Characterizing Non-gaussian Aquifer Model Parameters Based On The Ensemble Kalman Filter

Numerical modeling of groundwater flow and mass transport is increasingly becoming a reference criterion nowadays for water resources assessment and environmental protection. To render the model reliable for future predictions, the model structure and parameters have to be characterized as close to the reality as possible. The process of model identification by integrating measured parameters and observed model states is so called inverse problem. A series of methods has been proposed to solve the inverse problem in the past several decades such as maximum likelihood method, pilot point method, self-calibration method, Markov chain Monte Carlo method and gradual deformation method, and the evolution of inverse method is discussed in the thesis. The main point of this thesis is to propose a stochastic inverse method to estimate model parameters which cannot be described with a Gaussian distribution integrating nonlinear model observations.The normal-score ensemble Kalman filter (NS-EnKF) is constructed on the basis of the standard EnKF. The standard EnKF is widely used as a real time data assimilation technique due to its advantages, e.g., computation efficiency and ability to assess model uncertainty. However, it is known to perform optimally when the model parameters and state variables follow multiGaussian distributions. To extend the application of the EnKF to nonGaussian distributed state vectors, the normal-score transformation is introduced into the EnKF forming the NS-EnKF. The augmented state vector consisting of model parameters and state variables are normal-score transformed so that they follow marginal Gaussian distribution. Then, the transformed vectors serve as input to the EnKF, which now operates on marginally Gaussian distributed variables. The updated vectors are then back transformed to the original distribution space. The effectiveness of the proposed method is assessed in a synthetic bimodal aquifer, where the NS-EnKF is found to perform better than the standard EnKF in characterizing the bimodal structure of the hydraulic conductivities and in the subsequent flow and transport predictions.Sensitivity of the NS-EnKF to different parameters is analyzed, i.e., size of the ensemble, number of conditioning hard data and piezometers, variance, prior model, localization of Kalman gain and boundary conditions. In the sensitivity analysis we find that (1) when the ensemble size is small, filter inbreeding can happen; (2) influence of the variance of lnK is not serious in that the NS-EnKF works well even with a variance as high as near 10; (3) NS-EnKF is able to identify the main lnK structure even if no hard data are available although more piezometers are needed in this case; (4) with a wrong prior model NS-EnKF does not work as well as that with correct prior model; (5) NS-EnKF performs better after introduction of localization of Kalman gain; (6) NS-EnKF gives similar results with parallel flow and radial flow; (7) NS-EnKF deteriorates with less observation wells.