Climate Dynamics

, Volume 44, Issue 11–12, pp 3187–3210 | Cite as

A voyage through scales, a missing quadrillion and why the climate is not what you expect

  • S. Lovejoy


Using modern climate data and paleodata, we voyage through 17 orders of magnitude in scale explicitly displaying the astounding temporal variability of the atmosphere from fractions of a second to hundreds of millions of years. By combining real space (Haar fluctuation) and Fourier space analysis, we produce composites quantifying the variability. These show that the classical “mental picture” in which quasi periodic processes are taken as the fundamental signals embedded in a spectral continuum of background “noise” is an iconic relic of a nearly 40 year old “educated guess” in which the flatness of the continuum was exaggerated by a factor of ≈1015. Using modern data we show that a more realistic picture is the exact opposite: the quasiperiodic processes are small background perturbations to spectrally continuous wide range scaling foreground processes. We identify five of these: weather, macroweather, climate, macroclimate and megaclimate, with rough transition scales of 10 days, 50 years, 80 kyrs, 0.5 Myr, and we quantify each with scaling exponents. We show that as we move from one regime to the next, that the fluctuation exponent (H) alternates in sign so that fluctuations change sign between growing (H > 0) and diminishing (H < 0) with scale. For example, mean temperature fluctuations increase up to about 5 K at 10 days (the lifetime of planetary structures), then decrease to about 0.2 K at 50 years, and then increase again to about 5 K at glacial-interglacial scales. The pattern then repeats with a minimum RMS fluctuation of 1–2 K at ≈0.5 Myr increasing to ≈20 K at 500 Myrs. We show how this can be understood with the help of the new, pedagogical “H model”. Both deterministic General Circulation Models (GCM’s) with fixed forcings (“control runs”) and stochastic turbulence-based models reproduce weather and macroweather, but not the climate; for this we require “climate forcings” and/or new slow climate processes. Averaging macroweather over periods increasing to ≈30–50 yrs yields apparently converging values: macroweather is “what you expect”. Macroweather averages over ≈30–50 yrs have the lowest variability, they yield well defined climate states and justify the otherwise ad hoc “climate normal” period. However, moving to longer periods, these states increasingly fluctuate: just as with the weather, the climate changes in an apparently unstable manner; the climate is not what you expect. Moving to time scales beyond 100 kyrs, to the macroclimate regime, we find that averaging the varying climate increasingly converges, but ultimately—at scales beyond ≈0.5 Myr in the megaclimate, we discover that the apparent point of convergence itself starts to “wander”, presumably representing shifts from one climate to another.


Climate Weather Scaling Variability Paleotemperatures 



Roger Pielke sr., Gavin Schmidt, Daniel Schertzer and Adrian Tuck are thanked for their useful comments.

Conflict of interest



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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of PhysicsMcGill UniversityMontrealCanada

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