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

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 similar to 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 approximate to 0.5 Myr increasing to approximate 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 similar to 30-50 yrs yields apparently converging values: macroweather is what you expect. Macroweather averages over similar to 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 similar to 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.