## Thursday, September 21, 2017

### Beyond equilibrium climate sensitivity

New(ish, but I'm just getting round to writing about it) review article by Knutti et al on climate sensitivity. The detailed review of published estimates is impressive, a lot of work must have gone into that. It has been spotted that the Callendar estimate is wrong: the value in the paper is about 1.8C for a doubling of CO2, which is rather lower than the value plotted in the figure. (This calculation ignores changes in clouds, so it's impressively close to what we would estimate today for the same processes).

Probably the most important aspect of the update, however, is summarised in the figure of how radiative imbalance changes with temperature as a model warms up (after an abrupt quadrupling of CO2). Simple linear first-order modelling of the energy balance would suggest that the points should lie on a straight line, with the intercepts on the y and x axes being the initial forcing  and the equilibrium temperature change respectively (and these values can be halved to get those pertaining to a doubling of CO2). A handy consequence of this is that the equilibrium response could be estimated in a climate model, without the need to run the model to equilibrium. Based on this idea (often referred to as the “Gregory method ”), the equilibrium sensitivities of the CMIP models are typically estimated on the basis of a 150 year simulation following a quadrupling of CO2.

However models - and quite probably, the real world - doesn't behave like that. Instead, the points appear to cluster around a curve which implies the true equilibrium change is greater than that which would be estimated from analysis of an initial segment of the run.

I can't help wonder how rapidly and widely this method would have been accepted if it had been proposed by someone less eminent. I suspect there would be more of a “nice idea, but it doesn't really work that well”. Incidentally, the behaviour is nothing to do with quadrupling per se, you get similar results for greater and lesser forcing changes. I believe quadrupling was just chosen (rather than the more conventional doubling) to get a greater signal/noise ratio in the changes.

Paul Skeoch said...

Thanks for the write-up on this. I'm a bit confused by the Callendar estimate, or how it's understood. From my reading the paper is showing a no-feedback calculation - changing CO2 with water vapour held constant. He then does some hand-waving to suggest that water vapour + cloud feedback would amount to roughly nil (though I'm not sure he's actually talking about it in the context of a feedback due to CO2 increase): 'Thus a change of water vapour, sky radiation and temperature is corrected by a change of cloudiness and atmospheric circulation, the former increasing the reflection loss and thus reducing the effective sun heat.'

Paul Skeoch said...

Couple of interesting things about use of the Gregory method(s). Andrews et al. 2012 formalised the type of Gregory-method used in AR5 for model ECS estimates, citing Li et al. 2012 (which stems from Li's PhD thesis) in support, noting that a Gregory regression method calculated EffCS within 10% of the true warming having run a GCM out six thousand years after quadrupling CO2.

However, the Gregory method used by Li was quite different from that used in Andrews et al. 2012, in which they use abrupt4xCO2 simulations and apply linear regression from a cold start at year 1 over 150 years. Li introduced the CO2 transiently and started the regression only after reaching 4xCO2 at 140 years, at which point the model had already warmed by 6K. A linear regression was then performed over a period of several hundred years.

The other point is relevant to what you were saying about use of 4xCO2 simulations, because the figure that Li found using Gregory regression on a 4xCO2 run in the ECHAM5 model was 12.2K. Using the Andrews et al. 2012 method of converting that to 2xCO2 sensitivity (simply dividing by 2) suggests a model ECS of 6.1K, which is about 80% greater than the slab-ocean 2xCO2 ECS reported in AR4 for that model.

I tend to think the Andrews ECS estimates get close to the canonical 2-4.5C range due to competing biases, whereby the use of 4xCO2 sometimes enhances sensitivity (versus 2xCO2) while regression from an abrupt start dampens apparent sensitivity. The importance of one versus the other probably varies across models. Might also explain the bi-modal distribution of reported model ECS in AR5. About 2/3 of models reported slab-ocean ECS between 2.7 and 3.4K in AR4. Only 1/4 were within that range for Andrews ECS reported in AR5. Instead tending to cluster around 2.5 and 4K.

James Annan said...

Hi Paul, not sure about the Callendar thing, on a quick check of the paper your reading seems correct - what I wrote was based on a comment from someone else who generally knows his stuff so I'll maybe discuss it with him a bit more. In any case the plotted value in Knutti et al seems incorrect. As for the regression, even doing years 20-150 rather than starting at year 1 gets quite a bit closer to the long-term equilibrium value. But of course that doesn't fully solve the problem, as is clear from the figure I copied.

Paul Skeoch said...

Yeah, definitely incorrect. Looks like they either doubled the 1.8K (for some reason) or accidentally duplicated the 3.6K figure from Plass. Incidentally, Plass' estimate is also no-feedback, as covered by Gavin several years ago (also seems quite badly wrong, as far as we understand today).