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-order advection–dispersion equation (fADE) models were analyzed and compared systematically, including the space fADEs with either maximally positive or negative skewness, the time fADE with a temporal fractional-derivative 0 < γ < 1 , and the extension of the 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 multiple immobile phases and therefore record the temporal history of concentration “loading” (i.e., the time-nonlocality). We then applied the fADEs as models of anomalous dispersion to four extensively-studied, regional-scale, natural systems, including a hillslope composed of fractured soils, a river with simultaneous active flow zones and various dead-zones, a relatively homogeneous glaciofluvial aquifer dominated by stratified sand and gravel, and a highly heterogeneous alluvial aquifer containing both preferential flowpaths and abundant aquitards. We find that the anomalous dispersion observed at each site might not be characterized reasonably or sufficiently by previous studies. In particular, the use of the space fADE with less than maximally positive skewness implies a spatial dependence on downstream concentrations that may not be physically realistic for solute transport in watershed catchments and rivers (where the influence of dead-zones on solute transport can be described by a temporal, not spatial, fractional model). Field-scale transport studies show that large ranges of solute displacement can be described by a space nonlocal, fractional-derivative model, and long waiting times can be described efficiently by a time-nonlocal, fractional model. The unknown quantitative relationship between the nonlocal parameters and the heterogeneity, and the similarity in concentration profiles that are solutions to the different nonlocal transport models, all demonstrate the importance of distinguishing the representative nonlocality (time and/or space) for any given regional-scale anomalous dispersion process.
Advances in Water Resources – Elsevier
Published: Apr 1, 2009
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera
Read and print from thousands of top scholarly journals.
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
ok to continue