Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation
Abstract Hydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics re...
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| Format: | Article |
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Wiley
2024-03-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2023WR036089 |
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| author | Yong Zhang Xiaoting Liu Dawei Lei Maosheng Yin HongGuang Sun Zhilin Guo Hongbin Zhan |
| author_facet | Yong Zhang Xiaoting Liu Dawei Lei Maosheng Yin HongGuang Sun Zhilin Guo Hongbin Zhan |
| author_sort | Yong Zhang |
| collection | DOAJ |
| description | Abstract Hydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection‐dispersion equation” (IT‐fADE) to simulate HM‐HMs of TAD. The model is approximated using an L1‐based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT‐fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub‐diffusion arising from sudden shifts in hydraulic gradient within a regional‐scale alluvial aquifer, (b) transient sub‐ or super‐diffusion due to convergent or push‐pull tracer experiments within a local‐scale fractured aquifer, and (c) transient sub‐diffusion likely attributed to multiple‐conduit flow within an intermediate‐scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT‐fADE aptly capture the ephemeral nature and evolving memory of HM‐HMs of TAD by incorporating multiple stress periods into the model. The sequential HM‐HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT‐fADE to capture hot phenomena of TAD in aquatic systems. |
| format | Article |
| id | doaj-art-fabf51eebd2e4221bb1eec6cb691909b |
| institution | Kabale University |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | Wiley |
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| series | Water Resources Research |
| spelling | doaj-art-fabf51eebd2e4221bb1eec6cb691909b2025-08-20T03:30:53ZengWileyWater Resources Research0043-13971944-79732024-03-01603n/an/a10.1029/2023WR036089Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative EquationYong Zhang0Xiaoting Liu1Dawei Lei2Maosheng Yin3HongGuang Sun4Zhilin Guo5Hongbin Zhan6Department of Geological Sciences University of Alabama Tuscaloosa AL USAInstitute of Science and Technology Research China Three Gorges Corporation Beijing ChinaState Key Laboratory of Hydrology‐Water Resources and Hydraulic Engineering Hohai University Nanjing ChinaEIT Institute for Advanced Study Ningbo ChinaState Key Laboratory of Hydrology‐Water Resources and Hydraulic Engineering Hohai University Nanjing ChinaSchool of Environmental Science and Engineering Southern University of Science and Technology Shenzhen ChinaDepartment of Geology and Geophysics Texas A&M University College Station TX USAAbstract Hydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection‐dispersion equation” (IT‐fADE) to simulate HM‐HMs of TAD. The model is approximated using an L1‐based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT‐fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub‐diffusion arising from sudden shifts in hydraulic gradient within a regional‐scale alluvial aquifer, (b) transient sub‐ or super‐diffusion due to convergent or push‐pull tracer experiments within a local‐scale fractured aquifer, and (c) transient sub‐diffusion likely attributed to multiple‐conduit flow within an intermediate‐scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT‐fADE aptly capture the ephemeral nature and evolving memory of HM‐HMs of TAD by incorporating multiple stress periods into the model. The sequential HM‐HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT‐fADE to capture hot phenomena of TAD in aquatic systems.https://doi.org/10.1029/2023WR036089hydrologically mediated hot momentsanomalous diffusionfractional derivative modelaquifers |
| spellingShingle | Yong Zhang Xiaoting Liu Dawei Lei Maosheng Yin HongGuang Sun Zhilin Guo Hongbin Zhan Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation Water Resources Research hydrologically mediated hot moments anomalous diffusion fractional derivative model aquifers |
| title | Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation |
| title_full | Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation |
| title_fullStr | Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation |
| title_full_unstemmed | Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation |
| title_short | Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation |
| title_sort | modeling hydrologically mediated hot moments of transient anomalous diffusion in aquifers using an impulsive fractional derivative equation |
| topic | hydrologically mediated hot moments anomalous diffusion fractional derivative model aquifers |
| url | https://doi.org/10.1029/2023WR036089 |
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