We consider the problem of placing a limited number of sensors in a municipal water distribution network to minimize the impact over a given suite of contamination incidents. In its simplest form, the sensor placement problem is a p-median problem that has structure extremely amenable to exact and heuristic solution methods. We describe the solution of real-world instances using integer programming or local search or a Lagrangian method. The Lagrangian method is necessary for solution of large problems on small PCs. We summarize a number of other heuristic methods for effectively addressing issues such as sensor failures, tuning sensors based on local water quality variability, and problem size/approximation quality tradeoffs. These algorithms are incorporated into the TEVA-SPOT toolkit, a software suite that the US Environmental Protection Agency has used and is using to design contamination warning systems for US municipal water systems.
Heterogeneity plays an important role in groundwater flow and contaminant transport in natural systems. Since it is impossible to directly measure spatial variability of hydraulic conductivity, predictions of solute transport based on mathematical models are always uncertain. While in most cases groundwater flow and tracer transport problems are investigated in two-dimensional (2D) systems, it is important to study more realistic and well-controlled 3D systems to fully evaluate inverse parameter estimation techniques and evaluate uncertainty in the resulting estimates. We used tracer concentration breakthrough curves (BTCs) obtained from a magnetic resonance imaging (MRI) technique in a small flow cell (14 x 8 x 8 cm) that was packed with a known pattern of five different sands (i.e., zones) having cm-scale variability. In contrast to typical inversion systems with head, conductivity and concentration measurements at limited points, the MRI data included BTCs measured at a voxel scale ({approx}0.2 cm in each dimension) over 13 x 8 x 8 cm with a well controlled boundary condition, but did not have direct measurements of head and conductivity. Hydraulic conductivity and porosity were conceptualized as spatial random fields and estimated using pilot points along layers of the 3D medium. The steady state water flow and solute transport were solved using MODFLOW and MODPATH. The inversion problem was solved with a nonlinear parameter estimation package - PEST. Two approaches to parameterization of the spatial fields are evaluated: (1) The detailed zone information was used as prior information to constrain the spatial impact of the pilot points and reduce the number of parameters; and (2) highly parameterized inversion at cm scale (e.g., 1664 parameters) using singular value decomposition (SVD) methodology to significantly reduce the run-time demands. Both results will be compared to measured BTCs. With MRI, it is easy to change the averaging scale of the observed concentration from point to cross-section. This comparison allows us to evaluate which method best matches experimental results at different scales. To evaluate the uncertainty in parameter estimation, the null space Monte Carlo method will be used to reduce computational burden of the development of calibration-constrained Monte Carlo based parameter fields. This study will illustrate how accurately a well-calibrated model can predict contaminant transport.
We consider the problem of placing sensors in a municipal water network when we can choose both the location of sensors and the sensitivity and specificity of the contamination warning system. Sensor stations in a municipal water distribution network continuously send sensor output information to a centralized computing facility, and event detection systems at the control center determine when to signal an anomaly worthy of response. Although most sensor placement research has assumed perfect anomaly detection, signal analysis software has parameters that control the tradeoff between false alarms and false negatives. We describe a nonlinear sensor placement formulation, which we heuristically optimize with a linear approximation that can be solved as a mixed-integer linear program. We report the results of initial experiments on a real network and discuss tradeoffs between early detection of contamination incidents, and control of false alarms.