Mar 10 2008
4 of 4 Global Metrics Show Agreement in Trends
I go out of town to visit relatives with no Internet access, and the proverbial fit hits the shan. That’s perhaps over-stating the magnitude of the situation, but Anthony Watts has a new post that is extremely misleading and it would have been nice if I could have thrown this post together sooner. He posts at Watts Up: 3 of 4 global metrics show nearly flat temperature anomaly in the last decade. The one that doesn’t show “nearly flat temperatures” is GISS, which seems to cause undue concern.
He concludes by saying
Given some of the recent issues Steve McIntyre has brought up with missing data at NASA GISS, it also makes me wonder if the GISS dataset is as globally representative as the other three.
I previously posted a graph that showed the 4 global temperature anomalies (GISS, HadCRUT, RSS, UAH) all on the same plot: 4 Global Temperature Anomalies Say the Same Thing. I think the plot speaks for itself, so I’m going to reuse it here.
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I think it’s clear that all four products are doing basically the same thing. There are minor deviations between the four time series, especially around the strong ENSO event in 1998. GISS has the lowest peak for that year, and the MSU-derived products (RSS, UAH) show the highest peak. HadCRUT takes the middle ground.
Cherry Picking?
Remembering the title of the Watts Up post, it’s clear that any sort of trend analysis that he performed is going to isolate the ENSO event in 1998. In fact, the years he chose were January 1998 through January 2008. Side note: this is actually 10 years, 1 month and not 10 years as he states on his blog. The end points also correspond to very near the peak of the positive ENSO anomaly at the start of the time series, and a very negative peak due to the negative ENSO anomaly at the end of the time series.
If our goal is to diagnose the extent of global warming, fluctuations due to ENSO are noise. In fact, any semi-periodic phenomenon are noise including the PDO and NAO. Therefore, choosing the end points of the time series in this manner should give us a fairly negative trend. If this isn’t obvious, draw a periodic function, such as a sine wave, for a large number of periods. The trend of this function is zero. Now truncate the time series so that the first point starts at a peak and the last point ends at a valley. The trend for this time series is obviously negative.
I’ve shown previously that trends calculated over short intervals are meaningless. That analysis was done for HadCRUT data, but given the extreme similarities with the other data, the conclusions are very likely going to be similar. I concluded that trends calculated for time periods of less than about 13-15 years are not meaningful.
Trend Analysis Implications
But let’s look at the same trend analysis done for different periods. In fact, let’s do the same analysis for all possible periods. The current temperature trend was calculated using January 2008 as the end date, and the start date was varied from the beginning of the time series (Dec, 1979) to the start of the time series. For each time span, I calculate the trend and the 1 sigma error estimation in the trend value. The results are shown below.
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The long-term trend is clearly positive and somewhere around 0.2 C/decade for all four sets of data. As the number of years in the trend calculation decreases, the trend varies a little, but in general there is good agreement until less than 13 years are used in the calculation. At 10 years there is a wide disagreement between GISS and the other three metrics. And at 9 years there is wide disagreement between HadCRUT and the other three metrics. On extremely short time scales (< 8 years) there is disagreement between all four time series.
I did not do any statistical significance tests on the data. Any ‘disagreements’ above were solely due to the changes in trends. But by using less data points, we also change our confidence in the trends. This plot shows the ‘uncertainty’ in the trend calculations as a function of the number of years used.
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This plot isn’t really interesting. The one thing that sticks out to me is the bump in the MSU data for the ENSO event. I won’t speculate at this time about implications for that little bump.
Conclusions
From the above plots, it should be clear that choosing the timescale over which to calculate temperature trends should not be done capriciously and arbitrarily. Changing the period of interest from 10 years to 9 years results in drastically different conclusions. This is because of the effect of the strong ENSO event in 1998 which caused a minor divergence in the datasets. Since the ENSO signal is noise, much longer time intervals are needed over which to calculate the trend in order to minimize its effects.
By choosing the start of the time series at the height of the positive ENSO event and the end of the time series during a negative ENSO event, the calculated trend will be much smaller than reality.
Watts’ concern that the GISS data are contaminated is not apparent in this analysis. All four of the global temperature metrics show widespread agreement when more than 15 years are used in calculating the temperature trend. Previous work has shown that 15 years is about the timescale when the trends start to become important.
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15 Responses to “4 of 4 Global Metrics Show Agreement in Trends”
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Doesn’t this depend on your starting assumptions?
We are trying to predict future years based on history.
If annual temperature is randomly distributed then it is easy — might go up, might go down, even chance. Moreover stastical tests apply with ease because we have a randomly distributed population.
But your starting assumption is that it is not randomly distributed. You assume a long term trend (say 30-50 years) overlaid with random noise. OK maybe that describes the real world and your conclusions are correct.
But eyeballing the graphs it seems more likely that we have that trend overlaid with shorter term trends overlaid with random noise.
And if we look at an even longer term graph we see evidence of longer term trends. So we have perhaps three levels of trends plus random noise.
Pull our vision back to ice ages and we see another layer of trends. And so on, until we eventually reach the longest trend of all, a cooling trend — the earth formed from very hot gases, passed through a liquid pahse and is now solid.
What determines the next few years thus depends on the confluence and magnitude of a large number of trends of different wave lengths. Whether we denote some as “noise” and some as “trends” is arbitrary, or at least a perspective detrmined issue.
It is getting warmer here in Wisconsin — most of this week is predicted to have highs above freezing. Is that a trend or noise? I may not know, but the geese overhead are strongly suggesting it is an annual trend.
The last few years do tell us one thing. Whether the hiatus in global warming is the result of a short term trend, noise, or some combination of them, they are great enough in magnitude to counterbalance the warming trend offered as evidence of AGW.
I suspect that there might be statistical analyses capable of discerning and separating all these trends, but that such statistical analyses will pass into the realm of the supernatural. Not that the analyses would be incorrect, just that the inability to explain the methods to mere mortals would move them over into the supernatural
With that view, JL, you guaranteee that you will be permanently confused by short-term trends. Since short-term trends have considerable variability, you can also remain more or less permanently hopeful that the long-term trend could reverse at pretty much any time. Good luck with that.
Steve,
My point succinctly is that what is “a long term trend”, “short term trend” or “noise” is not determined mathematically or scientifically, but subjectively.
Putting aside selection to prove a point, I strongly suspect that individual human experience is a stronger influence than we might suspect.
My children, in their twenties and thirties, have only seen a warming trend, undoubtedly “long term” to them. I recently had a conversation with an 87 year old relative, who commented that temperatures were just getting back to what he remembered as a teenager. He implicitly regarded those as normal and the ~2 degree lower temperatures in the sixties and seventies as exceptional — “noise” of a sort.
The convention of “thirty years is climate, less is weather” might be influenced by the average age of climatologists .
Atmoz,
Very nice graphs – I especially like the # years in trend vs. trend o; very succinct.
John Lederer,
For choosing the length of time that’s appropriate to call a trend, see Atmoz’s prior post, linked above. In addition, what you designate as “signal” and “noise” is a function of your current interest and focus – if you’re looking for ENSO, you focus on 4-7 year patterns, and other things are “noise,” functionally speaking. If you’re looking for climate response to greenhouse gas increases of a certain rate, you look at longer trends and treat ENSO as part of the “noise.” One researcher’s noise makes another researcher’s career, to paraphrase an old saying. But the point is that there are physical justifications for focusing on one time scale or another, and selection of time scales is not arbitrary.
Your mention of the past winter temps that “counterbalance the warming trend” suggests that you’re confusing trend and anomaly – it’s closer to say that Jan/Feb temps were “back to average about average for the middle of the previous century.”
Last, I wouldn’t place too much stock in your relatives’ memories of the past climate (or in _anyone’s_ autobiographical memories of climate). Tons of research on human learning and memory of the distant past suggests that this kind of trend over time is _very_ hard to pick up through everyday experience. For example, your relatives’ memories of childhood climate (and mine, and yours) are likely to be shaped by a few extreme events that are now overrepresented in memory, rather than by any real knowledge of the trend.
“Your mention of the past winter temps that “counterbalance the warming trend” suggests that you’re confusing trend and anomaly ”
Sorry if I was not clear. By “counterbalance” I mean that something — a short trend, noise, an anomaly, whatever — has equaled in negative magnitude whatever positive long term trend there is, so average temperatures have essentially been equally distributed in increase and decrease for the past few years.
I appreciate your thoughts on memory’s frailty and generally concur. I took a quick look at the climate record for North Carolina where my elderly relative lives. It matches his memory well. He retired to the house where he grew up, and tends the same garden his mother did, so that may give him a good point of reference.
Atmoz, I did the same thing a while back but my curves looked different than yours ( I only did Giss) from 1880 to present all 5 year, 6 year, etc etc ..33 year trends, then looked at max trend, min trend, std dev of all trends. ( ah I dont think I transformed it to decadle trends, maybe thats why it looked different… rambling) Anyway,
In a warming century, and we have had a warming century, you of course will find that as you increase the time period the maximum warming slopes you see ( as a function of time) will outnumber the minimum warming slopes you see ( as a function of time.
For example, at 7 years, about 42 ( hand counted, so double check) of the 122 7 year slopes were negative.
At 30 years about 25 of the hundred or so series show a negative trend.
Let me put that another way. In a century of warming, If you randomly select a time peroid, you will always have a better than half chance of selecting a time period that shows warming. For any given time period the positive slopes outnumber the negative slopes. ( is that always true?? double check)
[Reply: I don't know if it's mathematically always true, but it is for these time series.]
Now we cant help but cherry pick the century we are in, but once that pick is made, then i think the second pick, which time period, will always look like a cherry picking event if you happen to select a time period that has a negative trend. Basically in a warming century the probablity of picking a cooling trend randomly goes up as you shorten the time scale and goes down as you lengthen it. So, warmists will argue for longer time scales and coolists will push for shorter time scales.
(Until the frequency of internal climate varibility is determined … ok dont want to go there )
It might be fun to redo your analysis with some white noise or some 1/f noise or some simple periodic functions to show folks.
Anyway nice post. I always enjoy your way of looking at things.
Time out, I just read your post on 5 year trends. Good job.
I should read before I post.. or not
Steve Mosher,
Just for clarification: you asked whether “In a century of warming, If you randomly select a time peroid, you will always have a better than half chance of selecting a time period that shows warming” - this is true if the rates of rise and decline are roughly equal and stable. (You may have meant this anyway by referring to the 20th century…)
I think the analysis is really interesting
- especially the trend graph
- so the question I have is what happens if you plot back further than 30 years…
- ok, so satellite data isn’t available, but you could plot the Giss data back (as steven mosher did)
- and see if the trend line keeps stable at 0.2deg/decade, or declines….
(which obviously it will)
- but then you need to analyze what the decline means
- the problem with the 30-year trend is that it only looks back as far as the end of the post-war cooling period
- so it’s bound to over-estimate any warming trend.
or, course, just revert to a 30 year rolling average
Atmoz–
I didn’t read carefully enough yesterday. (In fact, I read very badly. I thought you meant to apply the uncertainty bands to your first graphs, and I thought you’d left them off.)
But, today, the one thing I’d ask– did you multiply by “t” when getting your error bands?
For a ±30% bands, (roughly 1 sigma) you multiply the standard error for the “3 Year” average by t=1.963. In contrast, you multiply the 30 year uncertainty by t=1.037. (At least squinting at your graph and comparing what I got for data, it doesn’t appear you added these, but it’s hard to tell because we may define “number of years” shifted by 1.)
Anyway, multiplying by “t” amplifies the effect you intend to show. We do need quite a bit of data to small enough uncertainty intervals to learn anything at all.
The difficulty for your underlying argument is that using 30 years of data isn’t always better than 8 years! It all depends.
If we assume
1)there really is an underlying linear trend, and/or
2) there exists no “weather noise” with cycles longer your data set,
then you get a better and better estimate as you add more years and the rate drops more or less as you show.
However, if either of those two things are wrong, the whole analysis doesn’t work. Uncertainty does always drop as we collect more data but it doesn’t drop as quickly as you show. That’s a problem because it means 30 years maybe no good either!
Here is what happens if either assumption is violated:
If there is no underlying linear trend, there could be a “break” at any year (possibly 2001). Or, the real fit could be quadratic. Or, any number of other things would be true. In that case, the change in linear trend seen at 2001 could actually be due to hitting the top of a quadratic. (I don’t necessarily believe it is. But this can’t be excluded based on statistics.)
If there are multidecadal cycles in global weather– for example, the PDO– then the uncertainty intervals calculated using a simple linear regression that ignores these will be incorrect. In particular, they will be too small. Worse, you can’t “discover” that cycle by processing a data set that is shorter than the cycle and you can’t even widen your uncertainty bands enough by analyzing for the autocorrelation. It’s mathematically impossible because your time series is too short.
So, unfortunately, statistics is useful, and lets us test things. But, at best, the uncertainty bands we find are the minimum uncertainty, that exists only if our assumptions are correct.
Of course, that just means defining climate is even harder than one might think, and you can’t really close off arguments about what the change in trend after 2001 might mean by showing that uncertainty bands get narrower — because your uncertainty band calculations actually assume that whatever trend existed must continue to exist.
And that is actually the question!
Atmoz,
Pick 1941 or 1942 as the starting point.
.1C per decade or less right?
Do the same graph for 1910 to 1941.
.2C per decade.
What caused the 1910 to 1941 rise?
Was it the same mechanism as the 1970’s to 1998 rise?
[Reply: This post was to show that arbitrarily choosing a starting point when discussing the "current trend" is a bad idea because you can basically cherry pick to get the answer you want. The same point holds for choosing when to end the trend. I will not engage in discussion of obviously cherry picked results.]
[...] has been a lot of discussion about my recent post titled 4 of 4 Global Metrics Show Agreement in Trends. I had posted that in response to his post saying that 3 of 4 global metrics show nearly flat [...]
Dude: Watts is a second rater.
Until scientists can explain the last 10 years it is premature to look at all this trend data. The explanation that seem to fit that I have read is:
http://www.nbr.co.nz/home/column_article.asp?id=21153&cid=39&cname=NBR
If this is correct then the question is why did we see the temperature increase of the last 30 years? I presume with appropriate jigging of the model variables, forcing factors etc… that one can figure out how to get the latest 10 years data to look approx right. I presume this is what the IPCC will do in the next revision.
THere is a lot of self-analysis that is going to come from this gross mistake in the scientific community. Heads will roll. People will be called to explain how they were telling us it was going to be 2 degrees, maybe 6 degrees how they said they were 95% certain and that we were all about to spend trillions and change our lives to do something about nothing. This is going to have huge impact on the scientific establishments credibility. The science establishment has become massively politicized. They have an entrenched interest in promulgating a theory BEYOND their natural skepticism which is the way all scientists normally operate. We didn’t have that here. We had scientists running around with politicians claiming they were CERTAIN of things based on almost zero real data but computer models that have never worked.
This is the biggest scientific screwup in HISTORY. Scientists are never going to live this down. People for the next century are going to be joking about how they predicted this disaster or not funding things or changing the requirements to publish. Things will have to change about how science and politicians work together. This preaching of politics in the science classroom I see everyday has got to stop. Scientists have to up the standards and some will have to be eliminated who just did bad science.