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

Author

Listed:
  • Hidekazu Yoshioka

    (Shimane University
    Shimane University)

  • Kunihiko Hamagami

    (Iwate University)

  • Haruka Tomobe

    (Tokyo Institute of Technology)

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.

Suggested Citation

  • Hidekazu Yoshioka & Kunihiko Hamagami & Haruka Tomobe, 2023. "A Non-local Fokker-Planck Equation with Application to Probabilistic Evaluation of Sediment Replenishment Projects," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10006-5
    DOI: 10.1007/s11009-023-10006-5
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    1. Akdim, Khadija & Ez-zetouni, Adil & Danane, Jaouad & Allali, Karam, 2020. "Stochastic viral infection model with lytic and nonlytic immune responses driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    2. Smith, Martin D. & Slott, Jordan M. & McNamara, Dylan & Brad Murray, A., 2009. "Beach nourishment as a dynamic capital accumulation problem," Journal of Environmental Economics and Management, Elsevier, vol. 58(1), pages 58-71, July.
    3. Zhang, Hongxia & Xu, Wei & Han, Ping & Qiao, Yan, 2020. "Stochastic dynamic balance of a bi-stable vegetation model with pulse control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    4. Zhang, Hongxia & Xu, Wei & Guo, Qin & Han, Ping & Qiao, Yan, 2020. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    5. G. Guthrie, 2021. "Adapting to Rising Sea Levels: How Short-Term Responses Complement Long-Term Investment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 78(4), pages 635-668, April.
    6. Hidekazu Yoshioka & Yuta Yaegashi, 2020. "A growth rate control problem of harmful species population and its application to algae bloom," Environment Systems and Decisions, Springer, vol. 40(1), pages 107-124, March.
    7. Fahimi, Milad & Nouri, Kazem & Torkzadeh, Leila, 2020. "Chaos in a stochastic cancer model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Hidekazu Yoshioka & Yuta Yaegashi, 2018. "Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(3), pages 338-354, May.
    9. Straka, Peter, 2018. "Variable order fractional Fokker–Planck equations derived from Continuous Time Random Walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 451-463.
    10. Dragicevic, Arnaud Z., 2020. "The economics of the Sylvo-Cynegetic equilibrium," Forest Policy and Economics, Elsevier, vol. 120(C).
    11. Haddadchi, Arman & Kuczynski, Anika & Hoyle, Joanna T. & Kilroy, Cathy & Booker, Doug J. & Hicks, Murray, 2020. "Periphyton removal flows determined by sediment entrainment thresholds," Ecological Modelling, Elsevier, vol. 434(C).
    12. Lochana K. Palayangoda & Hon Keung Tony Ng & Ronald W. Butler, 2020. "Improved techniques for parametric and nonparametric evaluations of the first‐passage time for degradation processes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(4), pages 730-753, July.
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