Troy's Scratchpad

April 16, 2013

Sensitivity / CMIP5 comparison paper now in press at Climate Dynamics

Filed under: Uncategorized — troyca @ 8:24 pm

It is available online and titled “Observational Estimate of Climate Sensitivity from Changes in the Rate of Ocean Heat Uptake and Comparison to CMIP5 Models”.  Apparently Nic Lewis’s paper beat mine to online release by a day, and though my estimated confidence interval for equilibrium sensitivity is significantly wider, the median sensitivity in my paper also tends to be on the lower end relative to the IPCC AR4 likely value.  It is pay-walled, but please contact me if you need a copy and do not have University access.  Anyhow, a zip that includes all my code and data is available here.  From the abstract:

Climate sensitivity is estimated based on 0-2000m ocean heat content (OHC) and surface temperature observations from the second half of the 20th century and first decade of the 21st century, using a simple energy balance model and the change in the rate of ocean heat uptake to determine the radiative restoration strength over this time period.  The relationship between this 30-50 year radiative restoration strength and longer term effective sensitivity is investigated using an ensemble of 32 model configurations from the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting a strong correlation between the two.  The mean radiative restoration strength over this period for the CMIP5 members examined is 1.16 Wm-2K-1,  compared to 2.05 Wm-2K-1 from the observations.  This suggests that temperature in these CMIP5 models may be too sensitive to perturbations in radiative forcing, although this depends on the actual magnitude of the anthropogenic aerosol forcing in the modern period.  The potential change in the radiative restoration strength over longer timescales is also considered, resulting in a likely (67%) range of 1.5 K to 2.9 K for equilibrium climate sensitivity, and a 90% confidence interval of 1.2 K to 5.1 K.

To explain further on what I consider to be three of the more important conclusions of the paper:

First, there seems to be a relationship between the estimates of effective sensitivity from the last 30-50 years and the longer-term multi-century effective sensitivity (which is arguably more important than equilibrium sensitivity) as they are calculated in models.  To me, this gives hope that as the length of satellite record increases, we might start to narrow down a more accurate value for sensitivity that is relevant to the timescales of greatest interest.

Second, most of the CMIP5 models seem (albeit not without caveats) to show too high of sensitivity over this period.  From figure 3 of the paper:


This is showing the radiative restoration strength in the CMIP5 models examined (each X is a different run from that model), which is generally inversely related to sensitivity.  The solid gray line represents the likely value from observations, and the dashed lines represent +/- one standard deviation.  As can be seen, the vast majority of these runs fall below the observational likely value for radiative restoration strength, suggesting these CMIP5 models likely have too high a sensitivity relative to the observations.  Interestingly, inmcm4 and MRI-CGCM3 are both well above the line, and while they are among the CMIP5 models with the lowest sensitivity, they are not nearly as insensitive as the 50-yr radiative restoration strength would make them appear (which would be ~ 1.2 K for ECS if we performed a naïve calculation).  Obviously, the relationship between this radiative restoration strength and ECS can be complicated, as discussed previously at this blog and within the paper.

Finally, there is the estimate of ECS, for which I have tried to consider some effect of the potential change in Effective Sensitivity to ECS based on the CMIP3 relationships, although again I would argue that effective sensitivity is generally of more interest (but it is not the standard benchmark at this point).  Nonetheless, from figure 5 of the paper:


The gray indicates the pdf of “ECS” if we keep the radiative restoration strength fixed after the 50-year observational period, whereas the black line indicates the pdf for ECS if we take the uncertainty in the T_eff/T_eq into account based on this relationship in CMIP3 models.  The latter is reported in the upper right box and in the abstract.  The orange and purple lines represent the “likely” values for sensitivity when switching in the JAMSTEC or CSIRO OHC data rather using that from NOAA.

Clearly, the median estimate for ECS of 1.98K seems to match some other observationally-based estimates with a lower sensitivity, and the “likely” (67%) range of 1.5K to 2.9K is on the lower end as well.  Unfortunately, due to the large uncertainties in 0-2000m OHC data earlier in the record, this method continues to yield large uncertainties at the extremes, which due to the inverse relationship between sensitivity and the radiative restoration tends to increase the higher end of the range much more than the lower end.  Hence the 90% interval of 1.2K to 5.1K is not a particularly strong constraint.


  1. +1 Troy

    Comment by Steven Mosher — April 17, 2013 @ 9:20 am

  2. Nice job Troy! I look forward to reading Masters (2013) 🙂

    The range (1.5 K to 2.9 K for equilibrium climate sensitivity, and a 90% confidence interval of 1.2 K to 5.1 K) seems reasonably consistant with other papers using observational data (models and paleo stuff tends to give slightly higher ranges). The wider CIs also seem a bit more realistic than Nic’s estimates, which I think are a bit too narrowly constrained.

    It looks like 2013 might end up being the year of the citizen climate scientists, as we are on a bit of a roll so far.

    Comment by Zeke Hausfather — April 17, 2013 @ 10:03 am

  3. […] has a blog post [here].  This is my first visit to Troy’s blog, I’ve just added it to my blogroll, I […]

    Pingback by Meta-uncertainty in the determination of climate sensitivity | Climate Etc. — April 17, 2013 @ 12:51 pm

  4. Congrats Troy. Nicely done.

    Comment by Ron Broberg — April 17, 2013 @ 3:41 pm

  5. Thanks guys! It is definitely cool to see more bloggers / citizen scientists getting in on the publication action.

    Comment by troyca — April 17, 2013 @ 10:14 pm

  6. Thanks for this effort. I’m leading with this today on WUWT, feel free to come on over and join in discussion.

    Comment by Anthony Watts — April 17, 2013 @ 10:48 pm

  7. […] wants $39.95 for the privilege of reading it, so all I can do is to provide the abstract. From his blog however, Troy does show figure 5 of the […]

    Pingback by Another paper finds lower climate sensitivity | Watts Up With That? — April 18, 2013 @ 3:01 am

  8. Nic Lewis talked about “uniform priors” back in January on the RC blog.

    Does you study use these?

    Comment by DCA — April 19, 2013 @ 6:08 am

    • No, I believe he is referring to a uniform prior for the climate sensitivity. I do not use one…rather, the pdf is bootstrapped from Monte Carlo using informed priors for forcing and imbalance based on published uncertainties. The only uniform distribution I use is for the percentage of heat uptake by the ocean.

      Comment by troyca — April 19, 2013 @ 8:21 pm

  9. In Section2.R, there might be a bug in your code:
    imb<-1/runif(n=runs, 0.85, 0.95) * imbalance[i] * 10^22/ (365.25*24*60*60*510072000*(1000)^2)
    should perhaps be
    imb<-1/runif(n=runs, 0.85, 0.95) * imbalance * 10^22/ (365.25*24*60*60*510072000*(1000)^2)

    Comment by AED — May 5, 2013 @ 10:27 am

  10. One more: The line:
    OHC3<-window(ohc.ts, start=lastYr, end=lastYr)[1]+ rnorm(sd=window(, start=lastYr, end=lastYr)[1], n=runs)
    in doRadiativeResponseMonteCarlo seems to me should be:
    OHC3<-window(ohc.ts, start=startYear+10, end=startYear+10)[1]+ rnorm(sd=window(, start=startYear+10, end=startYear+10)[1], n=runs)
    or something like that. What do you think?

    Comment by AED — May 5, 2013 @ 3:12 pm

    • Hi AED,

      Thanks for giving this a close look! I think the first one you pointed out is indeed a bug, as by indexing into the array it is not including the uncertainty in Ncur for the most recent period from measurement noise, only from the percent of ocean heat uptake. Fortunately, this only affects the most recent Ncur (which is only 1 of several possible Ncur) and the measurement noise is small over that period, so it seems to only have a small effect (I’m getting a .06 K difference in the median).

      I don’t believe the second one is a bug though. I am actually setting lastYr to startYear2+10 a few lines above…the reason I use a different variable is because one of the OHC entries is missing the lastYr of data so I need to move it up one year to avoid indexing out of the array.

      Comment by troyca — May 6, 2013 @ 6:27 am

  11. where did you get the Levitus 2000-m data? there’s a text file in your zip achive, but I can’t find that on-line anywhere. if you downloaded it, can you let me know what the link is? if not, can you point me to the original data that you used to create the text file?

    Comment by AED — May 8, 2013 @ 8:02 pm

  12. Sorry to keep bothering you about this, but now I’m looking at the GISS data. The GISS temperature data I found are here: But this does not agree with the data in the file GISS_T.txt in your archive. Have you massaged the data?

    Comment by AED — May 9, 2013 @ 1:16 pm

    • The NOAA OHC website data and GISS temps are both updated (even past values) based on new data. This is one of the strong reasons to keep an archive of the actual data used in the paper. The NOAA OHC website says it was last modified 2/28/13…not sure if that is the data or just the website. Regardless, the data has almost certainly been updated since I submitted the paper in December. That being said, the NOAA OHC appears to have changed quite a bit, so I would be curious to run it with these updates to see what changes it might make. I highly doubt, however, the GISS changes would have much of an effect, since that is already averaged with 2 other temperature sets and is less volatile.

      Comment by troyca — May 9, 2013 @ 2:43 pm

      • Odd, it looks like I re-downloaded the NOAA data when I did the revision, which would have been more recent. It doesn’t seem like that data should’ve changed so much in that short period…I did a quick re-run with that current NOAA data up there and while the median and mode remain about the same, the upper bounds seems to decrease a decent amount:

        Comment by troyca — May 10, 2013 @ 8:47 am

  13. Your statement that it doesn’t make much difference is puzzling. With the new data, a lot more heat is being stored in the ocean. It seems that this would absolutely require less energy to be radiated back to space. That, in turn, would require a smaller lambda (larger climate sensitivity). Can you explain why your results don’t change?

    Comment by AED — May 13, 2013 @ 9:14 am

    • Well, for one, I’m not sure I agree with your claim that “with the new data, a lot more heat is being stored in the ocean.” If I calculate TOA imbalance using the “new data” (that currently up at the NOAA site, which is the black solid line) and my archived data (which is the dashed line), it seems this is not the case: . In fact, the “new data” actually appears to show a *lower* rate of ocean heat uptake. Second, my method calculates TOA imbalance using the *change* in the rate of ocean heat uptake over a variety of periods, so it is relatively insensitive to an offset in the rate of ocean heat uptake as long as that remains relatively constant throughout the record.

      Comment by troyca — May 13, 2013 @ 2:27 pm

  14. […] De studies die een lage klimaatgevoeligheid laten zien en waar veelvuldig naar verwezen wordt, zijn alle gebaseerd op meetdata en schattingen van de afgelopen anderhalve eeuw, het instrumentele tijdperk. Een bekende recente studie is Otto et al 2013, waar we hier eerder over bericht hebben. Zij kwamen op een Equilibrium Climate Sensitivity van 2.0 °C (95% range 1.2 – 3.9 °C), gebaseerd op het decennium 2000-2009 of 1.9 °C (95% range 0.9 – 5.0 °C) gebaseerd op de periode 1970-2009. Andere studies, die gebaseerd zijn op ongeveer dezelfde data, zijn die van Nic Lewis, 1.6 °C (90% range 1.0 – 3.0 °C) of Troy Masters, 1.98 °C (90% range 1.2 – 5.1 °C). […]

    Pingback by Eenzijdigheid en valse vrijbrief bij de ‘klimaatgevoeligheid-is-laag’ hype | Klimaatverandering — September 30, 2013 @ 8:22 am

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