How fast is the Earth warming?

The Slutsky-Yule effect?
Is that a thing?
I think there may be a joke there, but I am not gonna be the one…leastways not with Christmas just around the corner.

I think any rate of warming could only be meaningful if it was limited to a small region of similar climate. Once you average everything globally it loses all meaning. Imagine doing a study of the incomes of 100 people over a year. Assuming they start at the same income let’s say 10 people experience a 10% cut in pay, 80 people experience no change, and 10 people experience a 20 percent increase. It would never be correct to say that the whole group experienced an average 1% increase in pay.
Think about that while I try to mix up a batch of universally average paint color.

“Willis I think ignoring this sentence is in error. You cannot average temperatures from the Yukon and Belize and get any meaning.”
I am tending to agree with the skeptics here.
Although sweeping statements can often be parsed and examined to find an example of when the statement may not be true, in general there is a good point to be made here.
As for the Yukon and Belize…which is a fine example…how about if we consider the relevance of averaging the water temperature over the vast open ocean and the interior of the Antarctic continent, and the frozen center of the Arctic ocean, in all of their highly homogenized and guess-worked glory, and throwing those values into a big blender with the surface records?
If one could even get accurate readings from all these places, and then correctly work out in sufficient detail the thermodynamics of the heat content of the various layers and humidity levels…what does it really compare?

Mark, there are two reasons the general notion of using an average of air temperatures needs careful thought, one physical (intensive versus extensive) the other statistical (the meaning of an arithmetic average). Sorry if this discussion is a little long.
When folks think of the physical issue and have comfort averaging over temperatures, they invariably have made the tacit assumption that one is trying to describe a thermodynamically isolated, relatively homogeneous system, such as the room you mention. The tacit assumption is that the room’s temperatures are relatively close together at different locations and the air is at the same pressure and humidity and at equilibrium. Under that tacit assumption, indeed the heat content of the total air is closely approximated as proportional to the temperature and averages over the temperature in the room approximate the narrow distribution of air in the room. Notions of “warming” or “cooling” based on the average temperature have some support. The uncertainty in the average temperature (or heat) is closely estimated by the standard deviation of the temperatures measured. This is essentially morphing the intensive temperature into a good approximation of an extensive property for the particular assumed restricted homogeneous system. But let’s look at what happens when the system under consideration consists of a collection of systems (such as the poles, the tropics, hemispheric lands, and the ocean).
Let’s think of the poles, tropics, hemispheric lands, and ocean as different rooms and we want to know something about their thermodynamics. The air temperatures in each of those locations depends on a variety of thermodynamic quantities including humidity, albedo, convective mixing, aerosols, etc. etc. Call the poles Room P, tropics Room T, lands Room H, and ocean Room O, or just P, T, H and O for short and think of the air temperatures measured there (or anomalies, it doesn’t make a difference just modifies the statistics a little). Let’s say the measured temperature at P is -2, at T +2, at H +1 and at O it is 0.0, all degrees C (these are just hypothetical example numbers but they make the point). Assume these numbers are individually measured repeatedly with thermometers to precision 0.01 C. Now the average temperature is the average of -2, +2, 1, and 0, which is 1.0 C. The standard deviation (more about that later) of these numbers is 1.7 C. The uncertainty with which the average represents the distribution of the numbers (whatever they “mean”) is 1.7 C not 0.01 C. The reason the averaged numbers do not have a small standard deviation such as the individual temperature numbers is because they have not been individually related to the underlying extensive properties. If the average goes up or down one cannot say what it means thermodynamically unless one knows what the underlying distribution is doing. Hence the average number 1.0 C does not describe any thermodynamic system in any causal way and the uncertainty is much more than the measurement error of the thermometers. It does not describe the differential relationship between total system entropy and any of energy, volume, pressure, etc. So if the tacit assumption is not true (and it is not for the globe) then averages of air temperatures over the globe do not represent a thermodynamic quantity.
Now let’s address the statistics issue, i.e the notion of an average. What is commonly called an average is usually meant as an arithmetic average, i.e. the sum of a subset of some set of numbers, possibly all, divided by the number of measurements. There are other averages, such as a geometric average (the product) or a logarithmic average. All of these are simply prescriptions for calculating a number from some set of numbers. Now these prescriptions are, in statistics, generally used as estimates of parameters that characterize a presumed underlying distribution obeyed by the numbers. Arithmetic averages are usually used to estimate the mean of such assumed underlying distributions. Other prescriptions yield estimates of other parameters such as modes, quantiles, variances etc.
The prescription for calculating an estimate can be followed for any set of numbers. However, the utility of the number lies in its ability to estimate a parameter of the underlying distribution. The nature of that distribution is linked intrinsically to the utility of the estimate. Let’s use an illustrative example. If one calculates an average and standard deviation of the numbers 1,1,1,1,10,10 one gets an average of 4 and a standard deviation of 4.6. The prescription for calculating a standard deviation is the average over the deviations of the mean from each of the data points (actually the square root of the sum of their squares). If the assumption of an underlying Gaussian distribution is true to some extent, then this prescription yields a statistically “good” estimate of the standard deviation of the Gaussian whose mean was estimated by the average. (There is a slight nuance concerning sample size and whether we are thinking of the uncertainty of the estimator versus the underlying distribution parameter, but it is unimportant here.) For the example numbers above, it is obvious that these estimates don’t themselves give a clear picture of the underlying distribution (this is because in the back of our mind we are thinking of a Gaussian distribution). We could not draw the distribution of the numbers using just the average and standard deviation. So the utility of a number from the prescription depends on whether the underlying numbers at least somewhat obey the distribution we have in mind. (Another problem with this little example occurs a fair amount in climate science, such as in averages of precipitation amounts or the number of storms, namely the numbers are all positive, but that is another story. The usual Gaussian distribution goes from minus infinity to plus infinity. If the numbers are by definition positive, then some other distribution is needed (e.g. binomial, lognormal, etc.) and estimates of parameters describing those distributions are different.) Inferences drawn (e.g. trends) based on arithmetic averages of such quantities require a careful attention and are usually wrong if done using Gaussian based tools without assuring the underlying distribution is Gaussian on its face or by transformation. If the numbers are far enough away from zero, sometimes a Gaussian is a fair approximation, but otherwise not. Macroscopic temperatures are fairly far away from zero in the natural thermodynamic units of degrees K.
So to use an average wisely, such as global average temperature or temperature anomaly, requires examining the underlying distribution of the numbers. In my earlier post I looked at constant time global temperature distributions from UAH as an example. The statistical utility of the number is based on how well it estimates the distribution of temperatures. (Note that this is related to, but distinct from its physics utility.)

I’m afraid I’m stuck on simple . I’ve been accused of taking simple to the extreme and that definitely might be said to be the design goal of my 4th.CoSy language .
As Willis recently commented , http://wattsupwiththat.com/2015/08/24/lags-and-leads/#comment-2015825 :

Me, I’m a great fan of very simple models, what I call “Tinkertoy” models. I like them because i can use them to see where the earth does and doesn’t act like the model predicts. …

The thorough quantitative understanding of models significantly simpler than Tinkertoys is the classical method of physics . In http://cosy.com/y14/CoSyNL201410.html , I paraphrased from one of the classics I’ve bought after it was mentioned in a blog :

Goody makes the interesting observation , … , that there are two approaches to understanding planetary temperature , one starting from the measured phenomena and working to explain it . That appears to be the ubiquitous method . But without the other , the traditional analytical understanding of abstracted systems simple enough to be quantitatively confirmed by experiment , one never can be said to understand .

David Appell in particular has spammed my explication of calculating the temperature of a radiantly heated colored ball observing that a planet is much more complicated than a simple colored ball .
But , if you don’t know how to calculate the temperature of a radiantly heated colored ball — which can be easily experimentally tested — but which I venture to say many career “climate scientists” don’t , you are blowing smoke to claim you understand anything more complicated .
Averaging temperatures clearly has quantitative meaning . To claim otherwise would imply that it’s just dumb luck that our estimates of observed average global temperature is within 3% of the temperature calculated by
simply summing the energy impinging on a point in our orbit .
As has been pointed out , many intensive properties like temperature and density are intensive because they are ratios with volume or mass already in their definitions . That does not make doing arithmetic with them meaningless . I recently had an exchange with someone so confused by the intensive distinction that he could not understand the purpose of the Kelvin scale or that it was meaningful to say that one temperature was twice another . Such arguments reduce ( Lord Chris , what’s the Latin ) to the impossibility of constructing any temperature scale at all .

As an aside, Axel Kleidon has been doing some very interesting work using rigorous thermodynamics to explore the planetary (climate) system. One paper from 2012 focuses on free energy within the planetary system (an extensive quantity). It is titled “How does the Earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?” It was in Proc. Roy. Soc. but is available online in pdf at
http://rsta.royalsocietypublishing.org/content/roypta/370/1962/1012.full.pdf .
He published another interesting paper in 2011 on wind energy, “Estimating maximum global land surface wind power extractability and associated climatic consequences,” available online at
http://pubman.mpdl.mpg.de/pubman/item/escidoc:1693451/component/escidoc:1693450/BGC1565.pdf
Both are interesting, accessible reads and firmly grounded in thermodynamics. His work is neither pro-AGW nor anti-AGW. It is refreshing to think about the planetary system without the usual baggage of “hottest year evah!” … “no its not!” …. “yes it is!” etc. etc.

MarkW, absolutely, with enough sensors the atmospheric energy content can be measured. The question is how many would one need, could all the sensors be temperature sensors, and would the energy content be expressible as a simple sum of the temperatures.
For the case of a habitable room, HVAC systems are designed to hold the relevant quantities of temperature and humidity within comfortable bounds and to mix the air sufficiently so that the distribution of heat is as uniform as possible, despite the vagaries of day/night, amount of window area, inside/outside walls etc. So the HVAC controlled room air is designed to be a small region in a thermodynamic space. The control point is to keep the temperature (and humidity and mixing) within a small set of bounds. Under these conditions, a few temperature measurements (such as done by a few thermostats around the house or room) can fairly adequately capture the energy content. Given that the HVAC system keeps the room at some equilibrium state, the average temperature is a good proxy for the energy content. The uncertainty on the measurement would be the uncertainty on the control system bounds and the uncertainties of the temperature measurements. The temperature measurements could be made as precise as one wished, but the uncertainty of the energy estimate would generally be dominated by the variation allowed by the control system.
For the atmosphere, there is no human designed control system maintaining the system in global or local equilibria. Recall that temperature appears in a partial derivative in general and only in restricted systems in a total derivative. There are a variety of other thermodynamic variables necessary to characterize energy content of a system. Some of these are humidity, pressure, convection, turbulence, work being done by or on the air mass, etc. For example the specific heat of air varies with humidity by about 5 percent or so over atmospheric ranges. Atmospheric pressure and density varies with altitude exponentially, so we need to consider the size of the volume for which we want to measure the energy and measure the temperature as a function of the altitude desired. The work done on and by flowing air masses varies with the surface roughness, wind speeds, and characteristics determining the turbulence such as the height of the planetary boundary layer which essentially sets the Reynolds number of the local flow. Convective flow itself comprises a significant amount of the energy. So if we want to measure the energy content of some fraction of the atmosphere, we need to measure a lot of things, not just temperatures. Further, although we may be able to measure individual temperatures very precisely, say 0.001 degree C, the uncertainty of the energy estimate will be dominated by the variations in the other thermodynamic variables. A simple average of temperatures alone has large uncertainties as a measure of an extensive quantity like energy content over the globe. Given these uncertainties, there is no way to distinguish between variation in the temperature measurements due to the above stated factors versus the simple spatial variation over the globe and the strict statistical estimate of the uncertainty is quite large. I suspect this underlies the penchant for using even local anomalies, although that introduces another statistical quirk since anomalies are actually deviations. The issue of the distribution of temperatures about the calculated average and the import of that for inferences drawn is a part of another long conversation.
This is not to say that a simple average of temperatures is useless, just that it alone is not a thermodynamic quantity. (Unless the system is being artificially maintained in some narrow ranging equilibrium state like a habitable room.) Like the tide gauge measurements a historical record of temperature average can be used as an index and observed and searched for relationships to other things, under the assumptions that the underlying system is either cyclic, static, evolving, or whatever one wants to consider. Correlations to other variables can be examined. It is just how stock market players calculate the big price indexes, measures of debt/earnings, volatility indices, etc. and search the behavior over time for patterns relating them to consumer confidence, durable goods purchases, inventory levels or whatever.
The main problem with the simple global temperature index occurs when it, along with its statistical uncertainty, is thought of as a thermodynamic quantity and erroneous inferences are made.

Willis and E.M et. al. in this discussion thread: I think the discussion is needlessly contentious and we all actually agree as long as we are precise in our terms and understanding of what each of us is saying.
First, it is not the case that an average of intensive qualities is meaningless, or useless, certainly not in general. Second, it is also not the case that an average of intensive quantities over a heterogeneous or non-equilibrium system or set of systems is IN GENERAL a well-defined THERMODYNAMIC variable, even while maintaining its utility. Third, it can be the case that for a restricted or well defined SPECIFIC system or subsystem an average over intensive quantities is a good measure of the intensive property relevant to the specifically defined system.
To the first point, Willis has given a number of examples in which an average over intensive quantities is useful and indicative of some integrated behavior of the whole system. Water levels are good example. The historical record of high and low tides over a variety of meteorological conditions at a specific location is very useful as a guide to how to plan future construction, tidal surge amelioration infrastructure and the like. It doesn’t matter whether it is or is not a rigorously defined thermodynamic quantity. We take meaning from the historical record as an indicator of the likely future behavior. Even the much maligned global average surface temperature is useful and not without meaning. If it is calculated consistently and as accurately as possible it serves as a historical record of itself and provides a useful target for modelers attempting to model the heterogeneous non-equilibrium climate to try to reproduce it. As long as one keeps in mind, when assessing the uncertainty of the average, to differentiate between the measurement uncertainties of the instruments distinct from the uncertainty with which the average approximates a thermodynamic quantity there is no problem.
To the second point, even though an average of intensive quantities may be accurately calculated and we have historical records indicating its utility as an indicator of the evolution of the system, it is not in general (but see the third point) a thermodynamic quantity. There is no shame in not being a thermodynamic quantity. It is still useful and meaningful. It can still indicate some amalgamated underlying behavior. Not being thermodynamic simply means that the average itself may not appear in a thermodynamic equation based in physics. Alas we do not have equations to represent everything we want, else we would not be having this discussion.
To the third point, if the system under consideration is sufficiently restricted that the intensive quantity is constant enough over the system (meaning its variations over the system are small compared to the underlying dynamics) or the dynamics are represented in some kind of weighting system, then an average of an intensive quantity can be a good approximation of the intensive quantity relevant to that subsystem. Water level in a fixed tank is a good example. It may be the Nino index is another, in the sense that variations over the sea surface considered are small compared to the dynamics of the system – I honestly know nothing about that quantity. It doesn’t make any difference except for how we want to use it, as a term in a thermodynamic equation, or as an indicator to use to predict through correlation or through use of underlying detailed models. It is useful and meaningful in either case.
In summary, depending on the specific case an average over intensive quantities may represent a thermodynamic average intensive quantity or it may not represent an average thermodynamic intensive quantity. In either case, the number can still have immense utility and meaning. In a complicated world, not all numbers can be well defined thermodynamic quantities, but they are still useful. It remains for us to use the numbers wisely and try to avoid arguments when we all agree, at least when we understand what we each are saying.
To emphasize the point, the statement that “An average over intensive quantities has NO meaning” is incorrect. Also, the statement that “An average over intensive quantities is ALWAYS a thermodynamic variable” is incorrect.

Ditto me on that cooling trend Mark.
And I think the eyeroll is the perfect response to the inanity of the warmistas.
Toss in a good eyelash flutter for emphasis too.
The problem, or course, is that the inanity is the least of it.
This BS is serious shite nowadays.
The US economy and much of our energy infrastructure is being regulated out of business.

I like day to Dat better.
It says it all.

If I am interpreting this correctly, what it means is that if you wave your arms around in a big windmill fashion while talking real fast and using some big words and colorful charts…it is very impressive.

Honestly micro, I thought you were goofing him…my bad.