Stockwell asks: Is the Atmosphere Still Warming?

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:

Click to enlarge - Figure 1. Fluctuation process, structural change model and information measures determining the number of structural breaks for the five global temperature data-sets (CRU, GISS, NOAA, UAH and RSS).

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.

click to enlarge Figure 2. Linear vs. segmented regressions for the global temperature dataset CRU, with the timing of significant climatic events.

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.

click to enlarge - Figure 3. The fluctuation process, structural break model and information measures for global mean sea level, both barometric and non-barometric adjusted.

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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David Stockwell, how are you defining PDO?

Brian H

None are so “easily fooled” as those who desperately want to be!
But I think Anthropogenic Global Foolishness is definitely receding.

rbateman

There is nothing to prevent a big La Nina from stepping down the global temps.
A lot of folks who have been stressing out over natural changes will find thier hot air baloons gone cold, and the dizzying heights that they soar, with thier wild predictions, will mean a rapid descent to a hard and unforgiving surface.

Why does Figure 3, for global sea level, have an axis labelled “Temperature (C)”?
REPLY: It is segmented, top and bottom two different graphs, with the top graph sub-segmented for comparison. – Anthony

The AGW projections are so vague that their practicality is near meaningless. The projections are so well mixed in with the climate noise that it is impossible to separate any anthropogenic signal from variability.
You showed the rate of warming regressions for time periods, but a moving rate warming provides some interesting results.
http://theinconvenientskeptic.com/2011/04/2000-years-of-rate-of-temperature-change/
The current warming period is normal in both the magnitude and duration. What is most interesting is that there have been weaker periods of cooling over the past 400 years, well before any anthropogenic signal could have been impacting the climate.
Trying to focus on a 30 year period to predict climate is exactly why the warmists are so far off base. Their entire science is based on the current warming being caused by CO2. All of their efforts are for naught if the warming is 100% natural.

Murray, Oops – that should be sea level. I used the same routine on both sets of data.

Bob, I got the PDO dates from wikipedia. I don’t actually use the values anywhere, as only interested in it as an ‘event’ modifying the slope.

Robert of Texas

Your analysis of the data is based on some amount of trust in the data being correct. My biggest skepticism of Alarmist Global Warming AGW (not natural global warming) is that the data is too messy and inaccurate to draw any meaningful conclusion from it.
I suspect strongly that the urban heat island effect is underestimated. I suspect strongly that the closing of temperature stations has a larger effect than estimated. I find it curious that global warming has seemed to slow down or even stop about the time skeptics started really paying attention to how data is gathered – so I suspect the data since around 2000 is more accurate than the previous data. I am very suspicious of how the raw data is handled and bias accounted for.
Scientists studying global warming should be addressing all of these factors – instead some seem intent on avoiding a sensible discussion of these factors.
So while I find your analysis interesting, without some confidence in the data your conclusions about THIS data is not convincing, or even meaningful. You can’t analyze bad data and get meaningful results.
I do not mean any of this to be disrespectful of you and your work. I just need to trust the data first.

So, the middle graph of Figure 3 says the temperature has risen from -30C in 1995 to +30C in 2010? I don’t remember it being that cold in 1995. 60C sounds like a HUGE amount of gorebull warming,or am I totally missing something here?

JamesS

Not being a statistician — or even very good at the stats courses I took as a geology major — whenever I read an article like this that talks about a new statistical tool, I wonder “What did they test this against for correctness”?
So: what DO these stats wallahs run their brilliant new schemes against to see if they make sense at all? What are the sanity checks? Do they take a known curve or linear function and run it against them to see if the slope of the slope, or whatever they’re analyzing, stays constant over the range?
When I read these articles that basically say scientist X used a new tool to determine thus about so, my first thought isn’t about the results — it’s more along the lines of “Is that new-fangled meter stick really a meter long?”, or thoughts to that effect.
How DO we know these new tools are useful, and not just telling us things we want to see?

Thanks David, ignore my second post, timing issues.

tango

the only option is to move the temp recorders closer to the air conditioner units .why JUST do it, I am not going to get off the gravey train just do what you are told

P. Solar

Interesting analysis but why is there no legend on fig.1 and fig.3 ?
You present 5 data sets in fig.1 but there is no legend , no indication in the caption , not even an explanation in the accompanying text to say which is which.
Same in fig.3 , I’m interested to see how the barometric adjustments affect the data but which is which?
Also in fig.3 the middle segment y axis is labelled “temperature (C)” from -30 to +30 . Clearly this is supposed to be a plot of mean sea level not temperature.
The ‘click to enlarge’ images are nice and clear but then fig.3 loses it’s caption, it has no title .
This is incredibly sloppy work from a PhD (unless the doctorate was in sociology or something, I have not checked.).

Robert of Texas: While you could be right, a definite structural change down would be incontrovertable that something is wrong with the theory of AGW, nomatter what the deficiencies in the data, wouldn’t it.
JamesS: If you read some of the background material from the links I provide, these methods have been known to statistics for a long time and well researched. Contrast that with the ‘novel’ statistical approaches that demonstrate the so-called climate breakthroughs. Its chalk and cheese. Steve McIntyre has always been on about this. They need to use methods that have been around the stats literature that are well understood — what I have tried to do here — not roll their own for every new breakthrough.

P. Solar

Also what is the gray scribble on fig.2 ? Anybody’s guess.

George E. Smith

Well I am not much of a statistician; so I don’t play the lotteries. I figure that if I buy a ticket, I might win, and I might not; so its a 50:50 shot. If I don’t buy a ticket its a 0:100 shot that I don’t win.
I figure if I played the next million lotteries, that I am going to not win the vast majority of them; but I could win the next one; but only if I buy a ticket. It’s like I bought one ticket, and somebody else bought every other ticket, and he didn’t win; I did !
So much for the statistics.
So back to your premise “is the ATMOSPHERE still warming?” (my emphasis).
It would seem to me that the answer to that question is predicated on the assumption that we even know, or can know the Temperature of the atmosphere. We certainly can’t say if it is still warming until we know that we can even measure it.
I’m not aware that we have the means to measure it. Well I know for sure that Mother Gaia, knows exactly what the Temperature of the atmosphere is; she has a thermometer in each and every atmospheric atom/molecule, so for sure she knows what the (average) Temperature is; and at any instant of time too, so ergo, the average over any interval of time one could wish for.
But then she has no means of telling us what the Temperature is. And it’s for darn sure, that we don’t have nearly enough thermometers in the atmosphere to measure the Temperature. Well there’s that little problem of sampled data system theory, called the Nyquist Sampling Theorem. And we are sampling a field of two variables; time and space. And we don’t take enough observations often enough to satisfy the Nyquist criterion for either one of those two variables; let alone for both of them simultaneously.
And remember that, one only has to fall short of the Nyquist prescribed sampling rate by a factor of two to have the reconstruction of the sampled continuous function produce aliassing noise at zero frequency; which means that not only can we not reconstruct the continuous two variable function, but we can’t even obtain the correct average, without aliassing noise.
Other than that; it is an interesting question that you ask. In the long run, the properties of the H2O molecule will ensure that the answer to your question is NO !

David Stockwell says: “Bob, I got the PDO dates from wikipedia. I don’t actually use the values anywhere, as only interested in it as an ‘event’ modifying the slope.”
In looking at you Figure 1, the PDO switch that you’ve highlighted is the only event that lags the structural break.
Regardless, since the PDO is an abstract form of the North Pacific SST anomalies and does not represent them, there’s no mechanism for it modify the slope. The North Pacific SST anomalies peaked in 2005 and have been dropping since then.

Werner Brozek

“Both E&W and EFP agree that there is a small chance of flat temperatures for 10 years (EFP says around 5%)”
I believe it was once stated that the IPCC was 90% confident that CO2 was to blame for global warming. And even if we assume for argument sake that the temperatures were flat for only 10 years, does that mean the IPCC is now only 5% certain CO2 is to blame for global warming?

P. Solar: Tough crowd. I have sent in a new Fig 3 to replace the old one.

James Sexton

Great job, Dr. Stockwell! I thank you for post this! You saved me a ton of work and I don’t think my approach would have been as comprehensive as yours.
For those that wish a simpler view, similar to what I’m taking from the information,
go here, http://suyts.wordpress.com/2011/04/12/rss-going-negative/
No, it isn’t a blog per se, just some informative graphs that shows all of the recent “warming”. Hopefully, some people can come to an understanding that when a “scientist” speaks of “recent” warming on a global scale, they will know they are being entirely disingenuous. (Think about the explanation for the recent snowy years.)

P. Solar

The third segment of fig 1 and fig 3 have no label on the vertical axis. What does this represent?
Just for informational purposes , since axis ticks are usually marked with dimensionless quantities like 0,1,2… so the axis label should also be dimensionless, eg. temperature/C or MSL/mm .
As always when showing climate related data, no indication of the uncertainty of the data is given.
Perhaps that’s all we can expect form environmental “science”.

P Solar, the gray scribbles are: “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.”
The uncertainty of the breaks are indicated by the red bars over the x axis of the middle panels.

BravoZulu

No, S for brains. the atmosphere isn’t still warming.

Murray, did you ever get an answer to your -30C question? It’s a good on. Its probably in hundredths of a degree Celcius.

Alan

I’m sorry but could we stop “analyzing” the temperatures within such a narrow time frame window?… rising, or falling, or flat over a month, a year, or even a decade? It’s silly, populist, non scientific to me. In this planet’s history of climate and geology, anything less than a couple of centuries is just noise. Or weather. Are you bullish or bearish on stocks for this year, based on an analysis of the S&P 500 index yesterday between 2:30 p.m and 2:32 p.m?

Elmer: The sea level in in mm. There is a replacement graph with the correct axis label coming.
BarvoZulu; Not sure who you are addressing, but the idea is to approach the question in a principled way, not an opinionated way. The EFP indicates that we are getting very close to 95% confidence that the atmosphere isn’t warming.

P. Solar

It is unclear from your text and the graphs how you get from the EFP plot to your linear breakpoints. It would appear from the paper on strucchange that dates where the EFP breaks the boundary indicate a change in structure.
Now looking at fig. 1 , the most obvious dates are 1988 and 1997.5 , you chose to break at 1999 and 1988 falls exactly half way between two of your break points.
It appears from what is presented here that the EFP test and BIC has been used to suggest 4 break points but that the break points that were chosen were not derived from the results of the EFP plot.
Maybe you need to explain how you chose the break-points and how (of indeed if) these relate to the efp results.

P. Solar

David Stockwell says:
April 13, 2011 at 6:08 pm

P Solar, the gray scribbles are: “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.”

What AR model is that? How was it chosen , what does it mean? Why is it relevant?
Just showing a scribble plot “model” that has about the same amplitude does not prove/show anything unless you explain it.

The uncertainty of the breaks are indicated by the red bars over the x axis of the middle panels.

No, I meant the experimental uncertainty of the data. It’s an old-fashioned concept that used to exist in the hard sciences.
What you show with the red bars is the variable time lag between your apparently arbitrary breakpoints and the “events” you highlight.
Thanks for the reply.

James Sexton

Ric Werme says:
April 13, 2011 at 5:58 pm
http://www.facebook.com/event.php?eid=148669818520369
According to their Facebook page, 3,116 FB members will be attending, 2,426 may be attending. I clicked “See all” and it only showed me a few. Trying to friend them all would take a while.
=========================================
If you find one that wants to play, let the rest of us WUWT FB members know, wouldja?

Katherine

Sometimes these types of models are sensitive to the start and end point, so I re-ran the analysis with data from 1950.
If you re-run the analysis with data starting from 1930 or 1920 would the warming be similar?

Jeff L

I like this cross-diciplinary approach / analysis.
Key observations :
1) The current segment is way flatter than any of the other segments
2) It quantifies what is visually obvious
Very intriguing !

P Solar: The Zeileis approach, that I am trying to emulate, uses the EFP to determine if the slope parameter is unstable. If it is, by exceeding the 95%CL, then you proceed with the exploratory segmentation technique to get a model of how the trends might have been changing.
The EFP is not used for the dating of the breaks, which is just a brute force search based on the change in residuals for break vs no break.
EFP says it is not correct to fit a linear regression to the temperature — because it appears to be a process with structural changes, much like an exchange rate might change due to some government intervention.

Alan+Katherine on time frame: “I’m sorry but could we stop “analyzing” the temperatures within such a narrow time frame window?…”
Its OK when you ask a specific question. The change in slope from 2000 to 2010 is a significant departure from the steep slope from 1978 to 2010. The change in slope from 2000 to 2010 is not significant relative to the lower slope from 1950, or from 1900 for that matter.
That is why I say that there appears to be a significant departure from the 1978 slope, and of course, this is the fist that is supposed to be mostly caused by CO2 according to the IPCC. But CO2 is still increasing, but temperature is not, why?

Luther Wu
tommoriarty

“…subsequent revisions of Rahmstorf’s graph with longer smoothing, which had the unfortunate effect (for him) of removing the up-tick…”
Rahmstorf must be getting used to the idea of updated data taking all the fun out of his predictions. See, for example…
http://climatesanity.wordpress.com/2010/11/17/rahmstorf-2009-part-9-applying-three-corrections/

David Stockwell says:
“…I wrote on the failure of global temperature to meet AGW expectations.”
As Prof Richard Feynman explains regarding any new hypothesis: “We compare it directly with observation to see if it works.” If the hypothesis doesn’t agree with experiment, if it doesn’t agree with observation, it’s wrong.
The AGW hypothesis [and especially the Catastrophic AGW hypothesis] do not agree with experiment or observation. Therefore, they are both wrong.
The scientific method is ignored by the purveyors of the failed CAGW Hypothesis Conjecture. Their model is wrong, because it does not agree with observation. There is no runaway global warming, nor even warming. Despite a hefty ≈40% increase in CO2, temperatures are declining. Thus, the CO2=CAGW [and CO2=AGW] hypotheses are falsified; they do not agree with observation.
Who are you gonna believe? Michael Mann? Or Richard Feynman?

Smokey: That’s my view. If you haven’t had your favourite theories demolished a few dozen times, you are not a scientist.

mike g

@Alan
Well, Alan, then I’ve got just the videos for you. They’re of Bob Carter doing exactly what you are asking for. And, doing it very convincingly. No wonder media down under has him in the cross hairs.

And you can get the other three parts from Lucy’s fine site:
http://www.greenworldtrust.org.uk/Science/Curious.htm

P Solar on AR(1): This takes some explaining and not essential, but the literature on such tests (read B&V linked in the article) compares the realized temps to a presumed model of random variation. If you take the AR(1) model of the detrended temps, (ie Y_t= a Y_t-1) + e) then the a coefficient is about 0.7 and the SD of e is about 0.1C. Simulate that tons of times to get a feel for the spread of results due to pure, autocorrelated randomness. Thats the gray area in fig 5.
Most of the literature hovers around the 95%CL for tests of the realized temperature against random AR models (of various flavours).

Thanks, Dr. Stockwell. I appreciate your honesty.
Have you seen this knocking of heads between two environmental scientists on global warming? – http://college-ethics.blogspot.com/2011/04/two-environmentalists-knock-heads.html
I’d be interested in you thoughts on this.

Alice: I am more concrete about that sort of thing. The most basic assumption of linear regression is that the slope parameter m in y=mx+c is constant. It’s not. So the model is wrong. I fit a model with segments for each of the different slopes. Temperature is not increasing anymore. Either it increased from 1978 because of CO2 but has ‘maxed out’, or it was caused by the sun all along.

Lady Life Grows

David Stockwell says:
April 13, 2011 at 8:10 pm
“If you haven’t had your favourite theories demolished a few dozen times, you are not a scientist.”
I had a favorite T-shirt I got from a roommate that I called my “science T-shirt.” It showed a honey dripper and said “oh, Lord, make my words as sweet as honey, for tomorrow I may have to eat them.”
But I don’t feel sweet as honey when I consider that practical consequences of the AGW hysteria. Aside from fighting photosynthesis and risking extinctions, the econazis are burning so much corn as ethanol that world food stocks have declined and the Arabs countries are rioting. Tens to hundreds of thousands have been killed so far, and it may touch off larger wars that could kill millions or even billions of people.
That program is so inefficient that it would not reduce warming even if the hysteria were right. So maybe we can get the US congress to have mercy on the world’s poor and stop ethanol subsidies. We need to cut plenty anyway, and that is one good place.

P. Solar

David Stockwell says:
April 13, 2011 at 7:36 pm

P Solar: The Zeileis approach, that I am trying to emulate, uses the EFP to determine if the slope parameter is unstable. If it is, by exceeding the 95%CL, then you proceed with the exploratory segmentation technique to get a model of how the trends might have been changing.
The EFP is not used for the dating of the breaks, which is just a brute force search based on the change in residuals for break vs no break.
EFP says it is not correct to fit a linear regression to the temperature — because it appears to be a process with structural changes, much like an exchange rate might change due to some government intervention.

EFP says it is not correct to fit a linear regression to the temperature … but then you do. Including those areas that were found to be the most unstable , right across 1988 for example 😕
In fact it’s hard to see what use you make of efp once you’ve plotted it.
So the key work you do here is the “brute force” optimisation of segments, a process you don’t describe.
What is the rationale for the discontinuities you introduce ? What happens if you go to 8 or 10 segments, your optimisation does not seem to look beyond 5. That may well just be a local minimum, and a pretty shallow one at that.
I agree with the idea that post-2003 has been pretty flat but you don’t need a complex analysis to see that.
The rest of it just does not ring true for me. I don’t think this kind of method will be accepted as proving anything , apart from by some of the less critical minds here.

Bob K.

I am sure this: “H0: m1 = m2 VERSES the alternative H1: m1 not equal to m2” was ment to read: “H0: m1 = m2 VERSUS the alternative H1: m1 not equal to m2”.

Bob: “In looking at you Figure 1, the PDO switch that you’ve highlighted is the only event that lags the structural break.”
I wouldn’t take the location of the PDO shift as exact. When I say PDO I mean all those processes that PDO represents, that seem to explain the multi-decadal temperature fluctuations so well.

P Solar: “EFP says it is not correct to fit a linear regression to the temperature … but then you do. ”
EFP says it is not correct to fit a SINGLE linear regression to the temperature. So you need a model with more than one slope. Which is what the method does.
The EFP justifies the use of more than one slope. Its a critical step. The next step is dating of the breaks and is more exploratory — there are other criteria than BIC. But BIC should be a global optimum — it would always be greater with more parameters I think, unless it is a really weird type of series (I could imagine one I suppose if it was highly periodic).
The rational for a break, in the case of one test of breaks, is the supremum ration of the sum of squares for a single line vs. a broken line, and is an F statistic: F = RSS1/RSS2. However, this is not the only statistic either.
You really want to go to the literature if you want the details as its technical.

RoHa

“Stockwell asks: Is the Atmosphere Still Warming?”
And is his answer “No”?

Katherine

David Stockwell says:
That is why I say that there appears to be a significant departure from the 1978 slope, and of course, this is the fist that is supposed to be mostly caused by CO2 according to the IPCC. But CO2 is still increasing, but temperature is not, why?
Thanks for the clarification, Dr. Stockwell. I think I understand your article better now.

“I agree with the idea that post-2003 has been pretty flat but you don’t need a complex analysis to see that. The rest of it just does not ring true for me. I don’t think this kind of method will be accepted as proving anything , apart from by some of the less critical minds here.”
When I hear the words “pretty flat” or “pretty close” I immediately think “He must be a climate scientist”. As to whether it rings true for you, or me — who cares? The case for a segmented fit is this:
1. The model y=mx+c is WRONG as m is not a constant. Therefore you must use a model that allows m to fluctuate (and this goes for AR(1) with a constant drift term too).
2. The segmentation method “discovers” exogenous causes such as volcanic eruptions, without any knowledge of the timing of these events. So the method is interesting as it tells you something that you didn’t assume.
Now it could be that including TSI as a dependent variable explains enough of the variation that the EFP no longer crosses the boundary, then the case for a segmented model would not be so strong — I will have to look into that.
3. The method provides a way to evaluate the trends at the ends of a series without the problems that moving averages have. This is an important issue as we are most interested in what is happening at the ends, as that is the most recent data.

rogerthesurf

Does anyone know, according to the IPCC, how soon will it be before we are fully effected by the 7 meter sea level rise caused by the melting of the Greenland ice cap then?
Cheers
Roger
http://www.rogerfromnewzealand.wordpress.com