## Friday, January 15, 2010 ... //

### Global UAH: warmest January day on record

Many people think that the globe must be terribly cold these days. We've seen huge cold snaps and snowfalls in Britain, Eastern parts of the U.S., Western Europe, Central Europe, China, Korea, and India where hundreds of people have frozen.

So these are almost all the important places, right? (At this moment, the speaker forgets that there are places such as Latin America, Australia or the Balkans which have been warm.) So the globe must be cool - cooler than average, people could think.

However, the daily UAH global mean temperature shows a different story. The early January 2010 was warm. And on January 13th, which is the latest day whose temperature is known, we have seen the warmest January day on their record. The brightness global temperature near the surface was
T = -16.36 °C
which may not look excessively warm :-) but it is actually 0.11 °C warmer than the warmest January temperature recorded by UAH so far - which was on January 5th, 2007 (-16.47 °C). On January 14th, the temperature record was marginally improved to -16.35 °C. One day later, the figure even jumped to -16.29 °C while on January 16th, it was -16.27 °C (full 0.2 °C warmer than the previous 2007 record high) - and chances are above 50% that we will see even warmer figures this January.

(Update: I noticed that January 1998 was already missing in the UAH daily Java applet which only began in Summer 1998. It's plausible but far from certain that a January day in 1998 was warmer - but very unlikely that there was a warmer January day observed by UAH before 1998.)

By the way, you can see why this temperature anomaly could have been increased exactly by the extraordinarily high snow cover. The latent heat needed to create the extra snow in January 2010 could have heated up the atmosphere by as much as 0.2 °C.

Of course, some alarmists might feel happy for a while. They've been afraid that the worries about a new ice age could escalate. And they've been saved: the global weather is warm again. The strong El Nino episode (which is underway and approaching the 1998 levels of the ONI index) could have helped them - or someone else. It's important that they're saved. ;-)

However, there is another, more important consequence of these numbers. And it is the following: the global mean temperature is irrelevant for you and for everyone else, too. It didn't help the hundreds of frozen people in India, the passengers whose flights were canceled, and millions of other people in the European, Asian, and American civilization centers.

If you actually draw the monthly data from 1979 to 2009 - the global ones and those in e.g. Prague - you will find out that the correlation coefficient is just 0.17 - well below the maximum possible value of 1.00. It won't be much higher outside Prague, either. :-)

The Pythagorean average monthly anomaly in Prague has been something like 1.95 °C. Imagine that you want to use the global temperature in order to improve the estimate of the temperature in Prague for a given month. If you add the global anomaly and the expected local average temperature in Prague for the month, you will reduce the typical fluctuation from 1.95 °C to 1.92 °C or so - almost no change. The swings in the global temperature won't visibly help you to improve the predictions of the local temperature.

So while it may be fun to watch the global temperature - a meaningless game that many people began to play in recent years because of the AGW fad (and yes, your humble correspondent only plays these games because others do, not because it is scientifically important) - it is very important to realize that the changes of the global mean temperature are irrelevant for every single place on the globe. They only emerge when things are averaged over the globe - but no one is directly affected by such an average.

Even if you accumulate a whole century of changes, the relevance of the global temperature will be essentially non-existent. A 1.5 °C warming of the global mean temperature is still less than one standard deviation of the monthly average at a given place. And the "local" climate may also shift - the January 2100-2150 average may be warmer than the January 1950-2000 average in Prague by much more than those 1.5 °C. Different regional climates change differently and most of these changes have nothing to do with the changes of the global mean temperature!

By the way, it's almost certain by now that January 2010 will also be the globally warmest January on the UAH record - the anomaly will likely surpass 0.70 °C. It may even see the highest (or at least 2nd highest) monthly UAH anomaly since December 1978. I will print more exact predictions in a week or so.

#### snail feedback (7) :

Those satellites were conveniently adjusted taking as reference just the 1500 warmest surface stations out of 6000.

You know, Roy Spencer is actually doing these things, so he probably knows what he's doing.

The satellite data are not calibrated by the surface thermometer data at all. Moreover, even if they had been, your adjective "warmest" would be completely irrelevant for obtaining a warming trend. "Warmest" is not the same thing as the "most quickly warming".

I have a question about standard deviations and averages.

You say that “the relevance of the global temperature will be essentially non-existent. A 1.5 °C warming of the global mean temperature is still less than one standard deviation of the monthly average at a given place." And that “no one is directly affected by such an average.” Very clever and convincing statistical reasoning.

I am curious, however. It is said that chemical reactions and phase changes are temperature dependent. This must be wrong or at least an exaggeration. Your key insight seems to be that, when studying the implications of change, we should be comparing (a) the change in the average with (b) the value of the standard deviation. If the change is small compared to the standard deviation, then the change is of no consequence. We can apply this insight to the Boltzmann distribution. Heck, what’s a few degrees change in average energy compared to the huge standard deviation of molecular energies in room temperature gas? Paraphrasing your insight, no chemical reaction would be affected by the average.

Correct me if I’m wrong, but it seems we must conclude that refrigeration of food is completely unnecessary and that temperature control in manufacturing is a waste of time. Why have we been so obsessed with temperature? One of those alarmist things we got suckered into believing and never thought through. Why bother with observation when we can just reason through to the correct answer?

In fact, why even bother with the monthly standard deviation? We can argue from first principles that 1.5 °C has no practical effect on chemical reaction or phase change, and therefore no one is directly affected by the average.

Thank you for educating us with the statistical insight that a change in the average does not matter if it is small compared to the standard deviation.

Dear Ted, thanks for your kind words and questions.

I am confident that when the cooking or freezing is a part of the process to produce food, it has a significant impact - not only by many standard deviations but literally by orders of magnitude.

Try to calculate the number of bacteria that survive 1 hour at room temperature with those that survive at a higher temperature, and so on. Because their populations grow/decrease exponentially, when the temperatures are convenient/damaging, a small change of the exponent will translate into a big change of their population, which is why these things are important in the manufacturing process.

Be sure that my comparison of the "change caused by something" (signal) with the "standard deviation of the quantity" (noise) always gives you a sensible policy recommendation. You must just figure out what quantity is really relevant for you, and how it's affected by the policy and what its standard deviation is.

So if you wanted to prove that the Boltzmann distribution should be universally replaced by a constant, I surely disagree. ;-)

But if you wanted to say that 1.5 °C of change has no practical implication for pretty much anything in ordinary life, except for very fine pieces of industry that may require precision (and where you need to keep the temperature unnaturally constant - the constancy may beat anything that you could ever find in Nature), I agree wholeheartedly. 1.5 °C makes no difference. In Nature, everything fluctuates by 1.5 °C all the time, so everyone is ready to it and no one almost takes notice.

Cheers
LM

There are, of course, situations where a small movement in the mean (relative to standard deviation) is inconsequential. However, temperature dependent processes are not among them. Your signal-to-noise analogy is inappropriate and misleading when trying to understand phase change or chemical reaction rates. And those are what we need to concern ourselves with if we are trying to understand the significance of temperature change on Earth’s climate, geology, and biology.

"Temperature" (times a conversion factor) is the mean molecular kinetic energy from a Boltzmann energy distribution. It is easy to measure with a thermometer and gets a lot of attention. Focusing on the mean can be misleading, however, because rates of chemical reaction depend more on the distribution tail. When the "temperature" (mean energy) changes by 1K from 300K, the relative number of molecules within one standard deviation of the mean changes relatively little, because the function is relatively flat near the mean.

What changes dramatically and nonlinearly is the relative number of molecules at the tail of the distribution. This is easy to forget for healthy, temperature regulated creatures like you and me. For us, a few degrees change in ambient temperature is not a problem. As you say, we would not notice. But for natural chemical and physical processes and for the vast majority of organisms which have no temperature regulation, ambient matters a lot, because the molecular business end is the distribution tail. It is the small fraction of molecules that exceed the energy threshold that drive change. It is the small fraction of molecules far above the mean molecular energy that evaporate off the surface of water. It is the small fraction of molecules with enough energy to overcome the activation potential that causes iron to rust.

Imagine you could magically broaden the Boltzmann distribution function in an evaporation experiment. Apply your signal-to-noise analysis. The standard deviation would rise, so the signal-to-noise ratio would drop. If you wish to measure significance using signal-to-noise, then the broader Boltzmann function would predict reduced significance of warming. This is, of course, backwards. The issue is not what happens near the mean, but what happens near the tails.

Statistical mechanics is not the only field where distribution tails matter. If you are your company’s statistical process control engineer, and you want to reduce the defect rate to parts per million, you need to concern yourself with the distribution tails. When the mean moves a little, the number of production parts beyond five sigma changes nonlinearly and dramatically. Decreasing slightly the length of pins your factory produces may have no important effect on the mean length of pins you ship, but it can have a huge effect on the warranty return rate for pins that are too long.

I vigorously objected to your analysis because it is a common and bad misconception that understanding statistical significance only requires comparing movements in the mean relative to the standard deviation. So, when you say that “A 1.5 °C warming of the global mean temperature is still less than one standard deviation of the monthly average at a given place" and that “no one is directly affected by such an average,” I say you are not only wrong but you are contributing to that misconception.

Dear Ted,

I agree with you that the temperature is the mean energy and that the (arithmetic) average of a quantity is not enough to determine its impact if its impact depends highly nonlinearly - e.g. exponentially - on the quantity.

These things are important in chemistry, and so on, and so on. However, I don't think that they're too relevant in a discussion about the global mean temperatures and global warming which is why I consider your comments to be off-topic unless you demonstrate otherwise.

The nonlinearities - and e.g. the choice of the way how we calculate the arithmetic/other averages of temperature - can be seen to have "some" impact on some things but the impact is pretty small. Calculate it for yourself.

If you formulate the sentence properly and the sentence compares the signal with noise, and if enough data affects the quantities so that the central limit theorem is applicable, it is a *mathematical fact* that the statistical significance only depends on the "signal to noise ratio".

But even if one avoids rigorous mathematical propositions, it's another self-evident fact that if the accumulated temperature change is less than by the typical deviation of the average monthly (local) temperature from the "normal", (local) people won't be able to determine, with any significance worth talking about, whether the warming has actually occurred by looking at 1 month of the data. Do you really have any doubts about this trivial comment? Your comments start to be obnoxious.

Best wishes
Lubos

Yes. I thought about this later, and agree I got off track and out of bounds, and I think you appropriately took me to task for that. So, my apologies extended.

Bear with me, if you will. I still do not agree with you that either statistical significance or signal-to-noise is relevant. Well, it is relevant to the statistician who is trying to determine the statistics of temperature patterns, but that is not the issue. The issue is whether “changes of the global mean temperature are irrelevant for every single place on the globe. They only emerge when things are averaged over the globe - but no one is directly affected by such an average.”

Consider a simple experiment. Environmental chamber ‘A’ is set to a constant 20C for one month with a glass of water (representing physical processes) and potted bean seeds (representing chemical and biological processes). A lab technician measures temperature daily with a thermometer. Environmental chamber ‘B’ is set up the same but higher by 1.5C to a constant 21.5C. After one month, compare the measured temperatures, water loss, and plant growth. The results will be that more water will evaporate from the glass and the beans will grow more in ‘B’ than in ‘A’. The standard deviation of temperature will be zero in each chamber, and the difference between chambers will be statistically significant. The signal to noise will be zero. The statisticians are happy. The physical and chemical process rate differences are obvious.

Now run similar experiments in environmental chambers ‘X’ and ‘Y’ with one difference. You first get out your random number table and select random temperatures between 10C and 30C. You program chamber ‘X’ to change the temperature every hour according to the random numbers. You program chamber ‘Y’ to the same temperature schedule, except that you add 1.5C to all values, thereby making ‘Y’ 1.5C warmer than ‘X’. The lab tech measures temperatures in ‘X’ and ‘Y’. After one month, compare results. This time, the statisticians argue about whether there is a statistically significant difference between the temperatures in ‘X’ and ‘Y’. The standard deviation is now too high and the signal-to-noise too low. However, it is obvious that, because the temperature is always 1.5C great in ‘Y’, more water will evaporate and more plant growth will occur in ‘Y’.

Or, run a conceptually simpler and essentially equivalent experiment in which the temperature ramps from 10C to 30C in chamber ‘X’ and from 11.5C to 31.5C in chamber ‘Y’. Regardless of how you vary the temperature, you will notice significant physical and chemical process differences between the on-average warmer and on-average cooler chambers.

So, I disagree with you. The average does matter. Temperature variation may mask the difference to the thermometer, but it does not mask the difference to the physics and chemistry.

You write “… if you wanted to say that 1.5 °C of change has no practical implication for pretty much anything in ordinary life, … I agree wholeheartedly. 1.5 °C makes no difference. In Nature, everything fluctuates by 1.5 °C all the time, … and almost no one takes notice.” But, no, I would not want to say that 1.5C of change has no practical implication, because it seems to me that it clearly does.