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

Abstract

Abstract. At scales much longer than the deterministic predictability limits (about 10 days), the statistics of the atmosphere undergo a drastic transition, the high frequency weather acts as a random forcing on the lower frequency macroweather. In addition, up to decadal and centennial scales the equivalent radiative forcings of solar, volcanic and anthropogenic perturbations are small compared to the mean incoming solar flux. This justifies the common practice of reducing forcings to radiative equivalents (which are assumed to combine linearly), as well as the development of linear stochastic models, including for forecasting at monthly to decadal scales. In order to clarify the validity of the linearity assumption and determine its range of validity, we use last Millennium simulations, both with the simplified Zebiac–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 time scales from one to 1000 years. We also compare the statistics to multiproxy temperature reconstructions. The main findings are: (a) that the variability of the ZC and GCM models are too weak at centennial and longer scales, (b) for longer than ≈ 50 years, the solar and volcanic forcings combine subadditively (nonlinearly) compounding the weakness of the response, (c) the models display another nonlinear effect at shorter scales: their sensitivities are much higher for weak forcing than for strong forcing (their intermittencies are different) and we quantify this with statistical scaling exponents.