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We consider the effect of different temporal error structures on theinference of equilibrium climate sensitivity\footnote{ECS is defined as therealized equilibrium surface warming---globally-averaged surface airtemperature---for a doubling of CO$_2$}(ECS), in the context of an energybalance model (EBM) that is commonly employed in analyzing earth system models(ESM) and observations. We consider error structures ranging from uncorrelated(IID normal) to AR(1) to Gaussian correlation (Gaussian Process GP) to analyzethe abrupt 4xCO$_2$ CMIP5 experiment in twenty-one different ESMs. For seven ofthe ESMs, the posterior distribution of ECS is seen to depend rather weakly onthe discrepancy model used suggesting that the discrepancies were largelyuncorrelated. However, large differences for four, and moderate differences forthe rest of the ESMs, leads us to suggest that AR(1) is an appropriatediscrepancy correlation structure to use in situations such as the oneconsidered in this article. Other significant findings include: (a) Whenestimates of ECS (mode) were differrent, estimates using IID were higher (b)For four of the ESMs, uncertainty in the inference of ECS was higher with theIID discrepancy structure than with the other correlated structures, and (c)Uncertainty in the estimation of GP parameters were much higher than with theestimation of IID or AR(1) parameters, possibly due to identifiability issues.They need to be investigated further.

Dependence of Inferred Climate Sensitivity on the Discrepancy Model