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.

翻译：地下水流动建模常被用于计算地下水水头、估算地下水流动路径和运移时间，并为含水层内溶质运移过程提供见解。然而，由于地下非均质性和地质复杂性，加之测量数据缺乏或不可靠，驱动地下水流动模型的输入参数值往往高度不确定。这种不确定性会影响模型输出的准确性和可靠性。因此，在将模型作为工程工具应用前，必须量化参数的不确定性。本研究将不确定参数建模为随机变量，并采用贝叶斯反演方法获取参数的后验概率密度函数（pdf），该函数受数据约束：特别地，我们考虑的似然函数同时纳入井测量数据与关于研究区内泉域范围的先验知识。为控制模型与计算复杂性，我们假设参数后验pdf服从高斯分布。为验证该假设，我们对模型进行可辨识性分析：将反演流程应用于多组被不同噪声水平污染的合成数据，确定在何种噪声水平下能有效恢复参数的"真实值"。随后，我们转向真实井数据（来自意大利北部提契诺河流域，覆盖2014年夏季一个月），并以参数后验pdf为起点，对地下水运移时间分布开展不确定性量化分析。