1 Water Resources Research Institute, National Water Research Centre, El-Qanater El-Khayeria, Cairo 13621, Egypt

2 Department of Civil and Environmental Engineering, Imperial College London,
Exhibition Road, London SW7 2AZ, UK

3 Politecnico di Milano, D.I.I.A.R., Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

Abstract Nonstationarity of groundwater flow and transport processes is relevant in well capture zone design and wellhead protection. We introduce a State-Space First-Order approach as an alternative to numerical Monte Carlo methods to quantify the uncertainty associated with well catchment prediction. The mean and covariance of system state variables (i.e. head, pore water velocity and particle trajectory) are approximated by a first-order Taylor’s series with sensitivity coefficients estimated from the adjoint operator for a system of discrete equations (state-space equations). By employing numerical solution methods, it is possible to handle irregular geometry, varying boundary conditions, complicated sink/source terms and different covariance functions, all of which are important factors for real-world applications. Results obtained using the State-Space First-Order method compare favourably with those from Monte Carlo analysis and are considerably more efficient.

Keywords Monte Carlo method; nonstationarity; State-Space First-Order method; stochastic; well catchment