Liouville equation-based stochastic model for shoreline evolution

Xing Zheng Wu (Lead / Corresponding author), Ping Dong

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Long-term shoreline evolution due to longshore sediment transport is one of the key processes that need to be addressed in coastal engineering design and management. To adequately represent the inherent stochastic nature of the evolution processes, a probability density evolution model based on a Liouville-type equation is proposed for predicting the shoreline changes. In this model, the standard one-line beach evolution model that is widely used in coastal engineering design is reformulated in terms of the probability density function of shoreline responses. A computational algorithm involving a total variation diminishing scheme is employed to solve the resulting equation. To check the accuracy and robustness of the model, the predictions of the model are evaluated by comparing them with those from Monte Carlo simulations for two idealised shoreline configurations involving a single long jetty perpendicular to a straight shoreline and a rectangular beach nourishment case. The pertinent features of the predicted probabilistic shoreline responses are identified and discussed. The influence of the density distributions of the input parameters on the computed results is investigated.

Original languageEnglish
Pages (from-to)1867-1880
Number of pages14
JournalStochastic Environmental Research and Risk Assessment
Issue number7
Early online date24 Jan 2015
Publication statusPublished - Oct 2015


  • Liouville equation
  • Probability density function
  • Shoreline evolution
  • Total variation diminishing

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality


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