Dissertation/Thesis Abstract

Application of numerical stochastic differential equations to air and stormwater quality models with comparisons to current modeling methods
by McCullough, Cameron, M.S., California State University, Long Beach, 2014, 152; 1591607
Abstract (Summary)

Well known dynamic models for air and stormwater quality typically involve the application of deterministic differential equations (DDEs) or random differential equations (RDEs) that apply Monte Carlo simulation. An alternative to RDEs are stochastic differential equations (SDEs), which are DDEs that incorporate random noise. In this thesis, we develop air and stormwater quality models that employ DDEs, RDEs and SDEs numerically solved by finite difference methods. The numerical results of the model variants are compared to each other and empirical data. The outcome demonstrates the utility of the SDE approach. The stormwater model is based on a one-dimensional advection-diffusion partial differential equation (PDE) that simulates the stream transport of copper in a small area within Los Angeles. Two air models are implemented, an ordinary differential equation model based on the continuity equation and a two-dimensional advection-diffusion PDE. The models approximate carbon monoxide levels in Costa Mesa and the Coachella Valley in California. The numerical PDEs are solved with the Strang splitting method, where the Lax-Wendroff and Crank-Nicolson methods are employed for the advection and diffusion subproblems respectively. For the SDE case the Euler-Maruyama method is applied to the source term subproblem.

Indexing (document details)
Advisor: Kim, Eun Heui
Commitee: Gao, Tangan, Lee, Chung-Min
School: California State University, Long Beach
Department: Applied Mathematics
School Location: United States -- California
Source: MAI 54/05M(E), Masters Abstracts International
Subjects: Applied Mathematics, Atmospheric sciences, Environmental science
Publication Number: 1591607
ISBN: 978-1-321-83404-8
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