The Teeter-Totter of Temperature!
I thought I’d fiddle with my spread sheet and create a graphic I’ll be able to easily update month to month. This way, when the temperature trends flip to positive as predicted we’ll see that. Later, if and when the trend begins to increase to the level predicted by the IPCC projects, we’ll see that. 
Easy, peasy! The graph is shown below:
For convenience, I’ve also plotted the ENSO index from NOOA.
The cluster of negative slopes are the Cochrane-Orcut regressions for GISS Land Ocean, UHA MSU, NOAA, RSS, and HadCrut. Notice that GISS give the smallest negative trend: -0.4 C/century. HadCrut give the largest negative trend: -1.6 C/century.
Later this week, I’ll discuss other ways to look at estimating the trend and its uncertainty. I’ll also explain why I prefer to average all the data together, and why this is almost always preferable to selecting only one.
Updates
Someone requested a larger plot: GMST vs Time without the NOAA ENSO addition. (I’ll make a habit of making these larger and posting both larger and smaller versions.)
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22 Responses to “The Teeter-Totter of Temperature!”
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Chris Harrison March 24th, 2008 at 11:39 am
If you’re going to keep updating this interesting graph, please could you upload a higher resolution versions. Something like 1024×800 or so would be very helpful, thanks.
Alan S. Blue March 24th, 2008 at 12:34 pm
Could the confidence limits on the IPCC prediction be included? Adding the limits for everything would make the entire graph unwieldy, but having just that one set is a succinct summary of where we are.
lucia March 24th, 2008 at 12:38 pm
Alan– Sure. I’ll add those tomorrow. I’ll be discussing various possible confindence limits, and the ones I choose to show. This may surprise people, but of the three possible choices I consider defensible, I show the largest.
steven mosher March 24th, 2008 at 6:28 pm
Hi,
Spent some time today trying to explain to folks what exactly you had done. tammy was curious, not about the math,
not about the fact that you averged all the time series, but about the exact verbage of the IPCC. weird?
Leads me to believe that your math is solid and folks want some way to save the IPCC.
They wrote a bad report, they might have got some things wrong, fix the problem and get back to science. DUH!
Arrrg. Hey you know you can access to GCM results from UCAR? ( they are pretty ugly) But here is a thought.
On the supposition the the IPCC “forecast” is an average of multiple model runs, would it be better to reject
indivdual model results, rather than the IPCC average of them?
lucia March 24th, 2008 at 7:04 pm
Well… the exact verbiage of the IPCC report is in the IPCC report. I quoted it and linked in my post. I assume you told Tamino he could find it there?
Yes. I averaged them the temperature measurements. I should think that if Tamino is curious about the wording in the IPCC document, he could just read it, non?
The purpose is to minimize noise due to “instrument” error. (That is, it’s like averaging over 4 ensembles of thermometers.)
I don’t plan to access GCM results. I prefer to work backwards rather than forwards.
I want to compare data (aka observations) obtained after to “consensus” projections disseminated to the public. In principle, those working on the IPCC reports did whatever filtering or sorting of the GCM reports that are necessary or useful to create these projection. Either the data will indicate they succeeded or not.
If the people making the predictions did a good job, great. We note that. If not, we note that. In the event that the predictions were either poor or hold up, that’s information that I can use to make judgements that guide my hand at the ballot box, etc. I don’t particularly need to know whether the problem is in the paramerization for “X”, or the Validation and Verification or the “blah, blah, blah”.
Those would be interesting questions, but right now, what I want to figure out is if the process, as a whole, results in projections that pann out as the future unfolds.
On models themselves: I many be mistaken. However, I think the IPCC forecast is not simply an average of mutiple AOGCM model runs the way a normal person would describe a average of AOGCM model runs. It apppears that Tom Wigley and others came up with simple models — possible even better than “Lumpy”, and tuned those to AOGCM models.
We can call these “Fancier-than-Lumpy-Like” models.
In principle, these “Fancier-than-Lumpy-Like” models will regurgitate the average that an “ensemble” of AOGMCs would have regurgitated if one had actualy run these modles for the full 1-2 centuries at the suggested forcings. (One can also set the sensitivity on “Fancier-than-Lumpy-Like”. I guess…. I’m going by the brief descriptions in the IPCC reports.)
Anyway, after tuning these Fancier-than-Lumpy-Like” models, you “run” it, and get projections. Some sort of averaging is done. But, strictly speaking those curves aren’t direct output of AOGCM. (Or at least, I think they aren’t.)
So… if I’m understanding these correctly, it could even be the case that some AOGCM’s are perfect, but imperfections are introduced when one creates and tunes the “Fancier-than-Lumpy-Like” model.
steven mosher March 24th, 2008 at 7:14 pm
Lucia, I’ve been pretty mean to tammy so I’ve been trying to behave myself. I just told him to come here and ask you
directly. ( I dunno maybe he remebers the first time you tangled with him )
You will find it funny that when he propose a clmate bet
http://tamino.wordpress.com/2008/01/31/you-bet/
he suggest using ALL the indexes. ( read the comments )
hehe.
I thought the GCM interesting because the GCM are used to create that .2C trend you falisfy. so it follows……
lucia March 24th, 2008 at 7:18 pm
Sure. I’m working backwards because I figure I learn the most that way. Anyway, the primary issues are:
a) How much warming should we really anticipate.
b) What’s the uncertainty in our predictions.
I know people like Dan Hughes are very interested in the specific V&V and looking at snippets of code. You’d think with my background I might be too. But still when it come to down to brass tackes the question is: Given the current state of science, can we project into the future? To ±1C/century? ±2C/century? Or just “temperature are bound to go up!”
steven mosher March 24th, 2008 at 7:22 pm
argg, I should read your comments to the end. Fitting a model to model results? Someday I tell you about simple models of war and complex models of war. same kinda problems
lucia March 24th, 2008 at 7:23 pm
This would, in principle, be the job of whomever ultimately decides what the IPCC projections are. I only want to figure out if the IPCC projections end up giving useful guidance after they make them.
Knowing whether or not the IPCC projections are accurate or precise is important if we are to base decisions on their current, or future, predictions/projections.
steven mosher March 24th, 2008 at 7:27 pm
how much warming? Well, a naive forecast would say, .16C per decade ( starting from a 1964 start date)
To replace a stupid straightline model with a physics based model, you have to prove it has better skill.
something like that.
Roger W. Cohen March 25th, 2008 at 4:56 am
Visual inspection shows a periodic component to the data, evidently due to ENSO activity. This makes an analysis based on linear trend plus correlated noise suspicious, especially one that treats only first order autocorrelations like Cochran-Orcutt. How about a two-variable fit : T = m T + g ENSO + noise ? This model should better isolate the underlying trend and its uncertainty.
lucia March 25th, 2008 at 6:02 am
Roger:
I agree strictly linear is a problem. I selected linear because the IPCC’s projections are linear.
Do you have a model for ENSO? If someone wishes to do that analysis, or has done it, it would be interesting to read.
In my head, I’m planning a post to explain what the IPCC might do to include the uncertainty due to ENSO (or other cyclic projections) in the uncertainty intervals they disseminate to the public.
This would be easy for them to do. Basically, you estimate the contribution of “weather” with large periodicity to the variace of the slope <m’m'>, and add that. Once I’ve done this, I may be able to comment more precisely on how these long timescale features (like ENSO and the much longer PDO) influence the uncertainty in the measurement of the slope (m).
I think if the IPCC did this sort of thing and included the effect of these known weather phenomena in their 1-σ error bars, that would benefit the public understanding and aid policy makers.
I did do sort of back of the envelope estimate for how much this type of cyclic periodicity might affect the error in the estimation of the trend, in this particular time window with several cycles. I discuss that here. You can see that Atmoz’s graph shows the contribution of the error diminishes rapidly as we average over several cycles. It’s fairly apparent that at least two cycles have occurred. (One could argue more have occurred. But I want to be conservative, and consider the largest likely effect. )
Phil. March 25th, 2008 at 6:42 am
Just a thought Lucia, perhaps you could add the ‘last date updated’ to the graph?
lucia March 25th, 2008 at 6:57 am
Phil,
That’s a good idea. I was sort of planning on that because I know that even though you can tell the data “end” when they do, it’s still nice to have a date on there explicitly.
I need to figure out how to get EXCEL to put a time stamp on these so I don’t have to do it manually! (I’ve got some error bars on for the data.)
Roger W. Cohen March 25th, 2008 at 7:37 am
Lucia
I don’t know anyone who has done this for the recent epoch. There are a number of ways to go about it. The first two use the ENSO index itself as a model:
1. First detrend the data for the part that correlates with ENSO. This allows selection of the lag/lead that gives the maximum cross correlation (which I suspect is small or statistically insignificant). Then do OLS or Cochrane-Orcutt or Prais-Winsten on the detrended data. A test for whether you have ‘captured’ the main weather factors would be whether there is substantial excess autocorrelation beyond one month (there is now).
2. Do the bivariate regression: Temp = m t + g ENSO(t). This reduces to the same as #1 if there are no correlations between t and
ENSO(t). Visually it’s hard to tell.
3. A completely heuristic approach,similar to the spherical ENSO. For example, select the amplitude g’, phase p, and frequency w of the principal spectral component of the data, and do the bivariate regression: Temp = m’ t + g’ sin(wt + p)
I applaud your efforts to bring greater clarity to IPCC projections and their uncertainties.
lucia March 25th, 2008 at 7:56 am
Thanks Roger!
With each test, I need to learn more. What I’m doing is performing the analyses I know how to do now. Then, if someone advances a criticism, I try to address it. If their critcisms is purely qualiatative– like William C’s handwaving argument showing flat trends occur after volcanic eruptions, I respond with similarly qualitative argument. (To do otherwise, imposes the burden of perfection on me, and no burden on them.)
The ENSO issue Atmoz’ raised is interesting.
On the remaining autocorrelation: yes. It’s there. I noticed that generally, if I then do CO on the residuals (as on reference recommended) I narrow my uncertainty intervals. Soo…. I figured I should keep them wider, and so be less hasty.
What I do find a bit surprising is no-one has pointed to any peer-review articles (or even articles in the grey literature) that show comparisons of projections of this sort to data. (Except possibly Rahmstrof, which is.. well… I’ll discuss that later. I need to give that the ‘drawer’ treatment because everytime I compare what they did to what is in the IPCC I ask myself: Could a group of 6 authors, working together has made such a hash of the comparison?!)
steven mosher March 25th, 2008 at 8:08 am
CROSS POSTED at Tamino. see if he lets it through. pulling quates from Taminos YOU BET thread
This is a fun discussion. Lets suppose that it’s 2008. Oh it is. Do you think that 7 years from now we could reject a projection or prediction of warming? Is seven years too short a time period? Well it depends on the noise, and depends on the magnitude of the trend. Could we reject a projection of warming in a period less than 7 years?
Good Question! Let’s ask somebody who understands this:
“By 2015, the expected temperature from the regression-line fit and that expected from the “no change” hypothesis will be far enough apart that we’ll probably be able to distinguish between them with statistical significance. In other words, by 2015 either we’ll know that global warming has changed (possibly stopping, possibly reversing), or there’ll be no more of this “global warming stopped in 1998” malarkey.
It’s entirely possible that the numbers may give us statistically significant evidence even before 2015. If so, I’ll report the result. If it turns out that global warming is not continuing (which I seriously doubt), then I’ll readily admit that I was wrong. In fact, I’ll be keeping a close eye on the future evolution of global temperature and actively looking for such results, so if we do get valid evidence that global warming has stopped, I just might be the *first* one to say so.”
Very simply, If I bet that the next 7 years would show say .017C of warming per year on average,
or .17C per decade
AND IF, for example, we saw a couple years of zero warming, or Cooling, then as our author above suggests we could reject the claim that warming is proceeding apace at .017C per year,
AND we could reject this claim in a period shorter than 7 YEARS!.
Now, Which series would we look at? Just GISS? I dont know, Lucia makes a point to look at them all. let’s ask for some opinions. How should we determine the outcome with the HIGHEST RELIABILITY?
What would tamino say: We know, he said it a while back
“[Response: None of the metrics — popular or not — is 100% correct. And correcting the GISS Y2K error led to a net change in global average temperature anomaly of 0.003 deg.C.
As I said, I’m not betting money I’m trying to establish conditions under which we can confirm or deny various hypotheses. It was framed as a bet because that seems to be popular for discussion, and it does force one to be explicit about exactly what conditions will lead to a declaration for one or another hypothesis. For a bet, I think it’s better to keep it simple and agree on a single source of data for decision.
But for determining the outcome with highest reliability it’s better to use multiple data sets. I intend to keep track of GISS, HadCRU, and NCDC, and I’ll probably keep my eye on satellite data from RSS, UAH, UMd, and UW as well. I’ll report any significant results, regardless of the nature of the result or the source of the data. I expect they’ll end up telling the same story.]”
So, there you have it. It’s theoretically possible to reject a claimed warming trend, or cooling trend with less than 7 years of data ( it would be one hell of a rare event) and the most reliable method is to look at several measures ( giss, hadcru etc etc)
I dont know what you guys are arguing about. I agree with tamino
lucia March 25th, 2008 at 10:42 am
SteveM, I have a quibble with this:
Either, it would take a unusually rare cooling event ( this would be α error) or a hypothesis would have to be quite wrong.
Do notice that the event we have had is consistent with warming. It’s just not consistent with warming at a rate as high as that projected by the IPCC.
steven mosher March 25th, 2008 at 11:09 am
Lucia, Yes, I’m just trying to explina that this notion that 74 months of data “is not enough” is categorical
nonsense. A lousy projection will get you into trouble early, as you note. I think most people dont get that
even a small amount of data can be used to reject, IF the means are sepated by large amounts relative to the noise.
Also, I am amused by the number of peole who suggest that we have to wait 30 years to reject, but who want to
“accept” the underlying hypothesis when the data in the short run seem to confirm.
Ralph Becket March 25th, 2008 at 8:04 pm
Hi Lucia, I believe you can use the @today function in Excel to include today’s date (see here).
lucia March 26th, 2008 at 3:33 am
Thanks Ralph!
steven mosher March 28th, 2008 at 5:54 am
re 1338. Tamino has complained that my quote mispresents his position on 7 years of data being enough. After re reading the whole text I agree. I told him sorry and suggested that he should also apologize for misrepresenting that Lucia was falisifying the TAR, when she was in fact falsifying Ar4. lets see if he does