  A linearized energy-balance model for global temperature is formulated,
featuring a scale-free long-range memory (LRM) response and stochastic forcing
representing the influence on the ocean heat reservoir from atmospheric weather
systems. The model is parametrized by an effective response strength, the
stochastic forcing strength, and the memory exponent. The instrumental global
surface temperature record and the deterministic component of the forcing are
used to estimate these parameters by means of the maximum-likelihood method.
The residual obtained by subtracting the deterministic solution from the
observed record is analyzed as a noise process and shown to be consistent with
a long-memory time-series model and inconsistent with a short-memory model. By
decomposing the forcing record in contributions from solar, volcanic, and
anthropogenic activity one can estimate the contribution of each to 20'th
century global warming. The LRM model is applied with a reconstruction of the
forcing for the last millennium to predict the large-scale features of northern
hemisphere temperature reconstructions, and the analysis of the residual also
clearly favors the LRM model on millennium time scale. The decomposition of the
forcing shows that volcanic aerosols give a considerably greater contribution
to the cooling during the Little Ice Age than the reduction in solar irradiance
associated with the Maunder minimum in solar activity. The LRM model implies a
transient climate response in agreement with IPCC AR4 projections, but the
stronger response on longer time scales suggests to replace the notion of
equilibrium climate sensitivity by a time-scale dependent sensitivity.
