Application Of Stochastic Methods To Creating Models Of Contaminant Transport And Dispersion In Rivers And Groundwater

Purely stochastic methods can yield useful prediction models of contaminant arrival-time distributions derived from advective-dispersive transport in a variety of one-dimensional environments. Two different models are considered, both relating to dispersion of a brief pulse of conservative contaminant in a steady flow system. The first model considers the arrival-time of a contaminant pulse in a river channel with hydraulic interaction with an adjacent unconfined aquifer (hyporheic zone). The contaminant particles experience chance delays in the hyporheic zone where all particle movement is deemed to be at right angles to the channel. This model is mathematically equivalent to a one-dimensional random walk with positive, zero, or negative drift. Zero drift yields scale-invariant arrival-time distributions, with all other drift values giving inverse Gaussian arrival times. Negative drift implies some contaminant particles never escape the hyporheic zone. The case of zero or near-zero drift is of particular interest because the arrival-time distribution is then characterized by long t tailing over considerable time ranges. This gives a possible explanation of a recent river tracer experiment which recorded power-law tailing over a long period. The second dispersion model considers the case of temporal moments of contaminant arrival-time distributions when flow is partitioned into parallel stream tubes with independent advection-dispersion within each stream tube. This includes, for example, perfectly stratified aquifer systems or river systems where some flow moves along old linear channel deposits. This model yields the general result that the rth temporal central moment is an rth order polynomial function of contaminant travel distance. For example, the arrival time variance is a quadratic function of contaminant travel distance. This relation holds independently of arrival-time distributions and variations of hydraulic conductivity across the stream tubes.