  Groundwater flow modeling is commonly used to calculate groundwater heads,
estimate groundwater flow paths and travel times, and provide insights into
solute transport processes within an aquifer. However, the values of input
parameters that drive groundwater flow models are often highly uncertain due to
subsurface heterogeneity and geologic complexity in combination with lack of
measurements/unreliable measurements. This uncertainty affects the accuracy and
reliability of model outputs. Therefore, parameters' uncertainty must be
quantified before adopting the model as an engineering tool. In this study, we
model the uncertain parameters as random variables and use a Bayesian inversion
approach to obtain a posterior,data-informed, probability density function
(pdf) for them: in particular, the likelihood function we consider takes into
account both well measurements and our prior knowledge about the extent of the
springs in the domain under study. To keep the modelistic and computational
complexities under control, we assume Gaussianity of the posterior pdf of the
parameters. To corroborate this assumption, we run an identifiability analysis
of the model: we apply the inversion procedure to several sets of synthetic
data polluted by increasing levels of noise, and we determine at which levels
of noise we can effectively recover the "true value" of the parameters. We then
move to real well data (coming from the Ticino River basin, in northern Italy,
and spanning a month in summer 2014), and use the posterior pdf of the
parameters as a starting point to perform an Uncertainty Quantification
analysis on groundwater travel-time distributions.
