GCM's, macroweather, the climate and extremes

We are used to the weather - climate dichotomy, yet the great majority of the spectral variance of atmospheric fields is in the continuous “background” and this defines instead a trichotomy with a “macroweather” regime in the intermediate range ≈ 10 days to 30 years. In the weather, macroweather and climate regimes, exponents characterize the type of variability over the entire ranges and it is natural to identify them with qualitatively different synergies of nonlinear dynamical mechanisms that repeat scale after scale. Since climate models are essentially meteorological models (although with extra couplings) it is thus important to determine whether they currently model all three regimes. Using Last Millennium simulations from four GCM's, we show that control runs only reproduce macroweather. When various (reconstructed) climate forcings are included, in the recent (industrial) period they show global fluctuations strongly increasing at scales >≈ 10-30 yrs, which is quite close to the observations. However, in the pre-industrial period the multicentennial variabilities are too weak. A possible explanation is that the models lack of important slow climate processes such as land-ice or relevant and possibly unknown biogeochemical processes. The existence of three scaling regimes is of fundamental importance for the extremes. This is because a generic consequence of scaling processes is power law (“fat”) tails on the corresponding probability distributions. It is therefore not surprising that temperature fluctuations at monthly and longer scales are power laws. Empirical estimates of the power law exponents are about 5 ([Lovejoy and Schertzer, 1986], [Lovejoy and Schertzer, 2013]). This means that fluctuations of amplitude ten standard deviations will occur with probabilities only 10**5 times less often than fluctuations of one standard deviation. This is a huge amplification of probability with respect to Gaussian fluctuations for which the corresponding decrease in probability would be a factor of about 10**23. References:

Lovejoy, S., and D. Schertzer (1986), Scale invariance in climatological temperatures and the spectral plateau, Annales Geophysicae, 4B, 401-410. Lovejoy, S., and D. Schertzer (2013), The Weather and Climate: Emergent Laws and Multifractal Cascades, 496 pp., Cambridge University Press, Cambridge.