Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

On the multiple ecological roles of water in river networks

The distribution and movement of water can influence the state and dynamics of terrestrial and aquatic ecosystems through a diversity of mechanisms. These mechanisms can be organized into three general categories wherein water acts as (1) a resource or habitat for biota, (2) a vector for connectivity and exchange of energy, materials, and organisms, and (3) as an agent of geomorphic change and disturbance. These latter two roles are highlighted in current models, which emphasize hydrologic connectivity and geomorphic change as determinants of the spatial and temporal distributions of species and processes in river systems. Water availability, on the other hand, has received less attention as a driver of ecological pattern, despite the prevalence of intermittent streams, and strong potential for environmental change to alter the spatial extent of drying in many regions. Here we summarize long-term research from a Sonoran Desert watershed to illustrate how spatial patterns of ecosystem structure and functioning reflect shifts in the relative importance of different 'roles of water' across scales of drainage size. These roles are distributed and interact hierarchically in the landscape, and for the bulk of the drainage network it is the duration of water availability that represents the primary determinant of ecological processes. Only for the largest catchments, with the most permanent flow regimes, do flood-associated disturbances and hydrologic exchange emerge as important drivers of local dynamics. While desert basins represent an extreme case, the diversity of mechanisms by which the availability and flow of water influence ecosystem structure and functioning are general. Predicting how river ecosystems may respond to future environmental pressures will require clear understanding of how changes in the spatial extent and relative overlap of these different roles of water shape ecological patterns. © 2013 Sponseller et al.