A Non-local Fokker-Planck Equation with Application to Probabilistic Evaluation of Sediment Replenishment Projects

Hidekazu Yoshioka (), Kunihiko Hamagami and Haruka Tomobe
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Hidekazu Yoshioka: Shimane University
Kunihiko Hamagami: Iwate University
Haruka Tomobe: Tokyo Institute of Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-37

Abstract: Abstract We analyze a new mathematical model to evaluate performance of recent sediment-based environmental restoration projects from a stochastic viewpoint along with applications. We focus on unique jump-driven non-smooth dynamics governing streamflows and sediment storage subject to impulsive human interventions to replenish the sediment. We derive a non-local Fokker-Planck equation (FPE) governing the probability density of the coupled streamflow-sediment dynamics, which is a unique hyperbolic integro-partial differential equation subject to non-smooth coefficients and non-local boundary conditions. It admits measure-valued solutions. We propose a simple conservative discretization method of the FPE and verify it against Monte-Carlo simulation. The stationary probability density turns out to be singular along a boundary due to the non-smoothness and non-locality, which are effectively captured by the proposed numerical scheme. Based on public and experimental data, we finally apply the proposed model to numerical evaluation of replenishment strategies from a viewpoint of nuisance algae bloom.

Keywords: Sediment replenishment; Fokker-Planck equation; Monte-Carlo simulation; Non-smooth and non-local dynamics; Nuisance algae bloom; 60H10; 65 M08; 82C31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10006-5

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