Lagrangian Random Walk Methods in Hydrologic Settings

Multiscale heterogeneity is ubiquitous in hydrologic systems. Geological media exhibit structure on scales ranging from micrometers to hundreds of kilometers. Cor- rectly predicting large-scale behavior often requires a framework capable of assessing how the effects of heterogeneity propagate across scales. In this dissertation, we ex- plore the concept of Lagrangian random walk methods, which represent variability through a statistical description. We develop numerical particle tracking methods and theoretical descriptions relying on random walk theory and apply them to a va- riety of problems with an impact on the hydrologic sciences. Specifically, we address solute reactions and mixing in the presence of nonuniform background flow fields, mixing through bioturbation in freshwater systems, tracer tests in river and stream transport, and broad return time distributions in hydrologic and other settings.