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Geophysical Monograph Series



  • climate
  • weather
  • turbulence
  • emergence
  • multifractals
  • scaling

Index Terms

  • 4415 Nonlinear Geophysics: Cascades
  • 4440 Nonlinear Geophysics: Fractals and multifractals
  • 3309 Atmospheric Processes: Climatology
  • 3379 Atmospheric Processes: Turbulence



Low-Frequency Weather and the Emergence of the Climate

S. Lovejoy

Department of Physics, McGill University, Montreal, Quebec, Canada

D. Schertzer

We survey atmospheric variability from weather scales up to several hundred kiloyears. We focus on scales longer than the critical τw ≈ 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 τw is the lifetime of planetary-sized structures. At τw, 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 τc ≈ 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 τc) define climate states. However, at scales beyond τc, 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.

Citation: Lovejoy, S., and D. Schertzer (2012), Low-frequency weather and the emergence of the climate, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, edited by A. S. Sharma et al. 231–254, AGU, Washington, D. C., doi:10.1029/2011GM001087.


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