  We consider the effect of different temporal error structures on the
inference of equilibrium climate sensitivity\footnote{ECS is defined as the
realized equilibrium surface warming---globally-averaged surface air
temperature---for a doubling of CO$_2$}(ECS), in the context of an energy
balance 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 analyze
the abrupt 4xCO$_2$ CMIP5 experiment in twenty-one different ESMs. For seven of
the ESMs, the posterior distribution of ECS is seen to depend rather weakly on
the discrepancy model used suggesting that the discrepancies were largely
uncorrelated. However, large differences for four, and moderate differences for
the rest of the ESMs, leads us to suggest that AR(1) is an appropriate
discrepancy correlation structure to use in situations such as the one
considered in this article. Other significant findings include: (a) When
estimates 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 the
IID discrepancy structure than with the other correlated structures, and (c)
Uncertainty in the estimation of GP parameters were much higher than with the
estimation of IID or AR(1) parameters, possibly due to identifiability issues.
They need to be investigated further.
