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The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations
Carbone, F., A. Bruno, A. Naccarato, F. De Simone, C. Gencarelli, F. Sprovieri, I. Hedgecock, M. Landis, H. Shov, K. Pfaffhuber, K. Read, L. Martin, H. Angot, A. Dommergue, O. Magand, AND N. Pirrone. The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations. JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES. American Geophysical Union, Washington, DC, 123(2):764-774, (2018).
A number of studies show that long-term memory in atmospheric pollutant concentrations exists (Chelani  and references therein), that is, up to a limit the concentrations maintain a certain correlation over time. Usually a long-term memory process is defined by a strong coupling between measured values at different time lags, `, and the system’s dynamics are characterized by the presence of complex mesoscopic spatio-temporal patterns. These patterns are associated with the generation of high amplitude fluctuations over a broad range of spatial and temporal scales giving rise to scale-free relationships for statistical quantities [Monin and Yaglom, 2007; McComb, 1990; Frisch, 1995]. These mesoscopic processes occur within macroscopic phenomena, and their behavior evolves into a power-law decay of the autocor relation function. Conversely, in a short-term memory process the autocorrelation function decreases exponentially or to zero after a certain time, `. The dynamics of pollutant concentration variations depend on numerous processes, (for a review see Chelani ), however, due to their complexity it is not possible to precisely describe their behavior and properties over space and time. One of the principal characteristics of complex dynamical systems is the intermittency [Warhaft, 2000; Briggs and Beck, 2007; Carbone and Sorriso-Valvo, 2014; Carbone et al., 2016a; Manshour et al., 2016]. Intermittency represents the strongly correlated fluctuations that lead to deviations from a normal probability distribution function (PDF). In the atmospheric boundary layer, intermittency is an important part of a continuous spectrum of atmospheric motions [Wyngaard, 1992; Katul et al., 2006; Vindel and Yagu¨e, 2011]. Within large scale temporal variations of atmospheric motion, fluctuations in pollutant species concentrations result from interactions of a large ensemble of mesoscopic phenomena, occurring contemporaneously in the atmosphere: turbulence [Wyngaard, 1992], variation in anthropogenic and natural emission sources [Pirrone et al., 2010; Carbone et al., 2016b], variation in deposition velocity, loss through chemical reactions which is in turn determined by fluctuating reactant/oxidant concentrations, and other extreme events. In the specific case of Hg0 these extreme events would include phenomena such as convective storms, forest fires, and atmospheric Hg0 depletion events [Lindberg et al., 2002; Schroeder W. H. et al., 1998; Dvonch et al., 2005; Holmes et al., 2016; De Simone et al., 2017]. Understanding the dynamics of these emergent extreme events, meteorological, chemical and anthropological, represents the key to understanding complex dynamical systems.
The probability density function (PDF) of the time intervals between subsequent extreme events in atmospheric Hg0 concentration data series from different latitudes has been investigated. The Hg0 dynamic possesses a long-term memory autocorrelation function. Above a fixed thresh old Q in the data, the PDFs of the interoccurrence time of the Hg0 data are well described by a Tsallis q–Exponential function. This PDF behavior has been explained in the framework of superstatistics, where the competition between multiple mesoscopic processes affects the macro scopic dynamics. An extensive parameter ?, encompassing all possible fluctuations related to mesoscopic phenomena, has been identified. It follows a ?2-distribution, indicative of the superstatistical nature of the overall process. Shuffling the data series destroys the long-term memory, the distributions become independent of Q, and the PDFs collapse on to the same exponential distribution. The possible central role of atmospheric turbulence on extreme events in the Hg0 data is highlighted.