In groundwater applications, Monte Carlo methods are employed to model
the uncertainty on geological parameters. However, their brute-force
application becomes computationally prohibitive for highly detailed
geological descriptions, complex physical processes, and a large
number of realizations. The Distance Kernel Method (DKM) overcomes
this issue by clustering the realizations in a multidimensional space
based on the flow responses obtained by means of an approximate (computationally
cheaper) model; then, the uncertainty is estimated from the exact
responses that are computed only for one representative realization
per cluster (the medoid). Usually, DKM is employed to decrease the
size of the sample of realizations that are considered to estimate
the uncertainty. We propose to use the information from the approximate
responses for uncertainty quantification. The subset of exact solutions
provided by DKM is then employed to construct an error model and
correct the potential bias of the approximate model. Two error models
are devised that both employ the difference between approximate and
exact medoid solutions, but differ in the way medoid errors are interpolated
to correct the whole set of realizations. The Local Error Model rests
upon the clustering defined by DKM and can be seen as a natural way
to account for intra-cluster variability; the Global Error Model
employs a linear interpolation of all medoid errors regardless of
the cluster to which the single realization belongs. These error
models are evaluated for an idealized pollution problem in which
the uncertainty of the breakthrough curve needs to be estimated.
For this numerical test case, we demonstrate that the error models
improve the uncertainty quantification provided by the DKM algorithm
and are effective in correcting the bias of the estimate computed
solely from the MsFV results. The framework presented here is not
specific to the methods considered and can be applied to other combinations
of approximate models and techniques to select a subset of realizations