Abstract
WATER RESOURCES RESEARCH,
VOL. 45,
W08435,
13 PP., 2009
doi:10.1029/2008WR007668
Stochastic analysis of transport in hillslopes: Travel time distribution and source zone dispersion
Dipartimento di Scienze dell'Ingegneria Civile, Università di Roma Tre, Rome, Italy
Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Volcani Center, Bet Dagan, Israel
Dipartimento di Scienze dell'Ingegneria Civile, Università di Roma Tre, Rome, Italy
A stochastic model is developed for the analysis of the traveltime distribution f τ in a hillslope. The latter is described as made up from a surficial soil underlain by a less permeable subsoil or bedrock. The heterogeneous hydraulic conductivity K is described as a stationary random space function, and the model is based on the Lagrangian representation of transport. A first-order approach in the log conductivity variance is adopted in order to get closed form solutions for the principal statistical moments of the traveltime. Our analysis indicates that the soil is mainly responsible for the early branch of f τ , i.e., the rapid release of solute which preferentially moves through the upper soil. The early branch of f τ is a power law, with exponent variable between −1 and −0.5; the behavior is mainly determined by unsaturated transport. The subsoil response is slower than that of the soil. The subsoil is mainly responsible for the tail of f τ , which in many cases resembles the classic linear reservoir model. The resulting shape for f τ is similar to the Gamma distribution. Analysis of the f τ moments indicates that the mean traveltime is weakly dependent on the hillslope size. The traveltime variance is ruled by the distribution of distances of the injected solute from the river; the effect is coined as source zone dispersion. The spreading due to the K heterogeneity is less important and obscured by source zone dispersion. The model is tested against the numerical simulation of Fiori and Russo (2008) with reasonably good agreement, with no fitting procedure.
Received 18 December 2008; accepted 12 June 2009; published 26 August 2009.
Citation: (2009), Stochastic analysis of transport in hillslopes: Travel time distribution and source zone dispersion, Water Resour. Res., 45, W08435, doi:10.1029/2008WR007668.
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