Separating low-frequency internal variability of the climate system from the forced signal is essential to better understand anthropogenic climate change as well as internal climate variability. Here both synthetic time series and the historical simulations from phase 5 of CMIP (CMIP5) are used to examine several methods of performing this separation. Linear detrending, as is commonly used in studies of low-frequency climate variability, is found to introduce large biases in both amplitude and

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... hase of the estimated internal variability. Using estimates of the forced signal obtained from ensembles of climate simulations can reduce these biases, particularly when the forced signal is scaled to match the historical time series of each ensemble member. These so-called scaling methods also provide estimates of model sensitivities to different types of external forcing. Applying the methods to observations of the Atlantic multidecadal oscillation leads to different estimates of the phase of this mode of variability in recent decades.