Simulation of solute transport using a continuous time Markov process: 1. Theory and steady state application

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Abstract
A continuous time Markov process is developed and used to describe chemical movement through the soil under steady state water flow regimes. Theoretical considerations are made to include chemical and biological degradation, crop uptake, and adsorption as processes which affect the probability of movement of a molecule of solute between adjacent soil layers. Probability distributions of solute are given for each soil layer given the flux of soil water and the intensity of transition for the source and sink terms. Predicted solute concentrations of nitrate and bromide compared favorably with observed concentrations collected from a laboratory soil column study under steady state water flow. The model, however, shows a dependency on the number of layers used to simulate the soil profile. The approach offers substantial promise for description of spatially variable solute movement in field soils, which is examined in a companion paper.