Ok… so I just wrote that there will be a pause in posting– but obviously, I sort of lied. Curious from Cleathropes wrote me a question, and I told him I’d post his question to the blog for discussion. I’ll give a response to the question he actually asked and then let others chime in.
Lucia,
Would you be able to answer a question I have relating to the Global
Temperature “Signal”. I understand that to determine if there as been
a “significant” change in this signal (due to AGW) we would need to
consider the “nature” of the data / signal. e.g. if we concluded that
the data points were statistically independent we could simply could
calculate a linear trend and put confidence interval around this etc.In your articles on this matter (in particular the ones relating to
Doug Keenan) I seem to recall that you mentioned that the assumptions
that Doug used to indicate that the global temperature signal contains
no significant trend, where “physically not possible”?Now to the the question . . . When you refer to “physically not
possible” what does this in fact mean? Does it mean that we can prove
these are not possible (e.g. hence 1=0 and therefore this cannot be
true etc) or does it mean that we cannot at present think of a
physical mechanism that would produce this type of “signal”.I hope I have managed to explain myself correctly and apologies if my
terminology is not correct. I enjoyed maths a great deal right up to
my final year of Elec Eng Degree but have to admit that once we moved
on to Stochiastical (probably spelt wrong) processes – it flew
straight over my head!Many Thanks for any advice or information you are able to provide.
Happy New Year!
I’ll begin with a point of clarification: The assumption that was physically not possible was that what is colloquially called “weather noise” arising form “natural variability” could be non-stationary; more specifically that a non-stationary d=1 model with no drift could describe changes in temperature that are not driven by AGW. But, it worth noting it is not his model for the signal that is being criticized. It is his model for the noise.
By “physically not possible” I mean something stronger than merely ‘we cannot at present think of a physical mechanism that would produce this type of “signal” noise ‘. I mean that in order for this model for “noise” to be a correct model, we must revise our present understanding of conservation of energy,radiative heat transfer and what we believe to be the dominant energy source for the earth.
Mind you: I could be incorrect. I don’t thinks I am… but it’s happened before. Nevertheless, I don’t merely mean that we can’t think up a reason why d=1 plus no drift could be true. I mean that if our understanding of certain specific long accepted physic principles is correct, it can’t be true. With respect to the earth’s energy balance, these principles are:
- Energy is conserved. That is: we believe the first law of thermodynamics is correct.
- Nearly all incoming energy is from the sun.
- Nearly all outgoing energy is radiated away.
I have said I do not have a mathematical proof and as far as I am aware no one has a proof. Any mathematical proof would involve first putting forward a simple physical model. One could easily prove this for d=1 is not possible for many simple systems governed by conservation of energy and radiative heat transfer that is not driven by forcings that are not “driftless ARIMA d=1”. But as far as I can tell, no one who likes driftless ARIMA d=1 models to describe earth’s weather noise would accept that as a “proof”, while many who understand physics would accept it. (The latter mostly already know how to do the proof!)
Saying the forcings are driven with d=1 forcings then bumps the argument to the sun. The presents the question, why should forcings have no drift, d=1 noise? They can’t. We can advance positive physical arguments for that. So, this could turn the argument to people suggesting that that incoming energy might come from Mars, the moon, created by magical Leprechauns or by Scotty from Star Trek secretly creating an energy generator made from dilithium crystals in a vault and programming it to ooze out “forcing noise” that is “driftless d=1”. All of these suggestions would require either revising our understanding of physics or how Scotty might behave.
With that, I will leave the discussion to others. We’ve had it before; no reason not to have it again. 🙂
(Oh… once again. the lavender and yellow images. Can you see the lavender? Can’t see the yellow? Let me know.)
That’s not blue it is lavender! I see the yellow smiley and fluctuations in temperature have physical constraints that can be confusing, if one data set contains instrumentation or methods that are different than the other.
Evidently, LIG max/min thermometers must have a major problem, since the time of day they record the maximum and minimum doesn’t matter, but the time of day that record is written down does 🙂
I don’t know blue from lavender, but I see a pink/lavender square with an X. I also see a yellow smiley, but no other yellow.
And I love the discussions, but they mostly go way over my head. 🙂
I’m confused about the conversation. Are we discussing whether it is possible that observations have a natural component which has not been captured in an Arima fit? Considering the huge imbalance in ocean layer temperatures, isn’t it possible to have a long walk?
Long walks are nice after all and it seems reasonable that a well mixed ocean would cause a long cold walk. Doesn’t it seem possible that an unperturbed or perhaps a warmed ocean with a stabilized upper layer may achieve a walk in the opposite direction exceeding its own base level through perturbation? – a positive feedback.
I see lavendar – nice
There are two inter-woven discussions.
1. a signal for global warming amid the noise
2. a signal for anthropegenic global warming amid the noise and OTHER forcings
Defining what is “noise” is not simple and will be relative to the variable looked at. Over a few decades volcanic activity will be essentially random events. Over a much longer temr volcanic activity can itself have trends.
Re: Jeff Id (Jan 12 19:55),
As long as d is < 1, the process is stationary. But you could get long runs that when tested would fail to reject a unit root (d=1) and, of course, would also reject d = 0.
Lucia,
I haven’t forgotten that I promised you a post explaining why statistical tests “fail to reject” a unit root. I’m frantically busy at the moment!
Paul
@Jeff Id (Comment #88553)
Jeff,
If you didn’t catch it, you might want to visit a post I did on the physics and stats arguments against a strong white noise element in the temperature series.
http://rankexploits.com/musings/2011/noisy-blue-ocean-blue-suede-shoes-and-agw-attribution/
If one considers the input flux rather than the temperature series, then “non-physical” becomes a clearer term, I believe.
In the very low frequency region (ignoring the noise component), a constant flux term – which translates into a straight line on the temperature plot – implies unbounded increase in cumulative flux – an infinite energy source. A straight line in flux – which translates into a quadratic form in temperature – is equally non-physical. It has not stopped many people from using a linear or a quadratic form to fit the average trajectory of the temperature series, but this seems to be typically done without the author’s understanding the implicit “non-physical” assumption they are making.
An alternative common “non-physical” premise is to model a white noise component in the flux term which translates into a unit root in the temperature series. This can be ruled out as non-physical over the long-term. However, it is more difficult to counter an argument that says it may be an appropriate model for a short-time segment.
Lavender = yes, Yellow = no.
JeffId-
No. It’s specifically, which characteristics cannot be possible for the “natural” component. The difficulty with d=1 for “natural” it would mean that temperatures can go to + or – infinity for no reason at all and more over, they can stay there. With d=1, there is no preferred temperature for the earth. None.
To borrow a term from chaos– the earth’s temperature would have no “point of attraction”. If d=1 were literally true for “noise”, the earth’s temperature could wander to a temperature greater that that of the sun, and at that level, it would have no tendency to cool. It would be equally likely the temperature would drop as rise.
So, this isn’t a general ARIMA issue, it’s a specific one about non-stationarity inherent in “natural” variability.
A non-physical weather noise model may of course fit the data in the short term… But it is still wrong. While weather may be chaotic, it still must be constrained by physical reality; adopting an impossible model never makes any sense, even if it seems to fit the data. Time to examine the physical processes and find a model that makes sense.
Lucia said, “To borrow a term from chaos– the earth’s temperature would have no “point of attraction”” Would it have “points” of repulsion? The 1997/8 El Nino looks like a harmonic phenomenon, It appears to have triggered a climate shift. Point of repulsion?
dallas–
If you question about arima(p,d=1,q) is does it have a point of repulsion, the answer is no. I don’t know what a “climate shift” means exactly. But if someone wants to view warming as happening in “shifts” that have an upward bias, I don’t necessarily have any problem with that.
To all: Dreamhost was down. I don’t know why. Some of you blocked by cloudflare will have to wait a bit.
I see 4 pink quarters. My wife confirms.
Re: dallas (Comment #88564)
Dallas,
What do you mean by “harmonic” phenomenon in this context?
Interestingly, For GISS annual values from 1900 to 1970 (pre-AGW), it doesn’t appear that a model based on first order differencing would produce the best fit. Following the iterative ARIMA modelling process generates AIC scores for the alternative models with each step as follows:
AIC for arima(0,1,0) = -87.36
AIC for arima(0,1,1) = -98.57
AIC for arima(1,1,1) = -102.74
AIC for arima(1,0,0) = -104.74 with AR(1) = 0.5478
In the above process once you get to ARIMA(1,1,1) you encounter a unit root in the MA term so you bump back to ARIMA(1,0,0).
Besides the AIC score, the standard deviation is also minimized with ARIMA(1,0,0).
Note: I don’t use the arima function in R to do time series differentiation (per documented R issues here)
Oliver said, “What do you mean by “harmonic” phenomenon in this context?”
Harmonic may not be a great choice, but I am not sure exactly what would be the best. Rogue wave is what I was used to. It is a common non-linear quirk in chaos theory, the best I can tell. Every example I have seen is a doubling amplitude of the wave, peak to peak. It happens in fluids, solids and is even possible in thermal waves if Relativistic Heat Conduction is believable. Happens when quasi-periodic cycles “harmonize” or cycles match frequency and amplitude for a moment in passing.
The temperature profile of the super El Nino had the perfect signature slope leading in and out of its peak temperature. What was really neat with the super El Nino is that both the mid-tropopause and the lower stratosphere matched, nearly perfectly.
What is even more fun, the approaches for the El Nino following, were not perfectly symmetrical. Some might think it indicates a direction of a “shift” . My laptop crashed or I would upload a graph.
Now I better go before Lucia banishes me to another thread 🙂
Re: 88597
Dallas, are you talking about a standing wave, where two waves of the same frequency collide and the amplitude is doubled?
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html#c1
Those of us that have spent any time on the ocean know a standing wave when we see one but I am not sure how it relates to the 1998 Super El Nino. A standing wave usually involves a reflection.
ivpO, There are a variety of standing wave phenomena, but reflection is definitely a part. The reason I think in terms of harmonics is Chladi? patterns. So you can have an isolated stationary standing wave, moving standing waves, converging standing waves diverging etc. Pretty much any shape you can stimulate with sine waves, nature can duplicate with the same limits on amplitude it seems. So some of the “noise” in data can produce tricks on the eye for cyclomaniacs or be something worth deciphering.
Since all systems tend to have non-ergodic tendencies, Selvam, at least alludes to that, smoothing methods on data sets can hide information or produce false information. A great reason for using multiple methods in statistics, both to eliminate false positives and to indicate neat phenomena, which may be natural or artifacts 🙂
So comparing instrumental data to paleodata can lead to wonderful misconceptions or unbelievable information. The trick is which is which?
@ 88660
So maybe more of a harmonic resonance. Where a VLF periodic wave aligns in antinode with a shorter El Nino wave to produce an increase in amplitude. This is certainly possible and an interesting idea worth considering. Good call!
“As long as d is < 1, the process is stationary. But you could get long runs that when tested would fail to reject a unit root (d=1) and, of course, would also reject d = 0."
DeWitt and Jeff, I can vouch for an ARIMA model with d<1 that fitted a reconstruction for MXD from Briffa. Those models show long runs over parts of the series that appear just as a deterministic linear trend would and when you apply the Augmented Dickey-Fuller test you can reject the unit root, i.e. that d=1. Those long runs are what, in my mind, can make it rather easy (with a little selection discretion) to produce those blades for a hockey stick – pointed upward if you select and pointing downward and upward if you do not select.
Looking at a deterministic linear trend or faux trend within a longer series will reject for d=1, but I think that if you have 2 or more linear trends within a series that are separated with breakpoints and you test over the entire period you could conclude that the series is not stationary and you could fit a model with d=1.
I think Lucia, Carrick and PaulK have shown and concluded that a temperatures series with a random walk are physically impossible because the temperature becomes unbounded. Therefore you cannot apply a model with d=1 (or integer) because of a random walk or random walk with drift because that would be unphysical. If you have a true deterministic linear trend or a faux linear trend from long term persistence over the period being tested, a model with d=1 (or integer) also does not apply. And, of course an Arima model with d<1 tested over the entire period would reject a test for a unit root.
If what I contend above is true then I do not see where an ARIMA model with a unit root could ever apply to a temperature series – even though it could render a non stationary series stationary.
I get both colors.
Gary–
I think everyone should see both today. I uploaded a yellow image to deal with all the missing links issues after the experiment was done. Thanks.
Think of Zeno’s paradox. The process you are calling unphysical could be bounded by time (e.g. to reach extreme limits would take longer than the age of the universe)
Let’s see, before my martini I think I’ll conjecture that temperature is bounded on the low side at absolute zero. My high energy physics implies an upper limit for temperature, I think, but do not know what it is.
Time of the universe started at or before the big bang and will end when??
Kenneth, you could use the ocean’s boiling temperature (377 K) as a provisional upper bound.
AMac, I , like Eli, am way beyond the oceans boiling as I think we know what portends for us when the sun goes to a white dwarf by way of a giant red star.
Lucia
As host, it is your pre·rog·a·tive to change your mind and plans on what you do – without treating it as a “lie”. Enjoy the freedom.
David–
I don’t know what you are referring to when you tell me that it’s my perogative to change my mind. Of course it is, but are you suggesting I’ve recently changed my mind about something related to the current post?
(a bot tried to reload the blog page 27,493 times between 5:57 and 6:47 am today. So, I’ve been working on identifying it’s work around…)
Lucia – just responding to your first line:
“Ok… so I just wrote that there will be a pause in posting– but obviously, I sort of lied.”
David–Ahhh! Ok. That makes sense.
Here’s and oddity. I downloaded which IPs clasified as threats hit my blog in the last 4 hours:
{“response”:{“ips”:[{“ip”:”128.2.207.79″,”classification”:”threat”,”hits”:268,”zone_name”:”rankexploits.com”},
{“ip”:”184.107.248.202″,”classification”:”threat”,”hits”:88,”zone_name”:”rankexploits.com”},
{“ip”:“128.156.10.80”,”classification”:”threat”,”hits”:53,”zone_name”:”rankexploits.com”},
{“ip”:”193.205.203.3″,”classification”:”threat”,”hits”:35,”zone_name”:”rankexploits.com”},
{“ip”:”89.22.206.178″,”classification”:”threat”,”hits”:31,”zone_name”:”rankexploits.com”},
{“ip”:”158.234.251.71″,”classification”:”threat”,”hits”:26,”zone_name”:”rankexploits.com”},
{“ip”:”164.92.9.21″,”classification”:”threat”,”hits”:23,”zone_name”:”rankexploits.com”},
128.156.10.80 is cerf.grc.nasa.gov =>NASA!. I wonder if they’ve been hacked?!
That NASA IP sure is curious. If that request continues, I would suggest contacting them. I would use their “Abuse” EAddy/ phone in this case, but only if it continues or increases.
If not hacked, then a virus/trojan/worm.
I would recommend reporting it to their webmaster to fix because that threatens its own operations as well as others.
AFPhys–It’s not going to continue because I’ve blocked that IP at cloudflare.
David– Yes. I’m going to report it. They might want to start routinely looking at how cloudflare classifies their IP!