What could we learn about climate sensitivity from variability in the surface temperature record

We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used trends in observational time series to constrain equilibrium climate sensitivity, it has also been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed, and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. It is only when the sensitivity is very low that the variability can provide a tight constraint. Our investigations take the form of "perfect model" experiments, in which we make the optimistic assumption that the model is structurally perfect and all uncertainties (including the true parameter values and nature of internal variability noise) are correctly characterised. Therefore the results might be interpreted as a best-case scenario for what we can learn from variability, rather than a realistic estimate of this. In these experiments, we find that for a moderate sensitivity of 2.5 degrees C, a 150-year time series of pure internal variability will typically support an estimate with a 5 %-95% range of around 5 degrees C (e.g. 1.9-6.8 degrees C). Total variability including that due to the forced response, as inferred from the detrended observational record, can provide a stronger constraint with an equivalent 5 %-95 % posterior range of around 4 degrees C (e.g. 1.8-6.0 degrees C) even when uncertainty in aerosol forcing is considered. Using a statistical summary of variability based on autocorrelation and the magnitude of residuals after detrending proves somewhat less powerful as a constraint than the full time series in both situations. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity but suggest caution in the interpretation of precise results.