Every now and again, its nice to be reminded that no matter how irritating the overenthusiasm of the greenies can be on occaision, the real wackos are on the septic side. If you can't cope with the long words at [[Global Warming]] then you can always look at the pretty pictures. Or maybe you like numbers?. More probably, you like sticking your head in the sand.
I'm sorry, but this kind of nonsense is just tedious. The world is getting warmer. You can argue about just how fast, and there is certainly a lot of room to discuss how much of a problem this is and how best to deal with it, but try to avoid arguing with basic reality. If you're really naughty, you may end up on CNN.
[Update: lots of exciting fighting in the comments, but things are getting lost there. In particular, M offers us a bet, but its terms are obscure as is who its directed at. So I'm pulling it up here, and am interested in taking it up, if it can be clarified. As I understand it, M is offering If you think the naughties were normal, you should be quite willing to bet that the temperature over the next 5 years will average significantly above the average for 2002-2007. $1000 says it won't. But he hasn't defined "significant". I take it that is *isn't* prepare to bet $1000 that the 2008-12 average won't simply be higher than 2002-2007 (why is he using 6 year periods but talking about 5 year averages?). Assuming he isn't, I'm interested in the bet, provided we can agree a meaningful definition of "sig", and... we know who he is. You can't expect known people who can't run away to put up against an anon, who can cut-n-run.
More update: we negotiated over the terms of the bet, and came close, but only at the expense of taking the bet down to $100, which is trivia. At that level, we're only doing it for reputation, which is meaningless for an anon. So no bet -W]
-W]
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I have a 3 year old daughter. Her favorite response when told she can't have something is 'But I WANT it!!'.
I think I know who is coaching the Deniers in their arguments. I knew the laptop was a bad idea..
My head is clear. Tell me William, how do you conclude from the satellite temperature record that the earth is significantly warmer today than 30 years ago?
In case you are tempted to cheat, by "significantly" I mean that the increase is distinguishable from random fluctuations.
[It looks like reality is slowly creeping in. You've abandoned your original claim of no warming, well done. But now you don't know what you mean by significant. The std measure is the obvious: would a line, fit by least-squares, have a slope as large as it does by chance at a 95% level of chance?; by which measure the recent warming is indeed significant -W]
[BTW, I had a good chuckle at your numbers link: there's not a single error bar amongst those figures.]
You are clutching at straws. When someone speaks of "no warming" over a 30 year period, they obviously mean no significant warming. If you don't agree, then what did you mean by your similarly unqualified statement: "The world is getting warmer"? Should I interpret that as "The world is getting insignificantly warmer"? Apparently by your criteria for scientific debate I am entitled to do so.
Well, in this case you'd be using the wrong approach. But even allowing such a measure, I seriously doubt the slope on that UAH graph has only a 5% chance of being negative (unfortunately I don't have the raw data at my fingertips to confirm that).
But more generally, confidence intervals from a standard least squares fit assume an underlying model that is linear + normal iid - independent and identically distributed - errors. Temperature time series have way too much autocorrelation for such an error model to be valid, hence such a model will significantly underestimate the uncertainty in the trend.
I'm sure someone has done the appropriate analysis somewhere, but looking at this plot of residuals over the period 1970 to today (4th figure here: http://tamino.wordpress.com/2009/01/15/what-if/)
doesn't suggest much in the way of temporal autocorrelation. I don't think a statistical analysis would show any autocorrelation across two year periods, and I'm quite sure that if you used every third year and assumed independence, you'd still end up with P<0.5.
[You do need to take account of autocorrelation. Favoured method is to use dof_effective = dof * (1 - ac(0)) or something like that. I forget -W]
That is, "P less than 0.05" for the temperature regression, even if you used a two-tailed test (software didn't like a less-than sign, I guess).
"less-than sign" is the start of a tag - html no like.
Using every third year would make it equivalent to only a decade of data and very unlikely to be an only 5% chance of a negative slope.
How many times have you heard recently that a decade does not a trend make? Of course, that admonition is only heard in the down decades. The high priests of climate were strangely silent on the subject in the 90s.
Steve L, that tamino link has an extra parenthesis on the end. Now I unbroke it, the data discussed there is GISS which IMHO is less reliable than the satellite due to the more uniform sampling of the latter, and the lack of impact of human activities on same.
Thanks for fixing the link. I think it is very wrong --better than not even wrong, but still very wrong -- to say that one datum every three years over thirty years is equivalent to one datum every year over a decade, especially when people are arguing about an underlying trend with potential autocorrelation!
You are right. It's equivalent to 10 independent samples over 30 years which is not the same as 10 independent samples over a decade (30 years is more time to see the trend).
However, look at the UAH data: you're not going to get a significant positive trend whether you take 30 autocorrelated samples over 30 years or 10 (supposedly) independent ones, I suspect not even if you cheat and don't correct for the autocorrelation in the 30-sample.
Okay, I went and tried it with the data I could find:
http://climate.uah.edu/dec2006.htm
1979-2006 (28 observations): P less than 0.001, Rsq 0.40
1979-2006 (10 observations): P less than 0.01, Rsq 0.63
So, the first result is contrary to what you suggested. The second result is sensitive to what year you start.
If I take every third year starting one or two years later[1980-2004 & 1981-2005] I can only get nine observations with these data -- the 1980-2004 version is thrown by the 1998 El Nino (P is 0.16) while the 1981-2005 version is marginally significant 0.07. This range of results supports an argument against strong autocorrelation among years. These are two-tailed tests on the data set of your choice. We could argue about whether one-tailed tests are more appropriate or whether taking every second year for 14 observations is better, but I'd rather see someone do the analysis correctly. I see William has provided a hint.
The graph I linked to goes to the end of 2008. Things got a lot colder these past 2 years or so. But thanks for chasing down the dataset - the URL should have given you a clue as to where to find the latest: http://climate.uah.edu/dec2008.htm
I am going to do the analysis when I get a minute. (hint: if adding two years changes a significant result to an insignificant one, the analysis that suggests a significant result is likely incorrect).
Browsing UAH looking for data, I came across this:
Well well. Ain't that exactly what this "wacko septic" concluded was wrong with Hansen's paleo argument. Might be time for me to write a little paper.
I agree that a result that depends on a single data point doesn't permit robust interpretations. Feel free to jackknife the data. But you're a mathy guy -- now that you have the data, why don't you do the analysis correctly? Here are the results for the compromise method I suggested for the full period, 1979-2008, two tailed:
every year: P 0.0003, Rsq 0.38
79,82,85...06: P 0.0152, Rsq 0.54
80,83,86...07: P 0.0537, Rsq 0.39
81,84,87...08: P 0.0240, Rsq 0.49
What do I win?
GISTEMP, HadCRUT, and RSS all show trends of 0.16 degree per decade since 1979. UAH is the laggard at 0.13 degrees per decade. If the satellite data was as reliable as skeptics like to pretend, the results wouldn't differ to such a large degree from analysis to analysis (especially if you throw UW and UMD into the mix). But they do, so they aren't.
tamino's done all this several times, but most recently, the trend (via GISTEMP) since 1975 is 0.0164 +/- 0.0022 deg.C/yr if you take into account ENSO and volcanic influences and 0.0173 +/- 0.0042 deg.C/yr if you don't.
http://tamino.wordpress.com/2008/11/10/known-factors/
Hey Wacko, are you changing the subject? You're drawing support for your sanity from the statements of someone else who disagrees with you about whether the globe has warmed and who, in fact, is suggesting that the observed temperature increase is anthropogenic. And the person you're citing says that most of the warming has happened since 1998 -- I thought the world had supposedly cooled in the last 10 years.
Anyway, there's also very little water in the cold high atmosphere. Have you considered that? Have you considered that GCMs and other climate models predict the fastest warming in the northernmost third of the globe? Have you considered that the warming and its pattern support the theory?
Someone should mention the mistake-prone history of both the UAH data set and (on separate subjects) its authors. There.
Douglass et al did a similar study 4 years ago. They found 0.0077 K/yr, which deviates from climate orthodoxy and hence seems to be ignored.
As for the UAH data. Ignoring the obvious structure in the variance (ie, using a straight linear regression), I get warming of 0.013K/yr and yes, it is significant, using a one-sided F test (ie a test that the slope differs from zero in the positive direction).
Removing the effects of the structure is non-trivial. Steve L's suggestion of taking every 3rd value gives insignificant warming, again with a one-sided F test, but that's probably too tough a test.
More interesting is to note that if you end the series in 2001 or earlier, there is no significant warming trend.
Here's the last 7 year's temperature residuals:
20020.31
20030.27
20040.19
20050.34
20060.26
20070.28
20080.05
The difference from the average has fallen back to just 0.05K. If that persists, the trend will disappear again. Or to put it another way, the trend in the UAH satellite data from 1979-2008 is essentially due to one bubble from 2002-2007. Where I come from, that's not significant.
When I take every third year I get significance (see my comment at 5:35 PM), even with a two-tailed test. How come you get something so different?
Dunno. Here's my numbers:
1979 -0.07
1980 0.09
1981 0.05
1982 -0.15
1983 0.04
1984 -0.26
1985 -0.21
1986 -0.15
1987 0.11
1988 0.11
1989 -0.11
1990 0.07
1991 0.12
1992 0.02
1992 -0.19
1993 -0.15
1994 -0.01
1995 0.11
1997 0.05
1998 0.51
1999 0.04
2000 0.03
2001 0.2
2002 0.31
2003 0.27
2004 0.19
2005 0.34
2006 0.26
2007 0.28
2008 0.05
LINEST in excel (actually openoffice but it's the same thing) does the regression analysis. Taking every third year starting with 2008 and working backwards we have:
1981 0.05
1984 -0.26
1987 0.11
1990 0.07
1992 -0.19
1995 0.11
1999 0.04
2002 0.31
2005 0.34
2008 0.05
(which is pretty noisy - would not expect the trend to be significant).
Plug those into LINEST, and I get F=3.4, 8 DOF. Look those up in the F tables gives a minimum F of 5.318 for significance at 8 DOF.
oops - looks like there's a problem with the original data at http://climate.uah.edu/dec2008.htm: 1992 is repeated twice, but with different values, and there's no 1996. I just cut and pasted from the web page so probably a transcription error: one of those 92's should be 96's data. Since pinatubo blew in 91, I'd say the colder one is the real 92. That will affect things.
Not by much: full set is still significant + 0.013K/yr, although slightly smaller slope and slightly less significant. Second set is still insignificant with F=3.25 now.
mugwump,
Since you are apparently unaware, in 2005 the UAH analysis underwent the most significant of its numerous revisions. Here are three versions of UAH examining the same time period (to September 2001 which is the end of the oldest series that I have), with RSS in blue for reference (this too has been superceded with RSS 3.2)
http://cce.890m.com/uah-vs-self.jpg
You claim that there was no significant warming to 2001. The linear trends from January 1979 to December 2001 of the current RSS and UAH analyses are 0.10 and 0.14 degrees per decade for UAH and RSS respectively. GISTEMP, for comparison, was also 0.14 degrees per decade over the same time period.
If you want an example of wilful ignorance in the face of orthodoxy, look no further than people who cling to this demonstrably false notion that the satellites are "more reliable" than the surface record.
FYI, the raw data is here:
http://vortex.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt
http://www.remss.com/data/msu/monthly_time_series/RSS_Monthly_MSU_AMSU_…
And you might want to update your library:
http://pubs.giss.nasa.gov/docs/2008/2008_Lean_Rind.pdf
Okay, you're using excel. Fine. Which version? If the 2003 version, go to the tools drop down menu, select "data analysis" from the bottom of that menu, and then select "regression". It asks for the response variable first (anomaly) and then the X (year). An analysis will pop up in a new window. I get results somewhat different from what I presented before partly because of excel, probably, and also because I didn't catch 1992 at 0.02 actually being 1996. (By the way, if GISS or somebody had made an error like that, it seems to me there would have been a lot of noise made about it.)
every year: F 16.9, P 0.0003, Rsq 0.38
79,82,85...06: F 13.1, P 0.0069, Rsq 0.63
80,83,86...07: F 3.9, P 0.0845, Rsq 0.33
81,84,87...08: F 3.3, P 0.1089, Rsq 0.29
These are two-tailed probabilities. Almost 3 out of 3 significant if you use 1-tailed. Note, if I remember correctly, the 1-tailed F-test on the table is actually a two-tailed test wrt the data (testing whether the variance of the residuals to the line show significantly less variance than differences from the mean, regardless of whether the slope is positive or negative).
My numbers are the same, first and last. I didn't do the two middle ones because it really matters which year you end in, and seeing as we're trying to determine whether we're all gonna fry in the fires of hell, getting the latest data is important.
Specifically,
all data: F=16.869, 28 DOF
08,05,...,81: F=3.254, 8 DOF
The F-score from the 5%, 1-sided F-test table for one numerator degrees of freedom (DOF) and 8 denominator DOF is 5.318, which is a lot larger than 3.254, so the null hypothesis (no trend) is not rejected.
But like I said above, more interesting is looking at the prefixes of the series (here F is the actual F from fit, Fsig is the F required for a significant trend):
1979-1988: F=0.01 Fsig=5.32
1979-1997: F=0.58 Fsig=4.45
1979-1998: F=3.11 Fsig=4.41
1979-1999: F=3.13 Fsig=4.38
1979-2000: F=3.05 Fsig=4.35
1979-2001: F=4.44 Fsig=4.32 **
1979-2002: F=6.91 Fsig=4.30 **
1979-2003: F=9.29 Fsig=4.28 **
1979-2004: F=10.76 Fsig=4.26 **
1979-2005: F=14.26 Fsig=4.24 **
1979-2006: F=16.82 Fsig=4.22 **
1979-2007: F=19.79 Fsig=4.21 **
1979-2008: F=16.87 Fsig=4.20 **
So you can see, the trend only (barely) becomes significant in 2001. Now maybe, had Pinatubo not burped, the trend would have become significant earlier, but it is interesting that it is really just the "naughties" that are causing the trend. It also illustrates why "significance" is so hard to determine when the model is invalid. If this data really was generated by a linear model + iid gaussian noise, the near uniform sequence of temperature anomalies from 2001 to 2007 would be spectacularly unlikely.
Q: What if 2008 heralded a return to normality? How many years of zero anomaly will it take to wipe out the trend?
A: 8 more years (trend insignificant in 2016 if no more warming).
Nope, you have to divide the P-value you calculate by two because the 1-tailed F table provided is just to determine whether or not the line explains a significant amount of variation relative to the mean over the period (it's one tailed because you're dividing the variance of one approach versus the variance of the other, and you don't flip the approaches in the division). If, before you look do the analysis, you have a null hypothesis of: "there is no significant warming", then you have to examine only half of the probability space (the positive slope scenario) to do the appropriate 1-tailed test.
Regarding your comments about which data are important, not important, & cetera -- that is all a posteriori crap that invalidates the frequentist approach. It's cherry-picking.
William,
I have a comment that is stuck in moderation.
[Now unstuck -W]
Steve L, I don't follow.
Let's work it out another way. For 81-08, every third year:
slope = 0.0107
standard error = 0.0059
A two-sided 95% confidence interval for the slope is:
slope +/- standard error * t[8,0.025]
where t[8,0.025] is the t-statistic for 8 degrees of freedom and p=0.025. But our null hypothesis is that the slope is non-positive, so we don't care to bound the range on the positive side, so we want a 95% likely interval from â to some lower bound:
slope +â / -standard error * t[8,0.05]
t[8,0.05] = 1.86, so our lower bound on the slope is
0.0107 - 1.86 * 0.0059 = -0.00027
IE, there's a greater than 5% chance the trend is negative.
I made no claims about the relevant importance of data. I merely made an observation that without the naughties there's no trend, and that the shape of the temperature in the naughties is very unlikely for a linear model. To add to that observation, such behaviour is not unexpected for a complex dynamical system with multiple overlapping near-periodic oscialltions. When the various oscillators are in near phase, you expect prolonged periods of unusual behaviour.
cce, 1979-2000 (inclusive), UAH, t-test approach above, I get a 4.8% probability that the trend is negative. Accounting for autocorrelation, that's significant at the 5% level (there does seem to be a difference with my F numbers, but the conclusions are almost identical).
Interesting paper. Thanks for the pointer. Would be worthwhile applying it to the satellite data. At least they don't ignore the Douglass et al. paper I mentioned (although for some reason they do not refer to the most recent update), and in fact get similar value for the contribution of solar irradiance as does Douglass (hard to read from their figure 2, but it looks like 0.08 K/W/m2 compared to 0.1K/W/m2 for Douglass et al.).
The surface record is far more prone to manipulation. Would you accept data massaged by people who act like this?
[Senator Timothy Wirth describes preparations for James Hansen's 1988 global warming testimony]
Mugwump, don't obfuscate the facts and make nutty claims if you don't want someone calling you a wacko septic. First, for 1981-2008, you don't need to tell me that the error on the slope includes zero -- that's what dividing the P-value I provided suggests: P = 0.1089/2 = 0.0545 ... barely not significant at an alpha of 0.05 for a one-sided test. However, taking every third year starting in 1979 or 1980 gives you a statistically significant result. Focusing on only the version starting in 1981 is a cherry pick, given that your claim was about the last 30 years.
Second, you're talking about removing the 2000-2008 period and seeing what happens. You claim the recent years are highly irregular, but the residual plot does not support such a statement. You say removing the period eliminates the statistical significance -- but earlier, in justifying your cherry pick of starting in '81, you stated that including the most recent data was important.
Bollocks. You proposed the "every third year" approach, not me. If you want to end in 2008 - the most recent data and the first "normal" year in the naughties - you have to start in 1981.
Sure it does, as do the F scores I gave above. The fact that the F-scores shoot up in the naughties shows the naughties make the trend.
All the data are important. I am just saying the naughties were weird. If I had to bet, I'd say the next few years are unlikely to be as uniformly warm. Whereas, if you take the linear fit on face value, you'd predict it to be even warmer for the next few years.
cce, I would say it is exactly the opposite. Check out this latest post on Anthony Watt's blog: "GISS Divergence with satellite temperatures since the start of 2003"
Money Quote:
Admittedly, it's a very short period, but that's a huge divergence. The satellites ain't the problem.
"The surface record is far more prone to manipulation."
The facts say that the satellite record is far more prone to manipulation. But, again, skeptics are clearly not interested in facts.
If you would like to read an accurate account of Hansen's '88 testimony go here:
http://cce.890m.com/hansens-88-scenarios/
Yes, mugwump, I've seen that post. And like virtually everything posted on that site, it's grossly incompetent.
I will repeat once again that GISTEMP, HadCRUT, and RSS all show about 0.16 degrees per decade since January 1979. UAH shows about 0.13 over the same time period. So which series is divergent? Why GISTEMP of course! Certainly not UAH!
There are six year periods where the satellites warm faster than the surface temperature. There are periods where they cool faster. This is especially true when you look at the response to volcanic eruptions, the '98 El Nino, the '88/'89 La Nina, and the recent La Nina.
Maybe I should create a post talking about how warm the 1998 El Nino is in the satellite analyses, thus proving that they "exaggerate warming" compared to the very conservative GISTEMP?
If you would like to read the transcript in which Wirth made those remarkable revelations, go here [PBS]
Yeah, riiight. Most of the posts on Anthony's site are merely factual. Did you perhaps mean "grossly heretical"?
GISS, RSS, UAH: 1997--today
So why do the satellites read so much higher in 1998? (that plot does not support your other assertions).
mugwump,
I know Wirth said that. It's in my history that you apparently didn't read.
And no, I meant gross incompetence. The recent Goddard posts especially.
Which of my assertions does the plot from '97 to present not support?
You're seriously relying on articles by the likes of Watts and Goddard, mugsy? I'm afraid that marks your final descent into the sludge pit of trolling.
Since you haven't responded cce, my guess is the satellites read higher because they're measuring the temperature of a larger volume of the atmosphere. Just a guess. I shall investigate.
Better them than Mann. Check out the latest in the neverending hockeystick fiasco.
Watts also won 2008 best science blog. Realclimate was in the running - where did they place? Last? Second last? something like that. Sneering superiority is really working out for you guys, isn't it?
Tamino talks a bit about ways to compensate for autocorrelation here: http://tamino.wordpress.com/2008/03/22/autocorrelation/
Using Tamino's approach (as I understand it...), I tested mugwump's claim by downloading the UAH LT data and analyzing the annual average data (30 data points from 1979-2008).
(1) A linear fit to the UAH LT annual-mean data has a slope of +0.013, with a 95% CI of [+0.0064, +0.019].
(2) After removing that linear trend from the data, I calculated the correlation coefficient between (the residuals) and (the residuals shifted one year). This shows an AR(1) autocorrelation correlation of 0.075, assuming I'm understanding correctly. In other words, there's some, but not a lot, of autocorrelation in the annual data.
(3) To compensate for autocorrelation, I calculated a correction factor of (N-rho)*(N+rho) = 0.86. In other words, the original 29 degrees of freedom are actually equivalent to ~25 degrees of freedom for uncorrelated data.
(4) The original 95% confidence interval would then be sqrt(1/0.86) times as large. Thus, correcting for autocorrelation, we find the 95% CI for the 1979-2008 trend is [+0.0059, +0.019].
Conclusion: mugwump's claim that the UAH LT data show no significant warming since 1979 is clearly false, even after correcting for autocorrelation.
And, of course, as noted by others, all the other temperature data sets (RSS, UW, GISS, Hadley) show more warming than UAH.
a correction factor of (N-rho)*(N+rho)
Whoops, make that (1-rho)(1+rho) of course. The numbers are right, I just mistyped in the comment. Sorry.
Like I said above, it's the naughties that were weird. If you calculate the trend to 2001 (Dec 2000), it's not significant. The naughties bubbled up, and then back down again in 2008. If I had to bet, I'd say the next few years are likely to be well below the trend line.
What's your autocorrelation for 1979-2000 vs 2001-2007?
[As J said, this is dull. You're now down to removing warm years to try to make the trend insignificant. Give up; there are more interesting things to discuss -W]
Shorter mugwump: "There's no statistically significant warming trend, as long as you exclude the years when the warming trend becomes statistically significant."
Sorry, that's lame.
Over the past thirty years, temperature shows a rising trend with noise superimposed. It takes until ca. 2000 for the signal to rise two stdev above the noise level. That's a great demonstration of why (contra 90% of the posts at Anthony Watts's site) you shouldn't waste your time trying to overanalyze short-term trends in climate data.
What's your autocorrelation for 1979-2000 vs 2001-2007?
I have no idea, and I'm not interested in a game of cherry-picking to see who can fiddle around with small subsets of the data to score a point.
You made a claim; it was wrong. Now you're trying to weasel your way out of it.
Rubbish. For 21 of those 30 years there's almost no action at all. Things changed dramatically at the start of this century.
Why do you think temperature is linear + noise? It obviously has longer-term dependencies.
If you think the naughties were normal, you should be quite willing to bet that the temperature over the next 5 years will average significantly above the average for 2002-2007.
$1000 says it won't.
My original claim:
I should have been more explicit: there's way too much long-term dependence. Autocorrelation is just one form of dependence. Now, I don't doubt you'll consider them weasel words, but hey, I am willing to put my money where my mouth is.
"Bollocks"?! You talk about a 30-year trend. You pick one 28 year trend to represent that 30 years. I indicate that there are two other 28 year trends that represent the 30 years equally well. No, you reply, 2008 is the first "normal" year (according to some subjective criterion in your head), and the most recent, so we've got to include it. That would be like me trying to ignore the 1998 El Nino year. That's cherry-picking!
PS: I have no idea what your F-scores are supposed to indicate. The residuals are much more useful. There are too many moving parts in F scores, and besides it's unclear to me why you think it makes sense to discount the most recent third of the data when discussing the last 30 years.
PPS: Thanks to J for doing the corrected analysis. Looks like mugwump was wrong about the uncorrected 30 year trend and the corrected version. I suppose I'll have to work through it to understand it. It seems odd to me that you can look at only one lag step. Perhaps one gets a better evaluation of autocorrelation if one can look at shorter time steps; would monthly data be more helpful?
Dr. Kunihiko, Chancellor of Japan's Institute of Science and Technology said this: "CO2 emissions make absolutely no difference one way or the other ... every scientist knows this, but it doesn't pay to say so." Now why would a learned man say such a crazy thing?
[You are using "argument from authority". This is generally considered invalid; however, if you do believe it, you should apply it consistently, and therefore go to the highest authority, which is the IPCC report. So you lose -W]
This is where the looney left gets lost. Their mantra is atmospheric CO2 levels are escalating and this is unquestionably causing earth's temperature rise. But ask yourself -- if global temperatures are experiencing the biggest sustained drop in decades, while CO2 levels continue to rise -- how can it be true?
[We are not experiencing a sustained drop. 2008 was cooler than 2007, but that is just intereannual variablity. See http://en.wikipedia.org/wiki/File:Instrumental_Temperature_Record.png for example. From 1983, T dropped 0.2 degrees in 1984, 5 and 6. And then the trend continues upwards, as we know -W]
Ironically, in spite of being shown false, we must now pray for it. Because a massive study, just released by the Russian Government, contains overwhelming evidence that earth is on the verge of another Ice Age.
[You mean this twaddle: http://english.pravda.ru/science/earth/106922-0/ ? I don't see any "massive study". Perhaps you could point to the one you mean? -W]
Based on core samples from Russia's Vostok Station in Antarctica, we now know earth's atmosphere and temperature for the last 420,000 years. This evidence suggests that the 12,000 years of warmth we call the Holocene period is over.
Apparently, we're headed into an ice age of about 100,000 years -- give or take. As for CO2 levels, core samples show conclusively they follow the earth's temperature rise, not lead it.
[Sigh. This is just wrong. http://scienceblogs.com/islandofdoubt/2009/01/the_quick_and_dirty_on_th… says it fairly well, but in summary: we knew all this Milankovitch stuff before. There is nothing new. But interglacials don't last 10kyr always. And CO2 forcing outweights it anyway -W]
It turns out CO2 fluctuations follow the change in sea temperature. As water temperatures rise, oceans release additional dissolved CO2 -- like opening a warm brewsky.
[Did you notice that you didn't cite a single source for anything you said? -W]
No they don't - they end before the most recent data. But it doesn't really matter: the trends are either marginally significant or marginally insignificant - that's hardly a resounding confirmation of significance.
trent142, there's little doubt that rising CO2 levels cause warming, and that humans are contributing most of the increase in CO2. The real question is how much warming will the extra CO2 cause. Personally, I think there's precious little convincing evidence that we'll get anything much above that implied by a straightforward application of the StefanâBoltzmann Law
mugwump writes:
Did you even read what I wrote? I'm not interested in cherry-picking short-term subsets of the data and arguing over them. That's your schtick, not mine.
Out of curiosity, however, I did try assuming that the next five years' average was no higher than the 2002-2007 average. Forget about "significantly higher". Even with that assumption, your initial claim about "no significant warming post-1979" would still be wrong. In fact, the confidence intervals around the trend would actually be narrower than they are right now.
In other words, even if someone here took you up on your new "bet" and lost, your original claim could be even wronger than it is today.
If that was an effort to defend your original claim, it fails spectacularly.
mugwump writes:
Yeah? Well, "Argument from mugwump's gut-feeling" would be more convincing if you hadn't been proved wrong over and over again here, most notably in this very thread.
I'd recommend going with IPCC instead.
Umm, where have I been proven wrong in this or any other thread? If you assume the data is linear + iid noise you get a significant trend from 1979 to today, but the data is clearly not linear + iid noise so that "significance" is meaningless.
Playing Steve L's game of every third year shows no significant trend.
Trent142 writes: This is where the looney left gets lost.
He/she then proceeds to recycle a lot of nonsense from an article in Pravda.
Right-wingers citing Pravda approvingly! To disprove the claims of alleged "leftists", no less! For anyone who lived through the Cold War, the irony is amusing.
I don't doubt it. I already talked upthread about what has to happen over the next few years to eliminate the significant trend (under the false assumption of linear + iid noise).
In my bet I was talking about what you believe. I believe 2002-2007 was very unlikely under a linear trend + iid. You have stated that you don't, in which case, you believe:
A) that the linear trend to today is real, and
B) it will continue
and hence should be willing to take money from someone willing to bet against that.
mugwump writes:
I don't think you understand what "iid" means. The whole point of my analysis was that the data are not IID. Even after compensating for AR(1) autocorrelation, your claim was still wrong.
Steve's method (which he seems to have proposed just off-the-cuff) overestimates autocorrelation in the annual data. It implies that there's only 9-10 degrees of freedom in the annual data, which is clearly not correct.
That's funny. I have proved my fair share of theorems about iid processes (and non-iid ones too).
I don't think you understand what "not iid" means. It doesn't mean AR(1). There aren't just two types of time series in this world. There can be any kind of long-range dependence in the data.
Of course, if you make no assumptions about the process generating the data then you can draw no conclusions, so you have to stop somewhere. All I am saying is there appear to be long-range dependencies. Determining how they affect the trend analysis is difficult. I proposed one method (look at the likelihood scores). No-one seems to like that. So go on, humour me: do your auto-correlation analysis on 2001-2007 (inclusive). You'll see.
That said, I was wrong in my original claim, because I used the term autocorrelation when I should have used long-range dependence. But since we apparently can't have a useful debate about whether the naughties were unusual or not, all that's left is a bet. My $1000 offer is still on the table.
[Sorry, I've been letting you folks fight it out, I'd missed the money offer. As I understand it, you are offering If you think the naughties were normal, you should be quite willing to
bet that the temperature over the next 5 years will average
significantly above the average for 2002-2007. $1000 says it won't. But you haven't defined "significant". Do I take it that you *aren't* prepare to bet $1000 that the 2008-12 average won't simply be higher than 2002-2007 (why are you using 6 year periods but talking about 5 year averages?). Assuming you aren't, I'm interested in your bet, provided we can agree a meaningful definition of "sig", and... we know who you are. You can't expect known people who can't run away to put up against an anon, who can cut-n-run -W]
mugwump writes:
This is wrong in so many ways that it's hard to know where to start.
First off, I specifically assumed that the noise isn't IID. But that's beside the point.
Second, even if you assume a simple linear model with no autocorrelation, the expected value of the mean for 2009-2013 is 0.29, barely above the 2002-2007 mean of 0.28. In other words, even with no autocorrelation your "bet" would be essentially a 50-50 coin flip. I doubt many people would be interested in gambling $1000 on a coin toss.
Third ... well, all I can say is that you seem to have an obsession with cherry-picking short time spans that no amount of argument can break through. I'll put this as plainly as possible: We have 30 years of data. Those 30 years show an increasing trend, one which is statistically significant even after compensating for autocorrelation using an AR(1) model. That's really the beginning and ending of my argument. Further obfuscation or weaseling from you will probably be ignored.
J, the bet was directed at Steve L, However:
People do it on the roulette wheels all the time, and in that case the odds are stacked against them by as much as they are in your favour under my proposal. But if you want better odds, propose your own number.
So let me put it as plainly as possible. Statistical significance is fundamentally a function of how well your model reflects the truth. To see this, imagine that the underlying process is AR(1) as you claim, plus rare events in which the temperature increases (or decreases) for no readily apparent reason for a few years and then settles back. If you model the data since 1979 with such a model, the trend would not be significant.
Absent any other distinguishing features, my model is as good as yours. And my model has the virtue of "explaining" the naughties whereas yours does not.
Now, absent a physical explanation for the rare bumps, my model is a little ad hoc. But there are plenty of long-period physical processes in the Earth's climate that could be the culprit.
Steve L's off-the-cuff over-estimation of autocorrelation game/method finds one strongly significant result, one marginally significant result, and one marginally non-significant result. Somehow mugwump gets this:
"the trends are either marginally significant or marginally insignificant,"
but that then morphs to this:
"Playing Steve L's game of every third year shows no significant trend."
This seems dishonest. Wrong about, "When someone speaks of 'no warming' over a 30 year period, they obviously mean no significant warming." Wrong about, "even allowing such a measure, I seriously doubt the slope on that UAH graph has only a 5% chance of being negative". Wrong about, "Using every third year would make it equivalent to only a decade of data." Wrong in this repeated assertion, "you're not going to get a significant positive trend whether you take 30 autocorrelated samples over 30 years or 10 (supposedly) independent ones, I suspect not even if you cheat and don't correct for the autocorrelation in the 30-sample." Wrong about, "lack of impact of human activities on [UAH data]" And I only reviewed a small ways into the thread. You've been wrong several times! Now you're wrong in suggesting that you've not been wrong: "where have I been proven wrong in this or any other thread?" Being wrong is okay. Add dishonesty and I'm pretty much ready to ignore mugwump.
J, the bet was directed at Steve L
That's odd, you were responding to one of my comments and didn't mention Steve.
Absent any other distinguishing features, my model is as good as yours. And my model has the virtue of "explaining" the naughties whereas yours does not.
I don't believe you've actually defined a model for us, which makes it a bit hard to evaluate this.
But I still can't understand why you keep alleging that the post-2000 years don't fit in "my" model. 2004 is right on the trend line, 2001, 2006, and 2007 are just a hair above it, while 2008 is a bit below it. As far as I can tell, you're just handwaving.
Steve L, if you believe what you say, take the bet.
Things got interleaved - the original bet was towards Steve L. Anyway, it doesn't matter.
Well sure, once you've included those years the line will fit them. But that's cheating. If you calculate the best fit to 2001 (Dec 2000), and then compare that to the best fit up to end 2007, you see that things changed from no significant trend to a highly significant trend in a few short years. Every point from 2001 to 2007 lies well above the best fit you get using the data until end 2000. In other words, if you believed your linear regression in 2000, you would not have predicted what was about to happen.
I didn't know the bet was directed at me, either. And I didn't understand the bet. But, Mugwump, let me try to exaggerate a little bit to try and convey to you why some people might consider you a 'wacko septic'.
1. You've basically said, "It's not significantly warmer now than it was 30 years ago and if it is, then it's only because the years in the more recent third of the data have been so abnormally warm."
2. You've basically said, "In evaluating a 30 year trend, the last two of the 30 years are more valid to study than the first two years because the last year was cold -- and no, that's not cherry-picking."
3. You've basically said, "If you are concerned that I may be dishonest and worried that you're wasting your time with me, then you should make an incomprehensible $1000 bet with me."
4. You've basically said, "The data that I chose didn't support a prediction of warming for this new century, so the people who correctly predicted warming based on other data and a physical model were actually wrong -- they're a bunch of religious zealots who want to take away my freedom."
I've exaggerated a little because I wasn't getting through to you. Anyway, let's try the other way again for a minute:
If I waste my time some more and put the agreed UAH values into JMP or excel for 1979-2000, I get a P-value of 0.0479 (one-tailed). I'm generally a careful person (in contrast, it would seem, to you) so I'm unlikely to take you up on any bet. However, William has indicated an interest if you can spell out the details of the bet (see above in your 4:35 PM comment).
Cool! I missed this - was watching the inauguration.
Now, I am not made of money, and my wife might not be too pleased if I opened a book, so I'd be happy for one taker at US$1000. The original offer was to "Steve L" or "J", but since they haven't taken it up, you're it William.
6 year period and averages is fine. 2008-2013 vs 2002-2007. That puts it slightly more in your favour than 2008-2012 if your beliefs are correct.
As for significant, that's harder. We need to pick a dataset, and my strong preference is for UAH lower trop, global mean, 12 month anomalies (need to check what period the anomaly is measured against). I need to double check, but the values I have for 2002-2007 are:
20020.31
20030.27
20040.19
20050.34
20060.26
20070.28
mean: 0.275. std dev: 0.0509
Now, that standard deviation is artificially low compared to the entire 30 year series standard deviation of 0.181, so lets calculate it both ways. Critical t for 0.05 prob and 5 dof: 2.015. Critical t for 0.05 prob and 29 dof: 1.699.
So, with probability 95%, the mean for 2002-2007 is less than 0.275 + 2.015 * 0.0509 = 0.378, assuming std dev = 0.0509.
Assuming a std dev of 0.181, the mean for 2002-2007 is less than 0.275 + 1.699 * 0.181 = 0.583.
So, we have two candidates for 2008-2013 to be significantly warmer than 2002-2007: average anomaly above 0.378, or average anomaly above 0.583.
Obviously, I would be happiest betting against the latter.
Hmmm, I don't want to reveal my identity. There should be a way around that. Anonymous escrow?
[As a committed Deep Greenie, loyal to the Flag of IPCC, I of course believe in an increase of ~0.2-0.3 oC/decade. Lets say 0.3 for the moment, and ignore variability. So I think that 6 years on the average should increase by 0.3*6/10 = 0.18 oC. From a base of 0.275 oC (and ignoring for a moment my quibbles about UAH) that would mean 0.455 oC. So 0.583 oC is too high. I could just as easily have picked 0.2 oC/decade, which would have given me +0.12 oC in six years, which is 0.395 oC, so even your low offer of 0.378 oC isn't very attractive - that has about a 50% chance of occurring.
So it looks like we can stop worrying about escrow - your beliefs don't differ enough from IPCCs for an attractive bet -W]
The other option is to make the bet for a smaller amount, say US$100, and I will just mail you the money now. I feel comfortable mailing that little cash. Then, if you win (in 5 years time), you keep it. If not, you mail it back to an address I'll give you + another $100.
If you believe in 0.2-0.3 per decade (uniformly for the sake of argument although it doesn't matter much for this discussion what the shape of that belief is. provided it is symmetric), and you believe the naughties were normal, then you should believe that the middle of your range has 50% odds: 0.25 * 6 + 0.275 = 0.425C. So your statement that 0.395C has 50% odds is not consistent with your other stated beliefs.
Nevertheless, if you want to go the subjective route, I'll admit that even 0.378 seems pretty unlikely to me, so I'll accept a bet at half the lower end of your range, or 0.275 + 0.1 * 6 = 0.335C.
[Me getting the high side of 0.1 oC/decade is acceptable in principle. Now we have to argue over the details. First, I don't like UAH, and I don't expect their current series to be still going in 2013. They will have revised and rebased their algorithm by then, and the temps for 2002-7 will be revised (in my expectation, upwards). By contrast, I don't expect any substantial revision within the sfc records. Second, I don't want to keep your $100 for 6 years, I'd lose it or forget it; and $100 is too small a sum to bother tracking for that long -W]
That would be in your favour. But it does raise the issue of what to do if the records change. Why don't we just say that the 2008-2013 average anomaly has to be 0.06C higher than the 2002-2007 average anomaly, by, say, June 30 2014, as the data stand at that time (time for any revisions to 2013 to be made).
[It would only be in my favour if we used the old algorithm for 2002-7 and the new from 2008-13. But that would be silly. We'd have to use a consistent series for both periods. Your suggestion is the obvious one, but it does mean we have to bet (assuming my belief of likely change is true) on an unknown series -W]
I don't trust the surface records. I don't believe they are actively manipulated but there are plenty of ways for them to be passively manipulated. The latest observation from Anthony Watts is that GISS has been disproportionately losing stations in regions with cooling anomalies. Had they been warming stations you can bet the GISS folk would have been all over it.
[I don't trust UAH; and I don't trust Watts paranoia in the slightest -W]
Then spend it. I trust you to pay up if I win. The point of sending the $100 now is you don't trust anonymous me to pay up.
[But I have to remember that I owe you the money. Hopefully you'll be able to point me at this, so that would dispose of that problem. But the trivia problem arises: neither I nor you care about $100 over 6 years. We might as well forget the money. Which is unsatisfactory, as the money is suppose to focus our minds -W]
But we're both in the same boat so it's fair.
Watts opinion is irrelevant. The point is there are many more ways for surface records to be manipulated than there are for satellite records.
[Indeed, I certainly agree that Watts opinion is irrelevant. But your point is wrong. The actual point is that you choose to trust one version of the satellite record above all other records; I choose to mistrust that record above all others -W]
We have agreement on all but the dataset. Are you saying you would change what we've agreed so far if the money was greater?
If not, the amount of money is not important to the conditions of the bet. I've certainly devoted as much energy to quantifying my beliefs as I would have if there was $1000 on the table. I want to win. My intellectual pride is not inconsiderable. I doubt you are any different.
[You ought to realise that, whether or not the trend is present, winning or not involves the luck of interannual variation. You've shown yourself moderately flexible about the level; I want to check what I think is likely before I conside agreeing -W]
I can't exactly mail you $1,000 today. Even if it did make it to you, I will be wearing all the risk of non-payment. We also still have a significant point of disagreement over which dataset to use. UAH is fair given that this entire thread was about UAH - you dissed me after it was already known that I was talking about UAH.
[No... I dissed you for http://scienceblogs.com/stoat/2009/01/iron_fertilisation.php#comment-13… which is nothing to do with UAH. Or rather, its a statement referencing no particular record -W]
Some money is very different to no money. Take the bet as it stands. I'll mail you the $100. You can confirm here when you receive it.
Deal or no deal?
Great programme. Watch it every day (not).
Mugwump, I'm curious. Out of interest, if you set such store by your analysis, why not work it up into a paper and submit it to a journal for publication? Surely, that's what any reputable scientist would do, isn't it?
This little spat is not worth writing up. No-one would publish it, nor should they. But since you mention it, I am working on a more substantial piece at the moment. Slowly, since I have a day job and 5 kids, but it's coming along.
That my statement was based upon UAH I made clear shortly afterwards, here: http://scienceblogs.com/stoat/2009/01/iron_fertilisation.php#comment-13…
My bet proposal was made well after we had been discussing UAH for sometime. You never rescinded your "wacko septic" libel, so presumably you still consider my conclusions based on UAH to be indefensible,
[Yes. Of course I believe your original assertion that the world is not warming to be indefensible, even if you use UAH -W]
I don't believe I have ever made that claim. Here or anywhere else.
Saying that the data don't support significant warming in 30 years is not the same as asserting the world is not warming. I don't know if the world is currently warming.
[Sigh. The memory hole again. Who said "The world is no warmer than it was 30 years ago."? -W]
Sigh. Semantic games again. We already went through this. I obviously meant "The world is not significantly warmer than it was 30 years ago". If you don't believe me then, as above, I choose to interpret your claim that "the world is getting warmer" as "the world is getting insignificantly warmer" which would, among other things, make you a "septic" by your own definition.
[Errm yes, we already have been through this. Which is why I said memory hole. Why are you going through it again? -W]
Now, saying "The world is not significantly warmer than it was 30 years ago." is not the same as asserting that the world is not warming. It just means that if it is warming, it is doing it slowly enough for the warming to be indistinguishable from noise.
With all due respect, that's lame. What a waste of time.
It should be irrelevant to you what is meaningful for me. For all you know $1,000,000 could be a trivial sum to me, in which case any sized bet would only ever be about my reputation.
So, given that your stated reason for refusing the bet is clearly fabricated, I can only conclude that you do not believe at least one of:
1) the IPCC claims of 0.2C-0.3C per decade; or
2) that the temperature bubble in the naughties is significant.