This is a “quickie” post. It’s really just a placeholder, so I can put a couple of graphs on the web and refer to them elsewhere.
The graphs are trend rates determined from 10-year time spans of global average temperature data, together with error ranges estimated from an AR(1) error model. The errors are not actually AR(1), so the true error ranges are larger than those plotted — but these graphs will at least show “ballpark” error ranges.
The dashed lines show the upper and lower 2-sigma error ranges from linear regression for the time span 1975-present.
Here are the results for GISS data:
Here are the results for HadCRUT3v data:
Note that for each decade in the GISS analysis (from 1975-1985 to 1998-2008), and most of them using HadCRUT3v data, the error range for the decade overlaps the error range for the entire time span (as indicated by the dashed lines).
12 responses so far ↓
Brian Klappstein // May 18, 2008 at 3:42 am
Tamino:
Why the apparently significant difference between the HADCRU3 and GISS dataset? Don’t they dip from the same well of weather stations and SSTs?
Also, the declining trend for temperature growth. You wouldn’t sell much stock if you showed this as the recent price trend for a public companies product. At some point (maybe soon) the “error bars” won’t overlap anymore.
Regards, BRK
[Response: When the error ranges don't overlap, is the time to wonder why.]
steven mosher // May 18, 2008 at 12:46 pm
I’m confused. is the y axis decadal trends?
you show .02 I must be making a mistake. help.
[Response: The y-axis is the decadal trend (i.e., determined from a 10-year time span), in units of deg.C/year. Multiply by 10 and you have the decadal trend in deg.C/decade.]
kim // May 18, 2008 at 1:49 pm
Wonder is a cloudburst of reason; it poureth heavily on the hills and dales of consciousness, not just when error bars don’t overlap.
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Hank Roberts // May 18, 2008 at 4:52 pm
Put Brian’s phrase
> difference between the HADCRU3 and GISS
into Google shows these words are a popular current theme at the usual sites, much repeated.
Down the results page below those is an informative link to our host’s blog here:
http://tamino.wordpress.com/2007/05/11/best-estimates/
S2 // May 18, 2008 at 9:39 pm
I look forward to the follow-up posts.
Just out of curiosity - you are apparently plotting decadal trend rates based on the start point of the decade, whereas some people (e.g. Keenlyside et al. ) use the mid point.
I can’t see that it would make any difference - your graphs would (I think) look exactly the same, except for the values on the x-axis.
Is their any reason why either approach should be better than the other?
[Response: No reason. Only the x-axis labels would change.]
jws // May 19, 2008 at 12:21 pm
“Note that for each decade in the GISS analysis (from 1975-1985 to 1998-2008), and most of them using HadCRUT3v data, the error range for the decade overlaps the error range for the entire time span (as indicated by the dashed lines).”
I must be missing something but how can it be said that the 1998-2008 error range overlaps if the graphs stop at 2000?
[Response: The x-axis variable is the *starting* year of the 10-year period. Hence the final data point is the 1998-2008 value.]
George // May 19, 2008 at 6:44 pm
Have you analyzed that data to see if there is any statistically significant periodicity?
Perhaps that is where you are going with this?
[Response: I posted this only so I could refer to the graphs elsewhere. I haven't found any significant periodicity in the 1975-present temperature data.]
Arthur Smith // May 19, 2008 at 8:26 pm
On GISS vs HadCRUT3 differences, I happened to recently run Stephen Schwartz’s (2007-edition) time-constant calculation for GISS, GISS MET, and HadCRUT3 data - results can be seen here:
Autocorrelation:
http://inlinethumb02.webshots.com/41409/2931858850101763211S600×600Q85.jpg
“time constant”:
http://inlinethumb53.webshots.com/21364/2149964910101763211S600×600Q85.jpg
You’ll note the Hadley data is significantly more auto-correlated (longer time-constant); also note that what Schwartz published was based on the GISS Met station data, not the GISS Land+Ocean data, and seems to be less autocorrelated (shorter time constant) than the Land+Ocean series.
Crashex // May 20, 2008 at 4:20 pm
Why did you stop at 1975? You chit D’Aleo for not using a broader range of temperature data for his chart evaluating the connection of CO2 and temperature trends in a recent post. These plots look like a convienently narrow range , ignoring the “global cooling” trends of the 70’s.
Are you a salesman or a scientist?
[Response: 1975 was a turning point for global temperature, easily demonstrable with objective mathematical analysis and actually rather visually evident, starting a new episode of global temperature evolution. And as I said in the post, the purpose of posting is to put graphs on the web so I could refer to them elsewhere, which discussion was about temperature since 1975.
The claim of global cooling in the 70s is a myth.
Are you a curious citizen, or an idiot?]
Crashex // May 20, 2008 at 9:31 pm
Curious citizen.
Oh, so a 120 year range demonstrates four distinct trends of 30 to 35 years each and you chose the one that best suits your argument. And you’re certain that that trend in better and different from the other three, meriting linear extrapolation beyond the data range.
Obviously, global cooling was a myth in the 70’s; hindsight verifies that the learnered progonosticators of the day weren’t correct. They were just extrapolating trends from a recent temperature cycle and publishing theories regarding what generated that trend in a climate system too complex for them to completely understand or evaluate.
I wonder if history ever repeats itself?
[Response: The claims that the climate science community was prognosticating global cooling in the 1970s is another myth. Some were, but more of them were expecting global warming, and there was certainly no concensus on the issue. But since clearly you don't bother to do real research into the opinions you spout, it's no surprise you'd repeat that one.
As I said before, I posted these graphs in order to refer to them on another website discussion. Since that discussion was about the time span graphed, your moronic statement "you chose the one that best suits your argument" proves that you're simply interested in snarky denialism.
You are most certainly not a curious citizen. You're an idiot.]
cthulhu // May 21, 2008 at 7:33 pm
Here are 10 year trends for UAH and RSS too ( the x-axis here is the end year rather than the start year)
http://img.photobucket.com/albums/v235/ononelk782/trend10years.jpg
Reason I made it was over some dispute elsewhere about the trend divergance of GISS compared to the other records in the last 10 years. Usual claims of fraud, etc. Just wanted to show visually that it’s not that uncommon for the records to diverge in the past. Unfortunately noone really saw the graph for what it was and just complained that it wasn’t like any of the records they had seen, etc etc and so I became part of the “conspiracy”.
Richard // June 1, 2008 at 3:49 am
I don’t quite understand how the dashed lines can be called 2-sigma error bands. 2 sigma error bands enclose >90% of the data don’t they? In the GISS only 6 of 24 data points fall inside the error band. Linear regression requires also some independence doesn’t it? Each of the data points shares 80% of its data (10 year moving average) with its neighbours, so the data points cannot be called independent can they? Thanks for further explanation to a statistical neophyte!
[Response: The dashed lines give 2-sigma error ranges for the warming rate estimated from linear regression of monthly temperature data from 1975 to the present, not a fit to the data points plotted in the graphs of this post. It's nearly the same as linear regression on this data -- that graph is of annual data, but the results plotted in this post are based on monthly data.
The individual data points plotted in these graphs (with error bars attached) are the results of the same computation, but based on 10-year time spans (rather than the 33+ years 1975-present which give limits represented by the dashed lines).
It's true that for normally-distributed data, more than 90% (in fact, about 95%) of the data should fall within the 2-sigma confidence limits. But the 2-sigma limits indicated by the dashed lines are not for the dots plotted in the graphs, they're for the slope from a linear regression to the 1975-present data. We can expect that the uncertainty in the 33+ year trend will be considerably less than that of any 10-year trend, so it's no surprise that the dots (10-year trends) scatter over a wide range while the long-term trend is much more precisely bounded.
It's a bit analogous to computing an average from many data points; the average is more precise than any of the data points, and the more data we have the more precise it gets. Suppose, for instance, you flip a coin and assign a value of 0 to tails and 1 to heads, and you want to estimate the average result of a coin flip. In this case, all individual flips give a result of either 0 or 1. If you flip it 10 times and get 5 heads, you'd estimate the average as 0.5 with a 2-sigma error limit of +/- 0.316. If you flip the coin a million times and get half a million heads, you'd estimate the average as 0.5 +/- 0.001, much more precise than the result from only 10 flips. But in *both* cases, the 2-sigma limits for the *average* don't enclose 95% of the data points. In fact, since all the data points are 0 or 1, in both cases the 2-sigma error limits for the average don't include *any* of the data points!]
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