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<p>Stochastic differential equations (SDEs) driven by Gaussian noise have proven effective for studying the dynamics of river basin discharges, while accounting for uncertainties inherent in rainfall–runoff systems. However, these uncertainties clearly exhibit many non-Gaussian characteristics, necessitating the use of more complex noises to model various levels of variability and anomalies in river basin discharges, ultimately enhancing the assessment of extreme hydrological risks. This paper considers uncertainties in rainfall–runoff systems by developing a Langevin-type SDE driven by non-Gaussian <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="477_2025_2931_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-stable Lévy noises. The different methods’ applicability is demonstrated on the Ouémé at Bonou river basin, Benin. The SDE model parameters were estimated through a developed heuristic method based on a Monte Carlo simulation approach. To access extreme hydrological event risks, the equivalent fractional Fokker–Planck equation (FFPE) was derived and solved numerically using an adaptive finite difference method. The results showed that Lévy stable noises better capture uncertainties in rainfall–runoff systems, highlighting anomalous diffusion in daily river basin discharges. The SDE and FFPE model solutions were consistent, aligning with actual observations, and the risks of extreme events were evaluated in terms of daily and cumulative probabilities.</p>

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Lévy-induced stochastic differential equation models in rainfall–runoff systems for assessing extreme hydrological event risks

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Sianou Ezéckiel Houénafa,
  • Erick K. Ronoh,
  • Olatunji Johnson,
  • Stephen E. Moore

摘要

Stochastic differential equations (SDEs) driven by Gaussian noise have proven effective for studying the dynamics of river basin discharges, while accounting for uncertainties inherent in rainfall–runoff systems. However, these uncertainties clearly exhibit many non-Gaussian characteristics, necessitating the use of more complex noises to model various levels of variability and anomalies in river basin discharges, ultimately enhancing the assessment of extreme hydrological risks. This paper considers uncertainties in rainfall–runoff systems by developing a Langevin-type SDE driven by non-Gaussian \(\alpha \) -stable Lévy noises. The different methods’ applicability is demonstrated on the Ouémé at Bonou river basin, Benin. The SDE model parameters were estimated through a developed heuristic method based on a Monte Carlo simulation approach. To access extreme hydrological event risks, the equivalent fractional Fokker–Planck equation (FFPE) was derived and solved numerically using an adaptive finite difference method. The results showed that Lévy stable noises better capture uncertainties in rainfall–runoff systems, highlighting anomalous diffusion in daily river basin discharges. The SDE and FFPE model solutions were consistent, aligning with actual observations, and the risks of extreme events were evaluated in terms of daily and cumulative probabilities.