An Investigation Of An Ensemble Kalman Filter Coupled With Statistical Moment Equations For Subsurface Flow

Using ensemble Kalman filter(EnKF)to estimate aquifer parameter(e.g.hydraulic conductivity)is commonly confronted with spurious correlation.An ensemble Kalman filter coupled with exact statistical moment equations(MEs-EnKF)is developed for solving the spurious correlation issue.I doing so by: first,investigating the pros and cons of applying covariance and domain localization methods on parameter estimation for constant-/variable-density groundwater flow;second,develop the two-and three-dimensional parallel codes which rely on an improved scheme of statistical moment equations under transient state;third,developing a moment-equations-based reduced-order model(MEsROM-KL)to reduce the computational burden and verify the accuracies of numerical solutions of the second-order accurate moment equations;fourth,proposing MEs-EnKF and conducting comparisons between MEs-EnKF and traditional EnKF.The results of the uses of localization methods show two issues.One of them is that localization parameters used are previously unknown.Another of them is that domain localization method lacks a guarantee of global convergence when only salinity data is assimilated in variable-density flow.The numerical solutions of statistical moment equations agree well with their corresponding analytical solutions under steady state,while well with the Monte Carlo solutions under transient state.In addition,MEsROM-KL being free of selecting snapshot size outperforms the traditional snapshot-based reduced model when they cost the same time.These results indicate that the numerical solutions of moment equations are accurate.The result of the use of MEs-EnKF show that:(1)MEs-EnKf can be free of spurious correlation and does not need to turn any parameters in terms of the experimental settings;(2)the traditional EnKF method can reach the similar results as MEs-EnKF when 10,000 realizations are employed,however,the central processing unit(CPU)time for performing former is about 1,000 times of the latter;(3)MEs-EnKF shows the inability to assimilate head data being highly accurate,which is related to the closure problem of the second-order accurate moment equations.In general,MEs-KF is free of spurious correlation and can be an efficient alternative of traditional EnKF.