{"corpus_id":20821623,"paper_sha":"79c76ee44089cd1b0c9740100be103bf59555d01","doi":"10.1029/2008JF001246","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2125418826,"dblp_id":null,"acl_id":null,"title":"Fractional advection‐dispersion equations for modeling transport at the Earth surface","year":2009,"publication_date":"2009-12-01","venue":"","journal":{"name":"Journal of Geophysical Research","pages":null,"volume":"114"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Physics","Environmental Science"],"reference_count":62,"citation_count":292,"influential_citation_count":20,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2008JF001246","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/79c76ee44089cd1b0c9740100be103bf59555d01","s2_open_access_license":null,"s2_open_access_status":"BRONZE","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Characterizing the collective behavior of particle transport on the Earth surface is a key ingredient in describing landscape evolution. We seek equations that capture essential features of transport of an ensemble of particles on hillslopes, valleys, river channels, or river networks, such as mass conservation, superdiffusive spreading in flow fields with large velocity variation, or retardation due to particle trapping. Development of stochastic partial differential equations such as the advection‐dispersion equation (ADE) begins with assumptions about the random behavior of a single particle: possible velocities it may experience in a flow field and the length of time it may be immobilized. When assumptions underlying the ADE are relaxed, a fractional ADE (fADE) can arise, with a non‐integer‐order derivative on time or space terms. Fractional ADEs are nonlocal; they describe transport affected by hydraulic conditions at a distance. Space fractional ADEs arise when velocity variations are heavy tailed and describe particle motion that accounts for variation in the flow field over the entire system. Time fractional ADEs arise as a result of power law particle residence time distributions and describe particle motion with memory in time. Here we present a phenomenological discussion of how particle transport behavior may be parsimoniously described by a fADE, consistent with evidence of superdiffusive and subdiffusive behavior in natural and experimental systems.","claims":[{"public_id":"cl_c7394031f8fea416073969d4f846bb75","status":"active","text":"Particle transport at the Earth surface can be parsimoniously described by a fractional advection-dispersion equation consistent with evidence for superdiffusive and subdiffusive behavior in natural and experimental systems.","confidence":0.94,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_c7394031f8fea416073969d4f846bb75"},{"public_id":"cl_981804df1ecd91202e026214b454ce7e","status":"active","text":"Relaxing the assumptions underlying the classical advection-dispersion equation leads to a fractional advection-dispersion equation with non-integer-order derivatives in time or space.","confidence":0.93,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_981804df1ecd91202e026214b454ce7e"},{"public_id":"cl_805380818a7306a57ef5d1cbf120aa6c","status":"active","text":"Space-fractional advection-dispersion equations arise when velocity variations are heavy tailed and represent transport influenced by flow-field variation across the entire system.","confidence":0.92,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_805380818a7306a57ef5d1cbf120aa6c"},{"public_id":"cl_25f030aa54d7c46022b33b4c7260bee2","status":"active","text":"Time-fractional advection-dispersion equations arise from power-law particle residence time distributions and represent transport with memory in time.","confidence":0.91,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_25f030aa54d7c46022b33b4c7260bee2"}],"concepts":[{"public_id":"co_16663eb099729ed9e5a31747796cfe3b","status":"active","name":"space fractional ADEs","description":"Fractional advection-dispersion equations with non-integer spatial derivatives.","types":["equation","model"],"aliases":["space fractional advection-dispersion equations"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_16663eb099729ed9e5a31747796cfe3b"},{"public_id":"co_1d35635addf827724b4de756f55c6fa3","status":"active","name":"flow field","description":"The spatially varying hydraulic or velocity environment through which particles move.","types":["environment"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_1d35635addf827724b4de756f55c6fa3"},{"public_id":"co_22141c27ead7035216ed03d333e1f28d","status":"active","name":"non-integer-order derivatives","description":"Derivatives of fractional order used in fractional differential equations.","types":["mathematical operator"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_22141c27ead7035216ed03d333e1f28d"},{"public_id":"co_527d207f3887313ad530f3eea79e6add","status":"active","name":"superdiffusive and subdiffusive behavior","description":"Transport regimes in which spreading is respectively faster or slower than classical diffusion.","types":["phenomenon"],"aliases":["superdiffusion","subdiffusion"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_527d207f3887313ad530f3eea79e6add"},{"public_id":"co_5f101d067d8e0492a509500650a17795","status":"active","name":"heavy-tailed velocity variations","description":"Flow-field velocity variability with a probability distribution that has heavy tails.","types":["distributional property"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_5f101d067d8e0492a509500650a17795"},{"public_id":"co_615cdb78eec1d30891d507697c20a4a5","status":"active","name":"memory in time","description":"Temporal nonlocality in which present transport depends on past states.","types":["property"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_615cdb78eec1d30891d507697c20a4a5"},{"public_id":"co_81d385d70674c604f5fe79690a3bfc2a","status":"active","name":"time fractional ADEs","description":"Fractional advection-dispersion equations with non-integer temporal derivatives.","types":["equation","model"],"aliases":["time fractional advection-dispersion equations"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_81d385d70674c604f5fe79690a3bfc2a"},{"public_id":"co_883c11fc31c5529a57741b3018f4e487","status":"active","name":"particle transport","description":"The movement of an ensemble of particles across surface environments such as hillslopes, valleys, river channels, or river networks.","types":["process"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_883c11fc31c5529a57741b3018f4e487"},{"public_id":"co_99961e9028489c82bf7dc35861a8bf40","status":"active","name":"fractional advection-dispersion equation","description":"A nonlocal transport equation with non-integer-order derivatives in time or space.","types":["equation","model"],"aliases":["fADE","fractional ADE"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_99961e9028489c82bf7dc35861a8bf40"},{"public_id":"co_c602a7a6c8f863b6ad2079cd7b779a81","status":"active","name":"advection-dispersion equation","description":"A classical stochastic partial differential equation used to model transport by advection and dispersion.","types":["equation","model"],"aliases":["ADE"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_c602a7a6c8f863b6ad2079cd7b779a81"},{"public_id":"co_f11732516306c66b8d6572fd2848c704","status":"active","name":"power-law particle residence time distributions","description":"Residence-time distributions for particles that decay according to a power law.","types":["distribution"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_f11732516306c66b8d6572fd2848c704"}],"external_ids":{"DOI":"10.1029/2008JF001246","ArXiv":null,"PubMed":null,"PubMedCentral":null,"MAG":2125418826,"DBLP":null,"ACL":null},"open_access":{"is_open_access":true,"pdf_url":"https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2008JF001246","landing_url":"https://www.semanticscholar.org/paper/79c76ee44089cd1b0c9740100be103bf59555d01","source":"semantic_scholar","pdf_url_source":"semantic_scholar_open_access_pdf","license":null,"status":"BRONZE","reason":null},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":631055,"paper_uid":"c32d4c19-53b6-419a-abb9-d426c18d40b3","canonical_identity":{"paper_id":631055,"paper_uid":"c32d4c19-53b6-419a-abb9-d426c18d40b3","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/20821623"}