A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence th e spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribut ion, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolat ion experiments. The model does not require knowledge of the soil structure . A homogeneous or uniform distribution of a solute and/or soil-water is in dicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mea n. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 a nd heterogeneity is indicated by HI > 1. A large value for this index may i ndicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experimen ts and is, therefore, easily calculated. The index may also be used to desc ribe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several diffe rent leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserv ed.