3D Variational Analysis In Subsurface Contaminant Transport Model

Anup Saha, North Carolina Agricultural and Technical State University


Modeling of contaminant transport in a subsurface environment by a numerical model deviates from the real world environment because of the highly heterogeneous nature of the subsurface environment. In this study, the data assimilation techniques are integrated with the numerical model and are applied to the subsurface environment to predict the contaminant transport. The Forward Time Center Space (FTCS) model is used as a numerical approach to solve the classical advection-dispersion-reaction transport equation and the Kalman Filter, Ensemble Kalman Filter (EnKF) and 3D Variational (3DVAR) analysis are used for data assimilation purpose. A hybrid scheme, termed as EnKF-3DVAR is developed using EnKF and 3DVAR analysis. The EnKF is a Monte Carlo based sequential data assimilation technique that divides the state vector into N number of ensembles rather than computing one state vector. The 3DVAR analysis uses the EnKF mean state vector as the background state and uses a cost function to find out an optimal estimate of that EnKF mean state vector. The simulation is run using an ensemble size of 100 members. A Root Mean Square Error (RMSE) profile is used to evaluate the prediction accuracy of the models. This study shows that state predictions are better for both the EnKF and EnKF- 3DVAR when compared to those of the numerical and KF solutions. The introduction of 3DVAR analysis with EnKF is found to be effective in the reduction of the prediction errors. The EnKF-3DVAR model shows an error reduction of 22.3% from the EnKF solution. The mean RSME for the four models numerical, KF, EnKF and EnKF-3DVAR are 159.1 mg/L, 72.9 mg/L, 17.5 mg/L and 13.6 mg/L respectively.