How to pick cherries

The not-so fine art of contriving to support the conclusion you predetermined is cherry picking.  Really not a good thing for a scientist to do or condone, but pretty common in politics.  The latest example comes from politician (now presidential candidate) Ted Cruz, being condoned/defended (even praised) by scientist Judy Curry.

Suppose you're interested in global warming, just in understanding what's going on -- not in 'proving' that there is warming, or cooling, or that temperatures are unchanged.  You're an actual skeptic -- looking for evidence and where the evidence leads.  One thing you learn pretty quickly in your skeptical explorations is that you need 20-30 years of data to define a global climate temperature.  Shorter than that, and your answer depends sensitively on your averaging period.  As a skeptic, you don't want such unreliable methods.  Apply the 30 years to a number of data records (below), and you get the answer that climate has been warming, 1.3-1.7 K/century (2.3-3.1 F).

As a cherry-picker, committed to finding a particular answer, however, you go straight for the option of using short spans -- look for a record length that will give you the answer you want, then ignore the fact that your answer changes if a couple years are added or subtracted.

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Agriculture in changing climate

If you're one of the people who thinks that food grows in grocery stores, all the talk about climate change affecting agriculture is passing you by.  You'd be wrong to think so, but most modern industrial country people are not involved in agriculture.  Having grown up in the corn belt I'm perhaps a little sensitized to the fact that farming is hard work.  And that farming is extremely sensitive to details of the weather.  Anything sensitive to weather is sensitive to climate.

Many foods depend on extremely specific climates.  Not just current climates, but the history of climate for thousands of years -- soils to grow a good crop in develop over that time span.  The corn belt is where it is not just because of current (well, 1950-1980) climate but because in the thousands of years before that, the soil improved and developed to the point of being able to support such farming.  For something like corn, which is grown across a huge area, climate change can be an issue.  But someone, somewhere, will probably be able to grow corn 30 years from now.

But many items grow in relatively small areas, subject to the whims of local change.  Some of these are:

• Chocolate
• Beer (hops)
• Wine (grapes)
• Coffee
• Horseradish (85% of the entire world's supply grows in a single county in Illinois)

Such specialized crops are sensitive, to the point of perhaps being eliminated, to climate changes.

I invite readers to check the sources linked to above.  And to contribute their own crop types that are either sensitive to climate change, those which are insensitive, and those which would even benefit from expected changes.  Please do include links to your examples.

Harry Bulkeley: A few questions about global warming -- Answered

An opinion writer (a retired judge) asked a few questions in his Galesburg, IL local paper, and I'll provide some answers here.  As always, I encourage you to read the original.

The good judge, like the usually informative Mr. Krauthammer, starts off on a very wrong foot, with bad philosophy of science.  There are many facts in science -- the earth is round, the sun is hot, there is a greenhouse effect, and CO2 is a greenhouse gas.  All can be questioned -- but not in the trivial way that Bulkeley and Krauthammer seem to think.  'I question it' is trivial, and pointless.  If you have a _scientific_ question about these things, or any other, it is because, and only because, you have scientific evidence that the 'fact' is false.

Climate change, as even commenters in agreement with Bulkeley note, is indeed a fact.  Climate changes, that's a fact.  One of the tasks of science is to try to understand the hows and whys of that fact.

Let's see about the questions:
1) Average temperature has indeed gone up the past 15 years.  This is a question, apparently, because the author didn't bother to look at the data. One can experiment with time periods and trends at NOAA/NCDC.
http://www.ncdc.noaa.gov/cag/time-series/global/globe/land_ocean/1/2/1880-2014  
It's worth paying attention to the fact that climate trends are defined on 30 year periods, not 15.  Some discussion of why this is the case is at
http://moregrumbinescience.blogspot.com/2009/01/results-on-deciding-trends.html

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Consequences of the abnormal normal climate

In last Monday's note, I concluded that climate was only 'normal' from 1936-1977.  As with any science conclusion, this is not past discussion.  But, as we often do in science, let's take that part as true and see where it leads us.  If it leads us to something silly, then we have (more) reason to question our original conclusion.  On the other hand, if it leads us to things that make sense, it suggests that the original, tentative, conclusion is possibly better than we originally thought.

So, if climate were 'normal' only between that span, give or take, is there anything else that can be concluded?  Two things occurred to me pretty quickly; please do add more that you think of!  One is about psychology and the other is engineering.

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When was climate normal?

It's been a couple years since I took up the question of normal climate, so time for another go.  At that time, I used monthly data from Hadley, and arrived at the observation that if you're younger than 26, you've never seen a month where the global average as as cold as the 1850-2011 average, 317 consecutive months (at that point, now over 330) of warmer than 'normal' temperatures.  I'll cheat and give you some answers first, read on to see how they're established:

• Climate was 'normal' only between 1936-1977
• Every year 1987-present has been warmer than any year before that
• 1976 was warmer than any year before 1926
• 1978 (next coldest year of the recent run) was warmer than any year before 1940

Do read on to see what 'normal' winds up meaning; it's important!  One part of 'normal', as we intuitively think about it, is that you should some times above it, and sometimes below.  Having many consecutive years above 'normal' says that normal isn't really very good.  To help get quantitative about how to proceed, consider this plot of NCDC's data (warmer/colder than the 1880-2012 average -- the length of the entire record).

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Sea level's climate time scale

My 'reality-based decision making' post prompted a comment asking for my thoughts about sea level rise, which is more than sufficient excuse to turn to that.  An additional excuse is that it provides a chance to look at how to decide climate time scales for something other than temperatures.  For global mean temperature trends, I found that you need 20-30 years to determine a climate trend.  We'll see that it is 40-60 years, 60 for preference, for sea level.

My starting point for data was the University of Colorado sea level group.  They provide satellite data back to late 1992.  High quality data, but only for a short period of time.  If global sea level's time scales are like global mean temperature's, then it's only just gotten long enough to provide a climate number.  Fortunately they list links to other sea level groups, including the Permanent Service for Mean Sea Level.  They have three global reconstructions available.  I'll take this one -- published in the scientific literature as: Recent global sea level acceleration started over 200 years ago?", Jevrejeva, S., J. C. Moore, A. Grinsted, and P. L. Woodworth (2008), Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611 -- on the grounds that it covers the longest time period and has the most recent literature publication date.  It will be a good project for a reader to see if the conclusions here change, and how, if you use one of the others instead.

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Three feet of global warming

Now that that idiotic line is out of the way, let's do some thinking about what we should expect from climate change. I've been calling it climate change, rather than 'global warming', since at least 1993. A major reason being that there is more to climate than temperature, and changing temperatures affect more than just how hot it gets.

One of the things that temperature affects is how much water can be in the atmosphere. The hotter it is, the more water vapor you can have in the air before it starts to form a cloud. So one very simple expectation that we could have on climate is that warmer = more humid (absolute humidity that is). Since there's more than temperature to climate, we don't really expect it'll work out that simply everywhere, all the time. But it tells us one line of research to take -- look to see what has been happening to atmospheric moisture content.

Jeff Masters has written this up at his blog on the Weather Underground, and I'm relying partly on his notes in my write up.

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Fingerprinting climate change

I'll take up one of the questions from the question place, how do we 'fingerprint' current climate change as being from CO2, rather than from any of the many other things that affect climate?  Same questioner asked several other interesting questions, and they'll be topics for later posts.  One thing I've mentioned is that there are indeed many things which affect climate.  A few to start with are: CO2 (or, more generally, the non-water vapor greenhouse gases*), solar input, volcanic aerosols, and orbital variations.

I don't really like 'fingerprint' as the description, myself.  I think of the process more as the 'duck test' -- if it looks like a duck, walks like a duck, and quacks like a duck, it's probably a duck.  We start by finding out what would be true if a given candidate were driving climate change, the more implications the better, and then go look at what is going on in the atmosphere.  So I'll approach it that way.

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How not to analyze climate data

Preface
The paper that prompts this post (and the preceding Introduction to time series analysis is McLean, de Freitas, and Carter, 2009. A reader suggested, in email, that I take a look. I'll recommend that to others as well. I won't carry out all suggestions, not least because I don't know all areas well enough to comment, but they are indeed welcome. And do at times result in a post here. There'll be some following notes as this paper opens several issues. For now, I'll stay with just the paper.

Comments have already appeared at OpenMind, Initforthegold, and Realclimate. In a fundamental sense, I won't be adding anything new. But the approach will differ and might show some features in ways that you might have missed in the comments over there. For instance, I mentioned the crucial bit that I'll be exploring here in a comment at Initforthegold, and Michael missed its significance on first reading. The fundamental was staring him in the face, but fundamentals aren't always easy to notice. When he did, it was 'forehead slap' time.

I've tagged this 'doing science' and 'weeding sources', as well as 'climate change'. Some issues of peer review will show up, as will a flag or two of mine which I find useful in weeding sources. The nominal topic of the paper "Influence of the Southern Oscillation on tropospheric temperature" is climate change. Recently I posted about scientific specificity. While it's entirely true that it doesn't work well to take that line in daily life, it's exactly what one should do with a scientific paper. One thing it means is that we keep an eye on whether the data used, or are used, support the argument that is made.

Begin
We start by reading the abstract. As a matter of doing science, the abstract usually makes the most eye-catching statements in the paper. It is the advertising section of the paper, so to speak. You want to say something here that will interest other scientists and get them to read your brilliant work. In this case, "That mean global tropospheric temperature has for the last 50 years fallen and risen in close accord with the SOI of 5–7 months earlier shows the potential of natural forcing mechanisms to account for most of the temperature variation."

SOI is the Southern Oscillation Index. It provides a number that is connected to the El Nino-Southern Oscillation (ENSO), which can then be used for further research, such as this paper. There are different ways of defining an SOI, which might be an issue if the effects the authors were working with were fairly subtle. But, as they are referring to explaining 68-81% of the variance (figure depends on which records are matched, and how large the domain examined is), we've left the realm of subtle. As the authors duly cite, there's nothing new in seeing a correlation between SOI and global mean temperatures. This is well-known. What is new is the extraordinarily high correlations they find, and that eye-catching conclusion that most of temperature variation for the last 50 years is driven by SOI.

For atmospheric temperatures, they use the UAH lower tropospheric sounding temperatures (paragraph 5) and for SOI, they use the Australian Bureau of Meteorology's index (para 7). If the abstract were an accurate guide, we'd expect that with those two time series in hand, they computed the correlations and found those very high percentages of variance explained. Or at least that they were that high with the noted 5-7 month lag. And here's where we get to the time series analysis issue that I was introducing Friday.

Three different things are done to the data sets before computing the correlations. One is to exclude certain time spans for being contaminated by volcanic effects on the temperatures. No particular time series analysis issue here. But the other two both have marked effects on time series. First (para 10) is to perform a 12 month running average. This, as I discussed Friday, mostly suppresses effects that are 1 year and shorter in period. Second is to take the difference between those means, 12 months apart (paragraph 14). As I described on Friday, this suppresses long term variation, and enhances short term variation. They assert that this removes noise, while, in fact, it amplifies noise (high frequency/short period components of the record). Alternately, they are defining 'noise' to be the long period part of the records -- the climate portion of the record.

The combined effect of the two filters is that both the high frequency and the low frequency parts of the records are suppressed. What is left is whatever portion of the two records lie in the mid-range frequencies. To return to my music analogies, what has been done is to set your equalizer in a V shape, with the highest amplitudes in mid-range. While the result has a connection to the original data, it is certainly no longer fair to say, as the authors do in the abstract, that their correlations are between SOI and temperatures.

Demonstration of filter effects -- sample series
The next 4 figures show k) the original time series, which I constructed by adding up some simple periodic functions l) the 12 month running average version m) the 12 month differencing of the original data and n) applying both filters as the authors did (minus volcanoes).

Original


12 Month Smoothing


12 Month Differencing


Both Filters


As expected, the running average smoothed out the series. In music terms, it suppressed the treble. That's the job of an averaging filter. The differencing made for a much choppier series than the original. That, too, can be desirable. But certainly the authors' comment about 'removing noise' is ill-founded. If we look at the variance in the time series, the original has a variance of 4.25. The running average decreased that to 2.69 (eliminating 37% of the variance). The differencing increased the variance 50%, to 6.47 (again, increased variance means more noise). Applying both filters produces the final figure, which has little resemblance to the original series. Not least, while the original looks to have a substantial amplitude at a period of 30 years (that appearance is entirely correct, I put in a 30 year period), the final product shows no sign whatever of the 30 year period. That is one of the jobs of a differencing filter -- remove the long period contributions. The filters have also suppressed the 15 year period that I put in, and, in general, turned my original series, which had equal contributions at 5 months, 1, 2, 3, 5, 7, 10, 15, 30 years into something that looks mostly like a 3 year period (count the peaks and divide that in to the time span for them) with a bit of noise.

Filter effects on SOI series
That was a warm up with a test series, where we know that there are no data problems of any sort, and we know exactly what went in. The real data of course have problems (this is always true, and one of the aspects of doing science), but they may not have problems that affect our conclusions. The next figure shows the smoothed (12 month running averages again) and then differenced (as in the paper) Australian SOI (labelled 'both' -- both the averaging and the differencing applied to the original data) (Note that I'm not showing the full curve, only 1950 to present, instead of 1879 to present -- the paper's analyses only covered, at most, 1958-2008).



You see that with both filters applied there are new peaks, missing peaks, and even the sign of the index can change (positive for negative, or vice versa). These are all signs that the filters have fundamentally altered the data set, so that whatever conclusion is drawn can only be drawn about 'data as processed by this filter', not the original data -- in contradiction to the statements in the paper and elsewhere by the authors that it is SOI that explains an extremely high portion of the variation in global mean temperature. Further, since the correlation is largely driven by the peaks, the high correlations can by largely a matter of how the filter creates or destroys peaks rather than the underlying data.

Response function
I mentioned Friday the amplitude spectrum -- show the amplitudes of the contributions from each period. Filters change the amplitude spectrum. That's their job. One thing, then, that you do to describe the filter is divide the amplitude at a period after processing with the amplitude before hand (this is known as the response function). An ideal filter will show a 1 for all periods except the ones you're trying to get rid of, where it will be 0. Real filters don't accomplish this, but that's the goal. So, to see the performance of the author's filter, I took their original SOI series, processed it through their filter, and then found the response function in this way. Those are the next figures. First is looking at cycles per year (frequency), letting us see well what happens at high frequencies. Second looks at the period (from 1-15 years).

Frequency Response Function


Period Response Function




There are some spikes in the curves, which have nothing to do with the filter. All that is happening there is the these are periods/frequencies which have little signal in the original series, so numerical processing issues can have large effects there (dividing by small numbers is hazardous). But the smooth curve is a fair description. The averaging filter suppresses the signal (response is close to 0) for frequencies of 1, 2, 3, 4, 5, 6 cycles per year. (With monthly data, 6 cycles per year is the highest that can be analyzed -- 2 months period.). The differencing filter also suppresses the very low frequencies (long periods), as we expected even with just the basic introduction from Friday. But take a look between 1.5 and 7 years. The response is greater than the input! Look, too, at the periods which are being amplified. A usual description of ENSO is 'an oscillation with a period of 3-7 years'.

Summary
So what do we really have? It isn't a correlation between SOI and global mean temperatures. Both were heavily filtered. What the authors actually compute is the correlation between the SOI time series and global mean temperature -- if you over-weight (response function is greater than 1, so it's an over-weighting) both series towards what is happening in the ENSO periods. The conclusion should really be "If you look only in the ENSO window, you see that ENSO accounts for a lot of variation in global mean temperature." One problem is, that isn't a new result. We already knew that ENSO was important in the ENSO periods. More important to the paper, in so doing, the authors cannot make any conclusion about explaining "most of the temperature variation". They've filtered out much of it, and never examined either the response function nor the effects of their filter on the inputs.

If what was desired was an analysis of global mean temperature response to SOI at ENSO periods, then both the authors should have been clear that this was their window, and they should have used a more suitable filtering process. When one goes back to the paper, it's also clear that no justification was ever made for using either filter, much less both. The filters were arbitrary, and as I've mentioned, we prefer to avoid arbitrary decisions in our papers. If no objective basis for setting up the filters could be found, the authors should have demonstrated that alternate choices did not affect their conclusions.

So, some 'weeding sources', or 'scientific specificity' signs:
* When a paper makes a conclusion about the correlation between A and B, verify that it is A and B that they are correlating.
* If a filter is applied, look for the authors to discuss a) why a filter is being applied at all, and b) why the particular filter they chose was used.




As is my custom, I've sent an email to one of the authors (de Freitas, the only one whose email was given in the paper) about this comment.

Some of the following blog posts will talk about the peer-review aspects that let this paper through. For now, see my old article peer review. One of the other notes (no idea when) will be about how the process continues after a bad paper gets through the peer review process. That is the comment and reply process, and I'll be writing Tamino about that (he's said in his comments that he's preparing a comment for the journal).

Results on deciding trends

No, the delay was not because the results came out differently than I'd expected. Just the more mundane business that I've been doing a number of different things and getting the figures done up reasonably is taking some time as I change my mind about what constitutes reasonable.

In brief (in a journal paper, this would be the 'abstract'):

• You need 20-30 years of data to define a climate trend in global mean temperature
• Forward and backward trends are markedly different
• Therefore, to discuss climate trends in global mean temperature, you need to use 20-30 years of data centered on the date of interest.
  

As with any abstract, it's too brief to show you why any of these are true, just some simple declarations. Now, if you trust me absolutely (which I don't recommend -- and if I'm talking science, you don't need to), you can stop and move on to some other reading. But let's take a look at the whys. As before, I'm putting the data and programs on my personal web site and you can run the analysis yourself, and modify the programs to work on different assumptions, methods, data sets.

Let's consider the first point -- how long it takes to determine a climate trend in global mean temperature. We could define a trend with 2 minutes of data -- temperature at one minute, temperature at the next minute, and draw a straight line through the two numbers. We'd wind up with wildly varying trends, though, from minute to minute through the year. This is weather and turbulence. Make it daily or monthly averages, and we still have the wildly varying trends, and the magnitude of those trends will depend on what time period we chose. Rather than declare that 'this is the right period', we'll determine it by looking at the data itself.

If it is meaningful to talk about climate as opposed to weather, there has to be a time span over which our result for describing climate does not depend much on how long a time span we choose. For average climate temperature, we found 20-30 years as the appropriate time span. I didn't show the figures then, but it's in the program and output you can pick up from my web site that this is also the appropriate time span for deciding a climate temperature variance (how much scatter there is about the average; even if the average didn't change, we would probably consider it a climate change to have winter lows vary from -30 to +15 instead of -10 to -5).

Figure 1 here shows the trends for all years (remember I'm lopping off the first 31 and last 31 from the NCDC record) that I computed trends for, by all 3 methods, in terms of the length of data record used. So at 36 (months) we see a range in the computed trends between +15 C/century and -15 C/century. These are enormous values cmpared to what we think of for climate change. If I wanted to give you a wrong impression about climate, then, I could use such short records. The range declines as we take longer periods. And then flattens out for trend periods of 252-372 months (21-31 years -- remember I took only odd averaging periods). In this part of the display, the range is about +1.5 C/century to -1.5 C/century -- and it is independant of how long an average I took. This, then, supports that a) there is such a thing as a climate temperature trend and b) that you need 21-31 years to find it (we can round to 20-30, given how 19 years is close to 21 also, we expect 20 even to be so as well).



Statistical aside: To compute variance, we find the deviation of each observation from the mean, square it, and then add this value up for all observations and divide by the number of observations. (Or use the appropriate function in your spreadsheet.) This is a fundamentally meaningful quantity. If we then take the square root of this number, and the numbers have a normal distribution, then we have a standard deviation. We can always take the square root of the variance, but it will not always be a standard deviation.

In figure 2, I plot instead the maximum and minumum trends, and the square root of variance -- again in terms of how long a period is used to compute the trends. This shows fundamentally the same information, but perhaps a little more clearly. Aside: It's a good idea to look at your data from several different vantages. Sometimes the display method you use in one step can hide something that's blindingly obvious in another method. Again, we see that the figures (maximum trend, minimum trend, average trend, square root of variance in trend) all stabilize once the data length used is 20-30 years. And, conversely, that for periods of 3-13 years, the figures all depend sensitively on how long an averaging period you choose.



Choose is a key word in doing science. We try to avoid having choices. Choices can be made differently by different people, for different reasons, and not all those reasons will turn out to be good ones. Finding a scientific principle and then looking for how to satisfy that principle is far better. Here, the principle is that the length of data used should not affect your conclusion about what the climate trend is. This is a strong principle. So when you see someone violating it (say by using a 7 year span without doing some real work to justify it -- work like I'm doing here), they're probably not doing good science.

Now, in figure 3, let's look at what the trends are like if we use 7 years of data, versus using 25 years. I'm computing all these by using centered information -- data evenly on either side of the time of interest. We'll get to why this is best in a minute. The main thing I think this shows is that if you use the short period, you present a false impression that climate is highly variable, trends changing from some very high positive value to a high negative value in a span not terribly longer than the 7 years' data you used in either case. This makes no sense for climate, but does for weather, or for misleading people. Weather, we know, does change rapidly. We can be warmer than usual for a few days (or months, or years) and then cool a few days/months/years later. Nobody (scientific) has ever said weather was going to end. Go out to the 25 year data period trends and we see, instead, that the trends have more stable behavior. They do change, which is reasonable since we do expect that climate changes. But it's no longer large magnitude flip-flops. That, too, makes sense as climate is a big beast and turning on a dime has to be a rare if ever occurrence.



To look a little differently at it ... if someone shows you a trend over 3 years, about 90% of what they're showing you is weather (real trends of up to 1.5 C/century, 3 year trends of up to 15 C/century -- 90% of that 15 C/century is weather). For a 7 year trend, it's about 70% weather. Weather is interesting, but if you're interested in climate, and they're claiming to be talking about climate, then they're misleading you by those 70-90% of weather they've thrown in by using such short spans.


On to which data to use for computing trends (or, for that matter, averages, but I'm focusing on trends today). Figure 4 shows trends in degrees per century as computed with data forward from the date given, backwards from the date given, and centered on the date shown. It also shows, and this is why I went to degrees per decade -- the magnitudes come out comparable, the NCDC monthly anomalies. I computed the trends using 25 years of data (300 months).



We immediately see that, indeed, the forward and backward trends are quite different, as expected in the planning note 'deciding climate trends'. The curves themselves are actually the same -- but shifted by 25 years (the period used to compute the trend -- when I use 31 years, it's shifted by 31 years, and so on). The centered trends show, again, the same behavior, but now 12.5 years (half my data period) off from the forward, or backward trends. So, look at the data for anomalies versus the different trends as computed. If we look at, say, 1945 (month 780) -- a generally warm year, we see a modestly negative trend from the centered trends, an extremely negative trend if we look forward, and extremely positive if we look backward. What's happening? And which makes most sense for thinking about the 1945 climate trend?

Climate is about normal, our expectations. For 1945, then, would we describe the typical change as one of rapid warming? rapid cooling? a modest cooling? If we look around then, the best description of the tendency is that there's a modest cooling going on. 1930s were warm, 1945 was a particularly warm year, but going in to the 1950s, temperatures were cooler. The large trends, in opposite directions, the forward and backward trend computations give us, even though for an appropriate period, mislead us. The centered trend computation gives us the right idea of what is going on around 1945. Repeat this inspection for other years, and think you'll rapidly come to the conclusion that the best description of what is going on around any given time is the one from a centered computation. If a trend is downwards (negative numbers), then we expect that times before our year of interest are generally warmer than later times. If it's upwards (positive trend), the we expect later years to be warmer. Only the centered computation consistently gives us this result.

We now have 2 conclusions: trends should be computed with 20-30 years of data, and they should be centered on the date of interest. Let's see how it works, applied to as much data as possible. To cover the greatest time span possible, I'll take the shortest data length reasonable for computing trends -- 20 years. Since I'm doing centered computations, this lets me get to within 10 years of the start and end of the record (remember I had been skipping the first and last 31 years so that all three methods could be used, and because I didn't know if some number shorter than 31 years would be long enough). Figure 5 gives the result, in degrees per decade, and with the NCDC monthly anomalies as well.



The most recent year we can compute a good quality trend for is 1998. The trend then is a warming of 0.19 degrees per decade, 1.9 per century. We see that the trend is higher towards the end of the record (i.e., towards the present) than at other times, though we'd have to do additional work to decide whether the difference was physically meaningful. The thing which surprised me about the curve is that most of the time -- from 1890 to 1998 that we can compute a quality trend for -- the climate trend has been a warming. Not a matter of sometimes up, sometimes down, but rather a basically up except for a bit of down in mid-20th century. 70% of the time, we've been seeing warming.

By way of summary, or postscript, or some such ...

• Whether it is to compute the average climate temperature, the variance of climate temperature, or the trends in climate temperature, we need 20-30 years of data.
• On the other hand, it is possible to compute a climate with 20-30 years of data. This didn't have to be the case. I'll show in a later post a curve with no climate in the sense I've been talking about.
  
• Most of the time for the period of data, we've been experiencing a climate warming.
  

Conclusions are, of course, limited by how data were analyzed. In this analysis, I looked only at the global mean temperature data themselves. If I'd done something more sophisticated, like carefully removing the effects of some 'weather' (short term or from outside the climate system) processes such as El Nino-La Nina oscillations, volcanoes, and solar variability, and then looking at how long was needed to get a stable estimate of the mean, or trend, I might wind up with a shorter period. On the other hand, that shorter period would only apply when people did indeed do a careful analysis of the effects of those things on global mean temperatures. This can be done, but is more sophisticated than I wanted to start with. It's also vastly more sophisticated than the many blogs and such out there which are misleading people by doing sloppy short term analysis and pretending that it's climate they're talking about.

Update  13 February 2010: The data file I worked on and the program I used are in a tar file.  You'll need a fortran compiler for this, or translate it to a language of your choice.  Nothing very fortran-ish is being done and the program is short.

1970s Mythology

One of the more popular myths repeated by those who don't want to deal with the science on climate is that 'in the 70s they were calling for an imminent ice age' and such like nonsense, where 'they' is supposedly the scientists in climate. This has long been known to be false to anyone who paid attention to the scientific publications from the time, or even to William Connolley's efforts in documenting what was actually in the literature over the last several years. Now, William and two other authors (he's actually the second author on the paper) have put that documentation into high profile peer-reviewed literature -- the Bulletin of the American Meteorological Society. For the briefer version, see William's comments over at Stoat and web links therein. That page also includes a link to the full paper in .pdf format.

Evaluating a climate trend

After the second what is climate note and the second testing ideas note, how might one go about testing whether climate had changed, and, more specifically, whether a prediction of change were supported or not. At hand is the question of whether the IPCC projection (not forecast) of 0.2 C/decade for the first two decades of the century could be rejected by observations currently in hand. I concluded in the testing ideas post that the methods used there were not useful, as they hadn't compared like to like in making the tests, nor been working with climate variables.

Now that the second what is climate note is in hand, we can make a better sort of test. Still not rigorous, but better than the one I discussed. That is, let us take the 20 year average from 1981 to 2000 (IPCC was allowing 20 year averages, though preferred 30) and compare to the 7.6 year average from January 2001 to July 2008. The latter period is only 91 months, which is short for a climate definition, per our experience in the what is climate note. See again how wobbly the averages are for averages that are only that short.

I took the NCDC data again and computed the averages. (At least I hope so, I might have been off in my start periods, but probably only by a month or two.) For 1981-2000, the average was 0.277 C, with 0.155 standard error (if we also assume the terms are normally distributed, which is a question at this point). For 2001-present, the average was 0.540 with standard error 0.104. To compute the trend, we take the difference between those two averages (0.263) divided by the number of years between the midpoint -- 1990.5 and 2004.8, respectively. We wind up with 0.18 degrees/decade for our slope. Does that represent a significant difference from 0.2? Well, for starters, the 0.2 was a round figure from the IPCC -- their actual words were 'about 0.2'. 0.18 is 'about' 0.2. Eyeballing the spread of the different projections, a difference of 0.02 is within the envelope. Then, to be serious, we'd also have to allow for the errors of measurement that go in to computing the global averages.

The upshot is, to the extent that it's meaningful to test IPCC 4AR projection 13 years too early, observation of global average surface air temperature are pretty close to what's expected from this consideration. Allow for the fact that the sun's been quiet the since 2001 vs. warmer, and there's even better agreement.

One can definitely do a more rigorous test than this. And, for professional publication, would have to.

Testing Ideas 1

I was invited (challenged, whatever) to take a look at a site that proposed to have disproved the 'IPCC prediction', over in comments to my cherry picking note. Here's part 1 of the look I promised in my comment reply over there. If you haven't already, please do read the cherry picking note. (Not only for my tiny little ego boost from having more page views, but because I'll be assuming here that you understand what all I mean by the term and examples of it for climate.)

Testing ideas is one of the central processes for science. Coming up with ideas is awfully easy. Supporting them takes work. Strengthening them so that they stand up to all good tests is extremely hard. But, they do have to be good tests. Same as it's harder to come up with supported ideas than just an idea, it's harder to come up with a good test than just a 'test'.

'Good test' does not mean 'comes up with the result I like'. Maybe it does, maybe it doesn't. You're usually much better off to not have specified before hand how you want the test to come out. A good test is one that is aware of the system it is studying, knowledgeable about the idea that it is testing, and has been devised carefully enough to confirm or deny the idea while also giving an idea of how firmly it is supporting or denying. Before launching in to the climate case, let's look at something very much simpler.

You might have the conjecture (even more tentative than a hypothesis), after having read my mention that I'm a distance runner, that I'm tall and thin. How would we test that? How can we make it a good test? You could just ask me. But that isn't a good test. You have no idea what I think is tall, nor do you have any idea what I think is thin. So if I say 'yes', you still don't really know anything. Poor test. You could try asking me my height and weight. But then you've made a poor test because you didn't establish what constituted tall or thin. If you're biased about the conclusion, it is far too easy to say after the fact that whatever figures I gave you do, or don't, constitute 'tall and thin'.

So you have to be precise about declaring what you're testing, what constitutes a pass and what constitutes a fail. You might arrive at something like 'taller than 80% of men your age means tall and lighter than 80% of men your height is thin'. Someone else might want those figures to be 90%, but, since you've specified how you arrived at your labels (and, of course, you will be sharing your data), they can examine for themselves whether they agree with your conclusion. You're still not out of the woods, however, because you don't know how I'm measuring my height and weight. Perhaps I'm wearing thick socks, shoes, and standing on my toes. Maybe I'm weighing myself fully clothed and carrying a backpack. You need to specify the conditions of the measurement as well. Further, you'll have to tell me how to report it. I could be 5'7" (170 cm) and round to the nearest foot/meter to tell you that I'm about 6' (2 meters) tall. That sort of ambiguity can completely ruin your test.

In any case, even for something as simple as deciding whether someone is 'tall and thin', you see that there can be quite a lot involved. One last thing, which winds up often being important in looking at people's conclusions. After going through the work of making a good test, you can only draw your conclusion about the thing you were testing. Suppose you decided that I was indeed tall and thin. That was your test, so that conclusion is reasonably good. What you cannot do, however, is conclude that because I am tall and thin, I'm a good distance runner. You never tested that, and haven't presented evidence that all tall and thin people are good distance runners. (They're not, nor is it true that all short and not-thin people are poor distance runners. Now you have to go back to the drawing board and decide what 'good distance runner' means and how to measure it.)

If something that simple involves so much work, something as complex as climate probably takes quite a bit more care. So, irrespective of much else, one thing to look for in reports about what is or isn't the case about climate is whether the author showed as much care in making their tests as I suggested for something as trivial as deciding whether someone was 'tall and thin'. In part 2, finally, I'll get to the examination I was invited to make.

Climate Change Detection

You'll want some dice or a random number generator for our first efforts to think about climate change detection. Start with one six-sided die. We'll assume that it's a fair die -- that each face is just as likely as any other to turn up. If we toss it many times, the average of the numbers that shows up will be 3.5.

Weather and Climate
This is one of our distinctions between weather and climate. Weather is what we saw on any given throw and climate is that average. But 3.5 is not a number that you can get on any single throw. What's up with this? It turns out that this, too, is a reasonable thing for thinking about climate. If you look at some very small area, and only one parameter (say temperature), it's possible that you'll see the 'climatic norm' occur. But only for that small area and limited look. As soon as you look at a large scale, you find that although the weather (instantaneous state) can be generally close to climate, it is seldom close everywhere. See, for example, this sea surface temperature anomaly map(difference from climatology).

The 1 die model of climate doesn't work very well. On the map, we see that most of the area is near climatology, and that the farther away we are (hot or cold), the less area is present. A better model then is to use 5 dice (again 6 sided). In this case our 'climate' is a total of 17.5, which still doesn't happen as weather, although you can get close. The maximum is 30, and the minimum is 5. The maximum difference from climatology is 12.5. But most of the time we'll be close to climatology. Take 5 dice, throw them, add them up and record the result for a couple hundred throws. (If you're moderately quick with your addition, this takes only a few minutes; I've done it.)

Within your 200 totals, you'll find some runs of constantly increasing values, and about as many runs of constantly decreasing values. Some of the runs will be long, and some short. But the number of each is about the same whether it's increasing or decreasing. If you compute the average of the first 5 sums, then 10 sums, ... out to the whole 200, you'll see that the average wobbles around. It tends to be closer to 17.5 as time goes on (as you average more tosses) but only in a very jerky fashion.

Climate Change
Suppose I take one of your dice and tape a 6 over the side that should read 1. The average throw now totals 18.3333 (repeating), instead of 17.5. The minimum is now 6 instead of 5, but the maximum is unchanged. What will happen, though, is we'll see the high totals more often. Each of these is more or less a fair description of what we've seen in the climate of the last 120 years -- warmer minimum temperatures, higher averages, and not much change in maximum temperatures. (Not a perfect analog, but pretty good for only 5 dice.)

Repeat the exercise of tossing the dice and adding them up. How long do you have to do it before the average is obviously different from the first run? Remember that the first time the average jumped around for a while. You'll have to go on for longer than that this time.

How many throws do you need to make before you can tell that there are fewer low numbers? More high numbers?

In doing climate change detection professionally, these sorts of analyses are applied. Are there more extreme highs? Fewer extreme lows? Higher average? Just how many data points do we need to detect that in the statistics?

Final question: when did the climate change? When you have a long enough series of throws to detect it in the statistics reliably, or when you saw me tape over the 1 face with a 6?

Climate is always changing

The subject line is a comment that surface surprisingly often in the literature of folks who want to deny that climate is changing, or if it isn't, that any of it is due to human activity, or if it is, then it will be good for us. Whatever. The science of interest here is the notion of climate change, how fast, how much, how often, and the like. The human side of concern ... we'll get to a bit of that as well.

As we look through the period where we have thermometers (the last 100 or so years) recording temperatures, we see that there are indeed changes from year to year (though a year is too short really to call climate) and decade to decade (a better period to average over). But this includes the period of significant human activity (the now 6+ billion of us), so doesn't necessarily tell us a lot about what the climate does without human effects.

For longer range, say the last 600-2000 years, we have climate proxies that tell us about climate without being thermometers. Tree rings and ice cores are two such sources of proxies. When we look here, we see that climate does change decade to decade, century to century, and even millennium to millenium. The changes are small, tenths of a degree for the global average (and the longer a period you average over, the smaller the changes). But they're observable and present.

Even longer term, we still have ice cores (to 800,000 years ago), and then also start looking at marine sediments (to about 100,000,000 years ago). We see here that climate still changes, even on 10,000 to 10,000,000 year time scales. A very large change, 5 C or so global average, is associated with the northern hemisphere ice age cycle. About as much is associated with the start of the Antarctic ice cap about 35 million years ago.

The exact causes for the changes are a subject of study with some good answers and some not as confident. They include carbon dioxide (greenhouse gas) changes, orbital variations (the earth's orbit isn't exactly constant), continental drift, and land surface changes.

So what do we need to consider as humans with human interests regarding climate? As scientists, we want to understand everything, through all of time. But as citizens thinking about policy, we can look at a few things. One thing is, although there have been large changes to climate before, humans weren't around for it, certainly not 6+ billion of us, many living in large cities near the ocean. Another is, these large climate changes were also associated with large extinctions. We might not want to cause climate change sufficient to drive a large extinction. During the glacial to interglacial warming 10-18,000 years ago, global human population was likely only a few million, and were largely nomadic. So when climate got bad in one area, they simply moved (or died). Today, with 6+ billion people occupying the earth in stationary cities, it'd be difficult to move out of the way if climate got bad where you were.

Perhaps the strongest indicator of our time scale of concern is human life. If change were to be small over 70 years, we might not be concerned as little would be different between our birth and death. More quickly, we might want to ensure that there was reasonable stability between the time our kids were born and the time they reached adulthood, 20ish years. Given the two, 'a few decades' becomes our time range. Cities also point us towards the few decade time scale -- it is on this scale that urban infrastructures are built and rebuilt. If changes are slow enough that 'all' we have to do it rebuild the city further inland over the next 50 years, for instance, then relatively simple practices could get us there (but this would require some consideration on how to carry it out, as people who live now in the area marked not to be rebuilt might object!).

So, while I'm very interested as a scientist in, for instance, the 100,000 year cycles of the ice ages (my first scientific paper was on it), it's just too slow to be a concern to me as a citizen. As a citizen, I'd as soon that scientists did understand the 100,000 year cycle -- the more that is understood, the more likely that good estimates can be made of the futures. But the estimates that matter are those for the next few decades to maybe a century or two.

Climate is a messy business

I'll be making a number of posts prompted by a note from Dave in a different area. It'll be a number of posts because I'd like to take some care on each of the points.

Let's start with:
This topic of global warming has alot of problems... First of all you have a complicated science. It's not likely alot of people will truly understand the science well enough to be able to argue the points.

Climate certainly is a messy business. One of the things that makes it interesting to those of us who work on it is precisely that. Wherever you look, you find something that affects climate, regardless of whether you look at permafrost, sea ice, forests, farms, rivers, factories, sunspots, volcanoes, dust, glaciers, ...

So certainly we have a complicated science and certainly few people are going to understand enough of it to argue the finer points. This is true within the science as well, as few who study volcanoes and their climate effects are going to be able to argue the finer points about the role of sea ice in climate, or vice versa.

What does an honest and interested person do then? Two things as I see it. First, not all the science involved is difficult. For those parts of the science, learn the science. Anybody who can get through normal life, cook a recipe, balance a checkbook, etc., can understand the basics. One source is Jan Schloerer's summary at http://www.radix.net/~bobg/faqs/scq.basics.html Jan was not a climate scientist, but, as I said, you don't need to be one to understand the basics. One thing he did do (see his acknowledgements, for instance) is check with people who were to ensure that he'd gotten the science right (or at least correct given the limits of writing a general audience description). I'll come back to basics in a minute.

Second, for things that aren't elementary, start looking to expert opinion. No different than if your car is acting up and you can't figure out why, or you've got something like a cold but it isn't going away like one should. You go find an auto mechanic or doctor and use their expertise. If your concern is, instead, about climate, then find some climate scientists. While there aren't that many (even counting worldwide) they do exist. And it's not that hard to find their professional understanding. You'll see it more directly in journals like Science and Nature than Scientific American or Discover. But both can be gotten fairly easily, and both include summaries of the science which are written for laymen.

You can also look to the IPCC reports, the fourth having been issued recently. The first was the best, I think, in terms of explaining the science to non-professionals. As the basics haven't changed since then, you might want to look for the first edition. The summary for policymakers, in each edition, is the most readable and aimed for non-professionals. The drawback is that it necessarily includes fewer details about the science. Nevertheless, it (the IPCC report) does represent as good a summary of the state of the science as you'll find.