The need to reduce the computational cost of stochastic groundwater flow and mass transport
predictions calls for efficient upscaling techniques which can transfer the heterogeneity across scales while
preserving similar flow and transport behaviors. In addition, due to the scarcity of measurement
data, inverse modeling is commonly used to calibrate the parameters by conditioning on  direct
and indirect data and hence reduce the uncertainty of flow and transport predictions. In this work,
an upscaling technique is developed and applied both in a synthetic example and a real case; then
upscaling and the Ensemble Kalman Filter (EnKF, a method for inverse modeling) are coupled to handle a
high-resolution inverse model; and finally, the EnKF and its variant, the normal-score EnKF, is applied in the
context of multiGaussian and non-multiGaussian media. The work included in this PhD can be grouped in three blocks.

First, simple averaging, simple-Laplacian, Laplacian-with-skin, and non-uniform coarsening
upscaling techniques are reviewed and assessed in a three-dimensional hydraulic conductivity upscaling exercise.
The reference is a fine scale conditional realization of the hydraulic conductivities at the
MAcro-Dispersion Experiment site on Columbus Air Force Base in Mississippi (USA). This realization
was generated using a hole-effect variogram model and it was shown that flow and transport modeling
in this realization (at the fine scale) can reproduce the observed non-Fickian spreading of the tritium
plume. The purpose of this work is twofold, first to compare the effectiveness of different
upscaling techniques in yielding upscaled models able to reproduce the observed transport behavior,
and second to demonstrate and analyze the conditions under which flow upscaling can provide a
coarse model in which the standard advection-dispersion equation can be used to model transport in
seemingly non-Fickian scenarios. Specifically, the use of the Laplacian-based upscaling technique
coupled with a non-uniform coarsening scheme yields the best results both in terms of flow and
transport reproduction, for this case study in which the coarse blocks are smaller than the
correlation ranges of the fine scale conductivities. However, in some cases, we also observe the impossibility of reproducing transport at the coarse scale solely on the basis of a flow upscaling. For this reason, a methodology for
transport upscaling is developed for three-dimensional highly heterogeneous formations. The overall
approach requires a prior hydraulic conductivity upscaling using an interblock-centered full-tensor
Laplacian-with-skin method followed by transport upscaling. The coarse scale transport equation
includes a multi-rate mass transfer term to compensate for the loss of heterogeneity inherent to
all upscaling processes. The upscaling procedures for flow and transport are described in detail
and then applied to a three-dimensional highly heterogeneous synthetic example. The proposed
approach not only reproduces flow and transport at the coarse scale, but it also reproduces the
uncertainty associated with the predictions as measured by the ensemble variability of the
breakthrough curves.

Second, the ensemble Kalman filter is coupled with upscaling to build an aquifer model at a
coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had
been taken for the purpose of inverse modeling. Building an aquifer model at such scale is most
often impractical, since this would imply numerical models with millions of cells. If, in addition,
an uncertainty analysis is required involving some kind of Monte-Carlo approach, the task becomes
impossible. For this reason, a methodology has been developed that will use the conductivity data,
at the scale at which they were collected, to build a model at a (much) coarser scale suitable for
the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (i) generate
an ensemble of realizations of conductivities conditioned to the conductivity data at the same
scale at which conductivities were collected, (ii) upscale each realization onto a coarse
discretization; on these coarse realizations, conductivities will become tensorial in nature with
arbitrary orientations of their principal directions, (iii) apply the EnKF to the ensemble of
coarse conductivity upscaled realizations in order to condition the realizations to the measured
piezometric head data. The proposed approach addresses the problem of how to deal with tensorial
parameters, at a coarse scale, in ensemble Kalman filtering, while maintaining the conditioning to
the fine scale hydraulic conductivity measurements. The approach is demonstrated in the framework of a
synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities,
piezometric heads or both is analyzed.

Finally, the ensemble Kalman filter is applied to jointly update the flow and transport parameters (hydraulic
conductivity and porosity) and state variables (piezometric head and concentration) of a
groundwater flow and contaminant transport problem in a multi-Gaussian porous media. A synthetic
experiment is used to demonstrate the capability of the EnKF to estimate the hydraulic conductivity and
porosity by assimilating dynamic head and multiple concentration data in a transient flow and
transport model. In this work the worth of hydraulic conductivity, porosity, head and
concentration data is analyzed in the context of aquifer characterization. The results indicate that the characterization of the
hydraulic conductivity and porosity fields is continuously improved as more data is assimilated. Also
the groundwater flow and mass transport predictions are improved if more and different types of
data are assimilated. The beneficial impact of accounting for multiple concentration data is
patent, particularly for the identification of the porosity field. Moreover, the normal score Ensemble Kalman Filter (NS-EnKF) method, which was recently developed to deal with the non-Gaussianity of parameters and state vectors in the EnKF, is used to assess
the impact of prior conceptual model uncertainty on the characterization of conductivity and on the prediction of flow
in a synthetic bimodal aquifer. In addition, the effect of distance-dependent
localization functions and different set-ups of the boundary conditions in the aquifer are also examined.
The results are evaluated in terms of ensemble means, variances
and connectivities of the conditional realizations of conductivity and also looking at the uncertainty of predicted
heads after solving the flow equation in the conditional conductivity realizations. For the cases analyzed it is found that (i)
the patterns of simulated conductivity and flow prediction can be reproduced close to the reference
for both the correct and wrong prior model using either the NS-EnKF or localized NS-EnKF as long as a sufficient number of piezometric head data are used for conditioning, (ii) coupling NS-EnKF with the
localization function improves the conductivity identification, (iii) the performance of the NS-EnKF is
not affected by the types of boundary conditions used.