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At scales much longer than the deterministic predictability limits(about 10 days), the statistics of the atmosphere undergoes a drastictransition, the high-frequency weather acts as a random forcing on the lower-frequency macroweather. In addition, up to decadal and centennial scales theequivalent radiative forcings of solar, volcanic and anthropogenicperturbations are small compared to the mean incoming solar flux. Thisjustifies the common practice of reducing forcings to radiative equivalents(which are assumed to combine linearly), as well as the development oflinear stochastic models, including for forecasting at monthly to decadal scales.  In order to clarify the validity of the linearity assumption and determineits scale range, we use last millennium simulations, with both thesimplified Zebiak–Cane (ZC) model and the NASA GISS E2-R fully coupled GCM.We systematically compare the statistical properties of solar-only, volcanic-only and combined solar and volcanic forcings over the range of timescalesfrom 1 to 1000 years. We also compare the statistics to multiproxytemperature reconstructions. The main findings are (a) that the variabilityin the ZC and GCM models is too weak at centennial and longer scales;(b) for longer than  ≈  50 years, the solar and volcanic forcings combinesubadditively (nonlinearly) compounding the weakness of the response; and (c) themodels display another nonlinear effect at shorter timescales: theirsensitivities are much higher for weak forcing than for strong forcing(their intermittencies are different) and we quantify this with statisticalscaling exponents

Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcings