Troy's Scratchpad

May 9, 2014

On forcing enhancement, efficacy, and Kummer and Dessler (2014)

Filed under: Uncategorized — troyca @ 10:11 pm

A paper by Kummer and Dessler (2014) [KD14] has recently been accepted by GRL, with the primary claim being that observational estimates of ECS over the 20th century can be reconciled with the higher ECS of CMIP5 models by accounting for the “forcing efficacy” mentioned in Shindell (2014):

Thus, an efficacy for aerosols and ozone of ≈1.33 would resolve the  fundamental disagreement between estimates of climate sensitivity based on the  20th-century observational record and those based on climate models, the paleoclimate record, and interannual variations.

However, I think there is some fundamental confusion with respect to how the forcing enhancement should be applied within KD14, which I will focus on specifically for this post (ignoring what I believe to be other issues in the actual energy balance calculations for the mean time).  While I have noted previously that the spatial warming pattern appears to indicate a value of “E” (the Shindell enhancement) near unity, I would submit that even if it was significantly greater than 1.0, it has been applied in a way within KD14 that likely substantially exaggerates its effect on 20th century ECS calculations.  Here are the issues that I see:

1. ECS calculations are unaffected by the effective heat capacity, whereas TCR calculations are not

First, let’s take a look at the Shindell (2014) definition for the forcing enhancement (which KD14 refers to as “forcing efficacy”), which is the ratio of the inhomogenous forcing TCR to that of the homogenous forcing TCR:

(Eq. 1)        

TCR is calculated by dividing the temperature change by the forcing, without consideration of the TOA energy imbalance at the time of the calculation (this is often normalized to transient change for a doubling of CO2 by multiplying by F_2xCO2 (~3.7 W/m^2), but I will leave it simply in the units of K/(W/m^2) for this post):

(Eq. 2)       

And if we consider the simple one box temperature response to an imposed forcing at time t, we have:

(Eq. 3)      

Where F is the imposed forcing change, lambda is the strength of radiative restoration (the increase in outgoing flux per unit of surface warming), and C is the effective heat capacity of the system.  As can be seen by working back from equation 3 to 1, TCR and hence E  will be affected by both the difference in C (the heat capacity) and lambda (radiative restoration) between the homogenous and inhomogeneous forcings.  On the other hand, the equilibrium response (t –> infinity) to a forcing does NOT depend on C, only lambda.

If we go back to the simple energy balance equation for the top of the atmosphere (TOA) , re-arranging eq. 1 in KD14 to solve for lambda (with N representing this net TOA imbalance), we have:

(Eq. 4)     

which can then be inverted and multiplied by F_2xCO2 to find the ECS in terms of a CO2 doubling.  What should be quite clear from this determination of ECS is that one can dampen the transient temperature response by increasing the value of C without it affecting the estimate of ECS.  After all, If the temperature response is heavily damped in the first 50 years for a forcing (due, for example, to the bulk of that forcing being concentrated in an area with deep oceans), then it is true that the value for T will be lower than it might be for a scenario with less ocean damping, but  the TOA imbalance (N) will be larger due to less radiative response (from lambda * T), thereby decreasing the quantity (F-N) by the same ratio , and yielding the same value for lambda.  On the other hand, it is clear why such ocean damping *would* affect the TCR, which does not take into account the TOA imbalance (N).

The problem should thus be obvious: the “enhancement” factor calculated by Shindell (2014) can be greatly affected by the difference in effective heat capacity of the hemispheres, but this in itself would not create any bias in the ECS calculations.  So KD14 should certainly not be using the forcing “enhancement” factor of Shindell as a proxy for the equilibrium forcing efficacy!  Note that much discussion regarding Shindell (2014) focused on how the greater land mass of the NH corresponds to a lower heat capacity, thus producing a greater transient response for an aerosol forcing located primarily in the NH.   But this intuition has nothing to do with a bias in the equilibrium response.

Rather, as I mentioned above, E is affected by both the effective heat capacity differential (C) and the increase in outgoing flux per unit increase in temperature (lambda), only the latter of which actually affects ECS.  So the more we find that E is a result of the differing heat capacity, the less room that leaves for lambda to have a substantial effect, and the less bias this would actually produce in the ECS estimates.  Furthermore, there seems to be less of the way in intuition of why a differing lambda would be responsible for a substantial portion of E, if this were the case.  Nevertheless, it IS possible that for a larger E, at least some portion of this would come from a differing radiative response strength from homogenous and inhomogenous forcings, but that leads to the second issue…

2. The Forcing Efficacy “correction” in the estimate is applied directly to the TOA imbalance resulting from the forcing, thereby overcompensating in transient estimates

Per KD14, we read that:

To test the impact of efficacy on the inferred λ and ECS in our calculations, we multiply the aerosol and ozone forcing time series by an efficacy factor in the calculation of the total forcing.

What Kummer and Dessler (2014) have done here is simply inflated the magnitude of the aerosol and ozone forcings beyond the best estimates, rather than actually accounting for the forcing “efficacy” that may result from differing lambdas.  In the event that the TOA imbalance has already reached equilibrium, there is no need for this distinction.  But in transient runs, using the KD14 method will bias the ECS high, because it is compensating for the differing TOA response in the numerator of Eq. 4 that has not yet fully manifested!

Consider an example, where lambda is 1.5 W/m^2/K for GHG (~2.5 K “true” ECS), but the “forcing efficacy” for aerosols is 1.5 and entirely comes from differing lambda, such that lambda for aerosols is 1.0 W/m^2/K.  Now suppose we perform our calculation early on in the transient run, such that only 50% of the equilibrium response to a given forcing of 2.0 W/m^2 GHG and –1.0 W/m^2 aerosols has been achieved.  This will yield T_GHG = 2.0 / 1.5 * 50% = 0.67 K, and T_aero = –1.0 / 1.0 * 50% = –0.5 K, for a net T of 0.17 K.  Using the KD14 method with Eq. 4, we would have an F = 2.0 W/m^2 – 1.5 * 1.0 W/m^2) = 0.5 W/m^2, an N of (2.0 W/m^2 – 1.0 W/m^2)  – [0.67 K * (1.5 W/m^2/K) + (-0.5 K) * (1.0 W/m^2/K) ]= .495 W/m^2, leading to a lambda of (0.5 – 0.495) / (0.17 K) = 0.03 W/m^2/K, corresponding to a sensitivity of > 100K!  This extreme example highlights the large bias that the KD14 method can produce when applied to transient runs.  Currently, if one takes the last decade net TOA imbalance to be ~ 0.6 W/m^2, and the forcing up to now to be ~ 2.0 W/m^2, this implies we are about 70% equilibrated…under these circumstances I would still expect a large bias from the KD14 application.

Anyhow, to illustrate the bias we would expect from the different methods of calculating ECS given an E of 1.5, I have written a script here.  Essentially, it treats the two hemispheres as separate one-box models, with the historic non-GHG anthropogenic forcings applied entirely to a more sensitive NH.  I have tried to match this to some degree so that the ending TOA imbalance is around 0.5 W/m^2 (and hence around 70% equilibrated), similar to that observed, but it is also possible that these models have oversimplified things.  Nevertheless, here are the results:

image

What this illustrates is much of the intuition we have gone over in these two sections.  From the blue line, we see that as we increase the attribution of the calculated E  to the heat capacity differential, there is very little bias introduced when calculating ECS using the “traditional” energy balance method (per #1 above, this is because there is less attributable to the difference in lambda) .  On the other hand,  since we introduce a case here where we are still far from equilibrium, the KD14 method creates an overestimate in all cases.

Summary

Overall, I am quite dubious about the KD14 results, for 3 reasons:

1) Based on the observed spatial warming, it seems unlikely that E is far from unity.

2) Even if E were greater than 1.0, only a fraction of that E applies to ECS estimates (the portion stemming from differential lambdas and NOT heat capacities), and

3) Even if the full E did apply, it appears KD14 has applied it incorrectly, introducing a large overestimate in the transient cases

The shame of it all is that this actually hints at an interesting underlying question, which is whether the spatial pattern of warming in the real world has created a radiative response substantially different from the response expected from a uniform GHG forcing.  It seems that if one were interested in what models say, however, it could be calculated much more directly – comparing the AMIP simulated radiative restoration strength to that of the historicalGHG from the same models would likely be the way to begin along this path.

35 Comments »

  1. Interesting. I’m going to have to think about what you’ve done a little more, but I had wondered something similar myself. My current view is that when one considers corrections due to Cowtan & Way and the possibility that there may be some effect from inhomogeneities (even if small) it does seem as though the energy budget estimates are becoming more similar to the other estimates. Maybe not completely consistent, but it seems as though they’re not as different as it may at first have seemed.

    Comment by And Then There's Physics — May 10, 2014 @ 12:06 am

    • Hi Anders. I am not sure if you saw my sensitivity tests for Otto et al. using different temperature and OHC datasets, but it might be of interest to you. By my calculation, using the Otto method would produce about an 8% larger ECS calculation if one used Cowtan & Way (or BEST), but iI don’t know if the effect would be as pronounced in KD14 because of their use of integrals starting in 1958. Regardless, as you can see in my link above, while certain choices may move the estimate higher, other choices would move the estimate lower. For instance, I believe KD14 uses the Balmaseda et al, OHC reanalysis dataset, which creates the largest estimate when applied over the 2000s but seems most volatile / sensitive to the decade applied, and is most at odds with satellite data. If one uses the other OHC datasets I’ve shown, or if one uses OHC from the post-ARGO deployment era, I believe the agreement is generally better between all datasets, but the agreement is generally on the lower sensitivity ~2 K. It may be easier to reconcile paleo and energy balance estimates by assuming a large difference between ECS and effective sensitivity, and I’ve been pondering this for a future post…

      Comment by troyca — May 10, 2014 @ 9:53 pm

      • Thanks, I hadn’t seen that. It’s an interesting analysis. I’ve only just started to consider a difference between effective sensitivity and ECS, so would be interested to know what you have to say about that.

        Comment by And Then There's Physics — May 13, 2014 @ 7:15 am

  2. Troy – I’m handicapped by having access only to the Shindell and KD14 abstracts. However, I have a question about your equation 4 above. Is it correct that the quantity N is typically computed from OHC uptake data and an adjustment that assumes a fixed relationship between total heat storage and OHC, the latter being about 90% of total? If so, might the true value of N (and hence lambda) be inaccurately estimated from OHC observational data when the ratio of OHC/total changes due to a temporary imbalance between land and ocean heat uptake? I realize this doesn’t address other points you made.

    Comment by Fred Moolten — May 10, 2014 @ 6:08 pm

    • Hi Fred,

      I would not say that N is typically computed using a fixed relationship between total heat storage and OHC, as some specifically try to account for calculated energy stored in the cryosphere, atmosphere, and land, but I believe KD14 simply add a static 0.06 W/m^2. That being said, I think that because the vast majority of heat is stored in the ocean, this really has little influence. Over the span of a decade, it is hard to imagine that we would leave the 85%-100% range, so we’re looking at a max uncertainty of probably ~ 0.1 W/m^2 in the calculation of a single decade, and (depending on specifics) we probably would have a max uncertainty in ECS of ~0.15 K attributed to this , so < 0.1 K difference in either direction. But for the specifics of something like KD14, they use an integral method that should theoretically be insensitive to temporary variations in the OHC / N relationship. In my paper I actually accounted for the uncertainty in this OHC / N relationship in my Monte Carlo simulations, but I cannot say it contributed much uncertainty (the uncertainty was dominated by the magnitude of the aerosol forcing and uncertainty in the OHC data itself in earlier decades).

      Comment by troyca — May 10, 2014 @ 10:13 pm

  3. Hello. I confess I have not completely internalized everything you’ve written, but let me make sure you understood the point that we are making. Our goal is to determine the climate system’s response JUST to greenhouse gases (that’s how ECS is defined). If you want to do that using the 20th century observational record, then you are stuck with data during a period of strong transient warming. In this time period, Shindell calculates an efficacy > 1. If the efficacy calculated by Shindell is correct, and you want to use the 20th century record to calculate ECS, then you must account for more joules of energy being trapped per W/m2 of aerosol/ozone forcing than in GHG forcing in your calculation. Neglecting this will indeed bias the ECS you calculate from the 20th century record low. We are NOT taking Shindell’s results and assuming that the efficacy lasts indefinitely into the future.

    In some sense, KD14’s result should be obvious. Models with an average ECS of 3 K can reproduce the obs. 20th century temperature record. But if you take the forcing from the models and the same 20th century record and use it to infer the ECS, then you get an ECS of 2 K. How can this be? It’s because the models have an efficacy > 1, and this explains that contradiction.

    As far as your argument about the bias of our method, I would point out that we don’t take the endpoints of the time series in our calculations. Instead, the terms in our version of Eq. 4 are integrals over a time period. I think this makes a big difference. If you do the calculations with integrals and still find a bias, let me know.

    I do appreciate the feedback, though, and would be happy to discuss this further.

    Thanks,
    Andy Dessler

    Comment by Andrew Dessler — May 11, 2014 @ 7:17 pm

    • Hi Andrew,

      Thank you for stopping by and continuing the conversation. I believe I understand the point that you are making, but I think the first point of confusion is here:

      If the efficacy calculated by Shindell is correct, and you want to use the 20th century record to calculate ECS, then you must account for more joules of energy being trapped per W/m2 of aerosol/ozone forcing than in GHG forcing in your calculation.

      The problem is that the enhancement factor (E) calculated by Shindell does not necessarily show “more joules of energy being trapped per W/m^2 of aerosol/ozone”, but could be that the same amount of energy trapped from aerosols is dis-proportionally located in areas with a lower heat capacity (i.e., the NH), such that the *same amount* of “trapped” energy would have a larger impact on T in the transient. If this is the case, the effect would apply to TCR estimates, but not ECS estimates (for which we only care about the radiative response per unit T, independent of the time domain).

      To further illustrate this, let’s consider a simple example using Eq. 3. Suppose we have lambda_CO2 = lambda_aerosol = 2.0 W/m^2/k. By definition, this is a forcing efficacy = 1.0. But suppose we apply 2 W/m^2 of CO2 forcing and -1 W/m^2 of aerosol forcing, and that the aerosol forcing is applied primarily to the lower heat capacity areas (NH) such that the effective heat capacity for aerosols (c_aero) is only 50 W-yr/m^2, compared to 100 W-yr/m^2 for c_CO2. Now suppose we calculated our Shindell enhancement (E) over the transient run after 50 years. We have T_CO2 = 2 W/m^2 / 2 W/m^2/K * (1 – e^-(2 * 50 / 100)) = 0.63 K, and T_aero = -1 W/m^2 / 2 W/m^2/K * (1 – e^-(2 * 100/ 100)) = 0.43 K. This corresponds to a Shindell “enhancement” of TCR_aero/TCR_CO2 = 1.36, despite the forcing “efficacy” relevant to ECS being equal to 1.0.

      Now in this scenario, if one were to simply apply 1.0 W/m^2 of CO2, the “true” transient temperature change after 50 years would be 0.315 K / (W/m^2). For determining TCR in our “with aerosols” scenario, the transient change appears as (.63 K – .43 K ) / (2 W/m^2 + (-1 W/m^2)) = 0.2 K / (W/m^2) if we naively plug into Eq. 2, which is obviously an underestimate. So it makes sense that this value of E=1.36 must be accounted for in transient calculations. But for ECS, the net TOA imbalance will be the net forcing (F = 2 W/m^2 – 1W/m^2 = 1 W/m^2) minus the radiative response, or N = (1 W/m^2) – (T_CO2 * lambda_CO2 + T_aero * lambda_aero) = 0.6 W/m^2. Plugging this into equation 4 with a net T = 0.63 K – 0.43 K = 0.2K, yields lambda = (1 W/m^2 – 0.6 W/m^2) / 0.2 K = 2 W/m^2/K, which is no surprise as it is equal to the lambda of both aero and CO2, So our estimate of ECS is unbiased by the lower transient change due the lower effective heat capacity of the aerosol forcing. If one applied the factor of E = 1.36 by multiply the aerosol forcing by that amount, the calculation would change to F = 0.64 W/m^2, which per equation 4 would produce a lambda of only 0.2 W/m^2/K, corresponding to a sensitivity of around 18.5 K!

      However, since the Shindell enhancement is a function of BOTH the heat capacity (c_aero/c_co2) and differing radiative response (lambda_aero/lambda_co2), the enhancement factor *may* contain some portion of the latter, which would indeed need to be taken into account for the sake of ECS calculations. But obviously one must differentiate which portion comes from the heat capacity vs differing lambda prior to applying the method. It is possible to do this by simply calculating lambda from the hist_all and lambda from the hist_GHG runs in the models used for Shindell (2014), and in fact I can likely perform this calculation over the next week if it is of interest to you. However, what would be more interesting to me is calculating lambda from the AMIP simulations coupled to the specific pattern of observed warming to the lambda calculated from histGHG. That way, rather than relying on a modeled spatial warming pattern that deviates from the one observed, one could see whether the observed warming pattern actually corresponds to a bias in the ECS.

      Regarding your other points, I hope to post a response on those later today or tonight, as this reply has actually gotten quite long!

      Thanks,

      -Troy

      Comment by troyca — May 12, 2014 @ 9:34 am

      • Thanks for your very comprehensive reply. It seems to me that much of the disagreement here may be over the definition of efficacy. I confess that I have never seen that IPCC definition that you linked to, but it seems pretty clear to me from how it’s written that it only applies at equilibrium. The efficacy that we used (and Shindell uses) is what I’ll call a transient efficacy, defined in our paper as the ratio of warming from X per unit radiative forcing divided by the same warming from carbon dioxide. This is NOT the ratio of lambdas: it starts off at 1.0 immediately after imposition of the forcing and rises over time until it is equal to the ratio of the lambdas.

        It seems that the easiest way to resolve this may be for you to take a look at a quick demo I put together in Mathematica: https://www.dropbox.com/s/3f03srn1jxuani1/simpleCalcV1.pdf. This explains quantitatively how all of the terms are defined and how we use them. I put it together quickly, so pardon any dumb errors in it.

        Comment by Andrew Dessler — May 12, 2014 @ 2:28 pm

      • After re-reading your comment, I think we are in agreement: the efficacy can be thought of as coming from 2 sources, differing lambdas and differing heat capacities. For ECS, it is the former that matters. This is a useful clarification; I’ll add a sentence to the galleys saying this. Clearly, the next thing to do is to quantify the different lambdas in the models. If you do anything on that and want to collaborate on a paper, let me know.

        Comment by Andrew Dessler — May 12, 2014 @ 5:13 pm

      • Hi Andrew,

        Thank you, I do think that the clarification would help your manuscript. I plan to begin downloading the TOA fluxes for the histGHG, histAll, and AMIP simulations here soon, which should allow us to calculate the lambda ratios in the models based on their own warming spatial distributions (histAll), as well as the warming pattern observed (AMIP).

        However, while I think that pretty much covers Section 1 of my post, I think there is still an issue with how the efficacy is applied directly to the forcings in KD14 (per section 2 of my post), even if 100% of that Shindell efficacy were to be attributable to this difference in lambda. I believe this is why you are getting a slight underestimate in lambda in the final section of the demo you provide. The reason why the bias isn’t worse in that final section is because you have allowed 200 years to pass on a fixed forcing, so it is near equilibrium. However, if you keep everything else the same and simply use a linearly increasing forcing (from 0 to 3 W/m^2 for F_GHG , and 0 to -1 W/m^2 over the 200 years) instead of the fixed forcing, such that there is not as much time to equilibrate, you will notice a significantly larger bias when using the KD14 method.

        Unfortunately, I do not have access to Mathematica, but I have reproduced the first three sections of your Mathematica script in R (getting almost identical numbers), and have simply appended the last section at the end to highlight the issue I mention. It is available here.

        On another note, unrelated to specifically how efficacy is applied, Nic Lewis mentioned in the comments here that KD14 seems to be using the IPCC forcings (which are referenced relative to 1750) without adjusting them to the same 1880-1899 baseline that the temperature are referenced to. Is this is the case? If so, I fear this would have a significant impact, since the large volcanic activity from 1880-1899 (averaged ~ -0.6 W/m^2 according to GISS) means the forcing differential from 1880-1899 would actually be much larer than the forcing difference since 1750, despite the increase in anthropogenic forcings from 1750 to 1880. This would obviously reduce the ECS estimate substantially (to 1.5 C in the E=1.0 case according to his calculations, though I have not done these myself).

        Comment by troyca — May 13, 2014 @ 11:43 am

      • Troy – Maybe I’m misinterpreting your point about the use of the 1880-1899 baseline, since I don’t have access to the full KD14 paper. If I interpret it correctly, couldn’t one use a 1750 baseline for temperature to match 1750 forcings and find an increase rather than a reduction in calculated sensitivity? The temperature in 1750, although uncertain, was apparently lower than in 1880-1899 – http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0088(19980330)18:4%3C355::AID-JOC241%3E3.0.CO;2-B/pdf.

        Comment by Fred Moolten — May 14, 2014 @ 6:03 am

      • sorry for the incomplete URL. Try this – http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0088(19980330)18:4%3C355::AID-JOC241%3E3.0.CO;2-B/pdf

        Comment by Fred Moolten — May 14, 2014 @ 6:05 am

      • Reference is Rowntree, Int. J. Climatol. 18:355, 1998

        Comment by Fred Moolten — May 14, 2014 @ 6:08 am

      • Hi Fred,

        I don’t see where in your reference in shows observed temperatures back to 1750? The temperature figures I see that go back to 1750 are Figs. 8 – 10, but the observed data (solid line) in those comes from Jones and Wigley (1991), and only goes back to 1850. The other lines (I admit it is difficult to separate in black/white only the different lines) are simply the outputs of simulations using a low-order model (which are then compared to the observations starting in 1850), with input forcings that differ significantly from the latest best IPCC estimates.

        Regardless, if 1750 temperatures were indeed lower than 1880-1899 (and I suspect they might have been), this would likely imply a positive energy imbalance in 1750 to be compatible with those IPCC forcings (that the slight anthropogenic component alone would create a larger transient response for the small anthropogenic forcing than for the much larger volcanic forcing seems inconsistent with anything except huge heat capacities). This positive energy imbalance would need to be taken into account for the delta N portion (as it is, KD14 assumes a 0 energy imbalance in the 1880-1899, which is not strictly correct but would likely be smaller than the energy imbalance starting in 1750). So to perform your baseline relative to 1750, you would need to consider the T relative to 1750 (highly uncertain), as well as the N in 1750 (highly uncertain, but almost certainly positive), so I do not think it is a given you would get a larger estimate for ECS or even one that is useful for constraining ECS (uncertainties would be exceedingly high). This is why climate model simulations typically break off from the control experiment and start in 1850, and why almost all energy balance estimates are done using the second half of the 19th century as the base period.

        Comment by troyca — May 14, 2014 @ 9:32 am

      • Troy – Thanks for your reply. I agree we don’t have “observed” 1750 temperatures. Still, I think Mann and Marcott reconstructions suggest 1750 was cooler than 1880-1899, although that’s not conclusive proof. On the other hand, do we know N was positive in 1880-1899? That interval appears to have been followed by a significant drop in global temperatures, so unless the drop was due entirely to internal variability, perhaps N was negative. It seems to me that one implication of the evidence is that effective climate sensitivities are not only sensitive to uncertainties in forcing but also in delta N. I’m not sure that’s resolved by starting in 1850, long before we had direct OHC evidence. My larger point was that if sensitivity is so sensitive to all these uncertainties, it would be unwarranted on the part of a critic such as Nic Lewis to recalculate EFS baseed on the assumption of any given value of N at that time, or 1750 for that matter..

        Comment by Fred Moolten — May 14, 2014 @ 11:50 am

      • Hi Fred,

        I don’t know if the 1880-1899 was positive, but I believe the reason for the immediate drop in temperatures after that is a separate volcanic eruption beginning at the 20th century. I know you don’t have access to the full KD14 manuscript, but from the “accepted article” draft I have seen, they say the following under “methodology and datasets”:

        “The forcing time series is referenced to the late-19th, which means that the temperature anomaly time series must also be referenced to that same time. To do this, we offset each time series so that the 1880-1900 average is zero.”

        Clearly, referencing the forcings and the temperature series to 1880-1900 was the methodology that Kummer and Dessler determined, and was the methodology accepted by the reviewers. I think it is fair for Nic Lewis to point out that using the actual methodology accepted by the reviewers, if done correctly, produces the ECS (in actuality EFS) of 1.5 C for E=1.0 or 1.7C for E=1.5. I think this should be corrected so that the actual application corresponds to the method described. Changing the method after-the-fact because it ends up with an undesirable result is a big no-no, and I would be disappointed to see it happen in this case.

        Comment by troyca — May 14, 2014 @ 12:31 pm

      • Troy – Maybe I’m missing the point, but how can one calculate an EFS for the interval from 1880-1899 to the present without knowing what N was at that point? If N was negative – e.g. from the volcanic activity you mention above for that interval – delta N will be greater than if it was zero, and EFS correspondingly greater for a given delta F and delta T. I’m still not sure (not having the paper) whether KD14 used 1750 or 1880-1899 for their forcing baseline, since I interpreted your various comments as saying two different things for this question.

        Comment by Fred Moolten — May 14, 2014 @ 1:50 pm

      • To clarify my question, do KD14 calculate delta F be assuming radiative balance during 1880-1899 or 1750? If it’s the former, the offsetting you mention would permit the calculation you mention. The appropriate question for me should be whether the criticism they used 1750 for forcing and the later interval for temperature was correct.

        Comment by Fred Moolten — May 14, 2014 @ 2:13 pm

      • Hi Fred,

        I apologize if I have been confusing. KD14 *said* they calculated both T and F relative to the 1880-1900 baseline (hence the portion I quoted). But in actuality they calculated F relative to 1750, while calculating T relative to 1880-1900 (as confirmed in Andrew’s comment here). Nic pointed out if they had performed the calculation they said they performed, it actually would have resulted in an estimated ECS of 1.5 K.

        Re: how can one perform the calculation without knowing N at the time of the baseline…how indeed? More complete analysis such as Otto et al. estimated the value of N using modeled simulations that break off from the control earlier, but they were extra conservative in its use (that is, they halved the estimated positive imbalance for their reference period) reasoning that if the models are more sensitive than reality, the N for reality will be smaller (as you suggest, using a MORE positive N, such as the one that comes out of the model, would actually lower their ECS estimate further). In my paper, my earliest period is 1958, so I can use OHC to calculate N for that baseline. However, KD14 simply assumed that N = 0. I agree that this is another issue with KD14, but have not mentioned it because it is likely of smaller importance than the other 3 issues discussed. In truth, KD14 probably would have benefited from more detailed review, but that ship has sailed.

        Comment by troyca — May 14, 2014 @ 2:57 pm

      • Hi Fred, You write:

        “To clarify my question, do KD14 calculate delta F be assuming radiative balance during 1880-1899 or 1750? If it’s the former, the offsetting you mention would permit the calculation you mention. The appropriate question for me should be whether the criticism they used 1750 for forcing and the later interval for temperature was correct.”

        I see that you are again doubting my claim that a statement in an accepted paper is incorrect. But I do not make such claims lightly. I think you should become more sceptical of what you read in the ‘peer reviewed’ literature. I am correct in this case also. KD14 used 1750 as their reference period for forcing. There is no reason to doubt that they used, as stated, 1880-1900 as the reference period for surface temperatures, not 1750. None of the temperature datasets started before 1850, and two only started in 1880.

        Andrew Dessler has now admitted that I am right about the forcing reference period, writing at Climate Dialogue:

        “Your statement about the referencing period of the forcing is correct and that will be corrected in the galleys.”

        As Troy says, the referees passed the paper on the undertanding that the calculations were carried out on the basis stated in the text. To alter the galley proofs to change the described basis to agree with how the calculations were actually performed seems quite wrong to me. I find it surprising that a journal like GRL would find such practice acceptable. But maybe I am naive, or climate science is not like normal science.

        BTW, there are published model based estimates of ocean heat uptake in the second half of the nineteenth century. These show hat uptake to be quite significant in 1850 as the Earth was still recovering from centuries when volcanic and solar forcing were negative (relative to 1750) and the simulated temperature was significantly colder, but very low over 1880-1900 due to high volcanic activity causing estimated forcing to be quite negative then. I haven’t seen any similar estimates for 1750, but as the Little Ice Age was very recent then I would in any case have thought it a poor base date for temperature.

        Comment by niclewis — May 14, 2014 @ 3:20 pm

      • Nic – Yours is an unfortunate comment in what has been a constructive dialogue between Troy and me, with me asking most of the questions and Troy providing his perspective on the answers. Doubting you is not always unwarranted in my view, since I’ve found previous statements you’ve made to misrepresent the evidence or at least be susceptible to a false interpretation – examples include Soden and Held 2006 and Andrews et al 2012. Nevertheless, in this instance, I thought your claim was correct based on one of Troy’s comments, but I was confused by another of his comments which seemed contradictory, and I was simply asking him for clarification, which he provided. Your assertion I should read the literature more skeptically is strange, since my questions to Troy were based on my stated lack of access to KD14. As to radiative imbalance in 1880-1899, we don’t really know whether it was positive, negative, or zero. I think you’re saying it may not have been very different from zero, and I don’t have any reason to doubt that.

        Comment by Fred Moolten — May 14, 2014 @ 7:40 pm

      • Fred, I’m not seking to disrupt your conversation with Troy – I just thought you were having another go at me. But you might like to try Googling
        kummer dessler “The impact of forcing efficacy on the equilibrium climate sensitivity” filetype:pdf
        which I find provides a PDF of the accepted paper (maybe from Google’s cache). If it doesn’t, then I will willingly email a copy to any address you specify.

        According to AR5’s best estimates, total forcing averaged -0.53 W/m2 over 1880-1900. That is significantly negative.

        If you weren’t actually doubting my claim, then I apologise for saying that you were. As you suggest, comments are easily misinterpreted.

        Why not tell me what you think I’ve said wrong about Soden and Held 2006 and Andrews et al 2012?

        Comment by niclewis — May 15, 2014 @ 7:48 am

      • Hi Nic,

        I can’t get the KD14 pdf but your point that the 1880-1899 negative forcing relative to 1750 leads to an increased delta F in the energy budget equation is well taken, as is your criticism of KD14 on that score. My quibbles regarding your descriptions of SH06 and Andrews et al 2012 are too minor to inflict on the readers of Troy’s blog, but let me ask you a relevant question about the latter paper. In Figure 1, the relationship between N and delta T is more or less linear after an instantaneous forcing change when the process is followed over an interval 150 years from the time of the forcing change. However, in many models shown in the figure, the curves are non-linear “early” after the change, where “early” refers both to time and the rise in temperature. Since a substantial amount of the forcing change in the real world has been fairly recent, to what extent do you believe it justifiable to treat the real world responses as linear, and hence a good approximation for how the temperature would proceed to equilibrium?

        Comment by Fred Moolten — May 15, 2014 @ 8:58 am

      • Hi Fred
        Good question re Fig.1 of Andrews et al. The first thing to remember is that this shows the behaviour of CMIP5 coupled AOGCMs, not the real world. Also, I believe that the red crosses representing fixed-SST experiment forcing estimates, really belong pretty much on the y-axis, not displaced from it by 0.5 K or so, but I’ve forgotten why that is. So far as the model behaviour goes, and counting models in alphabetical order (by row), I would say that models 1, 2, 5, 6, 8, 9 and 11 show almost perfectly linear behaviour, and models 3, 4, 7 and 10 strongly non-linear behaviour, whilst models 12, 13, 14 and 15 are in between – non-linear, but not that far off linear. I may have allocated the last 4 models to either of the first two categories in the past.

        Would you agree with my analysis of the models?

        In many ways it is more relevant to look at warming in the second half of a 140 year experiment in which CO2 concentration increases at 1% pa, and see to what extent it exceeds that in the first half once warming-in-the-pipeline (WiP) at year 70 is allowed for. Tomassini et al (2012) Figure 1 graphs this experiment for a number of CMIP5 models. About half exhibit measurable non-linearity (acceleration of warming after allowing for emerging WiP), and half don’t.

        So far as the real world climate system goes, I’m not aware that current observational evidence supports the existence of the sort of strongly non-linear behaviour exhibited by a number of the CMIP5 AOGCMs. Moreover, the behaviour of most CMIP5 models seems at best marginally consistent with the real world – see, e.g., Figures 4 and 5 of my guest blog at Climate Dialogue (do come and join in this discussion of climate sensitivity, BTW). So I think it is reasonable to go with the linearity assumption at present.

        Comment by niclewis — May 15, 2014 @ 12:13 pm

      • Nic – I do agree with your description of the data. Regarding your statement that you’re “not aware that current observational evidence supports the existence of the sort of strongly non-linear behaviour exhibited by a number of the CMIP5 AOGCMs”, it’s a matter of judgment how much that tells us about the existence or non-existence of that type of non-linearity. As long as different approaches to climate sensitivity (“bottom up” modeling, paleosensitivity, energy balance) yield differing estimates that remain to be reconciled, my preference is to avoid calling them the same thing.. In particular, I would recommend referring to the energy balance results as “effective climate sensitivity” (EFS) – the term commonly used – and the other estimates as ECS (or anything else for that matter), and then, if desired, discuss why they might or might not differ substantially. Ironically, none of them is really an estimate of temperature change at equilibrium, since they all disregard the slow feedbacks (ice sheets, vegetation, carbon cycle) that would be expected to play an important role on millennial timescales.

        I tried yesterday to register at Climate Dialogue, but all I got was a login screen rather than a registration screen. Maybe there’s a problem with my browser’s security settings, or maybe the website itself needs to be modified. I’ll have to look into it further.

        Comment by Fred Moolten — May 15, 2014 @ 1:26 pm

    • Hi Andrew,
      Maybe you can clarify my confusion about the results in your recent (I have a post about it that’s linked at the bottom of Troy’s comment section here, if you’re interested). I was messing around with a very simply model to try and understand how the efficacy influences the ECS and TCR. As I understand it, the Shindell idea is that the inhomogeneous aerosol/ozone/LU forcings means that the change in temperature due to a particular globally averaged change in radiative forcing is smaller than if the aerosol/ozone/LU forcings were homogeneous. Hence, if you use the standard energy budget calculation to determine the TCR, it will be an underestimate – because the inhomogeneity will reduce with time.

      However, when I was trying to do the same with the ECS, what I seemed to find (with a very simple model, mind you) is that the the influence of the inhomogeneities in the aerosol/ozone/LU forcings produced a large energy imbalance (system heat uptake rate, if you like) than would be the case where these forcings homogeneous. Hence the standard form of the ECS energy budget equation produced a good estimate, while including the efficacy factor produced an over-estimate.

      Now, it’s completely possible that I’ve misunderstood something about this but it does seem reasonable that if the inhomogeneities produce a reduced ΔT, that a consequence of this will be an increased energy balance (compared to what would be the case were the forcings homogeneous) and hence it’s not completely obvious to me that the efficacy factor applies to the ECS in the same way as to the TCR. Alternatively, I’m just very confused – quite likely, to be honest.

      Comment by And Then There's Physics — May 13, 2014 @ 7:25 am

  4. Troy – I’ve now had a chance to read a draft of Shindell. I note that he attributes the lambda component of his efficacy factor to increased snow/ice albedo feedback strength in the NH, although without assigning a specified proportion of the efficacy to lambda vs heat capacity. I was intrigued to reread Armour et al and note that the authors describe striking regional variation in lambda. including a lower value (higher ECS) for land vs ocean at a given latitude, related to a reduced (less negative) Planck response. I’m not sure what the mechanism is, but it may relate to the lower infrared emissivity of land vs water. Are you aware of other mechanisms for this proposed difference?

    Comment by Fred Moolten — May 12, 2014 @ 11:48 am

    • Hi Fred,

      Not sure off the top of my head for the land vs. ocean difference, but in terms of spatial differences for lambda, Winton et al, (2010) [http://www.gfdl.noaa.gov/bibliography/related_files/mw1002.pdf] indicates that the high-latitude heat uptake results in a stronger cloud feedback and weaker temperature response for the model used (GFDL-CM2.1), which seem to contribute the bulk of the difference to the effective vs. equilibrium response in that model, rather than the snow / ice albedo feedback. It would not surprise, however, if the mechanisms were different across different models.

      Comment by troyca — May 12, 2014 @ 12:30 pm

  5. […] where Q is the system heat uptake rate – the energy imbalance. However, Troy Masters has a blog post that seems to suggests that this efficacy factor shouldn’t be applied to the ECS calculation. […]

    Pingback by I’m confused about Kummer & Dessler | And Then There's Physics — May 13, 2014 @ 1:43 am

  6. […] 2014/05/09: TMasters: On forcing enhancement, efficacy, and Kummer and Dessler (2014) […]

    Pingback by Another Week of Climate Disruption News – May 11, 2014 [A Few Things Ill Considered] | Gaia Gazette — May 13, 2014 @ 10:42 pm

  7. Dear Fred,

    I heard from Nic that you have problems registering at ClimateDialogue. Please contact me, than we can solve it. +31.6.50614657 or bart.strengers@pbl.nl

    Bart, project leader Climate Dialogue

    Comment by Bart Strengers — May 16, 2014 @ 3:13 am

  8. […] Dessler (2014) extension of the Shindell (2014) forcing “enhancement” from TCR to ECS (although as discussed previously, the enhancements in TCR and ECS are very […]

    Pingback by Estimating ECS bias from local feedbacks and observed warming patterns–example with GFDL-CM3 | Troy's Scratchpad — June 13, 2014 @ 10:45 pm

  9. […] Don’t worry, even senior climate scientists are. Anyway, what do the Paris negotiators mean when they say want to keep warming below 2ºC, starting […]

    Pingback by No, the greenhouse effect does not justify your pet idea — March 1, 2016 @ 2:33 am


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