The relevance of rooting for a unit root

by

So what if the global average temperature series contained a unit root? It would mean that ordinary least squares regression may lead to spurious results in terms of inflated trend significance. It would *not* mean that phsyics-based climate models are suddenly invalid or that AGW is suddenly falsified (just as gravity is not falsified by observing a bird in the sky).

On a previous post, ‘VS’ commented that

“(…) global temperature contains a stochastic rather than deterministic trend, and is statistically speaking, a random walk.”

He later clarified (updated):

I agree with you that temperatures are not ‘in essence’ a random walk, just like many (if not all) economic variables observed as random walks are in fact not random walks.

And later still:

“I’m not ‘disproving’ AGWH here.
I’m not claiming that temperatures are a random walk.
I’m not ‘denying’ the laws of physics.”

However, many commenters started chiming in with a sense of “Yeah, somebody is taking on climate science and seems to have refuted it all!” Uhm, no.

Basically, a random walk towards warmer air temperatures would cause either a negative radiative imbalance at the top of the atmosphere, or the energy would have to come from other parts of the earth’s system. Neither is the case. It’s actually opposite: There is a positive radiation imbalance and other reservoirs (e.g. oceans, cryosphere) are also gaining more energy. Which makes sense, in the face of a radiative forcing.

Explaining the increase in global average temperatures by a mere ‘random walk’ would violate conservation of energy.

Ramanathan and Feng describe the earth’s radiation balance as follows:

So the process of the net incoming (downward solar energy minus the reflected) solar energy warming the system and the outgoing heat radiation from the warmer planet escaping to space goes on, until the two components of the energy are in balance. On an average sense, it is this radiation energy balance that provides a powerful constraint for the global average temperature of the planet.

I.e. The global average temperature only changes over climatic timescales (multiple decades or longer) if there is an imbalance in the radiation budget. As is now indeed the case. Climate is to a certain extent deterministic, irrespective of unit roots.

The presence/absence of a unit root (dependent on the nature of the assumed trend amongst other choices) does not disprove/prove that the extra greenhouse gases we put in the atmosphere are warming the planet.

Update: This discussion has focussed on global average air temperatures, but changes have been observed in many other parts of the earth system that point to a changing (warming) climate: Sea level rise, ocean heat content, ice sheets , sea ice, glaciers, ecosystems, radiation budget. A statement along the lines of ‘nothing anomalous is happening’ should take all these changes into account.

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53 Responses to “The relevance of rooting for a unit root”

  1. RickA Says:

    I just started reading this blog yesterday – steered over by Bishop Hill.

    This thread and the other post you have on going on global average temperature increase compared is really informative.

    This unit root stuff is really interesting.

    Keep up the good work.

    I will be reading regularly.

    Thanks.

  2. Paul Tonita Says:

    Doesn’t the rebound after large volcanic eruptions like Pinatubo provide some indication that ther probably isn’t a unit root? The Wikipedia page on “unit root” shows curves with and without unit roots after a drop in output. The climate responds in a fashion more like the blue curve than it does the green curve. Though I suppose that could be a result of the aerosol falling out of the atmosphere. But that just book ends the fact that the climate is driven by radiative forcings…

  3. VS Says:

    Hi Bart,

    I appreciate the effort, as you can see from my last post, in the active thread (again, I would prefer to keep everything there, so I’ll continue posting over there).

    One thing though. If you are referring to Tamino’s latest post, at least also refer to my reply.

    Here you are implying that what Tamino did was actually (statistically) correct, while in fact it was (to use his terminology) complete bonkers.

  4. Arthur Smith Says:

    Hi Bart,

    I think one central issue here is the borderline between “weather” and “climate”. The definition of climate is as the statistical properties of the system (which can be in principle obtained by observation over a suitably long period of time), while weather is the particular current instance of the system. We know weather is chaotic; that means it is auto-correlated over short periods of time, but in detail unpredictable over long-enough times. From chaos theory you get characteristic time constants over which modes of the system diverge (the Lyapunov exponents, which measure the rate of separation of slightly different initial states). Once you get beyond the shortest time-constant, that particular mode is essentially random, i.e. it ergodically explores the phase space available to it, so averaging over a few times that shortest time constant should give you stationary statistical properties.

    Now for the atmosphere that time constant is essentially the limit of predictability, i.e. at most a couple of weeks. So monthly averages of weather should be reasonably stationary, and variations in cloud cover, etc. should always average out on that sort of time-scale. Except for the problem that the underlying parameters keep changing (seasonal variation in insolation, volcanoes, solar cycle, and other external forcings). So external variability imposes constraints that move what should be essentially stationary statistical properties of the atmosphere up and down.

    There is also the issue that for overall energy balance we have additional components beyond the atmosphere that are larger (in heat capacity) and therefore mostly decoupled – in particular the oceans. I don’t know whether ocean behavior has been shown to be chaotic, but in any case there are clear oscillations (like El Nino) with much longer time-constants than for atmospheric auto-correlation. Components with very long time-constants (ice sheets, say) could be considered just part of the system in whatever state they are in, but that state may mean unbalanced energy flows in the rest of the system for lengthy periods of time (ice sheets absorbing heat as they gradually shrink, or releasing heat as they gradually grow, deep ocean changes similarly).

    So the best time-scale for assessing statistical properties that you expect to be stationary (i.e. defining climate) isn’t a priori obvious. To the extent ocean behavior is chaotic then there may be quite long-term “random walk” components – at least several years based on El Nino behavior, and perhaps longer. An assertion of non-stationarity over century time-scales is implying something about the physical system, in particular long-term internal variability (presumably via chaotic ocean modes). Since these supposedly produce wide temperature swings with no change in external forcing, as I noted on the other thread, I believe the consequence of such an assertion is that the linearized climate sensitivity to actual external forcings should be very large.

  5. whbabcock Says:

    Picking up on Arthur Smith’s time-scale considerations, one must realize that the “global temperature” that VS refers to in the passage you quote at the beginning of this post is simply the global temperature over a very short period of time (150 years). Hence, temperature data may very well behave as a random walk (over the period of observation), yet those very same 150 years worth of temperature data could be created by the “phsyics-based” theories of climate that are working on time scales well beyond the period for which we have data. Again, the data are what they are, and have their observed properties – irrespective of any potential explanatory theories. On the one hand, we have “theory” that implies one set of relationships and on the other hand we have data that seem to be inconsistent with the theory. Seems like a typical scientific problem – particularly when a discipline is in its infancy.

    Physical explanations of why temperature cannot be a random walk may very well be correct, but they can’t change the statistical properties of the 150 years worth of observed data that VS used. To me, this is the key point. At this stage in time and research, we simply may not have actual data (of sufficient scope and precision) to statistically identify (i.e., not reject) physics-based hypotheses. This doesn’t mean that a physics-based hypothesis is incorrect. However, while VS’ statistical analyses and observations, by themselves, do not “disprove” or “deny” anything, they should cause everyone to reevaluate AGW claims for “spurious results in terms of inflated trend significance” as you state in the opening to this post.

  6. Tom Fuller Says:

    I have a lot of time invested in following this thread, and I was going to make more or less the same comment as WHBabcock.

    I don’t believe VS is attacking the fundamentals of climate science. I think he is calling attention to the limits of analysis that can be performed on various data series. For that he should be thanked. Not attacked.

  7. Chuckles Says:

    Tom Fuller,

    Amen to that, but as has been noted in the past, ‘We live in an imperfect world, M’lud.’

  8. Marco Says:

    @Tom Fuller,

    Perhaps this is what VS meant, but it most certainly is not what B&R claim. That paper, rather than put question marks with its own ‘prediction (equal forcings, vastly different T increase, one permanent, the other transient), just rejects AGW.

  9. Al Tekhasski Says:

    A.Smith wrote:
    “Once you get beyond the shortest time-constant, that particular mode is essentially random, i.e. it ergodically explores the phase space available to it, so averaging over a few times that shortest time constant should give you stationary statistical properties.”

    This is completely untrue. Ergodicity and invariant measures of attractors are concepts that require infinite time. Topology of attractor can be very complex, and Lyapunov exponents are not necessarily uniform everywhere along the phase flow. Just look a the Lorenz attractor: there are areas in phase space when the system is sitting on a nearly periodic orbit for a while, and only then rapidly escapes into a different subspace, to a different quasi-periodic orbit, with different mean values of state variables . During these relatively long periods between jumps the system could be falsely identified as strictly periodic if the observation time is too short. Various running averages of Lorenz attractor produce the same chaotic time series, just high frequencies are filtered out, but the low portion of spectrum remains no matter what, which means – unpredictable in the long run.

    More, a multidimensional dynamical system way beyond equilibrium will have a spectrum of Lyapunov exponents, so to get a stationary estimation of anything you must go beyond the longest exponent. My suspicion is that the longest exponent for climate is about 120,000 years.

  10. Bart Says:

    Hi Arthur,

    Your point about the different time scales is indeed important. I’m still trying to understand the implications of what you wrote here though. Are you saying that there are clearly constraints on the atmospheric “chaos” at timescales beyond a month, but that it’s less clear if a similar timescale exists for the ocean at all? And that *if* climate even on a century timescale would be random, that it implies a very sensitive system (since the existence of a random walk doesn’t negate the effect of a radiative forcing acting on the system). Did I understand you correctly?

    Any thoughts on the physical likelihood of it being random/stochastic indeed on such timescales?
    (for reference, Arthur’s previous comment is here.)

  11. Arthur Smith Says:

    Al, you’re right that things can get complicated when you run into strange attractors and some of the more interesting aspects of mathematically chaotic behavior. However, in practical chaotic systems, rather than mathematical idealizations, you have actual randomness (from things like changing external forcings in the climate case) in addition to the internal deterministic dynamics, and the main impacts of chaotic dynamics are then first unpredictability, and second mixing (realizations spreading through the available phase space). And note that the dynamics is dominated by the *largest* exponent, which is the shortest time-constant, not the longest time-constant. So in practice you’re not going to see confinement to a small part of phase space for more than a few multiples of the shortest time constant for the (well-coupled) system.

    That said, if there really are slower physical processes (oceans, ice sheets) that are not well-coupled to the fast one (the atmosphere) then you’ll have a second or third set of slow dynamics that may or may not be chaotic, but will certainly have longer or even much longer time constants. If the time scale is really long then they can probably be considered more as external constraints rather than internal variability. And that gives the potential for steady unbalanced energy flows). But for ocean dynamics in particular there’s certainly a question (at least to me) of what the relevant time-scales are, some of which should be considered part of the dynamics.

    Bart – yes, the slow dynamic response is almost always forced to lead to an amplification of response (because in the short term they absorb some of the energy imbalance, as the oceans do now), so the longer that slow dynamics is relevant, the higher the total sensitivity of the climate system. I think this is the ssence of Jim Hansen’s claims (which have been disputed) that sensitivity is really 6 degrees to doubling of CO2, rather than the IPCC’s 3, when you look at 100,000-year time-scales.

    And a true random-walk would have an infinite sensitivity to external forcing (over long enough times).

  12. Alex Heyworth Says:

    Followers of this and the previous thread may be interested to know that this issue was considered some time ago in this paper in the Journal of Climate http://ams.allenpress.com/archive/1520-0442/4/6/pdf/i1520-0442-4-6-589.pdf.

    [Reply: And discussed e.g. here.

    "To claim that something follows a random walk, one had better suggest a mechanism as to why this is so. Specifically one needs a reason why any disturbance in temperature has infinite persistance- equivalently, why tomorrow's temperature would be solely a function of today's temperature and a set of possible disturbances which have the SAME probability distribution regardless of the current temperature. A random walk theory is wholly incompatible with the sorts of feedback mechanisms discussed by the mainstream participants in this thread. (...) If in fact climate follows a random walk, we should not be reassured."]

    For the not so reassuring part, also read Arthur Smith’s comments. BV]

  13. Ian Says:

    Alex Heyworth – thanks, that paper is a nice find. It was interesting to see the comparison between simulated and real temp trends as well.

  14. dhogaza Says:

    Perhaps this is what VS meant, but it most certainly is not what B&R claim. That paper, rather than put question marks with its own ‘prediction (equal forcings, vastly different T increase, one permanent, the other transient), just rejects AGW.

    Yeah, and it appears the reject the principle of conservation of energy (if 1 w/m^2 radiative forcing from CO2 only warms the planet about 1/3 as much as 1 w/m^w solar input, where is that extra energy from the CO2-derived 1 w/m^2 going? Poof? So it appears).

    Actually they reject *any* bit of physics that contains “e” in an equation, because they’re insisting that “e” impacts systems differently depending on the source of the energy. You need “e[co2] e[solar]” etc etc …

    VS could be doing a real service here, by showing where B&R go wrong. He’s made it clear to us that he’s got the skills to do so because he’s many times better at statistics than Tamino, and since Tamino is a PhD full-time statistician, it must be true.

  15. Pat Cassen Says:

    Very nice Alex (March 18, 2010 at 22:56) (why didn’t the rest of us find this?!)

    Be sure to check out the more recent papers citing this one.
    http://scholar.google.com/scholar?cites=16132388654911283203&hl=en&as_sdt=2000

    [Reply: Interesting! I just 'randomly' picked one, and it happens to be by two economists. It sais (2002):

    it provides strong evidence that global temperature series have positive trends that are statistically significant even when controlling for the possibility of strong serial correlation.

    . BV]

  16. Alan Says:

    I want to put a ‘policy maker’ hat on.

    The discussion here and in the other thread focused on [my paraphrase] the proposition by VS that the temperature time series over 150 years is too short to infer trends relating temperature anomalies and CO2 … that, statistically, there are unresolved questions about the unit root thingie, taking into consideration inputs from Tamino.

    Bart has recently wanted to focus on the implications of this. As a policy maker (proxy only) I too ask “so what?”.

    My questions are:

    1. If the statistical analysis of the temperature record over the last 150 years is inherently limited, then to what degree is our confidence level in the AGW relationships reduced?

    2. If Q1 suggests that confidence reduces substantially, what scope of temperature record is required to enable an analysis which gives me reasonable confidence that AGW is real and forecasts over the next couple of decades don’t exhibit huge error fans?

    Lots of subjective words in there, I know … policy makers like me will reframe confidence levels into a risk management perspective intuitively.

    Point is, if I was advised that the ‘problem’ significantly reduced confidence levels in AGW relationships, then I would commission immediate and substantial further research to improve the AGW relationships analysis … assuming that were possible/required given the answer to Q2.

    I would look at VS and say “get your skates on, m’boy, and publish in a peer-reviewed maths journal so we can sort this ‘problem’ out … funding won’t be an issue!”

    Of course in reality I can’t promise the funding bit … but seriously, it is time to piss or get off the pot. I don’t make policy on the basis of a blog discussion over a couple of weeks.

    [Reply: I think the policy relevance of this discussion is nil, because a) it doesn't impact on our physical understanding of the system and b) the politics is lagging behind the science already.

    I once saw this guy’s t-shirt with the text: “Sex is like pizza. If it’s good, it’s really good. If it’s bad, it’s still pretty good”. Well, perhaps we could say that “Climate change is like Brussels sprouts. If it’s bad, it’s really bad. If it’s good, it’s still pretty bad”.

    See also this post about the policy relevance of scientific uncertainty. Nevermind the fact that more uncertainty means higher risk. BV]

  17. Alan Says:

    OK … I checked a couple of the links to papers from the citation list which Pat Cassen pointed to.

    [apologies in advance is formatting is crap – not sure of the html tags]

    The first is to a 2002 paper by Fomby & Vogelsang (appear to be economists) in the Journal of Climate titled The Application of Size-Robust Trend Statistics to Global-Warming Temperature Series

    The abstract reads:

    In this note, new evidence is provided confirming that global temperature series spanning back to the mid-1800s have statistically significant positive trends. Although there is a growing consensus that global temperatures are on the rise systematically, some recent studies have pointed out that strong serial correlation (or a unit root) in global temperature data could, in theory, generate spurious evidence of a significant positive trend. In other words, strong serially correlated data can mimic trending behavior over fixed periods of time. A serial-correlation–robust trend test recently was proposed that controls for the possibility of spurious evidence due to strong serial correlation. This new test is valid whether the errors are stationary or have a unit root (strong serial correlation). This test also has the attractive feature that it does not require estimates of serial correlation nuisance parameters. The test is applied to six annual global temperature series, and it provides strong evidence that global temperature series have positive trends that are statistically significant even when controlling for the possibility of strong serial correlation. The point estimates of the rate of increase in the trend suggest that temperatures have risen about 0.5°C (1.0°F) 100 yr−1. If the analysis is restricted to twentieth-century data, many of the point estimates are closer to 0.6°C.

    A second paper from the same list by Zheng & Basher (1999) in the Journal of Climate titled Structural Time Series Models and Trend Detection in Global and Regional Temperature Series

    The abstract reads:

    A unified statistical approach to identify suitable structural time series models for annual mean temperature is proposed. This includes a generalized model that can represent all the commonly used structural time series models for trend detection, the use of differenced series (successive year-to-year differences), and explicit methods for comparing the validity of no-trend nonstationary residuals models relative to trend models. Its application to Intergovernmental Panel on Climate Change global and latitude-belt temperature series reveals that a linear trend model (starting in 1890, with Southern Oscillation index signal removal and a red noise residuals process) is the optimal model for much of the globe, from the Northern Hemisphere Tropics to the Southern Hemisphere midlatitudes, but that a random stationary increment process (with no deterministic trend) is preferred for the northern part of the Northern Hemisphere. The result for the higher northern latitudes appears to be related to the greater climate variability there and does not exclude the possibility of a trend being present. The hemispheric and global series will contain a mixture of the two processes but are dominated by and best represented by the linear trend model. The latitudinal detectability of trends is oppositely matched to where GCMs indicate greatest anthropogenic trend, that is, it is best for the Tropics rather than for the high latitudes. The results reinforce the view that the global temperatures are affected by a long-term trend that is not of natural origin.

    So what? Well, putting my policy maker hat back on I’d say to VS “there seems to be a bunch of studies about the statistical analysis of the temperature data with specific reference to the unit root thingie … is there anything in the list of 27 papers cited that changes your views?”

  18. Alan Says:

    The links are dodgy … go figure!

    Fomby et al is at http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0442%282002%29015%3C0117%3ATAOSRT%3E2.0.CO%3B2

    Zheng et al ia at http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0442%281999%29012%3C2347%3ASTSMAT%3E2.0.CO%3B2

    [cross fingers]

  19. Pat Cassen Says:

    Alan – Your links don’t work (don’t know why), but anyone can get those papers the way we did, from the link at March 19, 2010 at 00:34:
    http://scholar.google.com/scholar?cites=16132388654911283203&hl=en&as_sdt=2000

  20. Alan Says:

    Apologies to all … don’t know what went wrong either … or if the following will suffer the same issue!

    Curiosity got the better of me, so I scanned some papers which cited Fomby et al and Zheng et al … just to see how things progressed.

    If you follow some cites from the Zheng et al paper (1999), we find stuff like this:

    In conclusion section of Liu & Rodriguez, Environmental Modelling and Software, 2005, Human activities and global warming: a cointegration analysis

    Another interesting result is the composition of the I(1) and I(2) trends. According to our results, both trends are essentially composed by a linear combination of greenhouse gases that are affecting the temperature series strongly. In an specific case, we find that the I(1) trend is driven by temperature and radiative forcing of solar irradiance, whereas the I(2) trend is driven by a linear combination of the three greenhouse gases or exclusively by the radiative forcing of carbon dioxide. The first component could be associated to inertial and/ or natural factors. In the case of the second component, it could be related to human factors.

    In abstract of Gay-Garcia et al, Climatic Change, 2009, Global and hemispheric temperatures revisited

    To characterize observed global and hemispheric temperatures, previous studies have proposed two types of data-generating processes, namely, random walk and trend-stationary, offering contrasting views regarding how the climate system works. Here we present an analysis of the time series properties of global and hemispheric temperatures using modern econometric techniques. Results show that: The temperature series can be better described as trend-stationary processes with a one-time permanent shock which cannot be interpreted as part of the natural variability; climate change has affected the mean of the processes but not their variability; it has manifested in two stages in global and Northern Hemisphere temperatures during the last century, while a second stage is yet possible in the Southern Hemisphere; in terms of Article 2 of the Framework Convention on Climate Change it can be argued that significant (dangerous) anthropogenic interference with the climate system has already occurred.

    In abstract of Gil-Alana, Environmental Modeling and Assessment, 2006, Nonstationary, long memory and anti-persistence in several climatological time series data

    In this article we examine the stochastic behaviour of several daily datasets describing sun (total irradiance at the top of the atmosphere and sunspot numbers) and various climatological anomaly series by looking at their orders of integration. We use a testing procedure that permits us to consider fractional degrees of integration. The tests are valid under general forms of serial correlation and deterministic trends and do not require estimation of the fractional differencing parameter. Results show that the series are all nonstationary, with increments that might be stationary for those variables affecting sun, and anti-persistent for those affecting air temperatures.

    If you follow some cites from the Fomby et al paper (2002), we find stuff like this:

    In the abstract of Visser, Atmospheric Environment, 2004, Estimation and detection of flexible trends

    Literature on the estimation and detection of linear trends in (environmental) time series is extensive, as overviewed by Hess and others in work published in 2001. However, not all data patterns behave in a linear fashion or, at least, a monotonous increasing or decreasing fashion. Therefore, it may be advantageous to analyse data with more flexible trends. Once flexibility is introduced the problem of detecting statistically significant increase/decrease becomes much more complicated: the trend may be alternating between being constant, decreasing or increasing. As a consequence, the problem of detecting significant increases or decreases cannot be summarised in one single figure or statistical test, as in the case of linear trend detection.

    In the abstract of Gao et al, The Econometrics Journal, 2006, Semiparametric estimation and testing of the trend of temperature series

    The application of a partially linear model to global and hemispheric temperature series is proposed. Partially linear modelling allows the trend to take a very general form rather than imposing the restriction of linearity seen in existing studies. The removal of the linearity restriction is based on the fact that it is well accepted that a significant trend is present in global temperature series. The model will allow for the data to ‘speak for themselves’ with regard to the form of the trend. The results initially reveal that a linear trend does not approximate well the behaviour of global or hemispheric temperature series. This is further confirmed through a formal testing procedure. The results suggest that little faith should be instilled in long-term forecasts of temperatures in which the trend of global and hemispheric series is assumed to be linear. All the current evidence suggest that temperatures will continue to rise in an unknown and probably nonlinear fashion.

    I confess – this quick scan is a bit of a random walk from Gordon & I have ‘cherry picked’ papers that (a) are free, (b) in English and (c) met my time constraints. I didn’t quote any of McKitrick & Michaels’ papers (which didn’t mention ‘unit root’).

    I’m OK with this, because it is not my intention to prove anything methodological – rather it is to illustrate a point which appears obvious … that the field of statistical analysis applied to temperature data sets appears to be very well covered (including considerations of the unit root thingie and papers by econometricians).

    So, has VS really said anything that has not been considered before? That’s my question.

  21. Alan Says:

    Only one boob …

    Link to Gay-Garcia et al, Climatic Change, 2009, Global and hemispheric temperatures revisited

  22. Alex Heyworth Says:

    There is also Kaufmann et al 2009,

    Abstract We evaluate the claim by Gay et al. (Clim Change 94:333–349, 2009) that “surface temperature can be better described as a trend stationary process with a one-time permanent shock” than efforts by Kaufmann et al. (Clim Change 77:249–278, 2006) to model surface temperature as a time series that contains a stochastic trend that is imparted by the time series for radiative forcing. We test this claim by comparing the in-sample forecast generated by the trend stationary model with a one-time permanent shock to the in-sample forecast generated by a cointegration/error correction model that is assumed to be stable over the 1870–2000 sample period. Results indicate that the in-sample forecast generated by the cointegration/error correction model is more accurate than the in-sample forecast generated by the trend stationary model with a one-time permanent shock. Furthermore, Monte Carlo simulations of the cointegration/error correction model generate time series for temperature that are consistent with the trend-stationary-with-a-break result generated by Gay et al. (Clim Change 94:333–349, 2009), while the time series for radiative forcing cannot be modeled as trend stationary with a one-time shock. Based on these results, we argue that modeling surface temperature as a time series that shares a stochastic trend with radiative forcing offers the possibility of greater insights regarding the potential causes of climate change and efforts to slow its progression.

    Full paper behind paywall at http://www.springerlink.com/content/h0tx44h508602755/

  23. Alex Heyworth Says:

    Oops, that should be http://www.springerlink.com/content/vl6g4g28v8215004/. Wrong tab.

  24. Scott Mandia Says:

    Outstanding thread and I thank Bart and all of the commentators for their time and input.

    Bart, your blog is rapidly moving up the Blog Billboard charts. :)

  25. Eli Rabett Says:

    We are looking at this the wrong way. In principle a thousand monkeys stumbling about randomly could reproduce the “observed” global temperature series. It can also be reproduced using a GCM and a set of “reasonable” forcings.

    So the question is which is more likely. The random walk explanation has no support, it just exists. OTOH, we can point to a cooling stratosphere, observed emissions from various parts of the atmosphere, the Arctic warming more than the tropics, and more predictions from the GCMs. We can ask the question what is the probability of a random walk in the temperature, a random walk leading to a cooling stratosphere, a random walk leading to strong warming in the Arctic and more.

    Eli submits the answer to that is fat chance. It is only by isolating the global temperature series that you get this discussion. It’s spinich.

    [Reply: Good point. I tried saying the same here (last point). BV]

  26. VS Says:

    The relevance of rooting for a unit root

  27. Pat Cassen Says:

    Putting on Alan’s policy-maker hat for a moment, I am faced with the following situation:

    In 1988, Jim Hansen testified before congress that “…warming during this time period is a real warming trend rather than a chance fluctuation…”, and “…the greenhouse effect has been detected, and is changing our climate now.” He then went on to present his predictions of temperature into the twenty-first century.

    Had he been an econometrician, perhaps he would have been obliged to say something like “There is no way can we distinguish, at this time, any deterministic trend. Hence, we do not know what the future holds.”

    In fact, VS says that, even now, “…statistically speaking, there is no clear ‘trend’…” and that “…global temperature contains a stochastic rather than deterministic trend…” (My emphasis.)

    And Beenstock and Reingewertz say that “Because the greenhouse effect is temporary rather than permanent, predictions of significant global warming in the 21st century by IPCC are not supported by the data.”

    So, according to them, impressive as Hansen’s predictions* http://pubs.giss.nasa.gov/docs/2006/2006_Hansen_etal_1.pdf may appear to the statistically naïve, they are really not much better than a lucky guess.

    Unless, of course, Hansen’s predictions were derived from information not explicitly displayed in, or in addition to, the purely statistical properties of the temperature data. Like the laws of physics. (Now please do not use his statement to launch diatribes on the shortcomings of complex physical models. We all know that useful useful models usually do some things quite well and some things not so well, and that is certainly the case here.)

    Now I do not mean to imply that physics automatically trumps statistics. But, judging from discussions on this blog, and in the literature as represented by the papers cited above, applying the right tests and underlying models in a statistical analysis can be a pretty subtle business itself. So how should the two disciplines constructively interact?

    Does anyone seriously doubt that there is a stochastic component to climate forcings? (Rhetorical question.) Climate scientists are convinced also that there is a deterministic trend, based on physics and the myriad of specific responses observed in nature (e.g., stratospheric cooling, polar amplification, rising tropopause, etc.) that physics predicts. So should not the proper partnership of econometrics and climate physics be directed toward the explication of the magnitude and properties of the stochastic component (‘natural variability’) relative to whatever deterministic trend might exist? This would seem to be a rich field for progress. But this end is not served well by conclusions which declare with finality that “there is no deterministic trend”, or statements that all predicted or perceived trends are spurious because they have not been derived by ‘the’ correct method, or, for that matter, by statements to the effect that econometric results are useless because they conflict with robust physics. If the latter is the case, there is at least an opportunity to refine the statistical analyses, and even perhaps some quantitative aspects of the physics. Judging from the papers cited above, this may be where things are headed. I’ll keep listening.

    And thanks to all, especially Bart for moderating (in the true sense of the word!) and Alex Heyworth who provided more than one lucid explaination along the way, and opened the door to relevant publications.

    *Update the comparison with predictions using this data:http://data.giss.nasa.gov/gistemp/graphs/Fig.A2.lrg.gif

    [Reply: Very well said. BV]

  28. dhogaza Says:

    And Beenstock and Reingewertz say that “Because the greenhouse effect is temporary rather than permanent, predictions of significant global warming in the 21st century by IPCC are not supported by the data.”

    So, according to them, impressive as Hansen’s predictions* http://pubs.giss.nasa.gov/docs/2006/2006_Hansen_etal_1.pdf may appear to the statistically naïve, they are really not much better than a lucky guess.

    You do understand how unphysical B&R’s claim is that the greenhouse effect is temporary, right?

    How much physics are you willing to throw under the bus in support of this one paper which has not been published, peer reviewed, etc?

    The notion that the greenhouse effect is temporary suggests that the quantum mechanical properties of CO2 change over time. If this is true, QM is flushed down the toilet. Yet, we have other, extensive data that suggests QM is true.

    For instance, tunnel diodes *work*. Many off-the-shelf electronics that you may use in your daily life are *built* around QM.

    If a paper like B&R were written about something other than time series related to the politically-charged field of climate change, or if VS were tilting and windmills meant to convince you that your UHF tuner doesn’t really work, you’d laugh them out of the playground.

    Does anyone seriously doubt that there is a stochastic component to climate forcings?

    Forcings? Which ones? CO2 etc does what it does, following the laws of physics, and there’s no stochastic component there at the macro scale, whatever the economics people believe. This is as pure as the physics get.

    If you want to discuss volcanic aerosols, fluctuating TSI levels, etc, sure, lots of stochastic stuff going on, and climate scientists didn’t need economists to tell them that this blindingly obvious fact is true.

  29. dhogaza Says:

    Now I do not mean to imply that physics automatically trumps statistics.

    Why not? For the most part, the physics is intrinsically observation-based.

    B&R and VS apply statistics to a limited time series … if they want to disprove physics, they should apply their statistical analysis to a wide set of relevant physical observations. Of course, if they did, they’d see that A refutes B while B refutes C while C refutes A or the like. Much simpler to analyze a certain short-term series of data of varying accuracy over time, varying noise, etc, and to say that “hey! a whole field of science is wrong! Because … we’re economists! And we rule science!”.

  30. dhogaza Says:

    Here you are implying that what Tamino did was actually (statistically) correct, while in fact it was (to use his terminology) complete bonkers.

    Yet, VS, he’s the PhD in Statistics whose real name is Grant Foster, while you continue to hide behind your handle “VS”, and are just some random internet poster who claims to have some economics and therefore more statistics than God himself, because after all, economics is the be-all and end-all of intellectual accomplishment.

    If you’re so smart, why do you refuse to show where B&R went wrong in their analysis that proves that much of modern physics (“modern” as in “the last 100 years”) is wrong?

    Why do you refuse to prove how smart you are?

    Meanwhile, Tamino continues to publish, while for all we know you haven’t finished your PhD yet …

  31. ScP Says:

    Dhogaza
    “Why not? For the most part, the physics is intrinsically observation-based.”

    Wish you could say the same of climate science ;-)

    Also re. anonymity, arent you a bit ‘pot calling kettle black’ here? Personally I dont mind who is anonymous and who isnt. So what. Tamino wont get fired for writing in his blog, maybe VS think he would do.

  32. Eli Rabett Says:

    To continue beating my drum. You cannot draw meaningful conclusions from the statistical behavior of a single parameter in a coupled system.

    Even in 1988, Hansen’s argument was more sophisticated, viz: using physical constraints the outputs of the theory follow observation of a number of parameters including global temperature. Since we are confident of the theoretical inputs, and reasonably confident of the drivers, the forcings, and the observables over multiple time scales, the three legs of the theory support each other.

  33. Pat Cassen Says:

    Calm down dhogaza.

    “You do understand how unphysical B&R’s claim is that the greenhouse effect is temporary, right?” Yes.

    “How much physics are you willing to throw under the bus in support of this one paper which has not been published, peer reviewed, etc?” None. I expect that B&R are wrong.

    “If you want to discuss volcanic aerosols, fluctuating TSI levels, etc, sure, lots of stochastic stuff going on…” That’s what I meant.

    Sorry, I guess I was being too nuanced :)

  34. dhogaza Says:

    Dhogaza
    “Why not? For the most part, the physics is intrinsically observation-based.”

    Wish you could say the same of climate science ;-)

    I can, will, and just did.

    Also re. anonymity, arent you a bit ‘pot calling kettle black’ here?

    It’s easy to find out who I am with google.

    But just to help the google impaired, I identified myself in the other thread on the VS BS. Feel better, now?

  35. DirkH Says:

    “Eli Rabett Says:
    March 21, 2010 at 17:05

    To continue beating my drum. You cannot draw meaningful conclusions from the statistical behavior of a single parameter in a coupled system.
    [...]”

    Wait. I’ve read that on the other thread already, didn’t i? Yes:
    “# Eli Rabett Says:
    March 21, 2010 at 17:23

    To continue beating my drum. You cannot draw meaningful conclusions from the statistical behavior of a single parameter in a coupled system.

    Even in 1988, Hansen’s argument was more sophisticated, viz: using physical constraints the outputs of the theory follow observation of a number of parameters including global temperature. Since we are confident of the theoretical inputs, and reasonably confident of the drivers, the forcings, and the observables over multiple time scales, the three legs of the theory support each other.

    on

    http://ourchangingclimate.wordpress.com/2010/03/01/global-average-temperature-increase-giss-hadcru-and-ncdc-compared/

    And there’s Bart, warning people (of the skeptic side) to regurgitate empty talking points… This is silly, i’m leaving, the regulars here are too regular for my taste…

  36. VS Says:

    Hi guys,

    For the record.

    I formally tested (see the ‘PPS’) the H0 that the GISS temperature series follows a ‘random walk’. There is also a link there to Alex’s post where he performed a similar evaluation.

    We both firmly rejected the H0 of a random walk.

  37. Alex Heyworth Says:

    Bart, you commented in your post that

    The global average temperature only changes over climatic timescales (multiple decades or longer) if there is an imbalance in the radiation budget.

    Isn’t this strictly true only of heat content? I know we use average temperature as a proxy for heat content, but strictly speaking, over a body the size of the earth, is it not possible for average temperature to change without a change in heat content, as a consequence of a redistribution of heat?

    [Reply: Good point, and I addressed that in my newer posts: If it were due to redistribution of heat, other segments of the climate system (oceans, cryosphere) should have lost eneregy. Instead, they gained energy as well. BV]

  38. Alex Heyworth Says:

    Thanks Bart. One more question: I know how we measure OHC, but when it comes to the cryosphere, the main component is the extremely large mass of Antarctica. How do we know what the heat content of the ice mass is?

    [Reply: Here's one example of a paper identifying ice mass loss of both the Greenland and Antarctic ice sheets. SkepticalScience has some more references about the situation in the Antarctic. BV]

  39. Alex Heyworth Says:

    Bart, my question wasn’t about the mass of the ice, interesting though that issue is. My understanding of that was that the Antarctic has been slowly losing mass since the end of the last ice age, with a consequent slow rise in sea level. I note that the paper you referred to does observe an increase in the rate of loss, which presumably is attributable to the recent warming.

    However, the Antarctic could be losing mass (because it is surrounded by sea, which melts the ice in summer) but could at the same time be getting colder (the ice mass that is, not the air above it). So what my question really was about was, is the temperature of the ice itself measured in any way? Or is it just assumed that its temperature is constant?

    [Reply: I don't know. But melting ice costs energy, so the increased melt points to an increase in energy (and so does sea level rise, which has sped up compared to the background of the past few thousands of years). BV]

  40. Eli Rabett Says:

    Eli suggests that Dirk go read the 1988 Hansen paper.

  41. Alex Heyworth Says:

    Bart, thank you. That’s pretty much what I expected. Not that I think there is anything odd happening with the ice mass. Just a matter of how complete our knowledge of the cryosphere is.

  42. Eli Rabett Says:

    Melting ice costs a LOT of energy 333 kJ/kg (half the number of the beast), OTOH to warm water 1 K costs 4.18 kJ/kg

  43. Alex Heyworth Says:

    ER,

    indeed. Fortunately the volume of ice melting is extremely small relative to the amount of water in the ocean.

  44. Alex Heyworth Says:

    Pat Casson said

    And thanks to all, especially Bart for moderating (in the true sense of the word!) and Alex Heyworth who provided more than one lucid explaination along the way, and opened the door to relevant publications.

    Pat, I am not the same person as ‘Alex’, so I can take only the very small credit due for finding the Gordon paper. Even then, I found that linked in an old post at W M Briggs’ blog.

  45. Eli Rabett Says:

    AlexH, so? that looks like a non sequitor to Eli.

  46. Alex Heyworth Says:

    Eli, so … at the moment, it is not having a significant impact on sea level.

  47. Al Tekhasski Says:

    A body of ice can lose its mass even if it receives the same annual/decadal/whatever energy, but the snowfall accumulation is decreased for whatever different reason.

  48. Luke Skywarmer Says:

    Short question, if CO2 stops heat loss from the air, how does it warm the oceans?

  49. Eli Rabett Says:

    Luke, what CO2 does is limit the rate at which the surface of the ocean can cool by radiation, resulting in a warmer ocean.

  50. philc Says:

    Alan(http://ourchangingclimate.wordpress.com/2010/03/18/the-relevance-of-rooting-for-a-unit-root/#comment-1823)

    Thanks for the nice,eclectic search. I think it well demonstrates that the statistical opinion on the temperature record runs the gamut from stochastic trend to deterministic trend and multiple analyses pointing both ways, although not surprisingly the number of papers favoring deterministic is larger. I think the point is that it is really difficult to tease out a signal from this data, but that regression fitting linear trends to any period is not a useful prediction method. The bottom line is that it appears we don’t have enough solid data for highly significant statistical testing at this time.

    Re: Arthur’s comment about the time scales of the various interactors in climate(solar, ice, ocean, GHG, clouds, etc.) and how they might interact. If something like the ocean circulation has a similar, highly variable pattern like the surface temperature, but in terms of years to multidecades, it is easy to see that a fluctuation in circulation that could have large effects on SST without affecting the overall heat in the oceans, but more than enough to affect air temperatures. Something like El Nino, but on a longer time scale that we haven’t even had a chance to observe once.

    Third point- A climate model has to be able to demonstrate the fluctuation between ice ages and the interglacial periods. If a climate model can’t encompass ice ages it has to be missing major components of the climate.

  51. Willem Kernkamp Says:

    Bart,

    Do you know if geothermal heating contributes to the energy balance of the ocean? Does the underwater vulcanism at the mid-atlantic ridge perhaps make a contribution both to oceanic heat and to oceanic CO_2? If so, this could be a source of the stochastic behavior that the statisticians tell us is present in the data.

    Will

    [Reply: That is a negligible source of heat on the global scale. BV]

  52. Eli Rabett Says:

    philc, yes, the GCMs can capture the cycle of recent ice ages. Problem is that the mechanism of escape from really deep ones in the far past (Snowball Earth) is still a matter of contention. Ray Pierrehumbert has done a lot of work on that.

  53. Harry Says:

    There is a very nice dissection of the laws of physics by Claes Johnson at http://claesjohnson.blogspot.com/, which may be especially challenging to the physiscs guys over here like Dhogaza and Eli. Quite refreshing, in the face of AGW.

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