Prediction of absolute unsaturated hydraulic conductivity of soils with Weibull pore size distribution

Abstract

Predicting absolute hydraulic conductivity solely from soil water retention is essential when no conductivity data are available. This study developed an approach to reliably predict saturated capillary conductivity $K_{\mathrm{sc}}$ only from the Weibull distribution based water retention. Three new $K_{\mathrm{sc}}$ functions were derived and then incorporated into the Peters-Durner-Iden (PDI) and Brunswick (BW) model systems. A model-specific saturated tortuosity ${\tau }_s$ value was determined via fitting each of the nine predicted conductivity models to 12 calibration soils. Using the generally effective ${\tau }_s$ obtained from calibration, one then predicted $K_{\mathrm{sc}}$ and finally absolute hydraulic conductivity for the 25 test soils only from optimized water retention parameters. Model-data comparison results showed that the PDI-based and BW-based models, accounting for both capillary and noncapillary flow, predict the conductivity data better than the capillary-based Weibull distribution conductivity models, particularly in the dry range where noncapillary flow processes predominate. In addition, the cut-and-random-rejoin model proposed by Mualem performed the best within the PDI and BW model systems, proving the wide application of the Mualem model in soil physics and hydrology.