An uncertainty analysis of contamination transport by using moment closure method
Journal
Journal of Taiwan Agricultural Engineering
Journal Volume
63
Journal Issue
3
Date Issued
2017-09-01
Author(s)
Abstract
The advection-reaction equation is often used for simulating the effect of velocity and biochemical reaction rates to contamination transportation in river flow. Due to the limited hydrogeological observation data and its high levels of uncertainty, the result of the simulation is also high uncertainty. By solving the stochastic differential equation, the uncertainty of contamination transportation caused by the parameter uncertainty could be analyzed. Usual analytical methods are (1) Implementation of the stochastic partial differential equation such as the Monte Carlo Method (2) Statistical moments of specific position estimation like Moment Closure Method and Perturbance Moments Method. The statistical moments in different spatiotemporal could be obtained by solving the Moment Equations because the feature of Moment Closure Method is to convert the physics equation into Moment Equations. This research uses Moment Closure Method to calculate the first three order moment of Advection-reaction Equation, and the moments of three simulation cases are validated by the Monte Carlo method. In case 1, the initial and boundary condition uncertainty exist. Case 2, besides considering the uncertainties in case 1, the uncertainty of reaction rates is also considered. Lastly, in Case 3, consider the uncertainty in Case 1 and velocity uncertainty. The simulation result is categorized into four types: (1) The Moment Closure Method could consider the moments of initial and boundary condition and parameters uncertainty simultaneously. (2) Results of the first three order moment by using Moment Closure Method and Monte Carlo Method have a high correlation. (3) Comparing to Monte Carlo Method, the Moment Closure Method could improve the efficiency of uncertainty analysis. (4) The uncertainty of velocity and reaction rate could increase the uncertainty of concentration simulation as well as positive skew. In conclusion, the first three order moment could be calculated by using the Moment Closure Method efficiently and precisely.
Subjects
Advection-reaction equation; Moment closure method; Moments
Type
journal article