Measurement network design including traveltime determinations to minimize model prediction uncertainty

Traveltime determinations have found increasing application in the characterization of groundwater systems. No algorithms are available, however, to optimally design sampling strategies including this information type. We propose a first-order methodology to include groundwater age or tracer arrival time determinations in measurement network design and apply the methodology in an illustrative example in which the network design is directed at contaminant breakthrough uncertainty minimization. We calculate linearized covariances between potential measurements and the goal variables of which we want to reduce the uncertainty: the groundwater age at the control plane and the breakthrough locations of the contaminant. We assume the traveltime to be lognormally distributed and therefore logtransform the age determinations in compliance with the adopted Bayesian framework. Accordingly, we derive expressions for the linearized covariances between the transformed age determinations and the parameters and states. In our synthetic numerical example, the derived expressions are shown to provide good first-order predictions of the variance of the natural logarithm of groundwater age if the variance of the natural logarithm of the conductivity is less than 3.0. The calculated covariances can be used to predict the posterior breakthrough variance belonging to a candidate network before samples are taken. A Genetic Algorithm is used to efficiently search, among all candidate networks, for a near-optimal one. We show that, in our numerical example, an age estimation network outperforms (in terms of breakthrough uncertainty reduction) equally sized head measurement networks and conductivity measurement networks even if the age estimations are highly uncertain.