CAREER: STOCHASTIC MODELING AND UNCERTAINTY ANALYSIS OF SEDIMENT TRANSPORT IN REGULAR AND EXTREME SURFACE FLOW ENVIRONMENTS

本CAREER提案的主要研究目标是表征泥沙颗粒的随机运动，并科学量化在规则和极端流动中流量和泥沙浓度以及输沙率预测的变化和不确定性。提出的工作重点是检验1997年诺贝尔奖关于期权定价理论的创新思想的适用性，以更好地描述极端事件中粒子的随机粒子跳跃扩散过程。我们假设自然河流中泥沙颗粒的位移遵循一个随机跳跃扩散过程，该过程由平均漂移项、湍流引起的驱动Wiener过程和响应极端水流事件的跳跃泊松过程组成。本文将建立一个基于物理的三维随机偏微分方程（SPDE）的悬沙输运模型，该模型由基于随机跳跃扩散的粒子跟踪模型、基于大涡模拟（LES）的水动力模型和质量输运方程组成。建议的模型将根据实验室测量和现有数据进行验证。改进的Rosenblueth方法将用于量化常规和极端事件流的沉积风险。本课题旨在解决以下关键问题：(1)在输沙模型中，如何有效量化流沙影响变量的时空变异性和模型参数的不确定性？(2)水流和泥沙特性的统计特征如何有助于为泥沙和水质控制提供更科学的风险评估和安全系数？(3)大部分沉积过程发生在洪水等极端水流事件期间。我们如何将极端事件发生的概率纳入沉积物输运模型？如何区分正常流动期间的沉积过程或水污染的不确定性来源与极端流动事件？这个职业建议的教育目标有三个方面：刺激学生？学习兴趣和提高他们的定量技能，使学生参与研究，并指导学生，特别是妇女和少数民族学生，在他们的职业发展。PI将通过创造性的教学方法改变教学和作为教师顾问、职业顾问和榜样的指导来提高教育质量。主要的教育活动包括使用？认知发现教学与学习？范式和？简单解决复杂？定量课程的教学理念、技术的创造性和创新性实施、将研究纳入教学、长期招聘和留用努力以及女性和少数民族学生的外联活动，以及学生参与研究。

The primary research goals of this CAREER proposal are to characterize the stochastic movement of sediment particles and to scientifically quantify the variation and uncertainty of flow and sediment concentration and transport rate predictions in both regular and extreme flows. The proposed work focuses on examining the applicability of an innovative idea inspired by the 1997 Nobel Prize work on Option Pricing Theory to better describe the stochastic particle jump diffusion process of particles during extreme events. We hypothesize that the displacement of a sediment particle in natural rivers follows a stochastic jump diffusion process consisting of a mean drift term, a driving Wiener process due to flow turbulence, and a jump Poisson process in response to extreme flow events. A physically based 3-D stochastic partial differential equation (SPDE) based model for suspended sediment transport will be developed, which is composed of an innovative stochastic jump diffusion based particle tracking model, a hydrodynamic model using large eddy simulations (LES), and a mass transport equation. The proposed model will be validated against laboratory measurements and existing data. The modified Rosenblueth method will be used to quantify the risk of sedimentation in both regular and extreme event flows. This research project aims to address the following critical issues: (1) How can the spatial and temporal variability of the contributing flow and sediment variables and the uncertainty of the model parameters be effectively quantified in sediment transport modeling? (2) How can statistical characteristics of flow and sediment properties assist in providing a more scientifically based risk assessment and safety factors needed for sedimentation and water quality control? (3) Most of the sedimentation processes occur during the extreme flow events such as floods. How can we incorporate the probability of extreme event occurrences into sediment transport modeling? How can one distinguish the uncertainty sources of sedimentation processes or water pollution during regular flow periods from the extreme flow events?The education goals in this CAREER proposal are three-fold: to stimulate students? learning interest and improve their quantitative skills, to engage students in research and to guide students, particularly women and minority students, in their career development. The PI will improve the quality of education through creative pedagogy changes to teaching and mentorship as a faculty advisor, career consultant and role model. Major educational activities include the use of the ?cognitive discovery teaching and learning? paradigm and the ?simplicity solves complexity? teaching philosophy in quantitative courses, creative and innovative implementation of technology, incorporation of research into teaching, longer-standing recruitment and retention efforts and outreach activities of female and minority students, and student involvement in research.