Low-Frequency Weather and the Emergence of the Climate

We survey atmospheric variability from weather scales up to several hundred kiloyears. We focus on scales longer than the critical tau(w) approximate to 5-20 day scale corresponding to a drastic transition from spectra with high to low spectral exponents. Using anisotropic, intermittent extensions of classical turbulence theory, we argue that tau(w) is the lifetime of planetary-sized structures. At tau(w), there is a dimensional transition; at longer times the spatial degrees of freedom are rapidly quenched, leading to a scaling low-frequency weather regime extending out to tau(c) approximate to 10-100 years. The statistical behavior of both the weather and low-frequency weather regime is well reproduced by turbulence-based stochastic models and by control runs of traditional global climate models, i.e., without the introduction of new internal mechanisms or new external forcings; hence, it is still fundamentally weather. Whereas the usual (high frequency) weather has a fluctuation exponent H > 0, implying that fluctuations increase with scale, in contrast, a key characteristic of low-frequency weather is that H < 0 so that fluctuations decrease instead. Therefore, it appears stable, and averages over this regime (i.e., up to tau(c)) define climate states. However, at scales beyond tau(c), whatever the exact causes, we find a new scaling regime with H > 0; that is, where fluctuations again increase with scale, climate states thus appear unstable; this regime is thus associated with our notion of climate change. We use spectral and difference and Haar structure function analyses of reanalyses, multiproxies, and paleotemperatures.