A SIMPLE CONCEPTUAL MODEL FOR PREDICTING THE CONCENTRATION AND TIME OF ARRIVAL OF PESTICIDES IN PREFERENTIALLY MOVING WATER

In calculating the arrival time and the distance travelled by pesticides in soils, it is important to know what is the cross-sectional area of flow. Under convective flow, the average distance travelled is expressed as

where L is the average distance travelled by solutes in preferentially moving water, m is the fraction of the total pore space taken up by the mobile fractional of the soil ( m = 1 for the Convection-Dispersion equation), m is the moisture in the mobile fraction of the soil after water is drained 24 to 48 hours after the rainfall event, q is the downward flux per unit area or specific discharge, and tr is the duration of the rainfall event. For preferential flow, we suggest that water and pesticides travelling in preferential paths move downward with a velocity close to the saturated hydraulic conductivity; an assumption that has been shown experimentally in finger-flow experiments (e.g., Selker, et al., 1992; Selker, et al., 1992; Selker, et al.,1992). Also, the wetted portion of the cross-sectional area, a_w, adjusts itself such that the product of the saturated hydraulic conductivity and the wetted cross-sectional area equals the flux;

Therefore, the distance can be expressed simply as

for t_r > t_d , and L = 0 for t_r t_d

where td is the time to fill the distribution zone and ks is the saturated hydraulic conductivity. Assuming that the depth of the distribution zone is constant, the peak-concentration of pesticide in the preferentially moving water may be expressed as

where C_ow is the concentration at the end of the mixing phase in the distribution zone and before the distribution starts (t = t_d) and can be expressed as C_ow = M_o / W_a where M_o is the initial amount of pesticides applied. W_a and W_d are the apparent moisture contents per unit area in the distribution layer during adsorption and desorption phases and are equal to

and

where ka is the adsorption-partition coefficient during the adsorption of water and solutes in the mixing stage and kd is the adsorption-partition coefficient during the distribution stage, and dd is the depth of the distribution zone. The distribution value, kd is the tangent of the desorption isotherm and ka is an average value over the entire range. For non-absorbed solutes the apparent water contents per unit surface area, are as expected, equal to the amount of water in the distribution zone. However, for pesticides, the use of different partition coefficients are obviously justified, even through they are only approximate.

References:

Selker, J. S., Leclerq, P., Parlange, J., & Steenhuis, T. S. (1992). Fingered flow in two dimensions, 1. Measurement of matric potential. Water Resources Research, 28(9), 2513 - 2521.

Selker, J. S., Parlange, J., & Steenhuis, T. S. (1992). Fingered flow in two dimensions, 2. Predicting finger moisture profile. Water Resources Research, 28(9), 2523 - 2528.

Selker, J. S., Steenhuis, T. S., & Parlange, J.-Y. (1992). Wetting front instability in homogeneous sand soils under continuous infiltration. Soil Science Society of America Journal, 56(5), 1346 - 1349.