Vladimir Cvetkovic: Stochastic modeling of hydrological transport

Hydrological transport refers to water and tracer transport that is a part of the hydrological cycle. The two principle components are atmospheric and terrestrial, our main interest being the terrestrial component with many practical applications. Hydrological transport is controlled by boundary conditions and structure of the terrestrial hydrosphere (topography, drainage networks, soil, rock, etc) that usually exhibit both deterministic and random features. Our focus is on the water or tracer transport time between specified locations. The flow velocity is random, in the general case fluctuating in both space and time. Tracer travel or residence time is treated as a random process subordinated to the water travel time. Different probabilistic approaches are compared, from the classical Lagrangian (Taylor) approach of random streamlines, to a time-domain random walk approach, and more generally the continuous-time random walk approach. Illustration examples are given and conditions are discussed under which any of the given approaches is more appropriate. Finally, we note a few open theoretical issues.