  Earth's temperature variability can be partitioned into internal and
externally-forced components. Yet, underlying mechanisms and their relative
contributions remain insufficiently understood, especially on decadal to
centennial timescales. Important reasons for this are difficulties in isolating
internal and externally-forced variability. Here, we provide a
physically-motivated emulation of global mean surface temperature (GMST)
variability, which allows for the separation of internal and external
variations. To this end, we introduce the ``ClimBayes'' software package, which
infers climate parameters from a stochastic energy balance model (EBM) with a
Bayesian approach. We apply our method to GMST data from temperature
observations and 20 last millennium simulations from climate models of
intermediate to high complexity. This yields the best estimates of the EBM's
forced and forced + internal response, which we refer to as emulated
variability. The timescale-dependent variance is obtained from spectral
analysis. In particular, we contrast the emulated forced and forced + internal
variance on interannual to centennial timescales with that of the GMST target.
Our findings show that a stochastic EBM closely approximates the power spectrum
and timescale-dependent variance of GMST as simulated by modern climate models.
Small deviations at interannual timescales can be attributed to the simplified
representation of internal variability and, in particular, the absence of
(pseudo-)oscillatory modes in the stochastic EBM. Altogether, we demonstrate
the potential of combining Bayesian inference with conceptual climate models to
emulate statistics of climate variables across timescales.
