Uncertainty estimation of well catchments in heterogeneous aquifers

Abstract

[1] The uncertainty in the boundary of two-dimensional, steady state well catchments due to the uncertainty of the spatially variable hydraulic conductivity field is investigated. The well discharge rate and the areal recharge rate are assumed constant. The catchment boundary is traced by backward particle tracking in the velocity field. The uncertainty bandwidth of the catchment boundary is approximated in first order by formulating the time-dependent longitudinal and transversal second moments of the particle displacements along and normal to the mean particle trajectory. Applications of the approach are presented for a set of simple configurations. The results are compared with the results from unconditional numerical Monte Carlo simulations. The comparison allows an assessment of the accuracy, the applicability, and the limits of the method. The approximation corresponds quite well with the Monte Carlo simulations provided that the distance to the domain boundary is sufficiently large.

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

“…Recent applications of first-order methods have been extended to the determinations of stochastic well capture zones (e.g. Kunstmann and Kinzelbach, 2000;Stauffer et al, 2002Stauffer et al, , 2004Lu and Zhang, 2003;Zhang and Lu, 2004;Lessoff and Indelman, 2004;Bakr and Butler, 2005;Riva et al, 2006;Kunstmann and Kastens, 2006;Indelman et al, 2006). Most studies on the subject dealt with depth-averaged two-dimensional problems (Kunstmann and Kinzelbach, 2000;Stauffer et al, 2002Stauffer et al, , 2004Lu and Zhang, 2003;Zhang and Lu, 2004;Bakr and Butler, 2005;Riva et al, 2006;Kunstmann and Kastens, 2006).…”

Delineation of Source Protection Zones Using Statistical Methods

“…Furthermore, procedures were developed, which allow conditioning of the statistical moments of the flow field and, therefore, of travel time moments, on hydraulic heads measurements and/or aquifer architecture (e.g., Hernandez et al, 2003;Winter et al, 2003). Stauffer et al (2002) investigated the uncertainty in the location of twodimensional, steady state catchments of pumping wells due to the uncertainty of the spatially variable hydraulic conductivity field by a semi-analytical Lagrangian technique. For the analysis it is assumed that the aquifer can be modelled as a steady-state horizontal, confined or unconfined system.…”

Assessment of uncertainty associated with the estimation of well catchments by moment equations

“…The effect of domain size (in terms of the correlation scale of the log conductivity field) on the prediction uncertainty is also analyzed. The results are then compared with the semi-analytical solution proposed by Stauffer et al [24,25] and an extensive suite of numerical Monte Carlo simulations.…”

“…Recently, Stauffer et al [24] proposed a semi-analytical method to compute the uncertainty associated with the prediction of a well catchment. They measured uncertainty of predictions in terms of the standard deviation of the displacement of conservative particles along the direction normal to the mean boundary of the well catchment itself.…”