Fifty years of hyporheic zone research have shown the important role played by the hyporheic zone as an interface between groundwater and surface waters. However, it is only in the last two decades that what began as an empirical science has become a mechanistic science devoted to modeling studies of the complex fluid dynamical and biogeochemical mechanisms occurring in the hyporheic zone. These efforts have led to the picture of surface‐subsurface water interactions as regulators of the form and function of fluvial ecosystems. Rather than being isolated systems, surface water bodies continuously interact with the subsurface. Exploration of hyporheic zone processes has led to a new appreciation of their wide reaching consequences for water quality and stream ecology. Modern research aims toward a unified approach, in which processes occurring in the hyporheic zone are key elements for the appreciation, management, and restoration of the whole river environment. In this unifying context, this review summarizes results from modeling studies and field observations about flow and transport processes in the hyporheic zone and describes the theories proposed in hydrology and fluid dynamics developed to quantitatively model and predict the hyporheic transport of water, heat, and dissolved and suspended compounds from sediment grain scale up to the watershed scale. The implications of these processes for stream biogeochemistry and ecology are also discussed.

Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation. Patterns that are induced neither by heterogeneity in soil properties nor by the local topography are generally explained as the result of spatial self‐organization resulting from “symmetry‐breaking instability” in nonlinear systems. In this case, the spatial dynamics are able to destabilize the homogeneous state of the system, leading to the emergence of stable heterogeneous configurations. Both deterministic and stochastic mechanisms may explain the self‐organized vegetation patterns observed in nature. After an extensive analysis of deterministic theories, we review noise‐induced mechanisms of pattern formation and provide some examples of applications relevant to the environmental sciences.

The impact of climate fluctuations can be observed in the dynamics of vegetation and most particularly in the sensitive environment of savannas. In this paper we present a model for the local competition for soil moisture among neighboring vegetation. The initial condition for the model is a random field where at each point the soil moisture is the mean water content when there are no spatial interactions between sites. The mean soil moisture values account for stochasticity of climate and losses from evapotranspiration and leakage which depend on the existing water content. A spatial dynamics is then implemented based on the explicit minimization of the global water stress over the region. This approach explains the coexistence of herbaceous and woody plants in savannas as well as the changes in canopy density that have been documented in the southwest of the United States as a function of regional climatic fluctuations.