How Fast is Earth Warming?

We’ve already studied the rate of global warming in the GISS surface-temperature data and the two best-known satellite lower-troposphere data sets. We even removed approximations of the impact of exogenous factors (namely, the el Nino southern oscillation and volcanic eruptions) on the data, for a clearer comparison. Now that GISS, NCDC, and HadCRU have reported their year-end figures, let’s repeat the exercise using all five major global temperature records: GISS, NCDC, HadCRUT3v, RSS, and UAH. Also, let’s include another exogenous factor in our analysis: variations in solar output.


Just as before, we’ll use MEI (multivariate el Nino index) to characterize el Nino, and the volcanic forcing data from Ammann et al. (2003) to characterize volcanic influence. Also as before, we’ll allow for an annual cycle in the data (a residual annual cycle) by including a 2nd-order Fourier fit.

We’ll characterize solar fluctuation by the international sunspot numbers. I selected sunspot numbers because most reconstructions of TSI (total solar irradiance) are annual values rather than monthly, and the satellite-based estimates of TSI don’t start until about 1979 — but we’d like to fit surface-temperature data from 1975 to the present. So, we’ll use sunspot numbers as a proxy for solar activity, and see whether or not the temperature time series show correlation with that index.

We’ll also allow for a lag in the influence of el Nino, volcanic forcing, and sunspot numbers. For each of these exogenous variables, we’ll try a range of lags (from 0 to 24 months for el Nino and volcanic, from 0 to 120 months for sunspot numbers) and use the lags which give the best fit.

First let’s see what the data look like when they’re not set on the same scale, or compensated for exogenous factors. Here are all 5 records (annual averages with trend lines) from 1975 to the present (the satellite records don’t start until about 1979):

The GISS and NCDC data show 2010 tied for hottest year with 2005, while HadCRU, RSS, and UAH still have 1998 as the hottest year on record. The reason they’re offset from each other is, of course, that they’re all using a different baseline (i.e., a different “zero point” for temperature). After we remove the estimated influence of exogenous factors, we’ll use the same baseline (1980.0 to 2010.0) for all 5 data sets.

If we estimate the global warming rate without accounting for exogenous factors, we get this (numbers in parenthese are 1-sigma standard errors in the final digits):

Data Set Rate (deg.C/yr)
GISS 0.0176(23)
NCDC 0.0171(20)
HadCRU 0.0169(23)
RSS 0.0163(41)
UAH 0.0141(43)

All the rates are comparable, although the UAH lower-troposphere data give a noticeably slower warming rate than the others. Also, the satellite data sets (RSS and UAH) have larger standard errors than the surface-temperature data sets (GISS, NCDC, and HadCRU).

When we do a multiple regression of temperature on MEI, volcanic forcing, sunspot numbers, a linear time trend, and an annual cycle, the fits are quite impressive. Here, for example, is the result for GISS data:

[NOTE: in this graph, the thin black line is the GISS data while the thicker red line is the model based on el Nino, volcanic forcing, solar variation, a residual annual cycle, and a time trend.]

The multiple regression enables us to do two useful things. First, it gives us a direct estimate of the rate of linear time increase, i.e., the rate of global warming. The estimates are:

Data Set Rate (deg.C/yr)
GISS 0.0172(13)
NCDC 0.0172(10)
HadCRU 0.0171(11)
RSS 0.0183(13)
UAH 0.0159(15)

Second, it enables us to remove the estimated impact of el Nino, volcanic eruptions, solar variation, and the residual annual cycle, leaving only the global warming trend and any remaining natural variation. This gives us an adjusted data set for each source. Here they are, for monthly data, for all five data sources:

We can also compute annual averages of the adjusted data sets, which shows just how strongly the different sources agree with each other:

One thing of note is that although the satellite lower-troposphere data indicate slower warming when using the raw data, when they’re compensated for all three exogenous factors the RSS data shows the fastest rate of warming. This is primarily because the lower-troposphere data show a much stronger response to the exogenous factors than the surface-temperature records, and the exogenous factors are tending to reduce the estimated RSS trend — when these factors are removed, what remains is stronger warming in the RSS data set. Also, the trend in adjusted UAH data is similary higher than in the raw UAH data, but even with this increase the UAH data still show the least warming of all 5 data sets.

Also noteworthy is that when compensated for exogenous factors, the 3 surface-temperature records (GISS, NCDC, and HadCRU) indicate nearly identical warming rates since 1975.

Another interesting point is that in the adjusted data sets, all 5 sources have 2010 as the hottest year on record. In fact, 4 out of 5 (all but NCDC) also have 2009 as the 2nd-hottest year — quite the 1-2 punch. Of course all trends are statistically significant — strongly so. The conclusion is inescapable: the globe is warming, and shows absolutely no sign whatever of stopping or even slowing its warming. Any talk of “cooling” or even a “levelling off” of global warming over the last decade is absolute nonsense.

All 5 major global temperature indices are in oustanding agreement not only about the overall rate of warming, but about the year-to-year fluctuations as well.

The lower-troposphere data (both RSS and UAH) really do respond much more strongly to exogenous factors than surface temperature data. Their response to volcanic forcing is about 50% bigger, and their response to both el Nino and solar variations is just about twice as large as that of the surface temperature records. In fact, for the surface temperature data the response to solar variation is not quite statistically significant, but for lower-troposphere data the solar response is definitely significant.

To answer the question posed in the title of this post: presently, Earth is warming at about 1.7 deg.C per century. There’s good reason to believe that it’ll be warming even faster in the upcoming decades. And there’s good reason to believe that this spells trouble for life on earth — including human life.

Update

A lot of good questions were posed in comments, so I’ll try to answer some of them. If I don’t respond to your individual question, please don’t take it personally — life’s too short.


Do you have graphs for the removed solar, volcanic, and el nino forcings? Are there any other regional patterns which can explain the rest of the short term variability?

Yes (see below), and I don’t know.


… I’m rather more interested in the ‘best fit’ magnitude and lag of the solar influence.

As the above graph shows, the peak-to-peak influence on surface temperature is about 0.07 deg.C, on lower-troposphere it’s about 0.15 deg.C. Those are eyeball estimates of the “smoothed” values, the absolute range for solar influence is 0.08 deg.C surface, 0.18 deg.C lower-troposphere (but I suspect some of that fluctuation is just an artifact of the curve-fitting).

The lags were very small (which surprised me), only about 2 months for solar, but this analysis is really looking for rapid fluctuations so it seems that it’s capturing the rapid response.


It would be nice to know more of the fitted parameters, such as lags and amplitudes for the exogenous factors. Does the temperature lag all the exogenous factors? Are the lags similar? If you estimate a conversion factor from sunspot number to total solar irradiance, you can estimate sensitivity of temperature to TSI for the fitted sunspot amplitude. Is it reasonable?

People (Roy Spencer, for example) have included other multi-year indices in such fits and they have found that these can remove most of the linear trend. How do you justify including or excluding any particular index?

Best-fit lags are different for different data sets, but the lag for el Nino is 3 or 4 months surface, 5 months lower-troposphere. For solar, 2 months except GISS 3 months. For volcanic, 8 or 9 months surface, 3 or 5 months lower-troposphere. Hence the lower troposphere temperature responds sooner to volcanic eruptions, later to el Nino, and at about the same time to solar.

Just a rough guesstimate: the variation in TSI during a solar cycle is about 1 W/m^2, but correcting for geometry and albedo that’s a variation in climate forcing of about 0.18 W/m^2. Since the surface response is about 0.07 deg.C, that indicates a sensitivity of about 0.39 deg.C/(W/m^2). In the lower troposphere the response is about 0.15 deg.C so the sensitivity is around 0.83 deg.C/(W/m^2). This is the prompt response, and is higher than the Stefan-Boltzmann response would be, so it appears there’s some amplification of the prompt response to solar variation. But all this is, of course, tentative — based as it is on a statistical rather than physical model.

Oscillations don’t create trends. Temperature increase is energy which, as we all know, doesn’t appear from nothing. But of course with enough degrees of freedom you can model anything you want (including an elephant). Spencer’s attribution of the trend is nothing but wishful thinking on his part.


Just curious – of the (apparent) peaks and troughs that are left how much of that variation could reasonably end up suffering the same fate of being legitimately attributed to specific climate processes and phenomena and end up subtracted in a similar way to this to reveal, undisguised, the underlying trend?

Again, I don’t know. This is a question best posed to a genuine climate scientist. I will mention that whatever set of exogenous factors is included, there will always remain some unaccounted-for noise.


Still like to see the cross-validated version though!

All things come to him who waits.


What is the remaining rms difference between the different datasets there?

Just as an example, I took the difference between the adjusted GISS and adjusted RSS data. The r.m.s. difference in monthly data is 0.13 deg.C. The r.m.s. difference in annual averages is only 0.05 deg.C.

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130 responses to “How Fast is Earth Warming?

  1. Thanks Tamino, really appreciate you taking the time to publish online when you could have been watching American Idol. Honestly I can’t wait for Albertosaurus to chime in on this one. Sorry couldn’t help myself.

  2. Do you have graphs for the removed solar, volcanic, and el nino forcings? Are there any other regional patterns which can explain the rest of the short term variability?

  3. Interesting stuff, but really I’m rather more interested in the ‘best fit’ magnitude and lag of the solar influence. Solar remains high on the climate change denial ladder and if you’ve quantified its influence, however arbitrarily it might be (this being a statistical tool to remove solar influence rather than an investigation of the mechanisms behind it), I’d like to know what results you got. Can we have a look-see?

  4. Thank you, Tamino. I would have missed at least in removing the yearly variation and probably also in adjusting the volcanic forcing. As I said, so many variables it’s easy to get confused. Kevin’s comment on PDO or AMO and aerosols in the previous post ‘Sharper Focus’ is also a thing I recommend people reading before commenting.

  5. Great post, sir. Well analyzed and very well written. This is the kind of clear, unequivocal statement we need to hear more frequently.

  6. Brilliantly clear analysis! Remove all the known noise signals and we get a near straight line – if that’s not proof of global warming then i don’t know what is!

  7. Another pitch for doing this to the various stratospheric temperature series (MSU/AMSU and SSU).

  8. Very interesting. It would be nice to know more of the fitted parameters, such as lags and amplitudes for the exogenous factors. Does the temperature lag all the exogenous factors? Are the lags similar? If you estimate a conversion factor from sunspot number to total solar irradiance, you can estimate sensitivity of temperature to TSI for the fitted sunspot amplitude. Is it reasonable?

    People (Roy Spencer, for example) have included other multi-year indices in such fits and they have found that these can remove most of the linear trend. How do you justify including or excluding any particular index?

    Of course, the more indices you include, the better the fit looks. With enough basis functions, you can fit anything; but the result is meaningless.

  9. My thanks also. Just curious – of the (apparent) peaks and troughs that are left how much of that variation could reasonably end up suffering the same fate of being legitimately attributed to specific climate processes and phenomena and end up subtracted in a similar way to this to reveal, undisguised, the underlying trend?
    I realise this is no substitute for climate modeling but as a tool for cutting through some of the BS in the broader public debate it seems to have some real value – failure to take into consideration natural variations being one of the usual accusations levelled at climate science as well as one the fundamental mistakes of vocal opponents.

  10. Nice work. The sunspot proxy makes the difference to my eyes when looking at the gradient over the last decade. As it should, given the last solar cycle.
    (Still like to see the cross-validated version though!)

  11. Great rundown of the data. I like the idea of removing the solar variation as this is important to be able to see what might happen when solar activity increases on the upswing of the next cycle. It seems we will be seeing very strong apparent warming in the latter half of this decade when the solar input is increasing and no longer obscuring the warming due to human activity.
    Keep up the good work Tamino.

  12. Nice analysis Tamino!

    There’s something funny with the residuals around 1982 – the model appears to have accentuated the dip in temperature that year. There still seem to be some significant year-to-year variations – perhaps some of the effects have more than one lag term in their effects? Or maybe you need to dig up some other indices (North Atlantic?)…

    I wondered, did you use the same lags for each time series?

  13. Hi Tamino, thanks for that.
    Two things that puzzle me:
    1. Your “result for GISS data” after multiple regression of temperature including on MEI and volcanoes still seems to show the early 1990s Pinatubo cooling and the 1998 El Nino spike. Surely one should expect these to have been removed?? (I assume the red line is a running twelve month smooth?)
    2. I was expecting the HadCRU trend to come out a bit lower than GISS since it (as far as I am aware) does not represent Arctic temperatures to the same extent as GISS. Any comments?

    [Response: The graph of the result for GISS data shows the unadjusted GISS data, and the red line which is not a 12-month running mean, it's the model based on el Nino, volcanic, and solar activity. It's a testament to the accuracy of this model, that you mistook it for a 12-month running mean of the data!]

  14. I have absolutely no reason to believe the following is relevant but it’s something which needs to be brought up in a Devil’s Advocate sort of way.

    Who says that el Nino is an exogenous factor? Those who argue that negative feedbacks of some sort will save us (Lindzen, et al) could say that actually the warming is flattening off and the mechanism that’s causing it is changes to the ENSO (tropical clouds and all that) but that you’re cancelling that out. In other words, to be fully water-tight you’d need to show that there’s been no longer-term (decadal) change in the behaviour of the ENSO.

    • Except that the correction for ENSO doesn’t seem to affect significantly the trends for most of the indices except for the satellite based data. If the Iris is supposed to save us, it ain’t workin’.

  15. Excellent stuff!

    What amplitude did you find for the influence of the solar cycle, based on the multiple regression?

  16. I know we would normally prefer 30 years or more of data to identify climate trends, in order to better distinguish the trend from interannual variability, but given the roughly 11-year solar cycle and the fact that global warming appears to be still accelerating after its mid-20th Century hiatus, I think it’s interesting to look at 22-year trends as well.

    Thinking of the two satellite series in particular, they started very close to quite a high maximum of solar activity (around 1980) and end during the current very low solar minimum, so I would think that the unadjusted trends over the entire series would therefore slightly underestimate global warming and that does seem to be the case – RSS and UAH are the two lowest of your five unadjusted warming rates at 0.0163 and 0.0141°C per year respectively.

    Looking at the latest 22-year trends for both satellite series, the unadjusted warming rates become (according to ‘woodfortrees.org’) 0.02°C per year in both cases. I tried adjusting GISS for solar variation and I got 0.02°C per year for that series as well, over the same period. The difference between 0.017°C per year and 0.02°C per year isn’t all that much, but it does indicate to me that global warming is not only continuing unabated, but also continuing to accelerate.

  17. Tamino, that “adjusted” graph is amazing! What is the remaining rms difference between the different datasets there? It suggests the actual precision in global temperature measurement may be much higher than I’d thought (random error in monthly numbers of around 0.01 C?)

  18. There are lots of interesting questions, I’ll try to answer many of them in an update to the post. I hope to get to it some time today.

  19. Tamino, you must feel bombarded with questions and requests for more information, additional analysis, etc. I just wanted to note that this is a really cool post in and of itself. If you have the time and interest to update this with responses to some of the questions, that’s great. But even without that, this is really nifty.

  20. Tamino, clearly everybody is assigning you a lot of homework. Might it be possible to get the raw numbers for the adjusted series so we can leave some of the exercises to the readers?

    One question I had that might be fairly easy would be to look at the standard deviation, skew and kurtosis about the linear trend. The standard deviation would of course give us some measure of “inernal” variability. The excess kurtosis might give us an idea of whether the sources are oscillatory or episodic, and the skew vs time might give us an idea of whether there are systematic deviations from the linear trend.

  21. I’d like to add my thanks for a very interesting post. I’ll look forward to the update!

  22. tamino,

    Great post. Actually, I’m amazed something like this hasn’t been presented as a paper (i.e. cancel out the noise, and the trend appears like magic). How does one explain the trend when the usual denial mechanisms have already been accounted for?

    This reminds me of a denial post I saw once which was very effective, although if you thought about it, it actually proved the opposite of what it tried to say. In fact, I can no longer find it on the Internet, so I suspect the author/publisher realized this, and killed it.

    But what that post did was to try to prove a theory of warming by subtracting, one by one, the different elements, just as you have done. Of course, all he was left with in the end was a trend… definitive, unexplained (without CO2) warming. He thought it proved that ENSO/volcanoes/etc. were the dominant factors in climate, but what it really proved was that they were the dominant sources of noise that when removed clearly revealed the trend.

    Anyway, what I remember was effective about that post was that it went step by step. Here (first) are the original temperature observations. Here is the MEI, and the lag, scaled to match. Here (second) are the temperature observations with MEI removed. Here is the volcanic influence, with lag and rescaling. Here (third)… and so on.

    By doing it step by step, a reader could visually follow the progression, as noise is incrementally removed. This was very effective in making one feel that what was being presented was not arbitrary, or somehow “faked” by the poster (no accusation, but you know that’s what most deniers will eagerly think when they are referred here).

    When all is said and done, one is left with an obvious, overall trend (your result), with maybe a bit of wiggle.

    Lastly, subtract the last factor, atmospheric CO2 levels (as deniers often do with the raw observations, to “prove” a lack of correlation)… and you get a flat line.

    I’d also love to see this back as far as possible before 1975 (which obviously then requires some factor for aerosols, which perhaps doesn’t exist or must be fudged with a very simple model/guesstimate).

    One last point, on that wiggle… starting around 1998, there seems to be a very clear, regular and pronounced oscillation of about 4 years. There are only three cycles, so it’s too soon to say, but it looks so regular that it will be interesting to see if there is another factor that could be removed to further flatten the curve. It won’t change the trend, but would remove a bit more of the noise.

    [Response: I agree that removing factors one at a time makes a more compelling narrative. But it's a statistically inferior approach, because different factors can correlate (or anticorrelate) with each other. In such a case, the best approach (statistically) is to remove them all simultaneously by multiple regression.

    Going back before 1975 would indeed require including other factors (esp. anthropogenic sulfate aerosols). It would also call for using a time-trend model which is not linear. And, my real interest is in the modern global warming rate. But maybe I'll get to that some time soon.

    As for the 4-year oscillation is the residuals, I did Fourier analyze them and it's not statistically signficant. Frankly, if you do a lot of period analysis you'll see such wiggles all the time, especially with red noise. False detection of apparent "periodic" behavior by visual inspection is commonplace.]

    • That sort of stupidity sounds like the work of Bob Tisdale. His latest attempt involves taking a subset of SST as some sort of magic proxy for some unexplained ENSO trend…. then subtracting it from the global temperature.

      Hmmm…. I wonder what happens when you subtract local temperature from global temperature?

      The WTF crowd ate it up.

      [Response: Don't be surprised if he subtracts arctic temperature from global temperature, in order to claim the world is cooling.]

  23. Horatio Algeranon

    It’s interesting (though perhaps just coincidence) that if you average the trends for the two adjusted satellite data sets together, you get 0.0171 (ie, same as for the adjusted surface trends).

    One would not necessarily expect that result since at least some of the error associated with the satellite trends may be systematic (eg, calibration “drift”).

    Clearly, much of the uncertainty associated with the satellite trends is due to the fact that the noise (from ENSO and volcanic eruptions) gets “amplified”.

    But why does that result in a lowering of the trends by a significant amount? (almost 0.01 and 0.03 C per decade for RSS and UAH resp)

    If the noise were truly “random”, wouldn’t one expect the associated uncertainty to decrease, but the “central” trend value to remain basically the same?

    A more general question: what does it mean when the (apparent) trends for any of the data sets change due to the noise removal? The changes for GISS and Hadcru are admittedly smaller than those for the satellites, but they do change, nonetheless.

    What, if anything, does it mean that the trend for NCDC remains essentially unchanged? Is that just coincidence or does it tell us something?

    The fact that the trends for the different data sets respond differently to noise removal is very interesting.

    [Response: Remember that the linear time coefficients are only estimates of the trends. As noise is removed, its impact on the trend estimate is also removed.

    The satellite data don't start until about 1979, when solar influence was high, and they end at the present day when solar influence is low. So the solar influence during that time span tends to reduce the apparent trend, its removal restores the trend estimate. The surface temperature data were selected to start in 1975, so the influence of solar variation on trend is quite small.]

    • Horatio Algeranon

      Thanks!

      Makes perfect sense.

      Over the period between 1980 and present, the solar output was declining by about 0.1 W/m^2/decade, (shown here (Skeptical science)) which means climate forcing due to the sun was declining by about 0.7*(0.1)/4 or a decline of about 0.02 W/m^2/decade.

      using a climate sensitivity of 0.8 C/W/m^2 means the decline in solar output would have been expected to produce a downward trend in global temperature of (0.02)(0.8) or about 0.02C/decade (assuming all the temperature change due to the drop in solar output has already been realized, undoubtedly not the case, but this is only a ballpark estimate at any rate)

      So, it seems that the downward trend in solar output since about 1980 would be in the right ballpark to account for the difference between the adjusted and unadjusted satellite trends shown above.

      RSS 0.0183 – 0.0163 = .002C/yr = 0.02C/decade
      UAH 0.0159 – 0.0141 = .0018C/yr = 0.018C/decade

      And between 1975 – 1980, there was an increase in solar output, so the overall effect on the surface trends starting in 1975 would be expected to be less than it was on the satellite trends.

  24. I wonder what happens if we test the idea that UAH is simply wrong, having introduced a step change by incorrectly splicing the satellites. That single choice, after all, accounts for most of the difference between RSS and UAH.

    Can someone remind me how UAH justified that decision?

  25. “peak-to-peak”
    Peak-to-valley?

    [Response: Indeed.]

  26. Does not include ice melt which is global warming without temperature change.

    Conventional wisdom is that such ice melt is small relative to the global heat budget. However, I think we have lost more “anchor ice”, (frozen sea water that sinks) than is generally recognized, because we could not have had the observed warming of the Southern Ocean without such ice loss.

    Until all the ice sheets are melted, temperature alone will not indicated the full extent of global warming.

    • Agres, do the math. Two trillion tons of ice melted in 5 years according to GRACE (and it might be lower). It’s a few percent at most of the added heat from the greenhouse effect.

  27. Wouter Lefebvre

    Tamino, would you mind if I would translate your text into Dutch, for use in a magazine for weather maniacs? Of course with all due references to your site.

    [Response: Sure, go ahead.]

  28. Tamino, just as you look at a bunch of different temperature indices, it might be useful to try the three main ENSO indices (MEI, NINO3.4, SOI).

    Having seen other comparisons of the three, I doubt the results would differ much. But it would make your findings look even more robust … and head off any attempts to explain this away as cherry-picking.

    (I’m not aware of alternative data sets on volcanic forcings, and don’t know much about the sunspots/TSI side of things. If there are alternative, widely-used data sets there, it might be worth throwing them into the mix, too … basically, just trying to help make this as ironclad as possible).

    [Response: I've done this in the past, trying MEI, NINO3.4, and SOI, and MEI gave the best fit, although the difference was very small.

    Since these are only approximations anyway, different sets of volcanic/solar influence should likewise give similar results. Basically, "all roads lead to Rome" (as long as you head in the right direction).]

  29. I wrote: Tamino, just as you look at a bunch of different temperature indices, it might be useful to try the three main ENSO indices (MEI, NINO3.4, SOI).

    Or maybe that should be four (MEI, SOI, NINO3.4, ONI)?

    http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml

  30. [Response: I’ve done this in the past, trying MEI, NINO3.4, and SOI, and MEI gave the best fit, although the difference was very small.

    Thanks. I’m completely unsurprised that the difference would be small.

  31. Pingback: Quora

  32. I’ve been meaning to point out that balloon records like ratpac also have
    an a larger response to enso,maybe there is a physical reason for there enhanced
    response?
    this is a quick correlation table from ratpac A tropics(30N-30S) and annual MEI for el nino

    0.31448920319984 surf
    0.24731338908107 850(MB)
    0.38931843488637 700(MB)
    0.44928487388779 500(MB)
    0.41141456921934 400(MB)
    0.47240113879487 300(MB)
    0.53665627882488 250(MB)
    0.59131169751323 200(MB)
    0.5287215063199 150(MB)
    0.17745269879012 100(MB)
    -0.08580502499885 70(MB)
    -0.06301633389738 50(MB)
    -0.05534997165204 30(MB)

    [1] for ratpac http://www.ncdc.noaa.gov/oa/climate/ratpac/
    PS: I am sure there are much more qualified people to check the validity of my point but I hope this helps

  33. How much of the difference between UAH and the other data sets goes away if the first few years are discarded. On wikipedia the claim is made that the discrepancies are largely attributable to this.

    http://en.wikipedia.org/wiki/File:Satellite_Temperatures.png

  34. Nice job Tamino. I’m loathe to say this, but did you consider including the PDO? It might be worth doing so, just to demonstrate to Spencer that it is not the panacea of global SAT increase.

    How much of the variance in the SAT record does your MEI, volcanic forcing, sunspot numbers model explain?

  35. Also thanks for taking the time to do this. Great presentation and writeup of the data for this layperson.

  36. Nice work, Tamino. I think it is in good agreement with Lean and Rind (2008 and 2009), although using slightly different data sources.

  37. I just regressed the difference between annual GISS and UAH temperature anomalies on sunspot number for 1979-2009 (N = 31). Only 13% of variance was accounted for, but it was significant at p < 0.05.

    Year GISS UAH Delta Spots
    1979 0.08 -0.07 0.15 155.4
    1980 0.18 0.09 0.09 154.6
    1981 0.26 0.06 0.21 140.4
    1982 0.04 -0.15 0.19 115.9
    1983 0.26 0.04 0.22 66.6
    1984 0.09 -0.26 0.35 45.9
    1985 0.05 -0.21 0.26 17.9
    1986 0.12 -0.15 0.27 13.4
    1987 0.26 0.11 0.15 29.4
    1988 0.31 0.11 0.20 100.2
    1989 0.19 -0.11 0.30 157.6
    1990 0.37 0.08 0.29 142.6
    1991 0.35 0.12 0.23 145.7
    1992 0.12 -0.19 0.31 94.3
    1993 0.13 -0.15 0.28 54.6
    1994 0.23 -0.01 0.24 29.9
    1995 0.37 0.11 0.26 17.5
    1996 0.29 0.02 0.27 8.6
    1997 0.39 0.05 0.34 21.5
    1998 0.56 0.52 0.04 64.3
    1999 0.32 0.04 0.28 93.3
    2000 0.33 0.04 0.29 119.6
    2001 0.48 0.20 0.28 111.0
    2002 0.56 0.32 0.25 104.0
    2003 0.55 0.28 0.27 63.7
    2004 0.48 0.20 0.28 40.4
    2005 0.62 0.35 0.27 29.8
    2006 0.54 0.27 0.27 15.2
    2007 0.57 0.26 0.31 7.5
    2008 0.43 0.05 0.38 2.9
    2009 0.57 0.28 0.29 3.1

    R^2 0.1294
    R^2' 0.09936
    SEE 0.06753 N = 31
    F = 4.310 p < 0.04687

    Delta^ = 0.2854 – 0.0004813 Spots
    t = 14.10 (p < 1.632 x 10^-14), -2.080 (p < 0.04687)

  38. Thanks for the update Tamino, I’m very glad indeed you listen to and respond to your readers. Top blogging.

  39. 2 months for solar is surprising. But you tested for nearly the whole cycle lenght, so I guess that’s correct, then. When I considered removing the solar influence, my eyeballing of the graph suggested much more, and I started to do it with some 50 month lags… goes just to show the power of thorough analysis and good technique.

  40. To add, after some tries I gave up, as my skills in multiple regressions isn’t quite adequate.

  41. Awesome work. Tamino solo approaches the quality of the RC group effort.

    [Response: I'm flattered! But I don't agree. RC does way more than I do, and does it better.]

    • That’s silly, you do different things. But your post frequency and quality is a bright light in the world of science blogs, where you can expect quantity or quality, but rarely both.

  42. Given the cold start, how do people think 2011 will track?

    • Nobody wants to talk about this. On RC today somebody made an argument for why 2011 was going to be like 1999: brr cold. Gavin responded, “Wanna bet?”

      A simple take on things is that 2011 could be pretty cold.

      If 2011 comes in between 2009 and 2010, my lay-person mind says something has changed, but what? What’s behind Gavin’s confidence?

      • If 2011 comes in between 2009 and 2010, my lay-person mind says something has changed, but what?

        Well, maybe there will be no El Niño in 2011. Starting the year off with the tail-end of a significant La Niña, followed by no El Niño perhaps, would lead one to think that perhaps 2011 might be a bit cooler than the record-setting 2010 year, which, after all, was influenced for about six months by a mild El Niño.

        I think it’s reasonable to expect that El Niño years are more likely to break high temp records than years without them.

        What’s behind Gavin’s confidence?

        The person at RC was arguing for La Niña lasting all year, “degrading to neutral in 2012″. It appears to have peaked already, and models show it disappearing soon, though affects will linger for awhile afterwards. My guess – and it’s only a guess- is that Gavin has more confidence in the official ENSO forecast than the poster’s insistence that it will last all year, leading to a 0.2C drop compared to 2010.

        Of course, when pressed, the poster refused to bet …

      • We’ll see. This La Nina did not seem to noticeably bite until December. Looks to me like 2010 ignored La Nina. Maybe 2011 will too. 2010 certainly was not like the fall of 2007 when RC overflowed with giddy anecdotal winter reports from the global coolers, and this La Nina seems stronger than that one.

        [Response: Keep in mind that there's a demonstrable lag between the el Nino/la Nina state and global temperature, so the impact of the strong la Nina during the latter half of 2010 will have most of its impact on 2011 temperatures.]

      • This La Nina did not seem to noticeably bite until December. Looks to me like 2010 ignored La Nina.

        Without that last-minute bite, 2010 was on track to be the unequivocally hottest year in the surface instrumental record.

        Tamino:

        Keep in mind that there’s a demonstrable lag between the el Nino/la Nina state and global temperature, so the impact of the strong la Nina during the latter half of 2010 will have most of its impact on 2011 temperatures

        Yes, in the first part of 2011 … but if the forecast model predictions are correct, La Niña won’t last long enough to negatively impact the *entire* year, as the poster over at RC was proclaiming (until Gavin offered to bet, at which point the poster became much less certain of his year-long La Niña prediction).

  43. your solar index / response is very similar to that derived using LDA by Tung and colleagues. K.K. Tung, J. Zhou and C.D.Camp; 2008: “Constraining Model Transient Climate Response using Independent Observations of Solar-Cycle Forcing and Response” Geophys. Research Lett., 35, L17707,doi:10.1029/2008GL034240

  44. It’s a pity that the “Riddle me this” post has gone into the black hole, because it would be very good to see how 2010 fits in the expectations and claims of a slowdown in warming. Any chance of this, Tamino?

  45. One post I really miss is Tamino’s intro to his 2-box model–“Not Computer Models”. It really puts the lie to the meme that evidence for climate change derives from ultra-complicated GCMs. Of course you can also point out that Arrhenius derived his sensitivity with pen and paper–and that the computer models wind up lowering the sensitivity rather than raising it. But then, lying sacks of rat feces don’t care about truth.

  46. Jeff Baranchok

    “Are there any other regional patterns which can explain the rest of the short term variability?”
    The response of temperature to the El Nino cycle is very spikey. A linear regression of temperature vs ENSO does not map the entire extent of the matching temperature peaks, so I conclude that the temperature response to El Nino is non-linear. I have no idea what response function would be a better fit.

  47. Hi,

    I got for the lag behind solar 17 month as optimal for the hadcrut3gl, 2 are only a local optimum. I got also 2 month first as global optimum (assuming all other lags are 0) but after finding the other lags this cnanges to 17 month. My results are 17 month for solar, 8 for volcano, and 3 for mei. Can you replicate this?

    I find that a residual annual cycle is insignificant, but an annual modulation of the mei factor is. (this means (a+b*cos(..)+c*sin(..))*mei )
    The correlation between SSN and TSI is not perfect which could reduce the amplitude of solar influence.
    Also a different TSI will influence more then one month of temperature data
    If I go back until 1950 a quadratic fit is significant better then linear.
    There is an amonalous warmth in the hadcrut3gl data in 1998 even after removing mei.

    Does the AIC provide an improvement for all the data used in the regression? So which data set should be included or not acording to AIC?

    Solar eclipses may be recognized in the noise reduced data. During the eclipses the total solar radiation reaching earth is reduced by a significant amount for some hours. This may be detectable. Have you an idea how to test this?
    The timing of the eclipse in a month may of influence.

    • Uli, by AIC do you mean Akaike Information Criterion? If so, it won’t tell you which data to include, but rather will give you an idea of whether the added complexity you are adding is really improving the model. It might be interesting to use the model to forecast what temperature will do if the current La Nina persists.

      • Ray,

        yes the Akaike Information Criterion, I think I can use it to compare the improvement including futher data, deside when I have to stop to include further date to aviod overfitting and also which data should be included first especially in the case of different degrees of freedom.

        I have tested other fits and the 17 month lag is reduced to 2 month for the solar for the last fit.
        I find that including PDO and NAO is improves the fit a bit acording to the AIC. Also a biannual cycle improves the fit.

        But the most significant improvement I get due including an annual cycle for the volcaning forcing.
        Tamino, have you tried to modulate mei and volcaning forcing with an annual cycle?

      • Don’t forget that if your data are correlated, AIC won’t help you much.

    • David B. Benson

      Uli | January 22, 2011 at 7:49 am — Various papers have suggested 12 +- 12 months, so 17 months is in agreement with that work. Try Tang & Cabin (2008) for (at least) the references.

  48. “Are there any other regional patterns which can explain the rest of the short term variability?”
    As it is quite established that most of the enhanced greenhouse warming goes in to oceans these would be changes in other ocean currents than the Pacific currents involved in ENSO. One such could be variations in Agulhas current, there are some, another might be the currents going into or out of the Arctic. But there isn’t much good and reliable data for these from the early 20th century, and that makes applying corrections for these near impossible, I guess. Statistical significance would be very hard to find out, since all these should be accounted for.

  49. On Agulhas variations, there is the quite recent doctoral thesis, reported here: http://www.eurekalert.org/pub_releases/2009-03/uadb-tac031009.php

  50. Could I suggest creating a permanent link, labelled ‘Open Mind Archive’ to

    http://www.skepticalscience.com/Open_Mind_Archive_Index.html

    on Open Mind?

    [Response: I've added it to the blogroll under "Global Warming"]

  51. Tamino,I have two questions:

    How is the response of global temperature is in comparison to volcanic forcing (i.e. the climate sensitivity) for each dataset?

    How are the climate sensitivities obtained from each dataset for solar and volcanic forcing in comparison to the IPCC estimates (roughly 3ºC per doubling of CO2 or 0.8ºC/(W/m^2)) ?

    [Response: The last three graphs (in the UPDATE) show the response (not the forcing) for GISS and RSS to MEI, volcanic forcing, and sunspot counts. The surface data sets all show similar response (similar to GISS) and both satellite data sets (RSS and UAH) show similar response. As I mentioned in the update, the surface response to solar variation is around 0.4 deg.C/(W/m^2), the lower-troposphere response is about 0.8 deg.C/(W/m^2). However, these are *prompt* response rates, and don't indicate equilibrium response.

    For volcanic forcing, I'll have to check the units used in the Ammann et al. volcanic forcing data, as well as the normalization I applied when computing the area-weighted global averages.]

  52. Fine analysis. You corrected for ENSO but not for the AMO. The AMO has considerable impact on NH temperatures and correlates strongly with global temperatures. Could you redo the analysis but now including the AMO?

    • What would be the point of trying to remove something that “correlates strongly with global temperatures”? That’s the braindead mistake Bob Tisdale keeps making.

      You want to exclude the noise, not remove the signal.

      That said, I’m looking at an AMO graph. Where’s the correlation?

      [Response: The AMO is a north Atlantic ocean *temperature* index. So, it'll include the global warming signal *because of global warming*. Tisdale wants to subtract that global warming signal from the global-temperature global warming signal, so he can claim no global warming -- as though AMO were the cause of global temperature increase.

      That's like monitoring your child's height, and the length of his legs -- then claiming that because all the height increase is proportional to the lengthening of his legs, your child actually isn't growing (in spite of going from 2 feet tall to 6 feet tall).]

      • “The AMO is a north Atlantic ocean *temperature* index. So, it’ll include the global warming signal *because of global warming*.”

        Isn’t the AMO just a climate OSCILLATION that alternates warm and cool phases, just like the PDO and ENSO?

        After all, according to this graph:

        http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Amo_timeseries_1856-present.svg/1000px-Amo_timeseries_1856-present.svg.png

        The AMO entered the “warm” phase in the mid-1990s, while modern global warming began in the mid-1970s.

        If the current “warm” phase of the AMO was just the warming of the Atlantic caused by global warming, wouldn’t the AMO have switched to the warm phase in the mid-1970s?

        [Response: From wikipedia:

        The AMO signal is usually defined from the patterns of SST variability in the North Atlantic once any linear trend has been removed. This detrending is intended to remove the influence of greenhouse gas-induced global warming from the analysis. However, if the global warming signal is significantly non-linear in time (i.e. not just a smooth increase), variations in the forced signal will leak into the AMO definition. Consequently, correlations with the AMO index may alias effects of global warming.

        And that's what Tisdale (and others) hope to exploit: they use an alias of the global warming signal, in an attempt to claim that the effect of global warming is its cause.

        It might be interesting to correlate AMO to short-term global temperature fluctuations, if AMO is detrended nonlinearly, or if only the modern era (1975 to present) is detrended separately. But then: the denialists' claim disappears.]

      • Hey, I have a better idea!

        If we want to exclude ocean temperatures from our temperature graph, why don’t we use a land-only analysis?

        *Falls off chair laughing*

        Yes, it’s not funny.

      • Slight warning here: “warm” and “cool” are misleading terms in these oscillations. This site shows a good picture of the “warm” and “cool” phase of the PDO:
        http://jisao.washington.edu/pdo/
        Note the distribution of temperature anomalies in the Pacific.

  53. The AMO rises from 1975 onward, the same year where the above temperature plots start. The AMO cycle is about 60 years and is already detrended. You cannot detrend just the rising part of the cycle. Therefore it would be interesting to see what remains when the AMO is included in the multiple correlation analysis.

    [Response: Don't take this personally, but: that's total bullshit.

    The increase in AMO from 1975 onward is because the detrending (an attempt to remove the global warming signal) is linear, but the global warming signal is nonlinear. Therefore the AMO increase since 1975 is because of global warming. Using it, without detrending the 1975-present segment separately, is exactly the problem previously described: using the effect of global warming as the cause of global warming.

    Your statement that "The AMO cycle is about 60 years" is wrong. The only reason you think so, is that the residue of the global warming signal in the AMO data gives the visual impression of a roughly 60-year cycle -- a mistaken idea for which there's no evidence other than wishful thinking on the part of denialists.

    It really comes down to another lame attempt to claim that some "natural cycle" is responsible for global warming. The cycle doesn't exist, the one you think you see is the residue of global warming in N.Atlantic temperature data. If you want to remove the impact of N.Atlantic fluctuations on global temperature, detrending the post-1975 AMO is the only way to do it right.]

  54. Tamino, are you saying that Atlantic Multidecadal Oscillation (AMO) do not exist?

    That is, that the AMO is just the manifestation of climate change (any climate change, not necessarily antropogenic) in Atlantic, not an intrinsic oscillation like ENSO and PDO?

    [Response: It exists, but it's not what you think it is. It's not a periodic phenomenon, and the sustained rises and falls are a result of global warming, not a cause of it.]

  55. Tamino,

    I was just reading Trenberth’s paper where he discusses this subject and I understand that making the assumption that the warmth in SST’s has been linear is wrong thereby probably causing issues with the derivation of the AMO graph. However the question is what is the best way to separate the actual AMO signal? For example using Trenberth’s methodology they indicate that the AMO was negative during the 1870s whereas the old AMO index indicates that it was positive.

    I have done work on correlating the AMO to temperatures in a region across the North Atlantic Seaboard and the correlation is very strong on a yearly level but yet you’re indicating here that essentially the AMO index I am using is incorrect. For me I see the 1880s in my region as being cold but not as cold as it probably should be for the extreme volcanism experienced then,yet I also see a predominantly positive AMO which to me was explaining why the cooling was more muted. If Trenberth’s methodology is correct suddenly my correlations fall apart. But having seen the Desole paper and some of the papers which include Latif and Chylek’s work on the subject, I find the whole idea of it being a statistical artefact of the recent warming a little hard on the head.

    We also have tree ring data going back 1200 years (http://meetingorganizer.copernicus.org/EGU2010/EGU2010-13508.pdf) which is also based on the premise that our AMO data right now is relatively accurate. For me it is not that I don’t trust your judgement because I do very much, but that I feel like I need a little bit more convincing before I write-off the current AMO paradigm. Certainly I am open to the idea but as you could imagine for someone who is using this data for day to day work, I find it difficult to ingest and may need some more reflection on the idea.

    I know you’re likely quite busy, but perhaps you could at some point do a blog post addressing the whole AMO issue because I think there is still quite a bit of confusion, especially with papers like Desole’s and Chylek’s (2009) having come out.

    [Response: It sounds like an interesting topic, I'll put it on the "to do" list.]

  56. Heard an interesting talk here at AMS by Dr. Antonello Pasini during the “Computational Intelligence Techniques for Data Analysis and Knowledge Discovery” session on climate change attribution. I know almost nothing of neural nets and CI stuff, but he basically showed that training a NN to replicate the observed temps absolutely requires a significant anthropogenic component – inherent variability like PDO/ENSO/AMO and even GCRs don’t do it. In short, from a completely different view, which has nothing to do with GCMs (which also require anthropogenic forcings to replicate the observed record), one cannot get the observations without us and our emissions. Just another strong piece of evidence that claims of “it’s all the sun” or “it’s just natural variability” are *wrong*.

  57. Tamino, you don’t appear to have convinced John McClean, you know, the John McLean that was decimated here

    As they say, you can show an ass water but you can’t make it drink.

    [Response: McLean isn't convinced? I'm shocked!

    He says stuff like this:

    No mention about whether a time-lagged ENSO signal was involved despite at least 5 papers (mine included) showing that there is a delay

    But the post itself says

    For each of these exogenous variables, we’ll try a range of lags (from 0 to 24 months for el Nino and volcanic, from 0 to 120 months for sunspot numbers) and use the lags which give the best fit.

    In the UPDATE to the post I note that a reader actually asks about the lags, so the UPDATE says

    Best-fit lags are different for different data sets, but the lag for el Nino is 3 or 4 months surface, 5 months lower-troposphere. For solar, 2 months except GISS 3 months. For volcanic, 8 or 9 months surface, 3 or 5 months lower-troposphere.

    I question McLean's reading comprehension. In fact, I question his comprehension, period.]

  58. Oops, looks like I linked to John McLean’s comment history (must check it out).

    His thoughts on your analysis is here

  59. Tamino,
    Could you please publish the adjusted data from this post for everyone to download?

    [Response: I'm preparing this for publication in the peer-reviewed literature, and of course I'll provide the data (and programs) as supplemental material. Also I may change one of the input data sources, from the Ammann et al. volcanic data to Sato et al. optical depth data -- it doesn't change the result in any substantive way, but it does use the same data used by other investigators doing similar research (in particular Lean & Rind 2009, Geophysical Research Letters, 36, L15708, doi:10.1029/2009GL038932).

    I want to avoid conflict publishing the data on a blog and in a journal. But I'd like to also post it here -- so I'll dash off an inquiry to one of the journal editors to make sure that's not a problem. Stay tuned.]

  60. Tamino,

    How much does a starting date of, say, 1940 rather than 1975 effect both the graphs and the details of the conclusion?

    [Response: I don't know. The global warming trend isn't linear over that time span, so you'd have to use a more complicated time series model, or replace the simple time trend with, say, an anthropogenic forcing estimate.]

  61. Horatio Algeranon

    The comparison on the graph between actual data for GISS and the modeled data is indeed impressive, but, in general, the “swings” in the model data seem to be smaller than those in the actual data.

    As I believe someone else pointed out, the red line almost looks like what one would get from a multi-year average.

    Appearances can be deceiving, but it looks like the impact of MEI and possibly volcanic eruptions on global temperature is being underestimated by a bit.

    Any ideas why this might be?

  62. Tamino,
    someone suggested you should make the adjustments for each of the hemispheres first, and then combine the results. Will you do that?

    [Response: It might be an interesting experiment. As for the claim that it "should" be done that way ... I'm skeptical.]

  63. Sigh,

    Have you seen this?

    http://wattsupwiththat.com/2011/02/02/a-challenge-from-dr-roy-spencer/#more-33053

    How many papers can we find ? ;)

  64. Tamino,
    you conclude that the earth is slowly warming. Others conclude that there has been no global warming during the last decade. Interesting questions are:
    To which extent is a possible continued global warming caused by human activity? Is it measurable and distinguishable beside the natural fluctuations? And most important: Is it dangerous?

    [Response: Those who conclude that there has been no global warming during the last decade are mistaken.

    Yes, it's caused by human activity.

    Yes, it's dangerous.]

    • Olof Lind,
      It is interesting to me that you can even wonder whether the warming is continuing when last year was the warmest on record. It is also interesting that despite the mountain range of evidence for anthropogenic causation, you still don’t buy it. It kind of makes me wonder whether you’re keeping up.

  65. Timothy (likes zebras)

    “”there will always remain some unaccounted-for noise.”

    The sound and fury generated over the annual temperature figures has always frustrated given the vast error bars attached to the HadCRUT3 figures for something as simple as “sampling uncertainty”.

    Given that, I’m surprised at how little noise remains in your adjusted figure.

    [Response: The error bars are not vast.]

  66. Tamino: How do you calculate (in a sentence or two) the standard errors (1- or 2-sigma, etc) for the slopes? What do you assume for the uncertainties in the temperature anomaly data?

    [Response: A sentence or two really isn't enough. Maybe I'll post on the topic.]

  67. I’ve just found this blog through a link to this “How Fast is the Earth Warming?” post. I’m impressed, and will have to visit more often.
    A comment above requested a more complete presentation of data, model, and results. You said you were looking to publish, and would check with the journal editor to see if you could post the data.
    Has anything come of that request? If so, I’d like a link/citation/whatever. Before I went over to the dark side and started doing administrative stuff, I used to actually have some research skills. It would be a pleasure trying to recover those skills through exploring an analysis using techniques with which I once was familiar on a problem in which I am currently interested.

    [Response: The paper is in preparation, and I'd guess it'll be submitted by the end of July (just a guess). If it's feasible to do so, I'll post data at that time.]

  68. Tamino: It seems to me that you’ve produced quite an impressive analysis of past global temperature just using the anthropogenic warming trend, the ENSO data, a volcanic index and solar irradiance. Can you therefore use the same kind of technique to project future warming, given future scenarios in these variables? It would be good if there was some way of being able to say, in 5 years’ time, “this is what I predicted and when I plug in the actual data, the predicted temperature trend matches observations perfectly”… if that makes sense.

    [Response: It makes perfect sense. Unfortunately, we can't predict ENSO or major volcanic eruptions, and even the solar cycle is uncertain.]

  69. For those who want to know how to calculate slope uncertainties and statistical significance, see this:

    “Statistical significance of trends and trend differences in layer-average atmospheric temperature time series,” B. D. Santer et al, Journal of Geophysical Research (2000) v 105 n D6 pp 7337-7356. http://www.arl.noaa.gov/documents/JournalPDFs/SanterEtal.JGR2000.pdf

    You can accomplish it in Excel with the LINEST function.

  70. Tamino,
    With another 6 months of data in the can, any chance you will update this graph? That is, if you have nothing else to do …

    Thanks!

  71. I was thinking about this today, and I think I see a problem.

    The calculation here is purely statistical – it has no physics in it. But you’ve done a more physical calculation already – the two box model calculation. It should be possible to use one to check the other.

    So I tried exactly that. I’ve got my own version of your two-box model calculation, using a different way of constructing the response function. So I drove that model using just the solar forcing, to see how big the resulting temperature oscillations were. And they come out at under 0.02degC peak-to-peak. Obviously you’ll want to check that in your version.

    By contrast, the peak-to-peak amplitude of the solar term in your multivariate analysis looks to be at least 0.06degC. I suspect that the solar term is being inflated in the multivariate analysis owing by a rough synchronisation with the lagged effects of El Chicon and Pinatubo in the 80’s and 90’s, and increases in anthropogenic aerosols in the 00’s. But you’re in a better position to test that than I am.

  72. A very convincing post showing what looks like a clear underlying linear trend of about +1.7c to +1.8c per century. A couple of questions from somebody of a questioning frame of mind:

    The underlying trend seems rather lower than IPCC central projection of 3c per doubling of CO2 and it does not seem to be accellerating. What is more, this is over a period of historically rapid warming compared to previous periods (for instance 1945 – 1975). Do we have the data to do this analysis over a longer period looking backwards? Should we really expect this linear trend to carrry on indefinately? I know that you would not do this, but others out there might. Extrapolating a linear trend into the future is generally considered bad practice in most fields (I consider both sides of this argument grievously at fault in this).

    A denier looking at this post might say that you are arguing that “the temperature would be rising if we remove from the calculation all those things that make it fall”. If I were a denier I would be saying “well duh!”.

    The point with regards to random volcanic activity is obvious, but the removal of the Nino/Nina oscillation needs more justification. Nino/Nina could be part of the expression of the underlying temperature trend rather than just random noise that needs filtering out. This “filtering” would be particularly difficult to justify if we move into a period where La Nina is more prominent than El Nino causing global temperatures to fall in a more consistent way, effectively resetting the “baseline”.

    Also the effect on the global air temperature of solar energy fluctuations is a very contentious issue at the moment, so making assumptions about its effect is open to question too.

    Not suggesting that this is not good work, just on close examination I think you would do better to present the graphs going back further in time and also with Nino/Nina signal left in for comparison purposes.

    [Response: I don't expect the linear trend to continue unchanged, nor do I trust extrapolation of purely statistical models. I expect the trend to accelerate over this century, for physical rather than statistical reasons.

    If you run the numbers (and I have) you find that the exogenous factors make only a tiny contribution to the trend, and they end up mostly cancelling each other as well because the (very slight) negative trend contributions of el Nino and solar variations are offset by the (slight) positive trend contribution of volcanism. More important, factors like el Nino *cannot* contribute to the trend in a *sustained* way. The climate forcing due to el Nino/la Nina is limited to a very small range, so it's just not possible for its forcing to show any sustained trend. Even a *permanent* la Nina condition would "set the dial to -2 and leave it there" -- creating a sustained decrease but not a sustained *trend*. It's wise to adopt a more "questioning frame of mind" regarding arguments such as that one -- they simply don't make sense. Since the whole point is to isolate the changes which are *not* due to known non-anthropogenic factors, your suggestion to leave in one of the known non-anthropogenic factors seems foolish.

    The effect of solar variations may be contentious, but nobody in his right mind has argued that the sun has no effect! This is about as basic as climate physics gets. And this analysis makes NO assumptions about the mechanism, its magnitude, or even the *sign* of the solar effect. So to be frank, your comment on "making assumptions about its effect is open to question too" raises doubts about your comprehension, your objectivity, or both.

    A similar analysis has been done covering a much longer time span -- since 1889 -- by Lean & Rind (2008), Geophys. Res. Lett., 35, L18701, doi:10.1029/2008GL034864. That used only 1 temperature data set but this analysis compares 5, 2 of which are only available for the modern era.]

  73. “Even a *permanent* la Nina condition would “set the dial to -2 and leave it there” — creating a sustained decrease but not a sustained *trend*.”

    First time I’ve seen that articulated, I think. An excellent point to keep in mind.

    • Was trying to picture a ”permanent La Nina” condition”. Strikes me as a state that ”permanently” would suck in heat to increase the OHC. Pros and cons, short and long term? Someone looking for a BAU excuse, for the time being.

  74. Good reply. Thanks for going into detail, very helpful and typically robust response!

    Was just playing devil’s advocate… anticipating what a denier might counter with so that I can make the right sorts of comments elsewhere. The point about a “permanent La Nina” is very well made, I will make sure I remember that one.

    The one final point they would come up with, and do frequently (particularly Spencer), is that we may be wrong to make the assumption that the residual trend (after removal of exogenous factors) *has* to be caused by C02.

    They state that there could be an as yet unknown and unmeasured natural variation in the climate system that may lead to periods of warming or cooling over sustained periods of many decades with or without rising CO2 levels. Is there any straightforward counter-argument to that (other than the obvious one that CO2 is sufficient to account for the trend)?

    Another point: I have seen a rather startling graph on the climate4you web site that shows the 50 year moving average of the trend. The rate of change is clearly rising over time but has very clear and linear movements up and down. What could be causing that? Particularly the rise in the trend that took place 1915-1950 during a period when CO2 rise had not really got off the ground. The 50 year MA would clearly take care of any small cyclic exogenous factors such as Nino, and volcanoes would be a very minor bump, so there must be some other factor at work.
    http://img696.imageshack.us/img696/1674/cyclictrend.jpg

  75. TLM,
    One must be careful when choosing a period for a moving average. First, since they have data for 2011, this must be a trailing average, and 50 years means they are sampling back to 1961–when sulfate aerosols from dirty fossil fuels were depressing warming. Also, what matters for climate with volcanism is not the impulse of the individual evvents, but the average level. Since eruptions are Poisson processes, they are subject to significant fluctuations–as happened early in the last century, and which exaggerates the warming rate through the 30s.

    Finally, never, ever attribute a periodicity to a series where you have less than several cycles evident. My favorite example again,

    Consider the following series

    1,2
    2,7
    3,1
    4,8
    5,2
    6,8
    7,1
    8,8
    9,2
    10,8
    Plot the ordered pairs. Is the series periodic. If you think yes, predict the next number in the series. The correct answer if 4, because the y values of each pair are the digits of the base of Napierian logarithms, and the x values are the ordinal position of the y value left to right.

  76. The one final point they would come up with, and do frequently (particularly Spencer), is that we may be wrong to make the assumption that the residual trend (after removal of exogenous factors) *has* to be caused by C02.

    They state that there could be an as yet unknown and unmeasured natural variation in the climate system that may lead to periods of warming or cooling over sustained periods of many decades with or without rising CO2 levels. Is there any straightforward counter-argument to that (other than the obvious one that CO2 is sufficient to account for the trend)?

    Sure. This is the ‘chocolate cake orbiting Jupiter’ principle–it could be there because we can’t prove it isn’t. But Occam’s razor instructs us not to multiply putative causes unnecessarily. Failing to heed that is especially egregious if we propose causes for which there is no evidence and no explanatory need–not even a speculative description! (Well, other than Tamino’s Leprechaun theory, of course.)

  77. This may be a dumb question but when you say you are subtracting after regression what exactly are you subtracting so that you can know the impact for each variable?

    This post here got me thinking about what would be an interesting thought experiment and potentially if it warranted more, some research. Considering we know (and you have demonstrated) that the impacts of Volcanic Eruptions, El Nino and SSNs affect the TLT record why not use them with the SAT to reconstruct the TLT record since the SAT began. I left out using the SSN record because it did not significantly improve the result and I chose to use NOAA because I don’t trust hadley and it regressed better than GISS. Nino 3.4 was used because it was available but in particular I used the winter months (this is done on the annual scale) because that more or less will deal with the lag issue (it seems to have dealt with it). As you can imagine the adjusted R2 is pretty high (about 0.96) so it makes me wonder whether this sort of thing could be a realistic method. I haven’t cross-validated it yet but I will.

    Predicted versus actual TLT
    http://img37.imageshack.us/img37/5219/predictedtltactual.png

    Hindcast Model 1880-2010
    http://img200.imageshack.us/img200/9484/predictedtlthindcastmod.png

    Predicted versus NOAA
    http://img838.imageshack.us/img838/9484/predictedtlthindcastmod.png

  78. Ray Ladbury, thanks for the explanation.
    Did a bit of digging and it looks like the graph is based on linear regression applied to the prior 600 monthly data points (50 years).

    Yes, two dips and one peak is not really enough to establish a “cycle”. There has been a recent dip in the 30 year linear regression line. We will have to see if this develops into a similar downslope to the one seen in the mid 20th Century.

    What surprised me was the ruler straight nature of the up and down slopes, but that may just be an artefact of the kind of analysis, I do not know enough about linear regression.

    I have to say I have always found the aerosols argument for the mid-20th century cooling difficult to swallow as an explanation for *global* cooling (as opposed to regional). The aerosols were mainly from north-west Europe and USA due to coal burning for domestic heating and power generation. Unaffected areas of the globe included almost all of the southern hemisphere and most of the warmer northern hemisphere south of around 45N and the unpopulated areas north of 60N. Has anybody done peer-reviewed research that shows how much of the globe was significantly affected?

    I was amused by the “chocolate cake round Jupiter” example, but absurd examples are rarely illuminating. I suppose a better example might be the fact that the presence of Pluto was long predicted through analysis of pertubations in the orbits of other planets in the solar system. If there really is a (yet to be proved) 60-65 year cycle in the rate of change of global temperatures maybe that is the equivalent of the planetary pertubations pointing to something there that we have yet to discover.

    I hope the above is not considered too provocative in this otherwise rather “convinced” forum. It is meant in a spirit of genuine enquiry. We never learn if we are not prepared to ask questions. I tend to be equally challenging the other direction when posting in WUWT!

  79. “I was amused by the “chocolate cake round Jupiter” example, but. . . I suppose a better example might be the fact that the presence of Pluto was long predicted through analysis of pertubations in the orbits of other planets in the solar system. If there really is a (yet to be proved) 60-65 year cycle. . .”

    If–aye, there’s the rub. Evidence of such a cycle might turn the cake a little more vanilla, and would certainly bring it down to Earth.

    P.S. Glad to have amused–the image comes from Kurt Vonnegut originally (I think).

  80. TLM,
    First, you do realize that you are arguing over physics that has been accepted and uncontroversial for over a century, don’t you?

    And you do realize that it is pointless to look for a “cycle” unless you have several periods of data, right?

    And you do realize that there is no strong evidence of such a cycle in paleoclimate data, right? And that even if such a cycle were found, it would not overturn the known physics of CO2 as a greenhouse gas, right?

    Finally, you do understand that the evidence for climate change is not restricted to the warming of the troposphere, right? There is also the cooling of the stratosphere, polar amplification, the diurnal and seasonal patterns of warming…

    I am all for the spirit of genuing inquiry. However, I’ve found that the best way to satisfy that spirit when it comes to established science is in a textbook rather than by trying to redo science that was done long ago.

  81. Ray, you clearly misunderstand my position in this discussion.

    And you do realize that it is pointless to look for a “cycle” unless you have several periods of data, right?
    Of course, as I state clearly in my last post.

    And you do realize that there is no strong evidence of such a cycle in paleoclimate data, right?
    There is no way that paleoclimate data is sensitive enough to reveal a -0.004 to +0.015c a year (i.e. tiny) cyclic variation in the rate of warming in global average air temperature. At best it can give you a rough approximation of absolute temperature, give or take a few degrees, in a particular region. The only way that such a minor cycle could become apparent is through further decades of direct measurement of air temperatures.

    And that even if such a cycle were found, it would not overturn the known physics of CO2 as a greenhouse gas, right?
    I have never doubted “the physics of CO2 as a greenhouse gas” that is causing a rise in global average air temperatures.

    Finally, you do understand that the evidence for climate change is not restricted to the warming of the troposphere, right? There is also the cooling of the stratosphere, polar amplification, the diurnal and seasonal patterns of warming…
    Absolutely. I use almost that exact phraseology when arguing with those who would deny the reality of global warming.

    I think it would be illuminating to look at what this graph would tell us even if there does turn out to be a 65 year cycle in the rate of warming (which I again strongly assert is not proved, I am just putting up a “what if”).

    An upward slope of the graph is not a rise in temperature, it is a rise in the *rate of rise*. Similarly a downslope is not a fall in temperatures, it is a fall in the *rate of rise* in temperatures.

    At best, if there is a cyle (big if!), we might see a fall in the rate of growth over the next 30 years or so and that we may not see a linear extrapolation of Tamino’s carefully ascertained 0.018c a year rise in temperatures indefinitely.

    However, even If we assume that we have reached a peak in the rate of growth, then we can join the tops of the two possible peaks and the bottoms of the two troughs and in both cases we get an up-slope, which is telling us that we are seeing an *accelleration* in the rate of growth in air temperatures of about 0.005c a year every 60 years.

    So even if the long term averaged rate of rise in temperatures is *currently* around the 0.006c a year implied by the graph this is accelerating to 0.011c a year by 2070 and 0.016 by 2130. That is, of course, if we don’t see an acceleration in the rate of acceleration!

    The alternative proposition, of course, is that the “cycle” is illusory and that Tamino’s chart continues to rise at the same rate towards a 1.8c rise in temperatures in the next 100 years.

    So, I hope you can see from the above that I am not in denial, but just keeping an “open mind”.

    • Uh, which graph is “this graph?” Most of the above are anomaly graphs, which show “temperature rise,” not “rate of rise.”

      Actually, I don’t see any in the post that don’t show temperature rise, but maybe you’re talking about some other graph? Anyway, I don’t follow.

    • TLM, actually, a cyclic variation–even a small one–ought to stand out in paleoclimate data precisely because we could look at several cycles. I have to say that I am extremely suspicious of “cycles” when they are based on limited data and do not have a known physical cause. Our brains love cycles so much that we see them whether they are there or not.

      The other thing you have to consider is that there is a tremendous amount of data showing CO2 sensitivity is about 3 degrees per doubling, and that is close to what we are seeing.

      Yes, it’s “interesting if true”, but a lot of things are. Meanwhile it doesn’t invalidate what we already know.

  82. TLM,

    Regarding the problem of determining the existence of the “65 year cycle” which I take to mean the AMO. Below is a link to a post from this site that critiques attempts to determine the cycle by curve fitting. The post was marked by an unfortunate circumstance because the author of the post under criticism the denialist Frank, elected to start his presentation by throwing some red meat to the rabble over at WTFUWT (the intended audience). So before even a serious review of his presentation could begin (see the comments) Frank starts out in this forum with his credibility completely destroyed. In spite of that the host of this site labored on and produced an excellent criticism of the problems associated with finding cycles by curve fitting:

    http://tamino.wordpress.com/2011/06/02/frankly-not/

    Check the links in that blog post. There point to some archived posts on spectral estimation that are are very worthwhile. Check the comments too there are some good points in there as well.

    Here are others.

    Here is an interesting paper that looks at the question of AMO as a statistical phantom:

    http://www.nonlin-processes-geophys.net/18/469/2011/npg-18-469-2011.pdf

    This is one that looks very interesting too but it gets a little deep. I haven’t looked at in a lot of detail myself but it is intriguing. Using empirical mode decomposition the authors estimate that up to 1/3 of late 20th century warming resulted from AMV (Atlantic Mutidecadal Variabilty ).

    http://www.springerlink.com/content/akh241460p342708/fulltext.pdf

    Both of these papers were sourced via Ari Jokimäki’s excellent site:

    http://agwobserver.wordpress.com/

    • Thanks for the links! I had heard of the AMO but not as an explanation of this variability over the last 60 or so years. Always good to have new sources of information and these were very useful.

      A lot ot the maths is way out of my league but I think I get the gist. The main one being that this isn’t a “cycle” but a more random variability with no set periodicity. That makes a lot of sense as it makes it more like the way ENSO seems to work.

      It does seem, however, that we have recently been in a “warm” phase and will almost certainly flip into a “cool” phase at some point. This will no doubt give the deniers something to hang their wilful misunderstandings upon and it is good to have this kind of information so we can let them know that although the rate of warming might slow in the short term, that it will inevitably flip back to a “warm” phase again. There is no “permanent AMO cold phase” just like there is no “permanent La Nina”.

      If I understand correctly, from these papers, it looks like around 1/3 of recent warming might be down to this Atlantic Multi-decacal Variability. Not much comfort in that, as it seems to be that the underlying rate of warming might be accelerating even as it varies.

      • TLM,
        There are many systems in nature that exhibit quasi-periodic behavior. For instance, if a system has energy E and is metastable in a state below energy E+dE, and it’s energy fluctuates with some probability distribution, it will often take a characteristic time before it fluctuates out of its metastable state. It is not periodic–in fact, it is stochastic, but the oscillations will tend to fluctuation around some given period.

  83. Very nice analysis. One thing that has long puzzled me is why the satellite and ground-based readings should agree so well. The satellite readings are all inferred air temperatures, while (I believe that) roughly 70% of the ground temperature time series is based on ocean water temperatures , not air temperatures. (At least, for the historical data in the Hadley SST series, they talk about the differences between buckets and engine cooling intakes, which I am pretty sure means they are measuring water temps.)

    Formally, and by eye, it’s clear the satellite data exhibit higher variance. I had casually noted that the higher variance typically took the form of higher highs and lower lows during warming or cooling events. Vague, that seemed reasonable given the large dependence of the ground-based readings on water temperatures. Yours is the first analysis I’ve run across showing that the systematically higher response of the satellite series to these exogenous or cyclical factors. I’m guessing that’s due to the dependence of the ground series on water temperatures. And, without even bothering to think about how El Nino should best be handled, given that the separate land and ocean temperature data are typically available, I’d be interested to see this re-run on that split. My hypothesis is that the higher response of the satellite series is limited to the ocean component.

    • Thanks, jyyh. It figures that in a global system of ocean currents, you can’t afford to focus too tightly a priori on any one sub-component, such as the North Atlantic currents. It’ll be interesting to see how these interacting sub-components ‘balance out’–and of course, given the importance of regional modeling to adaptation efforts, this is obviously of considerable practical importance.