IMO, the debate on climate sensitivity and TCR should still be very pertinent in the political context, even though it currently is not. When allied to the parallel debate on the level of carbon cycle feedbacks, which has barely started, lowish sensitivity/TCR estimates (in line with what AR5 forcing and heat uptake best estimates imply) point to global warming from now to 2081-2100 of little more than 1 K on a business-as-usual scenario.

The CMIP5 mean projected rise is about three times as great. Which is correct has huge implications for what the optimal policy response is.

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.

Thus, it is not surprising that it has become a touchstone in the political debate. If the equilibrium sensitivity was around 1C or below, then anthropogenically-forced climate change would be a rather slow process and we would have little committed change. If sensitivity is close to 6C or higher, then we would already have committed the climate system to huge changes and rapid, massive emissions cuts would be an extremely urgent priority. However, a broad range of evidence points to a sensitivity well inside these values (albeit somewhat towards the lower end) and the remaining debate concerning the precision of our estimates is not, or at least rationally should not be, so directly pertinent for policy decisions. We already know with great confidence that human activity is significantly changing the global climate, and will continue to do so as long as emissions continue to be substantial. ]]>

As a very last question I invited the experts – by e-mail – to give their personal opnion on the relevance of the debate on Climate Sensitivity to climate policy and policy makers.Their answers are given below. ]]>

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.

]]>I would like to discuss now another important line of evidence: paleo climate. Below I try to summarize the arguments that have been brought up in the guest blogs and in the discussion so far.

James argues that when averaged over a sufficiently long period of time, the earth must be in radiative balance or else it would warm or cool massively. This enables us to use paleoclimatic evidence to estimate ECS. Non-linearities in the temperature response complicate the comparison of paleo-climate to the current changes in climate, but James argues that nevertheless paleoclimate evidence can offer useful constraints to ECS, due to the relatively large changes in temperature and forcing. The evidence rules out both very high and very low sensitivities and provides a figure around the IPCC range which could be used as a prior for Bayesian analyses.

Nic basically rejects paleo climatic approaches based on what is written in the last sentence of paragraph 10.8.2.4 in AR5 where it is concluded that paleo studies support a wide 10–90% range for ECS of 1.0–6°C. Nic points to the fact that in general, AR5 states that the uncertainties in paleo-studies are underestimated because of 1) the difficulty in estimating changes in forcing and temperature and 2) past climate states are very different, that is, may differ from the ECS measuring the climate feed-backs of the Earth system today and therefore widening the uncertainty range (i.e. flattening the PDF) seems reasonable. Nic thinks the uncertainties are simply too great to support the narrower 2–4.5°C range mentioned by James.

John argues that paleo studies benefit from the large climate signals that can occur over millennia and that the paleo record provides a vital perspective for evaluating the slowest climate feedbacks. He emphasizes that sensitivity to nonlinearities, major uncertainty in proxy records (Rohling 2012), data problems, and uncertainty in forcing undermine any strong constraint on ECS and it is unclear whether progress on these fronts presents an immediate opportunity for reducing uncertainty in ECS in the near future.

A general question for all would be to discuss the pros and cons of paleo-estimates of ECS, in light of the arguments brought forward by the others.

Specifically:

James: Could you respond to the issues raised by Nic and to indicate why you think the uncertainties aren’t too great to support the 2 – 4.5 °C range.

John: What range of ECS estimates do you think can be derived from paleo-studies

Nic: AR5 is full of caveats (incl e.g. about Bayesian priors), so why should the caveated language about paleo-estimates of ECS be translated into them being rejected?

]]>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 states that the fact that Salvador Pueyo and I come to different conclusions based on what we both regard as being an objective prior provides corroborative evidence that an objective prior is not objective in the common use of that word. Although in most cases a completely noninformative prior may not exist, so that conclusions will depend to at least a modest extent on a subjective choice of prior, 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! (Of course, even where there is a unique fully noninformative prior, parameter estimation involves other subjective choices.)

Bart asks me to respond to Salvador’s criticism that if the prior depends on the experiment, it’s not strictly speaking a prior, but rather a reference distribution, which, in the absence of strong constraints by data (as is the case for ECS) causes a meaningless posterior distribution.

Where a prior is intended to be noninformative, not reflecting any prior knowledge of the parameter(s) being estimated, then it should depend on the experiment and nothing else. It is best regarded as a mathematical tool or weighting function, designed to produce a posterior PDF that reflects the data not the prior. Such a prior has no direct probabilistic interpretation: it should not be regarded as a probability density. A prior that is noninformative in this sense may or may not be a “reference prior” in the Berger and Bernardo’s sense. 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? It doesn’t follow that in the absence of strong constraints by data that means the resulting posterior distribution is meaningless. Quite the contrary. And the distinction that Salvador is making between what he calls respectively “reference priors” and “noninformative priors” makes no sense to me.

The whole point about a noninformative prior is that it is constructed so that only weak constraints by the data are required in order for the resulting posterior PDF for the parameter(s) to be dominated by (correctly-reflected) information from the data rather than information from the prior. Indeed, Berger and Bernardo show that reference priors have a minimal influence on inference, in the sense of maximising the missing information about the parameters.

Salvador’s arguments about a uniform distribution being noninformative for positions, and relating to symmetries, may be valid when parameters only have a finite number of possible values, but they fail in the continuous case because the relevant invariant measure is unspecified. Jaynes recognised this point (Section 12.3 of Probability Theory: The Logic of Science), and was only able to resolve the measure problem in special cases, in particular when a transformation group existed.

Bart also asks me to respond to James’ criticism that (in a radiocarbon dating example) the posterior PDF shows zero probability density at locations where the data show substantial likelihood but the prior pdf is zero. My 23 July comment already deals with most of what James said. When Jeffreys’ prior (the original noninformative prior) is used, the prior, and hence the posterior, is very low (not zero) in regions where the data are very uninformative about – change little with – the parameter(s). If no existing knowledge about the parameters is to be incorporated, the resulting PDF is correct, however odd it may look.

Suppose the data measures a variable (here radiocarbon age of an artefact), with known-variance Gaussian-distributed random errors. In the absence of prior knowledge about the artefact’s radiocarbon age or calendar age, use of a uniform prior for inferring the radiocarbon age of the artefact is both natural and noninformative. Use of a uniform prior results in a Gaussian posterior PDF, credible intervals from which exactly match frequentist confidence intervals for the same measurement. What’s not to like about that? But if one accepts that posterior PDF for radiocarbon age, one necessarily accepts the sort of odd-shaped posterior for the artefact’s calendar age that James rejects, since it follows from applying the standard transformation of variables formula.

James prefers what he views as realistic-looking posterior PDFs for parameters, even if the uncertainty ranges they produce disagree substantially with relative frequencies in the long run – and the posterior PDFs they imply for radiocarbon ages are most unrealistic looking.

I on the other hand prefer – , certainly for reporting scientific results – posterior PDFs that produce uncertainty ranges which are at least approximately valid in frequentist coverage (probability matching) terms upon (hypothetically) repeated independent measurements, so that they represent approximate confidence intervals. (Exact matching of confidence intervals is not generally possible using a Bayesian approach.) Of course, if there is genuine prior knowledge about the distribution of an artefact’s calendar age, then the position is different. But I don’t think a wide uniform distribution would convey such knowledge in any case.

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