It’s true. Every climate blogger knows it. Global Mean Surface Temperature have gone a bit flat. But is the recent flat trend statistically significant? Well, as my readers know, I took up Roger Jr.’s suggestion and set out to compare IPCC projections to data collected after the projections were made.
Over the weekend, I applied the Cochrane-Orcutt method to monthly GMST data, as reported by four separate groups (GISS, Hadley, UAH and RSS).
This analysis technique permitted me to estimate the best fit line that fits the monthly data and also includes 95% confidence intervals for the slope. I have now compared the trend line that best fits data collected after 2001 to IPCC projections for trends after 2001.
What’s important in the graph?
The short term IPCC projection is show with a red line which I superimposed on the IPCC chart. They predict that during the first 3 decades after 2000, the mean trend will be 2C/century; I indicated that with the straight line. (I extrapolate beyond 2030, so you can see the IPCC expect the trend to increase with thime.)
The shaded area on the IPPC graph shows the IPCC uncertainty intervals around their projected trend.
So, we should expect that if the IPCC trend is correct data trends will fall inside the shaded areas of the graph.
I estimate the empirical trend using data, show with a solid purple line. Not it is distinctly negative with a slope of -1.1 C/century.
But, more importantly, the IPCC projections for the mean trend, as indicated by the red line do not fall inside the 95% confidence intervals for the data. Those confidence intervals are bounded by the two purple dashed lines.
So, both the central tendency of the IPCC projections and the uncertainty intervals the IPCC applied to their projection fall outside the 95% confidence bands for the recent trend based on the data collected after the IPCC projections were made.
So, now, in answer to Roger Jr’s question posed in January:
What behavior of the climate system could hypothetically be observed over the next 1, 5, 10 years that would be inconsistent with the current consensus on climate change?
The current data appears at least somewhat inconsistent with the near term projections by the IPCC. The central tendency of the IPCC projection, m=2.0C/century, falls outside the 95% uncertainty intervals for trends estimed based on data collected since 2001. Moreover, the full uncertainty interval for trends projected by the IPCC fall outside the empirical uncertainty intervals.
Obvious follow on questions
When readers see this graph, I suspect these questions will come to mind:
- What does this mean in terms of IPCC projections: It appears that IPCC projections for the near term trend are high. I don’t know why they are high, but there have been no recent major volcanic eruptions. The climate modelers and NASA say that solar activity can no longer have a significant impact on the trend. “It’s in the pipeline” cannot explain a slowdown in the trend. The effect of thermal mass is to cause the temperature to rise more slowly initially, and then rise more rapidly later as the ocean begins to warm.
- Do I think AGW is ‘over’? Absolutely not.
The confidence interval for this data set are -3.3 C/century < m < + 1.1 C/century. The confidence intervals when I compute the trend with data from 1979 is +1.0 C/century < m < + 2.1 C/century. The newer data is not inconsistent with the longer term trend. (If it were, this would be surprising. I included the newer data when calculating the longer trend!) Nevertheless, based on data collected after the IPCC projections were first published, the IPCC projections appear to be on the high side. (That said: I would strongly prefer to defer full judgment on the consensus prediction. For many reasons, I prefer to use annual average data rather t han monthly data.).
It has always been a claim of skeptics that long term trends may exist in climate. If they do, any tests based on short series of data are problematic, because it is not possible to detect the true autocorrelation in temperatures from the data set. This applies equally to proving AGW exists and to falsifying it.
- Could different results be obtained with fancier statistical methods? Sure. Possibly someone will perform them.
The main purpose of applying Cochrane-Orcutt or any method to deal with serial autocorrelation, is to get a better estimate of uncertainty intervals. When serial autocorrelation exists, but is not corrected, the serial autocorrelation makes the uncertainty intervals appear to much too small.
It is also worth nothing that even though Cochrane-Orcutt widens the uncertainty intervals significantly, they may still be to small. The reason is that the uncertainty intervals I posted do not account for the uncertainty in the estimate for the serial autocorrelation on the uncertainty in the trend, “m”.
- Did I do lots of thorough fancy checks on this fit? No. I just assumed for the purpose of testing the IPCC model that the data should fit a linear trend and that the scatter around the trend is ‘noise.’ I recognized that the residuals for monthly data are serially autocorrelated and applied Cochrane-Orcutt to the data.
I didn’t check whether the residuals are normally distributed or do any additional checks. The residuals don’t need to be normally distributed to obtain a trendline that minimizes the sum of the square of the residual. However, the distribution of the residuals does matter if we are estimating uncertainty intervals on “m”.
That said, I’m not sure it’s worth a great deal of effort to do a whole lot of checks, at this point. I think it’s better to recognize the uncertainty in the empirical trend is quite large. It’s possible that if the uncertainty in the correlation coefficient were included in the estimate of the confidence intervals, they might widen. If they widened sufficiently, the IPCC projections might end up falling inside the uncertainty band for the data.
(It’s also worth understanding that temperature is not literally expected to vary linearly. However, the near term predictions by the IPCC are nearly linear. So, for the purpose of testing that projection, I assumed the near term trend is linear.)
What next?
Well, now that I think I have a handle on how to do this, I’ll be updating the evaluation rather regularly. We should expect that over the next few years, the confidence intervals on the trend will narrow. I suspect the trend will rise. After all the 30 year trend is positive, and radiative physics do argue strongly for some warming.
Still, as an empiricist, I do like to compare data to projections. So, I plan to do so.
Related posts
For new readers, here are links you might like to read:
- How I applied Cochrane Orcutt:http://rankexploits.com/musings/2008/correcting-for-serial-autocorrelation-cochrane-orcutt/>Correcting for Serial Autocorrelation.
- Why I start comparison in 2001: What Are The IPCC Projections? And How Not to Cherry Pick.
- My initial response to Roger Jr.’s hypothetical question. http://rankexploits.com/musings/2008/what-weather-would-falsify-the-current-consensus-on-climate-change/
References:
Updates:
- March 10: I adding a paragraph to better explain the graph. Later– modified graph for clarity and typos.
- March 11: Link to spreadsheet: GMST data after 2001
- March 11: Images for discussion in comments. (Click to enlarge)
Lucia, Your conclusion that “The current data appears at least somewhat inconsistent with the near term projections by the IPCC” appears to me to be at odds with the recent statement by Australia’s Professor Ross Garnaut (which I’ve quoted on another thread) that “Recent rises in global temperatures [have been] at the upper end of what was predicted [by the IPCC] in 2001.″ Do other readers agree? In particular, do the “real” statisticians agree that you’ve correctly applied the Cochrane-Orcutt technique to ascertain the trend that best fits the monthly data since 2001? (Incidentally, you’ve misspelled ‘Orcutt’ in your chart).
Ian–
The other two people did different analyses, but tell me I did C) correctly. I’ll fix the spelling!
I don’t see how anyone can think rate of change in global temperatures since 2001 is at the uppe end of what was predicted by the IPCC in 2001. If we don’t correct for serial autocorrelation, it’s flat. If we correct, it’s negative. If we look at annual data, it’s flat. How can this be at the upper end?
I guess I’d have to read more of what Prof. Ross said though.
Ian-
This reference you cite comes from Rahmstorf et al. 2007 and is cited on p. 21 of the Garnaut Interim Report. Rahmstorf et al. compare 2001 IPCC predictions with data since 1990. Two things make the analysis here different:
1. The inclusion of more recent data than used by Rahmstorf et al.
2. The 2007 AR4 predictions are a bit higher than those of 2001
Thus the statements here are not at odds with those in the Garnaut Interim Report, and if anything that report and its reliance on Rahmstorf et al. 2007 are now out of date.
Thanks Roger. I think we may be at cross purposes here. The 2001 ‘predictions’ for each of the six illustrative SRES scenarios were shown decade by decade in the tables in Appendix II of the WGI contribution to the TAR. These showed an acceleration of the projected temperature increase in the 2000-2010 decade compared with the (standardised) increase of 0.16 C for the 1990-2000 decade. At the Garnaut Review’s third public forum on 14 November 2007 (“Climate Change: What is the Science Telling Us? Is there a Need to Develop New Emissions Scenarios?”), at which I was a panelist, there was extensive discussion of the most recent report of the Global Carbon Project (Canadell et al in PNAS, 2007) and the claim in that paper that emissions since 2000 have been rising faster than in any of the SRES scenarios. This work was post-Rahmstorf et al. The Garnaut Interim Report modifies the Canadell et al conclusion somewhat (see the last complete para. on p. 15) – I suspect as a result of my comments at the forum and subsequently – but Ross has retained his view that post-TAR developments, including the observed increase in global mean temperatures, have strengthened the case for urgent action.
The statement I quoted on this blog was made by Garnaut to ‘The Age’ before the Interim Report was released (but I agree that he may have been relying on Rahmstorf et al as interpreted by Graeme Pearman, and may not have known of the observed decline in global temperatures in recent months).
I agree with you that if anything the Garnaut Interim Report may be out of date on this point, because of the more recent observational evidence as interpreted in Lucia’s analysis. That is why I am keen to learn of the verdict of expert statisticians on that analysis, and on what it does (and doesn’t) mean. I hope that some experts make submissions to the Review on this important matter.
It’s also worth noting that Lucia’s conclusion has an unambiguous meaning. If I have correctly understood her analysis, she has shown that, using the Cochrane-Orcutt technique to correct for serial autocorrelation, the mean estimate of the rate of change of global temperatures between January 2001 and January 2008 which provides the best fit to the observations during that period, and using the average of the four series as published by the respective sources, is minus 1.1 C/century. One can debate the reasons for this result, whether or not the number of observations is sufficient, et cetera, but at least the conclusion has a clearly defined meaning.
By way of contrast, the statement in the WGI contribution to AR4 that “Six additional years of observations since the TAR (Chapter 3) show that temperatures are continuing to warm near the surface of the planet” (Chapter 9, p. 683) is ambiguous. The ordinary meaning of this sentence, as constructed, is that the observational record shows that temperatures CONTINUED to rise DURING the six additional years following the TAR. But it appears from the full context that the meaning that the lead authors had in mind was that during these six years the world was warmer on average than in various earlier periods such as the first 50 years of the instrumental record or the first decade of the twentieth century or some other period. This says nothing about the trend DURING the six-year period concerned. It’s surprising that the lead authors of a chapter in a scientific report, and the various government and expert reviewers, were satisfied with such a fuzzy statement.
Hmmm, my numbers don’t quite match yours. I hope you don’t mind a question or two to track down the discrepancies:
Using monthly data, I get the following global trends from Jan 2001 to Feb 2008:
GISS: +0.83 C/century
HadC: -0.55 C/century
RSS: +0.41 C/century
UAH: -0.07 C/century
AVERAGE: +0.16 C/century
However, when I compute the trends from Jan 2002 to Feb 2008 I get:
GISS: -0.29 C/century
HadC: -1.67 C/century
RSS: -0.91 C/century
UAH: -1.71 C/century
AVERAGE: -1.14 C/century
From your article I’m not sure if you intended to start in Jan 2001 or Jan 2002. I believe your previous articles stated that Jan 2001 would be the start date. But it looks like you may have started in Jan 2002. Is that correct?
It’s amazing the difference a single year can make. 🙂
…or maybe I’m way off base and Cochrane-Orcutt can actually change the slope by that much.
John,
I’ll post figures of the least squares and Cochrane-Orcutt today. I have been known to make mistakes in my life, but looking at my spread sheet, my calculations do start in 2001. Feb 2008 data aren’t fully in yet, so I don’t have Feb 2008 in the calculation.
JohnV,
Yes. I do think it’s important to start in 2001. Picking and choosing years gives the analyst free reign to pick whatever the heck they want and screws up the basis for stating confidence intervals. (When there isn’t much data, it also screws up the trend– but generally shifting them within the confidence intervals.
Here are thumbnails of the charts. You can click to see larger images.
As you can see, we do get different trends for different data.
I added the spreadsheet above so you can check my numbers. (I downloaded the data from Watt’s site– as noted in my earlier post. Obviously, if something got corrupted in between, that would cause problems. But, I do start from Jan 2001.)
On your observation of the choice of year: YES. Right now, switching by a year makes a difference in conclusions. So, when Feb and March data come in, it may turn out that, while this “falsifies” in terms of hypothesis test, the later data show it just happened to be the 2σ event. (These happen– 5% of the time!)
Nevertheless, as Roger pointed out, for something to be called science, it must be at least hypothetically possible to falsify. Otherwise, it’s pseudo-sciece. Clearly, the IPCC does make projections that are at least hypothetically falsifiable, and I think it’s important to show how one would falsify and demonstrate what happens.
lucia, thanks for the extra details.
I was exhausted when writing last night and hope it didn’t come across as adversarial. The negative trend caught my attention because I’ve never seen that before.
JohnV,
You didn’t come off as adversarial. The negative trend stunned me when I saw it too!
Anyway, you and I both discussed checking the correlation in the residuals in the past. So, I happen to know you are very interested in this, as am I.
In all honestly, I’d love you to check my numbers. I think the issue of “how much warming” is important. You should also note that this result doesn’t say AGW is falsified; the upper uncertainty intervals clearly do include 0C/century.
The result says 2 C/century lies outside the bounds. So, if it’s correct, it gives us information to bound estimates and also to gauge how well the IPCC project and/or draws estimates their own uncertainty interval.
FWIW….. I’m waiting for February to come in. I have GISS, RSS and MSU data; I’m waiting for Hadley. I notice the numbers announced by the various agencies are susceptible to change the first few weeks after they are announced. 🙂
Still, I’ll be posting as soon as Hadley is in. I do know, based on “fiddling” that the “uptick” on the normal Temperature vs. Time plot looks small. It’s bitter on the Cochrane-Orcutt chart, because that takes into account the issue of correlation. Still, the new number is not going to reverse the negative value. That requires a change in the weather.
I’m also trying to learn some other methods– ARMA etc.
I’ve been able to confirm that we were working on the same numbers. (A small step, but definitely important). I will try to find time to understand C-O so I can check the rest. Today does not look good though…
BTW, now that we’ve cleared up the coincidence of OLS trends from Jan2002 matching C-O trends from Jan2001 I’m pretty confident that your calculations are correct. The spreadsheet *looks* right.
JohnV,
I found NOAA numbers, and I’m adding that to the average.
Also, I need to learn the other techniques. I helpful anonumous tutor says I should look at various other methods too.
Lucia,
Could you post your graphics in a larger size? Some of us don’t have the resolving power to see the details.
BarryW–
I make them smaller to save bandwidth. (I guess I’m used to blogging about knitting where the majority of my visitors always had the slowest connections.)
The full size graphics are also in the spreadsheet. So, if you download that, you can open in Excel and see the graphic. The link is in the “update” section.
Oh— Also, the graphic in THIS post started out in the IPCC document. It’s already blown up compared to their document. I added lines so we could have some hope of reading it.
Unfortunately, the IPCC isn’t to good about providing the sorts of numbers that make it easy to falsify of validate easily. To do a full t-test, I would need to actually read the values at the top and bottom of their uncertainty intervals to estimate what they are saying the standard error in their prediction is.
oh… heh. I just realized, you may mean the thumbnails in the update. Click on those, they’ll open to new windows with larger images.
Hey JohnV,
Do you think we can agree on a common format for these monthly anomalies. Some of the GISS stuff I have is
in a table ( year by month). The RSS and UAH stuff is in a table of year/month vectors. I prefer the hadcru approach,
a vector… ALSO, I just found out that Openoffice supports R extensions in its spreadsheet. FWIW
What do you think? Your Opentemp would be a good place to host it, being Open and all.
Something Like
Year Month UAH RSS GISS NOAA HADCRU
1850 1 xx xx xx xx xx
….
2008 2 xx
Not sure how you want to code missing data for those records that only go back to 1979 or 1880.
Anyway it would give folks who want to load it into a spread sheet and play around a good resource.
Or Lucia could do it.
Also Lucia, I’m unclear why you mean by Averaging these difference temperature indices, since they measure different
things. Not saying its wrong, but just asking for clarity
stevemoscher–
It would be nice if these were all in similar formats. But, they aren’t. Still, I find as long as all I’m looking for is monthly anomaly data, I find it and getting it into the spreadsheet isn’t anywhere the time sink that learning new ways to process data is. (Of course, getting the real temperatures is not so easy. OTOH, it’s really easy to find the little on line lectures telling us we shouldn’t want it. And that if we think we want it, we should realize we shouldn’t want it. No…. it’s not what we should want. 🙂 )
As for archiving: I’m not an appropriate person to be an archivist. It doesn’t suit my personality. . . Take my word for this! I’d be wretched.
The fact is, these data also sometimes sift. UAH found an error earlier this year, SteveMcYntire found errors in the NASA processing which caused them to fix an error. Who ever the archivist is, they will need to keep track of this stuff, and communicate it. I’m just not the person to do it.
What I’m doing currently is getting the data from an archive, slapping it into my spreadsheet, and after doing the analysis, uploading the current version of the spreadsheet to my wordpress logs. That way, if I screw up, at least precisely what I used is traceable. (I wasn’t even in this habit back in January. . .) I’m trying to remember to state where I got the data in the blog post when I report the data. But really, that’s about all.
For those wondering, I hunted down the NOAA monthly values and added them to my analysis. The 95% confidence bands for the trend, with NOAA added to GISS (Land/Ocean), Hadcrut, UAH and RSS are:
-3.0 C/century < m < 1.1 C/century. The best estimate based on this data is -0.9C/ century. So, NOAA to the average, the IPCC projections are inconsistent with this data.
Lucia,
Dont sell yourself short. you are the pefect person to do this work for the rest of us. and we would
all be ever so grateful…
Aint working huh? rats
How are you averaging? NOAA, GISS and HADcru are not independent measures, and UAH RSS measure something else..
Is there any connection between IPCC and Oil For Food?
The efforts appear to operate with remarkable similarity. Is it the same folks?
TIA
steven mosher,
Anthony Watts has done that at least back to 1979, see his very useful file 4metrics_temp_anomalies.txt which is in almost exactly the format you suggest. Let’s hope he or somebody else keeps it up to date as the new data comes in. Of course you are right that just averaging GISS HADCRU UAH RSS is a bit crude, but I think that’s what Lucia is doing and it seems as good as anything else.
Lucia,
I’m afraid I have doubts that these numbers are significant. If we just look at the simple least-squares trend I get -0.11 C / century from Jan 2001 – Jan 2008 (which I think agrees with the b in your spreadsheet). But if I start in Feb 2001, I get -0.28, and starting in March 2001 gives -.40. So the trends are all over the place, if you change your start by just one data point. But they are all less than +2 C/century, so maybe your conclusion still holds. Expert statistician needed – have you asked Briggs?
PaulM-
The error bands stated in the blog post are:
-3.3 C/century < m < + 1.1 C/century
The values you give (-1.1 C/century, -0.28 C/century and -0.4 C/century) all fall in the stated uncertainty intervals which were calculated using this method.
I think what you are seeing is precisely what those calculated uncertainty bands mean: We expect the value of “m” to vary “all over the place”– but within [-3.3 C/century, 1.1 C/century] based on this specific data.
So, yes, if what I’m claiming is true, I’d expect the various different choices to result in precisely the sort of scatter you are finding.
We could ask Briggs. He knows more than I do about this stuff. But, no, I haven’t asked him.
Chillguy33, yeah. They are both run by the UN.
Not surprised the Garnaut report is out of date already. It was never going to contadict from Stern.
If Garnaut was relying on an interpretaion by Graeme Pearman it would certainly be one of “dangerous warming”, of which Graeme has been an advocate for many years.
Ah well, it’s only taxpayer’s money.
At least the new PM has said it’s one of many inputs to climate policy. Hopefully the issues raised here will also also be considered before $zillions are committed to little or no effect.
Some of you may be interested in gustofhotair.blogspot.com which does statistical stuff with local data
Thanks Roger. I need to make clear that my comment about Garnaut relying on an interpretation of Pearman was based on the following statement by the Garnaut Review itself:
‘This section draws largely on the research of the Intergovernmental Panel on Climate Change (IPCC) as interpreted and presented by Dr. Graeme Pearman’ ( Issues Paper 3, p. 2. The section is headed “The Global Impacrs of Climate Change”).
Ian and Roger–
I plan to check that particular issue when I have time. It seems to me that there is lots of rhetoric on both sides, often not supported by any number of analysis. (Certainly, politicians rarely give citations when interviewed. I don’t actually expect them to do so.)
One of the difficulties is tracing down precisely what was ‘predicted’ in some of these documents. I’ve quickly examined the TAR, and didn’t find projections stated quite as clearly as in AR4. (I may find them yet, but so far… just not quite a clear.)
Some of the earlier documents are “unfalsifiable” in the scientific sense because they only predict things one could never even hope compare against empirical data.
For example, there is no really good empirical data to compare predictions of steady state climate sensitivity as a function of doubling of CO2. Schwartz (2007) gave it a good shot looking at post 1880. Hansen gave it a shot looking at glacial vs. interglacial. But to get really good data, we need to double the C02 and let the planet sit there for a while. Obviously, this experiment can’t be done! All we have for that is models.
Lucia, I think that you’ll find the TAR ‘predictions’ you’re looking for, decade by decade, in Appendix II (“SRES Tables”) of the contribution of Working Group I (“Climate Change 2001: The Scientific Basis”). These Tables show that, since 2000, emissions have increased more rapidly than in most of the SRES scenarios. This leads in turn to a faster-than-projected rise in atmospheric concentrations, in forcings and in the model average surface temperature (see Table II.4).
One way of looking at this is to imagine that, when representatives of the world’s governments met in Shanghai to approve the WGI TAR in January 2001, they were so seized with the urgency of the climate change emergency that they agreed to implement drastic immediate reductions in emissions of greenhouse gases. What would the consequence have been?
As the SPM of the WGI contribution to AR$ explains, “Even if the concentrations of all greenhouse gases and aerosols had been kept constant at year 2000 levels, a further warming of about 0.1 C per decade would be expected’ (p. 18, second sentence of emphasised paragraph).
If this had happened, the slashing of emissions would by now be being hailed as a great success. According to your analysis, the UPPER LIMIT of the increase in temperature since January 2001 has been at the rate of about 1.0 C/century – i.e. 0.1 C per decade. But this has been achieved in the face of an ACCELERATION of the growth of emissions, not a drastic reduction!
I think you’ve misunderstood the IPCCs pic. It doesn’t include natural variability uncertainty: http://scienceblogs.com/stoat/2008/03/all_quiet_on_the_climate_front.php
William,
My analysis assumes their error bars don’t include natural variability.
Lucia,
What has to happen in 2008 for the IPCC to get back on track?
what has to happen in 2009? in 2010?. there is clearly an envelope of futures
that puts the IPPC back in line with their projections. How probable is that?
I think I have a way of looking at this…empirically. lazy saturday
SteveM,
Interesting questions. It would take some fiddling to do active speculating! Maybe monday. But I may address the issue both William and Boris brought up: Weather noise, and how that relates to this. I think that may be more important than trying to figure out what hypothetical weather needs to happen to get IPCC back on track in by the end of the decade.
Lucia, I looked at the weather noise in a rather odd stupid way. I made every possible 30 year time series
from GISS 1880-2007 (t1-t30,t2-t31, etc etc ) I figure every 30 year sequence has got some climate trend
and some weather noise. Then I made a big spaggetti graph, grafting every 30 year sequence onto 2001.
A huge spread in data. ennormous variability over a 30 year span ( using an observationalist perspective)
Take away. The IPCC projections are based on GCM. GCM underpredict the variability of weather on short time
scales, and have not been tested on longer time scales.
Lucia, Steven,
Here is a model output that specifically includes ‘weather noise’:
http://en.wikipedia.org/wiki/Image:Climate_Change_Attribution.png
From the link:
This is from a Meehl et al., 2004 paper which is referenced numerous times in AR4. This should allow you quantify the weather noise built into the IPCC projections.
Raven,
If the bands are interpreted to include weather, then the IPCC did an even worse job at predicting the central tendency.
I will be discussing the weather vs. climate issue either on Monday or Tuesday. My hubby is mostly monopolozing the computer doing our taxes and our inlaws taxes today. And yesterday we were having a big get-together.
The weather/climate issue William discussed is a non-issues as the standard statistical techniques distinguish between year to year variability and trends. That’s actually the whole point of using this technique.
I have a few more questions:
1. If using the TAR estimates, why did you decide to use a graph from AR4? It’s not a big deal, but I am curious.
2. Where do you get the 2C century number for IPCC TAR’s projection? Does this number have error bars or a shaded area like the graph shown? If so, is it based on the ensemble mean? (The shaded area in the graph shown is based on the ensemble mean.)
3. Does the IPCC discuss “weather noise” in relation to their projection?
4. Does “during the first 3 decades after 2000” actually start in 2001? I assume so, but there’s a bit of ambiguity there.
Lucia,
“The weather/climate issue William discussed is a non-issues”
His point re your (mis)interpretation of the shaded area is an issue. The shaded area in the graph represents uncertainty in the climate sensitivity of the models. You are interpreting them as a confidence interval around the projected trend itself, but they aren’t and they don’t purport to be that. If I have understood correctly, they represent confidence about the model prediction, not in the model prediction. If I’m right then you would need to include this further uncertainty in order to compare like to like. And if you did, it seems plausible that the top of your error range would overlap the bottom of the IPCC range.
“IPCC projections
overpredictoverlap recent warming” is not such a snappy headline but you could still in principle falsify the projections with more data, and it would still be an interesting exercise. However I don’t know how you would go about quantifying the additional uncertainty in the prediction.Boris,
I use the AR4 because that’s the most recent one. Also, the AR4 itself, though published in 2007, calls what they are doing projecting the climate after 2000. (As you can see, the graphic includes data through 2000.)
The reason for the lag is the projections were not done fresh during 2007 and were published ain a previous document. The AR4 itself includes a graph with the 2C/century number and reiterates it in text several places.
As far as I am aware, the IPCC does not specifically discuss weather noise, but if you know differently, let me know. My understanding of their document is they discuss climate, as that is the issue of interest. In a previous post, I discussed what weather, measured using annual average data is consistent with the climate trends they project. In this post, I discuss the climate trends that are consistent with the weather measured at monthly intervals that we actually experienced.
Yes, the 3 decades are the first three of this century, and as you can see on the graph, that is the trend for this century, not the last decade of 1900. The whole thing is encapsulated in the graphic. As you can see, the graphic includes data up to and including 2000; the projections are for climate that occurs after.
For what it’s worth, I picked the start date for analysis before I obtained the monthly data and before I learned how to do Cochrane-Orcut. And obviously, if the temperature trends turn up, the falsification won’t “stick”. But right now, that’s what the projected climate is insistent with the recent string of weather we actually experienced.
Frank:
William says this:
I agree with William natural variability (weather noise) is not included in the IPCC projection. I agree with him the error bars are not supposed to constraint the year-to-year variation.
I agree with William that if the uncertainty intervals included natural variability, the uncertainty intervals would be larger.
So, William is confirming what I believed when I did my analysis: The projections do not include natural variablity. My analysis assumed this.
My analysis is specifically designed to detect which underlying trends (climate) are consistent with the weather we actually experienced. This technique is used in calibration, quality control and all sorts of other areas. It’s taught to undergraduates in engineering and science curricula, though the most painful lessons are generally driven home when doing laboratory experiments.
It is not clear to me why William thinks this makes my analysis incorrect. However, I’ll elaborate more, since this seems to be an area some have difficulty with.
As for your comment, could you explain whatever you think is the difference in ” confidence about the model prediction” and “confidence in the model prediction”?
I can’t image what the difference might mean, quantitatively.
I’m also a bit bemused that William says “Its not absolutely clear what the error bars are to me,”.
If a climate scientist at RealClimate doesn’t know what those uncertainty intervals mean, what was the public supposed to take away from that graphic? (That said: The text of AR4 says what they mean. I know because I read it. They apply to uncertainties in predicting climate. 🙂 )
Lucia,
“As for your comment, could you explain whatever you think is the difference in †confidence about the model prediction†and “confidence in the model predictionâ€?”
William put it like this:
We have a family of curves going into the future, of the nature of dT=CO2*f*t, for various values of f, where t is time. IPCC is graphing that. Missing from that is the weather noise, which corresponds to the throw of the dice for each year
In other words, there is some uncertainty about what the models actually predict in the first place – or maybe this is better stated there is a range of curves that could be used for prediction, and it is uncertain as to which one is the best one to pick if you want to make a prediction. It is this range of different model climate sensitivities that the shaded area represents. The mean is chosen as being the prediction likely to be closest to obs, but (since the climate sensitivities aren’t certain) it could be that a more accurate prediction lies in the shaded area. If that’s correct then the 95% confidence interval (shaded area) you’re using is just about the climate sensitivies.
The problem is that nothing about the process described above says what the error in the prediction (the difference between prediction and obs) is likely to be. It is just the process for making the prediction in the first place. (My understanding of it, anyway. I could be wrong.)
In any case, if I am right, then your use of the central trend in the IPCC graph should still be OK but you’re using the wrong error bars around their predicted trend, because the error bars you need aren’t stated at all in that graph.
Frank-
My purple lines are the 95% confidence intervals for climate trends that would be compatible with the weather we have had.
The IPCC shaded areas are their range of projections for the possible climate trends compatible with the different climate sensitivity. Yes. That’s how I interpret them.
Their range of projections for climate trends are not compatible with the weather we have had.
The IPPC trends are not weather predictions– they are climate predictions. So, of course they don’t tells us how well they predict weather. They tell us what the underlying trend– as expected given a range of climate sensitivies– is supposed to be.
So, in other words I have interpreted them exactly as you say I should.
Lucia, the text from the figure you’ve used says:
So the IPCC is clear on what the shaded area means, but this graphic is not the most suitable for your comparison.
Also, since it is a mean, the internal variability should be, to a large extent, averaged out.
I don’t agree that the IPCC made any predictions in 2001. They had a bunch of scenarios, and the temperature rises associated with those scenarios. But none of the scenarios matches the trends in the various climate forcing agents. For example, all the scenarios have higher atmospheric methane concentrations than have been observed, and most or all had higher black carbon emissions than have (likely) occurred.
However, on the cooling side, the most scenarios overestimate the SO2 emissions that have (likely) occurred.
If I say that there’s going to be a thunderstorm if the high temperature tomorrow hits 90 deg F, and a foot of snow if the high temperature doesn’t get above 30 deg F, it’s not possible to say how accurate those “projections” were, if the high temperature is 70 deg F tomorrow.
Boris:
We are all in violent agreement that the IPCC projections shows means and does not include weather noise. This method is meant to test the validity of hypothesis that predict a the underlying trend– a mean.
If we start comparisons after the IPCC made it’s projections, their central tendency and standard error bands fall outside the 95% confidence intervals of climate trends that are consistent with the noisy data. So, the data include weather noise, the IPCC graphic doesn’t. And the technique is supposed to explain whether that noise-less graphic is consistent with the noisy data.
As far as I can tell, this is precisely the graphic or sort of graphic that is suitable for testing.
If you think there is a different graphic, suggest it. Then we can discuss it.
MarkB–
If you read the document, you will find that they working group found projections for all scenarios were similar for the first few decades. They diverge afterwards.
In any case, the issue of predicting a thunderstorm and testing with 1 days weather is irrelevant. The IPCC graphs was predicting climate trends, not weather. Also, the test method uses a collection of data and the method results in confidence intervals.
Okay, but you seem to make a big deal that the IPCC’s confidence interval falls outside of the 95% error bars for the trend you calculated (emphasis mine throughtout):
And again:
And in another post:
(emphasis mine throughout)
I don’t think such comparisons are warranted.
If the IPCC put error bars based on internal variability, then the two ranges would overlap.
No Boris. That would be an inappropriate comparison. The correct comparison is to compare the climate trends that are consistent with the weather to the IPCC climate trends with no internal variability. That’s the way this test is done. By definition, climate trends do not include internal varibiability aka “climate noise”. So, the full confidence intervals for climate trends does not contain the additional variablity due to noise by definition.
There is also a specific test to compare two sets of weather data fit the same climate trend. But, in that case, we need two sets of weather data. By definition, the IPCC does not create weather data, the predict climate trends.
Lucia,
“The IPCC shaded areas are their range of projections for the possible climate trends compatible with the different climate sensitivity. Yes. That’s how I interpret them.”
But you also interpret them as an uncertainty range on their projection. But on short timescales, they clearly are not that. They can’t be. Do this:
Take a piece of paper and hide the graph prior to 2001. Take another piece of paper and slide it from the right until you are only including a single month or a single year’s worth of projections. Now, look at that. Does what you are looking at seem to you like the error bars that anyone in their right mind would put on an estimate of the central trend of one month’s or one year’s weather? Yet that is how you are using them – on longer timescales certainly, but still short enough to be a problem. I don’t think that sliding the paper out to 2008 makes that problem go away, though if you slide it out far enough then it should become insignificant.
Nor do I think the error bars in your analysis compensate for this. For example, please don’t tell me that if you did the analysis for one month or a year, *your* error bars would become so wide as to include the narrow bars between the pieces of paper – i.e. no harm, no foul. I am sure they would. The point I am making is that the IPCC error bars are in fact not present and these narrow bars are for a different thing, so your comparison (of the uncertainty ranges only) is not like for like in the first place.
“My purple lines are the 95% confidence intervals for climate trends that would be compatible with the weather we have had.”
Well, that’s another thing. The data you are measuring includes not just noise but the effects of physical phenomena that we know something about. Does your analysis assume that internal variability is uniformly distributed? If so then don’t we already know this assumption is wrong on these timescales? We know for example that summer is warmer than winter, and I think your data includes a little more winter data than summer data (one more winters than summers). We also know that a La Nina is recently cooling the data and hence the short-term trend (an effect that shouldn’t alter the long term trend). We could expect that both of these will bias your observed trend downward. We can also expect that had the IPCC really been attempting to provide error bars for the short term, they would have been wider to allow for these effects (which are well known and no surprise to anybody).
Frank,
Lucia may need to correct me but my understanding is Lucia is looking at the observed data and working backwards and figuring out what underlying linear trends are plausible given the actual data. This means she only really cares about it is the uncertainty in the underlying linear trends predicted by the models. Adding ‘weather error bars’ to the IPCC plot does not change anything when dealing with trends rather than an individual temperature measurement.
That said, Atmoz has a post where he superimposes a cyclic ENSO effect onto the IPCC trend and illustrates that a linear trend + large cyclic ENSO is consistent with the observed data. This is a reasonable premise, however, he is also implying that the simple linear model presented in the IPCC reports is wrong because it did not include a large cyclic ENSO effect. You cannot argue that a large cyclic ENSO effect is the same as ‘random weather noise’ because it is not random.
You argument wrt seasons is a red herring – all of these discussions are based on monthly anomolies which removes daily and seasonal variations from the picture.
A Compilation of the Arguments that Irrefutably Prove that Climate Change is driven by Solar Activity and not by CO2 Emission
Dr. Gerhard Löbert, Otterweg 48, 85598 Baldham, Germany. March 6, 2008.
Physicist. Recipient of The Needle of Honor of German Aeronautics.
Program Manager “CCV, F 104G” (see Internet).
Program Manager “Lampyridae, MRMF” (see Internet)
Conveyor of a super-Einsteinian theory of gravitation that explains, among many other post-Einstein-effects, the Sun-Earth-Connection and the true cause of the global climate changes.
I. Climatological facts
As the glaciological and tree ring evidence shows, climate change is a natural phenomenon that has occurred many times in the past, both with the magnitude as well as with the time rate of temperature change that have occurred in the recent decades. The following facts prove that the recent global warming is not man-made but is a natural phenomenon.
1. In the temperature trace of the past 10 000 years based on glaciological evidence, the recent decades have not displayed any anomalous behaviour. In two-thirds of these 10 000 years, the mean temperature was even higher than today. Shortly before the last ice age the temperature in Greenland even increased by 15 degrees C in only 20 years. All of this without any man-made CO2 emission!
2. There is no direct connection between CO2 emission and climate warming. This is shown by the fact that these two physical quantities have displayed an entirely different temporal behaviour in the past 150 years. Whereas the mean global temperature varied in a quasi-periodic manner, with a mean period of 70 years, the CO2 concentration has been increasing exponentially since the 1950’s. The sea level has been rising and the glaciers have been shortening practically linearly from 1850 onwards. Neither time trace showed any reaction to the sudden increase of hydrocarbon burning from the 1950’s onwards.
3. The hypothesis that the global warming of the past decades is man-made is based on the results of calculations with climate models in which the main influence on climate is not included. The most important climate driver (besides solar luminosity) comes from the interplay of solar activity, interplanetary magnetic field strength, cosmic radiation intensity, and cloud cover of the Earth atmosphere. As is shown in Section II, this phenomenon is generated by the action of galactic vacuum density waves on the core of the Sun.
4. The extremely close correlation between the changes in the mean global temperature and the small changes in the rotational velocity of the Earth in the past 150 years (see Fig. 2.2 of http://www.fao.org/DOCREP/005/Y2787E/y2787e03.htm), which has been ignored by the mainstream climatologists, leaves little room for a human influence on climate. This close correlation results from the action of galactic vacuum density waves on the Sun and on the Earth (see Section II). Note that temperature lags rotation by 6 years.
5. From the steady decrease of the rotational velocity of the Earth that set in in Dec. 2003, it can reliably be concluded that the mean Earth temperature will decrease again in 2010 for the duration of three decades as it did from 1872 to 1913 and from 1942 to 1972.
6. The RSS AMSU satellite measurements show that the global temperature has not increased since 2001 despite the enormous worldwide CO2 emissions. Since 2006 it has been decreasing again.
II. Physical explanation for the strong correlation between fluctuations of the rotational velocity and changes of the mean surface temperature of the Earth
Despite its great successes, the gravitational theory of the great physicist Albert Einstein, General Relativity, (which is of a purely geometric nature and is totally incompatible with the highly successful quantum theory) must be discarded because this theory is completely irreconcilable with the extremely large energy density of the vacuum that has been accurately measured in the Casimir experiment.
Seaon Theory, a new theory of gravitation based on quantum mechanics that was developed eight decades after General Relativity, not only covers the well-known Einstein-effects but also shows up half a dozen post-Einstein effects that occur in nature. From a humanitarian standpoint, the most important super-Einsteinian physical phenomenon is the generation of small-amplitude longitudinal gravitational waves by the motion of the supermassive bodies located at the center of our galaxy, their transmission throughout the Galaxy, and the action of these waves on the Sun, the Earth and the other celestial bodies through which they pass. These vacuum density waves, which carry with them small changes in the electromagnetic properties of the vacuum, occur in an extremely large period range from minutes to millennia.
On the Sun, these vacuum waves modulate the intensity of the thermonuclear energy conversion process within the core, and this has its effect on all physical quantities of the Sun (this is called solar activity). This in turn has its influences on the Earth and the other planets. In particular, the solar wind and the solar magnetic field strength are modulated which results in large changes in the intensity of the cosmic radiation reaching the Earth. Cosmic rays produce condensation nuclei so that the cloud cover of the atmosphere and the Earth albedo also change.
On the Earth, the steady stream of vacuum density waves produces parts-per-billion changes in a large number of geophysical quantities. The most important quantities are the radius, circumference, rotational velocity, gravitational acceleration, VLBI baseline lengths, and axis orientation angles of the Earth, as well as the orbital elements of all low-earth-orbit satellites. All of these fluctuations have been measured.
Irrefutable evidence for the existence of this new, super-Einsteinian wave type is provided by the extremely close correlation between changes of the mean temperature and fluctuations of the mean rotational velocity of the Earth. (see the figure referred to in Section I.4). Einsteinian theory cannot explain this amazing correlation between two physical quantities that seem to be completely unrelated.
While the rotational velocity of the Earth and the thermonuclear energy conversion process on the Sun react simultaneously to the passage of a vacuum density wave, a time span of 6 years is needed for the energy to be transported from the core of the Sun to the Earth’s atmosphere and for the latter’s reaction time.
As can be seen, super-Einsteinian gravitation reveals the true cause of climate change.
Raven,
“You argument wrt seasons is a red herring – all of these discussions are based on monthly anomolies which removes daily and seasonal variations from the picture.”
Right you are. (I was just about to post to retract that anyway, I forgot these were anomalies – that’s what I get for writing on the train.)
However I think that the point about ENSO is still valid on these time scales (especially as we actually know it’s been operating in these timescales).
You are correctly describing a procedure to estimate the error bars on the weather. I am using a statistical technique that tests the the uncertainty intervals for the climate.
Yes. In the limit of only less than 3 months data, my uncertainty intervals become infinite. With 3 months data, they are very, very, very wide. That’s the way the uncertainty bars for the trend work. This is because they are determined using a formula that contains the (N-2) in the denominator, with N = the number of data points in the fit.
In contrast, had the IPCC provided uncertainty intervals for the weather noise (which they did not) the uncertainty intervals for the weather noise remain more or less constant at all time intervals.
The anomaly are defined to deal with the summer/winter variablity. January is normalized to January etc. That’s what I understood when I read the literature and because I wanted to confirm it when trying another analysis, I actually emailed both Hansen and Kennedy about the monthly anomoly issue.
Honestly Frank, you are just trying to throw things out there.
1. Since you’ve chosen a graphic that shows only 1 SD, I’d say you don’t even have the full error bars for climate trends shown.
2. I realize how you are doing the test, but it’s an apples to oranges test and is pretty much meaningless. The climate trend is for 30 years for a reason–to eliminate weather noise.
3. Your comparison to IPCC error bars for the climate signal is misleading.
For instance, when you say the IPCC “overpredicts recent warming” how do you justify this given that the IPCC does not make a prediction for the recent warming? How can someone overpredict something they have not made a prediction for?
It must be frustrating not to be able to falsify the projections after several years, but that’s just the nature of climate.
Lucia,
“You are correctly describing a procedure to estimate the error bars on the weather. I am using a statistical technique that tests the the uncertainty intervals for the climate.”
No, I am describing how any projection of climate trend for such a short interval would look, because the climate trend would be drowned in the weather noise. Are you seriously suggesting that if you asked the IPCC, or anyone, for a projection of the data trend for just two months then slice of the graph I have just described (with those very narrow error bars) is what they would hand you?
If not then why do you think it is appropriate to compare to those error bars for any short timescale.
“Yes. In the limit of only less than 3 months data, my uncertainty intervals become infinite. With 3 months data, they are very, very, very wide.”
Exactly. And the uncertainty intervals of the IPCC projections for climate trend would look a lot wider on that timescale also, for precisely the same reason. The fact that they do not should tell you that they are not confidence intervals on the projected trend on short timescales.
“The anomaly are defined to deal with the summer/winter variablity”
Gack, yes I know, I already retracted that. Sorry about that. I realised that you were probably using anomalies after I’d posted, and indeed you are. Apologies for any confusion caused.
However I still think you may be neglecting components such as ENSO which on larger timescales don’t matter so much but in this case we can surmise are having an effect. It’s a bit like trying to test the hypothesis that a car will go faster when someone steps on the accelerator. No amount of stats technique will recover from failing to take account of the fact that we saw somebody step on the brakes.
Frank: If we assume a linear model applies, the underlying trend, and individual temperature data, related this way:
Ti= m ti + ei
“T” are the temperature, “m” is the underlying, aka climate, aka mean trend. the “ei” is the measurement noise. t is the temperature. The “i” subscripts denote a data triple. (Temperature, time, weather noise.)
The weather noise has a standard deviation– known as “weather noise”.
Based on any set of “Ti” and “ti” linear regression method estimates the true value of “m” and provides a best fit sample value for “m”. I get -1.1 C/century. That’s a “mean”. It doesnt not contain “weather noise”. If T had no weather noise, and was dictated only by climate and followed this trend, temperture would vary as show in by the solid purple line in my graph. That would be a “climate” prediction. It would not be a weather prediction.
Because this is statitics, based on a set of Ti and ti, I can also estimate the both the standard deviation in ei, associated with weather noise, (which we call se) and the standard error in the slope: sm.
The standard error in “m” the climate trend, sm tells us how close to the true “m” the best fit “m” is likely to be. Both the sm and se are provided by Linest, and t their meanings are explained in the “HELP” file in excel and undergraduate books on statistics.
sm have to do with climate. We obtain the confidence intervals for “m” from this. If we later wish to find uncertainties for individual temperature we look at ei.
If one wishes to test climate projections, one uses sm, and
The IPCC graphs contains “m” and “sm” type information only. It does not include “ei” data or “Ti” or “ti” data. That is: It does not contain any information about weather variability at all.
My uncertainty intervals test “m” information with “sm” type information. It is designed to test projections of “m” and sm tupe information, stripped of all weather noise.
You keep trying to explain that the IPPC chart doesn’t describe weather data. That’s right. It doesn’t. I have said repeatedly it doesn’t; I never thought it contained that data.
Had the IPCC chart included weather information (se) I would have had to subtract that out to do apply my hypothesis test.
As for ENSO: Enso introduced serial autocorrelation in the temperatures. This technique is designed to remove that from the estimate, and pump up the uncertainty intervals. Had I not corrected for the serial autocorrelation, my estimate on uncertainty in m (sm) would have been less htan 1/2 the value I used. It is because of Enso, that I corrected for serial autocorrelation.)
That this may be an outlier is true. Things that happen 5% ofthe time, do happen 5% of the time. If that is your point, we agree. This could be an outlier. If so, the falsification will reverse. But that doesn’t make this analysis wrong. It simply means that things that happen 5% of the time do happen, and it just so happened immediately after the IPCC made its projections.
There is really nothing I can do about coincidences. They happen.
Lucia,
“The IPCC graphs contains “m†and “sm†type information only.”
This is the key point I think. I say it doesn’t contain sm or even ‘sm-type’ information for your purposes, at least not yet. This is what I’ve been saying all along. And yes I’m talking about sm relative to the climate trend, as you are.
The proof, again, is if you look on some really short timescales, i.e. imagine the IPCC projection stopped in March 01 or Jan 02. If it really included sm type information, then sm would be much larger on those scales. (Not as wide as yours – for example never infinite as it would be constrained by physics – but wider than shown on the graph). Instead, eyeballing the graph, it looks like it starts out as small as 1/10 or even 1/100 of a degree. Does that mean that the IPCC is really saying that it or anyone else is able to project the climate trend in a few months or a year’s data to that accuracy – as in ‘what will the observed climate trend look like for the next few months’? No. Is the IPCC really betting that the 1 month or 1 year trend that you will see will be X + or – 0.01 degrees with a 95% CI? No. Nor is there any reason to take those error bars as representative of the IPCC’s CI around its projection on the ~7 years scale that you’re so far forced to use. They have simply not stated this CI.
Put it another way, forget about the IPCC graph. Look at your own analysis. You are trying to project the trend based on stats alone and look at the width of the error range that you have. What makes you think that anyone else trying to project the climate trend on the same timescale wouldn’t have similarly wide error bars? What makes you think that they can ignore the weather on this scale any more than you can? You’re both trying to project the same thing!
As Boris and I have pointed out, if you allowed the IPCC the same luxury of stating a real 95% CI with representative error bars for their projection, then your ranges would overlap.
“You keep trying to explain that the IPPC chart doesn’t describe weather data.”
No I’m saying that the confidence bars on that graph up there do not describe the 95% CI for the projection of the climate trend on short timescales. They could only do that on long timescales, i.e. in hindsight when the natural variability uncertainty has been averaged out.
Frank: You are still wrong.
My trends identify the trends consistent with a string of data colleted after the IPCC made their projections for “m”. Be cause I can only get 1 data point a month, my uncertainty intervals are infinite at time zero.
But the IPCC didn’t “project” using data starting after they made their projections. This specific limitation simply doesn’t apply to their uncertainty estimate.
The IPCC trends are supposedly, the result of processing ensembles of climate models of various sorts, looking at past data, and a variety of things. That means there is no reason their uncertainty in their projected “m” must be large at time =0. They
First: Are you suggesting the IPCC report can be read to imply that a trend of 0C/century fell within the “very likely limits”? Or some other trend?
Second: It’s impossible to discover the 95% confidence limits based on the IPCC document. Based on the curves appearance the intervals on the chart, the +1 sigma limit is larger than the -1sigma limit. Additional informaiotn is not provided. We know the distribution is not normal. So, it is not even possible to do as you suggest.
All we can do is test the limits they communicated to the public. If the wish to explain the fuller limits (possibly explaining that their projections really included the possibility of nearly indescernable warming) I suggest they clarify this.
If almost now warming is consistent with that document, I suspect policy makers would like to know this!
Third: For normally distributed randome variables intervals can overlap and still have their means. In fact, it happens all the time. I have a graph in my next post.
What I have shown is range of climate trends communicated to the public, falls outside the region supported by the data.
Lucia,
“First: Are you suggesting the IPCC report can be read to imply that a trend of 0C/century fell within the “very likely limitsâ€?”
Yes. Obviously so for the ultra short-term (a few months). How could it not? The observed trend could kick off in almost any direction. Any prediction on that scale would include almost any slope.
For the term of 7 years on your chart the CI might include 0C/century also. Certainly it seems likely that the CI for their slope would at least overlap your CI for your slope. How much they’d overlap is important but it is also not clear.
For the long term 0C/century is ruled out by their projection and the error bars on there would start to be appropriate to use.
“Second: It’s impossible to discover the 95% confidence limits based on the IPCC document.”
Probably true, but irrelevant. The fact you don’t have it doesn’t mean you don’t need it.
Frank– No. The fact that I don’t need it means I don’t need it.
The unalterable fact is: Their predictions and related uncertainty, as communicated to the public falls outside the support given by later data. The graph is their climate trend projections as published. If you think they blundered and should have created a different illustration, you’ll need to communicate that with them.
The trend in the weather could. And, if I computed a trend based on month 0 and month 1, the unceratinty in my estimate of the climate trends consistent with the estimate would be infinite. So, I would be unable to falsify the IPCC trend no matter what data I got. This is true even though the IPCC data for time zero appears to collapse to a point.
I’m hoping to have time to make a graphic to illustate it, but in the meant time, I’m afraid I’m not going to discuss this particular issue, because it’s clear we aren’t getting anywhere.
Hi Lucia-
You advise me, “If you read the document, you will find that they working group found projections for all scenarios were similar for the first few decades.”
I have read “the” document (the Fourth Assessment Report). In fact, I’ve read both documents. The document to which Ian Castles was referring was the Third Assessment Report, not the Fourth. This can be seen by the fact that Ian quoted Ross Garnaut as writing, “Recent rises in global temperatures [have been] at the upper end of what was predicted [by the IPCC] in 2001.″
Since the reference is to what was “predicted”(sic!) in 2001, it must be a reference to the Third Assessment Report, not the Fourth (i.e., not the one you’re referring to when you urge me to “read the document”).
I was merely pointing out that the Third Assessment Report made no predictions at all. Instead, they made pseudo-scientific projections. It you read any of the books of the “Limits to Growth” series, you’ll see the same type of pseudo-scientific nonsense masquerading as science.
As far as my analogy about thunderstorms or snowstorms, you misunderstood my point. (Perhaps I should have used something other than a weather forecast for my analogy. My apologies if the analogy created confusion, rather than providing explanation.)
My point was that the “predictions” (actually, “projections”) in the Third Assessment Report could be described as “conditional forecasts” (although “pseudoscientific rubbish” would be more accurate). A conditional forecast can only be falsified if the condition(s) upon which the forecast was made come to pass. If the conditions upon which the forecast was made do not come to pass, then the forecast can’t be shown to be wrong. To give an example unrelated to weather, suppose you were wearing blue near a bull pasture at 9 am last Sunday. And suppose I told you at 8:59 am that, if you were wearing red, the bull would charge you, because bulls always charge someone dressed in red on Sunday March 16, 2008 at 9:00 am. Well, you’d never know whether my conditional forecast was false, if you couldn’t get dressed in red by 9:00 am.
This problem, and another, occurs in coming-few-decades “prediction†of the Fourth Assessment Report. On page 7 of the Summary for Policymakers, the IPCC writes:
“For the next two decades a warming of about 0.2°C per decade is projected for a range of SRES emissions scenarios.â€
The first problem is that there is no definition of “about†in that sentence. If the exact level over the next 20 years is 0.1°C per decade, is that “about†0.2°C? What if the exact level of warming over the next two decades is 0.06°C per decade? Is that “about 0.2°C per decade�
There is also the problem that the temperature rise is projected “for a range of SRES emissions scenarios,†but does anyone know whether that “range of SRES scenarios†actually encloses the likely climate forcings over the next few decades? For example, as I’ve pointed out, the methane atmospheric concentrations in the IPCC TAR (and AR4) are likely higher than will actually occur in the next 20-30 years. Black carbon emission projections in the TAR were likely higher than will actually occur. (On the other hand, on the cooling side, projected SO2 emissions were also higher than will probably occur.)
So I appreciate what you’re trying to do, Lucia. But I think you’re dreaming if you think that a significant portion of the “climate change community†is going to accept that the IPCC “projections†were shown to be false…regardless of present or future data.
The whole point of what the IPCC has been doing for more than a decade has been to avoid making falsifiable predictions.
Mark
MarkB.
Ok. Sorry, I did think you were discussing the fourth report. Yes, if I understand, the fourth report is based on models run earlier and reported earler. The results of those models had been published, so they are “frozen”. It’s for that reason, the data stops long before 2007 when it was published.
I’ve looked through the TAR, and I did already comment that it’s difficult to dig up precise projections. I’ve been looking a bit, and I plan to post something at sometime, but the way blog discusion go. . . Well. . . 🙂
This is why I dredged up the graphic in the AR4. It at least shows some uncertainty intervals. I can’t find any discussions of their estimate of overall uncertainty using words.
I have no illusions about modifying the behavior of the IPCC. I like fiddling with numbers, I’m currently interested in this and I started a blog. I could have used my knitting blog, but I think my readers would have been bored. So, I started this one.
@JohnV
The mean of trends simply does not account for individual differences in their significance and error bars. Thus I suggest you redo your analysis.
I think Ian Castles has made an important point (at least in the Australian policy context). Our national enquiry into a response to ‘climate change’ is recommending drastic precautionary measures that are not proportionate to any threat that they have evaluated.
They claim both to be unable to do this evaluation and to accept (as I.C. points out) that the consensus trends are at the top end of an alarming range of forecasts. This is the worst way to make public policy: to adopt a dreadful (but at best contentious) threat uncritically as the justification for a dreadful (but certainly dreadful) attack on the well being of ordinary citizens.
I am not a statistician, and do not know what we should expect from the removal of autocorrelation errors. I note that Ian Castles, who is a statistician, does not endorse the conclusion, although he seems friendly toward it.
I am too. Lucia’s argument seems to plausibly fit the facts (of a halt and apparent fall in average global temperature anomalies). Could we have more responses from statisticians?
I am interested in what can be said with statistical validity about the entire record of IPCC projections, going back to the 1990 report. This would help address the objection: “7 years is too short,” no matter how valid the statistics. Certainly 20 years is sufficiently long to say something about the record of model projections, especially since they are the basis for end of century predictions and policy proposals based on them. So I did a rough calculation for all four IPCC report projections. Each calculation was similar to Lucia’s for the 2001 case. Differences were (1) I used only HadCRUT3 data, not the average of four data sets; (2) I treated month-to-month correlations per Lucia, assuming her 2001-2008 value (0.78) of the 1-month autocorrelation coefficient for residuals for all four epochs (one should really do it the way she did); and (3)I added the recently released Hadley February 2008 datum. For the IPCC projections I used Roger Pielke Jr.’s entries in his January 18 blog post. The result is:
1. Projected 2. Regressed 3. Approx. 4. Standard 5. Statistic
Central Slope Degrees Deviation ( 1. – 2. )/4.
IPCC Tendency HadCRUT3 of of Slope 2.
Deg./Decade) (Deg/Decade) Freedom (Deg./Decade)
1990 0.315 0.20 53 0.035 3.2
1995 0.17 0.14 38 0.071 0.4
2001 0.20 – 0.16 20 0.105 3.4
2007 0.20 – 5.34 2 2.47 2.2
A few remarks:
1. The table results are essentially Lucia’s analysis for 2001 (but for Hadley only) extended to the other three IPCC projections.
2. Of the four attempts, 1995 does the best, in agreement with visual inspection. The other three lie outside the usual range of statistical uncertainty.
3. The 2001 numbers appear to be very close to Lucia’s values. They should differ slightly because I used only Hadley data vs. her average of four data sets, and I included February 2008.
4. One might be tempted to throw out 2007 because of the small number of DOFs, but that effect is included in the large standard deviation. And it so happens that the r2 for the trend is pretty good (0.76) and correlations for this epoch are small. In any case, as will be seen below, it does not make much difference.
Now the question is, what do these values mean for the class of models? Can one make a statement about the collective accuracy of the models projections over nearly 20 years of records? I take the 4 IPCC projections as independent attempts to project the historical temperature trend in different epochs. This is not strictly true since the four epochs overlap to varying degrees. I use the four values of the statistic in the fifth column of the table to define a best estimate for the mean value of the difference between models and historical actuals, in units of the standard deviation of the historical actuals. Those four values also allow an estimate the standard error of the mean for the four attempts. This gives a mean of 2.3 standard deviations above the set of historical trend lines, with a standard error of the mean of 0.60. Then the statistic for the group of four “measurements†is 2.3 / sqrt ( 1 + 0.6^2) = 2.0. By this reasoning, the class of four attempts by IPCC models to project future climate falls outside statistical uncertainty; p = 0.98 that they are too high. This number drops only slightly to 0.97 if you throw out 2007.
I’ll welcome any comments on the validity of this approach or suggestions for how to deal with the model class problem. Even better I’d be happy if the pros did it.
I am interested in what can be said with statistical validity about the entire record of IPCC projections, going back to the 1990 report. This would help address the objection: “7 years is too short,” no matter how valid the statistics. Certainly 20 years is sufficiently long to say something about the record of model projections, especially since they are the basis for end of century predictions and policy proposals based on them. So I did a rough calculation for all four IPCC report projections. Each calculation was similar to Lucia’s for the 2001 case. Differences were (1) I used only HadCRUT3 data, not the average of four data sets; (2) I treated month-to-month correlations per Lucia, assuming her 2001-2008 value (0.78) of the 1-month autocorrelation coefficient for residuals for all four epochs (one should really do it the way she did); and (3)I added the recently released Hadley February 2008 datum. For the IPCC projections I used Roger Pielke Jr.’s entries in his January 18 blog post. The result is:
1. Projected 2. Regressed 3. Approx. 4. Standard 5. Statistic
Central Slope Degrees Deviation ( 1. – 2. )/4.
IPCC Tendency HadCRUT3 of of Slope 2.
Deg./Decade) (Deg/Decade) Freedom (Deg./Decade)
1990 0.315 0.20 53 0.035 3.2
1995 0.17 0.14 38 0.071 0.4
2001 0.20 – 0.16 20 0.105 3.4
2007 0.20 – 5.34 2 2.47 2.2
A few remarks:
1. The table results are essentially Lucia’s analysis for 2001 (but for Hadley only) extended to the other three IPCC projections.
2. Of the four attempts, 1995 does the best, in agreement with visual inspection. The other three lie outside the usual range of statistical uncertainty.
3. The 2001 numbers appear to be very close to Lucia’s values. They should differ slightly because I used only Hadley data vs. her average of four data sets, and I included February 2008.
4. One might be tempted to throw out 2007 because of the small number of DOFs, but that effect is included in the large standard deviation. And it so happens that the r2 for the trend is pretty good (0.76) and correlations for this epoch are small. In any case, as will be seen below, it does not make much difference.
Now the question is, what do these values mean for the class of models? Can one make a statement about the collective accuracy of the models projections over nearly 20 years of records? I take the 4 IPCC projections as independent attempts to project the historical temperature trend in different epochs. This is not strictly true since the four epochs overlap to varying degrees. I use the four values of the statistic in the fifth column of the table to define a best estimate for the mean value of the difference between models and historical actuals, in units of the standard deviation of the historical actuals. Those four values also allow an estimate the standard error of the mean for the four attempts. This gives a mean of 2.3 standard deviations above the set of historical trend lines, with a standard error of the mean of 0.60. Then the statistic for the group of four “measurements†is 2.3 / sqrt ( 1 + 0.6^2) = 2.0. By this reasoning, the class of four attempts by IPCC models to project future climate falls outside statistical uncertainty; p = 0.98 that they are too high. This number drops only slightly to 0.97 if you throw out 2007.
I’ll welcome any comments on the validity of this approach or suggestions for how to deal with the model class problem. Even better I’d be happy if the pros did it. Am sending this to Roger Jr. and Matt Briggs.
The table in 1198 came through as gibberish, but you can recover correct numbers from each horizontal sequence as follows:
Year IPCC Report: e.g., 1990
1. Projected Central Tendency Slope(Deg/Decade): e.g., 0.315
2. Regressed Historical Slope (Deg/Dec): e.g., 0.20
3. Approx. Degrees of Freedom: e.g., 53
4. Standard Deviation of Regressed Slope (Deg/Dec):e.g., 0.035
5. Statistic ( 1 – 2 )/ 4: e.g., 3.2
Hi Lucia,
You write, “I’ve looked through the TAR, and I did already comment that it’s difficult to dig up precise projections.”
That’s putting mildly! I’ve asked a fairly large number of climate scientists to label these assertions as, “true,” “false,” or “don’t know” regarding the projections in the IPCC TAR:
1) The IPCC thinks that there is an approximately 50/50 chance that the warming will be less than 3.6 degrees Celsius.
2) The IPCC thinks that there is an approximately 50/50 chance that the warming will be less than 3.1 degrees Celsius.
3) The IPCC thinks that there is less than a 10 percent chance that the warming will be less than 1.4 degrees Celsius.
4) The IPCC thinks that there is less than a 10 percent chance that the warming will be more than 5.8 degrees Celsius.
5) The IPCC thinks that there is more than a 50/50 chance that the warming will be less than 1.4 degrees Celsius,
6) The IPCC thinks that there is more than a 50/50 chance that the warming will be more than 5.8 degrees Celsius.
7) The IPCC thinks that there is more than a 99 percent chance that the warming will be less than 1.4 degrees Celsius.
8) The IPCC thinks that there is more than a 99 percent chance that the warming will be more than 5.8 degrees Celsius.
Only John Nielsen-Gammon had the honesty to (correctly) label all the assertions as “don’t know.”
That is, a reader can read everything in the IPCC TAR, and still not know whether the IPCC thinks that there is more than a 99 percent chance that the warming will be LESS than 1.4 deg C, or a more than 99 percent chance that the warming will be MORE than 5.8 deg Celsius.
In other words, the “projections” in the IPCC TAR are completely invalid, as a matter of science. The make no falsifiable predictions.
And the AR4 is no different. The answer would still be “don’t know,” because the IPCC AR4 makes no assessment of the probability of occurrence of any of their scenarios.
I have also offered to debate any climate scientist, in any forum, this assertion: “The IPCC Third Assessment Report’s (TAR’s) projections for methane atmospheric concentrations, carbon dioxide emissions and atmospheric concentrations, and resultant temperature increases constitute the greatest fraud in the history of environmental science.”
None has ever done so, because they’d lose.
It seems to me that future trends are most likely influenced by the lack of sunspot activity. I’m constantly amazed that the variations in our heat source – the sun – seem to be ignored, as if it’s some never varying heat source. The fact is that it does vary. How much this influences us seems to be unknown. However, the correlation between sunspot activity and the Maunder period is hard to ignore. Current data certainly indicates the possibility that we could be entering a similar phase.
It is now Oct, 2008.
The global cooling trends that began last year (2007) in earnest have continued, and winter 2008-2009 promises to be even colder, wetter than 2007-2007. (Notably, Solar Cycle 24 has yet to appear – and the sun remains sunspot free for more days than any since 1911, 1913 periods … Also years of very cold intervals. Solar Cycle 23 is over, Solar cycle 25 (maybe (just maybe) ending around 2030-2040 has been long promised by NASA to be very, very low intensity.)
Long term?
Since 1935-1940 (pick 1938 for convenience) we have had 70 years of steadily increasing CO2 concentration at just over 1% per year.
We have had 30 years of decreasing temperatures of about 1/2 of one degree.
We have had 28 years of increasing temperature of 1/2 of one degree: from 1970 to 1998.
We have had nine years of steady, slightly declining temperatures – followed by now two years of rapidly declining temperatures that have lowered averages back to their late 1980’s peaks.
So, any AGW theorist needs to answer: Why is their theory of man-caused, CO2-induced global warming only valid for 1/3 of the time? Why – if it FAILS to predict 45 YEARS of declining temperatures out of 70 – is it considered valid? 1 month? Clearly too short – one month IS “weather” not “climate”.
One year, two or three years? Still too short. But ten years of declining temperatures IS a valid trend. We just don’t know whether that trend is -.1 degree, – 2 degree, or – 3 degree yet.
Solar-magnetic-cosmic ray interactions predict EVERY short term and long term climate change. But these are rejected because the flat-earth societies are too busy eating cake as they grant each other grant money, igNobel Prizes for power point slide shows, and taxing us trillions of dollars.
It’s in the pipe! It’s in the pipe! Lookout!
Lucia,
You might like my post I just did which refutes the confidence intervals reported at tamino regarding the temp measurement trends.
Tamino made the point that the trend is not valid because of statistical uncertainty. I have demonstrated otherwise.
I didn’t know about your post. I got a somewhat different result by taking the difference between the three measurements RSS, GISS and UAH used at Tamino as the true uncertainty. (I believe this is a more accurate method) And I used the uncertainty of each value to demonstrate the 95 % confidence limit of the slope.
http://noconsensus.wordpress.com/2008/10/21/taminos-folly-temperatures-did-drop/
If you take the temperature trend to be the uncertainty including the short term but real temperature variations you get a much wider confidence interval. I am interested in what you think.
Jeff–
Unfortunately, subtracting one measurement from another doesn’t really give us an very good estimate of “noise”, no matter how we define it.
I don’t like the term “weather noise” but it’s endemic to blogs. But, subtracting doesn’t give that, as it is simply defined using some sort of set theory where we imagine a set of all possible weather conditions for some “earth”… blah… blah. The reason I say blah…blah…. is the precise definition for similar earths is rarely stated. Does Pinatubo erupt the same year on all these earths? Or are volcanic eruptoins random.
“Measurement uncertainty noise” is more specific. However, you can’t get that by subtracting either. The reason is the measurement groups draw from overlaping station measurements.
Over all, I think Tamino makes a poor case against Lomborg. However, he is correct to observe that you can’t prove the earth has entered a sustained cooling period based on the current 10 year record. But then, Lomborg doesn’t claim you we have.
Lucia,
I don’t make the point that the earth has entered anything sustained. The question from Tamino is, “how well do we know the trend?”. Several posts on my blog missed that point as well.
By subtracting the difference between three different measurements we can establish the “error” in the measurement accuracy – not precision. This is true because they are different methods. It is quite simple and different from the thinking — how well can we predict future trends or is this a long term trend.
The mistake in Taminos blog and others is using the SD of a single measurement to establish trend. I would like to invite you to come back in about 12 hours to my blog because I will use the full and (incorrect) Weather error to make exactly the same point. I planned to do it today anyway but I really thought people would figure this out on their own.
1- We do know the trend to a very high degree of certainty.
2- We also know the trend is slightly downward.
3- It doesn’t mean anything beyond that
j–
What you are saying about the measurement uncertainty would be valid if the measurements weren’t correlated. Unfortunately, the measurement uncertainty in GISS and HadCrut are correlated because all they do is process the same measurements differently. (Or, at least, they use many of the same measurements.)
I’ve looked at those differences too. I think it’s interesting to examine them, but unfortunately, you are likely to under-estimate the measurement uncertainty in that way. Though, who knows? Maybe the uncertainty associated with the algorithms used to calculate GMST from the measurements dominates the basic measurement uncertainties!
If you are saying that once can say the OLS trend from year N to year M is X, yes. You can. I think you’ll even get Briggs on your side on that one. You can certainly say the temperature on day A is greater or less than on day B without doing a any statistical analysis at all.
It’s only when you start comparing to predictions, projections, models, history etc. that you might want to use statistics to state categorically that models are or are not inconsistent with data.
My quibble with Tamino’s post is that he seems to be rebutting a strawman. To rebut what Lomborg actually says, Tamino needs to show the warming this century is worse than projected and that the amount by which it is worse is statistically significant. As far as I can tell, Tamino doesn’t even try to do that.
I agree about the measurements having some obvious correlation between GISS and HadCRUT because they start with some of the same data. I was refuting Tamino so I was forced to use his data.
Did you notice though that I took the independent RSS – UAH as the worst case in my post? I basically ignored the best fit GISS – UAH
We have 340 or so values by which we can check the SD of the measurement. I would say that because both SD are included we would be looking at a square root of the sum of the square of the SD of GISS and RSS leading to an ‘over estimation’ of the true error in my post.
Still, I appreciate your understanding of my point, it was missed by many people.
What I will show later today is that even with the full variation of temp included we know the slope is basically negative.
Regarding your last paragraph, Tamino just went after a decade temp trend and gave some bad math to prove it. I actually 100% agree with his previous post where he arma models temp trends and shows the ten year cycle doesn’t end the possibility that temps keep rising. Even though his linear model in that post pre-concludes his result.
Thanks.
J–
You can’t preclude a positive trend this century using AR(1) either. The ARMA(1,1) is required to bring the IPCC projections of about 2C/century into the 95% confidence intervals of observations. Even then, this just barely workds– unless you insist on padding the “noise” by estimating the parameters during a period with major volcanic eruptions and applying that uncertainty to the later period.
Lucia,
I was just pointing out that the trend in Tamino’s ARMA example was pre-concluded. It is on a different Tamino post. He could have achieved the same results with a different pre concluded trend i.e temp starts dropping long term.
On entirely different subject from my post, I still believe that the 95% confidence intervals using ARMA are overstated by using short term variation rather than temp uncertainty. We know the temp better than the variation demonstrates. I do understand the reasoning behind the methods.
Unfortunately for me, my position on this mirrors the problem which some people had with my recent post – a post which did not address this issue in any way whatsoever.