Restoration of river deltas involves diverting sediment and water from major channels into adjoining drowned areas, where the sediment can build new land and provide a platform for regenerating wetland ecosystems. Except for local engineered structures at the points of diversion, restoration mainly relies on natural delta-building processes. Present understanding of such processes is sufficient to provide a basis for determining the feasibility of restoration projects through quantitative estimates of land-building rates and sustainable wetland area under different scenarios of sediment supply, subsidence, and sea-level rise. We are not yet to the point of being able to predict the evolution of a restored delta in detail. Predictions of delta evolution are based on field studies of active deltas, deltas in mine-tailings ponds, experimental deltas, and countless natural experiments contained in the stratigraphic record. These studies provide input for a variety of mechanistic delta models, ranging from radially averaged formulations to more detailed models that can resolve channels, topography, and ecosystem processes. Especially exciting areas for future research include understanding the mechanisms by which deltaic channel networks self-organize, grow, and distribute sediment and nutrients over the delta surface and coupling these to ecosystem processes, especially the interplay of topography, network geometry, and ecosystem dynamics.

[1] One way to study the mechanism of gravel bed load transport is to seed the bed with marked gravel tracer particles within a chosen patch and to follow the pattern of migration and dispersal of particles from this patch. In this study, we invoke the probabilistic Exner equation for sediment conservation of bed gravel, formulated in terms of the difference between the rate of entrainment of gravel into motion and the rate of deposition from motion. Assuming an active layer formulation, stochasticity in particle motion is introduced by considering the step length (distance traveled by a particle once entrained until it is deposited) as a random variable. For step lengths with a relatively thin (e.g., exponential) tail, the above formulation leads to the standard advection-diffusion equation for tracer dispersal. However, the complexity of rivers, characterized by a broad distribution of particle sizes and extreme flood events, can give rise to a heavy-tailed distribution of step lengths. This consideration leads to an anomalous advection-diffusion equation involving fractional derivatives. By identifying the probabilistic Exner equation as a forward Kolmogorov equation for the location of a randomly selected tracer particle, a stochastic model describing the temporal evolution of the relative concentrations is developed. The normal and anomalous advection-diffusion equations are revealed as its long-time asymptotic solution. Sample numerical results illustrate the large differences that can arise in predicted tracer concentrations under the normal and anomalous diffusion models. They highlight the need for intensive data collection efforts to aid the selection of the appropriate model in real rivers.

Although sediment is a natural constituent of rivers, excess loading to rivers and streams is a leading cause of impairment and biodiversity loss. Remedial actions require identification of the sources and mechanisms of sediment supply. This task is complicated by the scale and complexity of large watersheds as well as changes in climate and land use that alter the drivers of sediment supply. Previous studies in Lake Pepin, a natural lake on the Mississippi River, indicate that sediment supply to the lake has increased 10-fold over the past 150 years. Herein we combine geochemical fingerprinting and a suite of geomorphic change detection techniques with a sediment mass balance for a tributary watershed to demonstrate that, although the sediment loading remains very large, the dominant source of sediment has shifted from agricultural soil erosion to accelerated erosion of stream banks and bluffs, driven by increased river discharge. Such hydrologic amplification of natural erosion processes calls for a new approach to watershed sediment modeling that explicitly accounts for channel and floodplain dynamics that amplify or dampen landscape processes. Further, this finding illustrates a new challenge in remediating nonpoint sediment pollution and indicates that management efforts must expand from soil erosion to factors contributing to increased water runoff.

Mathematical models improve our fundamental understanding of the environmental behavior, fate, and transport of engineered nanomaterials (NMs, chemical substances or materials roughly 1-100 nm in size) and facilitate risk assessment and management activities. Although today's large-scale environmental fate models for NMs are a considerable improvement over early efforts, a gap still remains between the experimental research performed to date on the environmental fate of NMs and its incorporation into models. This article provides an introduction to the current state of the science in modeling the fate and behavior of NMs in aquatic environments. We address the strengths and weaknesses of existing fate models, identify the challenges facing researchers in developing and validating these models, and offer a perspective on how these challenges can be addressed through the combined efforts of modelers and experimentalists.