will do so for the next 4 billions of years and beyond.
Perhaps somebody finds it fun to put a number on it . You could compute a geometrical average too, why not ?
The point what everybody is trying to explain to you is that this information about a global average is irrelevant aka useless.
I notice that you carefully avoided to engage my detailed explanation of why it was useless.
It is useless because it explains nothing and predicts nothing.
It cannot even be used to falsify theories because an infinity of theories where an infinity – 1 will be wrong will show the same averages.
So while it may have a value to satisfy the curiosity of somebody who wonders whether temperatures change or not and is not bright enough to already know that they do, it is of no value whatsoever to a scientist who asks questions about the dynamics of the system.
The parameter which encodes the relevant information is the whole temperature field – its average is irrelevant to everything.
For this reason it is of course important to measure temperatures and their distribution but it is absolutely not interesting to compute their arithmetical (or geometrical for that matter) averages. They are just mathematically accurate but physically meaningless numbers.
David:
Thankyou for your fine article.
I am now back in contact with the web and I write to point out something which directly pertains to your article. I have been saying this for years in many places (including on WUWT and in my review comments for the IPCC AR4). It is:
The observation of global temperature changes over the twentieth century could be entirely an effect of a change to the rate of horizontal heat transfer across the surface of the globe.
This possibility is because, as you point out, radiative flux is proportional to T^4. And, for radiative balance, the Earth must radiate energy to space at the same rate as it obtains energy from space (i.e. from the Sun). But the Earth receives most energy (per unit area) near the equator and emits least energy (per unit area) near the poles. Heat is transferred by oceans (and air) polewards from the tropics. Indeed, the tropics are net absorbers of radiation and the polar regions are net emitters of radiation.
Hence, a change to horizontal heat transfer (e.g. by oceans) across the globe will alter both the high and the low surface temperatures over the globe’s surface. These changes to local temperatures will provide a change to global temperature when the total radiative flux is a constant because radiative emission is proportional to T^4.
This possibility is important because it negates the ‘argument from ignorance’ which is used to support AGW. That argument says the rise in observed global temperature cannot be explained without including effects of increased GHGs (notably CO2) in the atmosphere. But it can: a change to the rate of heat transfer across the globe is an alternative explanation. And nobody knows what alters oceanic flows (e.g. ENSO behaviour cannot be predicted although the development of an initiated ENSO event can be predicted).
Richard
PS My use of ENSO as an illustration was not intended to invite discussion of epicycles.
richardscourtney;
Interesting comment. I came do very nearly identical conclusions via a somewhat different line of reasoning. The problem is disentangling two different processes.
We know from ERBE data and other sources that the arctic regions are net emitters of radiation and the tropics are net absorbers. For this to be true, energy must be transferred from tropics to arctic regions via air and water currents. We can actually measure those too, so no doubt that this is what happens.
So now the conundrum. When we observe a change in temperature in the arctic region, how do we quantify how much is due to direct effects of CO2 increases, and how much is due to changes in the amount of energy being transported from tropics to arctic regions?
The more I dig into the physics at this point, the worse it gets. For starters, the putative 3.7 w/m2 from CO2 doubling isn’t uniform. CO2 only has 150 w/m2 of upward bound LW to work with in the arctic regions, it has a whopping 450 w/m2 to work with in the tropics. So, the distribution of the 3.7 w/m2 direct effects of CO2 cannot be uniform. From there the math gets ugly. From an energy retention perspective, the change due to CO2 doubling in the tropics must be much higher than it is in the arctic regions, but because of the relationship to T^4, the temperature change is lower. Talk about counter intuitive! But worse still, the movement of energy from tropics to arctic regions must necessarily be driven by temperature differential which creates the high/low pressure cells and convective cells and so on that move air and water which in turn move energy around. So if the temperature differential between tropics and arctic zones gets reduced, then we’d expect LESS energy to be moved? Again, counter intuitive, because although less air and water gets moved, the energy density is higher…. at which point my head starts to hurt….
David:
Thankyou for the reply to me which you provide at August 30, 2012 at 9:58 am.
As you say, the issues are difficult to isolate but – with respect – that is my point.
For sake of illustration, consider that the tropics were to cool by 0.1 deg.C . Then the rest of the world must warm to maintain radiative output. The result is global warming of more than 0.1 deg.C because the tropics are the hottest region and radiative output is proportional to T^4.
Please note that I am not claiming the tropics have cooled. Indeed, the tropical oceans are near their limit of maximum temperature of ~31 deg.C. This limit seems to be a result of increased evapouration and cloud cover with increased thermal input (from any source). Therefore, the existence of this limit implies that variations in tropical temperatures are improbable.
However, the same effect would occur if the region of maximum temperature were to vary in area.
Importantly, there is no way to know if this variation happened over the last century. But it may have happened. And if it did then it may have happened such as to provide all the observed global warming over the last century.
Therefore, it is not true that increased atmospheric GHG concentrations are required to explain global warming over the last century. It would be equally true to assert that altered temperature distribution is required to explain global warming over the last century. In fact, neither statement is true: both effects – or neither effect – may have contributed to the observed global warming.
In my opinion, the major importance of your post is that it draws attention to the fallacious nature of the assertion that increased atmospheric GHG concentrations are required to explain global warming over the last century. Whenever that assertion is made it can be refuted by pointing out the other – also unlikely – possibility.
Richard
Data has been replotted for base periods from 1931 to 1995. The results are plotted here:
http://climateandstuff.blogspot.co.uk/2012/08/the-effect-on-slope-using-base-period.html
Using a base period of
1931 0.087K per decade
and 1961 0.077K per decade
So 1961 to 1991 seems a fair period to normalise to.
Richard;
A horizontal change in distribution of humidity would accomplish the same. Maybe moreso!
I am a lurker and I agree with ericgrimsrud, this article is fishy. And I believe it is justified to be said about an article which starts in the very beginning with a rather stron accusation of “lie”. Under this premise, there is no need to get personal towards Eric, David (August 29, 2012 at 8:58 am), since you set the tone yourself already.
So, again, why is this article fishy, also in my view: Because David denies a well developed method any possible merits. And David offers no better alternative. So, behind all scientific elaborations, he is on the simple rethoric trip to replace something with nothing. As far as I am aware, scientists are well aware that they have to work a lot with assumptions and uncertainities and that they nevertheless have to try to link factors based on this. This does not make them liers, and I believe this is still better than trying to assume – nothing.
So whats the point. To turn down on climate warning or to establish a new filosophy yourself? Whats it going to be with good old human observation keeping book by decades by now and testifying numberless climate changes without counting photons? Count bacterial and viral migrations if you really want to know about truth. There is no global math of any value or meaning but general.
Climate is of local importance in the continental part of the globe and the chain reaction to good or bad attached. Guess what, human kind is pretty much pending on this. And tell the US citizen. Half mid east burned down this year, sub soil dry as powder already. Oh yes, the number of photons on global output…. Seriously, we got to learn to be responsible while talking!