Potential Well in Poincaré Recurrence.

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

Thallium distribution in an estuary affected by acid mine drainage (AMD): The Ría de Huelva estuary (SW Spain).

This study investigates the behavior of Tl in the Ría de Huelva (SW Spain), one of the most metal polluted estuaries in the world. Dissolved Tl concentration displayed a general decrease across the estuary during the dry season (DS); from 5.0 to 0.34 µg/L in the Tinto and Odiel estuaries, respectively, to 0.02 µg/L in the channel where the rivers join. A slighter decrease was observed during the wet season (WS) (from 0.72 to 0.14 µg/L to 0.02 µg/L) due to the dilution effect of rainfalls in the watersheds. These values are 3 orders of magnitude higher than those reported in other estuaries worldwide. Different increases in Tl concentrations with salinity were observed in the upper reaches of the Tinto and Odiel estuaries, attributed to desorption processes from particulate matter. Chemical and mineralogical evidences of particulate matter, point at Fe minerals (i.e., jarosite) as main drivers of Tl particulate transport in the estuary. Unlike other estuaries worldwide, where a fast sorption process onto particulate matter commonly takes place, Tl is mainly desorbed from particulate matter in the Tinto and Odiel estuaries. Thus, Tl may be released back from jarositic particulate matter across the salinity gradient due to the increasing proportion of unreactive TlCl0 and K+ ions, which compete for adsorption sites with Tl+ at increasing salinities. A mixing model based on conservative elements revealed a 6-fold increase in Tl concentrations related to desorption processes. However, mining spills like that occurred in May 2017 may contribute to enhance dissolved and particulate Tl concentrations in the estuary as well as to magnify these desorption processes (up to around 1100% of Tl release), highlighting the impact of the mine spill on the remobilization of Tl from the suspended matter to the water column.

VENM: An Algorithm to Accurately Calculate Neutral Slopes and Gradients.

Mesoscale eddies stir along the neutral plane, and the resulting neutral diffusion is a fundamental aspect of subgrid-scale tracer transport in ocean models. Calculating neutral diffusion traditionally involves calculating neutral slopes and three-dimensional tracer gradients. The calculation of the neutral slope traditionally occurs by computing the ratio of the horizontal to vertical locally referenced potential density derivative. However, this approach is problematic in regions of weak vertical stratification, prompting the use of a variety of ad hoc regularization methods that can lead to rather nonphysical dependencies for the resulting neutral tracer gradients. Here we use a VErtical Non-local Method "VENM," a search algorithm that requires no ad hoc regularization and significantly improves the numerical accuracy of calculating neutral slopes, neutral tracer gradients, and associated neutral diffusive fluxes. We compare and contrast VENM against a more traditional method, using an independent objective neutrality condition combined with estimates of spurious diffusion, heat transport, and water mass transformation rates. VENM is more accurate, both physically and numerically, and should form the basis for future efforts involving neutral diffusion calculations from observations and possibly numerical model simulations.