Comparison of two methods for summarizing hydraulic conductivities of a layered soil

Abstract

Hydraulic conductivity data are frequently summarized using mathematical functions that quantify the relationship between water content (θ) and hydraulic conductivity (K(θ)). This study was done to determine the effects of the choice of the K(θ) function and to determine if field data from layered profiles could be summarized using only one parameter per depth. Three K(θ) functions together with a matching factor were fitted to hydraulic conductivity data from a field plot. The functions were Km(θ/θm)1/β, Km[(θm−θc)/(θ−θc)]1/n,and Km exp {α(θ−θm)}, where α, β, n, Km, θc, and θm, are parameters to be estimated. For each function, two methods were considered. Method 1 fitted a different value to α, β, n, and Km for each depth while maintaining θc at a fixed value. All hydraulic conductivity functions fit data from a Muir silt loam equally well, as evidenced by the coefficient of linearity (r2) values greater than 0.72, mean square error (MSE) values less than 0.97, and coefficient of variation (CV) values less than 50%. The fitting was accomplished using ln {K} as the dependent variable. Method 2 fitted values by depth only to Km, and all other parameters were held constant. The hydraulic conductivity functions performed equally well, with r2 values greater than 0.60, MSE values less than 1.2, and CV values of 50% or less. When some loss of precision can be tolerated, the number of parameters required to summarize data from a layered soil can be reduced.