PROBABILITY-DISTRIBUTION OF SOLUTE TRAVEL-TIME FOR CONVECTIVE-TRANSPORT IN FIELD-SCALE SOILS UNDER UNSTEADY AND NONUNIFORM FLOWS

This study addresses the development of probability distributions of t ravel times for one-dimensional (vertical) solute transport in soils. The field-scale soils are considered heterogeneous, with stationary fl uctuations of soil hydraulic properties in the horizontal direction bu t nonstationary fluctuations of these properties in the vertical direc tion due to layering of the soil, which induces nonstationary heteroge neity. Approximate ensemble probability distribution functions of cons ervative solute travel time for vertical convective solute transport w ere derived directly from the convective transport stochastic partial differential equation, under both deterministic and stochastic soil su rface water flux (infiltration rate) and under unsteady and nonuniform soil water flows. General depth-varying initial and time-varying boun dary conditions were used in these derivations. The magnitude of the a pproximation in the theoretical probability distribution functions of travel time is quantified mathematically. Utilizing the soil water con tent data from a University of California, Davis, field site, it is sh own that the mathematical condition for this approximation is satisfie d for this field. The spatial heterogeneity is represented through a n onstationary soil water content random field which covaries both in ti me and in space, Dispersion emerges naturally in the derived ensemble probability distribution functions of solute travel time, owing to the stochasticity of soil water content at field scale. Then the theoreti cal expression for mean solute concentration over a field is derived, by means of the theoretical solute travel time distribution, as a func tion of time and soil depth, under vertical transport with rectangular pulse solute loading for the upper boundary condition, Comparisons of theoretical probability density functions of solute travel time again st their empirical counterparts, obtained from field experimental obse rvations under steady but nonuniform soil water flow, shaw good agreem ent. Comparisons of theoretical mean solute concentrations, as they ev olve with time and soil depth, against field experimental observations also show good agreement. However, further field experiments under un steady flow conditions are required for the comprehensive validation o f the developed theory.