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A two-dimensional stochastic–diffusive energy balance model (EBM) formulated on a sphere by G. R. Northet al. is explored and generalized. Instantaneous and frequency-dependent spatial autocorrelation functions andlocal temporal power spectral densities are computed for local sites and for spatially averaged surface temperaturesignals up to the global scale. On time scales up to the relaxation time scale given by the effective heatcapacities of the ocean mixed layer and land surface, respectively, scaling features are obtained that are reminiscentof what can be derived from the observed temperature field. On longer time scales, however, the EBMpredicts a transition to a white-noise scaling, which is not reflected in the observed records. A fractional generalization,which can be considered as a spatial generalization of the zero-dimensional, long-memory EBM ofM. Rypdal and K. Rypdal, is proposed and explored. It is demonstrated that this generalized model describesqualitatively the main correlation characteristics of the temperature field reported in the literature and thosederived herein from 500-yr-long control simulations of the NorESM Earth system model. A further generalizationof the model, to include long-term persistence in the stochastic forcing, is also discussed

Spatiotemporal Long-Range Persistence in Earth’s Temperature Field: Analysis of Stochastic–Diffusive Energy Balance Models