Long‐term pollutant degradation in the unsaturated zone with stochastic rainfall infiltration

Given the discharge of a reactive material to the land surface, the fraction of the contaminant which reaches the underlying aquifer is uncertain due to variations in the rate of precipitation and infiltration. A stochastic conceptual framework is developed to estimate this variation. The framework relates the pollutant leachate fraction to the long‐term rate of infiltration and derives the probability of a given leacheate fraction from the probability of obtaining the associated infiltration rate. Application of the methodology is illustrated for the case where cumulative infiltration is represented by a compound Poisson process and pollutant fate is determined for one‐dimensional advective‐dispersive transport with linear equilibrium adsorption and first‐order chemical decay. The derived probability model for this case compares favorably to results from Monte Carlo simulations of a numerical transport model. Applications and limitations of the methodology with more sophisticated transport, reaction, and stochastic infiltration models are considered.