Application of The Stochastic Particle Tracking Model To Evaluate Particle Movement Uncertainty in Extreme Flows

In this study, modeling of suspended sediment particle movement in extreme flows is proposed by stochastic particle tracking modeling approaches. The proposed stochastic model is governed by a stochastic differential equation (SDE) composed of two random processes (a Wiener process and a Poisson process), and a random variable (i.e., flow magnitude) simulated by the extreme value Type I distribution. An extreme flow is defined as a hydrologic flow event (such as a flash flood) or a large flow perturbation with a low probability of occurrence and a high impact on its ambient flow environment. In the proposed particle tracking model, a random term mainly caused by fluid eddy motions is modeled as a Wiener process, while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process. Following previous work by Oh and Tsai (2010)[1] and Tsai et al. (2014)[2], this study is intended to modify the jump term, which models the abrupt changes of particle position in the extreme flow environments. It is proposed that the probabilistic magnitude of extreme events can be simulated by the extreme value type I (EV I) distribution. The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations. Our findings suggest that the ability to consider the probabilistic magnitude of extreme events can provide a more comprehensive and realistic estimate of the uncertainty of particle movement when extreme flow events occur. It is also found that the variance of particle position may be attributed to both the random magnitudes and occurrences of particle jumps in the presence of extreme flow events. It is demonstrated from this study that the proposed model can more explicitly quantify the uncertainty of particle movement by taking into considerations both the random arrival process of extreme flows and the variability of the extreme flow magnitude.

[1] Oh, J. S., and Tsai, C.W.(2010). "A stochastic jump diffusion particle-tracking model (SJD-PTM) for sediment transport in open channel flows." Water Resources Research, VOL. 46, W10508, 20pp, doi:10.1029/2009WR008443.

[2] Tsai, C.W., Man, C. and Oh, J.S. (2014). "A stochastic particle based model for suspended sediment in surface flows." International Journal of Sediment Research, 29 (2014), 195-207.