  The temporal fluctuations in global mean surface temperature is an example of
a geophysical quantity which can be described using the notions of long-range
persistence and scale invariance/scaling, but this description has suffered
from lack of a generally accepted physical explanation. Processes with these
statistical signatures can arise from non-linear effects, for instance through
cascade-like energy transfer in turbulent fluids, but they can also be produced
by linear models with scale-invariant impulse-response functions. This paper
demonstrates that on time scales from months to centuries, the scale-invariant
impulse-response function of global surface temperature can be explained from
simple linear multi-box energy balance models. This explanation describes both
the scale invariance of the internal variability and the lack of a
characteristic time scale of the response to external forcings. With parameters
estimated from observational data, the climate response is approximately
scaling in these models, even if the response function is not chosen to be
scaling a priori. It is also demonstrated that the differences in scaling
exponents for temperatures over land and for sea-surface temperatures can be
reproduced by a version of the multi-box energy balance model with two distinct
surface boxes.
