tag:blogger.com,1999:blog-7729093380675162051.post4115121610928553692..comments2023-11-27T20:33:09.759+11:00Comments on moyhu: More on global temperature spectra and trends.Nick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-7729093380675162051.post-76260708776917304612013-10-11T01:00:48.932+11:002013-10-11T01:00:48.932+11:00This is an example of an autocorrelation of a semi...This is an example of an autocorrelation of a semi-Markov series plotted in comparison to the SOI autocorrelation over the span of 130 years. The semi-Markov is completely stochastic, pulling random draws from a dispersive distribution, weakly centered about a mean period<br /><br />http://img513.imageshack.us/img513/1846/7sg4.gif<br /><br />The model above has a mean of about 5.5 years but lots of dispersive variance about that value.<br />This dispersion is high enough that it makes it difficult to predict the duration to the next peak or valley except perhaps probabilistically.<br /><br /><br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-21951015546188477842013-10-10T23:06:30.867+11:002013-10-10T23:06:30.867+11:00Yes, only since 1980 - basically for the reason Ta...Yes, only since 1980 - basically for the reason Tamino gave. If you go much further back, there is an obvious non-linear component. But I'm happy to look at longer periods when either the acf or power spectrum (my current focus) gives a clear separation between deterministic (approx) and stochastic deviation.<br /><br />As I've said, I was really looking at periodicity as something that confounds the stochastic modelling. That is up to about 4 years period. So there are plenty of periods in 33 years.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-9880463498142131042013-10-10T22:56:59.110+11:002013-10-10T22:56:59.110+11:00Nick, If I am reading your autocorrelation charts ...Nick, If I am reading your autocorrelation charts correctly, you only ran it for data from 1980. Any strong periodicities you see are likely merely artifacts.<br /><br />I spent the last year doing power spectral analysis on terrain features, and explored the whole range of Markov to semi-Markov disorder.<br />http://entroplet.com/context_select/navigate?category=fine_terrain<br />http://entroplet.com/ref/foundation/B-terrain_characterization.pdf<br /><br />I want to warn you about chasing phantoms on the temperature time series. Any predictive power will be low because there really is not a lot of data to generate a quality spectrum from, and like I said, the dispersion is high. <br /><br />The SOI is already detrended, so use that as a trial and see what you can find over the entire range.<br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-5809857918522810542013-10-10T20:48:57.862+11:002013-10-10T20:48:57.862+11:00I'm rather agreeing with Steve here. The acf&#...I'm rather agreeing with Steve here. The acf's show strong periodicity, which suggests "teleconnection" in the time domain - apparent correlation between well separated points. I agree that it can be subtracted as a fix, but that doesn't entirely help with the uncertainty estimate. For future climate, you could say that we'd do the same calc, but there is uncertainty associated with identifying the ENSO component.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-43708439332932996722013-10-10T20:41:15.038+11:002013-10-10T20:41:15.038+11:00WHT, thanks again for the link - I think we'r...WHT, thanks again for the link - I think we're looking at similar things. I hadn't heard of Eureqa, but it looks very powerful. It may be just what I need.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-4431727938074684172013-10-10T20:36:12.895+11:002013-10-10T20:36:12.895+11:00Thanks, Steve,
So far I haven't really been tr...Thanks, Steve,<br />So far I haven't really been trying to identify and explain the periodic effects, but just to separate them from the stochastics to get a better estimate of trend uncertainty - or at least the part of uncertainty that can be attributed fairly clearly to randomness. But a hemisphere separation would be interesting - I'll try it. I'm currently looking at trying to separate them in the frequency domain - it may work better.<br /><br />I think the periodicities you describe are indeed what I am seeing, and your suggested causes sound very interesting.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-58474746431985654462013-10-10T16:21:42.233+11:002013-10-10T16:21:42.233+11:00SteveF, I will meet you half-way and call it a se...SteveF, I will meet you half-way and call it a semi-Markov process. It is not quite memory-less but the randomness is strong enough that there are no identifiable periods. In other words, it is highly dispersive yet retains strong reversion to the mean properties. Take an FFT of the SOI process and it has a weak hump of a semi-Markov process but that's about it for structure. Here is the FFT along with a power spectral profile of a semi-Markov process that has a significant dispersion about a mean value.<br /><br />http://img822.imageshack.us/img822/4835/d6y6.gif<br /><br />The lack of structure is not too surprising as the majority of ocean waves are also highly dispersive (except for such types as ripple waves and cnoidal waves) , and don't show identifiable periods. This dispersion is all too frequent in nature.<br /><br />But all that really does not matter because the important point is that the SOI noise signal can be subtracted from the global temperature time series. This allows us to improve the SNR and estimate the AGW trend much more easily. <br /><br />Tamino and all the smart dudes are very excited by what Kosaka & Xie are doing. But it's not exactly overwhelming either, as it is so easy to do the compensation if one just wants to work with the SOI time series !<br /><br />And no more pause or hiatus, which is nice to be able to get rid of.<br /><br /><br /><br /><br /><br /><br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-69341348883183316832013-10-10T13:32:15.393+11:002013-10-10T13:32:15.393+11:00WHT,
The ENSO is neither a red noise process nor ...WHT,<br /><br />The ENSO is neither a red noise process nor an Ornstein–Uhlenbeck process; it is a pseudo-oscillation, and a causal, not random process. A strongly positive current ENSO state means that the ENSO state at a characteristic time in the future (corresponding roughly to the average "half-period" of the pseudo-oscillation) is most likely going to be negative (and vice-versa, for a strongly negative current ENSO state, of course). <br /><br />WRT Kosaka & Xie: they fix the ocean temperature in the tropical Pacific, and (lo and behold) their model better tracks the real world data; but considering that lots of people have shown very strong correlation between tropical Pacific temperature variation and global temps and rainfall patterns, I don't see there is much of a surprise there; it would be a surprise if forcing the model's tropical Pacific to match the Earth didn't make the model much better match the Earth. What Kosaka & Xie do not account for is the effective removal of heat from the model world when they force the tropical Pacific to cool (on average) to match the real world. Yup, take a bunch of heat out of the system, and the model temperature does not rise so quickly... I'm underwhelmed.<br /><br />SteveFAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-46276634447719952082013-10-10T10:16:16.303+11:002013-10-10T10:16:16.303+11:00I do hope to see evidence of your work Steve F.
...I do hope to see evidence of your work Steve F. <br /><br />Tamino's original work didn't click with me until I saw Keven C, Icarus, and Kosaka & Xie show how well the SOI fluctuations lined up with the global temperature time series, and also how well it worked all the way back to 1880!<br /><br />The SOI signal appears very close to a red noise source as it has strong regression to the mean and a mean that is stably near zero over the last 130 years. It may be straightforward to duplicate a random SOI-like signal by applying an Ornstein-Uhlenbeck process with a hopping rate and drag term. The SOI is unique in that its a linear combination of two other random processes, the Tahiti barometric pressure time series and the Darwin BP time series. If these two are not individually autocorrelated any more strongly then red noise, then the combination won't be either, as the two time series will get out of phase quickly. <br /><br />I posted my more complete analysis here:<br />http://contextearth.com/2013/10/04/climate-variability-and-inferring-global-warming/<br /><br />Thanks Nick for pointing out Tamino again. Hat's off to Tamino who has been pushing this idea of extracting the signal from the noise.<br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-27518705550691057822013-10-10T08:42:44.990+11:002013-10-10T08:42:44.990+11:00Hi Nick,
Interesting work. I have done some simp...Hi Nick,<br /><br />Interesting work. I have done some simple comparisons of residual variability in the temperature trends for CRUT4 after removing (as best possible) ENSO+solar and volcanic effects. I used centered moving averages of different lengths (3, 5, 7, 9.... 61 months) to try to see where there is significant periodic influence (when the length of the moving average filter is near the frequency the variability drops sharply. It looks to me like there are a few significant periodic contributions: annual, ~21-23 months, and ~47-49 months, which seem to correspond to some of the peaks in your graphic above. On further looking, the ~21-23 month contribution is ~100% in the northern hemisphere temperatures, is more common in winter than summer, and looks like it may be due to the stability of the polar vortex (the negative part of the oscillation seems to happen when there is a sudden stratospheric warming and loss of vortex stability, and the positive part when the polar vortex is more stable than usual). The ~4 year oscillation seems to mainly a southern hemisphere contribution; I have no idea of the physical cause.<br /><br />Anyway, applying your analysis separately to the northern and southern hemisphere data might be interesting. If you can grab the CRUT4 data by latitude and eliminate the tropics (look only above 30N and below 30S) nearly all the ENSO influence disappears, and the non-ENSO contributions may be clearer.<br /><br />SteveF (Steve Fitzpatrick)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-83732450411415796102013-09-12T10:38:47.448+10:002013-09-12T10:38:47.448+10:00Carrick,
Thanks - padding would help.
I mainly wa...Carrick,<br />Thanks - padding would help.<br /> I mainly wanted to show that the 3-4 yr cycle was real (I was surprised by the acf), and that it came down with F&R.<br /><br />What I'm maunly trying to get at with F&R is separating stochastic and other variation. In a way they both contribute to trend uncertainty, but the forcings part can't properly be modelled by stochastics.<br /><br />I've been trying to tease out whether AR(1) really is inadequate - it looks so, but the acf goes negative, which then makes it look more reasonable. However, that acf behaviour is probably due to the periodics etc. Actually, KC's warning is unclear, because I think he was already using ARMA(1,1). It may refer to something in the video, but I now can't see that. But yes, there remains a lot of interesting work to do.<br />Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-85957843245865838882013-09-12T04:35:24.918+10:002013-09-12T04:35:24.918+10:00Hi Nick,
Interesting work. First one gentle sug...Hi Nick, <br /><br />Interesting work. First one gentle suggestion -- add a zero pad factor of four to your Fourier transforms. The signal content in the transform is more readable by humans not endowed with Fourier interpolation skills when you zero pad. ;-)<br /><br />Secondly, it's not surprising that F&R (or any other smoothing algorithm) is going to reduce variance by subtracting some portion of it off. The question is by how much the trend that remains is affected by the smoothing algorithm. Reduced variance does not imply reduced absolute uncertainty.<br /><br />Three related posts to look at are:<br /><br /> <a href="http://troyca.wordpress.com/2013/05/21/another-reconstruction-of-underlying-temperatures-from-1979-2012/" rel="nofollow"> Another “reconstruction” of underlying temperatures from 1979-2012</a> by Troy Masters.<br /><br /><a href="http://www.skepticalscience.com/16_more_years_of_global_warming.html" rel="nofollow">16 ^more years of global warming</a> by KevinC.<br /><br /><a href="http://rankexploits.com/musings/2013/estimating-the-underlying-trend-in-recent-warming/" rel="nofollow">Estimating the Underlying Trend in Recent Warming</a> by SteveF.<br /><br />I think the warning by Kevin C is germane here:<br /><br /><i>Update 21/02/2013: Troy Masters is doing some interesting analysis on the methods employed here and by Foster and Rahmstorf. On the basis of his results and my latest analysis I now think that the uncertainties presented here are significantly underestimated, and that the attribution of short term temperature trends is far from settled. There remains a lot of interesting work to be done on this subject.<br /></i><br />Carrickhttps://www.blogger.com/profile/03476050886656768837noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-4538200706414615502013-09-10T07:42:58.549+10:002013-09-10T07:42:58.549+10:00Thanks, William, and for the suggestion, Yes, F&am...Thanks, William, and for the suggestion, Yes, F&R (but Gregory is easier to spell).Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-64944245484191551732013-09-10T07:05:23.431+10:002013-09-10T07:05:23.431+10:00Interesting follow-up, thanks.
> I'll do t...Interesting follow-up, thanks.<br /><br />> I'll do that here by looking at the Foster and Gregory residuals.<br /><br />F+R?William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.com