Climate Sensitivity and Transient Climate Response

First comments on the guest blog of James Annan:

I enjoyed reading James Annan’s guest blog on climate sensitivity. There is much in his post that I agree with and I found his discussion of nonlinearities in the paleoclimate record to be particularly interesting. I also agree with his characterization of our recent work (Fasullo and Trenberth 2012) as being primarily qualitative in nature. Given the likelihood that the CMIP archives do not span the full range of parametric and structural uncertainties, it seems unlikely that a more quantitative assessment would have been justified. It is clear however, from both our work and the work of others, that various GCMs have particular difficulty in simulating even the basic features of observed variability in both clouds and radiation. Given the importance of related processes in driving the inter-model spread in sensitivity we viewed this as a sound basis for discounting such models, which as it turns out were the only models in CMIP3 with ECS below 2.7. These models were also amongst the oldest in the archive and had been shown in other work to be lacking in key respects. As discussed below, this may present an opportunity for narrowing the GCM-based range of sensitivity.

I also agree with James’ point that an adequate estimation of uncertainty has been lacking generally, though I tend to view the problem of underestimation to be more common than that of overestimation. I think this challenge speaks directly to the question posed by the editors in their introduction as to why AR5 did not choose between the different lines of evidence in forming a single “best estimate”. Doing so would have required a firmer understanding of the uncertainties inherent to each approach than is presently available. Improved assessment of these uncertainties exists as a high priority in my view and one that is achievable in the not-so-distant future.

Lastly, while James makes a good point that there is not necessarily a contradiction or tension between the various approaches if different lines of evidence provide different ranges, it is here that I have reservations. Does this necessarily mean that the likely value in nature lies at the intersection of available ranges and does this also mean that the approaches should be given equal weight? In my view, given the issues regarding uncertainty mentioned above, the answer to both of these questions is likely to be “no”. Potential improvements in so-called “20th Century” approaches include a more thorough consideration of the adequacy of any “prior”, given the rich internal variability of the climate system, and the uncertainty in both forcings and their efficacy. There is also a need to more fully consider the sensitivity of any method to observations, particularly when using ocean heat content. As we show in a paper earlier this year, the choice of an ocean heat content dataset can change the conclusions of such an analysis from being a critique of the IPCC range to being consistent with it.

For paleoclimate-based estimates, as James points out, sensitivity to nonlinearities, data problems, and uncertainty in forcing undermine any strong constraint on ECS and it is unclear (to me at least) whether progress on these fronts presents an immediate opportunity for reducing uncertainty in ECS in the near future. Lastly, I view estimates involving GCMs to be somewhat of a mixed bag. Clearly, some GCMs can be discounted based on their inability to simulate key aspects of observed climate, as discussed above. One would be hard-pressed to argue that the NCAR PCM1 and NCAR CESM1-CAM5 should be given equal weighting in estimating sensitivity. Weighting or culling model archives based on various physically-based rationales is likely to play a key role in constraining GCM estimates of sensitivity in the near future. A major, apparently unavoidable, question for this approach however is whether existing model archives sample the full range of parametric and structural uncertainty in the processes that determine sensitivity.

First comments on the guest blog of John Fasullo:

John Fasullo focusses on the change lower limit of the IPCC AR5 “likely” range from 2 (in AR4) to 1.5 (in AR5), arguing that although it was understandable, it was wrong on the basis that models can reproduce periods of little warming. While I don’t presume to know what was going on in the IPCC authors’ esteemed minds, I believe it’s far preferable to consider the climate sensitivity estimation on the merits of the available literature rather than considering the previous IPCC AR4 estimate (and/or the GCM model range) as some sort of prior or null hypothesis to only be changed if and when the observational data become overwhelming. Whether we can still argue that the recent observed global mean temperature time series is consistent with the GCM ensemble (at some arbitrary level of confidence) is rather beside the point. The observed time series is indisputably close to the lower end of the range, and any reasonable estimate had better take that into account.

Some recent estimates, like Stott et al (2013), look beyond the global or hemispheric mean temperature change, and consider the full spatial pattern of response to different forcings. Fasullo’s arguments don’t appear to apply to this sort of detection and attribution approach at all.

Reference

Stott, P., Good, P., Jones, G., Gillett, N., & Hawkins, E. (2013). The upper end of climate model temperature projections is inconsistent with past warming. Environmental Research Letters, 8(1), 014024. doi:10.1088/1748-9326/8/1/014024

First comments on the guest blog of Nic Lewis:

Nic Lewis appears to be arguing primarily on the basis that all work on climate sensitivity is wrong, except his own, and one other team who gets similar results. In reality, all research has limitations, uncertainties and assumptions built in. I certainly agree that estimates based primarily on energy balance considerations (as his are) are important and it’s a useful approach to take, but these estimates are not as unimpeachable or model-free as he claims. Rather, they are based on a highly simplified model that imperfectly represents the climate system.

For instance, one well-known limitation of such models that effective climate sensitivity is not truly a constant parameter of the earth system, but changes through time depending on the transient response to radiative forcing. This introduces an extra source of uncertainty (which is probably a negative bias) into estimates based on this approach.

I would like to respond to John’s suggestion of exploring methods to estimate ECS from the observational record in a framework that is tightly constrained, using a model whose sensitivity is known and whose variability is thoroughly vetted. I concur, although depending on the approach used the realism of variability in the model with known sensitivity may not matter.

One approach is to use a detection and attribution method, comparing model simulations and observations for some “fingerprint” of the forcing of interest and using regression to find the best scaling factor. This provides estimates of TCR more readily than of ECS. If the scaling factor is for the response to greenhouse gases (GHG) over the last 60 or more years of the instrumental period, multiplying the scaling factor by the model’s TCR provides an observationally-based estimate of TCR. Figure 10.4 of AR5, panel (b), shows the GHG scaling factors (green bars) estimated by three such studies. The corresponding observationally-based TCR estimates for the nine CMIP5 GCMs studied in Gillett et al (2013), which uses the longest data time series, have a median of 1.45°C, close to median estimates of ~1.35°C that I have derived using simple energy balance approaches. A problem with such studies is difficulty in obtaining a complete separation of responses to different forcings. Incomplete separation between responses to GHG and aerosol forcing may lead to overestimation of the GHG scaling coefficient and hence of TCR.

An approach that avoids the separation problem is to systematically vary parameters of a climate model, varying the model physics so as to achieve a large number of different combinations of ECS, ocean vertical diffusivity (or other measure of ocean heat uptake efficiency), aerosol forcing and any other key climate system properties, and performing simulations for each – so-called PPE studies. Obviously, those properties must be calibrated in relation to the model parameters. The simulation results are then compared with observations and the best fit found. The fidelity of model variability is normally not critical since its effects are suppressed by using averages over ensembles of simulations. Real-world variability and covariability is then estimated from one or more separate much longer simulation runs, not necessarily by the same model, and appropriately allowed for.

This PPE approach can be used with full scale coupled GCMs, but the extensive supercomputer time required is very expensive. More seriously, it may prove impracticable to explore all combinations of climate system properties that are compatible with the observations. That was the problem with the Sexton et al (2012) and Harris et al (2013) PPE studies, as explained in my guest blog. often used In the idea is to minimise the effects of model variability by using ensembles of simulations, real-world variability then being allowed for using simulations by a more complex model.

It is more usual to use a PPE approach with models that are simpler than a GCM, typically resolving the globe horizontally only by hemisphere and land vs ocean, and maybe having a single layer atmosphere. However, several such studies have been carried out using the MIT climate model, which is in effect a 2D GCM, key parameter settings of which have been calibrated against 3D coupled GCMs. Longitude, which is not resolved, is generally far less important than latitude. Such studies include Forest et al (2002 and 2006), Lewis (2013) and Libardoni & Forest (2011, corrigendum 2013). Internal covariability was allowed for by the use of long control run simulations from full coupled GCMs, and multiple observations were used to constrain ECS, aerosol forcing and ocean effective diffusivity. Are such studies in principle more acceptable to John than observationally-based estimates using simpler numerical climate models or simple mathematical/statistical models?

Hi Bart,

Thanks for the additional questions. Firstly to clarify my position, I have indicated that so-called instrumental-record studies could play an important role in the discussion if they were more thoroughly vetted and understood. One need not use a GCM at all, though that approach could provide a useful well-constrained framework for such a vetting. The fact that this has not yet been done in any thorough sense to me is startling, given the sweeping statements that have been made based on such techniques and given how widely scrutinized other approaches (e.g. GCMs) have been.

My basis for the lower part of my estimated range is very much in line with Andy’s comments based on feedbacks – an approach I focus on in my original post. I know of no valid studies supporting the strong negative cloud feedback needed to arrive at a sensitivity well below 2C. I know of several claiming to show such a negative feedback that have been revealed (by myself and others) to clearly be wrong (Lindzen and Choi, Spencer and Braswell, among others). Lindzen himself has admitted to major errors in this work (http://dotearth.blogs.nytimes.com/2010/01/08/a-rebuttal-to-a-cool-climate-paper/?pagemode=print). From other recent work, (multiple works each by Soden, Webb, Romanski/Rossow, Sherwood, Brient/Bony, Gregory, Gettelman, Dessler, Jonko, Norris, Sanderson, Shell, Bender, Vechhi, Lauer …) that examine the issue across observations, cloud resolving models, and GCM archives of various sorts, there is persuasive evidence that the feedback is not strongly negative but rather is likely to be positive, perhaps strongly so. Clearly there remains a considerable range of uncertainty on the exact value of the feedback but in my view the evidence does not allow for a strong negative feedback. And so how does one construct a physical basis for a value well below 2?

My upper end of the range is based on my evaluation of models and related work in the literature (e.g. by many of the above mentioned authors). For instance, in my view, the CESM1-CAM5 ensemble that I present in my Fig. 2 shows no obvious bias in its reproduction of the surface temperature record yet its sensitivity is 4.1! Again, the main disparity between the observed record and the ensemble mean occurs during the hiatus, yet this does not accompany any reduction in the planetary imbalance (in nature or comparable model ensemble members) and therefore is not evidence for a strong negative feedback. It is therefore also not an indication of biases in model feedbacks and is not a basis for revising our sensitivity estimates downward. Moreover, the key processes that drive sensitivity are actually better represented in many of the high sensitivity models (Fasullo and Trenberth 2012, Sherwood et al. 2014) and the sensitivities of the poorest performing models in CMIP3 (e.g. 2.1 of NCAR PCM1 which we know has major problems) have not been reproduced by models in CMIP5, as a broader improvement (though not perfection) of key processes has been realized.

Regarding the work on efficacy, I’ll let texts from the abstracts do the talking, paraphrasing where useful.

Shindell: …transient climate sensitivity to historical aerosols and ozone is substantially greater than the transient climate sensitivity to CO2. This enhanced sensitivity is primarily caused by more of the forcing being located at Northern Hemisphere middle to high latitudes where it triggers more rapid land responses and stronger feedbacks. I find that accounting for this enhancement largely reconciles the {instrumental and GCM ranges}.

Kummer and Dessler: Previous estimates of ECS based on 20th-century observations have assumed that the efficacy is unity, which in our study yields an ECS of 2.3 K (5%-95%- confidence range of 1.6-4.1 K), near the bottom of the IPCC’s likely range of 1.5- 4.5 K. Increasing the aerosol and ozone efficacy to 1.33 increases the ECS to 3.0 K (1.9-6.8 K), a value in excellent agreement with other estimates. Forcing efficacy therefore provides a way to bridge the gap between the different estimates of ECS.

To James Annan:
Overall, I think I agree with James’ comments — I wish my argument were stronger. However, to be fair, it’s important to realize that there are no really strong arguments for any particular climate sensitivity range — if there were, we wouldn’t be having this argument. Rather, any argument about climate sensitivity requires you to evaluate conflicting arguments and decide one is right and the other isn’t. So while I think that ECS > 2°C, I understand the IPCC authors who decided the ECS > 1.5°C.

To Nic Lewis:
I appreciate your comments. Your statement about the referencing period of the forcing is correct and that will be corrected in the galleys. Assuming that the climate in the late 19th century is warmer than that in the mid 18th century (probable since radiative forcing is +0.3 W/m2 in the late 19th century), then referencing both time series to 1750 will increase the calculated climate sensitivity (I can explain why if it’s not clear). Thus, it does not affect our conclusion that incorporating efficacy has a significant effect on the inferred climate sensitivity.

I also agree that there is a useful clarification to be made between Shindell’s analysis and ours. The efficacy in Shindell’s analysis is a combination of a heat-capacity effect and an effect from differing climate sensitivities to aerosols/ozone and greenhouse gases. The effect due to differing heat capacities is not relevant for the ECS, but the other one is. Given the weaker radiative restoring force at high latitudes, I find it perfectly reasonable that there is a significant difference in sensitivity to these different forcers — and if there is, it resolves an otherwise confusing situation. As we say in the paper, determining this is should be a priority.

To John Fasullo:
I agree with just about everything you say!

Bart queries my comment that ‘I did not claim that observations alone can be used to generate a useful estimate of ECS.’ and asks what else is needed to generate a estimate for ECS. I think this is an issue of terminology. When I refer to observational estimates, I do not imply that a sound ECS estimate can be derived from observations alone. As I wrote in my guest blog, ‘Whichever method is employed, GCMs or similar models have to be used to help estimate most radiative forcings and their efficacy, the characteristics of internal climate variability and maybe other ancillary items.’

Let me take the example of an energy budget estimate of ECS, using Equation (1) in my guest blog. The change in global surface temperature is typically taken from a dataset that involves multiple measurement time series at different locations and a more or less sophisticated mathematical method of averaging the measurement, adjusting for inhomogeneities, etc. That method could be regarded as a model, but not in the normal sense of the word. Most people would view HadCRUT and other global temperature estimates as observational data, not model outputs. Planetary heat uptake / radiative imbalance in the final period can be calculated in similar ways. These may involving rather more processing and adjustments, but the outcome is still generally regarded as observational data.

On the other hand, it is generally necessary to rely on coupled GCM simulations to derive heat uptake in the base period, since that is typically in the second half of the nineteenth century, before proper observations of ocean temperatures at depth started. That estimate will have a first order dependence on the GCM’s ECS value. However, the absolute value of heat uptake in the nineteenth century is small, so it has only modest effect on ECS estimation, and an approximate adjustment can be made to the GCM’s simulated value by reference to the relationship of the GCM’s ECS to the energy budget ECS estimate.

The remaining term involves radiative forcings. Although the most important radiative forcings (those from greenhouse gases) can be estimated without use of GCMs, some radiative forcings cannot ,and nor can effective radiative forcing (ERF) – which is more appropriate for energy budget estimates – be estimated without use of GCMs. However, ERF estimates do not rely on the ECS values of the models involved. There is, for instance, a negligible correlation between ECS and F_2x (the ERF from a doubling of CO2 concentration) in the CMIP5 models included in Table 5, which have ECS values ranging from 2.1°C to 4.7°C, is negligible. And in any event, for most forcings (aerosol forcing being an exception) ERF is not estimated to be significantly different from plain radiative forcing.

So, to summarise, GCMs or similar climate models are needed for observationally-based climate sensitivity estimates, but their ECS values have very little effect on those estimates.

Bart also queries my implicit claim that even when a model and a method have been fixed, then in unsound studies ECS may not be completely determined by the observations. I should say that I regard a case where the model and method result in the best estimate for ECS potentially being substantially different from the value at which the model indicates a best fit to the observations as not completely determining ECS from the observations.

As I pointed out in a previous comment, there are two obvious ways that this situation can arise. One is where, a study is unable because of climate model limitations – properly to sample the entire space of values for ECS and other parameters being estimated alongside it that is compatible with the observations. This is a major problem with GCM-based PPE studies: varying the GCM’s parameters may not achieve even a moderately low ECS. I think James found this problem with a Japanese GCM.

Even if reasonably low ECS values can be achieved, they may always be accompanied by values for other climate system properties that make the simulated climate unrealistic. As I have shown, that is the problem with studies based on the UK HadCM3 model, which has been used a lot for such studies. HadCM3 seems unable to exhibit ECS values below 2°C whatever its parameter settings, although somewhat lower ECS values have been extrapolated by statistical emulation. But even with ECS reduced just to 2°C, the parameter setting required produce much more highly negative aerosol forcing, resulting in an unrealistically cool climate. This is probably because both low ECS values and high aerosol forcing result from low clouds being increased in extent and maybe having different properties. HadCM3 studies therefore simply cannot explore the combination of low-to-moderate ECS and moderate aerosol forcing that the observations point to.

The other obvious case is where the statistical method uses a highly informative prior. An obvious example is an expert prior for ECS. If one uses, as Tomassini et al (2007) did, a sharply peaked expert prior that falls to one-fifteenth of its maximum (achieved at an ECS of 2.5°C) at ECS values of 1°C and 6°C, then the best estimate – taken in AR5, correctly, as the median of the estimated (posterior) PDF for ECS – is obviously going to be pushed towards values somewhere in the middle of the 1°C and 6°C range.
But a uniform prior for ECS is also highly informative. The observable variables have a much more linear relationship to the reciprocal of ECS, the climate feedback parameter (lambda), than to ECS itself. It follows that a uniform prior in lambda is fairly uninformative. But if a uniform prior in lambda is uninformative for estimating lambda, it follows mathematically that for a prior in ECS to be uninformative it must have the form 1/ECS^2. That is, the prior should quarter each time the ECS value doubles. Even with a fairly well-constrained observational likelihood (the model–observation fit being good only over a limited range), the use of a uniform prior in ECS has a major distorting effect.

Compare the two ECS ranges shown (purple lines 3rd and 4th up from the bottom of the Instrumental section) in AR5 Box 12.2 Figure 1 for the Forster & Gregory (2006) study. The solid line, showing the study’s regression-derived original results, has a 5–95% range of 0.9–3.5°C and a best (median) estimate of 1.5°C. The standard regression method implicitly, and correctly, reflected a uniform-in-lambda prior. The dashed line, showing the estimate reported in AR4 – which had, for no valid reason, been transformed onto a uniform-in-ECS prior, has a 5–95% range of 1.2–7.9°C and a best estimate of 2.4°C. The best estimate is increased by 50%+ and the top of the uncertainty range is more than doubled!

I was not familiar with Nic Lewis’ 2013 paper, which figures strongly in his view of a low climate sensitivity, so I had a look at it. He uses the well-known method of Chris Forest to simultaneously estimate aerosol forcing, ocean heat uptake efficiency and equilibrium climate sensitivity from historical data, but extends it using more recent data and makes a few other changes to the method. Historical data is one of three constraints on climate sensitivity, the other two being information on prehistoric climate change (paleoclimate) and climate sensitivity calculated from first principles (climate models). Of the three, the estimates from historical data have generally been lower than those from paleo data or from models. Recently Otto et al. 2013 showed that the estimate drops still furhter when the most recent data are used, and Lewis shows an even larger drop, to a climate sensitivity likely near or below 2C.

The problem with estimating climate sensitivity from recent historical data is that the answer is very sensitive to aerosol forcing, which is poorly known, and (despite what Lewis says) such estimates also depend on models. The Forest/Lewis method assumes that aerosol forcing is in the northern hemisphere (establishing the “fingerprint”), so in effect uses the interhemispheric temperature difference to constrain the aerosol forcing.

In the last couple of decades, northern high latitudes have warmed dramatically while the southern high latitudes have warmed very little if any. Forest’s approach will implicitly attribute this to a positive aerosol forcing over that period, in contrast to the negative forcing that would be expected given the increase in aerosol precursor emissions over that time. This leads to a very small estimate of the climate sensitivity, since if I understand correctly, the method will believe that aerosols were adding to CO2 forcing rather than opposing it as we would normally think based on independent evidence including satellite observations of aerosol forcing. Such a large forcing, with less than 1C warming, would if it were true imply a low sensitivity.

The problem is that this interhemispheric warming difference since the 1980’s is almost certainly not aerosol-driven as the Forest/Lewis approach assumes. It is not fully understood but probably results from circulation changes in the deep ocean, unexpectedly strong ice and cloud feedbacks in the Arctic, meltwater effects around Antarctica, and/or the cooling effect of the ozone hole over Antarctica. Most of these things are poorly or un-represented in climate models, especially the MIT GCM used by Forest and Lewis, and these models display too little natural decadal variability. It is thus not surprising that GCMs have great difficulty simulating the recently observed decadal swings in warming rate (including the so-called “haitus” period where they overestimate warming, and the previous decade where they typically underestimated it). By implicitly attributing a pattern to aerosol that is probably due to other factors, Forest (and especially Lewis) are underestimating climate sensitivity. Other evidence such as the continued accumulation of heat in the worlds’ oceans is also inconsistent with the hypothesis that the slow warming rate in the last decade or two is due to negative feedback in the system as argued by Lewis.

A more general problem with Lewis’ post is that he dismisses, for fairly aribtrary reasons, every study he disagrees with. The fact is that no way of estimating climate sensitivity is solid, and we have to consider all of them (except Lindzen and Choi which is based on a ridiculous argument that is contradicted by their own data). Lewis dismisses climate models because they supposedly can’t simulate clouds properly, ignoring the multiple lines of evidence for positive cloud feedbacks articulated in Chapter 7 of the 2013 WGI IPCC report as well as the myriad studies (including my Nature paper from this year) showing that the models with the greatest problems are those simulating the lower climate sensitivities that Lewis favours, not the higher ones he is trying to discount.

If we look at all the evidence in a fair and unbiased way, we find that climate sensitivity could still be either low or high, and that it is imperative to better understand the recent climate changes and the factors that drove them. My money is on the models and the paleo data, not the estimates based on the 20th century. Although I hope I turn out to be wrong.

My concern is that ECS en TCS, as defined, can never be measured, because you cannot carry out the necessary experimentation with the earth. Therefore, they are strictly metrics describing the behaviour of climate models. Of course, a model with high sensitivity is likely to predict a larger temperature increase in response to an increase in CO2 as compared to low sensitivity model. Therefore, it is certainly of interest to compare sensitivities of different models. Discussing the climate sensitivity as a property of nature, however, is rather meaningless, in my opinion. It makes more sense to compare actual forecaste made with different models.
What I miss is a systematic discussion of the different studies comparing strong and weak points in 1. the particular definition of ECS/TCS; 2. the model used (even if you consider the model as a black box in which the temperature increase is proportional to the change of forcing this IS a model; quite poor and unrealistic in my opinion); 3. the particular observations (and or data derived otherwise) fed into the model; 4. the method used to feed data into the model.

In response to Gerbrand’s comment (2014-05-19 11:28:18) – yes, of course any number that we calculate for a physical system is based on idealization (which is why many of the above comments describe how every such metric must be based on a model of some sort). But that does not mean the physical system itself is not fundamentally behaving in a mathematical fashion – the experience of physics in a huge variety of realms from the tiniest particle to the largest systems in the universe shows things following explainable and precise mathematical laws. So the Earth should, in principle, have that same sort of mathematical character as any other physical system. Models attempt to match that but are of course always a simplification.

If you take away some of the complications of the real Earth – day-night, seasons, changes in solar forcing, etc. and think about how such a planet would respond to changes in its own atmosphere it seems clear there should be a range of responses on different time-scales. If, say, there’s an instantaneous forcing change (say from a volcanic explosion, change happening in a day or less) then the response to that “delta-function” forcing change will be spread out over time. The immediate effect is an energy imbalance (assuming all was in balance before the change) but no temperature change at first. Wherever the energy imbalance has a direct effect, for example on the surface if the forcing change is from reflective aerosols, will start to change in temperature (cool under increased aerosol forcing). That cooling will in turn change other energy flows – radiative and convective and other, that will start to address the energy imbalance and return things to balance. It will also have other consequences such as changes in water evaporation, precipitation, ice melting, etc. that add up to feedbacks that play out over a wide range of timescales. One of the really long timescales is the response of the subsurface – and in particular the oceans with their huge heat capacity. In principle the temperature change required to reach full equilibrium needs to be not just at the surface, but across the full range of planetary systems interacting through energy flows with the surface. For a planet like Earth that leads to timescales on the order of thousands of years, necessarily.

All that is in principle describable mathematically – as a response function of the planetary temperature field as a function of time T(x, t) ~ G(x, t) delta F(t=0) – though possibly other fields may need to be included as well (ice, cloud, fresh water, etc) to handle hysteresis effects. TCR and ECS are simplified metrics describing that full response function. Necessarily there will be uncertainties in any measure through observations that tries to get a handle on those numbers, and any model of the system similarly must have uncertainties thanks to discretization and parameterizations. It’s important in comparing models with one another, and models with observations, to be very clear (and generous, even) with accounting for those uncertainties before claiming a discrepancy. Nevertheless there is an underlying mathematical reality that these are trying to get to, so it really is a useful exercise. But I do agree it might be helpful, if possible, to think about other metrics than TCR and ECS to see if we can better characterize that fundamental response with measures that might be less subject to uncertainty and easier to compare.

@arthur smith

I appreciate your reacting (2014-05-19 16:23:24)to my comment.

I agree that the earth system behaves according to the laws of physics, first of all the laws of fluid dynamics, and then all the other processes that come in, but this does not provide an answer to my concern that you cannot measure ’the’ climate sensitivity. I also agree that you ‘can take away some of the complications of the real Earth – day-night, seasons, changes in solar forcing, etc. and think about how such a planet would respond to changes’ etc, but then you are really making a model. In reality it is simply impossible to do the experiment.

Maybe I am crazy, but this blocks me completely. How can one meaningfully introduce a quantity which can not be measured? I would argue, for model characterization only!

I have the same problem with the (IPCC) concept of radiative forcing. You can compute it, (‘with all tropospheric properties held fixed’) but there is no way you could actually measure it, because you can’t keep all tropospheric properties fixed if you perturb the actual system.

So, in summary, I fully agree, that there is an underlying reality, and also that climate sensitivity is useful for comparing models, but I do not see how you can measure it.

I thank Steven Sherwood for his comments. It is helpful to see some solid arguments made about my 2013 Journal of Climate study, to which I respond below. But before I do so, let me point out that the low best (median) ECS (and by implication TCR) estimates that study, and other such as Ring et al (2012) and Aldrin et al (2012) that also formed their own inverse estimates of aerosol forcing from observed spatiotemporal changes in temperature, arrived at are in line with energy balance derived estimates based on AR5’s expert best estimate of aerosol forcing.

I will quote what Steven writes in italics and put my responses in normal text.

Otto et al. 2013 showed that the estimate drops still further when the most recent data are used
That is incorrect. Otto et al 2013 reached best estimates for ECS of 1.4°C using data from the 1970s, 1.9°C using data from the 1980s, 1.9°C using data from the 1990s and 2.0°C using data from the 2000s. So using the most recent data gave the highest estimate of ECS, not a lower one. Using data for all four decades, the ECS estimate was 1.9°C.

The problem with estimating climate sensitivity from recent historical data is that the answer is very sensitive to aerosol forcing, which is poorly known, and (despite what Lewis says) such estimates also depend on models.
The suggestion that I claimed ECS estimates from recent historical data were independent of models is untrue. I wrote in my blog ” Whichever method is employed, GCMs or similar models have to be used to help estimate most radiative forcings and their effectiveness, the characteristics of internal climate variability and various other ancillary items.”

The Forest/Lewis method assumes that aerosol forcing is in the northern hemisphere (establishing the “fingerprint”), so in effect uses the interhemispheric temperature difference to constrain the aerosol forcing.
That is only partly true. The MIT 2D GCM used has a 4° latitudinal resolution, as good as many 3D GCMs of its day. Time-varying aerosol loadings are applied as a function of latitude, and will by no means be located only in the northern hemisphere. For the surface diagnostic used, the resulting surface temperature changes in four equal-area latitude zones, not just hemispheres, are compared with observed changes over each of five (Forest) or six (Lewis) decades. The upper air diagnostic uses temperature changes at eight levels and a 5° latitudinal resolution, but although giving similar results it adds little due to the larger uncertainties involved.

In the last couple of decades, northern high latitudes have warmed dramatically while the southern high latitudes have warmed very little if any. Forest’s approach will implicitly attribute this to a positive aerosol forcing over that period, in contrast to the negative forcing that would be expected given the increase in aerosol precursor emissions over that time.
Aerosol forcing estimation in the Forest/Lewis method is very stable and depends little on the periods used. Once the statistical methods in the Forest study are corrected, it produces a best estimate for aerosol forcing only 0.1 W/m² more negative using data ending in 1995 – almost two decades ago – as my study reaches using data extended to 2001. Over most of the diagnostic decades the surface temperature of the northern hemisphere was actually lower relative to that of the southern hemisphere than in the climatological (base ) period: the difference did not overtake the start of simulation period level until after 2001, and was particularly low in the decades to 1985 and 1995. So Steven’s objection is misplaced.

This leads to a very small estimate of the climate sensitivity, since if I understand correctly, the method will believe that aerosols were adding to CO2 forcing rather than opposing it as we would normally think based on independent evidence including satellite observations of aerosol forcing.
Steven does not understand correctly. Estimated aerosol forcing in my study is negative, as is usual. Moreover, the forcings used in the MIT model do not include that by Black carbon on snow and ice, which like aerosol forcing is concentrated in the northern hemisphere, and are stated in terms of average levels in the 1980s, since when as Steven says aerosol precursor emissions have risen. Those factors do not bias ECS estimation, but they do mean that my aerosol forcing best estimates need to be restated, adjusting them by about -0.2 W/m², to be comparable to aerosol forcing (ERF) estimates given in AR5. The so-adjusted aerosol forcing best estimates, of -0.5 W/m² using the Lewis diagnostics to 2001, and -0.6 W/m² using the Forest diagnostics to 1995, are well within the range of observationally-based satellite-instrument estimates cited in AR5.

The problem is that this interhemispheric warming difference since the 1980’s is almost certainly not aerosol-driven as the Forest/Lewis approach assumes. It is not fully understood but probably results from circulation changes in the deep ocean, unexpectedly strong ice and cloud feedbacks in the Arctic, meltwater effects around Antarctica, and/or the cooling effect of the ozone hole over Antarctica.
Indeed so, but as explained that has little or no impact on aerosol estimation in the Forest/Lewis studies. Incidentally, similar natural changes, in particular due to the AMO (which appears closely linked to quasi-periodic changes in ocean circulation) very probably accounted for at least part of the opposite changes in interhemispheric temperatures during the two decades up to the mid-1970s, rather than increasing aerosol forcing being responsible for the entire change in that period.

Most of these things are poorly or un-represented in climate models, especially the MIT GCM used by Forest and Lewis, and these models display too little natural decadal variability.
Agreed, but the decadal variability displayed by the MIT GCM is irrelevant. In fact averaging over an ensemble of simulations by it is used so as to reduce model variability. The estimates of decadal and other natural internal variability used in the Forest/Lewis studies come from full 3D AOGCMs. It may well be true that 3D AOGCMs also display too little internal variability, in which case my study’s uncertainty range for ECS may be too narrow. But that is not a reason to think that its ECS best estimate is biased.

It is thus not surprising that GCMs have great difficulty simulating the recently observed decadal swings in warming rate (including the so-called “haitus” period where they overestimate warming, and the previous decade where they typically underestimated it).
Indeed. However, the underlying problem is that GCMs seem to be oversensitive to forcing. GCMs only underestimated warming in the decade prior to the hiatus period if one takes that as starting in 1998, when real-world temperature were greatly boosted by the very exceptional 1997/98 El Nino, which was not included in the model simulations. If you take the hiatus period as starting any later than 1998, the average warming of the CMIP5 GCMs analysed in Forster et al (2013) JGR exceeded that in the real world. The 1991 Mount Pinatubo eruption distorts comparisons on a decadal basis; the twenty year period to the start of the hiatus offers a better comparison. Again, for all periods ending in 1999 onwards, the CMIP5 mean warms faster than the real world.

By implicitly attributing a pattern to aerosol that is probably due to other factors, Forest (and especially Lewis) are underestimating climate sensitivity. Other evidence such as the continued accumulation of heat in the worlds’ oceans is also inconsistent with the hypothesis that the slow warming rate in the last decade or two is due to negative feedback in the system as argued by Lewis.
Completely untrue. The continued accumulation of heat is not only perfectly compatible with a TCR of 1.35°C and ECS being (say) 1.75°C, it is actually implied by it. Surely Steven Sherwood must realise that? Upon substituting in Equation (1) of my guest blog using Equation (2), one obtains the relationship ΔQ = ΔT * F₂ₓ * (1/TCR – 1/ECS). This gives the increase ΔQ in ocean etc heat uptake between the base period (e.g., 1860-79) and the final period (e.g., 1998-2011) of an energy budget estimate as a function of the corresponding increase in global temperature (~0.75°C, the forcing F₂ₓ attributable to a doubling of CO₂ concentration (3.7 W/m²) and the values of TCR and ECS. Slotting in the numbers, this gives ΔQ = 0.75 * 3.7 /(1/1.35 – 1/1.75) = 0.47 W/m². Now, an estimate of ocean heat uptake over 1860-79 of about 0.25 W/m² can be obtained from Gregory et al (2013) GRL. Even discounting that by half to allow for their use of a sensitive model, the implied level of total heat uptake over 1998-2011 is 0.6 W/m², well up with observational estimates.

A more general problem with Lewis’ post is that he dismisses, for fairly aribtrary reasons, every study he disagrees with.
This is arm waving. I give specific reasons for dismissing each model. If Steven thinks any of them are wrong, I invite him to say so and to explain why.

Lewis dismisses climate models because they supposedly can’t simulate clouds properly, ignoring the multiple lines of evidence for positive cloud feedbacks articulated in Chapter 7 of the 2013 WGI IPCC report as well as the myriad studies (including my Nature paper from this year) showing that the models with the greatest problems are those simulating the lower climate sensitivities that Lewis favours, not the higher ones he is trying to discount.
Unfortunately, the “multiple lines of evidence for positive cloud feedbacks articulated in Chapter 7 of the 2013 WGI IPCC report” were not very persuasive to the AR5 scientists. As I wrote in my guest blog, “AR5 (Section 7.2.5.7) discussed attempts to constrain cloud feedback from observable aspects of present-day cloud but concluded that “there is no evidence of a robust link between any of the noted observables and the global feedback”.

Yes, some studies (including Steve Sherwood’s 2014 Nature paper) seem to show that certain specific features of the climate system are on the whole to be better/worse simulated by models that have higher/lower than average sensitivities. But it is a logical fallacy to think that implies higher sensitivity models correctly represent the climate system as a whole or that climate sensitivity is high. Moreover, the model simulations are often compared, not to observations, but to model-based reanalyses.

If we look at all the evidence in a fair and unbiased way, we find that climate sensitivity could still be either low or high, and that it is imperative to better understand the recent climate changes and the factors that drove them.
I have not claimed otherwise. I wrote that I thought it was unlikely – only 17% probability – that ECS (here effective climate sensitivity) exceeded circa 3°C. So I by no means rule out the possibility that it is higher. I entirely agree with Steven about the importance of better understanding climate changes and their causes.

John claims that my recent post is “riddled with errors in fact and framing”. I will let readers form their own judgements on that claim after reading my below responses to John’s points.

1. I suggested a mean planetary imbalance of 0.5 W/m², in line inter alia with the Loeb et al (2012) estimate for 2001-2010, but I wouldn’t argue with 0.6 W/m². Taking the rather longer 1998-2011 period, over which the various observational datasets agree reasonably well on the change in ocean heat content (OHC), reduces the uncertainty in the annualised imbalance. Using the AR5 energy inventory data and uncertainty estimates gives a 5–95% range for the imbalance of 0.59 ± 0.19W/m² over 1998-2011.

We clearly have different views on the ORAS4 OHC reanalysis, but John has not produced any evidence that what I wrote was incorrect.

2. AR5 estimates the change in indirect aerosol forcing from the start of the CMIP5 historical simulations to 2011 at -0.35 W//m² (deducting ERF_ari per the AR5 SOD from ERF_ari+aci). A planetary imbalance of 0.6 W/m² represents 30% of mean 2002-11 forcing per AR5 (about 25% based on estimated changes in both variables since the first few decades of the instrumental period). So allowing for the omission of indirect aerosol forcing in CCSM4, using AR5 best estimates, would reduce its 1.1 W/m² imbalance by ~0.1 W/m², to 1.0 W/m², still well above the ~0.6 W/m² observational estimate. To my mind, this certainly suggests that CCSM4’s ECS is too high, although other explanations are possible.

3. I didn’t suggest that “the CESM1-CAM5 indirect aerosol forcing is too high”. What I wrote was: “The CESM1-CAM5.1 model’s aerosol forcing was diagnosed (Shindell et al, 2013) as strengthening by -0.7 W/m² more from 1850 to 2000 than per AR5′s best estimate.” This relates to total aerosol ERF, not to that from aerosol-radiation interactions (direct forcing) and the sources are as stated. Shindell et al, 2013 diagnosed total aerosol ERF as changing by -1.44 W/m² from 1850 to 2000; the change per AR5’s best estimate was 0.7 W/m² smaller at -0.74 W/m². My point was that CESM1-CAM5.1’s higher-than-AR5-best-estimate aerosol forcing enabled it to match actual warming from the 1920s to the early 2000s despite having a high ECS and TCR. If the model’s aerosol forcing had evolved in line with AR5’s best estimate, it would have simulated unrealistically fast warming.

4. The magnitude of cross-equatorial heat transport is of relevance to climate sensitivity since high sensitivity AOGCMs typically require fairly high aerosol forcing (more negative than per AR5’s best estimate) in order to reproduce the historical record of global surface warming. Since aerosol forcing is concentrated in the northern hemisphere (NH), if a model’s aerosol forcing is higher than the actual level then it would need a larger northwards cross-equatorial heat transport to maintain temperatures in the NH at a realistic level in relation to those in the southern temperature (SH). Atmospheric cross-equatorial heat transport appears to be both fairly modest (southward) and better constrained than that by the ocean, because of its effect on the position of the ITCZ, the inter-hemispheric temperature differential, etc.

It is in any event surprising how similar the ocean cross-equatorial heat transport of almost all CMIP5 models is, perhaps because (as I understand) most of them share a common ancestor ocean model.

I wasn’t suggesting that ocean heat transport is a forcing. My point was that if 0.6 PW too much is transported across the equator that is equivalent, in terms of the rate of energy input, to an excessive inter-hemispheric forcing differential of 4.8 W/m² (more accurately, 4.7 W/m²).

I wouldn’t dispute that NCAR CESM1-CAM5 is, according a quite a few metrics, one of the best performing CGMs currently available. But that does not, IMO, imply that its ECS and/or TCR are realistic. They might be accurate, but the observational evidence suggests that TCR at least – which is better constrained by observations than ECS – is unlikely to be as high as 2.3°C (e.g., Otto et al, 2103, Energy budget constraints on climate response. Nature Geoscience, 6, 415–416).

Bart

Thank you for your latest, very relevant, questions. My answers are as follows.

1. You contrasted my statement, that over the period 1950-2013 CCSM4′s trend in simulated global surface temperature was nearly 85% higher than per HadCRUT4, with John’s statement that the decadal trends as simulated by the Community Earth System Model (CESM1-CAM5) of the National Centre for Atmospheric Research (NCAR) track quite closely with those derived from observations, referring to fig 2 in John’s guest blog.

These statements are not in fact contradictory. They relate to different model versions, and John’s statement relates to separate decadal trends in surface temperature, not to a single multidecadal trend.

My statement was based on a version of the CCSM4’s Historical/RCP4.5 simulation from the CMIP5 archive. It shows a linear trend in GMST of 0.197°C/decade over 1950-2013. That is 84% higher than the trend over the same period per HadCRUT4 of 0.107°C/decade.

A chart comparing surface temperature changes over 1850-2100 on the RCP8.5 scenario as simulated by CCSM4 and CESM1-CAM5 is shown in Hurrell et al (2013). Although CESM1-CAM5 has a higher ECS and TCR than CCSM4, its very highly negative aerosol forcing leads to its simulated temperature rise from 1850 not overtaking CCSM4’s until nearly the end of this century. Meehl et al (2013) give a more comprehensive comparison of projections by the two NCAR models.

2. This brings me on to point 5 of Bart’s summary, my assertion that NCAR CESM1-CAM5 model matches global actual warming reasonably well because the aerosol forcing was -0.7 W/m² more negative from 1850 to 2000 than the AR5′s best estimate (Shindell et al, 2013). Bart asks what I mean by ‘global actual warming’, and states that if I mean ‘global surface warming’ than my point 5 assertion seems to contradict points 2 and 3.

My assertion highlighted in Bart’s point 5 did refer to global surface warming. However, it related to the CESM1-CAM5 model, whereas my statements highlighted in Bart’s points 2 and 3 related to the CCSM4 model. These two model variants behave differently. CCSM4 has a lower ECS (2.9°C) and TCR (1.8°C) than CESM1-CAM5, which seems to have an ECS of 4.1°C and a TCR of 2.3°C. But CCSM4 does not simulate indirect aerosol forcing (aerosol-cloud interactions: ERF_aci). John says this means that its simulations in the CMIP5 archive shouldn’t be expected to replicate observed temperature records – or by implication future temperatures. These simulations do, however, form part of the ensemble used by the IPCC for projecting future temperatures, which is used for many purposes.

Although CCSM4 does not include indirect aerosol forcing, according to Lamarque et al (2011) its change in direct aerosol forcing from 1850-2000 was -0.81 W/m², in itself slightly higher that AR5’s best estimate of the change in total (direct + indirect) aerosol forcing over that period of -0.74 W/m².

Moreover, although Shindell et al (2013) diagnosed the 1850-2000 change in total aerosol forcing as -1.44 W/m² in CESM1-CAM5.1, Gettelman et al. (2012) note a total indirect effect of -1.3W/m² in CAM5 in 2000 compared to 1850. Although Gettelman et al. did not derive total aerosol forcing in CAM5, adding on to their -1.3W/m² indirect forcing the -0.8 W/m² direct forcing reported by Lamarque et al (2011) for CCSM4 would give a figure of -2.1W/m², much higher than Shindell diagnosed and outside the 5-95% uncertainty range given in AR5 despite that relating to changes since 1750.

3. Finally, Bart queries why I say that ‘observational evidence for cloud feedback being positive rather than negative is lacking’, pointing out that Steven Sherwood asserts that I have ignored ’the multiple lines of evidence for positive cloud feedbacks articulated in Chapter 7 of AR5′. The answer is simple. My concern is with the global level of overall cloud feedback and the observational evidence relating to it. Section 7.2.5.7 of AR5 “Observational constraints on Global Cloud Feedback’ deals with precisely this, discussing various approaches and citing many studies.

The first approach Section 7.2.5.7 discusses is to seek observable aspects of present-day cloud behaviour that reveal cloud feedback or some component thereof. Its conclusion: ‘In summary, there is no evidence of a robust link between any of the noted observables and the global feedback’; all it can point to is some apparent connections that are being studied further.

Section 7.2.5.7 then discusses attempts to derive global climate sensitivity from interannual relationships between global mean observations of TOA radiation and surface temperature, but notes studies contradicting the basic assumption of these attempts. It goes on to note all sorts of problems in finding acceptable cloud-response derived observational constraints on climate sensitivity, ending by stating ‘These sensitivities highlight the challenges facing any attempt to infer long-term cloud feedbacks from simple data analyses.’

References
Gettelman, A., H. and Coauthors, 2010: Global simulations of ice nucleation and ice supersaturation with an improved cloud scheme in the community atmosphere model. J. Geophys. Res., 115, D18216, doi:10.1029/2009JD013797.
Hurrell, J., and Coauthors, 2013: The Community Earth System Model: A Framework for Collaborative Research, Bull. Amer. Meteor. Soc., doi:
http://dx.doi.org/10.1175/BAMSWDW12W00121.1.
Lamarque, J.-F., and coauthors, 2011: Global and regional evolution of short-lived radiatively-active gases and aerosols in the representative concentration pathways. Climatic Change, 109, 191–212, doi:10.1007/s10584-011-0155-0.
Meehl GA et al (2013) Climate Change Projections in CESM1(CAM5) Compared to CCSM4. J Clim 26, 6287-6308
Shindell, D.T. et al, 2013. Radiative forcing in the ACCMIP historical and future climate simulations, Atmos. Chem. Phys., 13, 2939-2974

I’d like to come back to something in Nic’s earlier comments, which is also relevant to this recent comment of Chris Colose. Nic, you seem to acknowledge the possibility of a nonlinearity, or perhaps equivalently, that the effective sensitivity under the moderate recent warming, is different to the equilibrium result. However, my understanding is that your calculation ignores this. Is this a fair summary of your position? Do you think the effect is small enough to ignore, or are you omitting it in principle (ie, only attempting to estimate the effective sensitivity)?

I can see the source of the discrepancy regarding CCSM4 forcing in the Lamarque et al. reference. The -0.81 figure quoted by Nic Lewis refers to clear-sky forcing. This is not the same as the all-sky forcing being discussed by others because it masks out cloudy areas from the analysis, and therefore doesn’t represent a global average. For example, Bellouin et al. 2008 found clear-sky aerosol forcing to be -1.3 W/m2, and used a simple translation to obtain an all-sky forcing of -0.65 W/m2, 50% of the clear-sky figure.

Dear Nic,

Before you posted your last comment I asked John for some clarification on his last comment. In this mail he wrote the following, which is relevant, especially regarding your claim high negative aerosol forcing in CMIP5 models is necessary to match the observed global warming over the instrumental period. John wrote:

Given the uncertainties in observations (e.g. ocean heat content) and arising from aerosol interactions, it is an open question as to what the “right value” [of the total aerosol forcing] is. There is considerable uncertainty. The notion that the cooling needs to be excessively “high” to match observations is not reality. The simple fact is that simulations using aerosol forcing and indirect effects within our observational range, when compared with the observational record of surface temperature and ocean heat content, do not constrain climate sensitivity to Nic’s values. Despite Nic’s protests, the CESM1-CAM5 is a very tenable simulation. I agree that this basic fact is problematic for reconciling his values with a vast body of work.

I invite participants to read more about it at:

Meehl, Gerald A., and Coauthors, 2013: Climate Change Projections in CESM1(CAM5) Compared to CCSM4. J. Climate, 26, 6287–6308.
doi: http://dx.doi.org/10.1175/JCLI-D-12-00572.1

Hurrell, James W., et al. “THE COMMUNITY EARTH SYSTEM MODEL.”Bulletin of the American Meteorological Society 94.9 (2013).

Bart.

I am responding now to James’ query about effective climate sensitivity vs equilibrium climate sensitivity, and to the related part of Chris Colose’s comment.

My Journal of Climate objective Bayesian study did in principle estimate equilibrium sensitivity, since the settings of the parameter used to control sensitivity in the MIT 2D GCM were calibrated to equilibrium sensitivity. But my energy budget estimates based on AR5 forcing and heat uptake data do, as James says, estimate effective sensitivity and ignore the difference between that and equilibrium sensitivity.

The relationship between effective and equilibrium sensitivity varies between AOGCMs. The true equilibrium climate sensitivity is not known for most coupled CMIP5 models, and is usually taken from a ‘Gregory’ plot – the regression, typically for 140 years, of TOA radiative imbalance against GMST change following an abrupt 2x, or usually 4x, step increase in CO₂ concentration. One way of comparing effective and equilibrium sensitivity is to look at a model’s Gregory plot. If the regression line passes close to the initial point – the response is linear – then there is no indication of a material difference between effective and equilibrium sensitivity. Of the fifteen CMIP5 models for which Gregory plots are given in Andrews et al (2012), seven show almost perfectly linear behaviour, four show strongly non-linear behaviour, and four show fairly mild non-linearity. Virtually all the non-linearity is in the first few years; there is little evidence of sensitivity changing with the magnitude of forcing, at least up to a 4x increase in CO₂ concentration.

From a practical point of view, it more useful to know whether TCR, if correctly estimated from warming over the instrumental period (most of which has been in response to forcing over the last ~60 years), is likely to be a good guide to warming from now until the final decades of this century on scenarios with various changes in forcing. Allowance needs to be made for emerging warming-in-the-pipeline from past forcing when making such a TCR-based projection. What CMIP5 models suggest about the reasonableness of this method can be judged from how much warming during the second half of a 140 year model simulation in which CO₂ rises by 1% p.a. exceeds that in the first half. The below plot, Figure 1 from Tomassini et al (2013) shows the results of such an experiment for twelve CMIP5 models.

The amount of warming-in-the-pipeline after 70 years that will emerge over the second 70 years varies between models, but is probably ~0.4°C on average. About half the models show evidence of some increase in warming between the first and second 70 years in excess of 0.4°C. However, on average CMIP5 models show only a small degree of nonlinearity. Interestingly, CESM1-CAM5, although it warms faster than CCSM4, shows less evidence of non-linearity.

Who knows whether the real world will behave like any of the models? I think the IPCC scientists had it about right when they wrote in AR5 that the climate sensitivity measuring the climate feedbacks of the Earth system today “may be slightly different from the sensitivity of the Earth in a much warmer state on timescales of millennia”. Certainly, based on the results shown in Tomassini et al (2013) and the Gregory plots in Andrews et al (2012) it seems reasonable to ignore the difference between effective and equilibrium climate sensitivity when making projections over the rest of this century, at least.

Chris Colose referred to the Rose, Armour et al (2014) paper. Whilst interesting, it is based on artificial aqua-planet simulations with a mixed layer ocean. It is easier to relate time-varying effective sensitivity to the behaviour illustrated in the predecessor paper, Armour et al (2013), as that involves simulation by a CMIP5 model – actually CCSM4 – of the actual Earth, with a realistic ocean. In CCSM4, effective sensitivity increases over time, taking hundreds of years to approach equilibrium sensitivity. In simplified terms, the reason appears to be that ocean heat uptake (OHU) is stronger and more persistent – delaying the surface temperature rise – at latitudes where local sensitivity is higher. As the ocean in these regions eventually warms up then, because of the higher regional sensitivity, the surface temperature there has to rise further than the average elsewhere to compensate for the fall off in OHU. (This ignores important factors such as heat transport, and any variations in local feedbacks that occur as the pattern of OHU evolves.)

The prime region where this mechanism applies appears to be the Southern ocean, which at circa 50 degrees latitude absorbs heat particularly strongly and deeply. CCSM4 has a very high local sensitivity (very low climate feedback) at that latitude, as shown by the thick grey line in Figure 4 in Armour et al (2013):

However, the latitudinal pattern of feedbacks in CCSM4 is very different from most other CMIP5 models, as shown by Figure 3.f of Zelinka & Hartmann (2012), the thick black line being the multimodel mean:

The Zelinka & Hartmann graph is based on global rather than local temperature changes, so feedback should be scaled down towards the poles (north in particular). Nevertheless, the latitudinal pattern of feedback strength in CCSM4 per Armour et al is pretty much the opposite of that of most other CMIP5 models, which inter alia appear to have a low local sensitivity around 50 degrees south. That does not imply CCSM4’s feedback pattern is less realistic than in other models. All models may have the feedback pattern materially wrong. But it does seem that Armour’s reasoning for why equilibrium climate sensitivity can be expected significantly to exceed effective sensitivity is very much model-specific.

References
Andrews, T., J. M. Gregory, M. J. Webb, and K. E. Taylor, 2012. Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere-ocean climate models, Geophys. Res. Lett., 39, doi:10.1029/2012GL051607.
Armour, K. C., C. M. Bitz, and G. H. Roe (2013), Time-varying climate sensitivity from regional feedbacks, J. Clim., 26, 4518–4534.
Rose, B. E. J., K. C. Armour, D. S. Battisti, N. Feldl, and D. D. B. Koll (2014), The dependence of transient climate sensitivity and radiative feedbacks on the spatial pattern of ocean heat uptake, Geophys. Res. Lett.,
Tomassini, L et al, 2013: The respective roles of surface temperature driven feedbacks and tropospheric adjustment to CO2 in CMIP5 transient climate simulations. Clim Dyn, DOI 10.1007/s00382-013-1682-3.
Zelinka, M. D. and D. L. Hartmann, 2012: Climate Feedbacks and Their Implications for Poleward Energy Flux changes in a warming climate. Journal of Climate, 25, 608–624.

Can someone please explain the concept of “back radiation”, i.e. electromagnetic radiation (power transfer) in a direction of more intense electromagnetic field strength, at any frequency? Such concept is in opposition to all of Jimmy Maxwell’s equations. Such concept is also in defiance of Gus Kirchhoff’s laws of thermal radiation.
In addition such flux, (power transfer) has never been observed, detected, or measured. Where does such fantasy originate and why?

Dear Nic, John and James,

Let’s try to round off the discussion on aerosols and models.

For me, the crucial claim made by Nic in one of is his last posts is:

‘More generally, higher negative aerosol forcing in CMIP5 models compared to AR5′s best estimates seems to be the most important reason why many CMIP5 models have, until the last decade or so, broadly matched the observed global warming over the instrumental period.’

John’s reply to that was:

‘The notion that the cooling needs to be excessively “high” to match observations is not reality. The simple fact is that simulations using aerosol forcing and indirect effects within our observational range, when compared with the observational record of surface temperature and ocean heat content, do not constrain climate sensitivity to Nic’s values.’

@Nic: It is not clear to me how you draw this general conclusion. I went through several studies you referred to and there is one study – Shindell (2013) – that explicitly compares 7 models (including CESM1-CAM5.1) from CMIP 5 with respect to total aerosol forcing, summarized in figure 22 as follows:

This figure seems to confirm your claim that some (not many!) CMIP-5 models have higher negative aerosol forcing compared to AR5’s best estimate of -0.9 W/m2. However, the figure also shows that: “…there is an anti-correlation between historical aerosol RF and equilibrium climate sensitivity.”, which, in my eyes, seem to contradict the claim you make and seem to indicate there are (also) other reasons why these 7 CMIP5 models match observed global warming.

@John: it would be very helpful to me if you could elaborate a bit more on the interesting claim you make.

@James: I would like to ask to give your view on this matter.

Bart.

Reference
Shindell, D. T. et al, 2013. Radiative forcing in the ACCMIP historical and future climate simulations. Atmos. Chem. Phys. 13, 2939–2974

Dear Nic,

Just a short questions for clarification:

On may 15 you write: “If aerosol was known to have a current ERF of -0.9 W/m², in line with AR5′s best estimate…”
On may 21: “AR5′s best estimate of the change in total (direct + indirect) aerosol forcing over that period of -0.74 W/m².”
On may 27: “the AR5 best estimate for the increase in Aerosol ERF over …1850 to 2000 is -0.75 W/m²”
What explains the difference in numbers? Different periods?

Bart.

A few general thoughts on aerosol forcing:

1) Backing up what I believe is Nic Lewis’ general theme, aerosol forcing in some models, and in AR5 chapter7/8, is a substantial contributor to total net anthropogenic forcing. There is also a large spread of net aerosol forcing across the CMIP5 model ensemble (something like -0.3 to -1.6 W/m2, about 10 – 60% of net non-aerosol forcing). All else being equal a greater negative net aerosol forcing will reduce the amount of warming produced by the model, so aerosol forcing can be considered a major contributor to the spread of simulated historical warming amounts in the CMIP5 ensemble. Another major contributor is sensitivity. If we can get a decent idea of the correct aerosol forcing that should lead to narrowing of uncertainty on sensitivity.

2) How seriously should we take the best estimate for aerosol forcing given in AR5? I think it’s worth stating that the confidence level for forcing estimates of aerosol-cloud interactions RFaci and ERFaci are given as ‘low’ and ‘very low’. DirectRF or RFari was elevated to ‘high’ confidence though the uncertainty range expanded compared to AR4, and ERFari was given as ‘low’.

There is of course evidence which points to a total net aerosol forcing of about -0.9W/m2, but given these confidence levels the word “about” should be a major part of interpreting such a statement. I don’t think it’s realistic to regard -1.0, -1.1 or perhaps even -1.2W/m2, for example, as much less likely than -0.9, or to definitively discount larger (more negative) aerosol forcing as too high. That’s at least my reading of the relevant AR5 chapters taken as a whole.

3) Model (and observational, for that matter) aerosol forcing estimates can be a minefield, as earlier portions of this discussion can attest. One issue relevant to recent discussion here is timescale.

Modelling groups involved with the ACCMIP project submitted a set of time slice simulations representing anthropogenic aerosol emissions at various moments. They used the difference between the 2000 and 1850 time slice simulations to represent the aerosol forcing of the models. Since the IPCC AR5 forcing estimate uses 1750 as base year an adjustment is required for a like-for-like comparison.

Numbers for CMIP5 models not involved in ACCMIP (which is the majority) tend to be calculated by comparison between sstClimAerosol and sstClim simulations. sstClimAerosol is equivalent to the ACCMIP 2000 experiment, but sstClim is not equivalent to ACCMIP 1850 because it doesn’t include any anthropogenic aerosol emissions at all. That means the result represents the absolute anthropogenic aerosol forcing, as opposed to being relative to a particular moment.

Relevant to Bart’s recent question the different values given by Nic Lewis are indeed referencing different periods, -0.75 for 1850-present and -0.9 for 1750-present, according to the forcing profile presented in AR5 Chapter 8. As described above it is correct to use the 1850 figure to compare with ACCMIP numbers, but it is not correct for comparing with numbers for all other models. If anything the AR5 estimate requires a small adjustment the other way for comparison. Unfortunately AR5 chapter 7 makes the same error/confusion by listing ACCMIP and sstClimAerosol-sstClim results in the same table under the banner of 1850-2000 forcing.

—————————————-
One minor point of pedantry:

There are actually 3 versions of the GISS-E2-R model included in CMIP5 and aerosol setup/forcing is the key difference between the versions. It’s not entirely clear which, if any, of these was used in the ACCMIP submissions to produce the stated -1.1W/m2 forcing but if I had to guess it would be version 2, which produces about 0.7ºC warming in the historical run.

Dear Bart,
You query my different figures for the AR5 best estimate of aerosol forcing. As you suspect, the reason is mainly different periods. The current ERF of -0.9 W/m² is for 2011, the most recent year for which AR5 gives forcing data, relative to 1750, representing preindustrial conditions, where all the AR5 forcing data are set at zero.
The period I referred to on 21 May was 1850 to 2000, the same as for the figure I was comparing it with. Between those years AR5’s best estimate of aerosol ERF changed by -0.744 W/m², which I rounded to -0.74 W/m². Early today, I instead rounded the same 1850 to 2000 figure to -0.75 W/m², which looks a little less unrealistically precise than -0.74 W/m².
Nic

This enlightening dialogue has prompted me to offer first a specific and then a general comment.

First, I’m impressed with the call by Nic Lewis and John Fasullo for more effort focused on reducing the broad uncertainties surrounding aerosol forcing. Better accuracy should be most critical for TCR estimates based on regressing temperature change on forcing change. Aerosol forcing is of course also relevant to equilibrium sensitivity estimates, but these depend on many additional variables that are also uncertain. TCR is of particular relevance to changes expected over the remainder of this century (but see below).

Estimating the equilibrium temperature change resulting from a CO2 doubling most appropriately incorporates all relevant feedbacks. These include not only short term feedbacks such as changes in water vapor, lapse rate, clouds, albedo, and the modifying effects of varying atmospheric and ocean circulation patterns, but also longer term changes in ice sheets, dust/vegetation, and the carbon cycle. A strong dichotomy is sometimes assumed between the short and long term responses, but it is likely that every feedback follows its own time course, with no absolute dividing line. Curiously, these estimates have been termed “Earth System Sensitivity” rather than “equilibrium climate sensitivity” (ECS), with the term ECS misapplied, in my view, to three other types of sensitivity estimation that exclude the longer term responses from the feedback calculations. These three types may be of more immediate practical importance, but they are not true equilibrium estimates. I’ll refer to them as EFS, PCS, and FCS. The term “EFS” may already be familiar, but PCS and FCS are terms of convenience I’ve conjured up for this discussion, and may not have been used before in this context.

“Effective climate sensitivity” (EFS) attempts to derive a value for equilibrium temperature change from observations made under non-equilibrium conditions, based on an energy balance model relating changes in planetary energy imbalance N to those in forcing F and radiative restoring (the increase in heat loss to space from a surface temperature rise): N = F – λ ΔT, where the feedback parameter λ quantities the rate of increased heat loss per K warming. At equilibrium (N = 0), the temperature change is given as F/ λ, which for doubled CO2 is about 3.7/ λ. The equation is well known, but my point here is that it asks a specific question – If λ is constant, so that λ calculated from non-equilibrium data is the same as λ at equilibrium, what would the equilibrium temperature change be? In other words, EFS is a hypothesis about the consequences of a constant λ. Typical values have been in the range of 2 C. I should add that the range is broad due to uncertainties about the forcings, and broad uncertainty is also true for the values of PCS and FCS discussed below, but I prefer to leave that challenge to a different discussion.

PFS (my abbreviation for paleoclimate sensitivity) asks a different question. If the forcings from an earlier era (typically the LGM) can be used as surrogates for forcing due to doubled CO2, what temperature change would that allow us to predict for doubled CO2? PFS is a hypothesis about the relevance of changes under a different climate involving different forcings to our current climate forced by CO2. Typical values are closer to 3 C, again with substantial uncertainty.

FCS is my convenience term for “Feedback-based Climate Sensitivity” derived from “bottom up” models incorporating the short term feedbacks I cited above. It hypothesizes that these accurately capture the entirely of climate behavior (minus the long term feedbacks) in response to CO2 forcing, despite the known weaknesses of current GCMs. Typical values also tend to center around 3 C.

If I were to attempt a single assertion to illustrate the essence of what I’m describing, it would be that each one of these estimates, despite differing among themselves, might in theory be largely correct, because they each estimate something different – i.e., they each test a different hypothesis, which in none of the cases actually involves the true equilibrium response that Earth System Sensitivity aims for.

The most apparent disparity is between EFS and the other two metrics. Inaccurate forcing estimates may play a role in the disparity, but there is also reason to conclude that EFS, in hypothesizing a constant λ, is not accurately representing the real world evolution of climate responses to an imposed forcing. A number of groups have reported model-based evidence for the variation of λ with time and temperature in a downward direction, signifying an increasing value calculated for equilibrium temperature change. The very recent article by Rose et al that Chris Colose mentioned above suggests that it may be impossible even to evaluate the relationship between EFS and the other metrics on the basis of current evidence – transient sensitivity and ocean heat uptake. I don’t presume to judge the weight of evidence. Rather, I would suggest that since neither EFS nor PCS nor FCS is a true ECS and since none of them is necessarily addressing the same hypothesis as the others, their differences should be acknowledged. Specifically, a logical default position for entities that may not be identical would be, I suggest, that we not call them all by the same name, since that prejudges the issue.

This seems particularly relevant to recent literature, which increasingly has looked at EFS. The values are lower than values estimated for PCS and FCS, and this has led some to suggest that the latter two estimates are wrong. That may or may not be the case, but if it’s a case to be made, it should be done explicitly based on evidence, and not implicitly through the use of identical names for the different estimates.

Thank you, John, for responding to my explanation regarding Schwartz (2012). I will comment on that before responding to your other comments.

Schwartz (2012)
You exaggerate by claiming that I established a basis for excluding “some” of the forcing datasets used by Steve Schwartz. I only did so for a single forcing dataset (MIROC), and for ECS estimation by one method only. Steve himself had already excluded another forcing dataset (Myhre) for both ECS and TCR estimation, and had excluded the same forcing dataset as I did for ECS estimation by the other method.

You claim that forcing and surface temperature change need not correlate strongly at all. But Steve’s study is based on a simple model in which these variables do exhibit linear proportionality. So you are in effect rejecting the basis of Steve’s paper. Indeed, I wonder if you are actually rejecting the entire basis of estimating TCR and/or (effective) climate sensitivity from the warming observed over the instrumental period. That would be an extreme position and not, I hope, one that many climate scientists would support.

Contrary to what you suggest, Steve does find that “a rather robust linear proportionality is exhibited for most of the forcing data sets between surface temperature and forcing, but with different slopes”, although he finds that not to be so for the Myhre forcing data set. For the MIROC dataset he finds a reasonably strong relationship between surface temperature and forcing (R² of 0.47) when the regression is not constrained to pass through the origin, but (unlike for the other datasets, excluding Myhre) a much weaker relationship (R² of 0.29) when it is so constrained.

Steve wrote “The fraction of the variance in the temperature data accounted for by the regression forced through the origin is over 50% for four of the six forcing data sets. For most of the data sets, the intercept is near zero; constraining the regression line to pass through the origin results in little decrease in the fraction of the variance in the data accounted for by the regression”. He goes on to say that “A high correlation with zero intercept, that is, temperature anomaly proportional to forcing, is consistent with a planetary heating rate N that is likewise proportional to the temperature increase.”

Since for the MIROC dataset the correlation with zero intercept is low, in its case the relationship of temperature with forcing does not support the planetary heating rate being proportional to the temperature increase. Yet the assumption that the heating rate is so proportional is used to estimate ECS (although not TCR) from the MIROC dataset. The combination of the low correlation with zero intercept using the MIROC forcing dataset and the indication that that dataset is not consistent with the method used to derive ECS from it seems to me valid grounds for excluding that estimate. I note that in, relation to the MIROC forcing dataset, Steve wrote that the departure from linear proportionality, together with the observations of increase in temperature and planetary heating rate, are inconsistent with an energy balance model for which the change in net emitted irradiance at the top of the atmosphere is proportional to the increase in surface temperature – the model that underlies his study.

Contrary to your claim, my reasoning – which is close to Steve’s – is not circular. And it has nothing to do with bias – the basis for rejecting a forcing dataset is not related to whether the ECS estimate it produces is high or low. You might contend – although I would not – that the linear proportionality assumption made by Steve between changes in forcing, surface temperature and planetary heat uptake is unjustified even as an approximation over periods of under a century. But, having made that assumption, I think it is right to follow it through. Nevertheless, I don’t think a multiple-forcing-dataset regression approach is the best way to estimate TCR and ECS from observed warming over the instrumental period. As I wrote, the 1.1–3.1 K range for ECS given by Steve’s study if the MIROC dataset is excluded does not sample all the uncertainty in forcing, temperature change and heat uptake rates. I disregarded that range in my guest blog (and in the Lewis/Crok report). But if, as you seem to do, you reject the simple proportionality model underlying Steve’s study then you should certainly not conclude – as you do – that his uncertainty range stands.

As you say, internal variability affects the relationship between changes in surface temperature and forcing. There are also substantial uncertainties in forcing, especially aerosol forcing. Long AOGCM control runs are very useful for providing estimates of internal variability, in ocean heat uptake as well as in surface and atmospheric temperatures. However, even if they simulate multidecadal internal variability well (including, implicitly, in forcing as well as in ocean–atmosphere heat interchange), they cannot be expected to match its actual phasing. Therefore, estimates of ECS and/or TCR using temperature observations over the instrumental period are likely to be biased up or down if they span a period over which multidecadal internal variability (in particular, the AMO) has a significant positive or negative influence.

GCM ensembles can certainly be used as a surrogate for uncertainty in forcing, as was done in Otto et al (2013). But I think using the AR5 uncertainty distributions for forcings, now that they are available, is much preferable.

Cloud feedback
You query what negative feedback I envision that might not be included in any model physics. I do not go along with attempts to reverse the burden of proof. When the results of a model that is known to be imperfect disagree with observational evidence, the scientific default position is that the model needs to be modified. If the modellers claim that their model is correct and observational evidence is at fault then it is incumbent on them to prove so. It is not up to someone who accepts the observational evidence that the model is not a good representation of the real world to show where and how it misrepresents the real world.

You say that “On clouds, you seem to ignore the vast body of work aimed at bridging the scale separation between GCM and microphysical scales.” Such work is indeed valuable. However, the multi-authored Zhang et al (2013) paper giving results for low cloud feedbacks from the first phase of the international CGILS project, whilst interesting, inter alia concluded that “the relevance of CGILS results to cloud feedbacks in GCMs and in real-world climate changes is not clear yet. In a preliminary comparison to cloud feedbacks in four GCMs at the three locations, SCMs [single column models] results were uncorrelated to those simulated by the parent GCM”. If ultimately it proves to be the case that cloud feedback is positive rather than negative, then so be it. But there is a long way to go before cloud feedbacks are fully understood and correctly represented in GCMs. Additionally, as Figure 3 of my guest blog showed, GCMs have severe biases as to cloud extent.

It is remarkable how much GCM modelling of water vapour and cloud water content varies, particularly in the upper troposphere (UT). Per Jiang et al (2012), the modelled mean CWCs [cloud water contents] over tropical oceans range from ~0.03x to ~15x the observations in the UT and from 0.4x to 2x the observations in the lower/mid-troposphere (L/MT). Modelled water vapour over tropical oceans was within 10% of the observations in the L/MT, but mean values ranged from ~0.01x to 2x the observations in the UT. Moreover, Figure 6 of Jiang et al (2012) shows that all CMIP5 models analysed have specific humidity levels above the observational uncertainty range at pressure levels between ~150 hPa and ~250 hPa in mid (30°-60°) and high latitudes, as do all but HadGEM2, CNRM-CM5 and one other model in the tropics. For global cloud water content, many models simulate a level outside the observational uncertainty range above ~200 hPa, whilst NCAR-CAM5 is at or below the observational lower bound almost everywhere save near the surface – well below it between ~350 hPa and ~600 hPa.

Su et al (2014)
You mention the recent Su study. I read this when it came out, and thought it quite interesting. However, it seems odd that its metrics based on relative humidity profile in the tropics and sub-tropics rank the sensitive UK Met Office’s HadGEM2-ES model poorly. In the Jiang et al (2012) study, that model’s overall performance ranking was second only to the low sensitivity NCC NorESM model. A contact of mine at the UK Met Office who is knowledgeable about this area was unconvinced by the Su paper.

In Figure 10 of Su et al (2014), six high sensitivity models were placed within or adjacent to the boxes favoured by observational evidence in both performance metrics. For one of these models (NCAR CAM5) I do not have historical/RCP4.5 global temperature time series. The other five models (CSIRO Mk3.6, CanESM2, GFDL-CM3, MIROC-ESM and MPI-ESM-LR) simulated global warming over 1979-2013 with trends in the range 0.19–0.39°C/decade, averaging 0.295°C/decade. That is nearly double the observed HadCRUT4 trend of 0.155°C/decade. Moreover, 1979-2013 was a period over which the AMO exhibited a considerable warming influence on global temperature (Zhou & Tung, 2013), and uncertainty in the change in aerosol forcing was relatively small. However well they score on Su’s performance metrics, these high sensitivity models have badly failed the acid test of simulating global warming over a 35 year period.

References
Jiang, J. H., et al., 2012. Evaluation of cloud and water vapor simulations in CMIP5 climate models using NASA “A-Train” satellite observations, J. Geophys. Res., 117, D14105, doi:10.1029/2011JD017237.
Otto, A., F. E. L. Otto, O. Boucher, J. Church, G. Hegerl, P. M. Forster, N. P. Gillett, J. Gregory, G. C. Johnson, R. Knutti, N. Lewis, U. Lohmann, J. Marotzke, G. Myhre, D. Shindell, B Stevens and M. R. Allen, 2013: Energy budget constraints on climate response. Nature Geoscience, 6, 415–416.
Schwartz, Stephen E., 2012. Determination of Earth’s transient and equilibrium climate sensitivities from observations over the twentieth century: strong dependence on assumed forcing. Surveys in geophysics 33.3-4: 745-777.
Su, H., J. H. Jiang, C. Zhai, T. J. Shen, J. D. Neelin, G. L. Stephens, and Y. L. Yung (2014),Weakening and strengthening structures in the Hadley Circulation change under global warming and implications for cloud response and climate sensitivity, J. Geophys. Res. Atmos., 119, doi:10.1002/2014JD021642.
Zhang, M., et al. “CGILS: Results from the first phase of an international project to understand the physical mechanisms of low cloud feedbacks in single column models.” Journal of Advances in Modeling Earth Systems 5.4 (2013): 826-842.
Zhou, Jiansong, and Ka-Kit Tung. “Deducing Multidecadal Anthropogenic Global Warming Trends Using Multiple Regression Analysis.” Journal of the Atmospheric Sciences 70.1 (2013).

I’d like to respond to the most recent public comments, by Paul S and Fred Moolten, which raise some good points.

Dealing first with Paul’s comments, I agree that AR5 does not imply aerosol forcing levels moderately different from 0.9 W/m² are much less likely than that level. I view the probability density function (PDF) given for aerosol forcing as intended to represent the uncertainty, with ‘low confidence’ being reflected in the very wide PDF, in accordance with the Bayesian probabilistic approach used. Figure 8.16 of AR5 shows that the aerosol forcing PDF level remains above 70% of its peak value from 1.2 W/m² to 0.3 W/m².

On the basis of the AR5 uncertainty distribution, one can’t rule out any of the CMIP5 models’ aerosol forcings as definitely too high – nor as too low even for models that only include direct aerosol forcing. However, it should be borne in mind that the AR5 aerosol estimate, particularly its long negative tail, is influenced by aerosol forcing in CMIP5 and other models. The means for the model and satellite-based estimates used in formulating AR5’s aerosol uncertainty range were respectively 1.28 and 0.78 W/m².

The ‘likely’ (17-83%) ranges of circa 1.2–3.0°C for effective climate sensitivity and 1.0–2.0°C for TCR that I gave in my guest blog reflect, inter alia, the full AR5 uncertainty distributions for aerosol and other forcings.

Regarding Paul’s point about the aerosol forcing reference point for non-ACCMIP CMIP5 models, I have been unable to locate aerosol forcing estimates for most such models. Perhaps Paul can point to where estimates using the method he describes are to be found for the relevant models? For all the CMIP5 models included in my chart showing Historical warming vs Aerosol ERF, I believe the ACCMIP protocol with 1850 as the reference was used.

Paul’s point about GISS-E2-R is a good one, and rather worrying. I would have expected GISS to use the same version (1?) for ACCMIP as was used for the primary CMIP5 results, but he may well be right about it being version 2. Certainly, warming of 0.7°C in the Historical run would bring that model much closer to a best-fit line in my chart showing Historical warming vs Aerosol ERF.

Turning to Fred’s comments, I agree that the acronym ECS is, confusingly, used (in AR5 as well as by myself and others) to cover a range of meanings. IMO, the ECS concept is of most relevance for how global warming will develop over the next century or two. Projecting such warming requires incorporation of the ocean’s behaviour over that period, but not that of ice sheets and other slow components of the climate system. Apart from not being concerned with multicentennial behaviour, that corresponds to the IPCC definition of equilibrium climate sensitivity, which does not represent full equilibrium. As Fred says, there are a range of different timescales depending on the feedback. But atmospheric feedbacks are fast and the ocean can be modelled.

Although a few studies have emphasised evolution in the climate feedback parameter λ over multidecadal or even centennial timescales, the Gregory plots in Andrews et al (2012) show that, where CMIP5 models exhibit a nonlinear relationship between surface temperature change and radiative imbalance after a step quadrupling of CO₂, they mainly do so only over the first few years of the 150 year simulation. That suggests to me that what is involved is more likely to do with non-surface-temperature-dependent atmospheric etc. adjustments to CO₂ forcing, as discussed in Williams, Ingram and Gregory (2008): Time variation of Effective Climate Sensitivity in GCMs and/or to other relatively fast processes.

Whilst effective climate sensitivity is an imperfect measure, I don’t think there is reliable evidence that using it will lead to estimates for global warming over the rest of this century, and probably next century, that are materially inaccurate. Inaccuracy in estimating carbon cycle feedbacks is of much greater significance in projecting warming from different emission pathways. In the RCP8.5 scenario, carbon cycle feedbacks add about 60% to the increase in atmospheric CO2 concentration over 2012-2100. But it is unclear that there is much observational evidence for any carbon cycle feedback at all: Gloor et al 2010. What can be learned about carbon cycle climate feedbacks from the CO2 airborne fraction.

I thank Bart for his summary and will just offer a few clarifications.

On the observations vs models point, I certainly think it desirable to minimise dependence on complex numerical models so far as possible, although it is often necessary to rely on them to some extent. In science, observations determine to what extent models are valid, not vice versa. But there is a problem in that observations are very incomplete, span a limited time and are affected by internal variability. So up to now it has been difficult to rule out many of the possible models of climate behaviour

John’s and my view as to the ‘clear scientific understanding’ of why (CMIP5) models simulated too high warming rates, especially in the last 15 to 20 years are quite different. IMO, the correct scientific understanding is that the models have too high a transient climate sensitivity – and, since the Earth’s energy imbalance seems to be relatively modest – too high an ECS (here meaning effective climate sensitivity). The idea that the ‘vast body of work pointing at a positive cloud feedback’ is based on solid scientific observational evidence is contradicted by AR5’s conclusion about Observational Constraints on Global Cloud Feedback, that “there is no evidence of a robust link between any of the noted observables and the global feedback”.

There is also now a suggestion from experiments with fixed sea surface temperatures that part of what had previously been interpreted in models as positive cloud feedback to surface temperature changes is in fact a rapid atmospheric and land surface adjustment, probably better seen as part of effective radiative forcing. For instance, according to Vial et al (2013) the NCAR CCSM4 model actually shows negative overall cloud feedback, whilst on average across the models analysed cloud feedback, whilst positive, is fairly small – similar to albedo feedback. On the other hand, CCSM4 shows a large positive cloud adjustment, as (to a lesser extent on average) do most models analysed.

Turning to the Schwartz (2012) paper, I don’t think one should place too much emphasis on its precise results and whether or not a particular forcing dataset tells us much about uncertainty in climate sensitivity. To my mind, the take-home message from the paper is this. In general the relationship between forcing estimates and the global instrumental temperature record, along with estimates of heat uptake over the last fifty years, points to TCR and ECS being relatively low. However, there is substantial uncertainty in forcing estimates, related mainly to anthropogenic aerosols. As it concludes: “Confident determination of Earth’s climate sensitivities thus remains hostage to accurate determination of these forcings.” I agree. The observational evidence from warming over the instrumental period certainly points to sensitivity being more likely to be low than high, but one cannot at present conclude for definite that it is low.

Reference
Vial J, J-L Dufresne and S Bony, 2013. On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Climate Dynamics, DOI 10.1007/s00382-013-1725-9.

I agree with John that it is unclear how well F and T in Figure 10 of Schwartz (2012) should track each other on a timescale of one – or even a few – years, given internal variability. However, a regression best-fit line is determined more by the average values of points towards its ends than by values for individual years, particularly those whose points fall towards the middle of the data. Carrying out the regression on points representing averages of several years’ data is unlikely to change the best fit much. The worrying thing about the regressions for the MIROC data set is that the unconstrained best fit based on 1965-1998 data does not pass close to the origin, which it should do under the energy balance model underlying the paper.

I agree with Steve Schwartz that excluding forcing data sets on the basis that they do not fit the model used is not ideal. But I think that using just a selection of mainly GCM-derived data sets is more of a problem. I understand why Steve did so: at the time there were only a limited number of forcing data sets available. Even using forcing time series diagnosed from a much larger ensemble of CMIP5 models does not provide as wide, or as scientifically justified, a spread of possible forcing histories as the climate scientists involved in AR5 decided on, based on uncertainties for each individual forcing. Hence my preference for using the AR5 forcing data set, now that it is available, and its associated uncertainty distributions. For most climate variables, the idea that the CMIP5 ensemble provides a realistic uncertainty distribution is highly questionable.

FWIW, I believe Steve Schwartz’s views on the most likely levels of ECS and TCR are much closer to mine than to John’s.

Bart,

It’s important to note that your quote refers to 2005-2012, a rather short period of limited relevance to determining ECS/TCR. I’m sure there will always be some debate over how confident we can be of the observed values, but on the other hand it is also clear that the observations (or to be more precise, these particular sets of observations when analysed though energy-balance modelling) do point towards the lowish end of the commonly quoted range.

Apologies but I have been on travel and busy with end of term, so did not follow the blog after posting nearly a month ago. I would like to respond briefly to Nic’s main replies to my previous comment. Nic’s comments are very thorough and show that he has lots of time to devote to this. I am not so lucky and probably won’t have time to continue the dialogue beyond this post.

Nic claims that I am only “half right” in asserting that his method relies on the inter hemispheric difference in warming to tease out the aerosol and GHG/feedback signals. But how else can it work? If it uses some other fingerprint, please explain. In any case the method only works if the fingerprint is known correctly. The assumption that aerosol forcing is concentrated in the northern hemisphere, for example, could prove to be quite untrue (see recent paper in Science by Ilan Koren et al., which implies that cloud-mediated effects could actually have been stronger in the southern hemisphere because there is so much less background aerosol). If the method relies on some other, more complicated fingerprint then it is even more uncertain. I think Nic needs to be more forthright about what fingerprints are actually being used and what the results would be if others were used.

He also notes that if natural variability on decadal time scales (as seems to be the case) greater in reality than in most AOGCMs, this broadens the PDF but does not shift the best estimate. This is true if you have no information on what natural variations actually happened in recent decades. But we do have information on them, and as I explained, they have characteristics that will interact with the implicit aerosol assumptions to bias the result towards lower ECS and TCR. One commenter pointed out the recent paper by Matt England et al, which is also highly relevant here although not about the inter hemispheric warming difference. Nic’s statement that his results aren’t so sensitive to time period misses the point – recent asymmetric warming trends are strong enough to stand out no matter what time period is used, so his insensitivity to time period is just what I’d expect. Moreover, broadening of the pdf is not inconsequential as it reveals that the instrumental record is not a very good constraint on ECS.

He has also twisted the conclusions of AR5 Chapter 7 (of which I was a co-author). The multiple lines of evidence were not only based on GCMs, please read the chapter. We explicitly required observational evidence or back-up from detailed cloud simulations. The two feedback mechanisms we identified as having such support, are both positive (relating to the rise of the tropopause and the poleward shifting of cloud bands) have support both from observations and explicit models of the relevant processes. And as Andy Dessler points out in a comment, to get ECS < 2C you need very strong negative cloud feedbacks to come from somewhere in order to cancel out the known positive ones. We have no evidence for such a thing after decades of searching. The quote from our chapter given by Nic was taken out of context and does not imply there is no evidence for positive feedback. It applied only to one particular strategy that has been used. And in my view the statement would not even be true, due to advances made since AR5 went to press, which further support a climate sensitivity consistent with a stronger positive cloud feedback.

Finally, Nic challenges me to defend the studies he wishes to dismiss. All I can say is that one could dismiss every single study, including his, by cherry-picking some random imperfection in the methods or models used. These studies all passed peer review, which does not prove they are valid, but means that if Nic wishes to dismiss them the burden is on him to identify the key flaw and explain why it would have led to an overestimate of ECS rather than an underestimate.

Bart,

I pretty much agree with your additional comments on aerosols, but would like to add a few clarifications.

Your comment on aerosol forcing in Lewis (2013) (adjusted to 1750-2011, as per AR5) does not make clear that the study formed its own observationally-based inverse estimate of aerosol forcing rather than using an external estimate. Surface temperature changes in four equal-area latitude zones were compared with observed changes over each of six decades, rather than using an external forcing estimate. Steven Sherwood’s comment that I need to be more forthright about what fingerprints are actually being used and what the results would be if others were used is wide of the mark. The fingerprint (the spatiotemporal pattern of aerosol forcing) was determined by the Forest, Stone and Sokolov team at MIT, so he should look in the relevant publications by those authors to see what pattern was used. I simply used their 499 sets of 2D climate model simulations; there is no question of trying other fingerprints because no simulations run with different fingerprints are available.

I have only been able to locate aerosol forcing estimates for a dozen or so CMIP5 models. Excluding a few models that do not include aerosol indirect effects (e.g., CCSM4, bcc-csm1-1), the change in total aerosol forcing is typically above the AR5 best estimate, averaging -1.17 W/m² over 1850-2000 for the models analysed in Shindell et al (2013), significantly higher than the -0.74 W/m² best estimate per AR5 over that period.

I wouldn’t say that I doubt model ECS and TCR values directly because of their large aerosol forcing. Rather, I regard their large aerosol forcing as explaining why until the last few decades AOGCMs did not simulate excessive surface warming or ocean heat uptake despite having high ECS and TCR values, but have done so since then. However, their large aerosol forcing may have indirectly led to AOGCMs having high sensitivities, as the model developers chose model variants and tuned them with an eye on matching the historical temperature record.

Regarding constraining ECS and TCR from the instrumental period, it is in theory possible that a period over which there was confidence that aerosol forcing had changed little might enable ECS and TCR to be better constrained even if the change in aerosol forcing since, e.g., 1850 remained poorly constrained. In that connection, there is a general view that aerosol forcing has changed little over the last ~35 years. Unfortunately, that period has probably been strongly (positively) influenced by multidecadal internal variability in the form of the AMO and also has an asymmetrical volcanic forcing profile.

Reference
Shindell, D. T. et al, 2013. Radiative forcing in the ACCMIP historical and future climate simulations. Atmos. Chem. Phys. 13, 2939–2974

Another important subject we did not discuss yet is priors.

Nic wrote in his blog:
“Most of the observational instrumental-period warming based ECS estimates cited in AR5 use a ‘Subjective Bayesian’ statistical approach. The starting position of many of them – their prior – is that all climate sensitivities are, over a very wide range, equally likely. In Bayesian terminology, they start from a ‘uniform prior’ in ECS. All [instrumental based] climate sensitivity estimates in the AR4 report were stated to be on a uniform-in-ECS prior basis. So are many cited in AR5.[…] Use of uniform-in-ECS priors biases estimates upwards, usually substantially. When, as is the case for ECS, the parameter involved has a substantially non-linear relationship with the observational data from which it is being estimated, a uniform prior generally prevents the estimate fairly reflecting the data. The largest effect of uniform priors is on the upper uncertainty bounds for ECS, which are greatly inflated.
Instead of uniform-in-ECS priors, some climate sensitivity estimates use ‘expert priors’. These are mainly representations of pre-AR5 ‘consensus’ views of climate sensitivity, which largely reflect estimates of ECS derived from GCMs. Studies using expert priors typically produce ECS estimates that primarily reflect the prior, with the observational data having limited influence.“

According to Nic’s study (Lewis, 2013), a non-informative prior should be used because:

“The non-informative prior prevents more probability than data uncertainty distributions warrant
being assigned to regions where data responds little to parameter changes, producing better constrained PDFs”

In his guest blog James wrote:
“Further issues arise with his methods, though in my opinion these are mostly issues of semantics and interpretation that do not substantially affect the numerical results. (For those who are interested in the details, his use of automatic approach based on Jeffreys prior [which is a non-informative prior] has substantial problems at least in principle, though any reasonable subjective approach will generate similar answers in this case.)”

My interpretation of James’ remark is that the use of a non-informative prior can also cause substantial problems, but do not seriously affect the results as derived by Nic.

The question I would like to discuss is:

What are the pros and cons of informative, non-informative (or Jeffrey’s) and expert priors in the different types of studies (i.e. instrumental based or paleo based)?

WHY I DO NOT AGREE WITH LEWIS’ CHOICE OF PRIOR DISTRIBUTION (AND A DIALOGUE BETWEEN TWO ALIENS)

Most experts in climate sensitivity think that the “non-informative prior distribution” of climate sensitivity is what Nic Lewis uses, and that it results into a low climate sensitivity. I do not agree. Some time before Nic published his paper, I also published a paper on the non-informative prior distribution of climate sensitivity (Pueyo, S. 2012. Climatic Change 113: 163-179), and my conclusions were very different:

http://www.springerlink.com/content/3p8486p83141k7m8/

Unfortunately, estimates of climate sensitivity are very sensitive to methodological choices. When adopting a given methodology, climatologists are implicitly positioning themselves about issues in which there is no unanimity among the own experts in probability theory. This means that, if we want our estimates to be realistic, we have a difficult challenge ahead, which we cannot address in the usual ways, e.g. by increasing computing power. However, I hope the climatological community ends up addressing this challenge fully, and does it as soon as possible. To help climatologists bypass some hard texts, I once wrote a comic version of my paper on non-informative priors, featuring a dialogue between two aliens named Koku and Toku.

Also, some time ago, motivated by a conversation with Dr. Forest, I “transcribed” another dialogue between Koku and Toku, which sheds light on the difference between Nic’s and my own view of non-informative priors (I strongly recommend reading the comic above before reading this second dialogue; the comic is short):

Objective prior distribution of climate sensitivity, or… Koku and Toku looking for the shape of ignorance

There is one thing in which Nic, myself and many others agree: in that the uniform prior vastly overestimates climate sensitivity S. However, this does not mean that many estimates in the literature should be overestimates. The overestimation resulting from this prior is so obvious that, in practice, the uniform is assumed only between S=0 and some Smax, and a zero probability is assumed above Smax, with no explicit criterion to choose Smax (discussed in Annan & Hargreaves 2011, Climatic Change 104:423–436). With this correction, it is not so obvious that this method should overestimate sensitivity, but it is obvious that it is inappropriate. The conclusion of my paper was that the non-informative prior of climate sensitivity is proportional to 1/S. In contrast, Nic sustains that the non-informative prior depends on the dataset but that it will often be roughly proportional to 1/S^2 (see his comment 1048). My prior, S^(-1), is midway between the uniform S^0 and Nic’s S^(-2). If using my prior results into a probability distribution f(S), Nic’s will often give a distribution f'(S) proportional to f(S)/S. My conclusions are that Nic’s is not the correct non-informative prior and that, at least for some datasets, it results into a vast underestimation of climate sensitivity.

Let me add that, in fact, my proposal in Pueyo (2012) was not a direct use of 1/S. I proposed a middle way between the non-informative prior (proportional to 1/S) and subjective priors. My proposal was to start from the non-informative prior, and, then, to introduce explicit and well-justifed modifications (e.g. based on physics) before feeding the data. I hope someone tries this.

I thank Nic for his answer to my comment. The points he made will be helpful for some basic clarifications.

Nic refers to Bernardo and Smith’s authority to support the methods that he uses to obtain the “non-informative prior” for each dataset. However, Bernardo was careful enough to coin a new expression for what he (and now, Nic) was using: “reference prior”. Even though there is some confusion between both concepts in the statistical literature, they are quite different. The most important difference does not lie in how you calculate each of these “priors”, but in the meaning that you give to them. In the context of climate sensitivity, we might be able to progress more quickly in our discussions if, in his papers and posts, Nic says that he has been using the “reference prior” and that I sought (or that I found, but he does not seem to agree with this) the “non-informative prior”.

A non-informative prior distribution “sensu stricto” plays the original role of any prior distribution in Bayesian theory: it intends to tell how likely different options are (e.g. different values of climate sensitivity) without considering some given data (in the “non-informative” case, without considering any data at all). When you introduce the data, the prior probability distribution is updated and gives rise to the posterior distribution.

The reference distribution does not tell you the same. The reference distribution is a function that you can use in the place of the prior distribution “sensu stricto” when you cannot decide the later. It is intended just as a convention, as something that everybody is supposed to use when they don’t know what to use, so that everybody’s results are comparable (and, since the reference prior has several good statistical properties, you avoid some types of “accident”). This is a practical option when the posterior distribution is strongly constrained by the data. However, this is not the case of climate sensitivity. In the case of sensitivity, small differences in the prior can have a visible impact on the posterior. Since the reference prior cannot be given the strict meaning of a prior probability distribution, what you obtain by updating it cannot either be given the meaning of a posterior probability distribution. In fact, it is meaningless.

That the reference prior is not, strictly speaking, a prior probability distribution, is apparent from the fact that, as Nic emphasizes, it depends on the experiment. The probability that climate sensitivity is large cannot depend on some experiment that I am planning to do to measure it. Otherwise, climate policy would be much easier: rather than reducing emissions, just plan the right experiment to be carried out in a distant future: once you have it in mind, it should be unlikely that global warming will be severe. Well, at least this is what we would think if we interpreted the reference prior as a prior probability distribution “sensu stricto”, but this is not the right interpretation.

The confusion between reference prior and non-informative prior causes two serious problems. We have already seen one: that the final result (the posterior distribution) is given an unwarranted meaning. The second problem is that, as reference priors are different for different experiments, by using them you cannot combine different types of data. This is especially unfortunate in our case, because, without combining different data types (as Annan and Hargreaves 2006 began to do), it will be difficult for the data to constrain the posterior distribution enough to forget our discussions about the prior of choice (also, we will be more vulnerable to possible biases inherent to specific types of data).

In Pueyo (2012) I had already given an alternative: seek the actual non-informative prior based on Jaynes’ logic, and enrich it with well-justified pieces of prior information. Nic says that Jaynes’ approach “failed save in certain cases”, but I don’t know how he decides that it “failed”. However, even if we accepted that neither Jaynes’ nor any other method allow us to determine a true non-informative prior, there would still be something that we could do: to go ahead by putting together increasing amounts and heterogeneity of data up to the point in which the posterior is robust enough to our choice of prior. However, we cannot do this in the framework of reference priors.

Taking all of this into account, I invite Nic to rethink his current approach and his conclusion that climate sensitivity should be so low, and to consider exploring these other approaches.

James Annan, as I understood you, you focused on CS on the ground that it was “more relevant [than TCR] to stabilisation scenarios and long-term change over perhaps 100-200 years (and beyond)”. However you didn’t challenge the claim made in the Introduction that TCR is the parameter more relevant to policy. Furthermore I don’t believe those who did spend more time on TCR (mainly Nic Lewis among the experts) challenged it either.

So if I may I would like to challenge it here.

On the face of it, it seems quite reasonable to assume that CO2 will be compounding annually at a CAGR of 1% by 2050. Taking that as a lumped value applicable to the century as a whole, this would make estimation of TCR invaluable for forecasting global mean surface temperature in 2100.

But what is the basis for estimates of TCR? Nic rightly focuses on Box 12.2 of AR5, which is where the current report examines this question most closely, along with estimating both equilibrium climate sensitivity and effective climate sensitivity defined as varying inversely with the climate feedback parameter.

I had a very hard time following how the behavior of 20th C global surface temperature could be used to estimate any of those three measures of climate response to CO2. Problem 1 is that CO2 was rising last year at only 0.5%, at 0.25% in 1960, and even less before then. Problem 2 is that CO2 has risen only 43% since the onset of industrial CO2. And Problem 3 is that ocean delay, long recognized as a source of uncertainty, may be an even bigger source of uncertainty than assumed in interpreting historical climate data.

I do not mean to imply that these are inconsequential numbers, quite the contrary in fact, but rather that they invalidate overly naïve extrapolation from the previous century to this one.

A pathologically extreme example of how badly things can go when you neglect changing CAGR of CO2 can be seen in the 2011 paper of Loehle and Scafetta on “Climate Change Attribution”. They analyze climate as a sum of two cycles, a linear “natural warming” trend, and a steeper linear anthropogenic trend. Setting aside the cycles, the trends purport to model rising temperature before and after 1942, rising (in their Model 2) at respectively 0.016 C and 0.082 C per decade, obtained by linear regression against the respective halves of HadCRUT3.

The following argument justifies their attribution of pre-1942 warming to natural causes.

“A key to the analysis is the assumption that anthropogenic forcings become dominant only during the second half of the 20th century with a net forcing of about 1.6 W/m2 since 1950 (e.g., Hegerl et al. [23]; Thompson et al. [24]). This assumption is based on figure 1A in Hansen et al. [25] which shows that before 1970 the effective positive forcing due to a natural plus anthropogenic increase of greenhouse gases is mostly compensated by the aerosol indirect and tropospheric cooling effects. Before about 1950 (although we estimate a more precise date) the climate effect of elevated greenhouse gases was no doubt small (IPCC [2]).”

For reasons I will give below it is not clear to me that the influence of pre-1942 CO2 was so minor, but set that aside for the moment. Their justification for their linear model of post-1942 warming is as follows.

“Note that given a roughly exponential rate of CO2 increase (Loehle [31]) and a logarithmic saturation effect of GHG concentration on forcing, a quasi-linear climatic effect of rising GHG could be expected.”

The relevant passage from [31] is,

“An important question relative to climate change forecasts is the future trajectory of CO2. The Intergovernmental Panel on Climate Change (IPCC, 2007) has used scenarios for extrapolating CO2 levels, with low and high scenarios by 2100 of 730 and 1020 ppmv (or 1051 ppmv from certain earlier scenarios: Govindan et al., 2002), and a central “best estimate” of 836 ppmv. Saying that growth increases at a constant percent per year, which is often how the IPCC discusses CO2 increases and how certain scenarios for GCMs are generated (see Govindan et al., 2002), is equivalent to assuming an exponential model.”

In effect L&S have based their model of 20th century climate on TCR.

So how bad can this get? Well, ln(1 + x) is close to x for x much less than 1, but becomes ln(x) for x much larger than 1. The knee of the transition is at x = 1. Taking preindustrial CO2 to be 1, today we have a CO2 level for which x = (400 – 280)/280 = 0.43, and with business as usual should reach 1 (double preindustrial) around 2050.

So for the 19th and much of the 20th century ln(1 + x) can be taken to be essentially x. Since x is the product of population and per-capita energy consumption we can assume with Hofmann, Butler and Tans, 2009, that up to now anthropogenic CO2 and hence forcing has been growing exponentially. (Actually the CDIAC data show that the CAGR of CO2 emissions for much of the 19th century held steady at 15%, declining to its modern-day value of around 4-6%, but the impact of anthropogenic CO2 was so small in the 19th C that approximating it with modern-day CAGR of CO2 emissions may not make an appreciable difference. When I spoke to Pieter Tans in 2012 about extrapolating their formula to 2100 he thought a lower estimate might be more appropriate, which is consistent with the declining CAGR of emissions between 1850 and now, but estimating peak coal/oil/NG is far from easy, a big uncertainty.)

It follows that CO2 forcing to date has been growing essentially exponentially, not linearly, but that it will gradually switch to linear (or even sublinear) during the present century. Hence extrapolating 20th century global warming to the 21st century and beyond cannot be done on the basis of either a linear or logarithmic response to growing CO2, but must respect the fact that over the current century forcing will be making the transition from one to the other.

The sharp transition at 1942 in Loehle and Scafetta’s model is in this light better understood as the flattening out (as you go from 1950 to 1930) of an exponential curve. Even if aerosol forcing happened to approximately cancel the left half of the exponential, it would be preferable to put an estimate of the aerosol contribution independently of the CO2 forcing. Moreover if the feedbacks are capable of doubling or tripling the no-feedback response then this would entail aerosol forcing driving CO2, raising the possibility of estimating aerosols around 1900 by comparing the difference between the Law Dome estimates of CO2 with the CDIAC’s estimates of CO2 emissions, provided the difference is sufficiently significant.

There is also the matter of any delay in the impact of radiative forcing on surface temperature while the oceans take their time responding to the former (Hansen et al 1985). If forcing grows as exp(t) with time t, any delay d means that temperature actually grows as exp(t – d) = exp(t)exp(-d), introducing a constant factor of exp(-d) into observation-based estimates of climate response. In particular if exp(-d) = ½, as it might well, then failure to take this delay into account will result in underestimating the prevailing climate response by a factor of two. This on its own would entirely account for misreading a sensitivity of 3.6 as 1.8. That’s a huge contribution to uncertainty. If furthermore the delay varies with time (as it may well given the complexities of ocean heat transport) then so does the factor exp(-d), making the uncertainty itself a factor of time. One might hope that d varied if at all very slowly with time, and preferably monotonically, say linearly to a first approximation.

For such reasons I feel that if climate projections are to be based on climate observations, a third notion of climate response is needed, one that differs from TCR along the above lines, taking into account both the manner in which CO2 grows and the extent to which the ocean delays the response of global mean surface temperature (in degrees) to forcing (in W/m2).

James claims that my Climate Audit blog post about radiocarbon dating provides a “catastrophic failure” of the use of noninformative prior. That is because of the stress he places on probability density and the way he interprets low values of a (posterior) probability density function (PDF). I find it more useful to see how realistic the uncertainty ranges produced by a PDF are than what its values are in particular regions. Moreover, I think one should look at the likelihood function (and/or the prior) as well as the PDF, in order to understand where the likelihood is very low, implying the data is inconsistent with the parameter value, and where only the prior is low (implying, for a noninformative prior, simply that the data is uninformative about the parameter value).

Primary scientific results are normally stated in terms of a best estimate and an uncertainty range, with any PDF underlying the best estimate and uncertainty range being secondary. When a frequentist statistical method is used – as it is in a large proportion of cases – the uncertainty range is usually designed to be a confidence interval whose boundaries the true value of the (fixed but uncertain) parameter involved would fall below in the specified proportions of cases (e.g., 5% and 95%) upon repeating the experiment many times using random drawings from the data etc. uncertainty distributions involved. The method may or may not accurately achieve that aim (known as probability matching), but in most cases there is little disagreement of its desirability. When the IPCC AR5 scientific report states that it is 95% certain that more than half the global warming over 1951– 2010 was anthropogenic in origin, that is based on a frequentist confidence interval, not derived from a Bayesian PDF. If most scientists were told that a archaeological artefact had been shown by radiocarbon dating to be at least 3000 years old with 95% certainty, I think they also would expect the statement to reflect a confidence interval bound, with at least approximately probability matching properties, not a subjective Bayesian PDF.

As I showed in my radiocarbon dating blog post, the use in the case considered of the noninformative Jeffreys’ prior provided uncertainty ranges that in all cases gave exact probability matching no matter what percentage boundaries were specified or from what probability distribution and within what range the sample being dated was picked, unlike whatever method James prefers. Not my idea of failure!

James considers that a near zero probability density over 1200-1300 AD – a calendar period over which the radiocarbon age hardly changes, so that the data is very uninformative about the calendar age – is unrealistic. I suggest that view can only come from prior knowledge of the probability characteristics of calendar ages of samples. The method I was criticising was put forward in a paper that explicitly assumed that no prior knowledge about the probability characteristics of calendar ages of samples existed. But even if some such knowledge does exist, it does not follow that incorporating such knowledge into calendar age estimation (by multiplying an estimated PDF reflecting it, used as an informative prior, by the data likelihood function in an application of Bayes’ theorem) will improve results, even if the PDFs look more believable. As my Climate Audit post showed, doing so and then drawing samples from a segment of the known true calendar age probability distribution often produced estimated uncertainty ranges with probability matching characteristics that were not just worse than when using Jeffreys’ prior (inevitably, as that gave perfect matching), but substantially worse. It should be noted that although the Jeffreys’ prior will assign low PDF values in a range where likelihood is substantial but the data variable is insensitive to the parameter value, the uncertainty ranges the resulting PDF gives rise to will normally include that range.

It is important to understand the meaning of the very low (not zero) value of the prior, and hence of the posterior PDF, over 1200-1300 AD, or over any other period where the radiocarbon age, whilst consistent with the data in terms of having a significant likelihood, varies little with calendar age. It simply reflects that over the interval concerned the data is very uninformative about the parameter of interest, because the interval corresponds to a small fraction of the data error distribution. If some non-radiocarbon data that is sensitive to calendar ages between 1200 and 1300 AD is obtained, then the noninformative prior for inference from the combined data would cease to be low in that region, and the posterior PDF would become substantial in the calendar region consistent with the new data, resulting in a much tighter uncertainty range.

James’ statement that “It is clear that, despite many decades of trying, no-one has come up with a universal automatic method that actually generates sensible probabilities in all applications.” is true. But it masks the fact that in very many cases – probably the vast bulk of practical parameter inference problems – Berger and Bernardo’s reference prior approach does, in many peoples’ view, do so. In the one-dimensional case, Jeffreys’ prior is the reference prior.

James refers to probabilities produced using an objective Bayesian approach as having some “intuitively appealing mathematical properties”. I will single one of these out as a property that the vast bulk of physicists would support. Jeffreys’ prior, and some of the more sophisticated priors that remain noninformative for marginal inference about one parameter out of many in circumstances when Jeffreys’ prior does not do so, are invariant under one-to-one transformations of data and parameter variables. That means, for instance, that if a PDF is estimated for the reciprocal of climate sensitivity, 1/ECS, rather than for ECS itself, and the resulting posterior PDF for 1/ECS is then converted into a PDF for ECS by using the standard transformation-of-variables formula, the PDF thus obtained will be identical to that resulting from estimating ECS directly (from the same data). The construction of the noninformative prior (which will differ greatly in shape between the two cases, when both expressed in terms of ECS) guarantees that this invariance property obtains. A subjective Bayesian approach does not respect it, at least when data variables are transformed.

James’ claims that there is nothing in “Nic’s approach that provides for any testing of the method, i.e. to identify in which cases it might give useful results, and when it fails abysmally.” I beg to differ. I think most statisticians (and scientists) would regard the accuracy of probability matching as a very useful – and widely used – way of identifying when a statistical method gives useful results. There is a large literature on probability-matching priors, and the performance of noninformative priors is often judged by their probability-matching (Kass and Wassermann, 1996). Indeed, Berger and Bernardo (1992) refer to the commonly used safeguard of frequentist evaluation of the performance of noninformative priors in repeated use, as being historically the most effective approach to discriminating among possible noninformative priors.

References
Kass RE, Wasserman L (1996): The Selection of Prior Distributions by Formal Rules. J Amer Stat Ass 91 435:1343-1370
Berger J O and J. M. Bernardo, 1992: On the development of reference priors (with discussion). In: Bernardo J. M., Berger J. O., Dawid A. P., Smith A. F. M. (eds) Bayesian Statistics 4. Oxford University Press, pp 35–60

Thank you Bart (Verheggen) for your synthesis and questions. Let me just clarify that most of your mentions of “non-uniform prior” refer, more precisely, to “non-informative prior”.

I am grateful that Bart clearly separates my approach from Nic’s. Quite confusingly, they are often lumped together, e.g. in the recent post by James (perhaps because he posted it while my previous post, in which I emphasize the differences, was awaiting approval). As I said in my previous post, Nic’s would be more properly called “reference prior” than “non-informative prior”, while I did seek a “non-informative prior”. From my point of view, the concepts of “non-informative prior” and “reference prior” differ as much from each other as each of them differs from the concept of “expert prior”.

James and Nic have engaged in a discussion on whether or not it is a “catastrophic failure” that, in a given example (unrelated to climate sensitivity), Nic’s method assigns an almost null probability to the interval in which the only measurement lies, and larger probabilities to neighboring intervals. Behaviors like this occur because “reference priors” like Nic’s can be very complex, which makes clear that they are not “non-informative”. In fact, they contain a lot of information, but it is information on the measurement technique, which is completely unrelated to the original concept of “prior probability” (i.e. the probability to be assigned to the property to be measured before the measurement takes place).

James uses this example to criticize so-called “objective priors” in general, an expression that encompasses both reference priors and non-informative priors, and that he suggests to replace by “automatic priors”. I think my comment above makes clear that his point is valid only for reference priors, and cannot be extrapolated to non-informative priors. Furthermore, I will argue that, in some sense, non-informative priors are indeed “objective”, but are not “automatic” (unlike reference priors).

I will introduce my argument with the help of a thought experiment. Consider a set of objects whose positions have been decided by algorithms that are completely different and unrelated to each other. My intuition tells me that the frequency distribution of the coordinates of these objects will be uniform. Besides intuition, the rational argument to expect a uniform distribution is that it is the only one that preserves the symmetries of the problem. Therefore, the uniform should be the non-informative probability distribution in this case (according to Jaynes’ invariant groups logic), and it is so “objective” that it results into an observable frequency distribution.

I have suggested that there are several frequency distributions in nature that are almost non-informative because they result from putting together values with completely different, “idiosyncratic” origins (see a synthesis of previous papers in http://arxiv.org/abs/1312.3583). Often, the variable of interest is not a position, so the symmetries to be conserved are not the same, and give rise to a distribution that is not uniform. To predict this objective distribution, one needs to identify the symmetries of the problem, which is an objective but not automatic process.

We do not have a sample of “idiosyncratic” climate sensitivities allowing us to observe a frequency distribution, but we can still treat the non-informative distribution similarly to a frequency distribution, as we would treat the result of tossing a coin only once. As soon as we have this prior distribution (log-uniform, according to my results) and some measurements defining a likelihood function, Bayes theorem is very clear in that we have to combine the first with the second to know how likely different values of sensitivity are. The way measurements are taken affects only the likelihood function, not the prior probability distribution.

Nic’s technique does not deal with actual non-informative priors. Whether or not one agrees with my claim that non-informative priors do exist, one has to concede that using a different type of prior (reference prior) as if it were non-informative can cause serious trouble unless the amount of data makes the result quite insensitive to the prior, which is rarely the case with climate sensitivity. As I said, underestimation of climate sensitivity is especially likely when using Nic’s method.

Bart asked me to reply Nic’s claim that Jaynes’ prior is not suited to the “continuous parameter case”. In my previous post, I stated: “Nic says that Jaynes’ approach ‘failed save in certain cases’, but I don’t know how he decides that it ‘failed’”. Unless he clarifies this, I cannot fully answer his criticism. However, I have already given some reasons to think that Jaynes’ logic is valid.

Nic states “the main reason that Salvador and I come to different conclusions is that we have completely different views on what makes a prior uninformative, resulting in us selecting different priors. One of us must be wrong! ”. I had previously stated that the “reference priors” used by Nic aren’t “non-informative priors”. However, Nic says that “the distinction that Salvador is making between what he calls respectively ‘reference priors’ and ‘noninformative priors’ makes no sense to me ”. Let’s see the point of view of Bernardo, who introduced reference priors (building on Jeffreys), and is repeatedly cited by Nic as an authority. In his seminal paper on reference priors, this author stated that “a reference prior does not describe a situation of ‘non-information’ about the parameters of a model” (Bernardo 1979a, p. 126). The opinion that the introducer of reference priors has on non-informative priors is best expressed in the title of Bernardo et al. (1997): “Non-informative priors do not exist”. In the ensuing comments, Ghosh (1997) summarizes the position behind this title as a “concern with useful non-subjective posteriors instead of noninformative priors”. Indeed there has been much confusion between reference and non-informative priors in the literature (and even Bernardo has contributed to it at some points), but it is clear to me that this distinction does “make sense”.

I not only made the distinction between reference priors and non-informative priors, but went beyond and stated that “the reference prior cannot be given the strict meaning of a prior probability distribution ”. Nic writes “I think Salvador arguing that such a prior is not actually a prior distribution in the strict sense of representing a genuine probability distribution for the parameter(s). I wouldn’t disagree. But so what? ”. His interpretation is correct, but let me answer to the “so what?”. Bayes theorem establishes a mathematical relationship between probabilities. Therefore, if you pretend to apply Bayes theorem but your input is not a probability distribution, then you cannot use Bayes theorem to state that your output is a probability distribution. You are free to equate this output to a probability distribution, but this results from an extra step: a subjective decision. It is not an objective result.

Then, what is the usefulness of the “reference posterior” that you obtain using a “reference prior”? I had already stated two points: as a conventional way to express the information in your sample, and as a way to avoid some technical problems that some other priors pose in some cases. Bernardo mentions these uses, but actually, he emphasizes another one: it “is just a part – an important part, I believe – of a healthy sensitivity analysis to the prior choice” (Bernardo et al. 1997, p. 163). He means that the result of applying a reference prior is useful because it can be compared with the result of applying your subjective prior of choice, to check if the posterior distribution is sensitive to the prior.

We are having this lively discussion because of the consequences that different choices of prior may have for decisions in climate policy, including Nic’s choice, i.e. a reference prior. If the usefulness of reference priors is limited to the points that I described above, what are the implications of taking the resulting posterior distribution at face value for policy decisions? Bernardo (1979b, p. 140) was admirably honest: “it would certainly be foolish to use it in lieu of the personal posterior which describes the decision-maker opinions”. Of course, this assumes that we can reach well-founded opinions in other ways, probably with a sound expert prior, which is no less problematic in the case of climate sensitivity. So, which other alternatives do we have?

I mentioned two alternatives. For those who, unlike Bernardo and many others, think that non-informative priors do exist, the alternative is clear: using them (corrected with pieces of well-founded knowledge, Pueyo 2012). This is my opinion and I posit that such priors can be found by applying Jaynes’ logic. The problem that Nic sees in this option is that Jaynes admitted being only “able to resolve the measure problem in special cases, in particular when a transformation group existed.” In the case of climate sensitivity, we can consider the transformation group whose elements are changes in measurement units. These changes do not have to affect a non-informative prior. This leads to the result in Pueyo (2012).

The second alternative is accepting a posterior distribution only when it proves mostly insensitive to the prior (so we do not need to decide which prior is the correct one). Probably, we will need to combine different types of data to reach this point. Such combinations are forbidden when using reference priors, but are perfectly correct when assuming that we have a prior probability distribution sensu stricto, either non-informative or informative, whether or not we specify it.

References

Bernardo, J.M. 1979a. Reference posterior distribuitons for Bayesian inference. Journal of the Royal Statistical Society B 41: 113-128.

Bernardo, J.M. 1979b. Author’s reply. Journal of the Royal Statistical Society B 41: 139-147.

Bernardo, J.M., Irony, T.Z. & Singpurwalla, N.D. 1997. Non-informative priors do not exist. A dialogue with José M. Bernardo. Journal of Statistical Planning and Inference 65: 159-177.

Ghosh, J.K. 1997. Non-informative priors do not exist – discussion of a discussion. Journal of Statistical Planning and Inference 65: 180-181.

Pueyo, S. 2012. Solution to the paradox of climate sensitivity. Climatic Change 113: 163-179

Bart V asks me to justify my treatment of paleo-estimates of ECS. (I wouldn’t put any weight on what AR5 said about Bayesian priors, BTW.)

Bart has over-interpreted my position. I don’t exactly reject paleo-estimates of ECS. Rather, I agree with AR5’s caveats, and broadly accept their 1–6°C range, although I would be inclined to treat it as a 17–83% likely range rather than a 10–90% range.

However, AR5 gives little indication of the shape of the uncertainty distribution involved in paleo estimates. My view is that for paleo estimates the fractional uncertainty as to forcing changes and as to the relationship of climate feedbacks in different climate states (which AR5 does highlight) is likely in reality to be considerably greater than fractional uncertainty as to temperature changes. Assuming so, the overall PDF for ECS from paleoclimate studies should have a rather similar skew to that derived from instrumental period warming based studies, implying a median estimate far below the midpoint of the 1–6°C (or whatever) range.

That being so, even if the paleoclimate studies provide a completely independent overall estimate of ECS to that from warming over the instrumental period, the paleo estimate should not greatly affect the overall median and likely range derived from warming over the instrumental period. I’ve done some calculations based on the 1.7°C median estimate and 1.2–3°C likely range I put forward, which corresponds to uncertainty in the climate feedback parameter (the scaled reciprocal of ECS) having a normal distribution. If the overall 1–6°C paleo estimate shares that characteristic, then incorporating it would do little other than narrow my 1.2–3°C likely range at both ends. This is perhaps an extreme case, but it does illustrate my point.

On the subject of the relevance of the scientific debate on climate sensitivity to the political discourse, it is my opinion that the two are largely disconnected, at least here in the US. It is true that those advocating for the status quo often insist that sensitivity is low (or zero), but this is done largely out of convenience rather than being based on specific tidbits of convincing evidence. In fact, the latest shift in political tactic here is to disavow any knowledge of the science altogether (e.g. Marco Rubio’s and Rick Scott’s “I’m not a scientist” remarks). In truth, despite the differences voiced by Nic, James and I during our discussion, our viewpoints represent a relatively narrow portion of the US political spectrum, where half of Congress essentially deems the issue unworthy of further study – an opinion clearly voiced by members with vested interests that would change little if the scientific consensus were to become firmer. Given this reluctance to embrace even the broadly accepted facts on the issue (e.g. that humans have contributed substantially to Earth’s warming since the mid-20th C), any strong connection between the scientific debate and policy seems thus far to be elusive. It is both my hope and expectation that this will change.

I’m not an expert on the politics involved, but I give my personal opinion below:

The political situation in Europe (certainly in the UK) is different from that in the USA. The political centre ground is considerably to the left of that in the US. All the main parties affirm belief both in the science of climate change and the need to take action to reduce carbon emissions. In reality, very few politicians have any real understanding of the science, or of the merits of the costly climate policies that they legislate for. The government politicians in the UK listen to a fairly narrow group of advisers on climate change, and take no notice of the observational evidence that sensitivity may very well be lower than represented in the CMIP5 models. The highbrow media (BBC, Guardian newspaper) are committed believers in dangerous anthropogenic climate change and present only that viewpoint.
There are also various pressure groups warning of dangerous climate change and pushing for strong actions to reduce emissions. These include renewable energy groups and other subsidy farmers with vested interests, environmental NGOs and radical politico-environmental campaigning/protesting groups. So, at present, the scientific debate on climate sensitivity has a very limited impact in the UK political context. However, the few writers and bloggers who put forward the case for climate sensitivity being low, climate scientists and advisers being biased and/or policy being wrong-headed do get some attention, as does the Global Warming Policy Foundation think tank. The longer the hiatus continues, and the more energy prices are pushed up (and consumer choice reduced) by emission reduction policies, the less IMO the public is likely to believe climate scientists and to support policies to combat AGW. The politicians might then listen to a wider range of views within the scientific debate on sensitivity. Or a party with very different views on AGW might get to wield power, as in Australia.

I don’t think that any politicians in the UK, or for that matter Japan (where I lived and worked until recently) is paying much attention to the arcane debate in the literature about climate sensitivity. There are of course pressure groups who tend to distort the science as an alternative to debating honestly about policy choices, but thankfully they don’t seem to have much influence.