Academic Journal

Unveiling the Stochasticity of Bank Erosion: A Hybrid Deterministic and Stochastic Modeling Approach.

Bibliographic Details
Title: Unveiling the Stochasticity of Bank Erosion: A Hybrid Deterministic and Stochastic Modeling Approach.
Authors: Li, Zhi, Langendoen, Eddy J., García, Marcelo H.
Source: Water Resources Research; Nov2025, Vol. 61 Issue 11, p1-32, 32p
Subject Terms: Stochastic models, Fluvial geomorphology, Hydrodynamics, Environmental risk, Riparian areas, Deterministic algorithms, Erosion
Geographic Terms: Tibetan Plateau
Abstract: This paper presents a new hybrid deterministic‐stochastic river morphodynamics numerical modeling approach that integrates a hydrodynamic model (deterministic) with a bed morphodynamic model (deterministic) and a bank erosion model (Markovian stochastic). The hydrodynamic model solves the Shallow Water Equations and the standard k $k$‐ϵ ${\epsilon}$ model for turbulence closure. Bedload transport is estimated using the Meyer‐Peter and Müller formula, and bed evolution is solved using the Exner equation. The Markovian stochastic bank erosion model uses a new method to evaluate bank erosion risk. The approach was applied to a meander bend cutoff event in the Maiqu River on the Tibetan Plateau. Sixteen different bank‐material critical shear stress cases were considered, representing highly erodible banks (τ‾c=0.1 ${\overline{\tau }}_{c}=0.1$ Pa) to resistant banks (τ‾c=15 ${\overline{\tau }}_{c}=15$ Pa). Ten statistical realizations were performed for each case with different bank‐material erodibility to obtain ensemble‐averaged results. The flow field and bed evolution in the cutoff channel suggest that the model can successfully simulate bank erosion processes during cutoff channel evolution, and bank topographic irregularities are reasonably captured. A newly introduced calibration parameter is the ratio of mesh size to the coupling period between the bank erosion model and the hydrodynamic and morphodynamic model. Unlike the erosion rate calibration parameters used by traditional bank erosion models, the present model requires estimating the size of a typical slump failure to determine the size of the computational mesh. This new modeling approach enhanced existing tools for fluvial geomorphologists and river engineers focused on bank erosion with real‐world complex geometric features under intricate hydraulic conditions. Plain Language Summary: This article introduces a new method for estimating the likelihood of riverbank erosion. The new method is implemented in a computer model that simulates riverbank evolution by considering the topographic irregularities of riverbank lines. We tested the model on the observed evolution of a natural river on the Tibetan Plateau. We found that the model realistically captures real‐world bank features and can show how the river banks change over time. This model can help predict how riverbanks erode, leading to better ways of managing river erosion. Key Points: We introduce a new hybrid deterministic‐stochastic modeling approach, coupling hydrodynamics, morphodynamics, and a Markovian stochastic bank erosion modelThe bank erosion risk is controlled by probability density functions of the near‐bank flow and bank material erodibilityBank erosion is simulated with natural topographic bank features in a stochastic manner under complex hydraulic and geometric conditions [ABSTRACT FROM AUTHOR]
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  Data: Unveiling the Stochasticity of Bank Erosion: A Hybrid Deterministic and Stochastic Modeling Approach.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Zhi%22">Li, Zhi</searchLink><br /><searchLink fieldCode="AR" term="%22Langendoen%2C+Eddy+J%2E%22">Langendoen, Eddy J.</searchLink><br /><searchLink fieldCode="AR" term="%22García%2C+Marcelo+H%2E%22">García, Marcelo H.</searchLink>
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  Data: Water Resources Research; Nov2025, Vol. 61 Issue 11, p1-32, 32p
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  Data: <searchLink fieldCode="DE" term="%22Stochastic+models%22">Stochastic models</searchLink><br /><searchLink fieldCode="DE" term="%22Fluvial+geomorphology%22">Fluvial geomorphology</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrodynamics%22">Hydrodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Environmental+risk%22">Environmental risk</searchLink><br /><searchLink fieldCode="DE" term="%22Riparian+areas%22">Riparian areas</searchLink><br /><searchLink fieldCode="DE" term="%22Deterministic+algorithms%22">Deterministic algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Erosion%22">Erosion</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Tibetan+Plateau%22">Tibetan Plateau</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper presents a new hybrid deterministic‐stochastic river morphodynamics numerical modeling approach that integrates a hydrodynamic model (deterministic) with a bed morphodynamic model (deterministic) and a bank erosion model (Markovian stochastic). The hydrodynamic model solves the Shallow Water Equations and the standard k $k$‐ϵ ${\epsilon}$ model for turbulence closure. Bedload transport is estimated using the Meyer‐Peter and Müller formula, and bed evolution is solved using the Exner equation. The Markovian stochastic bank erosion model uses a new method to evaluate bank erosion risk. The approach was applied to a meander bend cutoff event in the Maiqu River on the Tibetan Plateau. Sixteen different bank‐material critical shear stress cases were considered, representing highly erodible banks (τ‾c=0.1 ${\overline{\tau }}_{c}=0.1$ Pa) to resistant banks (τ‾c=15 ${\overline{\tau }}_{c}=15$ Pa). Ten statistical realizations were performed for each case with different bank‐material erodibility to obtain ensemble‐averaged results. The flow field and bed evolution in the cutoff channel suggest that the model can successfully simulate bank erosion processes during cutoff channel evolution, and bank topographic irregularities are reasonably captured. A newly introduced calibration parameter is the ratio of mesh size to the coupling period between the bank erosion model and the hydrodynamic and morphodynamic model. Unlike the erosion rate calibration parameters used by traditional bank erosion models, the present model requires estimating the size of a typical slump failure to determine the size of the computational mesh. This new modeling approach enhanced existing tools for fluvial geomorphologists and river engineers focused on bank erosion with real‐world complex geometric features under intricate hydraulic conditions. Plain Language Summary: This article introduces a new method for estimating the likelihood of riverbank erosion. The new method is implemented in a computer model that simulates riverbank evolution by considering the topographic irregularities of riverbank lines. We tested the model on the observed evolution of a natural river on the Tibetan Plateau. We found that the model realistically captures real‐world bank features and can show how the river banks change over time. This model can help predict how riverbanks erode, leading to better ways of managing river erosion. Key Points: We introduce a new hybrid deterministic‐stochastic modeling approach, coupling hydrodynamics, morphodynamics, and a Markovian stochastic bank erosion modelThe bank erosion risk is controlled by probability density functions of the near‐bank flow and bank material erodibilityBank erosion is simulated with natural topographic bank features in a stochastic manner under complex hydraulic and geometric conditions [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Water Resources Research is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1029/2024WR039336
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
        StartPage: 1
    Subjects:
      – SubjectFull: Tibetan Plateau
        Type: general
      – SubjectFull: Stochastic models
        Type: general
      – SubjectFull: Fluvial geomorphology
        Type: general
      – SubjectFull: Hydrodynamics
        Type: general
      – SubjectFull: Environmental risk
        Type: general
      – SubjectFull: Riparian areas
        Type: general
      – SubjectFull: Deterministic algorithms
        Type: general
      – SubjectFull: Erosion
        Type: general
    Titles:
      – TitleFull: Unveiling the Stochasticity of Bank Erosion: A Hybrid Deterministic and Stochastic Modeling Approach.
        Type: main
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          Name:
            NameFull: Li, Zhi
      – PersonEntity:
          Name:
            NameFull: Langendoen, Eddy J.
      – PersonEntity:
          Name:
            NameFull: García, Marcelo H.
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          Dates:
            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
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              Value: 11
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