Data Assimilation Application to the Subsurface Flow and Solute Transport

A data assimilation method is developed to calibrate a heterogeneous hydraulic conductivity field conditioning on observation of a transient groundwater flow field or transient conservative solute transport field. An ensemble Kalman filter (EnKF) approach is used to update model parameters such as hydraulic conductivity and model variables such as hydraulic head or solute concentration using available data. A synthetic two-dimensional flow case is used to assess the capability of the EnKF method to calibrate a heterogeneous conductivity field by assimilating transient flow data from observation wells under different hydraulic boundary conditions. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating hydraulic head measurements and the hydraulic boundary condition will significantly affect the simulation results. The ensemble size should be 300 or larger for the numerical simulation in the study case. The number and the locations of the observation wells will significantly affect the hydraulic conductivity field calibration. Another synthetic case with the mixed Neumann/ Dirichlet boundary conditions is designed to investigate the capacity and effectiveness of a constrained EnKF by assimilating the solute concentration to identify a conductivity distribution. The study results indicate that the constrained EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating solute concentration measurements. The larger area for the initial distribution of the solute concentration, the more observed data can be obtained, the better the inversed results. The number of the actual observation wells needed to calibrate the hydraulic conductivity field through the constrained EnKF method via assimilating the solute concentration is very small. The data assimilation method can produce useful results in the first five or seven time step assimilation. The simulated results by the data assimilation method are still very similar with different observation errors. Based on the problems of the filter divergence in the data assimilation application, the localized EnKF method is applied. The covariance inflation and localization schemes are used to the transient state groundwater water flow. The synthetic study case of the transient groundwater flow is the same as the research before, but the assumed real conductivity values are correlated. The simulations by the data assimilation with and without localized EnKF are compared. The hydraulic conductivity field can be updated efficiently by the localized EnKF, while it cannot be updated via just the EnKF. The covariance inflation and localization are found to efficiently solve the problem of the filter divergence. The ensemble size for the localized EnKF method is 100 and less than that only in the EnKF before, which reduce the computer cost. The correlation length is found to affect the simulation by the localized EnKF method much more than the localization radius. Moreover, the updated results of hydraulic conductivity fields produced by the localized EnKF method with the greater correlation length and greater localization radius are a little closer to the real field. Based on the problems of the filter divergence and it is more reasonable to add error perturbations to the forward model because there are so many uncertainties and error sources in the reality, the model error perturbation is added to the EnKF. The synthetic study case and the real hydraulic conductivity field of the transient state groundwater flow are the same as above. The EnKF method by adding the model error perturbation is applied to the transient state groundwater flow to update the hydraulic conductivity through assimilating the observed data of the hydraulic head. After comparing the inverse results obtained via the EnKF by adding model error perturbations with the results produced by the EnKF and the results produced by the covariance inflation scheme via the EnKF method, the problem of the filter divergence is found to be improved to a certain degree by adding the model error to the EnKF method though the updated results at later assimilating time is not good. Even though big error has been added to the forward model, the EnKF method still can efficiently update the hydraulic conductivity field. The EnKF method by adding model error perturbations is more efficient than the EnKF method by the covariance inflation to update the hydraulic conductivity field via assimilating the observed hydraulic head data from the transient groundwater flow.