HR: 12:05h
AN: H12C-07    [Abstracts]
TI: Nonlocal transport captured by spatiotemporal fractional derivative models: Modeling approach and field-scale applications
AU: * Zhang, Y
EM: Yong.Zhang@dri.edu
AF: Desert Research Institute, 755 E. Flamingo Road, Las Vegas, NV 89119, United States
AU: Benson, D A
EM: dbenson@mines.edu
AF: Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401, United States
AU: Reeves, D M
EM: Matt.Reeves@dri.edu
AF: Desert Research Institute, 2215 Raggio Parkway, Reno, CO 89512, United States
AB: We investigate the spatiotemporal nonlocality underlying fractional derivative models as a possible explanation for regional-scale anomalous dispersion with heavy tails. Properties of four fractional advection-dispersion equation (fADE) models are analyzed systematically, including the space fADEs with either maximum or minimum skewness, the time fADE with a temporal fractional derivative 0<γ<1, and the novel extension of time fADE with 1<γ<2. Space fADEs describe the dependence of local concentration change on a wide range of spatial zones (i.e., the space nonlocality), while time fADEs describe dynamic mass exchange between mobile and immobile phases and therefore record the temporal history of concentration "loading" locally (i.e., the time nonlocality). We then apply the fADEs as models of anomalous dispersion to several extensively-studied, regional-scale, natural systems. Results suggest that large ranges of motion sizes require the space nonlocality, and long waiting times require time nonlocality. The unknown quantitative relationship between nonlocal parameters and subsurface heterogeneity, and the similarity in concentration profiles captured by different nonlocal models, all imply the importance of distinguishing the dominant nonlocality for the regional- scale anomalous dispersion process.
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting