A Simple Stochastic Model Predicting Conservative Mass Transport Through the Unsaturated Zone Into Groundwater

The development of a Randomized Plug Flow (RPF) model is motivated by the problem of large spatial variability in unsaturated zone parameters. The model utilizes a one-dimensional plug flow concept with conservative tracer applied as a delta function at i =0. Flow is defined as d = i / θ where d (L) is the depth to the tracer, i (L) is the net infiltration, and θ (L³/L³) is the field capacity of the soil. d, i and θ defined as random variables D, I, and Θ respectively. The percent of mass applied that has reached the water table as a function of i is determined by F_θ(i/z), where F_θ is the cumulative distribution function of θ and z is the depth to ground water. Similar results are presented using distributions of i and d.

Five experiments conducted at the Hancock Experimental Station in the central sands region of Wisconsin are presented. The first experiment compares the transport of tracer to pesticide Aldicarb. Soil water samplers were installed in triplicate at depths of 3, 6 and 9 feet directly beneath potato hills in a 50′ x 150′ plot. Three wells with 2 foot screens at the water table were installed in furrows. Potassium bromide and Aldicarb were applied in narrow strips over the emerging plants and immediately hilled. Samples were taken over 372 days. Transport of Aldicarb is similar to bromide at the experimental plot. Both substances were transported to the water table in significant quantities far in advance of average rates of transport through the unsaturated zone.

The second experiment tests the accuracy of model transport – predictions. Samplers were installed and tracer applied in a 60’ x 60’ plot as in Experiment 1. Samples were collected from 6 soil water. samplers at 3 feet and 7 samplers at 6 feet for 180 days to determine the – distribution of I. Ninety-one days after tracer application 23 soil cores a were taken. Bromide and moisture content were determined to define the – distributions of D and Θ respectively. Wells surrounding the field with two foot screens at the water table were sampled for 237 days after – application of the tracer to estimate transport of bromide to the water a table. Comparisons are made assuming log normal or normal distribution of I, D and Θ and using Jury’s Transfer Function Model, (TFM) (1982) to adjust distribution parameters. Normal distributions and distributions adjusted using the TFM show good agreement with the percent of mass transported to the ground water determined using well samples.

The utility of the method is illustrated in Experiments 3, 4 and 5. All three experiments use soil water samplers installed in triplicate at 3 and 6 feet to determine f_I(i). Potassium bromide is applied as in a Experiment 1. Experiment 3 compares mass transport to the ground water under 3 methods of potato cultivation; 20 inch disk hills, Lilliston cultivator hills and bed cultivation. Results are inconclusive due to large – natural variability and problems with sample apparatus. Experiment 4 – compares the effects of over irrigation on the three methods of potato cultivation. Transport under the hill treatments which apparently shed the excess water is not affected by 60% more irrigation. In contrast 200% more mass is predicted to reach the water table under the over irrigated bed treatment within 300 days of tracer application. Experiment 5 in furrow placement of tracer to the placement described in Experiment 1. Five hundred percent more mass is predicted to reach the water table within 300 days after application of bromide in the furrow.

The RPF model may be calibrated using estimates of readily obtained parameters. It will probably provide good estimates of conservative mass transport to ground water in sandy soils.