Guest post by Dr. David Stockwell
I suspect that the only really convincing evidence against global warming is a sustained period of no global warming or cooling — climate sensitivity and feedbacks are too esoteric.
I have followed the recent global temperature with some excitement, and started to prepare a follow up to a previous article I wrote on the failure of global temperature to meet AGW expectations.
The Nature publication “Recent Climate Observations Compared to Projections” by Rahmstorf, Hansen and others in 2007 claimed an up-tick in a graph showed that “global temperatures were increasing faster than expected”, and consequently climate change would be worse than expected. In “Recent Climate Observations: Disagreement with Projections”, using their methodology and two additional year’s data, the up-tick was shown to be an artefact of inadequate smoothing of the effects of a strong El Nino. Perhaps this rebuttal played some part in subsequent revisions of Rahmstorf’s graph with longer smoothing, which had the unfortunate effect (for him) of removing the up-tick, so they could no longer claim, “global temperatures were increasing faster than expected”.
Can we answer the question “Is the Atmosphere still warming” in a reasonable way?
From the field of econometrics comes empirical fluctuation processes (EFP), available to programmers in an R package called strucchange – developed to analyse such things as changes in exchange rates by the brilliant Achim Zeileis. The idea is to find a test of the null hypothesis that the slope parameter m for a section of a series has not changed over time:
H0: m1 = m2 versus the alternative H1: m1 not equal to m2
The idea is to move a window of constant width over the whole sample period, and compare local trends with the overall distribution of trends. The resulting process should not fluctuate (deviate from zero) too much under the null hypothesis and—as the asymptotic distributions of these processes are well-known—boundaries can be computed, which are only crossed with certain probability. If, on the other hand, the empirical process shows large fluctuations and crosses the boundary, there is evidence that the data contains a structural change in the parameter. The peaks can be dated and segmented regression lines fit between the breaks in slope.
I applied the strucchange function EFP to the five official global temperature data sets (CRU, GISS, NOAA, UAH and RSS) from 1978 using the latest values in 2011, and to mean global sea level. The results for the global temperature are below:
The fluctuation process (top panel) crosses the upper significance boundary a number of times, indicating that the trend parameter is unstable. For example, it crosses in 1998, coincident with the strong El Nino, and then relaxes. Most recently, three of the five data sets are at the lower boundary, indicating that at least the CRU, NOAA and RSS datasets have shifted away from the overall warming trend since 1978.
The middle panel shows the structural break model for the CRU data, with the optimal number of breaks given by the minimum of the Bayesian Information Criterion (BIC) (bottom panel). The locations of the breaks are coincident (with a lag) with major events: the ultra-Plinian (stratosphere reaching) eruptions of Mt Chichon and Mt Pinatubo, the Super El Nino and the Pacific Decadal Oscillation (PDO) phase change in 2005.
Sometimes these types of models are sensitive to the start and end point, so I re-ran the analysis with data from 1950. Figure 2 is the resulting structural break model for CRU. While the fluctuation process did not show the same degree of recent downtrend, the structural break model is similar to the shorter series in Figure 1, except the temperatures since 1998 are fit with a single flat segment.
The temperature is plotted over random multiple AR(1) simulations, showing the temperature has ranged between the extremes of an AR(1) model over the period.
Another indication of global temperature is the mean global sea level, both barometric and non-barometric adjusted. Global sea levels tell the same story as atmospheric temperature, with a significant deceleration in sea level rise around the PDO shift in 2005.
By these objective criteria, there does appear to be a structural change away from the medium-term warming trend. Does this mean global warming has stopped?
What are the arguments that warming continues unabated?
Easterling and Wehner in their article “Is the climate warming or cooling?” lambasted “Numerous websites, blogs and articles in the media [that] have claimed that the climate is no longer warming, and is now cooling” for “cherry picking” the recent data. They examined the distribution of 10 year slopes of both the realized and modelled global temperature. They argued that because there were a small number of periods of flat 10 year temperatures that the long-term warming trend is intact.
Both E&W and EFP agree that there is a small chance of flat temperatures for 10 years (EFP says around 5%) during a longer-term warming trend. What E&W’s are saying is that given a small chance at one time, the chance of flat temperatures at any time, over the last 50 years say, is much higher. This doesn’t alter the fact that to an observer during any of those decades when temperature was flat (as now) there would still be a 5% chance of a break in the long-term trend.
Breusch and Vahid (2008 updated in 2011) chimed in with “Global Temperature Trends”, stating “there is no significant evidence for a break in trend in the late 1990s”, and “There is nothing to suggest that anything remarkable has happened around 1998.” As hard as I looked I could not find any estimates of significance to back up their claim of significant evidence.
The statement is even more puzzling as the last 15% at the ends of the series are typically not tested for breaks due to low power of the test on the diminishing numbers of data. The 1990’s fall in the outside 15%. Breaks the size of the break in 1976 would not have been detected on their data.
Of course, there are a variety of other observations of the Earth’s radiative balance and ocean heat content, supporting of the “no warming” claim, by top researchers such as Douglass and Loehle. There does not appear to be any credible empirical evidence from the AGW camp that the atmosphere is still warming.
I suspect that as in “Recent Climate Observations” where climate scientists were fooled into thinking that “climate change will be worse than expected” by the steep up-tick in global temperatures during a strong El Nino, they have also been fooled by a steep but longer-term up-tick in global temperatures associated with a positive phase of the PDO.
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The most obvious, dominant feature of temperature records you have shown in fig 1 is the roughly periodic “humps” of about 3.5 years duration. So any attempt at average slopes of the scale you are attempting must be synchronised to these features otherwise the result will be dependant on the phase of this cycle where you start/end your sample.
The form of the troughs is much more defined than the peaks and so is a more well defined criterion. This would often be close (though different) to the intervals you have derived.
From figure 1: corresponding periods would be 1978?, 1985.5,1992.5, 2000, 2008
This is superimposed by the sunspot cycle which although not dominant probably contributes to the minima around 1985 and 97 and the maximum around 2003.
Any attempt at fitting straight lines is rather doomed to be wrong, however fancy or abstract the technique as I think you have shown with EFP.
A paper you may find interesting looked at trends in Antarctic peninsula base (Gomez dome).
E. R. Thomas et al (with UEA co-author)
GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L20704, doi:10.1029/2009GL040104, 2009
“Ice core evidence for significant 100-year regional warming on the Antarctic Peninsula”
They do a PC analysis based of isotope ratios at Gomez, then diverge into some speculative and subject commentary based on climate models to provide the now obligatory “unprecedented” mantra to ensure further funding.
However, if you study the first half of the paper where they were looking at real data and doing real science it seems to be both rigorous and objective. The result is a century scale warming that peaked around 2000.
Despite their trying to spin this as proof of warming in continental Antarctica, the climate at Gomez is still basically that of the peninsula (as noted in the paper) and dominated by surrounding ocean.
Though comments are made about the similarly chaotic nature of economic and climate data and your approach is interesting , I think figure 1 alone shows there is too much periodic behaviour in climate to take the analogy too far.
If you’re looking for a long term trend masked by significant cyclic phenomena, you need to remove the cyclic element first otherwise all attempts a straight lines will be corrupted. That is what you show by EFP.
Maybe running a 7 year gaussian would reveal the form you are looking for without sacrificing too much of the recent data.
Perhaps fit a line to each solar cycle: 1985-1995 , 1995-2009. Then look at the EFP for each segment.
Sorry 1997 http://www.leif.org/research/Active%20Region%20Count.png
thanks to Anthony’s encylopedic web site, I did not have to look far.
😉
P. Solar says:
April 17, 2011 at 4:40 am
“The most obvious, dominant feature of temperature records you have shown in fig 1 is the roughly periodic “humps” of about 3.5 years duration. So any attempt at average slopes of the scale you are attempting must be synchronised to these features otherwise the result will be dependant on the phase of this cycle where you start/end your sample. ”
Just let the window glide and show the gradient of the resulting trend for each window instance as a continuous curve.
The right way to do this is to try to fit the known sources of natural variation plus a straight line trend to the global average temperature data. Then subtract out the part of the temperature that is due to the natural variation and see if a trend remains. The natural sources of variation are volcanoes, El Nino Index, and the sunspot cycle.
http://tamino.wordpress.com/2011/01/20/how-fast-is-earth-warming/
When this is done the result seems like the global average temperature has a strong upward trend since 1975:
http://tamino.files.wordpress.com/2011/01/adj1yr.jpg
Dr Stockwell says,
I suspect that as in “Recent Climate Observations” where climate scientists were fooled into thinking that “climate change will be worse than expected” by the steep up-tick in global temperatures during a strong El Nino, they have also been fooled by a steep but longer-term up-tick in global temperatures associated with a positive phase of the PDO.
I think that you are mistaken here. Quoting from the 2007 paper you referenced the authors write:
The global mean surface temperature increase
(land and ocean combined) in both the
NASA GISS data set and the Hadley Centre/
Climatic Research Unit data set is 0.33°C for
the 16 years since 1990, which is in the upper
part of the range projected by the IPCC. Given
the relatively short 16-year time period considered,
it will be difficult to establish the reasons
for this relatively rapid warming, although
there are only a few likely possibilities. The first
candidate reason is intrinsic variability within the
climate system. A second candidate is climate
forcings other than CO2: Although the concentration
of other greenhouse gases has risen
more slowly than assumed in the IPCC
scenarios,
an aerosol cooling smaller than expected
is a possible cause of the extra warming. A third
candidate is an underestimation of the climate
sensitivity to CO2 (i.e., model error).
Accusing them of being fooled by the sources of natural variability that you mentioned, the PDO and El Nino, is clearly not justified.
In fact the definition of the PDO, which is derived from the average Sea Surface Temperature of the Northern Pacific Ocean , excludes the possibility that the index could contribute directly to warming of the global oceans.
http://jisao.washington.edu/pdo/PDO.latest
Updated standardized values for the PDO index, derived as the
leading PC of monthly SST anomalies in the North Pacific Ocean,
poleward of 20N. The monthly mean global average SST anomalies
are removed to separate this pattern of variability from any
“global warming” signal that may be present in the data.
A program that removes the seasonal (cyclical) component first is bfast: BFAST: Breaks For Additive Seasonal and Trend.
BFAST integrates the decomposition of time series into trend, seasonal, and remainder components with methods for detecting and characterizing abrupt changes within the trend and seasonal components. BFAST can be used to analyze different types of satellite image time series and can be applied to other disciplines dealing with seasonal or non-seasonal time series, such as hydrology, climatology, and econometrics. The algorithm can be extended to label detected changes with information on the parameters of the fitted piecewise linear models.
I tried it with these data and while it recognises and removes the seasonal component, the piecewise linear model is the same as strucchange, because the seasonal amplitude is small relative to the overall rise from 1950 to 2000. This is not the case for Arctic Ice, where the seasonal component is large relative to the multi-decadal change, and that result is interesting.
Of course, this will only fit short period cyclic components, as the long period will only be half cycles in this data, which is what I understand you are saying. Of course, a half cycle can be approximated with a piecewise fit, and the phase change in PDO should be those breaks that relate to the cyclical component. The only other breaks are “extraordinary” like volcanos and the “supe El Nino”.
I would see it as an advantage that you can model a longer cycle with piecewise fits, but not necessarily assume a long cycle. Whether the flattening from 2000 is due to the phase of the cyclic component, or a special feature of global warming (maxing out) is not a result of the approach. My concern was specifically whether it was rational to say that the atmosphere had stopped warming. It would be supported in both the cyclical and special case.
eadler says trust Tamino; Lucia does better:
http://rankexploits.com/musings/2011/hadley-march-anomaly-0-318c-up/
In respect of the furphy that PDO is only natural variation and can’t produce a trend see:
http://www.cgd.ucar.edu/cas/adai/papers/MonahanDai_JC04.pdf
http://www.atmos.ucla.edu/~sun/doc/Sun_Yu_JCL_2009.pdf
Here is a quick run of HadCrut3 (rather than atmosphere) with a 10y window 2.5 sigma gaussian filter.
I’d say we are definitely at the peak of the ~60 year cycle. Looking at the previous two peaks (c. 1878, 1960, 2002) we see that IPCC 0.7/cent is a con job. They are using the century time-scale like it’s a good idea because it’s a round number. Looking at the data we see it’s a clever ploy to measure trough to peak without actually saying so.
measuring peak to peak we see the rise over each cycle to be 0.2 then 0.4C , a total of 0.6/125 years. That 0.48C/century.
Now let’s be Al Gorey for a minute and assume (for no good reason) that GW is a run-away exponential growth. The next cycle will give us 0.8C in 62 years. That’s 1.3C per century assuming run-away exponential growth. Not 4 or 5 or 6C, but 1.3C.
Now lets assume (because IPCC tells us that “most” GW is due to man and most of that is CO2 and CO2 is increasingly at a steady linear rate) a linear progression : 0.6C in the next cycle, that’s 1C/century. That’s not going to frighten the horses.
But CO2 is well beyond the linear regime and steady increase will have progressively less affect. So let’s now be equally silly and assume the IPCC are right about the importance of CO2, we should probably expect between 0.2 and 0.4C over the next 62 years.
The way cycle 24 and 25 are projected, we may not be that lucky.
OK , let’s play silly buggers with wordpress filtering out hrefs, how about this?
[IMG]http://i55.tinypic.com/e7b8z7.png[/IMG]
[Reply: WUWT uses HTML (angle brackets), not BBCode (square brackets). That may be the problem. Also, no need for an IMG tag, just paste the link with a space before & after, like this: http://i55.tinypic.com/e7b8z7.png ~dbs, mod.]
[Post edited; you didn’t close the “a” tag. Also, you don’t have admin priveleges, so the link won’t load. ~dbs]
http://i55.tinypic.com/e7b8z7.png pretty please?
[See? It’s E-Z! ~dbs.]
http://i55.tinypic.com/e7b8z7.png
pretty pretty please?
Phew.
By the way , IPCC’s “the latter half of the 20th c.” is equally ingenuous move to measure peak to trough. If they’d used “last 60” they would have had 0.4 instead of 0.6 averaged over a longer period.
That masterly bit of the illusionists trade allows them to nearly double the warming trend without actually lying about it.
P Solar: The thing that is coming out of this discussion is how much we all can read things into something like a simple graph of temperature. I’ve done plenty of graphs of periodics like that, and while there is a signal there, there is also the abrupt changes, and the trends to contend with. To avoid taking one set of blinkers off and putting another on, perhaps bfast is better (1. remove seasonality and seasonal breaks, 2. remove linear breaks).
The “60 year” cycle from what I have seen is quasi-periodic, meaning its not really a definite period, but to me looks more like a drifting between two extremes, a bit like a snowboarder in a half-pipe. So if it gets to one extreme and “turns around” then the periodicity is well represented by breaks, as I am sure you have seen the figure of the PDO cycle represented as a zig-zag.
Seems like I am going to have to expand the motivation for a break model in any paper like this that I submit.
eadler: Accusing them of being fooled by the sources of natural variability that you mentioned, the PDO and El Nino, is clearly not justified.
Its an old trick, listing your disclaimers and then advocating the alarmist line anyway. Their conclusion is:
Previous projections, as summarized by IPCC, have not exaggerated but may in some respects even have underestimated the change, in particular for sea level.
If they were not fooled, why then did Rahmstorf consider it necessary to increase the length of the smoothing for the same figure in the Copenhagen Synthesis Report?
eader:
The right way to do this is to try to fit the known sources of natural variation plus a straight line trend to the global average temperature data.
Tamino’s analysis is nice and persuasive, but keep in mind that a straight line fit does not admit the possibility of a break in the trend. A series can have a significant long-term trend AND a significant recent break down from the trend. To ask a question, you need a model that is capable of answering it. The proof T gives that temperatures have not turned down since 1998 or 2004 is the calibrated eyeball test.
My approach is not to assume a single linear trend that you say is the correct way. You cannot test for a break in a linear trend, if you simply assume it.
And BTW, my analysis differs from T in a number of respects. I am saying that three of the temperatures are approaching 95%CL, its going to take a year or two more of no warming to become really significant. I am also not factoring out the sun, as I am only asking if global warming has stopped, not whether the effect of CO2 has stopped — different question.
cohenite says:
April 17, 2011 at 5:13 pm
eadler says trust Tamino; Lucia does better:
http://rankexploits.com/musings/2011/hadley-march-anomaly-0-318c-up/
The link you provided to Lucia is irrelevant to Tamino’s analysis. Lucia’s compares data to multi-model projections and includes a fudge factor for noise. Tamino’s analysis has nothing to do with multi-model simulations and noise.
In respect of the furphy that PDO is only natural variation and can’t produce a trend see:
http://www.cgd.ucar.edu/cas/adai/papers/MonahanDai_JC04.pdf
http://www.atmos.ucla.edu/~sun/doc/Sun_Yu_JCL_2009.pdf
I don’t see the relevance of either the SUN_YU or the MonahanDai paper to PDO. Both are about ENSO, which I recognize is a component of global temperature variation. There is no mention of PDO in either paper.
Are you trying to pull a fast one here? Did you actually look at these papers?
David Stockwell says:
April 17, 2011 at 9:10 pm
eadler:
The right way to do this is to try to fit the known sources of natural variation plus a straight line trend to the global average temperature data.
Tamino’s analysis is nice and persuasive, but keep in mind that a straight line fit does not admit the possibility of a break in the trend. A series can have a significant long-term trend AND a significant recent break down from the trend. To ask a question, you need a model that is capable of answering it. The proof T gives that temperatures have not turned down since 1998 or 2004 is the calibrated eyeball test.
My approach is not to assume a single linear trend that you say is the correct way. You cannot test for a break in a linear trend, if you simply assume it.
And BTW, my analysis differs from T in a number of respects. I am saying that three of the temperatures are approaching 95%CL, its going to take a year or two more of no warming to become really significant. I am also not factoring out the sun, as I am only asking if global warming has stopped, not whether the effect of CO2 has stopped — different question.
The purpose of science is to understand the natural and human caused forces driving the climate. This beats reliance on purely statistical analysis which does not have any rigorous predictive function. We know that the naturally occurring driving forces volcanoes and solar radiation drive imbalances of radiation that warm the earth and that the temperature will respond as a result. We also know that there are oscillations in the surface temperature of the pacific ocean, the El Nino/La Nina conditions, that also strongly affect the surface temperature. Using what we know to extract the long term trend after these known oscillating and impulse forces are removed, is a better way determine if a trend exists, than a simple statistical analysis that is totally void of scientific content.
The evidence is that there is a good fit and a long term trend can be extracted. Climate scientists believe that the trend is probably due to a combination of positive radiative forcing due to GHG’s and a decrease in aerosals since the 1970’s.
David Stockwell says: “To avoid taking one set of blinkers off and putting another on, perhaps bfast is better (1. remove seasonality and seasonal breaks, 2. remove linear breaks).”
Well , I don’t know what all this has to do with blinkers. Any data processing distorts the data so it is important to ensure the method is applicable to the data (does not assume some quality of the data that is not the case) and that the method does not in some way presume the result.
I’m not familiar with bfast, what is the “linear breaks” referring to? I don’t really see any breaks in the temperature records you used here. Several have already be adjusted, spin-washed and homogenised to the point where even their accuracy is doubtful.
You seem particularly interested in some volcanic events as discontinuities in the data. I don’t go with that. There is a discernible trace of these events but it far from being a step function either in reality or in the record and they are not of magnitude or duration that requires a separate analysis.
For example Mt Pinatubo had a limited effect that is visible for a couple of years. This hardly amounts to a regime change. It is a small perturbation. The long term impact of these kind of events (or absence thereof) are part of what makes up the long term trend. I don’t see merit in treating them as discontinuities.
PDO flip in 1976 may qualify as a systematic change of behaviour but again it was not huge ( and is outside the period you are examining). It is possible that 1995-1998 was also a change of structure. I think that one may be worth looking at to see if it fits that kind of analysis.
If you think the ~62 year cycle is better modelled as up and down slopes I see nothing wrong with that approach (or at least not that it is less valid than a cyclic analysis). What I had trouble with was the discontinuous drops and linear rises in your post since I found the lack of negative segments was not representative of the data and was indicative of a flaw in the method.
eadler says:
Climate scientists believe, real scientist prove.
eadler, ENSO is PDO:
http://www.esrl.noaa.gov/psd/people/gilbert.p.compo/Newmanetal2003.pdf
I read the papers and when I say I prefer Lucia to Tammy, that’s what I mean; stop looking for an argument.
I was under the impression that increased cosmic radiation warming the upper atmosphere would trigger an increase in cloud cover and precipitation down below. Like the biosphere popping a protective umbrella. There is no paradox here. They still can’t explain why the solar corona is a million degrees…while the solar surface is 10,000 degrees.