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Recent Advances in Subsurface Flow and Solute Transport Modelling
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Recent Advances in Subsurface Flow and Solute Transport Modelling

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydrology".

Deadline for manuscript submissions: 20 July 2025 | Viewed by 1338

Special Issue Editors

Dr. Jing Yang

E-Mail Website
Guest Editor
National Institute of Water and Atmospheric Research, Auckland, New Zealand
Interests: surface-groundwater interaction; hydrologic modelling; water resources allocation; groundwater trend and attribution; decision support
Dr. Channa Rajanayaka

E-Mail Website
Guest Editor
National Institute of Water and Atmospheric Research, Auckland, New Zealand
Interests: hydrogeological processes; groundwater-surface water interactions; integrated groundwater-surface water modelling; groundwater recharge
Prof. Dr. Kei Nakagawa

E-Mail Website
Guest Editor
Institute of Integrated Science and Technology, Nagasaki University, Nagasaki, Japan
Interests: hydrogeology; groundwater; soil and water pollution; reactive transport in groundwater; physical and chemical hydrogeology and heterogeneity; saltwater intrusion and subsurface dam; groundwater modeling; remediation of contaminated soils and groundwater
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ming Dou

E-Mail Website
Guest Editor
School of Ecology and Environment, Zhengzhou University, Zhengzhou 450001, China
Interests: groundwater mathematical model; water resources allocation; groundwater pollution; allowable groundwater exploitation; groundwater management

Special Issue Information

Dear Colleagues,

With increasing global water resource demand, declining groundwater level, and worsening water quality, there is a critical need to better understand subsurface flow processes and solute transport to support decision-makers in water resource and nutrient management. To address these challenges, this speccial issue invite papers on studies of groundwater recharge, groundwater flow and solute transport, ranging from statistical and physically based models to innovative method such as chemical or isotope tracers and machine learning. We seek contributions that model or elucidate groundwater recharge, subsurface processes, solute transport, and their interaction with surface water and human activity, ultimately supporting the setting of groundwater abstraction limits and water allocation. Submit your research and help shape the future of water resource management.

In this Special Issue, we welcome submissions on the following thematic areas, among other possible topics:

  • Using physically based groundwater models (e.g., MODFLOW) to simulate subsurface flow,
  • Applying physically based subsurface solute transport models (e.g., MT3D-USGS) to simulate solute transport,
  • Using statistical models (e.g., PASTAS) to study the subsurface flow and solute transport,
  • Develoing or using machine learning methods to support decision-makers in water resource management,
  • Using remote sensing data to quantify groundwater recharge or changes in groundwater storage,
  • Utilising methods/technologies (e.g., stream depletion model) to support water allocation and limit setting,
  • Employing chemical/iostope tracers to study water ages, transit time, age distribution etc.,
  • Implementing innovative technologies to support model calibration and uncertainty analysis.

Dr. Jing Yang
Dr. Channa Rajanayaka
Prof. Dr. Kei Nakagawa
Prof. Dr. Ming Dou
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • groundwater
  • solute transport
  • machine learning technology
  • statisical and physically based models
  • water allocation

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

22 pages, 4222 KiB  
Article
Simulating Anomalous Migration of Radionuclides in Variably Saturation Zone Based on Fractional Derivative Model
by Mengke Zhang, Jingyu Liu, Yang Li, Hongguang Sun and Chengpeng Lu
Water 2025, 17(9), 1337; https://doi.org/10.3390/w17091337 - 29 Apr 2025
Abstract
The migration of radioactive waste in geological environments often exhibits anomalies, such as tailing and early arrival. Fractional derivative models (FADE) can provide a good description of these phenomena. However, developing models for solute transport in unsaturated media using fractional derivatives remains an [...] Read more.
The migration of radioactive waste in geological environments often exhibits anomalies, such as tailing and early arrival. Fractional derivative models (FADE) can provide a good description of these phenomena. However, developing models for solute transport in unsaturated media using fractional derivatives remains an unexplored area. This study developed a variably saturated fractional derivative model combined with different release scenarios, to capture the abnormal increase observed in monitoring wells at a field site. The model can comprehensively simulate the migration of nuclides in the unsaturated zone (impermeable layer)—saturated zone system. This study fully analyzed the penetration of pollutants through the unsaturated zone (retardation stage), and finally the rapid lateral and rapid diffusion of pollutants along the preferential flow channels in the saturated zone. Comparative simulations indicate that the spatial nonlocalities effect of fractured weathered rock affects solute transport much more than the temporal memory effect. Therefore, a spatial fractional derivative model was selected to simulate the super-diffusive behavior in the preferential flow pathways. The overall fitness of the proposed model is good (R2 ≈ 1), but the modeling accuracy will be lower with the increased distance from the waste source. The spatial differences between simulated and observed concentrations reflect the model’s limitations in long-distance simulations. Although the model reproduced the overall temporal variation of solute migration, it does not explain all the variability and uncertainty of the specific sites. Based on the sensitivity analysis, the fractional derivative parameters of the unsaturated zone show higher sensitivity than those of the saturated zone. Finally, the advantages and limitations of the fractional derivative model in radionuclide contamination prediction and remediation are discussed. In conclusion, the proposed FADE model coupled with unsaturated and saturated flow conditions, has significant application prospects in simulating nuclide migration in complex geological and hydrological environments. Full article
(This article belongs to the Special Issue Recent Advances in Subsurface Flow and Solute Transport Modelling)
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19 pages, 4569 KiB  
Article
Characterization and Quantification of Fracture Roughness for Groundwater Modeling in Fractures Generated with Weierstrass–Mandelbrot Approach
by Yun Xing and Mingyu Wang
Water 2025, 17(7), 982; https://doi.org/10.3390/w17070982 - 27 Mar 2025
Viewed by 135
Abstract
Accurate characterization of fracture roughness is critical for modeling groundwater flow and solute transport in fractured rock aquifers, where subsurface heterogeneity significantly impacts contaminant migration and water resource management. This study investigates fracture roughness characterization by integrating the Weierstrass–Mandelbrot approach with 3D-printed experimental [...] Read more.
Accurate characterization of fracture roughness is critical for modeling groundwater flow and solute transport in fractured rock aquifers, where subsurface heterogeneity significantly impacts contaminant migration and water resource management. This study investigates fracture roughness characterization by integrating the Weierstrass–Mandelbrot approach with 3D-printed experimental validation and numerical simulation verification. Specifically, all the related parameters including fractal dimensions (D), frequency density (λ), segmentation accuracy (s), and summation number (n), which control the generation of fracture roughness, along with investigation scales (rs), were initially considered, and their corresponding impacts on the fracture roughness characteristics were examined. The results revealed that D is the primary factor controlling fracture roughness characteristics, while λ shows secondary importance when exceeding 1.3. The roughness remains stable when s ≤ 3 mm, n > 200, and rs ≥ 240 × 240 mm2. Two multivariate regression models were established to describe the relationship between fracture roughness and influencing factors. The proposed methodology significantly enhances the precision of groundwater flow and solute transport simulations in fractured media through advanced high-fidelity fracture characterization, offering substantial improvements in groundwater resource management and contaminant remediation strategies. Full article
(This article belongs to the Special Issue Recent Advances in Subsurface Flow and Solute Transport Modelling)
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26 pages, 18116 KiB  
Article
Evaluation of the Application of the Moving Particle Semi-Implicit Method (MPS) to Numerical Simulations of Coupled Flow Between Low-Permeability Porous Media and Surface Water
by Yoshihiko Hibi
Water 2025, 17(6), 863; https://doi.org/10.3390/w17060863 - 17 Mar 2025
Viewed by 189
Abstract
The moving particle semi-implicit method (MPS) has been employed to numerically simulate fluid flows. Further, some studies have used the MPS method to solve the Darcy–Brinkman equation, which also expresses fluid flow in porous media. However, these studies simulated flows only in porous [...] Read more.
The moving particle semi-implicit method (MPS) has been employed to numerically simulate fluid flows. Further, some studies have used the MPS method to solve the Darcy–Brinkman equation, which also expresses fluid flow in porous media. However, these studies simulated flows only in porous media with high permeability, not in relatively low permeability. Thus, this study developed a numerical simulation method that employs Navier–Stokes equations to describe flow in surface water and the Richards equations, derived from the Darcy law and the law of conservation of mass, to describe water flow in porous media, and it uses the MPS method to discretize those equations. This numerical simulation method was then evaluated by comparing the numerical simulation results with previously obtained experimental results for fluid draining from the bottom of a column, which was first packed with silica sand saturated with water and then filled with water to 25 cm above the top surface of the sand, which had an intrinsic permeability of 1.737 × 10–11 m2, a porosity of 0.402, van Genuchten parameters of 0.231 kPa–1 and 9.154, a residual gas saturation of 0.0, and a residual water saturation of 0.178. The numerical simulation was able to simulate the decrease in the level of the surface water above the silica sand in the column, similar to the column experimental results. However, the decrease in the saturated water in the silica sand obtained by the numerical simulation was almost consistent with the experimental results. Full article
(This article belongs to the Special Issue Recent Advances in Subsurface Flow and Solute Transport Modelling)
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19 pages, 11015 KiB  
Article
Calculation of Urban Groundwater Environmental Carrying Capacity Driven by Multiple Factors
by Yuze Zhou, Ming Dou, Ting Gao and Kaizi Ning
Water 2025, 17(6), 807; https://doi.org/10.3390/w17060807 - 12 Mar 2025
Viewed by 423
Abstract
Global urbanization has led to the overexploitation and pollution of groundwater resources, restricting the sustainable construction and development of cities. Groundwater environmental carrying capacity (GW-ECC) refers to the maximum total amount of pollutants that can be accommodated by a given groundwater system within [...] Read more.
Global urbanization has led to the overexploitation and pollution of groundwater resources, restricting the sustainable construction and development of cities. Groundwater environmental carrying capacity (GW-ECC) refers to the maximum total amount of pollutants that can be accommodated by a given groundwater system within a certain time period and under specified environmental goals. To better understand the changes in GW-ECC in the context of rapid urbanization, this study built a model of the urban GW-ECC driven by multiple factors. Taking the urban area of Zhengzhou as an example, rainfall infiltration and riverside seepage within the urban groundwater system were calculated considering the change in the impervious area over the past 20 years. The Mann–Kendall rank test was used to evaluate the varying trends of the two factors in the urbanization process. Based on this, the change in the GW-ECC in the current year was calculated, and the changes under different regulatory schemes after 10 years was calculated and evaluated. The results showed that the model constructed in this study could accurately simulate an urban groundwater system. With the acceleration of urbanization, the urban groundwater system recharges by precipitation, and rivers tend to decline. The GW-ECC of ammonia nitrogen in Zhengzhou exhibited an overall upward trend. By the end of 2030, the GW-ECC of ammonia nitrogen is expected to reach a maximum of 1964.5 t. Changes in groundwater resources caused by precipitation and extraction were the main factors driving variations in the urban GW-ECC. In areas with mature urbanization, measures such as increasing groundwater recharge and reducing groundwater extraction are more effective in improving the GW-ECC. Full article
(This article belongs to the Special Issue Recent Advances in Subsurface Flow and Solute Transport Modelling)
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