If I understand Gavin in comment correctly, he is requesting that I expand the features I consider to be included in the IPCC projections to include more information. The idea is that, by including features describing the variability of weather over time, the current trend could be found to fall into the range for weather. So, basically, in comments, I think he is requesting I check this hypothesis that climate since 2001 assuming all of the following are simultaneously true:
- there is a a deterministic trend in surface temperature of m=2 C/century.
- with weather noise is AR(1) and has a lag 1 autocorrelation of ρA=0.1 for annual averaged data
- the inter-annual variability, not explained by the trend, is σ=0.1C based on annual averaged data.
I’m going to give it a shot! To do this, I will use monthly data (as I always do), begin with Jan 2001 (as I always do), test up to three features.
- Is the observed lag 1 autocorrelation for annual averaged monthly data consistent with a lag 1 autocorrelation of 0.1 for annual averaged data? If the answer to this is “no”, the lag-1 autocorrelation Gavin proposed will be said to falsify. I won’t do any further tests using the suggested autocorrelation, because using an autocorrelation that has been shown inconsistent with the data makes little sense. However, it the lag-1 autocorrelation fails. I’ll continue.
- Assuming ρA=0.1 is does not falsify, I’ll test the residuals for the observed OLS fit to for GMST vs time consistent with σ=0.1C for annual averaged data. If the answer to this is “no”, once again, I won’t do any more tests. But if it passes, I’ll continue.
- Assuming both ρ=0.1 and σ=0.1 C pass, I’ll test furture trends using both these model values and observed values. If they don’t pass, I’ll test using best estimates based on empirical data.
For those wondering: One of the bones of contention is this. The models predict much larger variability in 8 year trends than indicated by the recent data. However, if the model variability is correct, then the current trend does fall within the range of variabilty of models. (Both Gavin and I agree on this.)
My first quick and dirty swipe at the data suggested that ρA falsified badly. However, I sat down to examine the effect of averaging over 1 year, and concluded that I can’t tell without doing the entire analysis. So, you will now be subjected to several truly boring analyses, which will be posted so that people can see what I have considered and not considered.
Based on the assumption that the earth temperature itself is an AR(1) process, but data are reported as averaged over a time “T” (i.e. 1 month, 1 year) I’ll post at least the following preliminary analyses:
- A boring analysis to relate the variance of averaged temperature to the underlying instantaneous variance. ( The purpose of this is to relate the variance of the monthly average to the annual average. This is necessary to test the first two questions above using monthly data.)
- A boring analysis to relate the lag 1 autocorrelation for averaged temperature to the autocorrelation for the continuous temperature series. (This is necassary to test whether ρA=0.1 is consistent with the monthly data since 2001.)
- A post to explain the values of the monthly data for σ and ρ that will be used to generate the montecarlo data.
- The likely less boring analyses that actually do the tests of ρA=0.1, σ and the trend itself.
Have I done the full test yet?
Nope! It looks like the test for ρ will be the most critical one. As I said, the initial back of the envelope things had it failing badly, but, if I do the steps in boring analysis 1 & 2, it like that knocks the lag-1 autocorrelation from ρM=0.82 to ρM0.73. I had previously run tests on ρM0.80 , which fails (miserably). But I haven’t run on 0.73, and just looking at the data roughly, it might just squeak through (or not!)
The purpose of the first few posts is to force myself to make sure my analysis to even get 0.73 is right! (I never quite trust my freshman year integration or even the though process that set up the problem unless I test it. Documenting will force me to check the first steps.)
So, plan to see some boring tests going forward. (I’ll have to interlace this with some ice-melt posts.) 🙂
“plan to see some boring tests going forward”
Lucia, you couldn’t write a boring post if you tried!
Whether they will be boring or not the procedures will not prove anything. Using a property of the models to validate or falsify the models is a logical fallacy known as a circular argument. If the variability of the models is much greater than the climate variability, as Gavin claims, then this fact demonstrates that the models do not replicate climate successfully. The fact that the variability of the climate in the models does not guarantee that the trend is wrong, but it certainly does nothing to convince any one that the models have the trend right. However, Gavin might know of a study that shows that climate variability since 1900 is much lower than it has been since, and he could rescue the larger error bars.
DougM:
Actually, the model can be falsified this way. It can’t be proven.
If the lag 1 auto-correlation of ρ=0.1 is inconsistent with data, that means this particular prediction is falsified. If it is not falsified, it means that we can’t prove it false. That doesn’t prove the prediction correct, but it would mean we can’t say it’s proven false (to any particular level of confidence we happen to pick. For blogging, I use 5% and two tailed. )
However, in my opinion, I still prefer to test the 2C/century and weather noise from the data.
Still, if the ρ=0.1 survives, I’m perfectly willing to admit it and carry it along. The earth will continue to rotate, and after a while, we’ll have more data. Either a particular hypothesis will survive, or it won’t.
I’ll eventually expand to reporting the “beta” (β or “type two”) error. This will let people judge just how much weight to extent to “fail to falsify”.
So let’s see.
“For those wondering: One of the bones of contention is this. The models predict much larger variability in 8 year trends than indicated by the recent data. However, if the model variability is correct, then the current trend does fall within the range of variabilty of models. (Both Gavin and I agree on this.)”
If you take that argument to it’s absurd conclusion , an ensemble of climate models with a very wide distribution could predict 0C/century as falling within prediction.
These climate modelers are a very silly bunch
watching ice melt is pretty dang interesting this year
In my mind the whole thing is a sterile exercise in mathematics. Whatever numbers one uses for variability are meaningless if we cannot associate the physical processes of variability to those numbers in a veriviable way. So basically, we now have an 11 year flat trend. Ajusting for ENSO still leaves us with a flat trend. Throwing more variability into the computations so that we can say that the models have not been falsified, when we cannot find the physical processes associated with that variability, seems pointless to me. I can see doing that for predictions, but doing it for a historical trend is simply saying that we should use large variability to avoid falsification. If we know enough about natural variability to build it into our models, then we should be able to look at the last decade, remove that variability from the signal and show that the signal is still there. We should not need to retain the same noise bands for historical data. Gavin is completely unable to provide a physical explanation for why the last decade is flat. I personally would not let him off the hook by giving him variability error bands that should only be used for prediction.
The bottom line is this, we have had a flat temperature decade. If you remove everything that we know about variability – ENSO, Solar, PDO, Volcanoes, aerosols, etc. it does not come close to overriding the supposed .2C per decade CO2 forcing trend. With everything that we know about removed, the .2C signal isn’t there. So we can either assume that we do not know enough about natural variability or that climate sensitivity is much weaker. Gavin has been asked to account for the natural variability that would give us a flat trend, on real climate, at least four times, by different people. And he has run away from the question.
Lucia has done a great job demonstrating how protean the AGW models are. They can’t be falsified in part because the rather substantial range of physical processes they do not capture are a double-edged sword. When skeptics /denialists /lukewarmists point out how little of actual reality the models capture, the alarmists say that simply means we need more time for the various unaccounted for “short term masking effects” etc to play out and let the “real” trend reveal itself. It is a kind of genius to be able to argue that the less my work jibes with reality, the longer you need to fund it. Is this a great country or what?
If the next two years continue to flat-line, I expect lots of language about “stair-step” patterns. Alarmists could do a partial rhetorical backtrack and give credit those undefined Gaia-like balancing tendencies that re-establish equilibrium on each higher stair step until overwhelmed again… In the alternative, they could go for a “sudden flip” theory in which all the bad stuff will happen at once instead of steadily, measurably over time.
If the IPCC is clever, the next round of AGW temperature graphs will be lucia-proof bar graphs in 50-year blocks showing big leaps over long time periods in undefined increments–(“falsify that, lady!”).
Natural climate variability and modification of the temperature record has been discussed in several places on this Blog. Spence_UK discussed the subject, as did Tilo Reber, among several others. I’m not sure where my thoughts go, so I’ll put them here.
I haven’t seen in the discussions what I consider to be an important aspect of the situation. An over-riding aspect, in my opinion.
Let me try to say it this way; Have the models/codes predicted during the time scale of interest the natural variability for which the measured data are being modified? If the applications of the models/codes have not resolved the phenomena and process responsible for natural variability, there are no basis for modification of the data. Actually, if the states of the climate system produced by the models/codes are not consistent, to some degree, with the states of the climate system during the times of interest, there might be no basis at all for attempting the comparisons. The use of a global solution meta-functional tends to make these kinds of comparisons somewhat iffy under the very best of circumstances.
I consider this a valid issue because resolution of the natural climate variability is a well known area of weakness for the models/codes. Michael Ghil and colleagues, and many others I’m sure, have addressed the problem. Here is what looks like a proposal to do some investigations into the problem and this seems to be a paper based on that work. The ‘proposal’ and the abstract of the paper have summaries of some of the issues.
It seems to me that there a few prerequisite conditions that must be carefully determined before the numbers calculated by GCMs can be assigned to climate variability of the real Earth system. It is my understanding that some of the results presented in the IPCC reports are not from general GCM calculations but instead are from special-purpose versions of the models/codes. Whatever the source of the numbers I think the following need to be determined.
(1) Do the numbers come from models/codes that even include modeling/application approaches that can accommodate the physical phenomena and process that are responsible for the natural variability of the Earth systems. I’m sure that some do and some don’t, but whatever the case, if the data record is modified for these it must be checked that the models have in fact calculated them for the time period of interest. The spatial resolutions used in many applications of GCMs are enormous and might not be sufficient for accurate resolution of natural climate variability.
(2) What are the important natural variability phenomena and processes that have occurred within the calculations and are these the same as those being used to modify the temperature record?
(3) Have the models/codes results from (2) been shown to correctly reproduce the natural variability that occurred during the time scale of interest for which the measured data have been taken. That is, have Validation exercises been conducted and shown that the models/codes correctly calculated the phenomena and processes that actually occurred during the period of the measurements.
Hand-waving invocation of ‘weather variability’, especially because the models/codes don’t resolve weather, and no other ‘justification’ has been offered for such an attribution, just doesn’t cut it for me.
More importantly the difficulties with proper resolution of natural climate variability by existing models/codes is well-documented in peer-reviewed papers.
Corrections for incorrectos will be appreciated.
Dan Hughes,
Don’t you get it? The computer generation rules! 🙂
Let me get this straight. Climate scientists can arrange an ensemble of climate models and come up with a wide distribution and claim that 0C/century doesn;t falsify their pet models? At the same time people like Hansen say the world is at a tipping point and we should believe him because of a climate model?
A strange bunch these model hacks.
You’re trying to determine if a 10 year trend is consistent with the expected long-term trend, correct? Here’s what I would suggest, if I may. For the years 1860 to 1998, you can get slopes looking 5 years ahead and 5 years back. For 1860, you’d get the slope between 1855 and 1865, and so forth. Then you repeat the excercise, looking 10 years ahead and 10 years back. Finally, you model the difference between the 10 year trends and the 20 year trends. You can get a standard distribution from this and draw some statistical conclusions about what we see now.
Joseph-
I’ve done a similar exercise– but limiting the test to periods without volcanic eruptions. If we restrict to periods without volcanic eruptions, then the uncertainties in the trend I find are supported by the test. If we include periods with volcanic eruptions it is not.
Of course, this is precisely what one would expect based on the phenomenology. When stratospheric volcanos erupt, the temperature plunges, and then, unless another volcano erupts, it rises.
This means the variability of 8 year trends rises dramatically. So, because we know the eight year variability should be different when stratopheric volcanos are or are not erupting (and later when the dust veil clears) we can’t treat those periods as “similar” from the point of view of statistics. With respect to testing the variability of 8 year trends, they are different.
So… if we correctly account for the volcanos, my variabilities look fine. Arguments are possible because a) there is not that much data in the first place and b) the amount of time not affected by the volcanic eruptiosn is small.
But what data we have says my uncertainty intervals are in the correct size range.
DougM,
In case you wanted to know why it can be falsified:
One of the principle laws of logic is the law of non-contradiction. This basically states that something can not be A and not A at the same time. In classical logic, this is utilized in reductio ad absurdum, which basically states Assume A, show a contradiction, therefore not A. If the contradiction cannot be shown, there is no logical argument to be made. (as Assume A, show no contradiction, therefore A is indeed a circular argument)
Because statistics deals in probability and not the absolutes of classical logic, this isn’t precisely the logical argument she uses but it really is close enough to get the gist of why it is possible to falsify.
Lucia-I would really be interested in what your method would say about a trend of .17 degrees per decade (say) as opposed to the .2 you’ve been testing against. Does the result differ? I think it will.
BTW, reading another thread here, it seems JohnV et al. want to have it both ways with “low frequency weather noise”-they want to say it gives false falsifications-but that this “low frequency weather” does not need to be considered when attributing trends to AGW in the first place. How silly. Many people seem to have trouble thinking consistently and clearly these days.
@Andrew (and perhaps JohnV?)
hmmm, so “Climate” is the weather (with its variability) integrated over a sufficient time to yield a state variable. And “low frequency” weather noise is something different from “CLimate”?
Is it assumed that the “low frequency” part is CHAOTIC in its nature?
If not chaotic, has frequencies been suggested?
If not chaotic, has causal mechanisms been suggested?
Cassanders
In Cod we trust
Andrew–
I tried to remember which posts had full tables. You can see one here:
April Test
You’ll see 1.7 falls inside for some measurement groups and outside for others. But I only did Cochrane Orcutt last month. If a test says y ± x, all you need to do is add and compare the bounds to any value to discover your answer.
But why do you want to test 1.7C/century? Did anyone suggest that currently applies? With frequentist statistics, it’s best not to pick your uncertainty intervals after doing the test. You pick what you want to test, then test, then say “accept/reject”. There is a reason for this– in some sense, the uncertainty intervals have uncertainty intervals.
So, I usually just talk about 2 C/century.
Looks like Joe’s plots are getting good use. Lucia maybe yours will be used someday 🙂
http://www.tech-know.eu/uploads/Letter_ … i-moon.pdf
http://www.tech-know.eu/uploads/message_to_Congress.pdf
Hi-yes, some people have suggested that. For instance:
http://www.worldclimatereport.com/index.php/2006/01/31/hot-tip-post-misses-the-point/
The result is about what I expected-this is approximately the trend over 1977-2005 on the surface. So I expected that to not be falsified by the surface measures. 🙂
Good article. It is always useful, when someones say things like the world is warming (faster/slower) than (unnamed) scientist predicted.
Whose predictions are you talking about?
When were they made?
What was the predicted rate?
And how fast has it warmed since them?
Certainly, right now, it’s difficult to find prediction followed by higher warming measured after the prediction was made. Given recent data, the only way to make IPCC predictions look like they underpredicted is to find data available before the prediction was made!
Predictions from the fourth assessment report may falsify. The AGW counter is that shorter term variations aren’t being accounted for correctly, and that over a longer time period the prediction will be better.
However previous predictions from the first, second and third assessment reports perform better. Lucia’s chart posted recently showed that the actual temperature has been above the lower bound predicted in each of these reports.
The improved performance of older predictions, based on less data, less computational power, and less scientific understanding, but a longer time period, lends support to the argument that a longer time period will lead to improved performance for the fourth assessment report predictions.
The trend is your friend – until it, without any warming at all, turns its back on you and joins the enemy…