Articles | Volume 28, issue 1
https://doi.org/10.5194/hess-28-179-2024
https://doi.org/10.5194/hess-28-179-2024
Review article
 | 
11 Jan 2024
Review article |  | 11 Jan 2024

Adjoint subordination to calculate backward travel time probability of pollutants in water with various velocity resolutions

Yong Zhang, Graham E. Fogg, HongGuang Sun, Donald M. Reeves, Roseanna M. Neupauer, and Wei Wei

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Cited articles

Adams, E. E. and Gelhar, L. W.: Field study of dispersion in a heterogeneous aquifer: 2. Spatial moment analysis, Water Resour. Res., 28, 3293–3307, https://doi.org/10.1029/92WR01757, 1992. 
Alijani, Z., Baleanu, D., Shiri, B., and Wu, G. C.: Spline collocation methods for systems of fuzzy fractional differential equations, Chaos Soliton. Fract., 131, 109510, https://doi.org/10.1016/j.chaos.2019.109510, 2020. 
Al-Qurashi, M., Rashid, S., Jarad, F., Tahir, M., and Alsharif, A. M.: New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method, AIMS Math., 7, 2044–2060, https://doi.org/10.3934/math.2022117, 2022. 
Atmadja, J. and Bagtzoglou, A. C.: State of the art report on mathematical methods for groundwater pollution source identification, Environ. Forensics, 2, 205–214, https://doi.org/10.1006/enfo.2001.0055, 2001. 
Ayaz, M., Ansari, S. A., and Singh, O. K.: Detection of pollutant source in groundwater using hybrid optimization model, Int. J. Energy Water Resour., 6, 81–93, https://doi.org/10.1007/s42108-021-00118-4, 2022. 
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Short summary
Pollutant release history and source identification are helpful for managing water resources, but it remains a challenge to reliably identify such information for real-world, complex transport processes in rivers and aquifers. In this study, we filled this knowledge gap by deriving a general backward governing equation and developing the efficient solver. Field applications showed that this model and solver are applicable for a broad range of flow systems, dimensions, and spatiotemporal scales.