Travel time distributions derived from particle tracking in models containing weak sinks

A travel time distribution based on a particle-tracking analysis in a ground water model containing weak sinks is often uncertain because whether a particle is discharged or allowed to pass through a weak sink is unresolved by particle-tracking theory. We present a probability-based method to derive an objective travel time distribution in models containing weak sinks. The method discharges a fraction of the particle at the weak sink and allows the remaining fraction to pass through the weak sink. The weight of the discharged fraction depends on the ratio of the sink flux to the influx into the weak sink cell. We tested this approach on a coarse (100 x 100 m) and a fine (25 x 25 m) horizontal resolution regional scale ground water model (34.5 x 24 km). We compared the travel time distributions in a small subcatchment derived from particle-tracking analysis with one derived from a transport model. We found that the particle-tracking analysis with the coarse model underestimated the travel time distribution of the catchment compared to the transport solution or a particle-tracking analysis with the fine model. The underestimation of travel times with the coarse model was a result of a large area covered by sink cells in this model and the more accurate flow patterns simulated by the fine model. The probability-based method presented here compares favorably with a solute transport solution and provides an accurate travel time distribution when used with a fine-resolution ground water model.