Extreme flow induced particle transport is stochastic in nature and enhances geomorphologic change, and intensifies local erosion and deposition processes. Therefore, the relationship between the stochastic characteristic of extreme flow events and sediment transport modeling has gained increased attention. While sophisticated deterministic models for particle transport are currently available, the predictions are likely to be associated with uncertainty, as the transport processes involve a multitude of highly varying and random factors. Most of the uncertainty analysis methods require substantial computation, but provide only limited tractability in their solutions. The following proposed stochastic modeling frameworks aim to quantify natural variability of flow and particles, and the uncertainty associated with predictions at a reasonable computational cost:

(1) A physically based stocahstic jump diffusion particle tracking model (SJD-PTM) was developed to accurately predict sediment concentrations, and quantify the uncertainty associated with estimating sediment concentration by simulating the stochastic property of sediment particle movement. We developed a means for evaluating the reliable range of concentration measurements and transport rates.

(2) The Perurbance Moments Method (PMM), which is an improved point-estimate method, was derived based on a discrete representation of the probability distribution functions of the stochastic input variable to quantify the uncertainty of predictions that arise from data variability and parameter uncertainty. A risk assessment was then conducted to systematically compute the probability of failure. 

(3) Several Markovian type models such as the Gambler's ruin (GR) model, and multiple state Markov chains (MSMC) were employed to estimate the probability of reaching designated water quality standards and maximum sediment carrying capacity under different flow conditions.

(4) A novel application of the Hilbert-Huang Transform (HHT) method for the analysis of nonstationary and nonlinear time series was introduced both to evaluate trends and to assess the cause-effect relationship between the studied system and external physical factors. The ability of the HHT to perform data based decomposition of the signal and transformation into the frequency-time domain provides insights into the time series characteristics such as the trend and multiple time scales of the flow and sediment concentration data.

Major achievements in education activities include the use of the "simplicity solves complexity" teaching philosophy, creative pedagogy changes to existing quantitative courses, development of three state-of-art gradaute courses in stochastic modeling, incorporation of research into teaching, training and professional development opportunities for female postdoctoral researchers, and student involvement in multi-disciplinary research.

Significance and Intellectual Merit: 

This project focused on addressing the following fundamental questions: (1) How can sediment transport knowledge be advanced beyond theories and models built upon the deterministic and steady flow premises? (2) How can modern probability theories be used to develop a novel approach to better quantify spatio-temporal variations of flow and sediment in rivers, and the uncertainty associated with model predictions? (3) Sedimentation processes such as erosion and deposition are more significant during extreme flows. How can the probability of occurrence and the magnitude of extreme flows be incorporated into sediment transport modeling?  

This project successfully developed various levels of physically based, stochastic modeling approaches for particle transport. In particular, the proposed SJD-PTM is one of the first few stochastic dif...

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