Scaling, extremes and mass extinctions in the megaclimate regime

Shaun Lovejoy (March 28, 2019)

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Our atmospheric environment is variable from milliseconds to the age of the planet, from tenths of a millimeter to its size: scale ratios of 1020 and 1010 respectively. The simplest assumption about wide space-time scale range processes is that its dynamics – even though complex and highly nonlinear - are nonetheless scaling (i.e. they respect a scale symmetry). The scaling principle can thus be used to classify the various dynamical regimes that are in operation.

Using modern instrumental and paleo data, and with the help of Haar fluctuations, in 2015 it was pointed out that the conventional picture of atmospheric variability - essentially a white noise “background� “continuum spectrum interspersed with oscillatory processes - was in error by a factor of at least 1015. Instead, modern data and paleo data show that there are 4 or possibly 5 regimes - from dissipation scales up to the end of the Phanerozoic eon (5.5x108 years): weather, macroweather, climate, macroclimate and megaclimate. The time scales transitional from one regime to another were broadly estimated as 10 days, 300yrs, 105 yrs, 5x105 yrs. (the 300 yr macroweather- climate transition is a pre-industrial estimate; in the anthropocene, it is closer to 20 years). It should be noted that the status of the narrow macroclimate regime is not clear; it may instead turn out to be a broad astronomically forced cycle.

Scaling regimes have a number of generic statistical properties that we outline. These include intermittent “spiky�, highly nonGaussian transitions as well as power-law extreme probabilities associated with “black swan� events. We show that this (real space) intermittency is associated with large, random spectral spikes that can easily be spuriously attributed to oscillatory processes. Indeed, we argue that sophisticated Fourier techniques combined with inappropriate null hypotheses have often misinterpreted random spectral peaks in terms of real physical phenomena.

We focus on the megaclimate regime whose statistical properties are investigated with the help of data from benthic stacks (ocean sediment isotope measurements) that cover the range of scales from roughly half a million to half a billion years. We show that in mega-climate the paleotemperature fluctuation exponent is positive indicating that the temperature is unstable, that it tends to “wander�: instead of tending to converge to any particular value, it tends to diverge. This already invalidates Gaia hypothesis – at least over the Phanerozoic. We also show that paleotemperatures are intermittent, we quantify this with (multifractal) scaling exponents and we also confirm that the extreme fluctuations are power laws. This implies that it is difficult to distinguish relatively frequent extreme temperature fluctuations from genuine tipping points.

Finally, we show that this picture is compatible with analyses of mass extinction events.