The topology of river networks has been extensively studied over the past decades using the suite of quantitative methods developed in the pioneering works of Horton, Strahler, Shreve, and Tokunaga. As a result, stream-ordering schemes and statistical self-similarity concepts have been explored to a considerable extent in hydrologic and geomorphologic sciences and have penetrated other areas of natural sciences. At the same time, questions related to how the static topology of a river network affects the dynamical processes operating on this network have been studied to a considerably lesser degree, while the impact of such processes is of the greatest interest from environmental, economic, and societal points of view. This project maintains a sustained research effort focused on environmental transport along river networks, in particular, and dynamic processes on hierarchical branching structures, in general. The main goal is to develop a theoretical and modeling framework that will facilitate predictive understanding of the relationships between the geometry of a network and dynamic processes that operate on it. The analytic methods to be developed and applied in the project arise from the theories of hierarchical aggregation and complex networks. The proposed transport modeling is based on the mathematical theory of Boolean delay equations (BDEs), a framework especially tailored for the mathematical modeling of systems that exhibit thresholds, multiple feedbacks and distinct time delays. The BDE modeling will provide a flexible basis for a preliminary assessment of land-use and climate change effects on resource attributes of a river system, including sediment grain size distribution, algae production and transport, nutrient loading, and fish population. It will also constitute a simple ?platform? for testing hypotheses and guiding further data collection efforts for improved prediction under uncertainty. The project will adapt concepts and tools from other disciplines, mainly dynamical and complex systems, to earth-surface research.
The proposed study opens a new direction in earth-surface modeling, focused on environmental transport on river networks. The intellectual merit of this project resides in the novel mathematical, modeling, and data exploration approaches, put forward by an interdisciplinary team toward predictive understanding of environmental dynamics on river networks. The critical societal and economic importance of network dynamic problems? in the geosciences and other areas of the physical and life sciences?adds substantially to the proposal?s intellectual merit. The project will result in better predictive understanding of environmental fluxes including precipitation, sediment bedload, nutrients, pollutants, etc., and provide new insight into rivers? habitat structure and food webs. The project will impact other science areas that involve network dynamics and hierarchical aggregation, including gene interactions, social networks, spread of diseases, and Internet security. The new results will be achieved by further developing a novel theoretical concept of dynamic networks, integrating this concept into concrete applications, and developing corresponding numerical models. The project PIs are actively involved in promoting interactions between mathematicians, physicists and researchers in geosciences and will further strengthen such interactions within this project. The collaborative and cross-disciplinary approach of this project makes it an ideal training ground for graduate students, post-docs and young scientists.
Landscapes contain networks of dynamically connected paths (e.g., fluvial, hillslope, subsurface) which play an important role in structuring environmental fluxes. In this work, we have proposed a framework for studying the topology (branching), the geometry (link lengths and distances), and the dynamics (temporal evolution of connectivity) on networks for the purpose of quantifying flux response functions in river basins using reduced complexity models. Specifically, a transport framework on networks has been generalized in our work in a way that accounts for the transport dynamics of different fluxes (e.g., streamflow, sediment, nutrients, biota) through a dynamic hierarchical connectivity of pathways considering process dynamics and space-time variable inputs. The developed framework has been demonstrated and applied to fluvial sediment transport in the Minnesota River Basin (MRB) which, despite being mostly agricultural land, has a pronounced localized spatial heterogeneity in geomorphic features, such as high bluffs and still evolving headwater channels, the remnants of a geologic history left behind by the last glaciation contributing to new sediment sources. At the same time, an accelerated hydrologic cycle (mainly due to changes in land-use) is making the response of the MRB to perturbations quite complex. Specifically, focusing on the transport of sediment (e.g., sand on the river bed), a sedimentologic response at the outlet of the basin has been computed revealing multiple peaks arriving at the outlet at times not trivially related to sub-basin distance from the outlet. Our preliminary results suggest a resonant frequency of sediment supply where the disturbance of one area followed by the disturbance of another (spatially disconnected) area after a certain period of time (resonance time), results in amplification of the effects of sediment source perturbation. Thus, this framework has identified an important vulnerability of the basin to spatial and temporal structuring of sediment inputs and can form the basis of guiding management decisions.
