Not NORMAL: Anomalous transport in hydrology, hydrogeology, and geomorphology

2017 Spring Cyberseminar Series

Rina Schumer / Desert Research Institute

Talk Description:

Across scientific disciplines, the diffusion equation is the default model for simulating the spread of particles around an average motion.  Since solutions to the diffusion equation are related to the Gaussian, or Normal, probability distribution, we refer to diffusive motion as ‘normal transport’. Not surprisingly, this single mathematical model fails to capture all relevant features of water, solute, and sediment transport across the earth. Instead, characterization of the ways in which transport deviates from normal diffusion is a tool in identifying significant environmental processes and the time and space scales over which they operate.  Identification of and origins of anomalous transport from physical and mathematical perspectives varies across subsurface, fluvial and overland systems. Anomalous transport in the subsurface can arise from the structure of porous media. Non-diffusive nutrient and sediment transport in rivers is frequently attributed to retention in transient storage zones or the bed. Nonlocal transport on hillslopes can arise when vegetation creates sediment capacitors. In all cases, anomalous transport leads to distinctive signatures in the macroscopic variables we measure. Interpretation of transport-mediated processes - including biogeochemical processing and reactions, persistence of environmental contaminants, and landscape evolution - is affected by the mathematical models we choose to describe transport. However, operational upscaling using anomalous transport equations is yet to come.


Dr. Schumer is a Research Professor at the Desert Research Institute in Reno, NV. Dr. Schumer’s primary research interests involve stochastic models for environmental processes. She uses mathematical models to enhance understanding of subsurface transport in porous and fractured media, surface-subsurface exchange, sediment transport, as well as geomorphic processes and their signature in the geologic record. Using her background in applied mathematics, she also has projects that employ optimization techniques, time series analysis, extreme value theory, and probability and statistics. Dr. Schumer received her B.S. in Earth and Environmental Sciences from Wesleyan University, M.S. in Hydrogeology and Applied Mathematics and Ph.D. in Hydrogeology from the University of Nevada Reno.

CUAHSI's Spring 2017 Cyberseminar Series on Heterogeneity, Complexity and Anomalous Transport in Hydrologic Systems

Real hydrologic systems are heterogeneous and hierarchical, leading to transport processes occurring over disparate and broad ranges of spatio-temporal scales. Many classical models of transport, while undoubtedly powerful and useful, are built on assumptions that simply fail to recognize these complexities.  As such they are incapable of predicting many features commonly observed in real systems. These behaviors are often called “anomalous”. They include processes with very large spatial jumps where solutes or particles quickly travel much larger distances than expected. Similarly trapping events can occur that hold back solutes and particles for much longer times than anticipated. Both the long jumps and trapping events are commonly characterized by power laws, rather than more conventional exponential and Gaussian distributions. Despite the name, anomalous transport is anything but that and is increasingly recognized as the norm across many disciplines in the hydrologic sciences, including flow and transport in highly heterogeneous aquifers as well as in flowing surface waters with hyporheic exchange. Additionally, such behaviors arise in related disciplines such as geomorphology in the fields of surficial processes and sediment transport. To overcome the limitations of classical modeling efforts, new classes of models have and continue to emerge, which successfully capture these so-called anomalous features. This cyberseminar series will focus on these efforts with expert speakers coming from the disciplines of subsurface and surface hydrology and geomorphology to outline these processes in accessible ways to the broader hydrology community.

The series was hosted by Diogo Bolster (Notre Dame University).