By Steven Mosher and Robert Rohde
One of the more interesting findings of the Berkeley Earth papers centers around volcanos and the climate reaction them. The proposition that volcanic eruptions, when conditions are right, cool the temperature of the globe is accepted by everyone who understands physics. Nevertheless, there are someways of looking at this problem where you can fool yourself and others. Start here with some back of the envelop glance at the problem. On the surface it seems to make sense. Volcano’s cool; line up the charts; and it should be clear. The approach fails, however, to take notice of the fact that volcanos appear randomly. If the climate was experiencing a warm year, say 1C above normal, and a volcano cooled the planet by .5C, it would be lost in the noise. It would be invisible to someone who didn’t want to find it. To be fair, Willis tried a second method, looking at the average of the two years prior and the average of the two years after a volcano. This too is a weak method of signal detection. Below, I’ll illustrate the problem with a little toy example, and then tell you a couple ways to find the volcano.
Below is a version of a toy world. In this toy world there are 120 time units. There is a “temperature†and “cooling effect†from volcanos. The red curve represents volcanic cooling that tapers off to 0 at 36 time units.
And as you can see the dips don’t exactly line up. In fact it gets warmer sometimes. Conclusion? Volcanos don’t cool? The volcanos above do actually cool that toy planet. I know they do because I created a truth world before I subtracted for volcanos. So below see the truth in blue and the result after we subtract the volcano. Volcanos don’t always make it cold, they make it cooler than it would be otherwise. And they don’t always align with spikes.
 
To be fair to Willis, it appears he was responding to Muller’s NYT editorial where he stated, “The historic temperature pattern we observed has abrupt dips that match the emissions of known explosive volcanic eruptions.†That is an unfortunate way of describing for a lay audience what was done in the paper.
Using Willis’ method you won’t have a good chance to find the volcanos’ signature in the data. But they are there. In the paper,   what a regression was done to see if the volcanos “explained†the data. They did. You can build your own little toy world as I did above and test that. Or you can get the temperature data and the volcano data and run some regressions.
If we want a simple method that is similar to Willis’ second approach, but done with some statistics, we can do the following. Rather than looking at each volcano separately as Willis did, we will stack the volcanos and align them all on a zero year basis. Then we simply average the  years before the volcanos and average the years after the volcano.
The red bars represent the average for the 3 years post and prior and 6 years post and prior to the volcano. All series are centered at zero for the time of the volcano. For the later part of the record we have this:
Next we wanted to test whether this change to temperature could occur randomly. To do that we use the temperature series to create a distribution of all 3 year periods. Then we perform a monte carlo and randomly select points in time and generate the probability of seeing the kind of shift we see in the data. In both cases the shift in temperature seen after a volcano doesn’t happen by chance.
In the Berkeley earth paper we showed that the volcanos helped to explain the data. In regressions they were significant. The way that claim is challenged is by looking at the regressions, not by constructing a method that cannot detect a volcano.
Update
Found a plot Robert created awhile back that might be interesting to folks:
Complementary analysis: cross-covariance of (detrended) temperatures vs. volcanoes.
.
The downward peak at lag 1 means that detrended temperatures at time t+1 are negatively correlated with volcanic intensities at time t.
I find this very odd indeed. We know the LOCATION of the volcanoes and we know the atmospheric transfer process is slow, >3 months from hemisphere to hemisphere.
The obvious thing to do is look at temperature changes near the eruption vs ones far away; the nearby ones should respond first, and more deeply, than the ones far away.
You have an internal control because you know where the damned things are.
Likewise, you can use the same methodology to locate the ‘unknown’ volcanoes, by looking where the Earth cooled first and deepest.
This all assumes that you record is good enough. If you can’t find the finger print of massive eruptions, then you really are not describing global temperature.
Amazing how weak and short lived the response is. I always thought it was a bigger event, but at least there is something. Then I’ve recently heard claims about volcanic eruptions that mysteriously increased global temperatures in geological past. Don’t really trust that.
I would be interested in seeing what happens if we try Doc’s idea; can we get a spacial distribution following the diffusion of the volcanic gasses post eruption over time?
Doc
One of the issues is that for the older volcano you have origins but not temp record at the origin.
The fundamental question is this. You have a temperature record.
You have an emissions record. Theory says the emissions should cause a temporary drop in temperatures. Does the data show that? yup.
Willis took an approach that is almost designed to fail when trying to find a small signal in noisy data.
next comes the question, how much can C02 ( scaled ) and volcanos explain. Answer. A good deal of the variance. Does adding solar forcing improve the fit? Nope.
I view this is as EDA. basically,
changing radiative forcing can explain a great deal of the record.
For one audience ( GHGS explain nothing ) this approach should give them pause. For another audience ( GHGs cause warming ) the chart confirms what we already knew.
ideally we wanted to do something that was a bit more spatially aware, but that would involve dispersion models.. and thats a whole different paper.
basically, every idea I’ve seen raised on the web was addressed at our meetings. Good ideas ALL, however, all the good ideas meant
“write a new paper focused on that”
basically, when we saw the record going back to 1753, one of us,
( zeke or me ) suggested looking at the volcano record. and then we ran down the various sources of data. That led to a chart. It could and probably should lead to a whole paper, but the paper as it stood was already long. The diurnal range chart should lead to a whole paper. etc
Volcano A: Cooling of 1C
Volcano B: Cooling of .5C
Volcano C: Warming of .5C
Average: Volcanoes Cool an average of .333C
Do Volcanoes cool the earth? Maybe. Sometimes.
Several issues with the toy model as I see it:
1. The assumption is that the effects of “noise” and volcanoes are additive. For measurement noise, this makes sense. However, for “weather noise” it does not-volcanoes are supposed to be changing the weather. The weather is the cause of the noise. See the problem here? The two components are not independent.
2. The second problem is how this model compares with reality. In the above, all three volcanoes appear to be hidden by the weather noise. But part of the problem with the BEST analysis is that it appears to be attributing cooling to volcanoes that isn’t hidden, but is not clearly due to the volcanoes. Put another way: in the observations there are cases where the noise appears to be exaggerating volcanoes. In three out of three cases, your toy model shows the noise hiding volcanic effects.
I would be interested to see how many volcanoes you have to combine in your last method in the toy model to get a very clear signal BTW-there’s clearly still some noise present in the plots.
OK, nobody bit on my “fresh new hockeysticks” link, so I am going to ask a question. It’s a bit OT, but I can claim to see a link with volcanoes (sort of).
Who/when has looked at the odd congruence (albeit lagged) between Length of Day and historical warming? Surely this has been put to bed on some skeptic debunking website.Graph here:
http://tinypic.com/view.php?pic=14mgeif&s=6
Red – “deltaT” – cumulative change in length of day from an arbitrary reference (something like year 1820, value = 10 to correspond with some previous method of record keeping). Blue – GISSTEMP annuals. Blue lags red by a couple of decades.
wtf
re: volcanic cooling. 1. I think Mosher et al already accepted that sparseness of data may exaggerate the effect of the cooling (Zekes second to last post?)
2. we have to distinguish between high and low latitude volcanoes. The large low latitude eruptions eject into the stratosphere and then a big concert begins up there … I’m not the person to write that up, so I for the moment just refer to Wunderground and Robock’s review from 2000 .
Gavin Schmidt published a short article about his climate model in Physics Today in January, 2007. In it he demonstrated the validity of his climate model by looking at Pinatubo’s eruption in 1991.
http://www.giss.nasa.gov/research/briefs/schmidt_04/
Some interesting things from that paper-
1. The paper shows that change in atmospheric optical depth peaked at 0.15, and tailed off to zero by 1996. Yet Hansen has claimed that Pinatubo is still cooling current temperatures.
2. The global optical depth increase gives a reduction in surface forcing of about 1362/4*0.7*0.15 = 35 W/m^2 for a period of nearly a year, and nontrivial reductions in forcing for several years. There must be tremendous negative feedback processes that limited global temperature changes to under 1 degree F/R/C/K.
3. Gavin claims “The 1991 eruption of Mount Pinatubo provided a good laboratory for model testing. Not only was the subsequent global cooling of about 0.5 °C accurately forecast soon after the eruption, but the radiative, water-vapor, and dynamical feedbacks included in the models were quantitatively verified.”
Yet Willis at WUWT sees only a 0.15 C dip in BEST data. Which is correct? Who knows.
4. It is impossible to verify a climate model if the transient response in the observational data varies by a factor of almost 4 around a well-understood transient natural forcing.
5. It is trivial to fit a climate model to any old transient response in observational data if you have a sufficient number of adjustable parameters in your climate model.
One of the big problems is that before say 1850 (and certainly before 1500) we really did not know the location of the volcanoes if they went off somewhere where there was not a record keeping civilization.
Also, since the step function has a bit of a delay, even from a big one, as the cloud is distributed through the atmosphere, looking at global records is probably not the best thing to do, but rather, dividing up the globe into NT, ST and Tropical zones and looking at them separately would be more powerful.
Mosh, I hope I didn’t come across as too negative, but I am a little unconvinced that you have teased the volcano signal from the Signal+Noise.
The problem is that your Signal:Noise ratio is variable during the reconstruction, I find it hard to believe you can determine what is a aerosol induced drop in temperature, temperature variation and noise that is a function of the size/location of your temperature sites.
I would, a prior, suggest that individual station monthly differences are a better way to go. If historically you know a big firework happened in June, then a series June-March and July-April, which are then homogenized would give a better determination.
I know you have to work with what you have, but in the time period of interest, you probably do not have enough stations.
I would only have ‘faith’ in your approach if you used exactly the same stations that you had in 1760, throughout; even knowing about changes in instruments and ToO.
Correlation does not mean causation.
The planet is quite capable of dropping 0.5C without any major volcanic activity. You only have to look at the drop from September 1988 to January 1989.
You point to the drop in temperature after the Pinatubo eruption and say “hey, look what Pinatubo did to the global temperature”, yet with other volcanic eruptions you have to go scratching in the dirt looking for anything that resembles a signature.
Can’t you see that there’s something not quite right with that?
Skeptikal–
No. But if you have a cause and effect theory you can often test the theory by checking whether the correlation exists.
Chris y, this has always confused me. Volcanoes are heterogeneous, but we know that hydrogen halides (HCl and HF principally) are injected into the atmosphere. Chloride and fluoride both alter ozone levels, so ozone levels at high altitude will tend to drop and ones lower down will rise. The penetration of uv into the lower will warm.
So dust reflects and absorbs incoming and outgowing radiation; cooling and warming; but cooling overall.
Halides and SO2 deplete ozone, cooling the upper and warm the lower atmosphere.
The life times of dust, sulphur and halides are different.
Now, that is a bitch to model, using modern instruments. Frankly, other than a back of an envelop guesstimate, its not doable.
Hum… It doesn’t seem difficult to see the effects of recent volcanoes in the satellite and seas surface records. This graphic: http://i48.tinypic.com/52grqt.png
shows an overlay of the RSS lower tropospheric trend over ocean only and the Hadley SST2 trend since 1979. Both trends were normalized to the same base and then adjusted by subtracting an estimate of the ENSO contribution to variation (I used the 4 month lagged Nino 3.4 anomaly multiplied by a constant to represent the ENSO influence). Note that much of the temperature variation from 1997 to present is gone (suggesting much of the variation is due to ENSO), an that both El Chichon and Pinatubo eruptions were followed immediately (the next month!) by drops in both trends. The volcanos seem to me to stand out pretty clearly. Interesting also that the ENSO adjusted trends are essentially flat for the last 15 years.
(The heavy smoothed lines are 11 month centered rolling averages, and the thin lines the monthly data with no smoothing.)
For what it’s worth, I have no doubt volcanoes cool things. I also don’t dispute BEST found evidence of volcanic forcing. There’s just a huge gap between that and quantifying the effect.
I like toto’s graph above, which shows an expected correlation. It also shows a stronger correlation between temperatures in the past and volcanic eruptions. That suggests either global warming causes volcanoes (37 years later), or the effect is difficult to tease out.
Simplistic curve fitting is fine, but there are limits on what you can conclude based on it. The new BEST paper draws conclusions its analysis cannot support.
“The new BEST paper draws conclusions its analysis cannot support.”
Welcome to Climate Science! 🙂 🙂 🙂
Andrew
SteveF, it appear that the think green line (Hadley SST2) was already heading down (more so for El Chichon) when the volcanoes erupted.
Andrew_KY, to be fair, some of what I take issue with could be defended as “not actually wrong.” For example, the paper doesn’t actually give an estimate for the climate sensitivity’s doubling of CO2. Instead, it says the “anthropogenic forcing parameter is 3.1 ± 0.3 ºC for CO2 doubling.” That’s true. Their model does give that as a parameter. As long as one doesn’t conflate that parameter with the actual climate sensitivity, things are fine. Of course, the paper then goes on to say that value is:
It’s still not technically wrong. It’s just grossly misleading to compare these two values as the paper does. The implication of comparing the two is the two results are comparable, and thus the reader should believe the authors have estimated climate sensitivity with an uncertainty range of only 10%.
In reality, they didn’t estimate the equilibrium climate sensitivity, and they didn’t estimate any sensitivity to a doubling of CO2 (they instead used CO2 as a proxy).
Brandon,
I like reading your comments as they usually are straightforward and have something meaningful to say. You’ll have to forgive me though, for the intrusion. I have been hangin around climate blogs for too many years, and have become a jaded old junkyard dog.
On my deathbed, I’m going to ask St. Peter for some time off Purgatory for the suffering Climate Science has inflicted on me and the rest of humanity. 😉
Andrew
Volcanoes are heterogeneous, but we know that hydrogen halides (HCl and HF principally) are injected into the atmosphere. Chloride and fluoride both alter ozone levels, so ozone levels at high altitude will tend to drop and ones lower down will rise. The penetration of uv into the lower will warm.
HF doesn’t have much effect on ozone because the F is too tightly bound (you don’t get much/any free F atoms.
HCl is extremely water soluble and pretty much rains out. Volcanic eruptions have more water in them than just about anything else.
So not much HCl gets up high enough
The life times of dust, sulphur and halides are different.
Now, that is a bitch to model, using modern instruments. Frankly, other than a back of an envelop guesstimate, its not doable.
If you mean measure that is just plain wrong. They each have very different signatures. Modeling, at least on a time averaged basis (weeks/months) is also possible
Andrew_KY, no forgiveness is necessary. I’m always happy to have lighthearted quips inserted into discussions.
By the way, I’m flattered. It’s nice to be appreciated!
chris y,
Unless Hansen has made a different statement I believe this is a misunderstanding of the ‘Pinatubo rebound effect’. The point is not that Pinatubo is cooling current temperatures but that the warming rebound from the forcing change as stratospheric aerosols were scrubbed from the atmosphere overshot a “stable” position, meaning that temperatures at around 2000 were warmer than they would have been without this rebound. The suggestion is that this works like a harmonic oscillator so following this warming rebound there is a restorative impulse to cool again.
Hansen treated this effect as being similar to a forcing change: There was a large forcing increase up to ~2000, followed by a smaller forcing decrease from then to present, exerting a cooling influence on the years which followed. Figure 18.e in Hansen et al. 2011 explains this pretty succintly in graphical form.
AndrewFL
I did the toy model to illustrate the problem with trying to “find” the effect of volcanos by looking for ALIGNED dips. the weather noise is high and if the response to a volcano is around the size of the weather noise, finding it by willis’ method will be futile.
I was going to make it really complex.. but in the end just wanted to illustrate in pictures what most of us known in our heads.
Oh bollocks Hare-brained one. Stratospheric HCl and HF life times depend on height, as liquid water solidifies with altitude. The difference between liquid/sold water to transport halides from altitude is rather difficult to model.
http://www.geo.mtu.edu/~raman/papers2/TextorJGR03.pdf
Now go a run a an equilibrium box model and pretend it reflects a steady state and don’t forget to eat up your own droppings*.
* Rabbits are one of the few mammals that actively seek out and eat their own shit, apt really.
Brandon. thank you for reading the caveated language of the paper.
I will say this; Richard tends to frame the results differently than the paper does. i’ve said elsewhere and it bears repeating.
there are three response to the chart
1. I knew that!
2. wow, thats a surprise
3. I dont believe it.
Richard definitely fell into number 2.
For me, I fell into # 1 and would like to see a more detailed ( read complicated) look at the issue.. like others have done by looking at the temp record and forcings.. BUT for that we need to throw n the ocean.
So, the most one can say is that the result confirms what we knew.
radiative forcings explain the data. going back further in time didnt upset known science. That’s a good result. I dont get why
mann and others have to get pissy about it and say ” we knew that”
Well, we clearly did know that. Now we know extending the temperature record doesnt upset that knowledge. Again, a good finding. Not the cover of nature or science.. that’s reserved for ..[self snip]
Agreed Eli.
we started down a path of looking at it in a way that was more sensitive to the spatial aspects.. and well, the tangent becomes a whole new paper. A couple of us (grin) suggested a paleo angle.
Lets put it this way. You have a results paper that confirms known science using an expanded dataset. You know what the complaint will be.
Doc.
I believe we had annual volcanic data. hmm I have to check.
I pointed robert at the Ar5 dataset and at NOAA paleo.
And zeke, as I recall, ran down the Gao numbers and then Robert and Gao communicated. Maybe Zeke will drop by and run down some more details.
That said, I guess the main point is that there are many ways to actually look for the signal. Willis picked two ways that really dont show cogent thinking through the problem. for whatever reason..
Bruce 101277,
The thick lines are 11 month centered smoothed (each data point is the average of the preceding 5 months, that month, and the five months that follow) the sharp drop the month after the eruption therfore influences the smoothed trend line in the preceding 5 months. If you look at the thin lines ( unsmoothed data) you can see a sharp drop in the month following each eruption.
As far as volcanoes go, we had both annual hemispheric and monthly gridded series. There were some discrepencies between the two, and I believe we just went with the annual series for the analysis.
Gao Annual: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txt
Gao Monthly: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2loadinglatheight501-2000.txt
Updated the post with a close-up of the early volcanoes.
Paul S-
Thanks for the link to the paper. The figure you reference describes various adjustments of parameters in a climate model. Arguing that a warming effect after aerosol cooling overshoots a mythical stability point to help explain tenth’s of a degree changes in global temperature (that is not known to that accuracy) and that should otherwise be there due to modeled energy imbalances that are on the edge of detectability is, shall we say, a faith-based exploration of climate model conjecture.
But thanks for the entertainment. It certainly reinforces my opinion of Hansen’s climate science.
Zeke, why is there sulphate in 1943, annual, but not monthly?
The Mexican ParÃcutin volcano was a cinder cone volcano and didn’t have much in the way of boom and tend not to release much gas.
Thanks for the updated figure.
Have you tried to run the tow traces as CUSUM plots?
Oh bollocks Hare-brained one. Stratospheric HCl and HF life times depend on height,
The HCl gets blown out in a cloud that is mostly water vapor and dust. As it rises there is condensation with the HCl solvated in the aerosol. Most of this falls as rain.
“Lets put it this way. You have a results paper that confirms known science using an expanded dataset. You know what the complaint will be.”
Actually Eli knows how the next to last paragraph in the paper starts:
In a paper to be published later. . . . 🙂
snap.
If the effect from volcanoes is so small and so short lived, what’s all the fuss about?
I think that to many of us non-specialists that if there is no way to tell from the temperature data even approximately when the volcanoes occurred, then it really doesn’t matter.
Paul S are you sure? Mosher could you or Zeke comment on this. It seems unphysical, in that sulphates are said to cool by light scattering. http://rankexploits.com/musings/2012/on-volcanoes-and-their-climate-response/#comment-101286
John F Pittman,
Yes, increased abundance of sulphate aerosols reduces insolation, causing cooling. What is at issue with the “rebound effect” are the consequences as the aerosols are being scrubbed from the atmosphere and insolation increasing. Hansen et al. describe it briefly in this paragraph:
Mosh, thanks for drawing attention to my post at WUWT. However, you seem to have missed the point of the post entirely. You say, for example,
You seem to have misunderstood my fundamental question, which was not what you claim at all. Conventional climate theory not only says that emissions should show a “temporary drop in temperatures”. Theory says the emissions should show a large temporary drop in temperatures. So the fundamental question is, does the data show the claimed large temporary drop in temperature?
Nope.
Which was my point. Sorry if you missed it, but I thought I had made it clear in my various posts on volcanoes. You see, I got started on volcanoes by claims from climate modelers, particularly the folks at GISS, that their models did a whiz-bang job at simulating the results of volcanoes. In fact, they hold up the model’s response to modeled volcanoes as evidence that their models are very accurate. But as I showed in “Prediction is Hard, Especially of the Future“, the actual response from volcanoes is much smaller than that claimed by the modelers.
I also showed here and here that using a “black box” type of analysis, a much more accurate result is obtained by reducing the modeler’s estimate of size of the volcanic effects. Again this refutes their claim that their models do a good job with volcanoes.
I followed this up by showing exactly why the volcanic response is much less than the modelers claim, in a post called “Pinatubo and the Albedo Thermostat“. In that post I showed how the climate responds to an increase in albedo due to volcanic eruptions. It responds by decreasing the albedo, which counterbalances the effect of the volcano to a large degree.
So in your foolish attempt to attack something that I never said, all you have done is make my point for me. The modelers claim that volcanoes have a large effect on the climate. But as you point out, all that they do is give us a “small signal in noisy data” … well duh, Steven, that’s what I’ve been saying all along.
See, the modelers are caught. IF climate sensitivity is on the order of 3°C per doubling of CO2 as they believe, then volcanic forcing should cause a large temperature excursion. But eruptions don’t change the temperature much, their best effort gives us what even you call a “small signal”.
SOOO … if you’d truly like to discuss my work, Steven, how about you use your marvelous averaging method to determine the climate sensitivity as indicated by the volcanoes, and stop faffing about with trying to prove that volcanoes have an effect. They do have an effect, everyone knows they do, and that’s never been the question in anyone’s mind (except yours, apparently).
The question is, how large is the effect? So how about you take the volcanic forcing claimed by Muller and the BEST folks, and you compare their claimed volcanic forcing to the GISS claimed volcanic forcings, and then you compare the calculated forcing to the tiny changes in temperature that we both agree occur from volcanoes, and you tell us what that means about the climate sensitivity?
Because claiming I’m wrong by attacking something I never said goes nowhere.
All the best to everyone,
w.
PS—In one of your figures (you really should number them so folks can discuss them) you show the results of a stack average of the four largest volcanoes prior to 1850, and give three year averages of the results. IF the vertical red lines are one standard deviation of error in the mean of the results, then there is no statistical difference between the “before the volcano” and the “after the volcano” results … which means that indeed, your claim above is correct, because even after averaging, what you describe as a “small signal in noisy data” is still lost in the noise …
PPS—Both at the top and the bottom of the page, it says that this post was not written by you and Robert Rohde, but by Zeke …
PPPS—You say you have used the “four largest eruptions 1760-1850” in your calculations. I only find three large named eruptions in that period, Laki, Tambora, and Cosiguina … what did you use for the fourth eruption?
Willis,
The uncertainties in both the temperature record in the 19th century and the extent of forcing from volcanic aerosols would seem to preclude calclating a sensitivity value with much confidence. Pinatubo (and even moreso the NEXT major eruption) seems to me to be more suitable for estimating response. I also think it it reasonable to adjust the temperature record to account for known contributions to short term variation, like ENSO, to better define the volcanic response (see my comment with link to a graphic above). I remember (I’m pretty sure) that you have objections to any such adjustment for known sources of variation, but I have never been able to understand your rational.
SteveF, 101292
I am quite sure the thin green line (and the think blue line) peaked before El Chichon and was heading down. Not quite as sure for Pinatubo.
Therefore the question is how far down it would have gone without an eruption. We have no idea.
Sorry willis. see the monte carlo.
you selected two rather weak ways of trying to detect the effect of volcanos in the record when you know full well that they wont work.
shame on you.
Steven Mosher (Comment #101315)
August 11th, 2012 at 11:28 am
Of course they won’t work, Steven, that was my point—the effect is so tiny that most methods don’t work, and in fact, even your method doesn’t show a statistically significant difference for the largest volcanoes in the record …
And I’d love to “see the Monte Carlo”, but since you haven’t made the code available, and have given only a very vague description of what you did, I can’t. Shame on you, and in fact, double shame on you, you are the man behind “free the data, free the code”, and in this case you have provided neither one …
How about you comment on the fact that your averaging method shows no statistical difference between before and after the 4 pre-1850 volcanoes you chose?
How about you explain how using Monte Carlo methods can explain away no statistical difference in your results?
How about you comment on the fact that you misunderstood what I was saying? You still haven’t gotten off of the incorrect idea that I was trying to show that volcanoes have no effects, which was just your poor reading comprehension at work. I made no such claim.
How about you do an analysis that shows what climate sensitivity would lead to your pathetically weak results, results that aren’t statistically significant?
How about you answer my question as to what you used as the fourth pre-1850 volcano?
In fact, how about you man up and stop with the cryptic three-sentence replies to complex questions? I can’t tell you how tired I am of you pretending to answer questions with your little dribbles of ideas, they don’t impress anyone but you.
w.
PS—Here’s another way to look at it, Steven, by answering a simple question, viz:
Is there a method by which we can identify the timing of volcanoes in the temperature data by analyzing just the temperature data itself?
I say that the volcanic signal is so weak that we can’t do that, but you seem to disagree (it’s hard to tell because your claims are so vague and you haven’t provided data or code).
If you think there is such a method, then enlighten us … what is the method we can use to analyze the BEST data and use it to identify the timing of volcanic eruptions?
And if there is no such method …
PPS—You say:
It may be “unfortunate”, but it was Muller’s exact claim. Now, if by “unfortunate” you mean “100% wrong”, then what are you arguing with me about?
I said Muller was wrong in his claim. You don’t have the clangers to say he was wrong, you wimp out and say he was “unfortunate”. He wasn’t “unfortunate”, Steven, that implies fortune had a hand in it. He picked and chose his words, one assumes carefully. He may be right or wrong in his claims, but you can’t invoke the winds of ill fortune to get your hero out of his own choice of words.
“He picked and chose his words, one assumes carefully.”
and…
“… but you can’t invoke the winds of ill fortune to get your hero out of his own choice of words.”
Steven – is Muller your “hero?”
Here are 10 year Zoom-ins of Berkeley land temperatures and the biggest eruptions of Laki, Tambora and Krakatoa.
Attribution is much over-blown when one views the high-res data.
http://s9.postimage.org/cm8kxoo3j/Berkeley_Laki.png
http://s11.postimage.org/9qij74xbn/Berkeley_Tambora.png
http://s13.postimage.org/s1ri4b11j/Berkeley_Krakatoa.png
Mosher (or Zeke): “If the climate was experiencing a warm year, say 1C above normal..”
That’s a scorching hot abnormal year. Has that ever happened?
Niels,
Perhaps we should have been clearer. “say 1C above normal” is meant hypothetically, to explain why the procedure of dipology is intellectually bankrupt. On a monthly basis you will see large excursions, on a yearly basis, of course, the excursions are less large.
The basic point is this. Since you dont know apriori the effect size of the volcano, and since its possible for the effect size to be less than the known weather noise, practicing dipology isn’t exactly what I would call a search for understanding. yet, some practice it.
Niels, the early TMAX monthly anomalies for global-land fluctuate from +3.5C to -6C ….
1833 5 3.466
1838 1 -6.073
As time goes on the fluctuations from month to month dampen down to at most +1 to -1 or so.
The interesting thing to me is that wide fluctuations still occur in US states such as Washington (and many others):
2011 9 2.722
2010 6 -2.067
Montana:
2009 9 4.509
2009 10 -5.056
If you look at the data for most countries, the temperatures fluctuate so little compared to US states I suspect that the non-US data has been tampered with or large fluctuations have been deliberately discarded.
I would say that explaining this to a lay audience is a tough job. heck, explaining to you why your approach is wrong headed is tough. explaining to mann why his approach is wrong is tough.
So, in fairness to you, I don’t mention that you actually don’t address the claims in the paper. you analyze press releases.
Perhaps you should have spent more time on the watts 2012 debacle. Muller implied the spikes line up. Thats wrong and unfortunate. They dont. I would not expect them to. In any case I am open to how you or anyone else would describe those results to a lay audience.. perhaps “we identfy and attribute some periods of cooling to the effect of large volcanoes”
That would be about right, but even there I am sure some clever person would then argue that the periods were not cool, some of them were warm. And so it goes.
And yes the method does show a significant effect. Do the regression. you will find that the variable is significant and does explain variance. And look again at the monte carlo. Its not that hard to figure out.
Further, if you read the paper you would see that we have a different e folding time than the models suggest. So, one can look at model results, as you have, and conclude that a first principles physics approach doesnt get all the details perfect for one volcano. You stop there. not a curious bone in your body. We took a different approach. We calculated a observation driven model of the effect given a first principles functional form. basically a spike with an exponential decay.
Its one thing to note that models get it wrong and to walk away smugly. It’s quite a different thing to tackle the problem with a different approach, an approach that seeks better understanding.
In the end you have this. you have a temperature series. you have a volcano emissions series and you have C02. A simple regression lets you see that given these two variables a good amount of the “natural variability” we see is explainable in simple terms. is everything explained? nope. Is it perfect? nope. does adding TSI have any explantory power? nope.
Folks will of course look at an exercise like this and comes away with different opinions. Its not dispositive in my opinion. It does however, raise the bar for alternative explanations.
Bruce:
Niels, the early TMAX monthly anomalies for global-land fluctuate from +3.5C to -6C ….
1833 5 3.466
1838 1 -6.073
As time goes on the fluctuations from month to month dampen down to at most +1 to -1 or so.
The interesting thing to me is that wide fluctuations still occur in US states such as Washington (and many others):
2011 9 2.722
2010 6 -2.067
Montana:
2009 9 4.509
2009 10 -5.056
###################################
Welcome to the law of large numbers
BillC
Here are 10 year Zoom-ins of Berkeley land temperatures and the biggest eruptions of Laki, Tambora and Krakatoa.
Attribution is much over-blown when one views the high-res data.
#############
more dipology.
There are many ways you can look at a signal to not find what is obvious. Theory explains why volcanos should cool the planet temporarily. You can test that theory two ways.
A. build a first principles model of the entire climate and see what it predicts. validate that against observations.
B) extract what you can from a noisy signal using well known methods.
If your theory is that volcanos have no effect on temperature, you are welcome to propose that and test it. you are welcome to explain from a physics first principles perspective why it should have no effect and then test that.
What’s clear to most people is that we have a physical theory that explains why volcanos should cool the planet temporarily. How much exactly, and for how long is a tough problem. I’ll suggest that solving this problem with dipology or running averages is not particularly fruitful. look at what toto did. That, my friend, is showing some care and thinking about the problem. looking at the years before and years after, as Willis did, is not particularly powerful. If you use a weak method to find a smallish signal, guess what? well duh.
But hope springs eternal, perhaps you or willis can prove that volcanos have no effect. That would be great.
Joshua
“Steven – is Muller your “hero?â€
Nope. I don’t know how anyone can come to that conclusion.
I like the inkblot he presents to various people( nicely put Joshua ). I’ll put it this way, if micheal mann contacted me tomorrow and said he would like some help with data I’d say yes. I’d still be critical of him, but the person who criticizes him is a different person than the one who would help him. hmm perhaps I have no loyalties. Judith comes close, as does SteveMc and Lucia; they come close to being heros.. carrick too cant forget him. and nick stokes. Zeke of course. each is heroic in a certain way to me, or to put another way, each has qualities I lack and I admire them for those qualities. is that fair? but on that criteria most humans are heroic to me, even you Joshua. just to piss him off I will exempt bruce. he is not heroic in any way.
Here’s how I read your comment about Muller’s statement being unfortunately, Steven.
I find it very hard to believe that you don’t have loyalties – and I don’t doubt that sometimes they affect your assessment of situations. But I think you were saying that it is unfortunate that Muller’s statement might lead some people to conclusions that are different than what are supported by his research. The statement had nothing much to do with your judgements about him at a personal level – it was about the potential outcome of his statement.
Is that right?
I have noticed that Willis has a habit of getting emotional and as a result, making highly implausible conclusions for which he has no supporting evidence. Such reasoning causes him to misattribute cause-and-effect. I think that his mistaken assertion as to the cause for why you made your statement serves as a good case in point.
BTW – is it true that you haven’t made code and data available?
Mosher: “Welcome to the law of large numbers”
Or, as I like to say, mix all the colors together and you get mud, which has nothing to do with what is actually going on.
@Steven Mosher (Comment #101323)
You don’t think the majority of fanboys at CA or WUWT actually understood what you were talking about there.
Steve, to put matters bluntly, you come off as a jackass in the comment threads of this blog. You have a good motivation: you want to be a ‘good skeptic’ and you don’t want to be tarred by association with the ‘bad skeptics’ but I find your haughty diatribes over the top.
If Muller wants to claim the peaks just line-up, he isn’t just talking down to an audience of the ignorant, he is overstating the strength of the case. That’s hiding the pea; it’s a con.
Willis was was dead to rights to test Muller’s claim as given. You want to change topics to some attribution paper that’s already been discredited, written by a group that’s been discredited–and despite your aforementioned goal of cutting out the flab from skeptic arguments–you insist on associating with and defending this group.
Look in the mirror and get a grip. Put your attitude in check.
What a revealing thread. Here is my take as an observer with no notable stats/climate skills.
Mosher expends considerable space in the head post derogating Willis analytical skills and continues to do so in the comments until Willis shows up a day later to defend himself with an extensive rebuttal.
Mosher fails to dispute the substance of Willis’ rebuttal or admit he misrepresented Willis position. Instead Mosher responds with a couple short remarks ending by telling Willis he should be ashamed. Mosher couldn’t even be bothered to answer the simple question about the name of the 4th eruption. I wonder if that is due to shear arrogance or is he hiding something?
Willis counters with another substantial comment which Mosher has up to this time ignored.
Since Willis’ last comment Mosher has commented directly to several other people, but not to Willis.
Tune in again tomorrow to see whether Mosher continues to ignore Willis or properly address his comments. Perhaps, if we are really lucky, Mosher might even condescend to name that mystery 4th volcano. Maybe he will even name all of them. Willis seems to be assuming the most substantial volcanoes are the ones used. I don’t think I’d want to assume that in this case.
As of right now, Willis comes off looking very well, Mosher not so much. Maybe that will change, but I’m skeptical.
QEd
Mosher is weaselling his way here not having the guts to respond to Willis’ true assertions that Mosher deliberately misrepresented Willis. And he re-directs the thread to irrelevant matters. Mosher comes off in this incident showing that he lacks integrity.
Mosher is claiming that Willis deliberately chose a method to make his point that he knew was not effective. If so, then the accusation is that it is Willis who lacks integrity.
Willis has shown his point exactly with facts and shown exactly what he said and Mosher said and Willis is right here. Mosher has not responded to Willis’ points and has resorted to obfuscations.
Tune in tomorrow for more lessons on how not to have a discussion.
Zeke, Mosh,
I can’t help thinking that for the present article, it would have been better to stop after the first part. It provided a simple demonstration of why temperature dips do not line up simply in time with volcanic eruptions.
Including the “monte carlo†argument without any explanation of the underlying model assumption does not help this explanation; instead, it adds a provocative argument in its own right.
I presume the level temperature series from BEST exhibits a unit root and strong serial correlation, since all the other instrumental series do. How many model terms did you include to account for autocorrelation in the difference series when generating the MC results? The way your description reads, it looks like you have just assumed independent random occurrence of change in the 3-year averages. If so, the significance calculated is spurious.
Does it matter that your methodology may be flawed? In this particular conversation, maybe not. I am happy to accept that volcanoes cause some temporary cooling, who’d a thunk it?
However, the correlation included in the original paper is pure unadulterated BS. The methodology rejects the last 50 years of improved understanding in theoretical stats to avoid spurious correlation in time series analysis.
I am working on my next paper to show via the application of simple MLR that the temperature series is in fact controlled by (a) volcanoes and (b) the logarithm of the number of registered births to unmarried mothers. It gives a better unadjusted R^2 than the BEST correlation with ln(CO2). I tested the inclusion of TSI and ln(CO2) and found that neither had any additional explanatory power. Who’d a thunk it? The only teensy-weensy problem I have is that my residual error term shows a high degree of autocorrelation and some annoying heteroscedasticity. But, hell, I’m not going to worry about a little thing like that before the press-conference.
Trying to get the relevant points, apart from the personal fighting, what do we have, and what are the different claims? What I see:
Willis:
(1) You couldn’t tell by the temp data alone when there were mayor volcanic events. And (2) the effect of volcanoes is clearly less than the models show.
Muller:
(3) The historic temperature pattern we observed has abrupt dips that match the emissions of known explosive volcanic eruptions.
Mosher explains this is an “unfortunate” way to put a right claim. Which is:
(4) CO2 and volcanic eruptions explain the trends (decade or bi decade, I guess) in global land temperature. And the sun doesn’t add to the explanation. (Without mentioning any other possible effect).
Mosher hasn’t addressed Eschenbach’s points, he just says they are irrelevant.
So there doesn’t seem to be any real discussion about 1 (Willis is right, but may be irrelevant … or not), 2 (Willis is right, but may be irrelevant … or not), and 3 (Muller is “unfortunate” – whatever that means). And we are left with 4, which seems to be the most interesting point. Can we really accept this claim from BEST, with this data? Paul_K doesn’t seem to think so.
“If the climate was experiencing a warm year, say 1C above normal, and a volcano cooled the planet by .5C, it would be lost in the noise.”
So this idea implicitely assumes and hinges on the proposition climate has a form of “momentum” that allows volcanic cooling to be overlayed on whatever other drivers are controlling the climate.
Paul K,
Maybe you could add the inverse of bikini size to the analysis. http://www.funpic.hu/en/categories/t-shirts-panties/27273_picture?mode=search&search=Global+warming&type=picture&all=1&position=8
No wait, the rate of births to unwed mothers could be inversely correlated with bikini size, and independent of warming. But don’t forget there should be a 9 month lag. 😉
It appears Mosher’s case is becoming less believeable the more it is examined.
Here is what I found in the volcano database located at National Geophysical Data Center / World Data Center (NGDC/WDC). http://www.ngdc.noaa.gov/nndc/servlet/ShowDatasets?dataset=102557&search_look=50&display_look=50
I searched only by date. 1760-1850 and 82 volcanos were returned.
The most explosive volcanoes in that period are
Tambora 1815 vei 7
Galunggung 1822 vei 5
Cosigüina 1835 vei 5
There are many which are vei 4. So, Willis question about the volcano names is very much on point. If those three I listed above were used, I’d like to know which vei 4 was cherrypicked to create that graph of the four largest eruptions 1760-1850. I’d also like know to which of these four vei 6 volcanoes (Krakatau, Santa Maria, Novarupta, Pinatubo) were used to create the graph of the three largest 1850-2000.
@Brandon Shollenberger (Comment #101338)
August 12th, 2012 at 4:18 am
[“shame on you.
Shame on you, and in fact, double shame on you
Tune in tomorrow for more lessons on how not to have a discussion.”]
Brandon, shame on you for trying to spoil all the fun! 🙂
ps, I agree.
Climate Grand Unified Theory (GUT)
http://www.youtube.com/watch?v=xZbKHDPPrrc
I agree with Bob Koss, volcanoes don’t add up at all.
I there was a major eruption this year, the temperature plateau since ~2000 would be attributed to the eruption by the convinced.
There are a couple of issues that have been brought up here that have been bothering me for quite some time.
1. Shouldn’t an accurate yearly anomaly measurement eliminate any weather noise? Mosher seems to be saying that the noise (weather, ENSO cycles, albedo effects, volcanoes, etc.) drown out anomalies. Eschenbach who knows that the anomalies aren’t accurate pokes holes in the warmer’s theories using their own false claims against them.
2. There seems to be something called ‘momentum’ in the warmer’s theories. What is the driver behind the gradual increase in temperature from the 1700’s? Obviously it can’t be an increase in CO2 because that wasn’t a factor until the late 1900’s and I certainly don’t know what it could be from a thermodynamics standpoint. Could ‘momentum’ simply be inaccurate anomaly measurements?
3. Is there any reason to suspect that the real TOA Global temperature anomaly isn’t stable or any broad scale Global anomoly measurement for that matter? It seems obvious to me that any anomaly measurement that can be changed by cycles in the system isn’t accurate.
4. What am I missing?
Laura S. (Comment #101331)
August 11th, 2012 at 11:41 pm
“Steve, to put matters bluntly, you come off as a jackass in the comment threads of this blog.”
That’s unfair to Willis who is at least as much the jackass. I’m reminded of Mad Comics Spy vs. Spy where two inept spies, one black one white, are constanty trying to kill each other and failing.
Pass the popcorn.
David Springer,
Your link doesn’t work.
I red some of the stuff above. I am not certain that most of it relates to what is actually important.
Volcanic eruptions are more a proxy than a cause of any significant climatic changes beyond a year or two.
http://www.vukcevic.talktalk.net/Ap-VI.htm
Ignore or take a note makes no difference to the climate, but it might help to the understanding.
On this point, I agree with Mosher’s analysis, I can’t say I agree with the common CA failing of attributing malice. I think Willis honestly believes his erroneous method was valid.
Ged (Comment #101250)
August 10th, 2012 at 11:49 am
“Then I’ve recently heard claims about volcanic eruptions that mysteriously increased global temperatures in geological past. Don’t really trust that.”
No mystery. If volcanic ash darkens a lot of snow/ice cover it will accelerate melt like a raped ape.
SteveF (Comment #101351)
August 12th, 2012 at 7:23 am
David Springer,
Your link doesn’t work.
The problem is on your end. It works fine for me with multiple browsers.
http://en.wikipedia.org/wiki/Year_Without_a_Summer
Mid-summer frosts in 1815 New York State. It doesnt’ take a PhD or USHCN records to connect the dots with a series of VEI 4+ volcanic eruptions in 1812, 1813, and 1814 culminating with VEI 7 Tambora in 1815.
All volcanoes are not equal however. Amount, composition, and height into the atmsphere all vary. This is a fool’s game hence the BEST team’s participation.
lucia (Comment #101270)
August 10th, 2012 at 4:03 pm
Skeptikal– Correlation does not mean causation.
No. But if you have a cause and effect theory you can often test the theory by checking whether the correlation exists.
—————————————————————–
Yes. Correlation remains a valuable diagnostic aid despite the lack of perfection.
The Year Without Summer should be renamed to the Decade Without Summer Potentially Caused By the Dalton Minimum.
July 1816 (at -2.5C) was the coldest July in the HadCET but there were other periods in the decade which had a greater low temperature anomaly such as January 1814 at -6.5C.
The Year Without Summer was just a period when temperatures were cold for the entire summer but there were other summer months in the decade which were colder. It does not look that unusual in this cold decade.
http://s11.postimage.org/u2tapz45f/Year_Without_Summer_Temps.png
David, the first VEI4 was St Vincent 1812 April 27.
The 2nd was Awu Aug 8 1812
For BEST TAVG New York, the 2 coldest months in 1812 were January and March.
1812 1 -3.364
1812 2 -2.752
1812 3 -3.939
1812 4 -1.855
1812 5 -2.908
1812 6 -1.582
1812 7 -1.720
1812 8 -1.197
1812 9 -2.239
1812 10 -1.899
1812 11 -2.429
1812 12 -1.755
As for the annual data:
1809 -1.2892500
1810 -0.7205000
1811 -0.5270833
1812 -2.3032500
1813 -1.0020000
1814 -1.1365833
1815 -1.6911667
1816 -1.9318333
1817 -2.1204167
If anything, the 2 VEI4’s in 1812 resulted in relatively warm 1813 and 1814 and the end of 1812.
Steven Mosher
August 11th, 2012 at 7:00 pm
Seriously? Your argument is that correlation is causation? Your claim is that a simple regression analysis is all that we need to explain most of the variation in climate? And you find my science lacking? Really?
Next, I did not “walk away smugly” after “noting” that the models get it wrong. After showing, not noting but showing that they got it wrong, I advanced a hypothesis as to why they were wrong, and supported it with data. My hypothesis is that the models overestimate the temperature change caused by volcanoes because the real climate responds, and responds strongly, to changes in temperature … as I linked above.
Regarding your Monte Carlo analysis, I had asked for the details of your analysis. Saying you have done a “Monte Carlo” analysis is as meaningful as saying you have done a “statistical” analysis. The devil is in the details, which is why I asked you for the data and the code that you used. You didn’t answer me, as is your habit. But I had hoped you might answer Joshua, who said:
Or you might have responded to Paul_K, who said:
I don’t know if the monte carlo code is available or not. I just know I haven’t seen anything resembling code for a Monte Carlo analysis. But despite that great lack, Steven, and despite Joshua and I and Paul_K all asking for it, you come back to say:
Not only can I not “look again at the monte carlo”, I haven’t been able to look at it at all, because you haven’t shown us exactly how you did it. Surely you know that the Monte Carlo method depends exquisitely on the model you choose for the pseudo-data, and you have not provided us with that model. And as to whether it is “hard to figure out”, it is not possible to figure it out from just your vague written description. You could have done something wrong without even noticing it, or you could be describing it from memory and not remember exactly what you’ve done. For you to advance the argument that you do not need to provide code for any reason, and particularly under the claim that you don’t need to provide it because your mystery method is “not that hard to figure out”, is a sick joke. You wouldn’t buy that from Phil Jones for one second, and yet here you are channelling him … do you realize how foolish that makes you look?
Nor can I “do the regression” on the volcanic variable as you suggest, because as far as I know, you have neither provided the dataset for “the variable”, nor have you explained where you got the dataset. All I can find is a handwaving reference to “volcanic sulfate emissions” … sounds good, but which ones? And how were they converted to temperatures? I just did a regression of the Dronning Maud volcanic sulfate record against the BEST data … epic fail, R^2=0.01. So what is the provenance of your “volcanic sulfate emissions” data, and where is it located, and how did you convert it to °C?
(In passing, I took the BEST data for my analysis from here … and I note that the BEST Folks have not completely removed the seasonal signal from the data. There is still a full degree C of annual swing in the data … why is that?
And what’s up with BEST not giving credit where credit is due? Someone on my thread noted that the BEST folks had screwed up the labeling of the volcanoes in the graph. Within 24 hours, it was fixed, without a comment or anything to indicate it was ever in error, much less a tip of the hat to the commenter who noticed the error. I suppose now that within 24 hours the annual signal will be gone from the BEST data, again without any notice, explanation, or a hat tip to anyone … but I digress.)
Finally, you still seem to be under the impression that I was claiming that volcanoes have no effect, or that their effect could not be seen in the temperature record, which I have never said.
Instead, I have shown, not said but shown, that the models and the current theory greatly overestimate the effects of volcanoes. How about you try dealing with that instead of your fantasies about my claims?
w.
“DocMartynâ€, it occurs to me that the impact of each volcano and temperature will depend on factors such as how high the gas/material that causes cooling is thrust into the atmosphere (thus what and where its effect is), what that gas/material is (thus what and where its effect is – I presume ash will precipitate out for example as it did downwind of Mt. St. Helens, much in eastern WA and heavy dusting southern AB etc. ), and where it goes (heavily dependent on where it starts from, then on air movement).
Many variables.
As seems usual in climate analysis, the statistical methods need to be examined by experts.
And correlation requires careful consideration before being considered a pointer to possible or probable cause.
FTR, volcanoes are only part of the picture – solar variation (in all its forms including orbital variation and various emissions such as those that might seed clouds), and of course the claimed correlation to CO2. (Which has many questions to be asked about, as errors have been made in timing and sources.)
Note as well that the Muller et al 2012 paper starts at the nominal end of a recognized cool period (the poorly named Little Ice Age) so it would be a big surprise if they did not show warming.
El Chichon – Warming or Cooling?
I’m not so sure one way or the other.
http://i50.tinypic.com/ieoy1h.jpg
“The eruption of El Chichon, Mexico, in 1982 conclusively demonstrated this idea was correct. The explosive eruption injected at least 8 Mt of sulfur aerosols into the atmosphere, and it was followed by a measureable cooling of parts of the Earth’s surface and a warming of the upper atmosphere.”
http://volcanoes.usgs.gov/hazards/gas/s02aerosols.php
Willis,
Just to be clear, I wasn’t really asking Mosh to provide code – I think I know what he has done. My question about how many terms he had used to account for autocorrelation was somewhat rhetorical. I was signaling that I thought what he had done here was questionable, since he has started with the assumption that, absent the volcanic input signal, there is no autocorrelation in the level dataset. I am sure he understands my message.
re:SteveF (Comment #101343)
August 12th, 2012 at 5:51 am
SteveF,
Thanks for the suggestion. It’s an area I’m working on.
A question for the knowledgeable. To what degree do the Yellowstone eruptions (VEI8) of the last 1M years show up in any proxy data? If data is available that far back.
Paul_K (Comment #101363)
August 12th, 2012 at 1:40 pm
I understand that you weren’t asking him to provide code. You were commenting on his lack of a description of his model for the Monte Carlo analysis, by saying:
I can only agree.
w.
PS—When I “think I know” what someone has done as you say above, far too often either I don’t know what they have done, or they haven’t described what they have done, or they don’t know what they have done. That’s why I’ve mostly given up trying to guess what someone has done.
I am amazed that many people in the comments, starting with Willis, are asking what was the “fourth” eruption and are even trying to guess it. It is obvious from the BEST plot (http://berkeleyearth.org/images/annual-with-forcing-small.png) that this eruption happens a couple of years before Tambora, and even on the wiki you can read about the putative 1809 eruption, see http://en.wikipedia.org/wiki/List_of_large_volcanic_eruptions_of_the_19th_Century.
Even more am I surprised by Willis’es accusation that BEST did not explain where they got the sulphate record from. Did you actually look in the preprint? I can post a link for your convenience: http://berkeleyearth.org/pdf/results-paper-july-8.pdf, line 269. Check out this citation in the bibliography list and you will see the direct link to the file with sulphate record, line 515 (“injection” record, to be more precise; I guess it is something like sulphate record after thresholding). See also line 292 regarding the fit.
BTW – Mosher –
“I like the inkblot he presents to various people( nicely put Joshua ).”
Actually, considering some of the comments I’ve read in this thread, it appears that you also have become an inkblot. Not sure if congratulations are in order or not.
Do you think it has something to do with having a last name the begins with “M” and ends with “R?”
“nicely put Joshua”
Warmer Salesman Mosher Pats Warmer Troll Joshua On The Back.
((Group Hug))
Andrew
amoeba
August 12th, 2012 at 3:55 pm
Thanks for that, amoeba. Unfortunately, the data that you link to above looks absolutely nothing like the dark line in the BEST overlay of co2+volcanic that you link to above … so it’s useless for the purpose. Remember that Steven Mosher said
The “variable” he is referring to is not the sulfate injections you link to. It is the volcanic forcing resulting from those injections … and unfortunately, despite your best efforts, we still don’t have that data. Yes, I now have your link to the record of stratospheric sulfate injections in Tg … but regressing that against the temperature shows an R^2 of 0.03 …
As a result your link, while interesting, is not what is being sought.
w.
PS—Next time, before you accuse me of not doing my homework, you might do yours …
amoeba
August 12th, 2012 at 3:55 pm
Thanks, amoeba. Since there is another eruption in about 1756 whose forcing is about the same size as that of the 1809 eruption, it is not at all “obvious” which one Steven is referring to. He could easily be referring to the earlier one, and the truth is, neither you nor I know which one he is discussing. You may believe that you know, but that is just belief, whether you turn out to be right or not.
Which is why I asked Mosh the question, and I didn’t ask you … because he and only he knows what he was referring to. You and I are just guessing.
w.
Did the 1809 unidentified eruption reduce temperatures leading into the cold 1810 decade.
Nope. It does not show up in the data.
The decade of 1800 to 1810 was also cold and there is no change in the trends at 1809 or 1810. I can’t see where the trend changed in this period. If anything, it goes back to 1798 or 1805.
Do you know how much of the stuff got blown into the stratosphere and how long it stayed there?
If we are discussing the paper linked below, I doubt that we really know enough about the details to be analyzing it in any depth. It certainly is a self admitted simplistic approach to modeling climate temperature by way of historical CO2 levels in the atmosphere and volcanic eruptions. I did not see any links to code for modeling or the modeling details so I might well be missing something here.
http://berkeleyearth.org/pdf/results-paper-july-8.pdf
This first excerpt clearly points to the caveats and I would not think it suffices to merely indicate that these simplification errors tend to cancel out. I do not believe it even considers the gross effects that Hansen has talked about where the volcanic effects on the climate successively overshoots the equilibrium temperature and oscillates to an equilibrium.
“In the simple linear combination, the anthropogenic term based on the logarithm of CO2 concentration has an effective response of 3.10 ± 0.34 ºC at doubled CO2 (95%
confidence). This is within the IPCC range for the equilibrium climate sensitivity at
doubled CO2 of 2-4.5 ºC; however, several important caveats apply. Firstly, the estimate provided here is based solely on land observations, and as such should be expected to overestimate the global change. Based on the last fifty years, IPCC observations suggest the land has warmed ~35% faster than the global average. Secondly, these numbers reflect the transient climate response to ongoing increases in CO2. Based on the global climate models runs reported by the IPCC, such a transient response will underestimate the equilibrium response by ~20-50%. Lastly, we reemphasize that CO2 is being used here as proxy for all anthropogenic effects, and is only reasonable because most anthropogenic effects are roughly proportionally to CO2. Despite these caveats, and the offsetting corrections for faster land warming and transient climate response, our very simple linear model is consistent with a climate sensitivity of around 3 ºC for an effective doubling CO2, consistent with the IPCC.”
The second excerpt indicates some serious posterior model fitting with the choice of the decay rate of the volcanic sulfate mass.
“A linear combination of volcanic sulfates and CO2 changes were fit to the land-surface
temperature history to produce Figure 5. As we will describe in a moment, the addition of a solar activity proxy did not significantly improve the fit. The large negative excursions are associated with volcanic sulfate emissions, with the four largest eruptions having all occurred pre-1850; thus our extension to the pre-1850 data proved useful for the observation of these events. To perform the fit, we adjusted the sulfate record by applying an exponential decay with a two year half-life following emission. The choice of two years was motivated by maximizing the fit, and is considerably longer than the 4-8 month half-life observed for sulfate total mass in the atmosphere (but plausible for reflectivity which depends on area not volume). It is likely that longer period reflects dynamic climate responses that are slower than the simple settling time of the total sulfate mass.”
The third excerpt again points to some simplifying and to not being able to assign a specific event to a peak at 1809. It was not clear what peak was being referenced here but I assume that the historical sulfate records are derived from ice core findings.
“Most of the eruptions with significant stratospheric sulfate emissions can be qualitatively associated with periods of low temperature. For most of these events, the volcano and year of emission is historically known. These include the eruptions of Laki in 1783, Tambora in 1815, and Cosiguina in 1835. The peak at 1809 does not have an associated historical event, and it might consist of two separate events [Yalcin et al., 2006; Cole-Dai, 2009]. The famous explosion of Krakatau in 1883 is smaller (measured in sulfates) than these other events. The temperature “forcing†of volcanic aerosols is a complicated function of latitude, altitude, season, and particle size; see Kelly et al. [1996]. However, the fit presented here can provide a rough estimate. We observe a response of -1.5 ± 0.5 ºC per 100 Tg of atmospheric sulfate emitted. The 95% confidence interval quoted here is primarily influenced by the uncertainties in the temperature data, however we also allowed the magnitude of each eruption to have a 1-sigma error of ±15%. A more sophisticated analysis of the forcings and the details of the climate response may be able to improve upon the crude estimate offered here based solely on the linear combination fit.”
I think that perhaps the authors were attempting to find new and unique ways to utilize the newly published temperature data set that is extended further back in time than the current major three. Perhaps the authors were trying too hard or maybe not hard enough. Time, details and further analyses will tell.
I have a minor bone to pick with Steven Mosher when he told me categorically that BEST uses no meta data. The fourth excerpt from the link above would indicate to me that they do.
“We also split records when there was a gap in record continuity greater than 1 year in duration, and at times when changes in station location or time of observation were documented.”
Unfortunately, the data that you link to above looks absolutely nothing like the dark line in the BEST overlay of co2+volcanic that you link to above […] Yes, I now have your link to the record of stratospheric sulfate injections in Tg … but regressing that against the temperature shows an R^2 of 0.03. As a result your link, while interesting, is not what is being sought.
Willis, did you take into account what is written on line 292 of the BEST paper, or did you just regress the temperature to the sequence of injection delta functions? “To perform the fit, we adjusted the sulfate record by applying an exponential decay with a two year half-life following emission”. Sounds quite clear to me, should be enough to reconstruct what BEST did.
The BEST paper is certainly deficient in its lack of a description of its extrapolation of pCO2 backwards in time. I was able to produce a reasonable facsimile of the dark BEST curve, by assuming that pCO2 varies linearly from 280 ppm in 1753 (start of BEST data) to the 315.97 ppm in 1959 (Mauna Loa value). This seems like number juggling to me; it seems much more plausible that the graph should exhibit upward curvature, as it has since 1959.
The equation for aerosols is a straightforward implementation of a “2-year half-life”, viz.
A(n) = 2^(-1/2)*A(n+1) + S(n),
where S(n) is the sulfate injection in year n, from the Gao et al. 2008 paper. [Link] It would make more sense to use the month of the forcing and monthly temperatures, though.
All of this seems rather inadequate as attribution and effects scaling in any case.
amoeba (Comment #101377)
August 13th, 2012 at 2:19 am
Thanks, amoeba. I did do that, but I was unable to replicate their results. See here for the details.
w.
Did you account for ENSO impacts in all of this?
There are a number of papers that have established from the paleontology that large tropical volcanoes usually initiate an El Niño event. So for any kind of analysis, the El Niño warming impact should be removed before trying to isolate the impact of the volcanic cooling.
Additional to the last comment:
The current hypothesis is the El Niño response in the Pacific occurs due to the cooling impact of the volcano. So in essence, the link is fairly good evidence that the volcano did cool the earth, and set off the El Niño response.
Also please remember, the proxies to determine ENSO events are different from the proxies for global temperatures.
my understanding is, that the link between enso-phase and volcanic eruptions (or rather the other way round) is highly disputed. However, years when Nina or Nino events and volcanic eruptions coincide complicate the analysis of the impact of either or the three (ENSO+,- and Volc).
It is probably a matter of confusion on my part but if one goes to the readme-gao for volcanic sulfates as estimated from ice cores there is a table that gives the forcing data by month, latitude and altitude that would seem to be a ready-made starting place for the BEST model. Was that information incorporated into the BEST model?
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/readme-gao2008ivi2.txt
“We then studied the spatial pattern of volcanic sulfate deposition on Greenland and Antarctica and combined this knowledge with a new understanding of stratospheric transport of volcanic aerosols to produce a forcing data set as a function of month, latitude, and altitude for the past 1500 years. We estimated the uncertainties associated with the choice of volcanic signal extraction criteria, ice core sulfate deposition to stratospheric loading calibration factor, and the season for the eruptions without a recorded month.”
Paul K.
Here is the code that Obert wrote for the post here. The point behind this is pretty much as we write in the post.
If you want to NOT FIND the effect there are many ways to Not find it. WIllis showed two ways not to find it. If you want a simple way to find it that is LIKE one of the methods Willis used ( there are other ways) you can stack the volcanos as Robert did.
Here is his code for doing that
v_full = [
1835.052054 % January 20, Cosiguina
1815.273972 % April 10, Tambora
1783.4356 % June 8th, Laki
1809.70833333333 % August(?) 1809, Mystery Eruption
1883.65479 % August 27th, Krakatoa
1963.208 % March 17, Agung
1991.454 % June 15, Pinatubo
];
v = v_full(1:4);
window = 6;
near = 3;
time_start = 1760;
time_end = 1850;
f = find( results.times_monthly v(1) – window );
combine = zeros( length(f), 1 );
for k = 1:length(v)
f = find( results.times_monthly v(k) – window );
combine = combine + results.values_monthly(f) – mean(results.values_monthly(f));
end
combine = combine / length(v);
level1 = mean( combine( end/2 – 12*near:end/2-1 ) );
s_level1 = std( combine( end/2 – 12*near:end/2-1 ) )/sqrt(near*12);
level2 = mean( combine( end/2 + 1:end/2+12*near ) );
s_level2 = std( combine( end/2 + 1:end/2+12*near ) )/sqrt(near*12);
level3 = mean( combine( end/2+12*near+1:end ) );
s_level3 = std( combine( end/2+12*near+1:end ) )/sqrt(near*12);
level4 = mean( combine( 1:end/2 – 12*near-1 ) );
s_level4 = std( combine( 1:end/2 – 12*near-1 ) )/sqrt(near*12);
level = level1 – level2;
scale = erfinv(0.95)*sqrt(2);
figure
plot( -window+1/24:1/12:window, combine);
ylim = get(gca, ‘ylim’ );
hold on
plot( [0,0], ylim, ‘k–‘ );
plot( [-near+1/24, -1/24] , [level1, level1], ‘r’, ‘linewidth’, 2);
plot( [1/24, near-1/24] , [level2, level2], ‘r’, ‘linewidth’, 2);
plot( [-2*near+1/24, -near-1/24] , [level4, level4], ‘r’, ‘linewidth’, 2);
plot( [1/24+near, 2*near-1/24] , [level3, level3], ‘r’, ‘linewidth’, 2);
plot( mean([-near+1/24, -1/24])*[1,1] , level1 + scale*[s_level1, -s_level1], ‘r’, ‘linewidth’, 1.5);
plot( mean([1/24, near-1/24])*[1,1] , level2 + scale*[s_level2, -s_level2], ‘r’, ‘linewidth’, 1.5);
plot( mean([-2*near+1/24, -near-1/24])*[1,1] , level4 + scale*[s_level3, -s_level3], ‘r’, ‘linewidth’, 1.5);
plot( mean([1/24+near, 2*near-1/24])*[1,1] , level3 + scale*[s_level4, -s_level4], ‘r’, ‘linewidth’, 1.5);
set(gca, ‘tickdir’, ‘out’ );
ylabel( ‘Mean Monthly Temperature Anomaly ( \circC )’ );
xlabel(‘Years Since Peak of Eruption’);
title({‘Temperature Anomaly Stack’, ‘Four Largest Eruptions 1760 – 1850’}, ‘fontsize’, 12);
fitPlot(gca);
loops = 50000;
level_test = zeros( loops, 1 );
for k = 1:loops
v2 = rand( length(v),1 )*(time_end-time_start) +time_start;
combine2 = zeros( length(f), 1 );
for j = 1:length(v)
f = find( results.times_monthly v2(j) – window );
combine2 = combine2 + results.values_monthly(f) – mean(results.values_monthly(f));
end
combine2 = combine2 / length(v);
level_test(k) = mean( combine2( end/2 – 12*near:end/2-1 ) ) – mean( combine2( end/2 + 1:end/2+12*near ) );
end
prob = sum( level_test > level ) / loops;
figure
hist( -level_test, -0.8:0.04:0.8 );
set(gca, ‘xlim’, [-0.8, 0.8] );
ylim = get(gca, ‘ylim’);
hold on
plot( -[level, level], ylim, ‘r’, ‘linewidth’, 2 );
set(gca, ‘tickdir’, ‘out’ );
xlabel(‘Temperature Change (\circC)’);
ylabel(‘Monte Carlo Counts’);
title( {‘Monte Carlo Temperature Shift’, ‘Four Random Dates 1760 to 1850’}, ‘fontsize’,12);
fitPlot(gca);
lb = boxedLabel( {‘Random Probability of ‘,[‘Apparent Shift: ‘ sprintf( ‘%0.2f%%’, prob*100 )]}, ‘northwest’ );
set(lb, ‘edgecolor’, [1,1,1]);
v = v_full(5:end);
time_start = 1850;
time_end = 2000;
f = find( results.times_monthly v(1) – window );
combine = zeros( length(f), 1 );
for k = 1:length(v)
f = find( results.times_monthly v(k) – window );
combine = combine + results.values_monthly(f) – mean(results.values_monthly(f));
end
combine = combine / length(v);
level1 = mean( combine( end/2 – 12*near:end/2-1 ) );
s_level1 = std( combine( end/2 – 12*near:end/2-1 ) )/sqrt(near*12);
level2 = mean( combine( end/2 + 1:end/2+12*near ) );
s_level2 = std( combine( end/2 + 1:end/2+12*near ) )/sqrt(near*12);
level3 = mean( combine( end/2+12*near+1:end ) );
s_level3 = std( combine( end/2+12*near+1:end ) )/sqrt(near*12);
level4 = mean( combine( 1:end/2 – 12*near-1 ) );
s_level4 = std( combine( 1:end/2 – 12*near-1 ) )/sqrt(near*12);
level = level1 – level2;
scale = erfinv(0.95)*sqrt(2);
figure
plot( -window+1/24:1/12:window, combine);
ylim = get(gca, ‘ylim’ );
hold on
plot( [0,0], ylim, ‘k–‘ );
plot( [-near+1/24, -1/24] , [level1, level1], ‘r’, ‘linewidth’, 2);
plot( [1/24, near-1/24] , [level2, level2], ‘r’, ‘linewidth’, 2);
plot( [-2*near+1/24, -near-1/24] , [level4, level4], ‘r’, ‘linewidth’, 2);
plot( [1/24+near, 2*near-1/24] , [level3, level3], ‘r’, ‘linewidth’, 2);
plot( mean([-near+1/24, -1/24])*[1,1] , level1 + scale*[s_level1, -s_level1], ‘r’, ‘linewidth’, 1.5);
plot( mean([1/24, near-1/24])*[1,1] , level2 + scale*[s_level2, -s_level2], ‘r’, ‘linewidth’, 1.5);
plot( mean([-2*near+1/24, -near-1/24])*[1,1] , level4 + scale*[s_level3, -s_level3], ‘r’, ‘linewidth’, 1.5);
plot( mean([1/24+near, 2*near-1/24])*[1,1] , level3 + scale*[s_level4, -s_level4], ‘r’, ‘linewidth’, 1.5);
set(gca, ‘tickdir’, ‘out’ );
ylabel( ‘Mean Monthly Temperature Anomaly ( \circC )’ );
xlabel(‘Years Since Peak of Eruption’);
title({‘Temperature Anomaly Stack’, ‘Three Largest Eruptions 1850 – 2000’}, ‘fontsize’, 12);
fitPlot(gca);
loops = 50000;
level_test = zeros( loops, 1 );
for k = 1:loops
v2 = rand( length(v),1 )*(time_end-time_start) +time_start;
combine2 = zeros( length(f), 1 );
for j = 1:length(v)
f = find( results.times_monthly v2(j) – window );
combine2 = combine2 + results.values_monthly(f) – mean(results.values_monthly(f));
end
combine2 = combine2 / length(v);
level_test(k) = mean( combine2( end/2 – 12*near:end/2-1 ) ) – mean( combine2( end/2 + 1:end/2+12*near ) );
end
prob = sum( level_test > level ) / loops;
figure
hist( -level_test, -0.4:0.02:0.4 );
set(gca, ‘xlim’, [-0.4, 0.4] );
ylim = get(gca, ‘ylim’);
hold on
plot( -[level, level], ylim, ‘r’, ‘linewidth’, 2 );
set(gca, ‘tickdir’, ‘out’ );
xlabel(‘Temperature Change (\circC)’);
ylabel(‘Monte Carlo Counts’);
title( {‘Monte Carlo Temperature Shift’, ‘Three Random Dates 1850 to 2000’}, ‘fontsize’,12);
fitPlot(gca);
lb = boxedLabel( {‘Random Probability of ‘,[‘Apparent Shift: ‘ sprintf( ‘%0.2f%%’, prob*100 )]}, ‘northwest’ );
set(lb, ‘edgecolor’, [1,1,1]);
Tommorow is my day at Berkeley. So I will ask Robert for his copy of the data that he got from Gao and for the rest of his code.
It is probably a matter of confusion on my part but if one goes to the readme-gao for volcanic sulfates as estimated from ice cores there is a table that gives the forcing data by month, latitude and altitude that would seem to be a ready-made starting place for the BEST model. Was that information incorporated into the BEST model?
ftp://ftp.ncdc.noaa.gov/pub/da…..08ivi2.txt
###############
Zeke covers this above. We looked at several sources
I supplied Ar5 data and Noaa paleo. as zeke says
As far as volcanoes go, we had both annual hemispheric and monthly gridded series. There were some discrepencies between the two, and I believe we just went with the annual series for the analysis.
Gao Annual: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
Gao Monthly: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
Seriously? Your argument is that correlation is causation? Your claim is that a simple regression analysis is all that we need to explain most of the variation in climate? And you find my science lacking? Really?
Next, I did not “walk away smugly†after “noting†that the models get it wrong. After showing, not noting but showing that they got it wrong, I advanced a hypothesis as to why they were wrong, and supported it with data. My hypothesis is that the models overestimate the temperature change caused by volcanoes because the real climate responds, and responds strongly, to changes in temperature … as I linked above.
Regarding your Monte Carlo analysis, I had asked for the details of your analysis. Saying you have done a “Monte Carlo†analysis is as meaningful as saying you have done a “statistical†analysis. The devil is in the details, which is why I asked you for the data and the code that you used. You didn’t answer me, as is your habit.
#########################
sorry Willis, but you seem to have missed the point of the post.
The point was simply this. You offered two methods of how not to find a volcano. Toto showed one interesting way. Robert shows another interesting way. In the end my point is this. You didn’t try very hard, in fact you tried hard not to find an answer.
Robert’s code is posted. I’d much rather it be put into SVN with the other code but that’s a much longer project that we are working on so that I don’t have to post code I just have to give the public SVN access. That way you won’t have to work through removing berkeley dependencies.
I have a minor bone to pick with Steven Mosher when he told me categorically that BEST uses no meta data. The fourth excerpt from the link above would indicate to me that they do.
“We also split records when there was a gap in record continuity greater than 1 year in duration, and at times when changes in station location or time of observation were documented.â€
################
noted Kenneth. I’m presently working on the data paper, so I’ll clarify that for you. I think the paper as written may be in error.
Station location would cause a split, but not by the “scalpel” That would most likely happen as a result of the merge process.
Willis.
“Seriously? Your argument is that correlation is causation? Your claim is that a simple regression analysis is all that we need to explain most of the variation in climate? And you find my science lacking? Really?”
Err no. The laws of physics provides the causation.
As you have argued elsewhere C02 will warm the planet and volcanoes will cool the planet.
How much? Well one simple way to see is to ask your yourself if you can “explain” the temperature record using those two variables.
Turns out, you can.
“Because of the simultaneous eruption and El NiËœno, the
climatic system felt the impacts of both, and it was difficult
to separate their effects on temperature. Normally a
large eruption like this would cool the global climate, especially
in the summer, but during the first year after the El
Chich´on eruption, no large cooling was observed, as the
El NiËœno produced large compensating warming. Studies of
these effects using climate models have improved understanding
of the climate system and increased confidence in
projections of global warming from anthropogenic greenhouse
gases, which are made with the same models.
The climatic effects also included winter warming of
Northern Hemisphere continents in 1982–1983, with the
temperature over North America, Europe, and Siberia much
higher than normal.
During the same winter, it was colder
than normal over Alaska, Greenland, the Middle East, and
China.
The volcanic aerosols in the stratosphere produced
heating, which changed the atmospheric wind patterns, to
one we now call the positive phase of the Arctic Oscillation”
http://climate.envsci.rutgers.edu/pdf/EGECElChichon.pdf
BEST NH data: http://i50.tinypic.com/ieoy1h.jpg
So … BEST found cooling for El Chichon?
Willis, the cites in the paper may help you
Gao, C., A. Robock, C. Ammann, 2008: Volcanic forcing of climate over the past 1500
513 years: An improved ice-core-based index for climate models. J. Geophys. Res.,
514 113, D23111, doi:10.1029/2008JD010239. Data available at
515 ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txt
The other dataset used as was mentioned on the previous thread is
here
http://data.giss.nasa.gov/modelforce/strataer/
Bruce:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txtftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txt.
Let me pull the data for 1982.
Stratospheric sulfate injection = 0.
1981 0.00000 0.00000 0.00000
1982 0.00000 0.00000 0.00000
1983 0.00000 0.00000 0.00000
So, we would show no cooling.
“On March 29th, April 3rd and April 4th, 1982, the El
Chich´on volcano in Southern Mexico erupted, injecting
about 7 million metric tonnes of sulfur dioxide (SO2) and
20 million metric tonnes total of particulate material into
the stratosphere.”
“El Chichon and Mt Pinatubo are the two largest eruption clouds measured by TOMS, but over 100 other eruption clouds have also been measured. The final explosive eruptions from El Chichon and Mt. Pinatubo produced approximately seven and twenty million tons of SO2 respectively, as measured by TOMS.”
And I’d love to “see the Monte Carloâ€, but since you haven’t made the code available, and have given only a very vague description of what you did, I can’t. Shame on you, and in fact, double shame on you, you are the man behind “free the data, free the codeâ€, and in this case you have provided neither one.
#################
Data is reference in the paper with a URL. I guess you missed that.
Code is posted for you. Hope that helps.
Opps sorry bruce.
You also have to look at the sato data
http://data.giss.nasa.gov/modelforce/strataer/
show that would indicate a slight cooling.
Willis:
“The “variable†he is referring to is not the sulfate injections you link to. It is the volcanic forcing resulting from those injections … and unfortunately, despite your best efforts, we still don’t have that data. Yes, I now have your link to the record of stratospheric sulfate injections in Tg … but regressing that against the temperature shows an R^2 of 0.03 …”
The R^2 will of course be small. Take my toy example where I combine noisy weather with a deterministic volcano signal.
What a regression will show you is that the variable is significant while the explained variance is small.. can you see why?
note all those years where there is no volcano signal but there is still noise. Even with the volcano signal set to the standard deviation of the weather noise, the R^2 are small. as they should be. But the variable is significant.
Steven Mosher (#101435)
As someone earlier pointed out, there is a readme file which notes that the Gao file which you mention as a source is deficient:”In particular, the 1982 El Chichón eruption is missing from our record, and should be added to the NH time series, with a loading of about 14 Tg H2SO4. ”
14 Tg would place it fourth in the modern (post-1850) list according to Gao et al. behind the three plotted in the top post (Pinatubo, Krakatau, Agung).
Mosher, I have only stacked three, but so far the >two years post-volcano temperature is greater than the years before the eruption.
There is no real change in temperature with volcanoes; what I believe is an absolute requirement of any temperature reconstruction.
If you can see a drop following a known incident causing cooling, then just what the hell are you looking at.
It will be interesting of the Watt et al., picked stations show a volcanic induced cooling.
Steven Mosher (Comment #101430)
August 13th, 2012 at 9:38 pm
Long ago I read that and forgot it. It would be a nice test of the scalpel, if one could modify the merge process to avoid doing this, and then see if the scalpel would find these breaks.
BTW you called Bill Illis BillC in an earlier comment. I don’t care, just posting this for posterity. (As if I have control over the handle BillC).
El Chichon clearly shows up in the stratosphere temperatures, as big as Agung but smaller than Pinatubo. The sulfate dataset also shows a 1976 eruption (Augustine?) but there were only smaller VEI 4’s in that year that were not stratospheric.
http://www.metoffice.gov.uk/hadobs/hadat/images/update_images/global_upper_air.png
Sort of echoing Steven here… it’s easy to get a non-detection of an event using a sub-optimally designed analysis algorithm.
Impulsive signals are probably the hardest that way… they are broad band and temporally short-lived, with a dominate period on the order of 1-2 years.
With volcanos, don’t trust GISS to model them correctly, they don’t typically produce much of a change in global forcings, unless they are violent and located near the intertropical convergence zone.
It may also be easier to see them if you combed precipitation indexes together with temperature using an analysis of multiple variance method. I have technical reasons to expect that, but it’d be interesting to look at regardless of my reasons.
If I were doing this, I’d construct a fairly short period time-domain analytic filter (that in real component is in phase, 90° out of phase component is Hilbert transform) with the climate response for both variables using a fairly short time-domain sliding window (and a Hann- or Blackman-weighting-funciton) and see if you get a peak where you expect a peak.
It’d also be interesting to break it down by at least latitude band to see if some bands show a more dominant effect than others.
And finally it’s important to remember that humans live in climate, and we don’t give a sh*t about global mean temperature, what happens to us locally is what matters. It could happen that what happens locally gets affected by volcanic eruptions, but not in a way that coherently produces a global climate change.
That is, averaging over global mean temperature may itself be obscuring a real and important signal. (Mathematically you can have basis functions that describe climate variability that average to zero globally. In most basis function expansions that “span” the solution set, 1/2 of the basis functions do this.)
Steven Mosher some of your links above are not working for me.
Muller on NPR right now (10AM ET, per my local station), national show with Diane Rehm show, pretty extensive interview with Q&A
Steven Mosher (Comment #101437)
August 13th, 2012 at 10:22 pm
It certainly would help … if I knew where it was posted. I searched all through the code that’s posted on the BEST website, but I couldn’t find any monte carlo analysis of the volcano results, although it’s possible I missed it, there’s lots and lots of lines of code there.
So perhaps you could post a link to your monte carlo code, and if it is buried in thousands of lines of code, the chapter and verse where I can find it, rather than a handwaving assertion that it is posted somewhere?
And let me say again that your cryptic, two-sentence style of reply does not redound to your credit. Clear links, with page numbers if necessary, beat vague claims any time.
w.
Willis,
http://rankexploits.com/musings/2012/on-volcanoes-and-their-climate-response/#comment-101425
Re: Carrick (Comment #101446)
Willis has a new post at WUWT that shows, rather dramatically, the difference between the forcing GISS attributes to volcanos, and the “forcing” one can infer from the BEST temperature record. It’s an order of magnitude.
Several of us have noticed this before: the W/m^2 of “radiative forcing” that GISS assigns to volcanic events clearly cannot be treated on the same footing as other forms of radiative forcing. It is not (just) a matter of timescales. It is really not something that can be dealt with by any kind of linear theory. If one takes the GISS figures at face value, then some kind of nonlinearity or saturation effect needs to be invoked to bring those volcanic spikes into agreement with the temperature record.
I find it perplexing that this should be so obvious to all of us “amateurs,” yet (to the best of my knowledge) no “real” climate scientist has ever commented on it or even acknowledge that the problem exists…
kenneth. do what i did. I read the paper. I went to the footnotes
and I clicked on the link. how fricking hard can that be
Thanks carrick.
i want to folks to do a thought experiment. combine a long monthly series with mean 0 and SD 1. Add to that a long series that is zero everywhere, but take on a value of 3 at a few points in time. Now do a regression. tell me what you find and explain why.
“To do that we use the temperature series to create a distribution of all 3 year periods. Then we perform a monte carlo and randomly select points in time and generate the probability of seeing the kind of shift we see in the data. In both cases the shift in temperature seen after a volcano doesn’t happen by chance.”
The above excerpt from the introduction to this thread mentions randomly selecting points in time for the monte carlo calculation. If point E depends on the preceding point D and perhaps preceding points C, B and A, would not selecting random individual points break this dependency and present a false monte carlo picture? Perhaps this was discussed or alluded to above.
Maybe I do not recognize that consecutive points in the series were taken together. How about a bootstrap calculation using random selections of data representing 3 years worth of consecutive data? I might even attempt that one myself.
Willis.
The Monte carlo code for this post is exactly where it should be.
connected to this post.
and the data, well check the footnotes to the paper. duh.
Hopefully later to day I might get a package put together of the code run for the paper. but for this post, the code as run is above
Kenneth.
The point of the exercise is this post was not to design an optimal volcano detector. the point was to show how Willis’ method of averaging years before and avergaing years after can be improved.
Simply, if your wedded to looking at things willis way we suggest an improvement. And you can design your own monte carlo to test it.
Lets be clear. the paper uses regression. That’s probably what we should be discussing. However, since Willis introduced two hokey methods. dipology and averaging the months before and after.
this post shows TWO things
A. dipology wont work
B. if your going to average as willis suggested, pick a better approach.
Steven Mosher (Comment #101427)
August 13th, 2012 at 9:22 pm
“ftp://ftp.ncdc.noaa.gov/pub/da…..08ivi2.txt
###############
Zeke covers this above. We looked at several sources
I supplied Ar5 data and Noaa paleo. as zeke says
As far as volcanoes go, we had both annual hemispheric and monthly gridded series. There were some discrepencies between the two, and I believe we just went with the annual series for the analysis.
Gao Annual: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
Gao Monthly: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt”
Steven Mosher none of these links work for me. How difficult would it be for you to go back and click on them and if they do not work for you, fixing them or if they do work for you letting me know that it must be a problem at my end?
Lately you seem to be very put off by people asking for details on subjects that you have brought up and you appear to want to make some kind of statement beyond the technical discussion at hand.
Mosh, I can’t even see the damn volcanoes using a CUSUM plot
http://en.wikipedia.org/wiki/CUSUM
Steven Mosher (Comment #101461)
Steven I am not discussing the Willis approach. I am discussing the approach described in this thread.
As far as the regression approach is concerned it appears to be based on an admittedly over simplified model given the existing literature of the climatic effects of volcanoes. Further I was very concerned about the statement that the selection of the half life for the volcanic effects was based on what gave the best fit to temperature. That is not good statistical practice and should automatically invoke some sensitivity tests that show the results of using other selected half lives.
Mosher,
Check yourself.
Kenneth the cite is in the footnotes.
Do what I did. read the paper. go to the citations. see the citation.
click the citation. Your browser should open as mine just did
and bring you directly to the data.
check with your ISP if you are having trouble. tech support is 100 bucks. I know, I’ve just spent two days fixing a NIC card before I cried uncle and paid them
Willis, the cites in the paper may help you
Gao, C., A. Robock, C. Ammann, 2008: Volcanic forcing of climate over the past 1500
513 years: An improved ice-core-based index for climate models. J. Geophys. Res.,
1: Year (A.D.)
2: NH stratospheric sulfate aerosol injection (Tg)
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Steven Mosher (Comment #101468),
Did you really need to flood the page with that shit?
Works just fine for me Doc.
read the paper. read the footnotes. click the link.
not rocket science
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txt
or if you are too lazy click on the link I gave to bruce. That works as well.
Then, forget to read the readme, forget what Zeke and I told you the other day about the Sato data. Forget the fact that I’ve told you I’m going to try to get it all in one neat little file so that you can take the data, do some work, and never share back.
As for CUMSUM. Let me suggest that you FIRST test whether that tool can detect the signal. make yourself a toy world. use truth data and see if CUMSUM can do what you are asking it to do.
Skeptikal (Comment #101469)
August 14th, 2012 at 1:40 pm
Steven Mosher (Comment #101468),
Did you really need to flood the page with that shit?
###############
If people cant read the paper, read the footnotes and click the link as I’ve suggested, then I see no other way right now of helping them out. Unless you want me to open an account to rehost the data for them because they refuse to read the paper, read the footnotes and click on the link. I’ll probably end up doing that, but not this morning. too many other things to work on
BillC (Comment #101444)
August 14th, 2012 at 7:23 am
Steven Mosher (Comment #101430)
August 13th, 2012 at 9:38 pm
I’m presently working on the data paper, so I’ll clarify that for you. I think the paper as written may be in error.
Station location would cause a split, but not by the “scalpel†That would most likely happen as a result of the merge process.
Long ago I read that and forgot it. It would be a nice test of the scalpel, if one could modify the merge process to avoid doing this, and then see if the scalpel would find these breaks.
######################
yes in fact that question has come up and I think we may be working on it. The merge process is the most complicated aspect of all of this and filled with pitfalls from a programming and assumptions standpoint.
The first link never worked for me until I edited it a lot. The link in comment 101470 did work.
But since El Chichon is missing and it is only annual values, I saw no point in wasting my time with it.
As far as the regression approach is concerned it appears to be based on an admittedly over simplified model given the existing literature of the climatic effects of volcanoes. Further I was very concerned about the statement that the selection of the half life for the volcanic effects was based on what gave the best fit to temperature. That is not good statistical practice and should automatically invoke some sensitivity tests that show the results of using other selected half lives.
############################
I will have to check with Robert and Richard about their exact technique. A first principles approach ( GCMs) gives you an e folding time that is pretty short. As Willis has shown probably too short. Another way to look at it is what do you have to assume about e folding time to maximize the fit. One approach is bottoms up. The other approach is top down. In the scope of this paper I dont think they had space to show all the various fits they tried, but they tried multiple fits. That’s part of the reason why I would not lean too heavily on the conclusions as Muller does. It goes as far as it goes. Theory gives us a functional form for the expected effect. exponential decay. Theory gives us some guesses for initial values for the peak and the falloff. The fit gives you an estimate made from information in the data. The probalem is obviously more complex than a two variable solution, but what is shown is that a two variable solution explains a good portion of the data. Nothing more, nothing less. I don’t happen to agree with how far muller pushes it. Neither did Judith. But I recognize it for what it is. As I’ve said before for me is more like EDA. Nothing more nothing less. And the point about Willis’s approach is very germane in that context. His EDA is aimed at not finding anything. That much, if you are honest, you must agree with.
That is, if theory tells you that the effect is small relative to the noise, if your math sense tells you that R^2 will be small ( cause the volcano signal is 0 80% of the time) what do you make of an approach like Willis used and what do you make of discussions about R^2.
In fact I’ve got a a few nice graphs. Its simple.
create a volcano series. 7 volcanos in 100 years.
with a 36 month fall off
decay <-function(a,rate){
timeSeries <- rep(0,35)
for( i in 1:35){
timeSeries[i]<-a*exp(1)^(rate*i)
}
return(timeSeries)
}
set.seed(1)
Months <- 1200
occurances <- 7
Eruptions <- sample.int(Months-36, occurances, replace = FALSE)
Volcano <- rep(0, Months)
Volcano[Eruptions]<-1
decrease <- decay(1,-.2)
for(i in 1:length(Eruptions)){
print(Eruptions[i])
Volcano[Eruptions[i]:(Eruptions[i]+34)]<-decrease
}
Volcano <- ts(-Volcano, start = 1800,frequency = 12)
plot(Volcano, main = "Volcano")
Baseline <- ts(rnorm(Months,mean = 0, sd =1), start =1800, frequency = 12)
plot(Baseline, main = "Baseline")
Combined <- Baseline+Volcano
plot(Combined,col ="grey", main = "Final Temperature 7 Volcano")
lines(Volcano,col="red",lwd=4)
Model |t|)
(Intercept) 0.9075511 1.8556044 0.489 0.624870
time(Volcano) -0.0005049 0.0010030 -0.503 0.614813
Volcano 0.9784126 0.2946635 3.320 0.000926 ***
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.003 on 1197 degrees of freedom
Multiple R-squared: 0.009403, Adjusted R-squared: 0.007747
F-statistic: 5.681 on 2 and 1197 DF, p-value: 0.003503
Lousy r^2 just as you expect. has to be lousy.
Now do that 1000 times
Est<- numeric(length = 1000)
for(test in 1:1000){
Truth <- ts(rnorm(Months,mean = 0, sd =1), start =1800, frequency = 12)
Combined <- Truth+Volcano
Model <- lm(Combined~time(Volcano)+Volcano)
Est[test]<-Model$coefficients[3]
}
plot(density(Est), main = "Estimate of Volcanic Effect")
summary(Est)
summary(Est)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.01439 0.78920 0.99170 1.00100 1.19200 2.08300
Re:
Steven Mosher (Comment #101425)
August 13th, 2012 at 9:13 pm
Mosh,
Thanks (sincerely) for this, but…
(1) I clarified to Willis that I really didn’t need a copy of the code, because i thought it was obvious what you (or Robert) had done. Your code confirms it.
(2) I was pointing out that you were adding a provocative argument. Having stepped through the code which you helpfully provided, this is still apparent. You should have set up a stat model (ARMA) based on the observed auto-correlation in the temperature series, and then generated for each volcano the MC distribution of expected responses for each volcano, based on the observed temperature history for each volcano prior to eruption. You can then MC sample from the 3 (or 4) distributions for your aggregate reaction.
(3) Do I care a lot about my point in (2) above? No, not a lot. I am sure that the most rigorous tests would still show a cooling reaction from volcanoes.
(4) I am more concerned about the totally KEERRAPP fit of an MLR model to the level temperature series despite all of the red stop lights saying that you have a spurious regression, and that the residual series has loads of statistical structure – autocorrelation, heteroscadisticty and cyclic structure.
(5) You mentioned that Robert was going to provide his code. Again, I don’t need his code to duplicate the trivial regressions produced. What I would dearly like to see is any and every justification provided by David Brillinger for this piece of garbage. He was thanked in the acknowledgments section of the paper. He used to be a heavyweight in this area and should certainly be able to understand the specific issues related to spurious correlation here. Is he actually standing behind the conclusions from this paper????
Mosh, CUSUM, in chart form, is used all the time to find the initiation of signal. It is a rather nice method to sort signal from noise.
I can see you have been having a hard time of it today.
Mosher’s links in #101427 (and other comments) are bad. I have no idea why he would get snitty with people for pointing out the links he gave were broken. He says if people aren’t willing to go find the data themselves, he can “see no other way right now of helping them out.”
I have a simple way for him. Learn to post links that work. When people point out your links don’t work, acknowledge it and post the right links.
Or, I guess he can just throw a fit every time he makes a mistake and say it’s everyone else’s fault.
Mosher in the post: “In the paper, what a regression was done to see if the volcanos “explained†the data. They did.”
Your regression is detecting a volcanic signal but is Willis right that the signal is far weaker than expected from the forcing values?
Or as julio comments above:
“Willis has a new post at WUWT that shows, rather dramatically, the difference between the forcing GISS attributes to volcanos, and the “forcing†one can infer from the BEST temperature record. It’s an order of magnitude.”
http://rankexploits.com/musings/2012/on-volcanoes-and-their-climate-response/#comment-101456
Do you think that your regression in the paper shows that the volcanos “explain” the temperature data in the sense that the magnitude of the temperature response is as expected? Do the the volcanos “explain” the temperature data if the response is much weaker than expected from the W/m2 change and you have to chose an odd extended half life for the volcanic effect to achieve the fit.
By the way, Mosher shouldn’t be blamed too much for his links not working. They got broken because of something WordPress does. Compare these two lines:
ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
ftp://ftp.ncdc.noaa.gov/pub/1-2000.txt
If I did that right, the first will be broken while the second works.
Edit: Yeah, that shows what happened. Because of the ellipsis in the text he assigned the link to, WordPress* borked and screwed up the link itself. He shouldn’t be blamed for that. His attitude on the other hand…
Steven Mosher you appear to react lately like one who has (too) much on their plate. I would not be ascribing laziness to people who are simply attempting to learn from you and obtain the details they need to better accomplish that task. You appear to come across, to me anyway, as one who has put a lot of time and effort into these analyses and thus you expect the same of others. Think of the process as analogous to having a paper reviewed. You are the expert and the paper’s author and when the reviewers ask you for more detail you are going to be more than happy to provide it because that is how the system (should) works. You are not going to tell them not to be lazy and then give some vague or circuitous route to the information requested. Be a Ryan O’Donnell to us Eric Steigs out there – as in the review and not the blog battles.
Zeke, Mosh,
I have now written privately to Professor Brillinger to ask him where he stands on certain issues. He sits in the (rather large) population of people who could easily convince me that I am behind the times on statistical theory in general or time series analysis in particular.
Despite all my adverse comments, I will repeat my congratulations to both of you for a worthwhile effort on producing your very best attempts at an objective interpretation of the instrumental series.
P.S I still thin the attribution argument is KERRAPP
“By the way, Mosher shouldn’t be blamed too much for his links not working. They got broken because of something WordPress does. Compare these two lines:”
I would assume that the links would be as broken for Steven as they were for me.
Kenneth Fritsch, no doubt. Mosher’s responses aren’t justified by the fact his links getting broken was caused by a bug. He could have easily gone back and tried them. Once he did, even if he couldn’t figure out why his links got broken, he’d at least know not to be snitty with people because of it.
Just to clarify about the links and WordPress…
WordPress automatically creates links if you enter a string which looks like a URL. Usually, the text which is associated, is the actual URL. Example: http://rankexploits.com
.
But WP abbreviates the link and inserts an ellipsis in the text if the URL is exceptionally long. Example:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2totalloading501-2000.txt
.
The link above works just fine. But if you copy-and-paste that section, you get the text with the ellipsis, not the entire URL. It may look the same, but it’s a busted link.
.
Zeke posted good links in #101293. Mosher evidently tried copy-and-paste of those links in #101427, and that produced busted links. In #101470 (for example) he entered the whole URL and that link is good.
HaroldW, while what you describe is true, it’s not the case here. As I said, it’s a bug. To test this, try placing the correct URL with the same text Mosher used. When I do, I get this:
ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
Despite putting the correct link in in the href tag, I get a broken link. It’s not due to anything I’ve done wrong. It’s due to a bug in WordPress.
Berkeley needs to compare their volcanic impacts to their own high-resolution temperature data to see if it is actually valid. If temperatures fall in 1781 and 1782, it is not caused by Laki in 1783. If temperatures rise from a low point in 1808 to a high point in 1809 and 1810, the 1809 eruption did not cause a temperature decline in 1809 and 1810. El Chichon needs to be in the dataset as well as Novarupta in 1912 which was a significant eruption.
And Berkeley also needs to double-check their data against other known temperature series. For some reason, the algorithm produces significantly higher warming rates than other series.
I feel as if there is an over-confidence problem here.
well good news and bad news
good news. i habe a copy of the gao data cimplete with the changes detailed
in his paper. i alsi will have the coeffs
for the regresion.
bad news. the current code posted
doesnt have all the routines needed. so we will meed to update that. robert estimstes two weeks including test.
basically we have to test that the entire
system will work for people. we had
planned opening svn to the public. now we will take some
time to just create a tarball and see what kind of
support issue that causes.
phone posting. so data will go up later after i get back home and find a good hosting service.
bill el chicon figures are in the gao paper and have to be added
by hand. posting later
i predict this contest will end with both Mosh and Willis pissing in the cistern. In the meantime, Paul K has drilled a hole in the bottom of the cistern without either of them noticing.
Paul_K,
I agree with your assessment of the attribution part of the paper; really not very good, and it only detracts from the part that is good. As to the volcanoes… do they cool? Well, sure. So, is that really something new? I don’t think it is. An analysis that shows how much (with some confidence) volcanoes cool would be interesting.
SteveF,
“An analysis that shows how much (with some confidence) volcanoes cool would be interesting.”
The paper states, “We observe a response of -1.5 ± 0.5 ºC per 100 Tg of atmospheric sulfate emitted.”
So what then are you looking for?
Maybe SteveF means an analysis, in which the highly educated and highly intelligent, Steve F, has some confidence.
Follow me, Harold?
kenneth.
“think of the process as analogous to having a paper reviewed. You are the expert and the paper’s author and when the reviewers ask you for more detail you are going to be more than happy to provide it because that is how the system (should) works. ”
you fundamentally misunderstand my position and role.
I’m basically your go-fer. I go fer things that you cant get on your own.
https://docs.google.com/spreadsheet/ccc?key=0AtIIrBCUsRhIdEpqXzlFMkM0Rm5ubGFuSVB0My0zMEE
Let me know if you have any trouble getting it as my network card has been acting up for the past 3 days. If this doesnt work for you then I will find another way to share it.
@Brandon Shollenberger (Comment #101480)
August 14th, 2012 at 3:00 pm
Edit: Yeah, that shows what happened. Because of the ellipsis in the text he assigned the link to, WordPress* borked and screwed up the link itself. He shouldn’t be blamed for that. His attitude on the other hand…
His attitude is the same it always was. People just don’t like it when they are on the receiving end rather than climate scientists.
(5) You mentioned that Robert was going to provide his code. Again, I don’t need his code to duplicate the trivial regressions produced. What I would dearly like to see is any and every justification provided by David Brillinger for this piece of garbage. He was thanked in the acknowledgments section of the paper. He used to be a heavyweight in this area and should certainly be able to understand the specific issues related to spurious correlation here. Is he actually standing behind the conclusions from this paper????
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I suppose it would depend if you are talking about the “conclusions” in the press or the description of what was done in the paper. For me, the analysis is an interesting approach to the data. Hardly conclusive proof of attribution, in fact I dont think you can prove attribution this way. There are a bunch of ways to criticize the approach, I don’t think Willis’ were very strong as they tend to lead people to believe that volcanos have no effect.
Conversely, I dont think the approach used in the paper settles any matter about the effect, its another way of coming at a estimate.
Not perfect of course, but better than averaging the years before and after or even stacking the years as we did in this simple approach. So for me its an entirely different question. Attribution isnt even on the table. The question is what ways can you estimate.. pros and cons. You try an approach, describe that, note its weaknesses and suggest something better. If you have a worse suggestion I’m going to point that out and suggest a way to improve your bad method. If you have a better suggestion, then I’ll listen and look at that. Not that hard really in my view of things once you take the attribution question off the table.
The spurious correlation is an permanent problem. It builds confidence however if you select variables that theory tells you should be causally related to the dependent variable. In fact its our causal understanding that tells us about the spurious correlation problem to begin with. without a causal understanding we would not even recognize spurious correlation.
HaroldW (Comment #101500)
August 14th, 2012 at 7:51 pm
SteveF,
“An analysis that shows how much (with some confidence) volcanoes cool would be interesting.â€
The paper states, “We observe a response of -1.5 ± 0.5 ºC per 100 Tg of atmospheric sulfate emitted.â€
So what then are you looking for?
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I hope not a link to the paper.
hey bugs do me a favor and click the link I posted in this comment
http://rankexploits.com/musings/2012/on-volcanoes-and-their-climate-response/#comment-101502
let me know if that works.
Here’s an open link to Steve’s file “Forcing Comparisons”.
Plenty of SOX and NOX being emitted from power plants. Can you remove the heat input signal of the exhaust gasses and warming effects of the Co2 and NOX exiting the stack and see if there is a net cooling effect around the area of the plant caused by the SOX only?
thanks carrick.
guys you can use the link carrick provided. otherwise click on my link and I’ll give you permissions.
cyclone, I think this is related to your question. Let me know if it doesn’t help.
Carrick
Re: Steven Mosher (Comment #101504)
August 14th, 2012 at 9:47 pm
Mosh,
Abstract from Muller’s NYT Op-ed:
“Our results show that the average temperature of the earth’s land has risen by two and a half degrees Fahrenheit over the past 250 years, including an increase of one and a half degrees over the most recent 50 years. Moreover, it appears likely that essentially all of this increase results from the human emission of greenhouse gases.
These findings are stronger than those of the Intergovernmental Panel on Climate Change, the United Nations group that defines the scientific and diplomatic consensus on global warming….”
Evidently Richard Muller sees no problem with using this approach for attribution – to the extent of a massive challenge to the orthodoxy.
The actual paper itself is only slightly more nuanced. By implicitly assuming the validity of its statistical model, the paper permits Muller to draw the conclusions on attribution that he has.
I do not have a serious problem with the empirical methodology applied to fit the volcano temperature response. Equally, if the paper had restricted itself to analyzing the lag between a detrended land series and the AMO, I would be quietly admiring the result. It could even have gone one step further for me, and written something like:- “We have fitted a simple linear regression model to (a function representing temp response to) volcanoes and log(CO2). This is included merely to forestall the argument that such a correlation does not exist. The authors make no claim with respect to the abstraction of any useful information from such regression, given the structural diffences between the datasets, and the difficulty of eliminating the likelihood of spurious regression and lurking variables.”
Instead of which, the paper sets out a statistical model, assumes its statistical validity, and tests the significance of other independent variables against that model with irresponsible abandon.
You also wrote, Mosh:-
“The spurious correlation is an (sic) permanent problem. It builds confidence however if you select variables that theory tells you should be causally related to the dependent variable. In fact its our causal understanding that tells us about the spurious correlation problem to begin with. without a causal understanding we would not even recognize spurious correlation.”
Since the 1980’s, there have been some excellent tools developed which provide objective tests to avoid the problem of spurious correlation. The problem with your ad hoc approach is that it will always give self-fulfilling confirmation. Take any two time series which have a generally positive rising trend in time. You think that one is controlling the other. You run a linear regression to confirm, and bingo, you find a high degree of correlation between them. This then confirms your conviction with respect to causality. But is it true? The following landmark paper is a good place to start:-
http://www.uta.edu/faculty/crowder/papers/Engle_Granger_1987.pdf
Paul
“Carrick (Comment #101510)
August 15th, 2012 at 1:03 am
cyclone, I think this is related to your question. Let me know if it doesn’t help.
Carrick”
Somewhat……. But do the same for SOX and not for Co2. However,in the Co2 experiment did they remove the cooling signature of the Sox that was present?
Mosher, I used the spreadsheet linked to by Carrick. The formula is the correct regression result but it produces a flatter fit than the data presented in the “Fit” column. It is lower by 0.8C in 2011.
In addition, the coefficient for CO2 produces an instantaneous 3.09C per doubling so something needs to be looked at.
Don Monfort, HarroldW,
I should have been more clear. I wanted to say an analysis which relates volcanic cooling to climate sensitivity. It has been noted by many that ENSO seems to shift to an El Nino phase following a major eruption, which minimizes the effect of aerosols on average surface temperature. Is this effect real? I don’t know, but it would seem to be important in analyzing the effect of radiative forcing on average surface temperature. I think that most published work on the energy balance following a major volcano is speculative, since there is no good estimate of how the ocean heat content changes due to the aerosol forcing. It will be the next major volcano (comparable to Pinatubo) that settles the question… assuming ARGO is still collecting data and satellites and ground sensors are still able to collect reasonably accurate data on albedo and solar obscuration. Of course, nobody knows when the next Pinatubo might take place.
.
With regard to relating Ln(CO2) to the temperature history: It ignores the influence of other well mixed GHG’s, land use changes, and man-made aerosol effects (direct and indirect), all of which are known or suspected to be important. Indeed, a wide range of assumed aerosol effects are routinely used to explain how the temperature history is consistent with GCM diagnosed climate sensitivity (anywhere from 2 to 4.5 C per doubling!), and with observed ocean heat uptake vs. GHG forcing. I just don’t see that an analysis which attributes the temperature history to Ln(CO2) alone is in any way informative. The paper would be much better if the entire attribution effort were removed.
Mmmmm, pretty tough crowd here lately. I think this in-depth analysis from several different perspectives is refreshing. Perhaps The Blackboard will become the de facto Peer Review process for climate science papers moving forward.
SteveF –
Thanks for the clarification. I’m also uncomfortable with mere linear regression of average temperature as attribution. It’s suggestive, certainly, but the climatic system is far too complex to label all other factors as “noise” uncorrelated with whatever causative agent is being considered.
I bet a neat contribution that BEST could add would be a non-model based version of the “20th century AMO vs. anthro aerosols” argument. Given the long time series.
Okay, I figured out why Mosher’s formula in the spreadsheet is not working. It should be based on “ln” rather than “log”. Works okay after that.
If you use monthly data rather than 12 month moving averages, the volcanic influence now reverses to a small positive rather than a -1.5C per 100 Tg negative.
Stephen Mosher or Zeke, I have been doing some monte carlo/ boot strap calculations on the BEST temperature data attempting to determine the probability of obtaining by chance the results you did by stacking the periods before and after a volcanic event. What is not clear to me (and perhaps it will be after I look at the code provided) whether you pulled 36 month periods randomly but as consecutive months or whether you pulled 36 months randomly. I also am not clear on your criteria used in your histogram plots for a success or failure. Obviously you used a lowering of the mean temperature in the 3 years before and after the volcanic event, but were there any further criteria like a reversion to the mean for the 3 to 6 year period after the event back towards the 3 year period prior to the event.
I have proven to myself that using random 36 consecutive month periods gives a very different result than using 36 randomly selected months.
Kenneth,
Autocorrelation?
BillC,
“I bet a neat contribution that BEST could add would be a non-model based version of the “20th century AMO vs. anthro aerosols†argument.”
Maybe. But first, they need to get rid of the new-style hockey-stick. The fit after 1959 (the Mauna Loa data, I presume) aliases a chunk of the upturning AMO cycle into a CO2 response. Pre-1959, the model fit cuts off the highs and lows of the AMO. This is clearly visible in Figs 5 and 6. Post-1959, the AMO conveniently stops (?) for the modellers, and the model fit tracks and then overshoots the actual temperature.
BillC (Comment #101523)
Probably auto correlation and deterministic trends in the data are the major factors, but I have not done the analysis.
Paul_K,
What about prediction/extrapolation using the MLR fit? Say, re-run the fit to 1959. It won’t help with the unit root and cycles, but might give a back of the envelope on the overshoot. I’m thinking of using their volcano fit per the spreadsheet Carrick posted. Will it predict Chichon and Pinatubo? How about the overall warming post 1960?
Evidently Richard Muller sees no problem with using this approach for attribution – to the extent of a massive challenge to the orthodoxy.
The actual paper itself is only slightly more nuanced. By implicitly assuming the validity of its statistical model, the paper permits Muller to draw the conclusions on attribution that he has.
##############################################
Well, Suffice it to say that more nuance was suggested. I would expect reviwers to suggest either more nuance or expansion.
In the end Muller, I suppose, would refer to the statistician who said that all statistics is really EDA and you have to pick a model and defend it.
“I do not have a serious problem with the empirical methodology applied to fit the volcano temperature response. Equally, if the paper had restricted itself to analyzing the lag between a detrended land series and the AMO, I would be quietly admiring the result. ”
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quiet admiration is what I live for. that way the discussion can be drowned out by dipologists and then you can practice quiet acquiesence. Steve called that silence of the lambs
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It could even have gone one step further for me, and written something like:- “We have fitted a simple linear regression model to (a function representing temp response to) volcanoes and log(CO2). This is included merely to forestall the argument that such a correlation does not exist. The authors make no claim with respect to the abstraction of any useful information from such regression, given the structural diffences between the datasets, and the difficulty of eliminating the likelihood of spurious regression and lurking variables.â€
however there is useful information. basically an empirical bound on effect size and effect duration. Someone, say hansen, who wants to argue that the effect duration last longer than 3 years would have some explaining to do.
Did that: that is, used Carrick’s spreadsheet to run the regression up to (actually) 1959, when the MLO data starts.
BEST’s fit using all the data is T=8.34 + 4.47*CO2 – 0.015*Volcano
My fit using all data until 1959 is T=8.36 + 4.86*CO2 – 0.015*Volcano
CO2 and Volcano in above are proxy for the actual data used by BEST (ln CO2/CO20 and sulfate decay model)
It overestimates the trend since 1960 a bit, resulting in an overestimate in 2011 of about 0.12K. Interestingly, it gets the volcanoes “right” according to the full model. But this could be a result of the sulfate “fit”. Would have to run the sulfate fit for the same time period.
I tried going to 1912 and predict the next century. Not so good on CO2, but still good for volcanoes.
Bill Illis (Comment #101514)
August 15th, 2012 at 7:58 am
Mosher, I used the spreadsheet linked to by Carrick. The formula is the correct regression result but it produces a flatter fit than the data presented in the “Fit†column. It is lower by 0.8C in 2011.
In addition, the coefficient for CO2 produces an instantaneous 3.09C per doubling so something needs to be looked at.
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If you do any work that is the result of my volunteer efforts I would appreciate it if you share and share alike or share back.
The whole point of being open with data and methods is to BUILD on what others do. Not take what is shared and hide your work on it.
Once you start to practice sharing back your appreciation for the difficulties created by sharing will be enhanced.
Good Kenneth. Now read this:
If you do any work that is the result of my volunteer efforts I would appreciate it if you share and share alike or share back.
The whole point of being open with data and methods is to BUILD on what others do. Not take what is shared and re hide it.
Once you start to practice sharing back your appreciation for the difficulties created by sharing will be enhanced.
Kenneth:
“Stephen Mosher or Zeke, I have been doing some monte carlo/ boot strap calculations on the BEST temperature data attempting to determine the probability of obtaining by chance the results you did by stacking the periods before and after a volcanic event. What is not clear to me (and perhaps it will be after I look at the code provided) whether you pulled 36 month periods randomly but as consecutive months or whether you pulled 36 months randomly. I also am not clear on your criteria used in your histogram plots for a success or failure. Obviously you used a lowering of the mean temperature in the 3 years before and after the volcanic event, but were there any further criteria like a reversion to the mean for the 3 to 6 year period after the event back towards the 3 year period prior to the event.
I have proven to myself that using random 36 consecutive month periods gives a very different result than using 36 randomly selected months.”
I will have to ask Robert. His task and goal was pretty simple.
If somebody DOESNT WANT TO DO THE REGRESSION, if somebody insists on doing things the way willis did them ( averaging before and after ) can we come up with any improvement on THAT METHOD. not that we suggest that method, we didnt use it in the paper. but if you want to do things his way, How can you improve it ( stack the volcanos ) and then How can you test that easily. For us the regression is the better approach, but if somebody insists on a different approach, how can you improve that. I’m surprised nobody asked the question ” why didnt you also select small volcanos?” That’s an obvious flaw in the approach.
Suffice it to say that if you change the monte carlo and the significance goes down to 75%, then the conclusion will be
The method of looking for the effect by averaging years before and years after doesnt work that well if the volcano effect is small.
HaroldW (Comment #101517)
August 15th, 2012 at 8:34 am
SteveF –
Thanks for the clarification. I’m also uncomfortable with mere linear regression of average temperature as attribution. It’s suggestive, certainly, but the climatic system is far too complex to label all other factors as “noise†uncorrelated with whatever causative agent is being considered.
#####################
That is the fundamental argument that someone like Judith Curry and others (ahem) made against the simplistic approach. However, the physiscists in the discussion were very much in favor of the simpler is better approach. In one way they look at the simple curve and say.. this phenomena is dominated by radiative forcing, the rest is details than other folks can worry themselves about, but the idea that the rise is so complex as to defy explanation is not supported by the data it is only supported by conjecture.
To people who say the rise has nothing to do with GHGs, to people who say the sun explains everything.. well, it would help their case if they had something that showed that in a straightforward fashion. As Muller argues it raises the bar.. FOR THEM. for people who concern themselves about the wiggles to a certain extent they already buy the notion that GHG forcing matters.
Re: wiggles.
CO2 regression coefficient from MLR of BEST data (CO2 + volcanoes, as above) ending the fit in:
1950 5.05
1960 4.86
1970 4.71
1980 4.24
1990 4.78
2000 4.41
2010 4.45
With regard to relating Ln(CO2) to the temperature history: It ignores the influence of other well mixed GHG’s, land use changes, and man-made aerosol effects (direct and indirect), all of which are known or suspected to be important. Indeed, a wide range of assumed aerosol effects are routinely used to explain how the temperature history is consistent with GCM diagnosed climate sensitivity (anywhere from 2 to 4.5 C per doubling!), and with observed ocean heat uptake vs. GHG forcing. I just don’t see that an analysis which attributes the temperature history to Ln(CO2) alone is in any way informative. The paper would be much better if the entire attribution effort were removed.
##################
see page 4 of the spreadsheet. the correlation between C02 and all other forcings is .97.
the argument was made ( ahem) that we should just include all forcings. The counter argument was that using ln(Co2) as a proxy for all forcings was sufficient because of the correlation between ln(C02) and all forcings. in short, the answer didnt change much by making it more complex.
There were other more complicated approaches suggested. One or two might be an intersting project. Here is the key
You’ve got a record that now goes back to 1753 ( NH dominated) with some pretty large error bars and some apparent high amplitude excursions. Is there any useful information in there. It seemed to us that lookinng at how the record tracked with volcanos was a useful exercise. and to get a better look at that signal it made sense to try to detrend the whole series. pulling out the trend due to increased GHG forcing seemed like a interesting approach.
The ln(CO2/CO2orig) coefficient can be restated as the instantaneous CO2 doubling rate.
X.XC per doubling = 4.46*ln(2) = 3.09C per doubling.
So, the coefficient is too high, doesn’t incorporate lags, or the temperature (land) actually increased at a faster rate than would be expected with CO2 doubling.
One could also look at this coefficient as being made up of two terms – the IPPC derivation is
0.81C/W/m2 * 5.35 Ln (CO2/CO2orig) W/m2 = 3/ln(2) * ln(CO2/CO2orig)C = 4.33 * Ln (CO2/CO2orig) * C
4.33 is lower than 4.46
The paper was rejected on technical/methodology grounds by one reviewer [whose views were disregarded, and who was subsequently identified by Ms Muller..] and one of the key authors withdrew her name from the publication because in her considered scientific opinion the conclusions on attribution are not supported by the data and its analysis.
What more is there to ask? Other than: is it OK for the Mullers to have a consulting company that offers advisory services in the field in question? Conflict of interest, anyone?
The rest of the discussion here is about how many fairies you can get on the head of a pin with Mosher defending the indefensible.
I can’t stand stupidity and this what this volcanic cooling talk amounts to. There are several things you first have to teach yourself before you are even qualified to talk about it. The first thing you should understand is the nature and behavior of ENSO. ENSO is a harmonic oscillation of ocean water from side to side in the equatorial Pacific. Trade winds pile up warm water in the Philippines-New Guinea area where it forms the Indo-Pacific Warm Pool. This is on the westward swing of the wave. When it has crested the reverse flow begins along the equatorial countercurrent. This is the El Nino wave and it runs ashore in South America. There it spreads out north and south along the coast, warms the air above, interferes with trade winds, mixes with the westerlies, and we notice the start of an El Nino warm period. But any wave that runs ashore must also retreat. As the El Nino wave falls back water level behind it drops by half a meter or more, cold water from below wells up in its wake, and we notice the start of a cool La Nina period. This has been going on as long as the equatorial current system has existed, which is to say since the Isthmus of Panama rose from the sea. The period of the oscillation is about five years and the amplitude can be around half a degree or so. Which means that the entire recorded temperature curve is made up of a succession of these El Nino peaks. They are not completely regular because other things in the ocean can interfere. If the interference is severe enough to block an El Nino wave on its way to South America entirely it will spread out in the middle of the ocean, warm the air as it would near he coast, and create an El Nino on the spot. This is called an El Nino Modoki or Central Pacific El Nino and will complicate temperature records. What is important for volcano effects is this: ENSO oscillations cause periodic cooling on roughly five year schedule as La Ninas appear. Volcanoes are alleged to cause similar cooling after each eruption. Question: how does volcanic cooling interact with ENSO? Lets say, for example, that an eruption takes place and is followed by a global cooling that peaks two years later. If the eruption coincides with an El Nino peak the cooling it generates should coincide with the La Nina cooling that follows. Will the volcanic cooling and La Nina cooling add? In the opposite case, if the eruption should come at the same time as a La Nina cooling, will its volcanic cooling wipe out the El Nino that follows? We are lucky that by chance two eruptions occurred in the late twentieth century that allow us to answer these questions. First, Mount Pinatubo. It erupted at the peak of the 1990/91 El Nino and was followed by the 1992/93 La Nina. That La Nina looks normal and belongs in the ENSO sequence. But to Self, who studied Pinatubo, writes in “Fire and Mud” that “Pinatubo climate forcing was stronger than the opposite, warming effects of either the El Niño event or anthropogenic greenhouse gases…” This of course is complete nonsense but the assignment stuck. And then comes El Chichon. It happened to erupt at the low point of the 1982 La Nina which was immediately followed by the 1983 El Nino. No cooling from that volcano at all. Self does not understand why but remarks that “…surface cooling is clearly documented after some eruptions, for example Gunung Agung, Bali, but not others like El Chichon, Mexico…” So what should we conclude from this? There is only one logical conclusion that fits: the so-called “volcanic cooling” simply does not exist. All volcanic cooling that has been reported is nothing more than a coincidental match with a La Nina cooling. It can be of various degrees from nothing, as in El Chichon, to a full La Nina, as in Pinatubo. Basically it is a lottery and the time of eruption relative to a local El Nino peak determines whether or not that particular volcano gets any “cooling” assigned to it or how much it is allowed to have. These “coolings,” even Krakatao included, are all segments of La Nina phases of ENSO and that is why I laid the emphasis on knowing your La Ninas. I suspect someone will now want to know about that year without summer that Tambora is supposed to have caused. It is reported to have lowered global temperature by 5 degrees Fahrenheit or 3 degrees Celsius. I checked both Armagh and Central England temperature records and they simply do not show any such temperature lowering. Armagh is quite good at showing ENSO oscilllations that far back and when you zero in on it you find that it shows an El Nino peak in 1815 and no three degree cooling anywhere near it. Apparently that Tambora cooling is a myth and it is not guilty of causing anything like a year without summer. Someone ought to find out what really happened then.
Re: Steven Mosher (Comment #101533)
That’s because, of course, this is the (theoretical) physicist’s basic approach to the world: look for the largest contributor to any particular effect and see how much you can explain based on that alone. This assumes (implicitly or explicitly) that the next-order corrections will be small and/or tend to cancel out (as, in this case, other GHGs and aerosols will tend to cancel out). Also, it is mindful of the fact that adding poorly known data (such as aerosols) to a model does not make the model more accurate.
So far so good. But including volcanoes violates all this logic. They are a small, random effect that does not contribute anything substantial to the trend that you are interested in. If you are going to include something at that level of insignificance, then you have no valid reason to exclude much larger things, such as other GHG’s, or even things like solar variation. And if you are going to implicitly acknowledge that the effect of volcanic aerosols is poorly understood (since they just calculated a regression coefficient, rather than try to use the equivalent forcings available in the literature), you might as well include all other aerosol estimates multiplied by an adjustable “effective forcing” parameter to see what happens.
Overall there is much good in the BEST project, but I agree that the attribution part is no better than the sort of thing Tamino might jot down on a napkin on a random day.
“I will have to ask Robert. His task and goal was pretty simple.
If somebody DOESNT WANT TO DO THE REGRESSION, if somebody insists on doing things the way willis did them ( averaging before and after ) can we come up with any improvement on THAT METHOD. not that we suggest that method, we didnt use it in the paper. but if you want to do things his way, How can you improve it ( stack the volcanos ) and then How can you test that easily. For us the regression is the better approach, but if somebody insists on a different approach, how can you improve that. I’m surprised nobody asked the question †why didnt you also select small volcanos?†That’s an obvious flaw in the approach.”
I think your vendetta with Willis which in turn led to your pushing of the monte carlo method overcame the desired tendency to dispassionately look at the methodologies used by all parties. I am surprised that you have defended the monte carlo used in this thread without knowing the details of how it was carried out.
Your arguments come across weak when you imply that the stacked approach with the monte carlo confirmation can be defended because it is a better approach than Willis used. You then revert to: Well the paper uses regression and we used the monte carlo here just to show there is a better way than the Willis way. That spin on things in turn ignores the problems with the regression. How about we critique the Willis way, the monte carlo (when we obtain sufficient information on how it was performed) and the regression in the paper as separate issues.
In my read on the regression in the paper, I continue to be perplexed that the volcanic half life was selected based on fitting the model and without any results with other half lives as would be required in a sensitivity test.
The rest of the discussion here is about how many fairies you can get on the head of a pin with Mosher defending the indefensible.”
Huh. It should be pretty clear to you and others that I prefer a more complicated approach and I dont agree with pinning an attribution argument on to this. I would say I agree with Judith, but I see the point the physicists made. I don’t believe anything is served by misunderstanding their thinking and their reasoning. I may disagree with it but FIRST I have to understand it. I have to understand it to the point that I can explain their position as they would since they are not here to defend themselves. It would be easy for me to say.. Oh crappola, but thats not my role.
My role is to voice my opinion openly in the staff meetings. make my arguments there. In the end all sorts of decisions will get made that I disagree with. I get faced with a choice. take my ball and go home; or stay engaged and continue to argue for what I think; or pretend I dont disagree. Since I prefer to stay engaged I have a duty to explain the position of those I disagree with fairly.
If everyone took their ball and went home when the group disagrees with them, then what would happen?
If everyone was silent about their disagreement, well you would not like that.
So, I stay engaged, I speak my piece, and Im in a position where I can speak for those I disagreed with. I try my best to be fair to them.
Try that sometime.
Arno, back when Eli was looking at such things, there was at least a hint that the little ice age was initiated by volcanic eruptions but stretched out by low solar insolation, so yes, two forcings in the same direction can have synergistic effects.
“Rather than looking at each volcano separately as Willis did, we will stack the volcanos and align them all on a zero year basis.”
Does the excerpt from the thread introduction above mean that the data were detrended? That is not how I interpreted it but…
Re: Eli Rabett (Comment #101545)
“there was at least a hint that the little ice age was initiated by volcanic eruptions…”
Based on what we have seen in this thread and elsewhere, I find that extremely hard to believe. I know there is a paper with that idea making the rounds, but to me it sounds just crazy…
Eli Rabett (Comment #101545)
August 15th, 2012 at 1:08 pm
Arno, back when Eli was looking at such things, there was at least a hint that the little ice age was initiated by volcanic eruptions but stretched out by low solar insolation, so yes, two forcings in the same direction can have synergistic effects.
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as you can well imagine the recent work on that was brought up.
but thanks for reminding me.
interestingly when you push back before 1850 you can well imagine the interest it stirs up. resistence and interest.
Kenneth
Read what I wrote.
“.
Using Willis’ method you won’t have a good chance to find the volcanos’ signature in the data. But they are there. In the paper, what a regression was done to see if the volcanos “explained†the data. They did. You can build your own little toy world as I did above and test that. Or you can get the temperature data and the volcano data and run some regressions.
If we want a simple method that is similar to Willis’ second approach, but done with some statistics, we can do the following.”
I’m wondering what part of this you dont get. So, start with your criticsm of Willis approach. Add in your comments about focusing on r^2, show your work on Monte carlo, and then tell everybody here what you did with the volcano data provided for you.
Then explain why you think volcanos will have zero effect on the weather. explain why a result that was only 90% confident would change physics? The simple fact is that the physics tells you why volcanos should have an effect. If you looked for the effect and found a result that was 94% confident would you say that evidence contradicted physics? flip your test around. test for zro effect or negative effects. or better yet. given the theory, given the data, estimate the effect.
kenneth.
“Your arguments come across weak when you imply that the stacked approach with the monte carlo confirmation can be defended because it is a better approach than Willis used. You then revert to: Well the paper uses regression and we used the monte carlo here just to show there is a better way than the Willis way. That spin on things in turn ignores the problems with the regression. ‘
I dont revert to the regression. I say if you want to talk about the regression start by doing some toy models. Like I did. why? well the first thing you learn is that looking at r^2 will fool you. it fooled Willis and since you were silent I assume it fooled you.
yup R^2 is low. has to be because the volcano signal is 0 for 80% of the time period. simple experiments will show you that.
Then I say.. if you WANT a simple approach like willis’ try this approach. The problems or limitations are not being ignored.
You have the volcano data, fire away. show the limitations of the regression approach and suggest improvements, refinements or whatever, but show your work.
So you have the sequence of things backwards. Reverting to the regression implies that I started with something else. wrong.
I start with the regression, prefer to talk about it, gave you data so you could talk about and then offered a suggestion to people who want to do something different. that’s offering an option. Dont like it, good. then stick with my first suggestion.
Steve Mosher,
“see page 4 of the spreadsheet. the correlation between C02 and all other forcings is .97. the argument was made ( ahem) that we should just include all forcings. The counter argument was that using ln(Co2) as a proxy for all forcings was sufficient because of the correlation between ln(C02) and all forcings. in short, the answer didnt change much by making it more complex.”
.
Well, that correlation sounds impressive, until you realize that there are a wide range of different “aerosol histories” that are purported to explain everything; I do not know which BEST used, but there are others that are substantially different. I say again: there is a substantial range of other effects which could plausibly and substantially impact the historical temperature record.
.
A couple of years back Julio and I kicked this issue around at The Blackboard in some detail. Julio, a physicists, was naturally looking for the simplest explanation (as he noted above 😉 ), and plotted Ln2(CO2) versus historical temperature, and he got the same kind of correlation with historical temperatures as BEST did. So, no surprise in the BEST results (Bill Illis did much the same 5 or 6 years back, and with similar correlation). Still, I refer you to Julio’s comment #101540 for his current thinking, which I completely agree with.
.
IMO, there is just too much else going on to draw a simplistic conclusion based on Ln(CO2).
Mosher
It is certainly laudable to make the efforts you make and to be able “to see the point the physicists made”. That does not make them right, however and the conclusions/attributions drawn from the BEST data/analysis are deeply flawed and tantamount to science-as-[socio political]-messaging.
McKitrick was correct in his rejection on technical grounds and Judith did absolutely the right thing.
In doing what it did and how it did it, the BEST team is well on its way to putting itself on par with Hansen in terms of shot credibility [ref his recent PNAS pseudo scientific musing on “Perceptions…”] and attention seeking advocacy [ref Muller’s “conversion” Op-Ed in the NYT].
All of the above is fair comment.
Steve Mosher,
Zeke prudently stated that he was not wild about the attribution part of the paper. He clearly shows wisdom beyond his years.
yes steveF i have said the same about the attribution.
i dont think you can do attribution this way. and i don’t
think using gcms helps much. in fact attribution
isnt very important in my mind
Steve Mosher,
” in fact attribution isnt very important in my mind”
.
I must admit to being a little surprised by this, considering the many comments above. If attribution is not very important, then what is?
tetris. interesting that you make unqualified
statements about who is right and wrong. i suppose
somebody considers that important. I’m
not particularly impressed by the idea that you
have to agree with everything in a paper
to have your name on it. Ive got my name on stuff
that i disagreed with. in my world authorship
denotes that you contributed. tom wrote stuff in climategate
that i would take issue with. big deal.
its only a big deal in some sort of quasi religious
world view.
Unqualified statements? Judith did withdraw and criticise the attributions. Mc.Kitrick did state as a reviewer that the paper was methodologically and technically wrong and should not be published. And the paper was rejected. So where’s tetris making unqualified statements?
Stratospheric volcanoes clearly have a temperature impact. It is just smaller than the initial theoritical constructs would say (surface solar insolation falls by very large numbers but temperatures fall by much much less than the solar impact says should happen).
And then you can’t see this smaller impact in the noise. Someone mentioned the ENSO above. The last two volcanoes occurred at the start of two major El Ninos (one a super-el Nino of which there is only about 6 known about). Temps should have increased by about 0.25C in the 1982-83 El Nino but they declined marginally instead due to El Chichon.
Even then, Pinatubo’s impact was probably only around -0.4C. Tambora might have been 0.75C (and we would have more luck seeing that if we knew what the ENSO, what the AMO was doing at the time – but there is no reliable data going back this far). But temperatures were already falling fast in the 10 years leading up to Tambora. The moving average fit (and the low resolution charts) take some of the earlier natural temperature decline and assigns that to volcanic forcing instead which is clearly not the way to do it.
And I don’t like using any moving averages (unless you really, really have to). Land temperatures are extremely variable and some sort of moving average has to be used. Try a 5 month moving average instead. Let’s also get a reliable ENSO and AMO dataset (the AMO is actually more important the ENSO).
Mosher,
You don’t owe that publicity hound ( Muller) anything. Let him carry his own water. It’s not like you are getting paid. You aren’t really a member of the team. More like the eager equipment manager.
Your considerable talents, intelligence, and good intentions could be put to better use elsewhere. Please watch this, Steven:
http://www.youtube.com/watch?v=X-Xfti7qtT0
OPSEC could use your help. Those who are currently serving in our intelligence and special ops services can’t speak out against these security breaches for fear of retribution from hack politicians. They need our support.
Venter, Tetris,
“Mc.Kitrick did state as a reviewer that the paper was methodologically and technically wrong and should not be published. And the paper was rejected. So where’s tetris making unqualified statements?”
As far as I know, Dr McKittrick has not formally reviewed THIS paper. He was one of the reviewers involved in the 4 papers released as BEST preprints last fall.
Mosh,
I’d like to say that I understand where you are standing at the moment. But I can’t, because I don’t think you are standing anywhere and I think that’s causing you some problems. However, from your various comments, I do think I may have insight into some of the personal challenges you are facing at the moment.
You are torn between your own beliefs, your own analytic skills, your sense of team loyalty and, I presume, some personal loyalties. You are trying to walk a path through the mire that allows you to retain your own sense of personal integrity as well as personal credibility.
My strong advice is to make some clean declarations of where you stand. You can make them public or make them just to yourself, but in any event, keep them very clear.
At the moment, I suspect that you do not have them clear in your own mind because your writing is sending very mixed signals to the readers here, a pretty strong indicator.
I’ll offer you the same advice I have given to many people over decades. If you are asked to be an advocate for something you don’t support, then don’t do it – unless you are a lawyer where personal integrity is not an issue. If you are compelled to do it, and circumstances permit it, then state clearly up front that you are adopting the role of advocate with the intention of presenting and defending a case in the best light that you can; you don’t necessarily fully endorse all aspects of the case presented. If you are compelled to do it, and circumstances do not permit you to state that you are acting as an advocate, then buy a large economy pack of vallium and be prepared to take some mental damage.
Free advice, but worth every penny.
Paul
Well Paul_K the review is like this:-
1) we have a measurement for large volcanic eruptions
2) We know that the volcanic injection of sulphates into the stratosphere causes cooling
3) This sulphate induced cooling can be seen in individual thermometer temperature records.
4) These cooling events are not present in the global temperature reconstruction based on thermometers.
5) These cooling events are not present in the global temperature reconstruction based on non-thermometer proxies.
Don posts a video.
http://www.youtube.com/watch?v=X-Xfti7qtT0
New Group With GOP Ties Tries To Swift Boat Obama
By Aviva Shen on Aug 15, 2012 at 10:08 am
http://thinkprogress.org/security/2012/08/15/692461/new-group-with-gop-ties-tries-to-swift-boat-obama/?mobile=nc
Mosher: In fairness, I think I see why Muller might want to look at volcanoes. You know when they went off and you expect that they will have a cooling effect, so it is a reasonable check to see if they show up in your temperature reconstruction: if they do, it will make you that more confident that your reconstruction is (at least somewhat) reliable.
The problem is that, as Willis and others have pointed out, the effect of volcanoes is for practical purposes indistinguishable from natural variability, so you wouldn’t even know that a volcano has gone off from looking at the record alone–you need the timing information and some more or less sophisticated statistical techniques to tell that they are there. And then you are in trouble, because basically you wanted to use the volcanoes to increase your confidence, and now that you’ve brought them up the statisticians in the audience will (rightly) ask you to quantify your “confidence level,” and to use standard “approved” methods to do so…
Too much detail about something too vague, but anyway:
I find it odd that the volcano fit doesn’t change much when you don’t include the 20th century, and it still predicts a pretty good Pinatubo effect.
This indicates to me that there may be some sort of unconscious “tuning to Pinatubo” in the model. (or, it’s really good). Who knows where? In the Gao data? In something BEST did? So for example, assigning Pinatubo-like characteristics to some of the larger eruptions in the early 1800s (e.g. decay time).
In the distant past (>100YA) there looks to be significant unexplained variance in the model. There are large upsurges, large downsurges not related to volcanoes. We could hypothesize that these are artifacts of spotty temperature records, since they don’t show up in the 20th century data. The fit is fairly impressive for the 20th century, particularly the latter 20th century. It does indeed leave a residual that looks like the AMO, which goes back beyond the supposed aerosol cooling of the early 20th century. The fit is also very strong in the post-Pinatubo era, which you would not expect if the 1945-1975 plateau was an aerosol effect (I would expect it to overshoot).
None of the above is to say that a more sophisticated statistical analysis wouldn’t shed light on this. Also – I guess BEST used the GISS solar forcing data, per the statements on Sheet 4 of the spreadsheet – and it does look like it helped a bit.
To further summarize:
Hypothesis: The Earth is warming- Yes, in fact global land temps are warming at nearly twice the rate of global SSTs or global atmospheric (UAH measurements) over the last 30 years. Attribution- CO2? UHI? Undetermined
Hypothesis: Volcanic aerosols cause temporary global cooling which can be seen in the global temp record- Undetermined. Indistinguishable from natural temp variation and oceanic processes.
What have we learned: We still have a long way to go to truly understand all the mechanisms of climate change.
“julio
The problem is that, as Willis and others have pointed out, the effect of volcanoes is for practical purposes indistinguishable from natural variability”
That is not a problem, it is a means of falsification of various hypothesize.
In addition, that the variation in temperature dwarfs the volcanic signals tells us that we cannot treat the system as an equilibrium and that the system does not display thermal inertia.
Instead changes in temperature in the record appear to be caused by changes in the distribution of heat in the system.
ivp0: I think one can definitely say that some of the warming is due to CO2. The question is (as always) how much. You cannot really answer that unless you include, at a minimum, the other GHGs and some estimate of aerosol cooling, which BEST has not done. To simply say that they should partly offset each other is fine for a back-of-the envelope calculation, but not for a research article.
UHI, on the other hand, is a dead horse that people should really stop flogging, IMO. BEST has done a lot to lay it to rest, and we should all be grateful for it.
DocMartyn: I tend to agree that the relative smallness of the volcanic signal is potentially very interesting. It immediately casts doubt on the recent volcanic explanation of the LIA. It may also call into question the predictions of GCMs that may be overestimating the volcanic cooling. It may even be that all theoretical estimates of aerosol cooling–not just volcanic–need to be revised (although personally I think this is unlikely). In any case, it is definitely not something a good scientist would want to sweep under the rug.
Doc, “In addition, that the variation in temperature dwarfs the volcanic signals tells us that we cannot treat the system as an equilibrium and that the system does not display thermal inertia.
Instead changes in temperature in the record appear to be caused by changes in the distribution of heat in the system.”
I don’t understand. There is thermal inertia that delays the changes in the rate of distribution of heat energy in the system.The volcanic “signature” would vary with the system inertia as Mosher mentioned. Since the system is bi-stable, response at the higher set point would be different that at the lower set point. Mid-range between the two set point should have the largest and most uniform variance. That just means the range of natural variation is likely underestimated.
Julio,
I agree that CO2 must cause warming along with other atmospheric GHGs. Global SSTs and atmospheric warming rates are probably our strongest indication of this. The fact that global land temps are warming at a much faster rate than the other two global temp series is still quite puzzling to me. We expect to find inertial lag in the oceans but not the atmosphere yet these two series track very closely in terms of warming rate over recent history. Global Land temp warming rate is the clear outlier especially in the US and Europe. Why? If not UHI, land use changes, widespread use of HVAC then what? Even though the BEST study did a good job of documenting and confirming global land temp accuracy it is still a significant climate outlier. I am uncomfortable using global land temps in defining AGW attribution for this reason.
Mosher
Pls spare me the bit about “quasi religious” world views”. In my 60s I certainly have my views about the world, but as an agnostic with a libertarian bent, quasi religious doesn’t apply. You would have to talk to environmentalists and socialists to get a proper insight into how the the quasi religious bit works in practice.
I have made it my business to either withdraw my name from a co-authored paper/study if I disagreed with its findings or explicitly state my reservations/disagreements up front -started that practice in my undergrad days, through my PhD and continued it into my private sector work which included a good bit of make or break scientific and corporate due diligence in venture capital [the “find-the-fatal-flaw-and-find-it-early” approach over time singularly fine tunes your BS detectors]. I asked that those who reported to me do the same. Doesn’t necessarily make you friends or get a lot of brown nose points, but tends to make things starkly clear and allows everyone concerned to sleep with a clear conscience. So as far as I’m concerned, Judith did the right thing, and it is absolutely fair comment for me to say so.
Bottom line, the BEST paper is scientifically dubious and its attribution findings are fundamentally flawed. And Muller is making Hansen jealous because of the publicity he’s receiving without needing to get himself arrested.
Here is the BEST land temp divergence. What are we missing here?
http://www.woodfortrees.org/plot/best/from:1978/to:2012/offset:-.2/trend/plot/uah/from:1978/to:2012/trend/offset:0.2/plot/hadsst2gl/from:1978/to:2012/trend
Ike,
Thanks for the link to the unbiased opinion of some clown from the non-partisan thinkprogress. Try this one:
http://www.youtube.com/watch?v=4VPd0YpN8E8
The two political hacks, who attend NSC meetings wearing their little re-elect the boss at any cost hats, need to be hooked up to lie detectors. Their names are Valerie Jarrett and Tom Donilon. They don’t have one clue about national security between them.
julio,
“UHI, on the other hand, is a dead horse that people should really stop flogging, IMO. BEST has done a lot to lay it to rest, and we should all be grateful for it.”
Remain serious! UHI is largely responsible for the evolution of continental surface temperature. All proxies show it with the divergences (including TLT). As the BEST work on UHI, the methodology is inadequate and the first result showing an UCI properly ridiculous.
ivp0,
I agree it is puzzling. My best guess is that there may be some feedback mechanisms that are particularly strong over land. Evaporation from irrigated crops? Changes in vegetation distribution? I know “hardiness zones” over the US have been changing in recent years. Human activity may be to blame in part also, but then one would have to look beyond the simple classification of “urban” and “rural”–the phenomenon seems to be quite widespread.
Another question is, how long could this go on? The different warming rates would lead to an increased temperature gradient between the land and the sea. Is this sustainable? What effects would this have on weather/climate in the long term?
I don’t know the answer to any of these questions 🙂
Julio, Pielke Sr. is bringing to his blog some new papers about a different kind of UHI. Not properly urban (say cities) but definitely about temperature effects of human’s landscape transformation.
I remember three, I think during July and August. Looks like they may bring UHI to life again. A different sort of UHI, for sure, which is apparently not addressed by BEST or any others. Who knows?
Also, let’s not forget that most of the global warming has, for various reasons, concentrated in the Arctic. It is natural for some of that to “bleed” southwards into the US and Europe. This would show strongly on the land temperatures (as most land is in the Northern Hemisphere), whereas it would be diluted in the global land + sea average…
The current warm period is indeed primarily Arctic and NH warming so you may be right. Simple atmospheric heat distribution is being observed in NH land temps. A good topic for the next climate change paper: “Dissecting the BEST land temp divergence.”
Re: Steven Mosher (Comment #101427)
The link for the annual contains loading data for Laki 1783, BUT all the links that I can find for monthly data has 0.0000 (no forcing) for Laki 1783, 1784 etc. What am I missing?
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/gao2008ivi2/ivi2loadinglatheight501-2000.txt
http://climate.envsci.rutgers.edu/IVI2/IVI2LoadingLatHeight501-2000.txt
Supplement v1.0: http://pmip3.lsce.ipsl.fr/
Julio
Either that, or it shows that in GCMs, responses to transient changes in forcing are smaller than actual sensitivity to long-term change in the forcings. As it should be. I understand that two-box models are frowned upon in this place, but you catch my drift.
“most of the global warming has…concentrated in the arctic.”
That would make it Regional Warming.
Andrew
julio: I see what you’ve described as important but only part of the problem.
I see the the rest of the problem is that volcanic events represent a short period transient on a complex system.
While it is true volcanic eruptions can, and do, have discernible effects only climate, see TLS for example (guess what happened in 1984 and 1991?) it isn’t always the case they will show up equally in all metric.
The effects seen in TLS are more like step changes, they are what happen when you have a system in quasi-equilibrium, and you “bang” it with a hard enough impulse. When it returns to equilibrium, it won’t necessarily return to the same one. These sort of responses of complex system aren’t tidily represented using transfer functions. (I believe some people refer to this shift in equilibrium/operating point as hysteresis. It’s not, as least as that term gets used in nonlinear oscillator theory, but same general class of concepts.)
In addition, we know what we call “climate” is the low-frequency component of the rather chaotic coupled atmospheric-ocean-land-surface-biosphere system. Because this transient is relatively high frequency you wouldn’t necessarily expect it to have the same amplitude of response as a step wise change in forcings (e.g., equilibrium climate sensitivity).
This is easy enough to visualize by looking at the transfer function for a typical low-pass system. I’ve plotted the example of the transfer function for the response of a first order low-pass filter, e.g.
$latex T(t) = {t_0/t \over 1 + i t_0/t}$
where $latex t_0 = 2 \,\hbox{years}$ is the “knee-point” or response time of the system, and t is the period.
The radiative-cooling aerosol component for a volcano is typically 1-2 years, for this example, we could expect a substantial attenuation in the climate response to the volcanic eruption compared to a steady-state change in forcings.
Equally important, it won’t be in phase with the forcing. That is you can’t simply use correlation between forcing and response to determine whether there is an effect or not In this example, for forcings much less than a year, the response will be 90° of phase, and the correlation coefficient will be approximately zero. This is the basis behind my comment about needing to compute the complex correlation coefficient. Basically this involves calculating $latex c_a = Corr(f + i g, x)$ where f is your assumed forcing function g is the Hilbert transformed version of it (90° phase shifted) and x is the data you are correlating against. [Fortunately, there is a very tidy way to do this using the discrete Fourier transform.]
Notes:
By the way, comparing TLS and TTS, , and seeing that there isn’t a downward shift in TTS commensurate with that of TLS is evidence against there being a significant “corruption” of the TTS band by the TLS one, a point argued on this blog previously.
It’s also interesting to consider the “expected” radiative forcings associated with volcanos, these are decidedly more complex than the oversimplified versions that some people have assumed. There is a pre-erruptive phase (which tends to be a positive forcing), an immediate post-erruptive phase (which tends to be a negative forcing, how global this is depends on a lot of factors, including the type of material ejected, what latitude band the volcano is in, and even the season and prevailing weather conditions), a long-term post eruptive period (reabsorption of GHGs released by the volcano by the biosphere).
OK, I have data to look at. Laterz.
The edit and latex functions seems disabled, which together with the lack of a preview, makes writing long comments a bit like shooting blind. Sorry for any typos.
Here’s a second try at the transfer function as the link above appears broken.
I had a typo in my transfer function too (not that it matters if you can’t read LaTeX. I wrote the transfer function for a high-pass filter. My results were for a low-pass one though.)
Here’s the proper formatted latex (hopefully):
equation
toto:
Well I don’t frown on them! I think they are quite useful in understanding short-period versus long-period responses.
Here’s a plot of real, imag and total correlation, that is c_r = Corr(f, x), c_i = Corr(g, x) and sqrt(c_r^2 + c_i^2).
Figure.
If you start dividing climate up in terms of fast and slow response components, as toto has pointed out, there is an additional dilution of the measured response in the global mean surface air temperature.
You can throw into this, excitation of modes that have zero global mean by volcanos. Just comparing volcanic eruptions to global mean surface air temperature, not seeing an effect, and concluding there is no effect, is bloody naive.
“dallas
‘Instead changes in temperature in the record appear to be caused by changes in the distribution of heat in the system’.
I don’t understand”.
The Earth cannot store temperature, but it can store heat.
The Earth is highly heterogeneous and an even distribution of heat would not translate into an iso-thermal system.
The ups and downs in temperature, observed by Spencer in the satellite record and in the various temperature reconstructions are not causes by changes in influx/efflux of photons; the temperature changes are caused by movements of heat from different thermal reservoirs. What causes the changes in ocean currents or in the semi-stable air currents, I have no idea, but it is obviously these that change the year to year temperature. As such year to year temperature changes dwarf changes resulting from volcanoes, what we mean when we talk about average needs to change.
todo,
I do frown on two box models a bit… too big a simplification, with a risk of drawing inferences which are quite a bit off. IMO only a range of response rates can reasonably simulate reality.
SteveF, two-box models aren’t perfect, but they are a h*ll of a lot better than assumptions that reduce to one-box models being used on this thread. Of course they are a simplification (even AOGCMs are simplifications in that sense), but a useful one as long as you remember their limitations.
Carrick,
” Of course they are a simplification (even AOGCMs are simplifications in that sense), but a useful one as long as you remember their limitations.”
Fair enough, but sometimes limitations seem to be forgotten.
Carrick, do tell what you mean by ‘forcing’.
“I dont revert to the regression. I say if you want to talk about the regression start by doing some toy models. Like I did. why? well the first thing you learn is that looking at r^2 will fool you. it fooled Willis and since you were silent I assume it fooled you.”
I have not commented on the Willis way because instead I was interested in the details of the what was posted here at the Black Board. I had not even read the Willis methods until recently as I seldom read the Watts blog.
As you have noted many, many times the Willis methods are not optimum or efficient for finding the evidence of the volcanic activity/events effects on global temperatures given other methods pointed to here and including stacking the data. The fact that Willis could not find it, and you, or an associate of yours, presented an alternative does not in itself mean anything unless we can be sure how the monte carlo was performed and whether it was correctly carried out. Again I am surprised, based on your initial comments, that you are not aware of these critical details.
Anyway my interest in these exercises is for the monte carlo method: knowing whether the method used random 36 consecutive months that were in turn stacked and not randomly selected individual months and whether any detrending of data was used in the observed and monte carlo calculations.
For the regression method I am interested in knowing how the authors justified selecting the half live parameter based on well it made the model fit and why in doing that they did not show what other half lives would have produced. Also why were not the results of the model given in the paper where other sources of sulfates and/or volcanic forcing were used. If you can obtain answers for my questions on these items from the authors I would be most satisfied.
You could, I suppose, tell me to do my own sensitivity testing, and while I might just do that, I think it is appropriate for the authors to have done or at least contemplated doing those tests.
By the way just to be clear I agree with the physics that show that volcanic activity can reduce global temperatures. My arguments and questions are related to the methods discussed here that are used to show and quantify those effects.
Carrick, toto,
Multibox models are definitely not the answer. Many of us have tried them (myself, Paul, Tamino, etc.) and the results (for volcanoes, that is) are always crappy, no matter how many boxes or timescales you add.
Box models are particular instances of filters where the impulse response is an exponential or sum of exponentials. Carrick’s example of a low-pass filter is a more nontrivial sort of transfer function, and it might be worth a shot. My impression is still that some kind of nonlinearity (like what audio engineers call “clipping”) must be involved, though.
DocMartyn:
“Radiative forcing”
The standard definition used in climate science. See e.g. here.
In general, you can think of it as the inhomogeneous terms in a system of differential equations, which happened to be normalized to have a common set of units and measured at one altitude in order to simplify comparison of the relative magnitude of the contributions to the inhomogeneous terms.
SteveF:
Based on comments made on this blog, it’s the opposite that happens. People forget that climate is more complex than a single box model. I’d rather they thought in terms of two-box models and forgot about that system’s limitations instead of equating transient system response with equilibrium system response.
At least they’d recognize the amplitudes of the two won’t necessarily be equal.
julio:
That depends what what what question you are asking. 😉
If you want to illustrate short-versus-long period responses, they do a nice job of that.
Are they are a quantitative substitute for more complex models? No.
To clarify my previous post: if you start with the GISS model E volcanic forcings and try to fit them to the temperature record, no linear filter scheme (multi box model) that I am aware of will allow you to “kill” the spikes so as to fit the global temperature record, without also removing all other variability from the fit (i.e., reducing it to a straight line punctuated by spikes).
I believe this will be the case for other linear filters as well.
The only way to get a good fit is to multiply the volcanic forcing by an adjustable parameter, as the BEST team has done here. There are only two possible rationales for this:
1. The GISS estimate of the equivalent radiative forcing for volcanos is way off.
2. The system response is nonlinear, so the very large spikes get “clipped” not just because they are sharp but because they are large.
julio:
Actually, the single-pole low pass filter is just an example of a single box model, just represented in terms that allows one to (hopefully) more intuitively understand how that particular system responds to forcings with different periods.
A two box model could be thought of a two pole representation of the transfer function. (And of course, we could have an N-pole model.)
Not if the response is small. Here we’re having difficulty (some of us anyway) even finding a signal. In such cases, the system will either behavior linearly, or quasi-linearly, even if nonlinearity is otherwise required to maintain stability in the system.
julio:
I think the volcanic spikes can be explained by a linear system. If you’re talking about the “high-frequency” noise, no it doesn’t capture that, but I don’t see why that’s relevant for long-term climate variability.
E.g., here’s my two-box model. The high-frequency noise is associated with short-period climate fluctuations, which my model doesn’t incorporate (and I’m sure I’d get b*tching about making the model too complex were I to add them!).
I’m not sure why not including that “climate noise” sector would bother you, unless you thought the “climate noise” were contributing to the secular trend itself. (And even then, that would only be an issue if you wanted to discuss quantitative predictions instead of qualitative behavior.)
Carrick,
But a small response to a large driving can be an example of a nonlinearity!
(Agreed on the single-pole thing, of course. I didn’t recognize the notation at first.)
Carrick, just to be clear here. When you use the term ‘forcing’ you are talking about the difference in the influx of radiation from the stratosphere into the troposphere and efflux from the troposphere into the stratosphere?
Re: Carrick (Comment #101629)
Well–is there any trace of the solar cycle left in your fit after you put it through your two-box model? And if so how does its amplitude compare to the temperature record?
julio,
“1. The GISS estimate of the equivalent radiative forcing for volcanos is way off.”
I think even the GISS folks will admit that the uncertainty is quite high, especially in the early part of the record. The SATO index, combined with the GISS assumed conversion of that index into forcing (in watts/M^2) leads to WAY too much volcanic response in late 1800’s early 1900’s for any heat uptake model which does a reasonable job in the late 1900’s. My guess is that the SATO index is just terribly wrong (way overstated) in the early part of the record. I have not looked at the BEST sulfate-in-ice record; maybe that is better than the SATO index.
.
If the Pacific responds to a strong volcanic event by going immediately into an El Nino phase of the ENSO, that could certainly represent a natural “clipping” of large responses.
julio:
Aren’t we getting into a contradiction here?
People are saying the response to the spikes aren’t even measurable. And now you’re saying they are large enough to invoke nonlinearity in the response.
Put another way large forcings does not equal large nonlinearity in response. You get large nonlinearity only if the response is large, not the forcings.
That said, I’m happy to see nonlinearity, I find it interesting when I see it. “Complexity is my friend”, said the scientist thinking about a long healthy career with a multitude of unsolved problems to work on.
Carrick (Comment #101629),
Your two box model looks to me like it dampens the response to volcanoes far too much. Look at the pattern of residuals between model and GISS temperature.
SteveF:
Since you’re discussing the excitation of a mode, that sounds like a linear response to me.
DocMartyn:
Those are your words, but they sound similar to what I would say (only in my own terms). As effectively as I can, I am using radiative forcing in the sense defined by the IPCC, though the particulars of that definition don’t matter, if what you are discussing is qualitative rather than quantitative features in the response of a system to an external stimulus.
julio:
There is if your assumed radiative forcings includes them, I haven’t compared it (though it is very small in the SAT record as you probably know), nor—and this is the point I’ve been trying to make—is it important to understand whether the two-box models agrees numerically with the temperature data for the purposes of understanding qualitative features in data.
(I can discuss a lot of essential features of nonlinear systems using a driven van der Pol oscillator, without having to worry about the particulars of whether the system I’m describing really obeys the VDP equation.)
SteveF:
As I said, I see it as a qualitative model, not a replacement for GCMs. That said, I’m using GISS Model E’s volcanic aerosol histories. If there is modal excitation (two-years for volcanos lines up with the short-period component of ENSO), then you could see an enhancement in the response of the physical system. Simplified models like this one will fail to capture such physics.
Carrick,
The last time I looked at this (years ago, I admit), it seems to me that to get the spikes to a level comparable to the one your model shows I had to dampen the high frequencies so much that the forcing due to the solar cycle basically disappeared. Anyway, we could simply look at the Fourier transform of the GISS model E total forcings, and compare it to the Fourier transform of the temperature record, and try to see what kind of filter would transform one into the other while at least preserving the physically meaningful peaks. I think I convinced myself that no reasonable filter would work, but I may just not have been clever enough.
Regarding nonlinearity, I don’t think I am contradicting myself–you are trying to get a large response from the system, and you find you can’t get past a certain point–at least on this particular variable–which actually happens to be pretty much the “natural variability” scale. You don’t get an el Niño effect larger than a certain value, etc.–your response is limited by the resources available. That’s nonlinearity.
jules, bringing up the solar cycle raises lots of interesting issues here, and ones that aren’t at all unique to any particular model (including 2-box models).
As Lief Svalgaard explains there is considerable controversy about the magnitude of the solar forcings themselves.
Given that, for a particular model, there is plenty of opportunity to “tune” the amplitude solar cycle-associated solar forcings to match virtually any temperature variation you are interested in. (And by “tune” I mean pick the published solar forcing history that gives the best match of your model to data.)
In any case the solar cycle effect on SAT is pretty small, and has a factor of two uncertainty itself (based on variability between different reconstructions using nearly the same exact temperature data sets!).
I’d say there’s plenty of wiggle room for the deft modeler to fit his model into the existing error bars on this one.
Doc, since they are using land only temperatures the changes in heat capacities would be amplified. Volcanic would be amplified, CO2 would be amplified, land use would be amplified, so any “fit” they get with temperature should be larger than life. Once they get around to a realistic sea surface temperature data set, then they will have to scale back estimates of impact a touch to relate temperature to heat capacity.
http://i122.photobucket.com/albums/o252/captdallas2/climate%20stuff/joethevolcano.png
That is the BEST volcanic with HADSST2 and RSS NH and SH. You can see the RSS NH shows the amplified impact of the volcanoes, about twice as large as SST and SH. My choice of baseline makes that chart a little more interesting. Since it appears that current temperatures are at the higher bi-stable set point for the oceans, the impact of the volcanic forcing would decrease. By assuming 1951-1980 was NH “normal” they will over estimate the impact, if the little ice age was due to volcanoes. Like I said in a bi-stable system variance would decrease as either if the two “set points” is approached and the largest variance would be between “set points”.
I am not sure what Zeke or Mosher think, but to me not knowing what “normal” should be looks like a serious problem since “forcing” at temperature a does not have the same impact at temperature b.
julio:
This is true, but only interesting in the sense of “clipping nonlinear response” if you saturate the ENSO response. Is there evidence the ENSO response was saturated after the 1984 or 1991 eruptions?
Certainly the super-ENSO of 1998 was much larger in magnitude, so I would suggest “probably no.”
The excitation of a mode is not a nonlinear phenomenon in the sense your “clipping nonlinearity” unless unless you are moving energy out of one frequency region into another. That is an essential property of the “clipping” nonlinearity you are describing.
[One way to sharpen the discussion is if you drive a system with a signal $\latex sin(\omega t)$ and get nonzero equilibrium response at frequencies other that $latex \omega$, then you can say the system has responded nonlinearly to your stimulus.]
Re: Carrick (Comment #101644) 

Perhaps a “clipping nonlinearity” is not the right way to think about it, but one might expect (in a linear system) that “half” the forcing triggers “half” the modal response. Do we see half-El Niños?
Carrick:
Maybe, but one could also interpret what happened in 1998 as a stepwise move to a new equilibrium state plus an overshoot oscillation around that state. The amplitude of the oscillation then does not look excessively large.
Either way, of course, there had to be enough energy stored in the system to allow for such a large response–maybe more energy than what’s normally available? So normally you can only go so far up or down, before saturation sets in, but meanwhile (because the radiative forcing keeps increasing) energy is piling up somewhere where it is not immediately available–and then, at some point, it does become available.
(I don’t know, perhaps I should just say that it all looks very nonlinear to me, but everybody who is happy with the look of your two-box fit should just feel free to ignore everything else I have said here…
:-))
Carrick,
“This is true, but only interesting in the sense of “clipping nonlinear response†if you saturate the ENSO response.”
Humm.. Could not the volcano itself make an El Nino run out of steam? I mean, the sudden drop in solar energy could (plausibly) initiate an El Nino, but then when the Pacific warm pool water spreads eastward, the cooling of that water would be enhanced (compared to a normal El Nino) because the aerosols would still be reducing the total solar energy reaching the surface. In terms of a “natural mode” of oscillation, the volcanic effect could change the behavior enough to limit the size of the resulting El Nino.
Oliver:
We see different strengths of El Ninos. RIght? E.g., the 1998 super ENSO.
The question is how you measure the amplitude in a way that you could answer the question of whether nonlinearity is playing a role in governing the response of the system to volcanic forcings (which is what I think julio is getting at, pardon me if I’m off base).
julio:
It is all nonlinear, otherwise the modes would “explode”. The existence of a mode doesn’t mean it doesn’t have an amplitude defined that is independent of the existence of a particular circulation pattern.
I’d guess Oliver or somebody else would be better than me at discussing how one measures the strength of the mode, but I’d suggest one way would be the measured amplitude associated with that mode on e.g. SAT.
SteveF:
That can happen with linear mode suppression too.
Again, to qualify, the mode itself exists and has a finite amplitude in the presence of an energy source such as the sun because of the finite reservoir of thermal energy that can be stored in the Earth’s ocean. That is a type of nonlinearity, but it itself has nothing to do with modal excitation, and not too much to do with responses to climate from “saturating”/”clipping” nonlinearity (which in their essence transform energy of the external driver from one frequency band into another).
You can get an enhancement (or suppression) of the response of the system to an external stimuli without having to directly invoke nonlinearity into the description of how that happens. Sometimes you need to invoke nonlinearity to explain things, it just depends on how large the external driver is.
It’s my impression that the impact of volcanos is pretty weak, likely only involves short-period components of the climate system (which is why I agree with toto on discussing the paradigm of the 2-box model in this context), and the weakness of the response in general has less to do with the underlying nonlinearity than with the relatively high-frequency nature of the driving itself.
In respect to a comment that you yourself made, it might be the case than for some volcanic eruptions that the existence of the ENSO actually enhances what might otherwise be an even weaker climate response… this is the opposite of what’s expected from saturating/clipping nonlinearities.
I think that last paragraph summarizes the issues without us getting lost in the meaning of words.
In essence here is the the observation—-the response of the climate system to volcanos is weak.
The models posed are:
1) the response is weaker because of saturating nonlinearity effects.
2) the response is weaker because of the high-frequency nature of the external driver.
2a) the response is weak, but stronger than otherwise expected, because the volcanic driving is invoking a response from the ENSO system.
I just read this. I like the zero year analysis. Very cool.
Re: Carrick (Comment #101654)
I think that sums it up well, keeping in mind that it could still be a combination of all three! Your nonlinear oscillator could also function as an amplifier–linear until it saturates… And the frequency response will almost certainly play a role as well.
In complete agreement here julio. And at this point I have no compelling reason at this point to reject any combination of these hypotheses.
To follow up slightly on evidence that might contribute to a better understanding of the mechanisms responsible for the climate response to volcanic driving(*): The main evidence for nonlinear saturation would shifting of energy into higher frequency bands.
If for example you had a roughly Gaussian looking spectrum associated with the volcanic forcing with a peak around 2 years, and if you saw double-peaked climate response, with a peak at 1 and 2 years, that would be evidence for saturation (there would also in principle be higher harmonics at 2/3, 1/2, 2/5, etc of a year).
The observation of the fundamental in the climate response, but absence of higher frequency harmonics would suggest the response of the system is dominantly linear.
(*) I’m leaving out the term forcing here, because that’s unnecessarily specific and has appeared to lead to some confusion above.
This seems to be a given amongst various commenters but I’m still not sure what it actually means. Weak compared to what? Weaker than expected? Expectations from what?
Paul S, as I’ve used it, “weak” with respect to temperature sensitivity to forcing, i.e., comparing volcanic to say temperature sensitivity to CO2 forcing. It is also weak with respect to signal to noise, which means it’s not a robust signal (and hence detection is more sensitive to the algorithm choice used for detection).
Carrick, Julio,
With a simple single-pole LTI model there is no substantial discrepancy observed in the forcing responses, unless you want to count a 74% efficacy factor that needs to be applied to volcanic forcings relative to GHG’s. Moreover, I have just overlaid the GISS-E volcanic forcings (expressed in the form of incremental flux) over the top of the total incremental flux forcing values inverted from the instrumental temperature series, using parameter values matched to the GISS-ER model. This does not show anything abnormal, Julio. Specifically, re the point you raised, elimination of the spikes due to strat aerosols does NOT materially affect the rest of the high frequency data. In other words, I see no major problem here in relative forcing contributions to temperature change .
As Carrick has suggested, the explanation for the APPARENT discrepancy is the high frequency nature of volcanic forcing. A large forcing is applied for months to a year. The system responds with only a fraction of its expected full response to the forcing before a large negative forcing is applied in the following year(s) to return the cumulative forcing to zero. Hence the magnitude of the spike is not in simple direct proportion to the magnitude of the volcanic forcing. It is also a function of the response time of the system; the longer the response time, the smaller the spike.
There is no need to invoke nonlinear dynamics to explain this behavior, and despite Carrick’s comments, the temperature data can be matched perfectly well with a single-pole LTI system.
What I am saying is that the basis for the “observation†that there is a weak volcanic response is spurious. It appears to be based on a misunderstanding of the BEST curve-fit and a flawed attempt to interpret the regression coefficients of the fit. The physics does not suggest a linear temperature response to cumulative forcing other than when the cumulative forcing itself is increasing linearly. Under this specific condition, the regression coefficient should (asymptote to) be proportional to the rate of increase of the forcing and inversely proportional to the total feedback of the system. If the condition of linearly increasing forcing is not met or the response time of the system is large, then interpretation of the regression coefficient as a climate sensitivity is fraught with problems even for the low frequency variation of CO2. In the case of the high frequency volcanic response, the regression coefficient has nothing to do with climate sensitivity, or almost nothing. It includes the (unknown) factor related to the realworld response time which controls the magnitude of the spike – what I described above as “the fraction of its expected step function response before a large negative forcing is applied in the following year(s) to return the cumulative forcing to zero†. This should not be confused with the modeled half-life response time built into the volcanic function. This latter controls the dissipation of aerosol effect in the statistical model, but the regression coefficient has to control the magnitude of the spike, and hence it “picks up†this timing response factor.
In summary, (a) you can’t compare the regression coefficients in the BEST model to test the consistency in climate response between volcanoes and CO2 and (b) especially since the correlation is spurious.
Re: Jeff Condon (Comment #101655)
August 16th, 2012 at 3:37 pm
Hi Jeff,
I’m quite surprised at your comment. I gave Mosh a hard time for failing to recognise that the temperature series is autocorrelated. If you know that the series is strongly autocorrelated do you think it’s fair to assume that the next 3 year period can be randomly sampled from all such 3 year periods, when for each volcano, you know the actual temperature history upto the point of eruption?
“Paul_K
I gave Mosh a hard time for failing to recognise that the temperature series is autocorrelated”
OK, Tell me the coupling between Decembers a year apart.
Re: Paul_K (Comment #101668)
Thanks, Paul, for the long explanation. I guess I misremembered your results from awhile ago; in particular, I thought the “efficacy factor” that you mentioned was a lot smaller than 74%. That’s a factor that could probably be accounted for by the general uncertainty with which so many things are “known” in climate science, without the need to invoke a “clipping” nonlinearity.
It’s still somewhat remarkable that the volcanic response (at least as seen in the global temperature record) never seems to exceed the amplitude of the ENSO oscillations, but I suppose that could be a coincidence…
Re:DocMartyn (Comment #101670)
August 16th, 2012 at 6:32 pm
OK Doc. Are you doubting that there is a significant autocorrelation in the data? It would make this temp series unique.
Paul_K,
I sure hope nobody thinks the temperature data is not autocorrelated, especially since it is pretty well known that much of the short term variation (<~1 year) is driven by ENSO with a bit of lag.
.
julio,
I think that it is not too surprising that ENSO driven variation in global average temperature is larger than observed volcanic forcing. The internal variabIlity is controlled by the physical processes that make up the ENSO. I don't see any reason a priori why those processes and the resulting internal variability should be smaller than the variability caused by volcanic eruptions; the two seem to me unrelated, unless a large volcano usually causes an immediate shift to El Nino (and that is widely disputed).
Julio,
The 74% was indeed my matched factor, but Hansen then reported an efficacy factor of 75% for volcanic forcing – same thing.
I had a look at the BEST temperature data – without the fitted line – and tried to pick out the years of volcanoes. I got most of them wrong. I agree with SteveF that it’s just simply that the natural variability is very large (2 sigma is about 0.8C) relative to the temperature response to volcanoes.
Carrick (#101642)
“In any case the solar cycle effect on SAT is pretty small”
I must be thinking in the wrong direction — there’s a 4 K variation (peak-to-peak) in SAT over the year. Can you please clarify?
Zeke (Comment #101293)
“As far as volcanoes go, we had both annual hemispheric and monthly gridded series. There were some discrepencies between the two, and I believe we just went with the annual series for the analysis.
Gao Annual: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
Gao Monthly: ftp://ftp.ncdc.noaa.gov/pub/da…..1-2000.txt
”
I realize that these links are probably broken but please go to Zeke’s original comment and click on these two links.
The discrepancy seems to be NO Laki volcano eruption at 1783 on the monthly data! I don’t understand the monthly data available for GCMs compared to the annual data. Can someone please explain this discrepancy. This is the data (Gao 2008) that BEST used for volcanic data, but if they had gone with the monthly data (instead of ‘just going with the annual’ like Zeke said) there would appear to have been NO volcano in 1783. I am so confused…
Paul_K:
Can you post an figure please? I would like to judge this for myself.
I seriously doubt, from experience, you can really match both short-period and long-period response with a single-pole system. It’s a studied problem, and I think my comment reflects many other people’s experiences.
You’ve lost me on this one too. You are claiming it is a linear system, and at the same time saying “the magnitude of the spike is not in simple direct proportion to the magnitude of the volcanic forcing.” ???
For a linear system, they have to be proportional, as with your LTI system.
That’s enough comments till I get a better idea of what you’re really saying.
Sue,
Two potentially useful papers on Laki (one of which Gao is a coauthor on!):
http://pubs.giss.nasa.gov/cgi-bin/abstract.cgi?id=om02000x
http://pubs.giss.nasa.gov/cgi-bin/abstract.cgi?id=tr08100v
HaroldW:
The solar cycle is a term of art and refers to the roughly 22 year fluctuation in solar irradiance (the sunspot cycle is 1/2 of this or 11 years).
What you’re thinking of is the annual cycle.
Carrick:
Thanks!!
Andrew_KY (Comment #101595)
August 16th, 2012 at 10:43 am
said
“most of the global warming has…concentrated in the arctic.â€
That would make it Regional Warming.
And therefore extremely unlikely to be due to CO2.
Zeke, are you saying you are surprised about the discrepancy?
Alex Hayworth,
It is a bit more complicated than that. GHG forcing is (of course) not a regional effect. However, even though the forcing is everywhere, the warming can be less than uniform do to heat transport. For example, most formation of cold deep ocean water takes place in the northern hemisphere, especially in the north Atlantic, while upwelling takes place more in the tropics and southern hemisphere. So when the ocean surface temperature rises, more heat is carried to the northern hemisphere at high latitudes by thermohaline circulation than to the southern hemisphere. So more warming in the arctic. There are other issues for sure, but a non-uniforn rate of heating does not disprove GHG forcing.
Paul_K, I’m out in the field most of the day pulling data. I did have one other term I was hoping for clarification, namely the term “efficacy”.
It’s an uncommon term, used in fields other than physical sciences, so could you provide an explanation of what 75% efficacy means?
“And therefore extremely unlikely to be due to CO2.”
Alex Hayworth,
You completed the logical process appropriately. 😉
Andrew
“the forcing is everywhere”
SteveF,
Sounds like Star Wars. And probably just as imaginary.
Andrew
Paul_K:
Your post yesterday finally triggered back my memory. IIRC, sometime ago you showed that you could produce an excellent fit to the output of GISS model E (which, as everybody knows, is a general circulation model with more boxes than one can count, and nonlinearity as a matter of course) just by applying a single-pole LTI model (or single-box model, or one-time-constant linear response model) to the GISS forcings, provided you multiplied the volcanic aerosol forcings by a “fudge parameter,” which you said above was 0.74 but I misremembered as being a lot smaller (0.4 or so).
At the time I took this fudge (or “efficacy”, as you say) factor to be an indication of the nonlinearity of the system: that is, the only part of the system’s response (as modeled by the GCM) that could not be accounted for by a linear response model.
[I may also be misremembering this, but it seems that also at the time the question of using more boxes (more poles, or more timescales) came up, and the conclusion was that it did not improve the fit–reducing the volcanic spikes “by hand” was still necessary.]
In any case, I am curious about your statement that “Hansen then reported an efficacy factor of 75% for volcanic forcing”. Does this mean that he multiplies the volcanic forcings by 0.75 before feeding them to the model, or (what I would prefer to believe) that the internal dynamics of the model result in volcanoes being somehow less effective (by 75%) at driving temperature changes than other radiative forcings? If the latter, some kind of nonlinear clipping might still be taking place (although this is, of course, not the only possible explanation, and the effect seems relatively small in any case).
Re: Carrick (Comment #101693) and julio (Comment #101696):
See Hansen et al. (2005), Efficacy of climate forcings, J. Geophys. Res., 110, D18104, doi:10.1029/2005JD005776:
To everybody,
In an attempt to set the record straight, I would like to “withdraw” parts of several postings I’ve made over the past few days, especially comments #101456 and #101580. Now that Paul has set me straight (not that toto and Carrick didn’t try), I can see that Willis’s “order of magnitude” discrepancy between the regression factor he needed to use for the volcanic forcing and for the CO2 forcing is really nothing to get excited about, and I’m sorry I ever said otherwise.
As Paul (Comment #101668) has noted (and toto and Carrick before), if you have a linear response system with a time constant T and drive it with a pulse of duration tp << T, the response will be smaller, by a factor of the order of tp/T, than what you would get for a constant driving of the same (peak) amplitude over a time longer than T. If the volcanic spike has tp ~ 1 yr, and the climate system's shortest response time is ~ 5 yr, you automatically expect the response to be about 1/5, or 0.2, smaller than to a constant radiative forcing of the same magnitude.
Add to this Paul's efficacy factor of 0.75 (or rather, multiply by it), and presto, a factor of 0.15 (or about an order of magnitude) difference between the regression coefficients for volcanoes and CO2 forcing.
Moral of the story: pay more attention to toto and Carrick, and less to WUPT, and think before you post.
Hi Carrick,
Your simple question first…
for definition of radiative forcing efficacy, see:
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-8-5.html
I am using it in the same way Hansen used it – a ratio of globally averaged effective forcing to the commonly quoted “adjusted forcing (Fa)”.
P
In attempting to look closer at what Steve Mosher presented in this thread with the approach of stacking the 72 months of BEST global mean temperatures zeroed at the volcanic eruption for comparing the mean temperatures of the 36 months before and after the eruption, I have looked at 9 volcanic eruptions. The list of volcanoes, eruption dates, and results for the before and after mean temperatures are given below.
Laki: Erupted June,1783 Before minus After = 0.640 Degrees C
Tambora: Erupted April, 1815 Before minus After = 0.304 Degrees C
Cosiquina: Erupted January, 1835 Before minus After = 0.441 Degrees C
Krakotoa: Erupted August, 1883 Before minus After = 0.248 Degrees C
Santa Maria: Erupted October, 1902 Before minus After = 0.374 Degrees C
Novarupta: Erupted June, 1912 Before minus After = -0.135 Degrees C
Agung: Erupted February, 1963 Before minus After = 0.124 Degrees C
El Chico: Erupted March , 1982 Before minus After = 0.139 Degrees C
Pinatuba: Erupted June, 1991 Before minus After = 0.201 Degrees C
BEST temperatures stacked for all nine volcanoes for 36 months before and 36 months after eruption date from above Before minus After = 0.259 Degrees C
In order to determine the probability of these differences occurring by chance I did a monte carlo by randomly selecting an eruption date and then comparing the 36 months before and after for 72 consecutive months from the BEST mean global temperatures. I used the entire BEST series for my monte carlo. I stacked 3 and 9 events and did 1000 samples for each where I calculated the stacked differences in mean temperatures for the 36 months before and after the event and give some quantile results below.
Stacked 9 high:
Prob=0%,Diff =0.282; Prob=1%,Diff=0.220; Prob=2%,Diff=0.202; Prob=5%,Diff=0.165; Prob=10%,Diff=0.125
Stacked 3 high:
Prob=0%,Diff=0.592; Prob=1%,Diff=0.344; Prob=2%,Diff=0.316; Prob=5%,Diff=0.256; Prob=10%,Diff=0.198
Since I did not know how the monte carlo was performed in the thread above I also calculated probabilities where I selected individual random dates for the 36 months before and after, stacked the temperature results, and calculated differences in means. Those quantile results are shown below:
Stacked 9 high:
Prob=0%,Diff=0.184; Prob=1%,Diff=0.156; Prob=2%,Diff=0.135; Prob=5%,Diff=0.112; Prob=10%,Diff=0.090
Stacked 3 high:
Prob=0%,Diff=0.383; Prob=1%,Diff=0.270; Prob=2%,Diff=0.234; Prob=5%,Diff=0.194; Prob=10%,Diff=0.146
From the foregoing: I conclude that you can reject the hypothesis that the differences in global means for the 36 months before and the 36 months after a volcanic eruption of these 9 volcanoes averaged together occurs by chance.
I also conclude that the same hypothesis would be rejected if you used a 3 or 4 high stack of these volcanoes for some of the 9 volcanoes but not all 3 and 4 volcano selections.
I finally conclude that using random individual dates/temperatures in the monte carlo greatly and improperly reduces the barrier for hypothesis rejection. I cannot say conclusively that the monte carlo results given in the thread introduction above used random individual dates/temperatures because it also used different parts of the BEST temperature series than I used. I would guess they used random individual dates/temperatures, but it would be a guess at this point.
julio (Comment #101698)
Julio, I plan to go back and carefully read what you posted so that I can completely erase it from my mind to avoid unconsciously recalling and using that information at later date.
Seriously, as a layperson I enjoy these discussion as they sometimes introduce me to new ways, for me anyway, of analyzing and looking at problems. I also realize that ideas and conjectures are being thrown around without the formalization that might be required for publishing a paper. My only problem from these discussions is that I never get a summary or for someone to outline what they judge would be a proper way of investigating a problem.
Thanks, Kenneth. These debates can certainly be enlightening if you can follow them all the way through–which for me is not always the case. It is interesting (but also occasionally frustrating) how all of us from different technical backgrounds have our own jargon. Sometimes I feel I need a translator more than anything else 🙂
Thanks for posting the results of your Monte Carlo analysis, also!
Andrew_KY (Comment #101695),
Too bad Lucia lets you make obnoxious comments devoid of substance again; it was much better when you were blocked.
Andrew_KY.
I know I’ve been distracted and I can see the back and forth has been a bit more.. uhmmm… personal than it ought to be. I just got in from mowing, and I can see that you are posting substance-free quips. Could you try to increase the amount of substance and eliminate the parts that most people would see as nothing but snide pointless quips? Bot #101694) and #101695 are examples of “snide pointless quips”.
lucia (Comment #101714)
“I just got in from mowing, and I can see that you are posting substance-free quips.”
It is a beautiful cool summer day here in Northern IL, but if it were one of those near 100 degree F days we have been having and Lucia comes in from mowing I say the guy gets dump. Heck, she might even dump me for this substance free remark.
OK Lucia.
I can understand you wanting to maintain a level of decency on your site. Believe me, I can sympathize. Try leaving a couple non-conformist comments on a pro-abortion page. It’s like I was blaspheming on a Muslim extremist site. You guys find me annoying. They hate me.
Andrew
Thanks Paul_K and Oliver for the clarification on “efficacy” used in this context.
Paul_K, while you mull over my other comments, could you post the zero-pole structure of your LTI?
julio, I think your explanation is right on target for why the driving is smaller than expected from equilibrium sensitivity.
I got great data today btw. It’s embargoed for now.
Where I’ve been working:
Gila River,
Superstition Mountains,
Ray Copper Mine and
more cactuses.
And yes I got stuck plenty of times.
(Stuck by cactus needles. My truck is still functioning, I’m happy to report.)
julio,
thank you (THANK YOU) for your couple of comments above. I thought from Carrick’s questions that I had finally crossed the line into Alzeimer’s. Mosh made a comment above about my comment on being “quietly admiring” of a result. The truth is that it is always nice to hear someone playback and build:- “I heard you say this, and that means…”
P
Carrick,
I apologise for the delay in my response, but I am working all out on something at the moment. As I write, it is 1:45 in the morning, so my response may not be fully coherent.
Again, dealing with your easy questions first, my LTI is the linear feedback equation for a single heat capacity system. For a step forcing, F, the (delta) temperature response function is:
T = F*(1 – exp(-t/tau)).
This satisfies all the requirements for being (single-pole) LTI.
Next easiest question. You wrote:-
“You’ve lost me on this one too. You are claiming it is a linear system, and at the same time saying “the magnitude of the spike is not in simple direct proportion to the magnitude of the volcanic forcing.†???
For a linear system, they have to be proportional, as with your LTI system.”
I am not challenging any mathematical orthodoxies, I assure you.
Let me restate the issue a little differently.
For the LTI system, the long-term response from an input STEP forcing is always proportional to the magnitude of the input step. Agreed.
For the LTI system, the peak response to an IMPULSE forcing varies linearly with the magnitude of the impulse forcings, provided always that the duration of impulse is the same. Agreed.
However, the relationship between response (temperature) and input (peak cumulative forcing) are completely different for the two cases – the step-forcing case and the impulse-forcing case. Do you agree?
You can consider these two relationships in loose terms as a reflection of two different frequencies of inputs. The impulse is very high frequency and the step forcing is very low frequency. The problem I am highlighting – which Julio has clearly grasped from his latest comment – is that linear regression coefficients (applied to cumulative forcings) from, on the one hand, something akin to a high frequency forcing and, on the other hand, something akin to a low frequency forcing cannot be directly compared.
If that doesn’t work for you then we can do some simple maths examples on the actual LTI I am thinking of. But, I am really tired, and I am hopeful that five minutes on a spreadsheet will allow you to convince yourself of what I am saying.
Erratum.
I should have written…
“my LTI is the linear feedback equation for a single heat capacity system. For a step forcing, F, the (delta) temperature response function is:
T = F*(1 – exp(-t/tau))/lambda where F is the step forcing, tau is the e-folding time and lambda is the feedback sensitivity in W/m^2/deg K, inversely proportional to linear climate sensitivity. “
Andrew_KY
People elsewhere may love or hate you. Either way, I prefer you avoid non-substantive quips. I did cut off the OT topic on the other thread.
Paul_K: I think Carrick just had a problem of translation. I’m sure we’re all on the same page now.
Carrick: beautiful scenery! Too bad about the cacti, though… 🙂
THanks for your detailed comments Paul_K.
That’s basically the same structure I use, only I have two poles. Like julio I think we’re all on the same page now. Like he said, there’s a lingo issue, different areas reuse the same word to mean different things (and it really gets confusing when people in different fields insist the different usages mean the same thing!).
I’ve some thoughts how to test all of this, but one interesting thing to look at would be compare the response of a step-function from your model to that of a more physically based one, like the AOGCMs.
julio, other than being stuck by them, I really enjoyed being around the cactuses. They are quite beautiful.
Carrick,
What are you doing out in the middle of the Sonoran Desert in August?? A little toasty today? It is really quite vast and beautiful especially when the afternoon T-storms roll in. We used to travel through there every February on our way to Puerto Penasco Mex. for a sailing regatta.
ivp0, I’m involved with a large scale infrasound sensor deployment that’s going during the month of August. Here’s a short blurb from the public release statement: “The purpose of these tests [to be performed at the White Sands Missile Range] is to study the effects of large scale explosions by collecting and analyzing seismic, acoustic, and blast damage data.”
We’re interested in being involved in the project because it gives us a chance to study the effect of sound propagation through the atmosphere (troposphere, stratosphere and thermosphere). Arizona is to the west, and there is a large summertime stratospheric jet that goes as fast as 100 m/s at about 45 km up and this produces ducted propagation that results in large signals at ranges of about 220 km (first bounce) and 450 km (second bounce). I’m doing “second bounce” measurements.
We were originally going to be up on the Mogollon Rim, but truthfully the USFS guy that handled the request for permits was completely incompetent, so we moved this part of the deployment down to the Phoenix area. (As usual, the Bureau of Land Management people were extremely competent and had quick turnarounds on requests for land usage.)
And yes it’s been “toasty” here. Daytime highs over 110°F for most of the deployment. We did a work stoppage when temperatures exceeded 105°F. Just a safety thing.
Carrick
For very good Mexican food, try El Charros corner of W 1st and Country Club in Mesa
Thanks Don, I will try that one. Mexican food turns out to be a really good choice for field work in these conditions (it just does, I’m sure there’s food science reasons why).
Carrick
Because you tend to drink copious amounts of really good Mexican beer with it I suspect
Interesting. So you are studying the acoustic effects of large scale explosions from White Sands. I suppose the stratospheric bounce is somewhat similar to a thermocline sonar bounce in the ocean. I can see how this might draw your interest into the study of climate change.
Enjoy your stay in the wild west. Don’t leave Phoenix without having a proper western cowboy steak.
Don: That’s me!
ivp0: It is pretty much the same problem except z -> –z 😉
Kenneth,
Thanks for posting the MonteCarlo results.
.
Paul_K,
You seem pretty far from Alzheimer’s. The only issue I have with a single time constant model is that we know the system has a multitude of time constants, and how well the temperature data fits any single time constant model will depend on the length of time over which we try to fit the model. A two time constant model ought to be more physically accurate, but still may not be terribly accurate. I think that a heat balance based model of heat uptake, which is reasonably consistant with the measured ocean temperature change over time and depth, would automatically yield an accurate response to applied forcing at all ‘frequencies’, from impulse to solar cycle to gradual GHG forcing. It is something I have been working on/thinking about for about 6 months (off and on).
Based on your above comments on writing very late at night, it appears you are writing in Europe. But you write English like a native speaker writes. Were you raised in the UK or the States?
Carrick,
“I’ve some thoughts how to test all of this, but one interesting thing to look at would be compare the response of a step-function from your model to that of a more physically based one, like the AOGCMs.”
I’ve already done this, albeit in an ad hoc way. Three AOGCMs (GISS-E, NCAR and CCSM) show a near perfect match to the linear feedback model throughout their entire forcing history. However, if one then considers future extrapolation of the results with forcing level held fixed (via the 20th century commitment runs) the flux response to temperature starts to deviate from this model to yield a much higher final temperature response than would be predicted from the linear model fit to history.
Similarly, if one compares predicted net flux behaviour from the linear feedback model for a fixed step forcing with the 2*CO2 scenario, one again sees that the AOGCMs in future prediction show a strong deviation from the linear model. Specifically, the net flux response to temperature change defines a curve, rather than a straight line for a fixed step forcing.
If you recall, Carrick, this was the central point I was making in this article:-
http://rankexploits.com/musings/2012/the-arbitrariness-of-the-ipcc-feedback-calculations/
So what is groundtruth here? I still don’t know. The fact remains that a single pole LTI will fully explain the historical temperature data (or the AOGCM matches to historical data). In future projections, the AOGCMs display a flux response to temperature change which cannot be described using a simple linear response term. Either you need to postulate a nonlinear temperature response or a linear temperature response moderated by time-dependence or a non-linear response moderated by time-dependence or the AOGCMs are simply giving wrong answers in prediction mode. Take your pick.
My statement : “There is no need to invoke nonlinear dynamics to explain this behavior, and despite Carrick’s comments, the temperature data can be matched perfectly well with a single-pole LTI system.” This was based on the application of Occam’s Razor. I should probably have emphasised that I was NOT saying that the single-pole LTI is the correct model – merely that you did not need to go to a more sophisticated model to explain the historic temperature behaviour – and in particular the relative contributions of volcanic and GHG forcings.
Re:SteveF (Comment #101773)
August 18th, 2012 at 8:04 am
Hi SteveF,
Your deduction is correct my dear Watson.
I live in the Dordogne in rural France. Retired engineer. Born and raised in the UK. Worked and lived in various parts of the US over the years, as well as about 15 other countries. 1 wife, 4 daughters, 1 son, 3 grandchildren, 6 dogs, 1 cat.
“I think that a heat balance based model of heat uptake, which is reasonably consistant with the measured ocean temperature change over time and depth, would automatically yield an accurate response to applied forcing at all ‘frequencies’, from impulse to solar cycle to gradual GHG forcing. It is something I have been working on/thinking about for about 6 months (off and on).”
I think we are going to have to agree to disagree on this one, SteveF. We’ve sort of had this conversation before. The measurements you are talking about should give us a more accurate estimate of total net flux, and hence a better constraint on short-term response. However, all of the observation-based estimates of climate sensitivity based on a linear model assumption yield very similar sensitivities in the range 1.3 to 1.8 deg K for a doubling of CO2. The large difference between these estimates and the AOGCM values of around 3 deg K arises from the non-linearity of the Earth’s flux response with rising temperature in the AOGCMs. Unfortunately, IMO, more accurate ocean measurements may assist in narrowing down uncertainty in the first, but can’t help with the latter.
Paul_K,
I hope then your house looks a bit like this: http://en.wikipedia.org/wiki/File:Beynac_chateau_1.jpg 😉
With regard to modeling: I am thinking about a little different approach. If you can approximately model the heat uptake over a range of time scales based on measured ocean temperature changes with depth versus measured ocean surface temperature changes, then you have (more or less) constrained the temporal system response over a range of time scales, independent of any assumptions about climate sensitivity. You can then look at different specified applied forcings and assumed climate sensitivities using a simple surface heat balance model (eg the response to a volcano, a specified step change, or a 1% per year increase in CO2 to doubling) combined with the expected ocean heat uptake, and compare the temporal evolution to what the GCM’s predict. Some preliminary results suggest that with an ocean model which reasonably matches measured heat uptake history you can’t reasonably fit both impulse response and long term response using a high sensitivity value (>3C per doubling) combined with large aerosol offsets, and the most reasonable fit is closer to 2C per doubling or a bit less, combined with much more modest aerosol offsets. The typical long term climate model response (~60% transient, ~40% extending out to several hundred years and more) seems to be duplicated only if you assume a high equilibrium sensitivity value; reducing the assumed sensitivity, with the same ocean model, weights the response much more in the transient period and less long term. One surprising thing: if you assume high climate sensitivity, then El Chichon and Pinatubo still today have a significant influence on surface temperatures. If you assume a lower sensitivity, then the influence of those volcanoes today has to be minimal.
Hi SteveF,
No we don’t live there, but clever of you to find a picture of our gamekeeper’s cottage.
I would agree with absolutely everything you wrote if I knew for certain that we could ignore areal effects.
I am always harping on doing sensitivity testing and to that end I decided to do the following:
A. Calculated the differences in the BEST mean global temperatures for the 12, 24, 36, 48, 60, 72 and 84 months before and after the 9 volcanoes listed in my previous post. The before and after series for each of the 7 period renditions were stacked 9 high with all 9 volcanic periods as described in previous post on the subject.
B. I did a Monte Carlo calculation by randomly selecting a month-year for the BEST global mean temperature series and then stacked 9 high the months before and after that date, using in separate calculations the 12, 24, 36, 48, 60, 72 and 84 month periods as I did for the volcanic eruption dates.
C. Calculated the Pearson correlation statistics for the mass of the sulfate ejection to the stratosphere for each volcano versus the average temperature differences I calculated in B above for each volcano for all 7 periods.
I obtained all the data for sulfate aerosol ejected into the stratosphere by volcano for all volcanoes except for El Chicon from this link:
http://climate.envsci.rutgers.edu/IVI2/IVI2TotalLoading501-2000.txt
For El Chicon I used the data from this link:
http://climate.envsci.rutgers.edu/IVI2/IVI2ReadMe.pdf
The results of my calculations are listed in the link below:
http://img140.imageshack.us/img140/1631/volcanostats.png
Taking the results together in the two tables in the link it can be seen that the before and after difference in temperatures for the average of all volcanoes falls off from a high in the 1 year period to low for the 7 year period. Using the periods greater than 5 years before and after an eruption does not allow the rejection of the null hypothesis that the difference can occur by chance and thus it appears that volcanic effects on temperature are mainly dissipated after 5 years. The lack of dissipation of the temperature effects for the Laki eruption centered at 1783 would appear to defy the more general pattern we see in the average for all volcanoes. There is considerable temperature noise in all the volcanic time series and thus the average result is probably more meaningful.
The non parametric Pearson correlation of 0.692 for sulfate ejections to the stratosphere versus before and after temperature difference while reasonably high has a very wide confidence interval of 0.048 to 0.929 – since I only had 9 data points.
In my post above I inadvertently used the Pearson correlation coefficient when I intended to use the Spearman non parametric correlation. Using the Spearman correlation I obtain a correlation of 0.617 and p.value of 0.0857 which does not allow me to reject the null hypothesis that that correlation can occur by chance.
“which does not allow me to reject the null hypothesis that that correlation can occur by chance.”
This is more normally stated as: which does not allow me to reject the null hypothesis that the correlation is zero.
Lucia, what happened above? It appears that a cat has taken over the graphs.
Hello, hello (echo) (echo). Is this thread dead?
I wanted to comment that the average in my linked table above for the 12, 24, 36, 48, 60, 72 and 84 months’ differences (that I used in the correlation against the ejected sulfates) is, in effect, weighted by 7, 6, 5, 4, 3, 2, and 1, respectively for these months’ periods – and intentionally so.
Re: Kenneth Fritsch (Comment #101865)
August 20th, 2012 at 5:35 pm
Kenneth,
I think it is admirable that you try to replicate and test the result presented, but I have the same concerns about the validity of your methodology as I had for the one presented in the original article.
Your first method does not fully account for autocorrelation. Your second method has the same problem, but introduces a new moot question which is about the theoretical underpinning for direct correlatability between sulphate peak and temperature response, a question which may equally be raised in connection with the main paper.
Let me try to set out what I believe should be the EDA for the test.
(1) test the temperature series for autocorrelation
(2) test for integration order for the observed level of autocorrelation
(3) fit the best ARMA or, more likely, ARIMA model
(4) run out the best ARIMA model upto the first volcano
(5) replace the calculated error terms with random seed and generate (MC) multiple realisations of the next n years of temperature data
(6) run out the best ARIMA model upto the second volcano and repeat (5) above
(7) Repeat (6) for the rest of the volcanoes
The multiple realisations for each of the volcanoes now give the expected values CONDITIONED BY the temperature data prior to eruption. These values can be compared with the actual realised values to assess likelihood.
The big difference is that the original approach assumes that any particular 3 year series is equally likely. This fails to recognise that the likelihood of any 3 year period is conditioned by the temperature series immediately prior to that period.
I hope this helps. I am not planning on running out an analysis myself, since I just can’t get too excited by the volcanic response. Ultimately it is just an excursion from the main temperature trajectory, I feel.
Kenneth and Mosh,
I would add that the first three steps above should have been carried out by the authors of the original paper as a matter of course. This should have been followed by standard tests to avoid spurious regression. All of this should have been included in the original paper.
If I were asked to review this paper, my first request would be for inclusion of these analyses. Without such analyses I would reject the curve-fitting part of the paper as junk science.
Paul K, my approach in the first post with 36 months periods before and after was to simply select 9 random month/years and then compare 9 stacked before and after 36 months BEST temperatures of 72 consecutively occurring months to determine the probability of obtaining those differences by chance. I have used actual temperature data whereas you are using data that is simulated from an ARMA or ARIMA model. My intention of using consecutive months was to capture the effects of auto correlation and any deterministic trends in the data.
My question to you is how you would handle any deterministic trends that might periodically occur in the temperature series and at various levels? You suggest an ARIMA model. I doubt that we could use an ARFIMA model since any long term persistence would require observations over a considerably longer time period than we have for the BEST series and thus that leaves us with an ARIMA model with d equal to an integer to account for deterministic trends. My question more specifically to you then becomes how you would handle several different deterministic trends in a time series? I assume here that the BEST series will be non-stationary. As I recall some of these more complex time series with multiple and varying trends have to segmented for analysis.
Also I want to be sure that we all understand that my calculation exercises were in answer to the calculations given in the thread introduction here and in an attempt to determine whether the month/years were chosen consecutively for the reasons I give above, or individually, which would not capture auto regression and deterministic trends.
Also to be clear the exercise in the thread introduction here and mine are separate from the paper where a model relating BEST temperatures to CO2 levels and evidently sulfates from volcanoes was presented.
I am disappointed that Steven Mosher has not yet responded to my specific questions related to the exercise here about consecutive versus individual months and the question about the paper in question authors selecting a 2 year half life for the volcano effects in order to obtain a best fit of the model to BEST temperatures and if sensitivity tests with other half lives were performed and if so what were the results.
“With an eruption at low latitudes, like Pinatubo, these fluctuations are caused by the increased temperature difference in the stratosphere between high and low latitudes. The results of detailed atmospheric studies after Pinatubo indicate quite complex patterns of pronounced summer cooling in many parts of the Northern Hemisphere but also pronounced winter heating in continental interiors. For example there were a few degrees of summer cooling over the US and Europe, and winter warming over Northern Europe and Siberia. ”
http://www.geolsoc.org.uk/gsl/education/page3042.html
I have plotted the monthly BEST global mean temperature series as anomalies and included the 12 month centered moving average series, the breakpoints found at January 1808 and November 1963 and the three resulting linear trends lines. The plots are in the link below.
Looking at the segmented series shows that it is probably not a good practice to pull random samples from over the entire series when doing a Monte Carlo but rather to confine the selection within the segments where the trend and monthly variations are closer to the volcanic period of interest.
Following up on PaulK’s inputs, I plan to attempt to fit ARIMA models to the 3 segments of the BEST series as defined by the 2 breakpoints after detrending those series.
http://img209.imageshack.us/img209/4417/bestglobmeanbreakpts.png
Using the auto.arima and arima functions in R from library(forecast) and library(stats), I was able to find the best AIC score for ARIMA models for the 3 detrended segments of the monthly BEST global mean temperatures as defined by the breakpoints at Jan 1808 and Nov 1963. For the 3 segments in order starting with the earliest to the latest, I fit the following models and coefficients:
ARIMA(1,0,0) ar1 = 0.341071589, intercept = -6.455950211, slope = 0.003288914
ARIMA(1,0,1) ar1 = 0.53243951 , ma1 = -0.14058056, intercept = -11.96950382 , slope = 0.00615074
ARIMA(2,0,2) ar1 = -0.17737517, ar2 = 0.46722475, ma1 = 0.54305672, ma2 = -0.12056645 , intercept = -47.21998130 , slope= 0.02394701
It becomes obvious that when analyzing the volcanic events that these segment differences should be taken into consideration. Depending on which segment the event falls into I would suppose one could use replications of simulated data to determine the probability of the temperatures for the times around the event occurring in that pattern by chance.
After looking at the first 2 segments of the BEST global mean temperature series as defined by the breakpoints at Jan 1808 and Nov 1963, I decided that my ARIMA model could probably not reproduce faithfully the structure I see in the BEST series. I therefore resorted to using the empirical data from the series but this time restricting my random selections of a month/year by the location of the individual volcanic eruption data in the series. I used the periods leading up to the eruption which I ended in the month before the eruption and which I started 3 years after a previous eruption or a month after the breakpoint whichever one was closest to the eruption data. I restricted my Monte Carlo analysis to 24 months before and after since the periods are not as long as in my previous analysis. As I did in my previous calculations, I made a random data selection and then compared the 24 months before and after the date. I repeated this for all nine volcanoes and obtained an average. I repeated this 1000 times and obtained a histogram of data and a calculated quantile listing the probability of obtaining a given temperature difference in the 24 months before and after an eruption for the 9 volcanoes.
The results I obtained are listed here and are very close to what I obtained using the entire BEST time series to draw random selections. I thus conclude that one can show a statistically significant difference in temperatures before and after an eruption when using all 9 volcanoes.
0% ,0.32 ; 1%,0.24 ; 2%,0.21 ; 3%,0.20 ; 4%,0.19 ; 5%,0.18 ; 6%,0.17 ; 7%,0.16 ; 8%,0.15 ; 9%,0.15 ; 10%,0.14.
I want to look closer at the BEST series and determine whether I need to further segment the 3 already segments parts of the series in order to obtain a reasonably good fit with an ARIMA model. The question is: are those lower frequency changes we see in the series due to deterministic trends or can that structure be emulated with an ARIMA model without assuming a trend?
As an aside, I think correlating the amount of sulfate emitted during an eruption to global temperature changes will be difficult because of the uncertainties in both the sulfate and temperature estimations.
Hi Kenneth,
Let me first try to explain by simple example why Mosh’s method is flawed, and why your first attempt at improvement retains the same problem (of not fully accounting for autocorrelation). We can see that the actual series has a lot of cyclic character. Suppose that we consider instead a different simple series, which consists of (just) a sine series plus a normal random error term; the sine series has a periodicity much greater than 72 months, and the error term has a standard deviation of less than a quarter of the amplitude of the sine cycle, say. Your null hypothesis is that volcanoes do not cause any change in temperature. You sample segments of 72 months from this series at random, and test the change in average temperature between the first 36 months and the second 36 months for each segment. You will find that you have a symmetric distribution for this change in temperature, since you are equally likely to sample from the rising part of a sine curve as from the falling part of a sine curve. Now suppose that in terms of the timing of your 9 volcanoes, 7 of them happen to sit on the falling part of the sine curve and 2 on the rising part. Clearly, for this hypothetical example, the expected aggregate outcome from your volcanoes should be a falling temperature even under the null hypothesis that they don’t have any effect at all! This yields a very different likelihood from that obtained by taking 9 samples from your symmetric distribution of differences, where the expected outcome is zero change. The error is arising because of the failure to account for the conditioning of the actual temperature data immediately prior to each volcanic eruption.
You asked: “My question more specifically to you then becomes how you would handle several different deterministic trends in a time series?”
If you KNOW that there are several different deterministic trends in the time series, or your argument is based on prior assumption of such trends, then you build them directly into the statistical model. Generally, however, this is not known. More specifically, in this instance, it is not known and cannot be assumed, and so it becomes a leap of faith to go for piecewise trends, especially since the data themselves are telling you that the residual structures are quite different for the three segments you have defined. The three apparent trends might be better described by a low-order difference model with a drift term. Who knows unless you test for it?
The critical requirement is to find a statistical model such that the random error terms end up as independent, unbiased, and homoscedastic; they should also satisfy minimum variance (or maximal information) criteria. This is not always easy, but it is an essential precondition for rigorous application of the sort of test which Mosh first proposed, and which you are seeking to improve on.
One of the things you might try as a shortcut is to reverse out the AMO temperature (with appropriate time-offset) from the land temperature series, and then try to fit the residual series with a statistical model. You may then find that you do not have to deal with a difference series – only a polynomial fit plus the level of autocorrelation in the high frequency data. So you fit the residual series and you then add the AMO temperature back in to form your final model. Test the error residuals, and if they are OK you have a model you can use for testing the effect of volcanoes.
Just as a parenthetic comment…
You wrote: “I have used actual temperature data whereas you are using data that is simulated from an ARMA or ARIMA model.” That was not my intention. I would use the actual temperature data right upto the point of (each) eruption by the simple expedient of fixing the error values in the ARMA or ARIMA model to fit. After eruption I would define the distribution of outcomes by allowing the error term to vary in accordance with its calculated statistics.
I hope the above helps.
Paul
PaulK, I have not studied your latest post, but below are my results using simulations of the Arima models with trends that obtained in an exercise above.
I looked closely at the Arima simulations of the BEST global mean temperature data from the 3 segments described in previous posts and decided that the models do a reasonable job of emulating the structure of the BEST series except for some trend like features in the first 2 segments. For completeness I used the Arima models for the segment in which the volcano eruption period resides in place of the empirical data used in my previous Monte Carlo analysis described above. I did 1000 replications with a different simulation of the appropriate Arima model for the 9 volcanoes. I took means for the 24 months before and after an arbitrary date in the series generated by the Arima model. I calculated the probability quantiles with the corresponding difference in means for the 9 volcanoes together that would be expected if the difference occurred by chance.
The results are listed below and are very close to those I obtained using empirical data. The result confirms that the effects of the average effect of 9 volcanoes can be shown to be statistically significant. The closeness of the results of the modeled and empirical approaches would indicate that the segmenting with breakpoints and modeling does a reasonably good job of emulating the BEST series.
0% ,0.33 ; 1%,0.24 ; 2%,0.21 ; 3%,0.20 ; 4%,0.19 ; 5%,0.18 ; 6%,0.17 ; 7%,0.17 ; 8%,0.16 ; 9%,0.15 ; 10%,0.14.
PaulK, thanks for taking the time to make some comments and suggestions on my analyses. Your point on a cyclical structure in the BEST temperature series and the problems that might impose on Monte Carlo methods is well taken, although off-the-top of my head I do not see where the Monte Carlo that I did, as opposed to what we think Mosher (and Robert) did, would not pick up this cyclical structure by making the larger mean differences in 24 months before and after a random date more likely to occur by chance than would be the case without extensive cycles. That might even be a case against using an Arima model that does not account for cycles in the series. Actually though I was surprised how well the Arima models visually fit the structure of the BEST series except for a couple trend like structures. Regardless, your point implies that one needs to do a spectral analysis of the BEST temperature series and with that I agree.
The drift term and removing it by differencing hits, I think, on a point we have had in discussions at the Black Board before. I am of the supposition that a drift term that could potentially be removed by differencing implies a random walk and I thought it was decided by some at least that a temperature series could not have a random walk. I was of the opinion that a model for a temperature series could be trend stationary, i.e. the residuals of a detrended series can be stationary, but that an Arima model for a temperature series could in effect never validly have a d=1 or higher integer term. If we consider Arfima models, a fractional d value could be considered for a temperatures series. That would imply long term persistence and I am not sure that we have temperature series sufficiently long to test that proposition. Anyway my point is that if I can produce a trend stationary series by detrending than a deterministic trend must exist in the temperature series or the trend has long term persistence. There are other ways, I believe, of determining whether a trend exists in a shorter series, but unfortunately I believe I have already shown for my own benefit that I can take a short segment of a series with long term persistence and no deterministic trends and obtain a positive test for a deterministic trend.
Paul_K, what happens when you add an external trigger to your example? (We have one here.)
Using the Augmented Dickey-Fuller test in R – library(tseries) and function adf.test – shows that the 3 segments and entire BEST global mean temperature series are trend stationary. This result is more indicative of a deterministic trend than for the existence of drift.
Of course, as I noted before if the BEST temperature series is a segment from a longer series (and unmeasured or validly proxied at this point in time) with long term persistence, the trends in that series could fool the ADF test. I think the ADF test can handle an Arima model, as opposed to an Arfima one, but I would have to test that supposition.
Actually the ADF test would supply the correct answer for a trend resulting from a short segment of a series with long term persistence and without a deterministic trend by rejecting the null hypothesis that the series has a unit root. The problem would come from assuming a deterministic trend.
I would think it is fairly safe to assume that the effects of GHGs will produce a deterministic trend in the later parts of the instrumental temperature record even if we might argue about the size and persistence of that trend.
Carrick,
“Paul_K, what happens when you add an external trigger to your example? (We have one here.)”
Not a problem if you are referring to the volcanoes as the “external trigger”. Under the null, they have no effect. Hence it is completely legitimate to set up the statistical model under the assumption that they have no effect. Their effect is then measured as a statistically unlikely deviation from expected values.
Kenneth,
I will respond to your longer post in a moment, but can I say that I am very surprised by this result:-
“Using the Augmented Dickey-Fuller test in R – library(tseries) and function adf.test – shows that the 3 segments and entire BEST global mean temperature series are trend stationary.”
The lag-order in the ADF test is critical. You need to test the entire BEST series for the degree of autocorrelation before you apply the ADF test. The ADF test works by testing for the significance of a non-zero regression coefficient of the lag-1 temperature term AFTER accounting for the autocorrelation terms. If you apply the test with too few autoregressive terms included, this increases the likelihood of a non-zero coefficient for the lag-1 temperature term. This translates into an increase in the likelihood that you will reject the presence of a unit root. So the big question is:- what lag order did you use for the ADF test on the full series, and on the basis of what test(s)?
This is an important question. All of the global temperature series test I(1)done by genuine experts. This particular land series has the same “structural characteristics” at first sight, so I am very surprised at your result.
Paul, below is a link to the documentation of how ADF is handled in R.
The pertinent details are excerpted here (I used the default value for k):
“The general regression equation which incorporates a constant and a linear trend is used and the t-statistic for a first order autoregressive coefficient equals one is computed. The number of lags used in the regression is k. The default value of trunc((length(x)-1)^(1/3)) corresponds to the suggested upper bound on the rate at which the number of lags, k, should be made to grow with the sample size for the general ARMA(p,q) setup. Note that for k equals zero the standard Dickey-Fuller test is computed.”
The lag orders were as listed below for BTS (the entire BEST series), W1(the earliest occurring segment defined by the breakpoints), W2(the middle segment) and W3(the latest occurring segemnt):
adf.test(BTS)$parameter
Lag order = 14
adf.test(W1)$parameter
Lag order = 8
adf.test(W2)$parameter
Lag order = 12
adf.test(W3)$parameter
Lag order = 8
http://127.0.0.1:25740/library/tseries/html/adf.test.html
Re: Kenneth Fritsch (Comment #102092)
August 24th, 2012 at 2:05 pm
Hi again Kenneth,
You wrote:-
“PaulK, thanks for taking the time to make some comments and suggestions on my analyses. ”
Thank you for your thanks. I will re-emphasize that I am not seriously challenging your conclusions. I would be very surprised if rigorous testing failed to show a significant volcano effect. I am only having a friendly conversation about the methodology employed, and possible ways to eliminate the weaknesses.
With that said, it may be helpful if we could establish some common definitions applied in time series analysis. Some of your usage seems to be a little idiosyncratic.
In TSA jargon, typically a “drift” or “stochastic drift” refers to a constant in the statistical model of the difference series. A “stochastic trend” refers to a function of t included in the model of the difference series. A “deterministic trend” refers to a function of t included in the level series. A “random walk” is a very specific time series. It has a unit root. Not all series with a unit root are random walks, but all series with a unit root have some component in the model which has unbounded variance over an infinite time-frame.
“The drift term and removing it by differencing hits, I think, on a point we have had in discussions at the Black Board before. I am of the supposition that a drift term that could potentially be removed by differencing implies a random walk and I thought it was decided by some at least that a temperature series could not have a random walk.â€
I THINK that you are saying something like the following.
“The use of an ARIMA model implies infinite variance over time, and I thought it was decided by some at least that a model with unbounded variance could not be reconciled with the physics. “
I am in broad agreement with this. You cannot fit an ARIMA model and then use it to produce a convincing explanation of the physics underpinning the series. However, that is not what we are trying to do here. What we are trying to do is to find the best statistical model of the series, using the actual statistical properties of the time series, in order to quantify the likelihood of any particular realisation within that particular series. The best way of doing this may be to use a deterministic trend plus an ARMA model of the residual or it may be an ARIMA model with or without a drift term in the difference model. However, you don’t get a free choice in the matter. Whatever model you choose must satisfy the actual properties of the series. You can’t for example elect to ignore a positive test for a unit root just because you don’t think it conforms to your idea of the physics. One way or the other, you have to apply a transform which gives you a stationary residual series. The critical requirement is that the final error terms are stationary, unbiased and satisfy minimum variance or maximal information criteria. If you ignore a unit root you will not be able to do this. However, you do get some choice in the methodology applied to effect this transform.
From the general to the specific… You wrote:-
“…off-the-top of my head I do not see where the Monte Carlo that I did, as opposed to what we think Mosher (and Robert) did, would not pick up this cyclical structure by making the larger mean differences in 24 months before and after a random date more likely to occur by chance than would be the case without extensive cycles. That might even be a case against using an Arima model that does not account for cycles in the series. “
I would agree that your algorithm should get closer to the truth than Mosh’s. However, if I have understood what you did, you are still not using the specific temperature data before a volcano to predict the realisations after its eruption. My main point was not about the cyclic nature of the data. It was that you are still sampling from the marginal distribution, when you really need the conditional distribution. Specifically, you want to know the distribution of outcomes in the three year period after a volcano GIVEN the temperature series before that volcano happened. My sine example was merely to illustrate that the answers can be very different if there is strong autocorrelation in the dataset.
Hope this clarifies a bit.
Re:Kenneth Fritsch (Comment #102117)
August 25th, 2012 at 9:06 am
Kenneth,
As a sense check,
(1) try testing ARMA significance on the annual (12-month average) series and then calculating the appropriate lag-order for an ADF test on the annual series.
(2) try testing ARMA significance on the monthly series and inputting the appropriate lag-order found
I suspect that with the monthly data, you may be running into sludge with such an enormous number of degrees of freedom being used.
Well said Paul.
Paul_K:
OK that’s something I agree with.
Time-aligned averaging based upon eruption date may not be a perfect method (because the climate response from each eruption isn’t identical, so you lose signal as well as noise by the averaging process), but it’s certainly something that can be justified based on statistical arguments.
Paul, I am layperson attempting to learn as much as I can about these matters here and I appreciate the comments and suggestions I receive at these blogs. And, of course, my layperonish is laid bare by your comment below:
“Some of your usage seems to be a little idiosyncratic.”
I intend to follow up on your suggestions and report my results at this thread. In the meantime I have a few comments and questions on your replies.
I believe the arima models I used for the BEST series and the 3 segments produce error terms that are stationary and I’ll show you results in a future post. As a hypothetical, if I could produce stationarity of a series with either a differencing or by detrending which would be the better candidate? I would think detrending because differencing implies a unit root and a unit root implies an unbounded variance or temperature in this case. I have looked at arima models for the BEST data with detrending and differencing and while I would need to show this with results of objective tests, as I recall detrending gave better fits with more simple models.
Paul, when you say the following you will have to give me specific details on how one would go about using the empirical data prior to a volcanic eruption to predict the data after the eruption. I suppose I can see how one might attempt this with a model, but in this instance I am drawing a blank.
“Specifically, you want to know the distribution of outcomes in the three year period after a volcano GIVEN the temperature series before that volcano happened.”
hi Kenneth,
“As a hypothetical, if I could produce stationarity of a series with either a differencing or by detrending which would be the better candidate?”
The answer is the one which offers maximum information – or more formally minimum loss of information. In simple terms, if both models really do produce a white noise residual, and they use the same number of degrees of freedom in the fit, then the model with the smaller variance in the residual should be preferred. This concept is extended to the comparison of models with different degrees of freedom by selecting the model with the smaller AIC value.
The methodology for calculating realisations conditioned by preceding values…
No matter how complex the model you end up defining, there should be a white noise error term in it, εt, say, with mean zero and standard deviation, σ. The value of σ is routinely calculated as part of the model fit. In the run up to the first volcano, these values can be calculated as the difference between the “observed” value and the model-predicted value without the white noise term. At the point of eruption of the first volcano, you therefore know all of the antecedent values of temperature and error terms – necessary inputs to your model. To predict the temperature at the next timestep, you use your model to predict the temperature without the white noise term, and then add in the white noise term in the form of a random sample from a normal distribution N(0,σ^2). You now have all the information to predict the next timestep, again using a random sample for the error term. You repeat this process for 3 years, say. You now have a single realisation of the 3 year period, conditioned by the temperature data and the error information prior to the eruption. You abstract the statistic of interest, in this case the mean over the three year period. You repeat this process 1000 times, say, and you now have the expected distribution of mean temperatures GIVEN the temperature data prior to the eruption of the first volcano.
You can now move onto the second volcano to do the same thing, but you use the actual recorded temperatures upto the second volcano, ignoring all the work you did on possible realisations from the first volcano. You repeat the Monte Carlo process for the second volcano to obtain the expected distribution of mean temperatures GIVEN the temperature data prior to the eruption of the second volcano.
Once this is completed for all of the volcanoes of interest, you can compare the actual temperature outcomes for each volcano with the corresponding conditional distribution you have obtained; this allows you to test whether the actual outcomes are statistically unlikely (or not).
Carrick,
“Time-aligned averaging based upon eruption date may not be a perfect method (because the climate response from each eruption isn’t identical, so you lose signal as well as noise by the averaging process)…”
I agree. I am in response mode, in this instance responding to the proposition offered by the article (and further developed by Kenneth) that the presence of a volcanic signal can be shown in the data on the basis of a statistically unlikely shift in the 3-year block-averaged temperatures before and after. To be fair, though, I think that if the shift could be shown to be highly unlikely against a credible statistical model which fully accounted for autocorrelation, I would accept the validity of the argument notwithstanding the signal-smearing issue.
Steven Mosher (Comment #101251)
August 10th, 2012 at 12:44 pm
Theory says the emissions should cause a temporary drop in temperatures.
The Temperature Anomaly Stack makes sense and appears to confirm this. Why is the drop in temperature temporary? The lost energy is gone, so why does the temperature recover quickly to the same level? Doesn’t that support Willis’s thermostat idea?
Has anyone stacked temperatures around El Niños and La Niñas in the same manner?
Ledite,
The deop in temperature is temporary because a drop in temperature reduces heat loss to space. The loss of heat increases when the temperature rises. You do not need to appeal to Willis’s thermostat or Richard Lindzen’s iris to have a net positive change in loss rate with rising temperature. As with all things ‘climate’, the devil is in the details: how much does the rate of loss rise as the temperature rises? There are lots of conflicting data…. not to mention conflicting models. The honest answer is nobody knows for sure. I guess ~ 2 watts/M^2 per degree rise. The modelers estimate between 0.8 and 1.8. This should become clearer over the next 50 years.
SteveF, ” Nobody knows for sure.” Give that man a prize. Food for thought. a one degree rise in surface temperature over the oceans should produce a 4% increase in precipitation, which depending on the surface temperature of the water could result in about 3.4Wm-2 of additional surface cooling. Which would negate the warming.
With the NH having more obvious response to volcanic impact you can see the ~3 year aerosol forcing, but there is ~5-8 year global settling time as energy is transferred from the southern hemisphere. The most stable temperature region on Earth is 44-64 S, so I would think you would need to follow the “thermal wave” so to speak. Not all that simple.
Paul_K, I will give a status report on what I have done to date and give more detail on using AIC to determine the best model in response to your comment below.
“The answer is the one which offers maximum information – or more formally minimum loss of information. In simple terms, if both models really do produce a white noise residual, and they use the same number of degrees of freedom in the fit, then the model with the smaller variance in the residual should be preferred. This concept is extended to the comparison of models with different degrees of freedom by selecting the model with the smaller AIC value.”
What I have found is that more than one model candidate can, not infrequently, have an AIC score almost the same as another. The excerpt below from the Wikipedia link illustrates what I am attempting to point out. The closeness of scores that I refer to are often closer than that shown in this example. My question then becomes: Given that the AIC score cannot determine the best model fit which one is then chosen in a temperature series where the choice is between differencing and detrending?
http://en.wikipedia.org/wiki/Akaike_information_criterion
“As an example, suppose that there were three models in the candidate set, with AIC values 100, 102, and 110. Then the second model is exp((100−102)/2) = 0.368 times as probable as the first model to minimize the information loss, and the third model is exp((100−110)/2) = 0.007 times as probable as the first model to minimize the information loss. In this case, we would omit the third model from further consideration. We could take a weighted average of the first two models, with weights 1 and 0.368, respectively, and then do statistical inference based on the weighted multimodel;[3] alternatively, we could gather more data to distinguish between the first two models.”
I have looked at the BEST series on a yearly basis with the Augmented Dickey-Fuller test for unit root and the p.values for the entire series was 0.016, while for the segments (as defined by the breakpoints) of the BEST series as they occur in time were respectively, 0.344, 0.030 and 0.010. Obviously as the degrees of freedom decrease it is more likely for the ADF test will fail to reject the null hypothesis that the series has a unit root. For analyzing the effects of volcanoes on temperature over relatively short periods I would think that monthly should be preferred for use over yearly data.
As an aside I have noted that the variance of the data in the 3 segments of the monthly BEST temperature data, as defined by the 2 breakpoints, is very different (I should do an F test to show statistical significance). Besides the breaks in the data the change in variance is another reason for doing the analysis of volcano effects on temperature by using segments and not the entire series as if it were homogeneous.
Before proceeding, I need to look in depth at your suggested conditioning of the model data with the observed and determine how different that approach is from the one I used and reported above where I modeled data in the 3 segments and then use that modeled data prior to a volcanic eruption to determine with a Monte Carlo how likely that the differences in mean temperatures in the 24 months before and after the volcanic eruption would be.
Paul_K, I am about ready to attempt your suggested method conditional on the temperature data prior to the eruption, but I am unclear on what prior data to use. From your coments it appears I should use all the BEST temperature data prior to a given volvano eruption and further that I should fit a new model for each volcanic eruption.
Paul_K, the standard deviations of the segments of the monthly BEST series from earliest to latest are 1.348554, 0.6589793, 0.468976. These differences are shown by an F-Test to be statistically significant. Would this change your mind on how to proceed with your method?
Kenneth,
While I consider some of your earlier comments, let me take your last point first to save you some time.
“From your coments it appears I should use all the BEST temperature data prior to a given volvano eruption and further that I should fit a new model for each volcanic eruption.”
The first part of this sentence I agree with – you should be using the entire dataset to define a model. The second part – absolutely not. You should be applying the SAME model to the entire series.
Kenneth,
You wrote:-
“I have looked at the BEST series on a yearly basis with the Augmented Dickey-Fuller test for unit root and the p.values for the entire series was 0.016, …”
Again I would ask, at what lag-order? And what specific tests did you use to assess the appropriate value?
Paul
Re:Kenneth Fritsch (Comment #102157)
August 26th, 2012 at 1:34 pm
Kenneth,
“Paul_K, the standard deviations of the segments of the monthly BEST series from earliest to latest are 1.348554, 0.6589793, 0.468976. These differences are shown by an F-Test to be statistically significant. Would this change your mind on how to proceed with your method?”
Not yet. This should actually be telling you that your segmented detrending of the level series is PROBABLY not the best approach to choose as your main atttack. I say “probably” because you would need to complete the process of decorrelating the residuals in the three segments to be certain that you have a problem of heteroscedasticity in the final “white noise” error term. My strong suggestion is that you drop segmentation for the moment as your FIRST approach, and search for a model which gives you a stationary residual over the entire series. After sufficient search, you may have to declare that such a model does not exist (i.e. you can’t find it); after that you apply transforms to eliminate heteroscedastity; if that does not work, you then use a formal breakpoint analysis to define a segmented model.
But note importantly that the fact that the residual series you have here display different variance across the different segments does not mean DE FACTO that you have a problem. These residual series are not white noise series. You only know you REALLY have a problem with heteroscedasticity after you have reasonably exhausted the attempts to explain the variance in terms of autocorrelation in these residuals.
Kenneth,
“Obviously as the degrees of freedom decrease it is more likely for the ADF test will fail to reject the null hypothesis that the series has a unit root. For analyzing the effects of volcanoes on temperature over relatively short periods I would think that monthly should be preferred for use over yearly data.”
Having read your results in more detail, I would just like to fix some stuff before I return to a suggestion for a radical change of course.
Your first sentence above is not an “obviously”. In fact with reasonably well-behaved series, the opposite is true. The R version of the ADF test fits a model with a bunch of AR terms plus stochastic drift plus stochastic linear trend to the difference series. It then tests for the significance of the presence of a non-zero coefficient of the lag-1 term. If this term is clearly non-zero then the unit root is firmly rejected. If you underestimate the lag-order (decrease the degrees of freedom in your terminology), then there is an increased chance of an erroneous non-zero value attributed to the lag-1 AR coefficient. In other word, there is an increased chance that you will reject a unit root, when it is actually present. As you increase the lag-order, the likelihood of this “Type I” error should diminish, and the likelihood of Type II error – accepting a unit root when it is not present – should increase.
Unfortunately, for real world time series, this tendency is not universally true, and hence the results (p-values vs lag-order) are never perfectly monotonic. So in reality you cannot escape the need for a rigorous pre-analysis of the appropriate lag-order to be applied to test for a unit root. This requires an analysis of the ARMA characteristics of the series (or detrended series) to which the ADF test is to be applied..
With respect to your second comment, I agree. However, I think that here you need to go through a downscaling process to test reality. With the monthly data, you are pushing the envelope on several sides. Many of the assumed asymptotic distributions which underpin statistical theory break down if you are eating up a large number of degrees of freedom – even if this number is small as a proportion of the total dataset. The monthly analysis is likely to be focused on, or side-tracked by, any seasonal variation which is left in the monthly dataset. Also numerical error and significance smearing.
Paul_K (Comment #102159)
The lag orders for the yearly BEST data weres 6, 3, 5 and 3, respectively, for the entire series and segments 1, 2 and 3. The test was as described above for the R function adf.test and library (tseries).
I will calculate the standard deviation of the residuals of the models I found best fitted the 3 segments and do the same using the model that best fitted the entire BEST series.
Paul_K, I have calculated the standard deviations of the residuals for the best fitted models for the 3 segments of the monthly BEST series as defined by the break points at Jan 1808 and Nov 1963. The differences in standard deviations of the residuals are shown to be statistically significant. The R code and results are listed below.
ARIMA(1,0,0) ar1 = 0.341071589, intercept = -6.455950211, slope = 0.003288914
ARIMA(1,0,1) ar1 = 0.53243951 , ma1 = -0.14058056, intercept = -11.96950382 , slope = 0.00615074
ARIMA(2,0,2) ar1 = -0.17737517, ar2 = 0.46722475, ma1 = 0.54305672, ma2 = -0.12056645 , intercept = -47.21998130 , slope= 0.02394701
AR1=arima(W1,order=c(1,0,0),xreg=time(W1))
W1ResSD=sd (AR1$residual)
W1ResSD
#[1] 1.266132
AR2=arima(W2,order=c(1,0,1),xreg=time(W2))
W2ResSD=sd (AR2$residual)
W2ResSD
#[1] 0.5432009
AR3=arima(W3,order=c(2,0,2),xreg=time(W3))
W3ResSD=sd (AR3$residual)
W3ResSD
#[1] 0.2953904
var.test(AR1$residuals,AR2$residuals)
F test to compare two variances
data: AR1$residuals and AR2$residuals
F = 5.4364, num df = 660, denom df = 1869, p-value < 2.2e-16
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
4.803938 6.175667
sample estimates:
ratio of variances
5.436395
var.test(AR1$residuals,AR3$residuals)
F test to compare two variances
data: AR1$residuals and AR3$residuals
F = 18.384, num df = 660, denom df = 575, p-value < 2.2e-16
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
15.68607 21.52706
sample estimates:
ratio of variances
18.38396
var.test(AR2$residuals,AR3$residuals)
F test to compare two variances
data: AR2$residuals and AR3$residuals
F = 3.3816, num df = 1869, denom df = 575, p-value < 2.2e-16
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
2.955682 3.850879
sample estimates:
ratio of variances
3.381646
Kenneth,
You don’t have to work overtime to convince me that your segmented series produces heteroscedastic residuals. Your results look eminently reasonable. Sit back for a moment and ask yourself what they are telling you about the data.
My suggestion for a radical change of course…
Think again about removing the AMO data from the land temperature series and testing what is left. While there is no way that one could do this to support an argument for low frequency causality in the dataset, that is not what we are trying to do here. We are trying to develop the best stat model in order to assess the likelihood of certain short-term realisations.
I think therefore that one could legitimately argue for a model that consists of the AMO plus whatever is left. The “whatever is left” is almost certainly a high frequency corrrelated series, which requires a good quality model fit. I suspect that this may provide a fast shortcut to your search.
In the interim of a search for finding a single model fit for the entire series what if I did what you first suggested but now use the volcano appropriate segment (and the corresponding model) in place of the entire series?
Would not an alternative explanation for the changing variance in the data merely be a result of the BEST data set using more stations with better spatial coverage going forward in time? I have a problem at this point seeing how backing the AMO effects out of the land temperatures will change the differences we see in the high frequency variations in the model residuals of the 3 segments.
The AMO data goes back to 1857 and the BEST series goes back to 1753. Also 3 of the volcanoes occur before 1857.
hi Kenneth,
If you’re still tuned in…
Working backwards…
The fact that the AMO dataset only goes back to 1857 is limiting, but I suspect that it is still a valuable thing to test for the 6 volcanoes in the common period with a solid basis for a model if one can be found.
“I have a problem at this point seeing how backing the AMO effects out of the land temperatures will change the differences we see in the high frequency variations in the model residuals of the 3 segments.”
It won’t eliminate the high frequency correlation. Whichever model(s) you choose will have to fit these high frequency data. However, it should/may eliminate a lot of the multi-decadal structure, which is where your main challenge lies, and leave you with an easier series to fit. Ideally, it should leave you with a trend-stationary residual with low order auto-correlation. (Your tests to date are still unconvincing in this regard. You need to test for a unit root at and around your best estimate of lag-order – not at the maximum possible upper bound based on rule-of-thumb.)
Fitting the multidecadal data is likely to be very difficult – but it is essential for what you are trying to do. The two broad options are that you explain the multidecadal variation using an ARIMA model or you eliminate or suppress the variation using the AMO data. If you go the first route, you will, I believe, have a large residual variance and a consequently weak test for volcanoes. The latter seems likely (to me) to be more certain, but I could be wrong. I am prejudiced by the fact that for the two global series which I have tested, (HADCRUT3 and GISSTEMP), it is the multidecadal data which leads to a failure to reject a unit root in the series.
“Would not an alternative explanation for the changing variance in the data merely be a result of the BEST data set using more stations with better spatial coverage going forward in time?”
It is very likely that the measurement uncertainty increases as one goes back in time, and there is possibly some bias introduced by the different geographical distributions of thermometers; these two things could certainly be part of the explanation for an increased variance way-back-when. But how are you going to distinguish between this measurement error problem and a true change in the data structure? What model are you going to postulate to separate the two? From a pragmatic viewpoint, you should try to fit the entire dataset with the minimum number of assumptions. If you then end up with residuals which are heteroscedastic, you FIRST check that it is not sourced by model mis-specification, and you SECONDLY consider the use of a proxy variable which eliminates the heteroscedasticity (like the AMO perhaps?). Only after that might you consider the use of one of the common cures for heteroscedasticity by transform or crude segmentation of the dataset.
“In the interim of a search for finding a single model fit for the entire series what if I did what you first suggested but now use the volcano appropriate segment (and the corresponding model) in place of the entire series?”
By all means, try it, Kenneth You may gain insight into the data structure, as well as the sensitivity of the volcano test to some assumption of correlation. My advice however is not to delude yourself at that stage that you have a bulletproof model.
Paul
Paul_K as a place holder here I am in the process of summarizing my findings using your suggested conditioning method but using segments of the BEST temperature series as defined by the breakpoints and not the entire series as you advised and comparing those results with my earlier methods using empirical and model data for 72 consecutive months and then comparing 36 months before and after means. All methods confine the models to the segments in which the volcano occurred.
In the link below I present the results of using Monte Carlo approaches to determine the probabilities of the mean in the Best monthly land temperatures 36 months before and after a volcano eruption date (or in one case 36 months after the event) occurring by chance for 9 major volcanoes with event dates within the BEST series.
In all cases the Monte Carlo calculations were confined to the 3 segments of the BEST series as defined by the breakpoints at Jan 1808 and Nov 1963. Three different Arima models were obtained using the data within each segment. Monte Carlo results are listed in the table linked below and were compiled for each of the nine volcanoes, combined 9 volcanoes, combined 6 latest occurring volcanoes and the combined 5 latest occurring volcanoes. These results were obtained using 4 different approaches which are described in the linked table and below in this post.
The first approach used observed data prior to the volcano event and within the segment in which the event resided except in a couple of cases noted in the table where the data were sparse and produced very skewed results. For those 2 events the data used were prior to the event and extended into the period between that event and the next occurring one. The general approach was as described previously and involved randomly selecting 72 consecutive months and then calculating the differences in the mean temperatures for 36 months before and after the centered event.
In the second approach the general procedure was the same as the first one described above except here the data used was from the realizations from simulations of the segment appropriate Arima model. The standard deviation used in the model was calculated from the observed data prior to the event and within the segment in which the event occurred.
In the fourth approach the procedure used was per Paul_K’s suggestions described above except here the instead of using all the data in the BEST series prior to the event it was limited to the segment in which the event occurred but prior to the event data. The model data for the 3 months following the event were obtained using the same segment appropriate models used in the second approach except here the model was conditioned by the observed data prior to the event in the event appropriate segment. Instead of using the standard deviation from the observed data the standard deviation used was calculated by difference in the prior observed data and the model with the white noise removed.
The third approach was the same as the fourth approach except here the conditioned model was used to generate realizations of the model for 72 months of consecutive data with 36 months before and after the event used to calculate, in turn, the before and after mean differences. The third approach was used to determine whether that approach would move provide results closer to the first and second approaches.
I should also point out here that the trend data specific to the segments were incorporated into the Arima model realizations for approaches that used models.
The results show that few if any individual events show a statistically significant effect on temperature following the event in the four approaches used, but when all 9 are combined together the result does show statistical significance. The results for significance are mixed depending on approach when the latest 6 and 5 occurring volcanoes are combined. The result of all four approaches tended to be in general agreement on probabilities with the increasing order tending towards more significant results going from the second, first, third and fourth approaches. I did observe from the histograms (not shown here) that distributions for the Arima model realizations where less skewed than those from the observed approach and particularly where the data was more limited.
I think it might be more realistic to work with 72 consecutive before and after months than 36 months after, but to show that more conclusively I would need to put together some toy models where the truth was known. Using 72 consecutive months with the conditioned model in approach three did move it closer to approaches one and two and away from approach four.
I want to follow this post up with a closer look at why or why not a single model can be used for the entire BEST series.
http://img407.imageshack.us/img407/2002/montecarlovolcanoeeffec.png
Hi Kenneth,
Can you clarify:
“Instead of using the standard deviation from the observed data the standard deviation used was calculated by difference in the prior observed data and the model with the white noise removed.”
Can you also explain how you have calculated the “summed” probabilities for the 5 (or 6) summed volcanoes. There are at least three possible methods for doing this.
Thanks
Paul
Paul_K, in answer to your first question I used your suggestion as noted in the following excerpt from your post. I used the model specific to the segment within which the volcano occurred and the observed data prior to the eruption date but within the segment the volcano occurred. For the 36 months following the eruption, the comparison with the observed result to determine the probability of that result occurring by chance was made to 1000 realizations using the segment appropriate model with the standard deviation as calculated per your suggestion. When I did a 36 months before and after the eruption date difference I used the same calculated standard deviation but now applied it to 72 months of model appropriate realizations over 36 months before and after the eruption.
“In the run up to the first volcano, these values can be calculated as the difference between the “observed†value and the model-predicted value without the white noise term.”
In answering your second question, I combined all 1000 of the realizations of means or mean differences for each volcano into a 1000 by 9 or 1000 by 6 or a 1000 by 5 matrix and averaged across the volcanos to obtain 1000 realizations of the grouped volcanos. I compared those probable means or mean differences to the average observed means or mean difference for the group.
Paul_K, I have been looking into the issue of heteroskedasticity in the BEST series and came up with the plots shown in the link below. The four plots are: monthly (1) and annual(2) mean land temperatures and the standard deviation of the monthly data for each year (3) and the standard deviation of 10 years of data for each year(4). It is easy to see that the standard deviations start high and approach a plateau that starts around 1875 for both the yearly and decade basis.
Below I show the results of the Breusch-Pagan test for heteroskedasticity (HSD) for the entire monthly series and the windows for the segments I used and in addition the window from 1880 to 2011. The entire period 1753 to 2011 shows HSD as do the periods of 1753-1807 and 1808-1963, while the periods 1963-2011 and 1880-2011 do not.
It becomes obvious that the 2 earliest occurring segments I used, as defined by the 2 breakpoints in the BEST series, exhibit HSD within the segments. Also it is obvious that the period that BEST extended back in time from 1875 or so (which is near the ending date used in the GISS, CTU and GHCN temperature series) to 1753 is period problematic for HSD. Did the BEST paper in which regressions where performed on CO2 and volcano effects take the HSD into account?
I would think the proposition could be tested whether the changing variations can be attributed to changing spatial/geographic coverage. My question to you Paul_K: Is, while using models to test the hypothesis that the differences in temperatures could occur by chance would be affected by HSD, would not using a Monte Carlo on the observed data to make this determination be less susceptible to HSD?
library(lmtest)
SW1=window(BTS,start=c(1753,1),end=c(1807,12), frequency=12)
Het=bptest(SW1~time(SW1))
Het
studentized Breusch-Pagan test
data: SW1 ~ time(SW1)
BP = 13.3848, df = 1, p-value = 0.0002537
SW2=window(BTS,start=c(1808,1),end=c(1963,10), frequency=12)
Het=bptest(SW2~time(SW2))
Het
studentized Breusch-Pagan test
data: SW2 ~ time(SW2)
BP = 220.744, df = 1, p-value < 2.2e-16
SW3=window(BTS,start=c(1963,11),end=c(2011,11), frequency=12)
Het=bptest(SW3~time(SW3))
Het
studentized Breusch-Pagan test
data: SW3 ~ time(SW3)
BP = 0.1275, df = 1, p-value = 0.721
SW4=window(BTS,start=c(1880,1),end=c(2011,11), frequency=12)
Het=bptest(SW4~time(SW4))
Het
studentized Breusch-Pagan test
data: SW4 ~ time(SW4)
BP = 0.027, df = 1, p-value = 0.8696
Het=bptest(BTS~time(BTS))
Het
studentized Breusch-Pagan test
data: BTS ~ time(BTS)
BP = 374.8861, df = 1, p-value < 2.2e-16
http://img689.imageshack.us/img689/7109/bestmonthannualsdchange.png
Hi Kenneth,
Let me re-emphasise that the heteroscedasticity on which you should be concentrating is that which remains in the residual error term after you have fitted your best model. Many time series which are structurally very simple will fail a test for homoscedasticity, when applied to the level series. The important thing is that if you claim, say, that you have a valid model of the form:-
Tk = Tk-1 + uk
uk = f(Tk-2, Tk-3,Tk-4, … εk-1, εk-2, εk-3…) + εk
then you need to show that your εk term defines a white noise series, including passing a test for HSD.
One reason I have chosen an example model above with MA terms was to clarify the language: ““In the run up to the first volcano, these values can be calculated as the difference between the “observed†value and the model-predicted value without the white noise term.†This was intended to mean that each successive value can first be calculated without the white noise term, and the white noise term can then be calculated as the difference between the model (without white noise) and the observed value. This white noise term is then used to calculate subsequent values in the series (depending on the model) as one forward-calculates the series.
For ARMA models, this is not generally the same as running the model out with the white noise term eliminated! The standard deviation of the white noise term is then calculated from the succession of calculated “sample” values.
I was just a bit concerned by your statement:-
“Instead of using the standard deviation from the observed data the standard deviation used was calculated by difference in the prior observed data and the model with the white noise removed.†If this latter point did not cause you any confusion then please ignore it.
Paul_K, I made an effort to quickly guess what might be the source of the changing variability in the monthly BEST mean land temperature series. That variability goes from more to less going from 1753 to the present time and definitely tests positive for heteroskedasticity (HSD). The HSD persists into the first and second segments of the BEST series as defined by breakpoints. All HSD tests were performed in R using the function bptest in library(lmtest) which is referenced to the Breusch-Pagan test.
My first guess was that the spatial coverage could be a major source of the changes in variability and to that end I compared the global land (and designated here as GL), and the land areas bounded by 80W-110W and 40N_60N (part of US and designated here as USP) and 0E-30E and 40N_60N (part of Europe and designated here as EUP) for standard deviations and HSD. These temperature series were obtained from the KNMI site and are from the monthly GISS data sets using a land mask. The time period used was from 1880 to present.
First of all I found that GL had significant HSD (p.value=0.003) that could be reduced to insignificance for the 4 segments defined visually (and not by breakpoint analysis) with p.values, respectively, of 0.11, 0.12, 0.96, 0.95 for the windows in the series from,1880-1899, 1900-1939, 1940-1969 and 1970-2011. The standard deviations for these windows in the series and in the same order were, respectively, 0.45, 0.32, 0.37, 0.33. F-Tests for the ratios of these standard deviations showed significance (at p.value<=0.05) for all pairings except the second and fourth windows.
Secondly, I compared the standard deviations of the land areas of USP and EUP with that for GL which, respectively, were 2.03, 1.40 and 0.45. The p.values for the test for HSD for USP and WEUP, respectively, were 0.51 and 0.15.
In summary, I think that the results here show that going back in time as data was added from the various parts of the global land area that the standard deviations would decrease and that the areas that were most available for the earliest parts of the BEST series (probably mainly Europe) were and are sufficiently variable to provide the higher standard deviations seen in the early BEST series. Obviously to do a rigorous test of this supposition would require going back and finding the areas that BEST started the series with and then those added and accumulated over time.
The KNMI site and relevant page are linked here:
http://climexp.knmi.nl/start.cgi?id=someone@somewhere
http://climexp.knmi.nl/select.cgi?id=someone@somewhere&field=giss_temp_250
Paul_K (Comment #102531)
I believe I am comprehending your suggestion on conditioning the model with observed data and doing it accordingly.
I have a problem with determining/fitting a model with data in a time series that shows significant heteroskedasticity and using the residuals from that model to determine whether that series exhibits heteroskedasticity (HDS). My question is: Would not the presence of HDS effect the assumptions used for modeling the original data series and particularly where the model is required to use a regression when the original series is trend stationary.
Also if the HDS is caused by changing spatial coverage in the BEST series I do not see a simple model removing it. As a layperson in these matters I have never made the calculations but I have heard of HDS compensating models like ARCH and all its variants – and also as a layperson would not be confident in properly applying that method if indeed it applies to a case at hand.
Paul_K on further reading on this matter, I think it is the heteroscedasticity (HDS) of the residuals of a model that effects the assumptions for the model much like the auto correlation of the model residuals effects the assumption that error terms are independent. My question would, however, remain: Given that in could be shown that the changing variation in the BEST series is from spatial coverage considerations could a relatively simple model be found that would provide residuals without HDS?
Kenneth, I haven’t check the best data, but in GISS LOTI, RSS and UAH there is a reduction in variance when the hemispheres approach relative equilibrium. The northern hemisphere has a higher sensitivity to forcing due to lower thermal mass. The can oceans can lose heat energy more rapidly than they can regain the energy, especially in the northern hemisphere where the summer solar forcing is lower than in the southern hemisphere.
Since you are using the best data you should see a reduction in variance around the 1940s and again in the 2000s. Before 1930 (NH) and 1958 (SH) the data is too noisy to be of much use.
http://s122.photobucket.com/albums/o252/captdallas2/climate%20stuff/?action=view¤t=joethevolcano.png
That is RSS plus HADSST2 using a 2002 to 2010 baseline which provides a decent look at the difference in volcanic impact. The Wm-2 conversion was just an attempt to scale volcanic impact, probably useless though.
BTW, using a 1995 to 2010 baseline shows better the increase in NH heat capacity recovering from the earlier volcanic forcings.
Here I want to quickly summarize some analyses I did comparing the GISS global mean monthly land temperatures from 1880-2011 (as linked to in the post above) to the BEST global monthly mean land temperatures over the same period. The thought behind this analysis and using this time period was to determine if the BEST series was better behaved relative to one of the major 3 data sets after leaving the early time period of BEST were the spatial coverage was much reduced and probably contributing in a major way to the changing variation in data coming forward in time.
What I found for the entire GISS series was that I was able to model that data as trend stationary with an Arima (1,0,1) model where ar=0.815 and ma=-0.478. The entire GISS series which had heterodecasticity (HSD) by the Breusch-Pagan test in R (p.value=0.01) did not exhibit HSD in the arima model residuals (p.value=0.56). The acf bar graphs in R and the Box.test showed some significant lag correlations in the residuals out past lag 10 for the arima model, but overall the acf looked reasonable (in this layperson’s estimation).
I also did a breakpoint analysis of the entire GISS series and attempted to model the segments derived from the bearkpoints. The breakpoints occurred at April 1936 and Jan 1977 and defined 3 segments of the series. The segments were all trend stationary and fitted from segment 1 (the earliest) to segment 3 (the latest) with the models Arima(1,0,1), Arima(1,0,1) and Arima(2,0,0). The acf bar graphs and the Box.test showed these segments had little or none of the correlation in the residuals beyond lag 10 as exhibited by the entire GISS series. The problem with the segment approach was that for segment 1 the residuals showed significant HSD (p.value=0.01) counter to the segments 2 and 3 which did not show significant HSD.
I could not fit a reasonable model to the entire BEST land series from 1880-2011 due to the residuals for the optimum model of trend stationary Arima(1,0,1) exhibiting HSD (p.value=0.04) and showing very significant residual correlations in acf and the Box.test at lag 10 and beyond. The BEST series from 1880-2011 itself did not exhibit HSD. The lag correlations in the BEST 1880-2011 model residuals as viewed in the acf plots were much more pronounced than those in the GISS series model over the same time period.
Next I did a breakpoint analysis of this BEST series and derived the breaks at Sept 1902, Oct 1944 and Jan 1977 which defined 4 segments identified as, from the earliest to latest, segment 1,segment 2, segment 3, and segment 4. All of these segments where trend stationary and none exhibited HSD. The optimum fit for these segments to an arima model were Arima(1,0,0), Arima(1,0,1), Arima(2,0,0) and Arima(2,0,0), respectively, for segment 1 through segment 4. None of these segments exhibited HSD in the model residuals. All models except that for segment 4 showed statistically significant correlations in the residuals beyond lag 10 and at a level nearly the same as for the entire BEST series 1880-2011.
What I conclude from this analysis is that, while authors are quick to point out how similar the temperature data sets are (and it appears the major 3 are or at least should be because they use nearly the same data), there are apparently some major differences exposed when attempting to model these series.
It is a disappointment to me that Zeke H and Steven M have apparently moved on and are not here to discuss these developments.
Kenneth,
Your ref:-
http://img689.imageshack.us/img689/7109/bestmonthannualsdchange.png
I have been puzzling over the two plots you made of sd over each 12 month period against calendar year and of sd over each 10 year period against calendar year, and have tentatively concluded that the data prior to about 1850 is so different from the later data that, EITHER it has been taken from a different sample population OR there is a problem with the BEST methodology.
In the early years, and particularly before 1850, the data reflect the seasonal and decadal variation of largely the northern hemisphere; see Figure 2 in the original paper. After 1850, the data reflect the sum of both NH and SH anomaly measurements. Your plot shows a REMARKABLY WELL-STRUCTURED decline in variance of the intra-annual anomaly values between the start-year and 1850.
It is a simple fact that the seasonal (intra-annual) variation of average temperature in just the NH or in just the SH is naturally an order-of-magnitude larger than the seasonal variation of average global temperature (because temperatures at corresponding southern and northern latitudes are approximately 180 degrees out of phase). It is less obvious to me why this should also be true for average values of temperature ANOMALY.
Your plots would suggest two possibilities:-
1) There exists a strong compensating correlation between southern and northern temperature anomalies which shows up on a monthly basis; in loose terms, a hotter-than-average summer in the north is typically matched by a colder-than-average winter in the south.
2) The BEST methodology leads to a systematic over- or under-shoot in the calculation of temperature anomaly depending on whether the anomaly is increasing or decreasing. The magnitude of the error arising (in the average anomaly) decreases as a function of the number of samples available.
I don’t know which of the two possibilities is true, and I may be missing something.
The first possibility can be readily tested. If it turns out to be true, and of the correct magnitude, then it would explain your plot. It also means however that all of the data prior to 1850 should be treated as a different population sample from the “global†data after 1850. On the other hand, if it turns out to be false, then the BEST team may need to re-examine their methodology or find an alternative explanation for the shape of your sd plots.
Zeke or Mosh,
Can you take a look at my comment above to Kenneth. It’s got nothing to do with volcanoes or spurious regression, but may raise an important question for you guys about BEST methodology and data integrity.
Paul
I’m not sure how relevant this would be for the current exchange, but not long after the newest BEST paper came out, I highlighted an issue I think is relatively important. I noticed BEST’s temperature record does not have a consistent correlation structure throughout its entirety. Its correlation with regions/countries changes over time. My interpretation is this means BEST fails to fully account for spatial biases. If that’s true, the expected response in the record to something like volcanic eruptions would change over time.
I have no idea how large an effect it would have, so I don’t know if it would be discernible or relevant, but I’ve brought the issue up before (Zeke said he’d get back to me on it, but I think he forgot), and no answer was had at the time. That means it’s a poorly understood source of uncertainty.
Just thought I’d share.
PaulK
“2) The BEST methodology leads to a systematic over- or under-shoot in the calculation of temperature anomaly depending on whether the anomaly is increasing or decreasing. The magnitude of the error arising (in the average anomaly) decreases as a function of the number of samples available. ”
It should, the ocean time constant is different and the source of ocean heat uptake is different. The magnitude of the overshoots should decrease as the average ocean heat capacity equalizes. So would the decreasing error magnitude really be due to the number of samples or due to heat capacity? The way I see it, there should be a reduction in the standard deviation leading into 1940 and 1995.
because of the phase of the ocean oscillations.
Dallas,
I hadn’t missed your previous point, and I’d like to return to it at some stage, but it is a different issue, I think, which largely effects the change in multiannual variance, and particularly the pseudo 20-year and 60-year cycles.
Paul_K, I have found a seasonal component in the models that I have used for arima modeling BEST , GISS and now GHCN monthly mean global land temperatures. All 3 data sets were modeled for the time period 1880-2011. The seasonal component shows in the afc and pacf plots rather clearly and I am currently working on using a seasonal adjustment in the models.
What is interesting here is that the seasonal component is most pronounced early in the series (where I have model segments as defined by breakpoints) and diminishes coming forward in time and further is most pronounced for the BEST series and less with GISS and GHCN. The residuals of the arima models without seasonal adjustments for entire series in all data sets fail the Box.test in R for independence at 24 lags, while the seasonally unadjusted arima model residuals for the 3 segments of GISS and 4 segments of GHCN show independence at lags 24. The arima model residuals of the 3 earliest of the BEST segments fail the Box.test at 24 lags, while the arima model residuals of the latest occurring BEST segment show independence at 24 lags.
I eventually will have modeled all of the 3 major land temperature data sets and BEST over the same time periods using both monthly and yearly data.
Paul K, It may be a different point. Kinda hard to tell before 1960 because of the SH coverage. I have been using a 1995 to 2010 baseline to take advantage of the AQUA and other more current data and work backwards on the oscillations.
http://i122.photobucket.com/albums/o252/captdallas2/climate%20stuff/sst2gissandbest.png
When I compared GISS to HADSST2 it appeared that GISS overly smoothed the data. Also the GISS 64-90S data wildly varies when compared to 64-90N prior to 1960. That is when I started comparing sequential standard deviations (20 and 11 year) of the GISS LOTI regional with the idea that the SD should decrease as a change point is approached, if a thermal capacity limit is the cause of the change. I had noticed that in the UAH and RSS data, BTW and thought it may be a reasonable way to search for climate shifts in the longer term surface data.
http://redneckphysics.blogspot.com/2012/09/standard-deviation-as-estimate-of.html
So it may not be related, then again?
Paul_K,
I think the opposite is true, if I understand what you’re saying. See this scatterplot of NH and SH anomalies from UAH. It would appear to me that there is a positive correlation. It doesn’t surprise me, as wouldn’t the difference be mostly due to ENSO?
BTW, the Pearson correlations are 0.62 for the hemispheric monthly anomalies, 0.37 for land only by hemisphere, and 0.65 for ocean only by hemisphere. So at most, the land anomalies would appear not to be strongly correlated. Again, if I have interpreted correctly.
re: Kenneth Fritsch (Comment #102687)
Kenneth, what do you see as far as seasonality or heteroscedasticity if you subtract the breakpoint residuals of GISS and GHCN from the BEST breakpoint residuals?
Brandon Shollenberger,
I know you said you commented on this somewhere else, but can you clarify? Particularly the second sentence, “correlations with regions/countries”. Correlations between countries or regions? So for toy example, England used to correlate with Continental Europe but now with USA?
Perhaps one should first subtract the series and then look for structural breaks, HSD and seasonality.
BillC:
Sure! You left out an important word at the start of that sentence, “Its.” You’ll note the sentence before refers to “BEST’s temperature record.” That means I was looking at the correlation between BEST’s (global, land) temperature record and the records created for regions and countries.
That wasn’t what I was saying as I was comparing the global record to countries/regions, but it is true as well. However, it isn’t as large a difference as you portray. For most of the examples I saw, things that were correlated stayed correlated (one would certainly hope so given the planet should have similar trends throughout). What changes is how strong a correlation there is.
To demonstrate, we can look at the two countries you listed (there are two different series for UK based on how the border is drawn, but it doesn’t affect anything discussed here). First, copy the data from 1800 on into the same spot (spreadsheet, programming shell, whatever). Next, check the correlation over the entire period. Then check the correlation over subsets of that period. Here are some examples:
1800-1850: .35
1800-2011: .33
1850-2011: .27
1900-2011: .26
1900-2000: .22
1900-1950: .19
The assumption made by the BEST team is the correlation structure for the planet’s temperature should remain the same over time. Either that assumption is wrong, or their methodology has failed in some way.
If we cannot qualify which it is or quantify the effect it may have, it makes any analysis with BEST’s data more tenuous and difficult to justify.
By the way, if you want to test with different countries/regions, you can get data for all of them here:
http://berkeleyearth.lbl.gov/country-list/
It’s quite convenient, and without it, I doubt I’d have noticed this issue.
Re:BillC (Comment #102689)
September 6th, 2012 at 12:03 pm
Hi BillC,
Your scatterplot is showing (positive) correlation between NH and SH temp anomalies on an annualised dataset. This is to be expected. It means that the low frequency multi-annual movements in each hemisphere track each other (to some extent).
The point I am trying to make is that the INTRA-annual data is showing a much higher variance in the early years than in the later years (after 1850). This relates to the high frequency (seasonal) fluctuations of temperature once any secular trend or low frequency cycles have been removed.
I sincerely doubt that there has been a real change in the variation of the annual cycle by a factor of 4 over the last 200 years. The explanation therefore has to be sought in sampling error, estimation error or methodological error.
Paul_K – those are monthly anomalies.
Paul_K,
Sorry for the hasty reply, I was in transit. I re-read your answer and I interpret you as saying you think my plot is annual anomalies. It’s monthly anomalies. My mistake if I am in turn misinterpreting. Of course, my plot says nothing about the temporal evolution of the correlation and furthermore is only for the 30+ years of the UAH data.
Brandon,
Thanks for the replies. That does clear it up. And thanks for the example, that is interesting. It would be beyond my current ability to systematically test what you demonstrated an example of, but it is interesting. A quick thought is if we tried to match correlation intervals with known cycles or phenomena such as oceanic
emulti-decadal oscillations, what would we see? Maybe I’ll play with it some.BillC,
Whoops. I missed that they were from UAH – I just roughly counted the number of points and leapt to an unfounded assumption.
However, your plot is still the wrong plot to test the issue, since it carries the multi-annual trends within it.
OK. I have just finished testing the (same) UAH dataset, but with a different and more direct approach. This time I took the global land series, the NH land series and the SH land series, and I calculated the variance and standard deviation for EACH year in the series. The result shows that the variance in the global temperature anomaly is smaller than the variance in either the SH or the NH measurements across the entire period. This can only happen if the intra-annual variation between the NH and SH are negatively correlated. Assuming that this result can be extended to the BEST land series, it has implications for the reliability of the early data as a measure of global temperature. Effectively it is being sampled from a different population. It is worth noting that this particular structural uncertainty is NOT incorporated in the BEST methodology for the calculation of uncertainty bounds.
I’ll post a couple of plots in a moment to show the results from the UAH data.
PaulK, http://i122.photobucket.com/albums/o252/captdallas2/climate%20stuff/UAHoceansStandardDeviation.png
You might find that interesting then.
Herewith a couple of plots to go with comment #102710.
Global temp variation stays inside the SH and NH variation. The calculated yearly sd values confirm the picture.
http://img812.imageshack.us/img812/8824/uahland.gif
Dallas,
Don’t know what to make of your plot (#102711). What do you think is happening?
BillC:
Glad to help.
I doubt you’d see much of anything. If I’m correct, the problem is one of spatial biasing. That would mean natural cycles would most likely have no discernible impact (on the correlations). Of course, I could be wrong.
Now I’m curious how one should go about testing for changes in correlation over time. If the changes were constantly in one direction, say, always getting weaker, they’d be easy to find. But what if there are just periods where something happens that breaks it?
As a quick test, I decided to use a “ten-year rolling correlation.” Instead of smoothing, I took the correlation for every ten year period. The results were interesting. For the first ten years worth, the average value was .46. For the entire period, the average was .2. To make things more interesting, the standard deviation for the ten years was only .07, but for the entire period, it was .12.
I imagine the results would be even more striking if I grabbed all the data rather than just the data starting at 1800, and I know there are examples of much larger shifts in correlation structure, but this is enough for me to believe there’s a problem that needs to be addressed. And I don’t want to be the one to do so.
Layman Lurker (Comment #102690)
Not sure where you are going with this LL, but the breakpoint segments for these series do not line up perfectly. I agree that differencing series is a better way of pinpointing differences, but I think if I went that route I might start by taking the difference between the series and then modeling the difference. Anyway I need first to attempt to find a seasonal model to use in conjunction with the series model to satisfy the Box.test for independence of the lags out to 24.
What I find a bit surprising and interesting is that if you plot the the temperature data set series together you might not suspect the differences you obtain from modeling the series, or at least for the time period 1880-2011 for the BEST, GHCN and GISS series.
PaulK, I am pretty sure it is an equalization of heat capacities between major SH and NH oceans. I have been playing with the sequential standard deviations and sequential linear regression to isolate internal ocean oscillations. In the GISS regional, annual, I haven’t tried monthly, the 64-94S band is almost perfectly stable due to the circumpolar current and the high average surface wind velocity.
Working back from there, using the 1995-2010 baseline because of the regime change, I can follow of few of the oscillations and what appears to be return thermal waves, for lack of a better term. So I am putting on with my glacial/interglacial model
http://redneckphysics.blogspot.com/2012/09/it-is-not-rocket-science.html that is a basic diagram.
Since the thermal equator is south of the true equator, there is a lag in ocean heat transfer northward. With the lower NH thermal mass, it is more sensitive to atmospheric forcing and the SH is more sensitive to solar forcing. Of course none of the data sets consider thermal mass and the annual solar cycle so I am just trying to see what I need before wasting a bunch of time.
Anywho, figuring out the internal oscillations looks like the real deal before estimating a lot of other crap.
The sequential SD is pretty spiffy though.
Paul_K, relating to negative correlations, individual stations when correlated with each other often have negative correlation functions at large distances. When you globally average across correlation functions, whose correlation scale varies with latitude, as BEST does for their kriging method, one thing you find is that regions of negative correlation tend to get “blotted out” by the correlation method.
You can see what I mean here.
Regions of negative correlation are extremely important in getting the right total variance, but they are very sensitive to “over averaging”, especially if you aren’t mindful of the underlying physical reasons for presence of the negative correlation to start with.
Carrick,
“When you globally average across correlation functions, whose correlation scale varies with latitude, as BEST does for their kriging method, one thing you find is that regions of negative correlation tend to get “blotted out†by the correlation method.”
I went through the BEST methodology for the first time last night, and it has left me with more questions than answers as yet. I do not fully understand the methodology as yet. (I am very well acquainted with kriging, having developed and applied packages in earnest for geostatistical mapping.)
The authors have included a latitude-dependent term in their equation for C. The flattening of the semi-variogram MAY not be too important if the correlogram was generated and applied to the residual temperatures after correcting for the latitude (and altitude) dependence. I am more trying to understand whether the latitude-correction is actually valid. The form suggests that the authors have tried to make it valid (only) for the high frequency temperature movements. I am still looking at the implications of this.
Carrick,
Does the plot you linked to (102718) not consider direction as well as distance – is this what you have discussed in the past about assuming distance correlations to be the same in all directions?
Paul_K, I know they considered it, see e.g. this, which comes from their work. For some reason (it’s been a while since I’ve looked at it), it’s my impression they opted for just using the global mean. Steve Mosher had some discussion of this a while ago, wish I could locate it now.
I ended up deciding I’d have to go through the code if I wanted to understand what they’ve really done. Haven’t had the time or energy for that yet. Of course their code has changed since the original draft (as I understand it, there were methodological errors in the code).
BillC, I am pretty sure they assume axisymmetric correlation functions, even though you can see from the above figure it isn’t close to axisymmetric.
Paul_K, I have finally been able to fit an arima model to the entire global monthly mean temperature data sets from BEST, GHCN and GISS for the time period 1880-2011 by using a seasonal component. The residuals from the modeled data series all are free of heteroscedasticity, show independence in the Box.test out to lag 24 and have well contained lags in the acf plot with CIs. The models for all series are arima(1,0,1) with a seasonal component of (1,1,1). A case might be made for a seasonal component of (2,1,1) as the aic scores are close.
The BEST series definitely shows more seasonality than GHCN or GISS. I am not at all sure I understand why the breakpoint segments for GHCN and GISS fit arima models reasonably well without seasonal adjustment while the entire series requires it. Also when using monthly anomalies I was a bit surprised to see seasonality in these series.
Next I could attempt to model the entire BEST series back to 1753 by including a seasonal component and use that model to test for volcano effects on temperature and/or confine my analysis to the volcanoes occurring after 1880.
Kenneth,
Sounds like progress! I am currently working my way through the BEST methodology and believe that I may be able shed some light on the issue of seasonal variation, but I am not ready yet.
If I were you, I would focus on the data after 1850 (or 1880, if you wish). I do not believe that the earlier data is representative of global temperature variation, but in any event it is unlikely that it can be represented with the same statistical model as the later data.
One thing you might want to return to is to compare your model residuals with a model fitted after removing the (time-shifted) AMO as a proxy for the multidecadal cycles
BillC, Carrick,
Yes, the BEST methodology assumes isotropy in spatial correlation (or axisymmetric correlation functions, if you prefer), but the correlation is applied to data which is locally de-seasonalised as far as I can tell, and which has been “detrended” by the subtraction of a time-invariant but latitude dependent temperature function. The hope is that these two elements should remove the main source of anisotropy in the temperature DIFFERENCE field.
This approach is clearly not fully effective, as revealed by the strong (residual) dependence of spatial correlation on latitude.
Paul_K, I have not been able to find an arima model, with or without a seasonal adjustment, that produces residuals without very significant heteroscedasticity when modeling the entire global mean monthly land temperatures from 1753-2011. I thus will move on and await the results of your analysis of the BEST data set.
I would like to play with the AMO index in modeling the GISS, GHCN and BEST data sets from 1880-2011. My first inclination would be to use the AMO index(es) available at KNMI. Do you have any preferences on data and general methodology to use?
I have read a post at Tamino’s where he is critiquing the BEST paper on its AMO analysis and doing one of his own. I believe the BEST paper assumes a zero lag whereas Tamino’s analysis and close scrutiny sees the AMO lagging the temperature change. I have linked the post below.
http://tamino.wordpress.com/2011/10/24/decadal-variations-and-amo-part-i/
Hi Kenneth,
The Tamino article is not super helpful. The AMO data has high frequency content which should offer high correlation with close to a zero lag, and lower frequency data where the lag should be several years. For your volcano tests you should be interested ONLY in the low frequency data from the AMO. In fact it is essential that you filter out the high frequency data before fitting.
Do you recall the magic trick that Bill Illis did in a comment on one of Zeke’s articles? The article is here:-
http://rankexploits.com/musings/2011/the-atlantic-multidecadal-oscillation-and-modern-warming/
See (Comment #70625) and the follow-up conversation. Bill Illis produced a plot of detrended Atlantic SST vs detrended Hadcrut3
http://img689.imageshack.us/img689/9449/hacrut3detrendedandthea.png
We should expect that detrended SST should track the detrended LAND temperatures very well. I was merely suggesting that you use that fact as a shortcut to define a proxy variable which would account for the multidecadal change in the BEST LAND temps, while retaining the high frequency information from the BEST LAND series.
So the method should entail something like:-
Choose an AMO SST dataset.
Apply a 7 or 9 year moving average to produce series “AMOFiltered”
Fit a model to the BEST LAND temp data of the form:-
Temp = a + bt + c*(AMOFiltered +lagshift) + eps
Parameters are a, b, c, lagshift.
The residual eps values should hopefully mostly be carrying just high frequency data from the BEST LAND series. Now apply an ARMA model to the residual eps values to produce your final model for the volcano tests.
As for the choice of Atlantic SST data, I don’t know. I would be inclined to test a couple – KAPLAN and HADSST2 – and choose the model that produced the best statistics of fit.
Paul_K, thanks for the suggestions on an approach for me to proceed with modeling the temperature series for subsequent analysis of the volcano effects on temperature. I plan to follow up on it and to use BEST, GHCN and GISS.
I have some ideas of my own for an analysis here, where I might attempt to use the residuals of the breakpoint segments of the original data used to produce the AMO index and further comparing that index with similarly produced residuals of the temperature data sets.
Paul, when you say, “Choose an AMO SST dataset” , I assume you mean AMO index and not the original temperature data from which the index was produced.
Interesting I find that a ccf analysis of the various AMO data sets available shows a high frequency (monthly) lag of AMO on detrended temperature series from 6 to 12 months depending on AMO set used and over the period 1880-2011. The lag varies little by changing the temperature data set from BEST, GISS and GHCN. The peak correlations depending on AMO data set varies from 0.08 to 0.20.
Tamino and the BEST paper authors, I believe found a correlation of approximately 0.40 with no or only a few months lag (AMO lagging temperature) by detrending with a 5th order polynomial. Also posted at the Tamino thread was a poster who used a second order polynomial and found lags of longer than 12 months for AMO lagging temperature. I do not recall he posted the peak correlation from the ccf graph but he did provide R code for doing the analysis.
The fact that one can obtain different answers using different approaches does not set well with me and particularly where a physical based hypothesis is not presented to rationalize the particular approach.