Troy's Scratchpad

August 31, 2012

Comment on “The phase relation between atmospheric carbon dioxide and global temperature”

Filed under: Uncategorized — troyca @ 10:36 pm

This may seem a bit trivial, but since Humlum, Stordahl, and Solheim (2012)) was published in Global and Planetary Change, I thought it may be worth addressing, particularly while I still have access to these paywall articles.  From the “highlights” on that link, I will note the following points:

► The overall global temperature change sequence of events appears to be from 1) the ocean surface to 2) the land surface to 3) the lower troposphere. ►Changes in global atmospheric CO2 are lagging about 11–12 months behind changes in global sea surface temperature. ► Changes in global atmospheric CO2 are lagging 9.5-10 months behind changes in global air surface temperature. ► Changes in global atmospheric CO2 are lagging about 9 months behind changes in global lower troposphere temperature. ► Changes in ocean temperatures appear to explain a substantial part of the observed changes in atmospheric CO2 since January 1980. ► CO2 released from use of fossil fuels have little influence on the observed changes in the amount of atmospheric CO2, and changes in atmospheric CO2 are not tracking changes in human emissions. 

My bold.  Essentially, the method in HSS12 is to compare the “DIFF12” values for each time series – that is, for each month they find the difference between the last 12 months and the 12 preceding months.  In general, they find that the fluctuations in DIFF12 of temperatures lead the fluctuations in DIFF12 of atmospheric CO2, and then conclude:

In general, we find that changes in atmospheric CO2 are lagging behind changes in any of the five different  temperature records considered. The typical lag is 9.5-12 months for surface temperatures and about 9 months for lower troposphere temperatures, suggesting a temperature sequence of events from the surface to the lower troposphere.

As cause always must precede effect, this observation demonstrates that modern changes in temperatures are generally not induced by changes in atmospheric CO2. Indeed, the sequence of events is seen to be the opposite: temperature changes are taking place before the corresponding CO2 changes occur.

In case one may mistake this to mean “temperature changes on a short-term scale”, they discuss later:

A main control on atmospheric CO2 appears to be the ocean surface temperature, and it remains a possibility that a significant part of the overall increase of atmospheric CO2 since at least 1958 (start of Mauna Loa observations) simply reflects the gradual warming of the oceans, as a result of the prolonged period of high solar activity since 1920 (Solanki et al. 2004).

For me, the easiest way to prove that the conclusions don’t follow from a particular method is to use a simple model where we know the actual causes and parameters, and then see if using the particular method will accurately diagnose the “cause.” 

Here, I’ll dust off that old one-box energy balance model.  Script is available here.  Some key aspects of this demo:

  • I’ve set the increase in CO2 due to anthropogenic emissions to increase at a nearly linear rate of about 2 ppm / year, with some slight curvature for realism.
  • I’ve included ENSO variations for temperature changes, using the actual Nino34 index.
  • I’ve set the atmospheric CO2 value to respond slightly to temperature after 11 months.

Running the “simulation” yields the following temperature response:


And here is the annual atmospheric CO2 for the run:


As you can see, that annual CO2 seems to vary little from temperature changes. But what happens when we use the DIFF12 method from HSS12?



Well, according to HSS12, this graph would imply that most of the CO2 increase over the model run must be due to surface/ocean warming (and not the other way around), since temperature diffs clearly lead those CO2 DIFF changes by 11 months!  Furthermore, anthropogenic CO2 would appear to have almost no effect on total atmospheric CO2!  Of course, there’s one huge problem with these conclusions: we know that they are wrong, because we set the parameters for the model.  In fact, we can calculate precisely the percent of the atmospheric CO2 increase that was caused by surface warming by subtracting the “resulting” atmospheric CO2 from the anthropogenic CO2: 0.33 ppm out of 62.2 ppm, or 0.5%.  In other words, 99.5% of the CO2 increase in this model run is the result of the programmed anthropogenic emissions, despite what the DIFF12 chart would appear to show.

Clearly, the HSS12 “DIFF12” method is not able to diagnose the long-term cause vs. effect.  Rather, it is quite easy for a small CO2 response to temperature, particularly one which will have no long-term impact, to create results in the DIFF12 graphs that make them appear (incorrectly) to provide great explanative power.  In other words, the method chosen in the paper does not support its conclusions.

So, does anybody with an academic grant for page fees want to take lead author on the reply for some easy publication credit? :)  



  1. Has it ever occured to you that your calculations is simply wrong? Does observations mean anything to you?

    Comment by Slabadang — September 1, 2012 @ 1:26 am

    • Indeed, I always allow for the possibility that my “calculations” are wrong, but I don’t believe this is the case here. It sounds as though English is not your first language, so I’m not sure if you mean to suggest that you have found a mistake, or if you are merely insisting that I consider the possibility that such a mistake may exist. If it is the former, please elaborate on any mistake you think is present…

      Observations are indeed, important, as you can see in many of my other posts. However, it is standard practice to validate methods against “pseudo-data” where the underlying properties are known. I’ve shown that the method used in this paper yields misleading results and fails “validation” for answering the particular questions that the authors are trying to answer. Why then would we have any confidence that such a method would work on “real world” observations?

      Comment by troyca — September 1, 2012 @ 3:58 pm

    • Slabadang,
      Real world data used as per Humlum et al 2012. (Usually 2 clicks to ‘download your attachment’) Does this show changes in CO2 are tracking global surface temperatures, as Humlum et al assert?

      Comment by Al Rodger — September 12, 2012 @ 6:07 am

  2. It would also be interesting to see, whether the behaviour is also seen in a 21C scenario in the CMIP3 or CMIP5 archive. Would make it even more compelling.

    However, for a comment one should also consider the observations to clarify what property of the data results in the suggestive visualization.

    Comment by ob — September 2, 2012 @ 9:40 am

    • Thanks ob, I was considering doing something similar, but couldn’t seem to find any output variable from CMIP that was associated with atmospheric CO2 concentration: The concentration is prescribed in several scenarios, and since I believe the effect we’re seeing here is ENSO’s impact on atmospheric CO2, I’m not sure that many of those GCM’s even attempt to simulate that process. However, I can’t say its something I’ve looked deeply into.

      Comment by troyca — September 5, 2012 @ 1:59 pm

  3. Does GPC charge page fees?

    I’ve had unhappy experiences with writing comments. The original authors can be allowed to write almost anything.

    I asked an editor – comments are peer reviewed at GPC. But if that means they give it to the same clowns that recommended publishing the original then that is as good as useless.

    Comment by richardjamest — September 5, 2012 @ 3:22 pm

  4. GPC does not charge page fees, unless you want the article to be open access, which costs a whopping 3000 euros.

    Considering the fact that the comment can be really short, it’s worth a try. In essence you can just show your model, which has CO2 before T change, and show that with their method the conclusion is reversed. In short: their method cannot show what they claim it shows.

    Regarding ENSO: perhaps it needs a reference to Foster et al, the comment to McLean, Carter and De Freitas’ similarly flawed method: (published in 2010)

    Richardjamest is right that you have the possibility to run into the same reviewers that allowed the original through. But this does not mean they will just reject it. I’ve probably accepted papers that contain some kind of methodological flaw, and would have no hesitation to recommend a comment that sets the record straight. In fact, I would likely *strongly* recommend it, just to correct my own original mistake.

    Considering the simplicity of your proof of the problems with the approach of Humlum et al, I also think the authors will have a major problem defending their approach. And remember, if comments are peer reviewed, so are the responses!

    Comment by Marco — September 6, 2012 @ 1:35 am

  5. The Humlum et al paper is so obviously faulty that in my view it should be withdrawn, not just a comment published, and you might want to suggest that to the editor. It would be interesting how they respond – please publish the response here.

    Your simple box model provides one elegant demonstration for why the paper is faulty, but the fact is obvious to anyone with basic science training even without using a model. The paper simply mixes up time scales, and the same mistake has been made in a number of “climate skeptics” papers. The method by design specifically analyses short-term variability, the DIFF12 approach effectively filters out any longer time scale. So of course the result only applies to this short-term variability and cannot tell us anything about the long-term trend. The short-term variability in atmospheric CO2 clearly is partly caused by variability in oceanic CO2 uptake which correlates with sea surface temperature, hence their result would not surprise anyone familiar with the carbon cycle. However, their conclusion about the long-term trends is demonstrably false. If – as they surmise – the long-term trend in CO2 was caused by outgassing of CO2 from the ocean due to warming, then the oceanic CO2 content should have gone down as the atmospheric CO2 content has been going up. That is disproven by measurements: CO2 content is increasing both in the atmosphere and in the ocean. And of course we know where the added CO2 is coming from: from fossil CO2 that enters the ocean-atmosphere system as a result of burning fossil fuels. That, by the way, has been proven already in the 1960s by isotope analysis, which demonstrates that the added CO2 has a fossil origin and does not come out of the ocean.

    Comment by S. — September 6, 2012 @ 5:49 am

  6. Nice demonstration!

    The reason the method fails is because correlations are only sensitive to the variations of the data around its mean, but it is the mean value of DIFF12CO2 that corresponds to the long term linear trend in atmospheric CO2. So even a correlation of 1 only explains the variation in the growth of CO2 around the linear trend, i.e. practically nothing.

    Secondly, a constant airborne fraction suggests that a constant fraction of annual anthropogenic emissions “stays” in the atmopshere, so the annual increase in atmospheric CO2 (i.e. DIFF12CO2) should be proportional to annual emmisions. However, instead of correlating with annual anthropogenic emissions itself, they correlate with diff12 of annual anthropogenic emisions. I can’t see a good reason why the annual increase in CO2 should be correlated with the *rate of change* of anthropogenic emissions.

    Comment by dikranmarsupial — September 7, 2012 @ 9:47 am

  7. Thanks all. See my latest post – – for a similar demonstration using a CMIP5 experiment, per some of the discussion above.

    Regarding page fees and publication, I find myself with little free time, and I don’t have much desire to be lead (or sole) author again and deal with the whole write-up, formatting, and submission process that seems to take up the bulk of that time, I’ve found that being a contributing author suits me much better 🙂 So again, if any qualified individual would like to do a write-up and take lead author, I’d be more than happy to include my demonstrations in the response.

    Comment by troyca — September 8, 2012 @ 10:07 am

    • Troy, try to contact Tamino, he might be interested. Or Gavin Schmidt?

      Comment by Marco — September 8, 2012 @ 10:37 am

      • another taming paper would indeed be nice (and it would be thorough). If I hadn’t also your time constraints, I would be tempted to volunteer…

        Comment by ob — September 8, 2012 @ 11:05 am

  8. Two remarks:
    (1) You test the HSS-method with a model that has known correlations between the variables. In the real world the correlations are not known with certainty. The generally assumed correlation between greenhouse gas emissions and temperature is a theory, not a proven fact. There is no doubt that CO2 absorbs infrared radiation, but the interactions with numerous other mechanisms are too complex to a assume a simple coupling between CO2 and temperatures.
    (2) Correlation analysis shows, that the correlation between CO2 emissions and increase of atmospheric CO2 is poor. Take the annual emissions and calculate the regression coefficient. I found r2 = 0.44 for the period 1959 – 2008. Do the same for the temperature and atmospheric CO2 and you will find r2 = 0.57. This indicates, that about 44% of the variance in atmospheric CO2 can be explained from emissions and 57% from the rising temperatures (regardless what caused the rising temperatures). Isn’t this a nice example of the truth being somewhere in the middle?

    Comment by Frans — September 11, 2012 @ 5:27 am

    • Frans,

      (1) Indeed, I test the HSS-method with a model with known properties, because this is the only way one *can* test a method. Suppose some group shows you a rock with unknown properties, but they claim it is filled with gold because their device says it is. However, you test their device on your rock that you KNOW has no gold inside, because you manufactured it yourself, but their device says this rock is filled with gold as well. Would you trust their device’s diagnosis of the first rock? You shouldn’t. Would you claim that your test is invalid because you knew the properties of your rock ahead of time, but didn’t know the properties of the original rock? Obviously that would be absurd, because the whole point of the test is that you knew the properties of your rock ahead of time.

      (2) The correlations in my model are not meant to be realistic, but merely to show the limitations of the DIFF12 method they’ve employed. I am not sure what data you are using or on what time scale to say that “the correlation between CO2 emissions and increase of atmospheric CO2 is poor”, but in my initial attempt to correlate the accumulated emissions vs. Mauna Loa atmospheric CO2 data I got an r^2 of 0.999. This seems almost too high that I’m wondering if the CDIAC data I’ve used is derived from the Mauna Loa data, except that HSS reference the data (gridded, monthly) that originates from the same annual data I’ve used here. See for yourself (R script):

      emissions.ts<-ts(read.table(" ", skip=227)[[2]], start=1950)
      emissions.ts<-window(aggregate(emissions.ts, nfreq=1)/12, start=1959)<-window(diffinv(emissions.ts), start=1959)
      CO2.ts<-window(ts(read.table(" ", skip=57)[[2]], start=1959), end=2008)
      test.lm<-lm(CO2.ts ~

      Comment by troyca — September 11, 2012 @ 12:58 pm

      • My friend,
        The data I used are:
        emissions 1959-2008:
        2462 2577 2594 2700 2848 3008 3145 3305 3411 3588 3800 4076 4231 4399 4635 4644 4615 4883 5029 5105 5387 5332 5168 5127 5110 5290 5444 5610 5753 5964 6089 6164 6252 6147 6155 6273 6400 6525 6633 6591 6573 6750 6916 6981 7397 7782 8086 8350 8543 8749 (see:
        CO2-increase 1959-2008:
        0,74 0,93 0,73 0,81 0,54 0,63 0,42 1,34 0,77 0,89 1,58 1,06 0,64 1,13 2,22 0,50 0,91 0,97 1,73 1,63 1,38 1,90 1,43 1,11 1,62 1,57 1,45 1,33 1,79 2,46 1,45 1,26 1,32 0,79 0,68 1,68 1,99 1,74 1,11 3,02 1,65 1,26 1,67 2,10 2,61 1,74 2,24 2,09 1,86 1,87 (the difference between the annual average of the Mauna Loa data, see
        temperature 1959-2008:
        1,63, 1,41, 1,84, 1,83, 1,95, 0,62, 0,95, 1,25, 1,27, 1,20, 1,87, 1,63, 1,09, 1,67, 2,29, 0,97, 1,19, 0,80, 2,03, 1,70, 2,23, 2,35, 2,55, 2,08, 2,86, 1,90, 1,82, 2,17, 2,89, 2,87, 2,55, 3,23, 3,01, 2,35, 2,52, 2,84, 3,35, 2,69, 3,74, 4,63, 3,51, 3,39, 4,03, 4,27, 4,32, 4,22, 4,37, 4,11, 3,99, 3,63 (HadCrut3, see
        Correlation analysis gives
        r2= 0.44 for emissions versus CO2-increase,
        r2= 0.57 for temperature versus CO2-increase
        So, the correlation between increase of atmospheric CO2 and temperature is better than between atmospheric CO2 and emissions. From a statistical point of view HSS do have a relevant point!

        Comment by Frans — September 11, 2012 @ 2:48 pm

      • Frans,

        Well, it looks like we were indeed using essentially the same data, where my last comment showed that the accumulated CO2 emissions explains 99.9% of the overall variance in atmospheric CO2 over that time period. Now that you’ve explained what you’ve done, it is clear that you have used the DIFF values again for atmospheric CO2, which as shown in my post confound any long-term trend causation diagnosis. Furthermore, you have correlated the atmospheric CO2 diffs against temperature anomalies, which would imply that actual atmospheric CO2 somehow depends upon the integral of temperature…even HSS did not suggest this, but rather tried their correlation against DIFF’d temperature anomalies. Their method does not prove what they claim it to prove, based on tests against known model outputs. Furthermore, we’ve seen that atmospheric CO2 correlates extremely well (r^2=0.999) with the accumulated fossil fuel emissions…I would submit that we don’t need to continue playing these statistical games with derivatives.

        Comment by troyca — September 11, 2012 @ 3:44 pm

      • Troy,
        If the increase of atmospheric CO2 were mainly due to CO2 emissions, we would expect that in years with small emissions we see a small increase atmospheric CO2 and in years with large emissions we see a large increase. But that is not what is happening. The atmospheric CO2-concentration is rising monotonously, with only a poor relationship with the annual emissions, as I show with the correlation between the DIFF-values.
        If, on the other hand, the increase of atmospheric CO2 were mainly due to outgassing from the oceans – as HSS asume – we would expect a positive correlation between the global temperature (better: ocean surface temperature) and the increase of atmospheric CO2. My correlation analysis shows that this correlation is poor too, though a bit better than the other correlation.
        So, my conclusion is that the truth lies somewhere in the middle: the rise of atmospheric CO2 is partly caused by CO2 emissions and is partly a result of outgassing from the oceans.

        Comment by Frans — September 13, 2012 @ 12:28 pm

      • Troy, the reason that the correlation between cumulative emissions and Mauna Loa CO2 concentrations is so high (your 0.999) is that this is essentially a test of the hypothesis that the airborne fraction has been constant over this period. See the remark of Dikran Marsupial @ Real Climate and his earlier piece at Skeptical Science.

        Comment by Gestur — September 12, 2012 @ 4:41 pm

      • @Frans (September 13, 2012 @ 12:28 pm)

        I encourage you to read again the demonstration in this post, as it directly addresses why those conclusions from HSS are not supported.

        “If the increase of atmospheric CO2 were mainly due to CO2 emissions, we would expect that in years with small emissions we see a small increase atmospheric CO2 and in years with large emissions we see a large increase.”

        All else being equal, yes this would be expected, but there are other variables involved. One such variable is ENSO, which may introduce higher frequency fluctuations that dominate rate-of-change on the *annual scale* but have a miniscule long-term impact. Please look again at the final figure in my post. The green line, “Anthro CO2 Diff12”, represents the anthropogenic CO2 emissions programmed into the model. If you regress this against the atmospheric CO2 Diff12 from the model you get r^2=.033. Does this mean that we have determined only 3.3% of the model’s increase in atmospheric CO2 is the result of emissions? Certainly not, because we know the model’s true values, which show that 99.5% of the increase in atmospheric CO2 is the result of emissions! This is not meant to represent the “true” value of the real-world system, but only to show that regressions against the DIFF12 atmospheric CO2 are worthless for this diagnosis.

        Comment by troyca — September 13, 2012 @ 4:18 pm

      • [troyca: I have removed this comment, per Gestur’s request].

        Comment by Gestur — September 14, 2012 @ 1:52 pm

      • Hi Gestur,

        Sorry for the slow weekend reply. Thank you for the support, although I would discourage future remarks disparaging other commenters (I don’t have the traffic to really worry about a “blog policy”, but I suppose this would be in it). If Word accepts the graphs, I might recommend saving that as a PDF and then linking to them on a public host (Skydrive, Dropbox, etc.)? I say that because many people might be wary of downloading Word docs that are macro-enabled.



        Comment by troyca — September 15, 2012 @ 1:50 pm

  9. Troy, you are wanted over at Realclimate. Or rather, you may want to talk to Rasmus Benestad, who has had something to say about the Humlum et al paper:

    Comment by Marco — September 11, 2012 @ 11:12 pm

    • Thanks Marco, that’s an interesting post, not sure I would have much to add other than my couple of demonstrations.

      Comment by troyca — September 13, 2012 @ 9:43 am

  10. Hi Troy. Thanks for the interesting post.Regarding your reply to Frans you state:

    < Furthermore, you have correlated the atmospheric CO2 diffs against temperature anomalies, which would imply that actual atmospheric CO2 somehow depends upon the integral of temperature…

    Thinking this through – isn’t it the proper relationship that of temperature levels corresponding with co2 increments rather than co2 levels? Using the ocean component as an example, presumably co2 sinks and sources would balance at a certain sst level. A step rise (no trend) of sst beyond that level would then imply an ongoing constant imbalance of sinks over sources which would then accumulate in the atmosphere at a constant rate (trend). The next step rise in sst would imply an increased trend in atmospheric co2 accumulation. If this is correct then the proper regression relationship would be co2 derivative with sst, or integrated sst with co2 levels. IIRC this is the point which Murray Salby makes.

    Comment by Layman Lurker — September 15, 2012 @ 8:58 pm

    • Thanks Layman. What you say seems plausible enough, although I’d say the process is complex enough that one (e.g. HSS) would not necessarily need to see it that way. They could argue just as easily that a step change in temperature results in a one-time release of gas from the ocean that could dominate (and otherwise keep things at equilibrium – or at least close enough that the imbalance would not contribute much). Indeed, from figures 2-10 of HSS, this appears to be what they are doing (where they compare DIFFs of temperatures and CO2), so it was a bit confusing to me that Frans seemed to be defending the HSS method while suggesting different physical relationship from them.

      Also, as you suggest, from an imbalance perspective this would suggest there is a set SST for equilibrium, and any increase from this would result in continued accumulation of CO2 in the atmosphere…and it would seem to be pretty sensitive to this as well! I don’t know that the ice core data would support this at all, but I confess I haven’t studied much on the subject. As you can see from my post, I don’t find either argument that compelling in terms of ocean warming contributing to current CO2 increases.

      For what it’s worth, you could run the script for my model above and then correlate T with the derivative of atmospheric CO2, then correlate emissions vs. CO2 diff:

      cor(T[12:348], total_CO2.diffs) #alignment of T with CO2 diffs
      cor(ACO2.diff, total_CO2.diffs)

      You’ll notice that despite a much higher correlation between T and atmospheric CO2 than “emissions” and atmospheric CO2 in this model, we again know that 99.5% of the increase in this model is the result of “emissions” and not T.

      Comment by troyca — September 17, 2012 @ 11:29 am

      • [troyca: I hesitate to delete any comments, but since you have requested it and it arose from confusion over e-mail to me vs. the blog, and nobody has directly replied to to this comment or the one above (other than myself), I don’t see much harm. It appears that if you subscribe to comment replies and WordPress sends an automatic e-mail update, a reply to that e-mail will submit it as a comment to the blog. I have not modified the WordPress settings much, but I will see if this message is an easy thing to change to add a warning or something. Nor do I have any moderation on, so a message will get posted immediately unless the Spam filter finds reason to place it in moderation. The e-mail I use for this blog is troy_ca at live dot com. Thanks.]

        Comment by Gestur — September 17, 2012 @ 3:40 pm

      • Thanks for the reply Troy. I understand what you are trying to portray in your model. But I doubt very much that physical reality behaves this way – at least with oceans. How is it that co2 can be shown conclusively to fluctuate with temperature but yet not accumulate when we know temperature levels are much higher now then they were 50 odd years ago? FWIW I am still open to argument on this (up till a month ago or so I had just taken anthropogenic related co2 increases as a given) but I think many have just quickly dismissed the co2 derivative connection because it ‘removes the trend’ without considering that any imbalance related to increasing temperatures must necessarily be integrated by the atmosphere. At this point at least, I consider the co2 derivative to be prima facie evidence of such an imbalance.

        I think it would be interesting to run multiple regression of temp plus human emissions on diff(co2) and I may may look into this myself if I get time. Thanks again For your great blog Troy.

        Comment by Layman Lurker — September 17, 2012 @ 5:00 pm

      • Layman,

        Below is a script to do the multiple regressions you are asking. However, again I would caution not to over-interpret this…using DIFFs is going to highlight what causes the bulk of the changes on a year-to-year basis, not on a long-term scale. Perhaps I will do a similar test on the GISS ESM when I have a chance:

        emissions.ts<-ts(read.table('', skip=227)[[2]], start=1950)
        emissions.ts<-window(aggregate(emissions.ts, nfreq=1)/12, start=1960)
        CO2.ts<-window(ts(read.table('', skip=57)[[2]], start=1959), end=2008)
        temp.ts<-window(aggregate(getNOAA(), nfreq=1)/12, start=1960, end=2008)
        test.lm<-lm(CO2.diff ~ emissions.ts + temp.ts)

        [troy: WP keeps garbling the code in those read table URLs. Just delete the extra stuff after .txt and .ems up to the comma.]

        Comment by troyca — September 18, 2012 @ 10:55 am

  11. The above should read sources over sinks rather than sinks over sources.

    Comment by Layman Lurker — September 15, 2012 @ 11:23 pm

  12. Well done.

    How would you respond to a similarly based argument that solar energy factoring is flawed because they only measure the watt energy? According to the World Center for Geomagnetism in Kyoto, earth’s protective interface with energy from space [our magnetosphere] is 10% weaker than it was in the 1600s, which is also when the over-hyped magnetic polar wander began [legitimately happening, but not a catastrophic thing]. Furthermore, it is well accepted that the solar magnetic fields are weakening simultaneously, the NSO has suggested that the next solar cycle may not have sunspots. While this has a moderate affect on watt energy [0.1% total variance from solar max to min] the real affect is that the weaker heliosphere allows more cosmic rays to enter the system [ENAs as well]. I am a professional researcher – I cannot find anyone who combines the factors I have listed above. I do not have the sophistication to model it statistically or do a design of experiment to test it.

    Can you help or point me in the right direction?

    Comment by Ben — February 27, 2013 @ 3:39 pm

  13. […] but I haven’t had much time for blogging lately!).   For those of you who have already read this blog post, or the one at RealClimate by Rasmus, the contents should not be much of a shock.  Sadly, the […]

    Pingback by Our comment on Humlum et al. in press at Global and Planetary Change | Troy's Scratchpad — May 16, 2013 @ 8:35 am

  14. […] is gratifying, however, to see troyca’s assessment of the same situation, and how it comes out right. And he’s a software engineer.  There’s hope […]

    Pingback by Powerful and Proper Time Series Statistics | Hypergeometric — June 21, 2013 @ 3:04 pm

  15. Payoff takes as little as several hours or up to 48 hours during
    high-volume times.

    Comment by Alyce — January 2, 2019 @ 5:22 am

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