Convergence assessment of numerical Monte Carlo simulations in groundwater hydrology

Numerical Monte Carlo simulation is considered to be one of the main tools to be used in groundwater hydrology (1) to quantify the uncertainty in the flow predictions due to imperfect knowledge of aquifer architecture, hydraulic parameters, and forcing terms or (2) to assess the reliability of approximated moment-based equations for flow and/or transport. While the Monte Carlo framework is conceptually straightforward and very flexible, it is recognized as lacking well-established convergence criteria. Here we propose a methodology for convergence analysis of Monte Carlo simulations and therefore for the reliability assessment of the inferred statistical moments. The methodology, based on simple rules of statistical inference, is described with reference to a typical groundwater flow problem and can be extended to different application fields.