Date of Award

2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Civil Engineering

First Advisor

Chang, Shoou-Yuh Dr.

Abstract

Contaminant transport modeling of a conservative solute in the subsurface is investigated by applying a Kalman filter (KF) with time correlated measurement errors. The usual method or assumption often employed is white Gaussian errors, but time correlated measurement errors were used instead for this research, since some hydrological observation data exhibit time correlated error characteristics. An observation data was generated from a two dimensional analytical solution with an additive time correlated random errors. This was used as the measurement Equation for the KF with time correlated measurement errors and the KF with white Gaussian errors. The measurement differencing algorithm was adopted in deriving a discrete time varying KF with time correlated measurement errors for a two-dimensional contaminant transport prediction in the subsurface. An expression for the correlation coefficient matrix for colored noise, termed as “Time correlated operator matrix”, is derived instead of using a traditional diagonally assigned one. A computer code was generated for both KF with white Gaussian errors and KF with time correlated errors. Simulation results indicated an improved root mean square error (RMSE) profile of KF with time correlated errors over KF with white Gaussian errors. The KF with correlated errors reduced the errors in prediction by 11.4% compared to the KF with xii white Gaussian errors using only 9 observation points in the entire 20×20 space domain. Further investigation revealed that the performance of the KF with time correlated observation errors was improved when the measurement errors standard deviation was reduced.

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