How big, and how long-lasting, will an extreme burst above threshold be ? Lessons from self-organised criticality

The idea that there might not be a typical scale for energy release in some space physics systems is a relatively new one [see e.g. mini-review of early work in Freeman and Watkins, Science, 2002; & Aschwanden, Self Organized Criticality (SOC) in Astrophysics, Springer, 2011]. In part it resulted from the widespread approximate fractality seen elsewhere in nature. SOC was introduced by Bak et al [PRL, 1987] as a physical explanation of such widespread space-time fractality. SOC inspired the introduction into magnetospheric physics of "burst" diagnostics by Takalo [1993] & Consolini [1996]. These quantified events in a time series by "size" (integrated area above a fixed threshold) and "duration", and revealed a long tailed population of events across a broad range of sizes, subsequently also seen in solar wind drivers like Akasofu's epsilon function [Freeman et al, PRE & GRL, 2000]. Spatiotemporal bursts have an interest beyond SOC, however. Estimating the probability of a burst of a given size and duration bears directly on the problem of correlated extreme events, or "bunched black swans" [e.g. Watkins et al, EGU, 2011 presentation at the URL below]. With a view both to space physics and this wider context we here consider an interesting development of the burst idea made by Uritsky et al [GRL, 2001]. These authors adapted the spatiotemporal spreading exponent [e.g. Marro & Dickman, Nonequilibrium phase transitions in lattice models, 1999], calculating a superposed epoch average of surviving activity in bursts after their first excursion above a threshold. In a 1D time series, the 1-minute AL auroral index (averaged over 5 minutes), they found scaling behaviour up to ~ 2 hours. We investigate the relationships between exponents found by this method and other, more widely known exponents governing a fractal (or multifractal) time series such as the self-similarity exponent H and long-range dependence exponent d. We conclude by discussing the applications of these techniques to problems such as the forecasting the probability of a single short-lived large burst versus that of a long correlated sequence of more moderate exceedences above a threshold.