Understanding the relationship between climate and weather is important in climate science.
Here’s NASA:
The difference between weather and climate is a measure of time. Weather is what conditions of the atmosphere are over a short period of time, and climate is how the atmosphere “behaves” over relatively long periods of time.
And again:
Climate is the average of weather over time and space.
Who could argue with that succinct statement? Easy for all of us to understand.
Now Tamino, in his long running blog, says:
Time and time again, peoplewhodontagreewithus-ists try to suggest that the last 10 years, or 9 years, or 8 years, or 7 years, or 6 years, or three and a half days of temperature data establish that the earth is cooling, in contradiction to mainstream climate science…
Of course that raises an interesting question: how long a time span do we need to establish a trend in global temperature data? It’s sometimes stated that the required time is 30 years, because that’s the time span used most often to distinguish climate from weather. Although that’s a useful guide, it’s not strictly correct. The time required to establish a trend in data depends on many things, including how big the trend is (the size of the signal) and how big, and what type, the noise is…
Well, I agree with the statistical principles involved here. But his comment does raise a very interesting point.
Is the global temperature value measured for a year just noise on top of the climate signal?
If the global temperature value measured in 2009 is less than that measured in 2008 did the world actually cool that year (relative to 2008), or is it just noise ?
Digression on Noise and Signal
For those not so familiar with the technical terms it’s worth explaining signal and noise a little. Let’s choose a non-controversial topic and suppose we want to set up a radio communications link. We have a receiver which amplifies the tiny incoming radio signal so that we can hear it – or retransmit it – whatever we want to do with this signal.
The noise is the random element that get mixed in with the signal. In amplifiers they are frequently the random movement of electrons (that increase with temperature). In reception of the signal they are the other radio waves at similar frequencies that have been reflected, diffracted and otherwise distorted their way to your receiver.
In this case, noise is stuff that is NOT the signal. It threatens to stop you measuring your signal – or at least make it less accurate. Noise can have a systematic bias or it can be random. And in the real world of engineering problems, dealing with noise is often a significant problem to be solved.
Signal and Noise in Climate
We are thinking here specifically of the average global temperature. Often known by its acronym, GMST (global mean surface temperature).
What Tamino appears to be saying is that the temperature from year to year is just the “noise” on top of the climate (temperature) signal. Well we don’t want noise to upset our measurement so in that case we do need to call on statistical processes to give us the real signal.
But is it true? Is this the right way to look at it?
Other commentators and scientists have made a similar point. Easterling’s paper Is the climate warming or cooling? submitted to GRL (2009) says:
Numerous websites, blogs and articles in the media have claimed that the climate is no longer warming, and is now cooling. Here we show that periods of no trend or even cooling of the globally averaged surface air temperature are found in the last 34 years of the observed record, and in climate model simulations of the 20th and 21st century forced with increasing greenhouse gases. We show that the climate over the 21st century can and likely will produce periods of a decade or two where the globally averaged surface air temperature shows no trend or even slight cooling in the presence of longer-term warming.
But there’s a very interesting paper in Current Opinion in Environmental Sustainability (2009) from Kevin Trenberth on the global energy budget. It’s worth paying close attention to what he has to say, and for anyone interested in the subject of the global temperature, read the whole paper. From the introduction:
The global mean temperature in 2008 was the lowest since about 2000 (Figure 1). Given that there is continual heating of the planet, referred to as radiative forcing, by accelerating increases of carbon dioxide and other greenhouses due to human activities, why is the temperature not continuing to go up? The stock answer is that natural variability plays a key role and there was a major La Nina event early in 2008 that led to the month of January having the lowest anomaly in global temperature since 2000. While this is true, it is an incomplete explanation.
In particular, what are the physical processes? From an energy standpoint, there should be an explanation that accounts for where the radiative forcing has gone. Was it compensated for temporarily by changes in clouds or aerosols, or other changes in atmospheric circulation that allowed more radiation to escape to space?
Was it because a lot of heat went into melting Arctic sea ice or parts of Greenland and Antarctica, and other glaciers? Was it because the heat was buried in the ocean and sequestered, perhaps well below the surface? Was it because the La Nina led to a change in tropical ocean currents and rearranged the configuration of ocean heat?
Perhaps all of these things are going on?
Interesting.
Trenberth is saying that we need to understand what happens to the global energy “account” in shorter time periods than decades. In fact, it’s essential. Because if we don’t know whether the earth warms or cools in one year, there might be important aspects of the climate that we haven’t understood in sufficient detail – or we aren’t measuring in sufficient detail. And if the earth has warmed but we don’t know where the energy actually is that is a problem to be solved as well.
All of which leads to the inescapable conclusion that the average global temperature value for one year is not “noise”. It is the “signal”. (See the technical note on temperature measurement at the end of this post)
After all, if there is a radiative imbalance in the earth’s climate system such that we take more energy in than we radiate out it must be warming. But if this energy is not being stored somewhere then the earth hasn’t warmed in that year. In fact, if there is less heat in the climate system, we radiated out more than we received in. There isn’t some secret place that is storing it all up.
Roger Pielke Sr has made that point (probably many times).
What I’m not saying is that earth is on a long term cooling trend. And I’m definitely not saying that the cold weather yesterday means the earth is cooling.
But if the global temperature in one year is cooler than the global temperature in the previous year then the earth has cooled. It’s not noise.
It’s only noise if we can’t measure temperature accurately enough to be sure whether the temperature has gone up or down.
Possibly I have misunderstood Tamino. I did post a comment on this topic to his recent blog post (twice) but possibly due to a moderating snafu, or possibly because there were much more important questions to be answered, it didn’t get published.
Conclusion
As NASA says, the climate is the average of the weather.
Monthly and annual averages of specific values like temperature and total heat stored in the climate system can change in apparently random ways. But that doesn’t mean that these changes don’t reflect real changes in the system.
I can draw a trend line through a longer time series and show lots of deviations from the trend line. But that doesn’t give some kind of superior validity to the trend line. I could take 10000 years of climate data and show that 100 year periods are just noise.
What is the climate doing? It’s apparently random, but actually always changing. Over the last 40 years it has warmed. For the more recent shorter period that Trenberth covered, it cooled. Over the last 20,000 years it has warmed. Over the last 10 million years it has cooled.
If there’s less heat in the earth’s climate at the end of 2010 compared with 2009, the planet will have cooled. And if there’s more heat at the end of 2010 compared with 2009, the planet will have warmed. Not noise, it really will have changed.
Why the total heat stored goes up and down, and how that heat is distributed is at the heart of the complex subject known as climate science.
Technical Note
More on this on a later post, but as many physicists will point out, taking the average temperature around the world is a little odd. That might seem strange – how else can you see whether the world is warming???
As a thought experiment, if you have 5 places to measure temperature, nicely distributed, the average temperature,
Tav = T1 + T2 + T3 + T4 + T5.
But it’s not really meaningful. T1 might be measured in a big lake – and water stores a lot of energy per unit volume. T2 might be measured on a big piece of plastic and be storing almost no energy.
Adding up these different numbers and dividing by the number of measurements is not really a useful number. Sure if you keep calculating this same average it kind of gives you a clue where things are headed. But it could be misleading. The piece of plastic might go up 10°C and the lake might go down 5°C so the average has gone up. But the total heat in the system will have gone down.
Two more useful methods would be:
- Sum up the energy actually stored -as Trenberth does in his paper – but it’s tougher
- Average the fourth power of the temperatures – T4
Energy is radiated out as the fourth power of temperature, so averaging this value gives you more idea how much energy the system is radiating – as a proxy for the energy changes in the system. It’s easy to show that global average temperature can go up while total radiated energy is going down. Just have the colder places heat up more than the warmer places cool down and Tav increases while T4av decreases. More on this in another post.
The Science of Doom 
“Warmest Decade on Record” and the Layman’s Guide to Autocorrelation
Posted in Commentary, Measurement on January 4, 2010| 4 Comments »
In many debates on whether the earth has been cooling this decade we often hear
(Note: reference is to the “naughties” decade).
This post isn’t about whether or not the temperature has gone up or down but just to draw attention to a subject that you would expect climate scientists and their marketing departments to handle better.
An Economic Analogy
Analogies don’t prove anything, but they can be useful illustrations, especially for those whose heads start to spin as soon as statistics are mentioned.
Suppose that the nineties were a roaring decade of economic progress, as measured by the GDP of industrialized nations (and ignoring all problems relating to what that all means). And suppose that the last half century with a few ups and downs had been one of strong economic progress.
Now suppose that around the start of the new millennium the industrialized nations fell into a mild recession and it dragged on for the best part of the decade. Towards the end of the decade a debate starts up amongst politicians about whether we are in recession or not.
There would be various statistics put forward, and of these the politicians out of power would favor the indicators that showed how bad things were. The politicians in power would favor the indicators that showed how good things were, or at least “the first signs of economic spring”.
Suppose in this debate some serious economists stood up and said,
What would we all think of these economists?
The progress that had taken the world to the start of the millennium would be the reason for the high GDP in the “naughties” decade. It doesn’t mean there isn’t a recession. In fact, it tells you almost nothing about the last few years. Why would these economists be bringing it up unless they didn’t understand “Economics 101”?
GDP and other measures of economic prosperity have a property that they share with the world’s temperature. The status at the end of this year depends in large part on the status at the end of last year.
In economics we can all see how this works. Prosperity is stored up year after year within the economic system. Even if some are spending like crazy others are making money as a result. When hard times come we don’t suddenly reappear, in economic terms, in 1935.
In climate it’s because the earth’s climate system stores energy. This is primarily the oceans and cryosphere (ice) but also includes the atmosphere.
Auto-Correlation for the total layman/woman who doesn’t want to hear about statistics
For those not statistically inclined, don’t worry this isn’t a technical treatment.
When various people analyze the temperature series for the last few decades they usually try and work out some kind of trend line and also other kinds of statistical treatments like “standard deviation”.
You can find lots of these on the web. I’m probably in a small minority but I don’t see the point of most of them. More on this at Is the climate more than weather? Is weather just noise?
However, for those who do see the point and carry out these analyses to prove or disprove that the world is warming or cooling in a “statistically significant” way, the more statistically inclined will be sure to mention one point. Because the temperature from year to year is related strongly to the immediate past – or in technical language “auto-correlated” – this changes the maths and widens the error bars.
Auto-correlation in layman’s terms is what I described in the economic analogy. Next year depends in large part on what happened last year.
Why mention this?
First, a slightly longer explanation of auto-correlation – skip that section if you are not interested..
Auto-Correlation in a little more detail
If you ever read anything about statistics you would have read about “the coin toss”.
I toss a coin – it’s 50/50 whether it comes up heads or tails. I have one here, flipping.. catching.. ok, trust me it’s heads.
Now I’m going to toss the coin again. What are the odds of heads or tails? Still 50/50. Ok, tossing.. heads again.
Now I’m going to toss the coin a 3rd time. At this point you check the coin and get it scientifically analyzed. Finally, much poorer, you hand me back the coin because it’s been independently verified as a “normal coin”. Ok so I toss the coin a 3rd time and it’s still 50/50 whether it lands heads or tails.
Many people who have never been introduced to statistics – like all the people who play roulette for real money that matters to them – have no concept of independent statistical events.
It’s a simple concept. What happened previously to the coin when I flipped it has absolutely no effect on a future toss of the coin. The coin has no memory. The law of averages doesn’t change the future. If I have tossed 10 heads in a row the next toss of this standard coin is no more likely to be tails than heads.
In statistics, the first kind of problems that are covered are ones where each event or each measurement are “independent”. Like the coin toss. This makes analysis of calculation of the mean (average) and standard deviation (how spread out the results are) quite simple.
Once a measurement or event is dependent in some way on the last reading (or an earlier reading) it gets much more complicated.
In technical language: Autocorrelation is the correlation of a signal with itself
If you want to assess a series of temperature measurements and work out a trend line and statistical significance of the results you need to take account of its auto-correlation.
What’s the Point?
What motivated this post was watching the behavior of some climate scientists, or at least their marketing departments. You can see them jump into many debates to point out that the error bars aren’t big enough on a particular graph, with a sad shake of their head as if to say “why aren’t people better at stats? why do we have to keep explaining the basics? you have to use an ARMA(1,1) process..”
But the same people, in debates about current cooling or warming, keep repeating
as if they hadn’t heard the first thing about auto-correlation.
Statistically minded climate scientists, like our mythical economists earlier, should be the last people to make that statement. And they should be the first to be coughing slightly and putting up a hand when others make that point in the context of whether the current decade is warming or cooling.
Conclusion
Figuring out whether the current decade is cooling or warming isn’t as easy as it might seem and isn’t the subject of this post.
But next time someone tells you “This decade IS the warmest decade on record” – which means in the last 150 years, or a drop in the geological ocean – remember that it is true, but doesn’t actually answer the question of whether the last 10 years have seen warming or cooling.
And if they are someone who appears to know statistics, you have to wonder. Are they trying to fool you?
After all, if they know what auto-correlation is there’s no excuse.
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