Title Supplementary Data and Code for 'On The Estimation of Internal Climate Variability During the Preindustrial Past Millennium'

We use an ensemble of simulations of a coupled model (NCAR Community Earth System Model) driven by natural radiative forcing estimates over the pre-industrial past millennium to test the efficacy of methods used previously to remove forced variability from proxy-based climate reconstructions and estimate residual internal variability (e.g. a putative "Atlantic Multidecadal Oscillation"). Within the framework of these experiments, the forced component of surface temperature change can be estimated accurately from the ensemble mean, and the internal variability of each of the independent realizations can be accurately assessed by subtracting off that estimate. We show in this case, where the true internal variability is known, that regression-based methods of removing the forced component from proxy reconstructions will, in the presence of uncertainties in the underlying natural radiative forcing, fail to yield accurate estimates thereof, incorrectly attributing unresolved forced features and multidecadal spectral peaks associated with them to internal variability.