Long-range persistence in global surface temperatures explained by linear multi-box energy balance models

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.