Prediction of absolute unsaturated hydraulic conductivity – comparison of four different capillary bundle models

Abstract. To model water, solute, and energy transport in porous media, it is essential to have accurate information about the soil hydraulic properties (SHPs), i.e., the water retention curve (WRC) and the soil hydraulic conductivity curve (HCC). It is important to have reliable data to parameterize these models, but equally critical is the selection of appropriate SHP models. While various expressions for the WRC are frequently compared, the capillary conductivity model proposed by Mualem (1976a) is widely used but rarely compared to alternatives. The objective of this study was to compare four different capillary bundle models in terms of their ability to accurately predict the HCC without scaling the conductivity function by a measured conductivity value. The four capillary bundle models include two simple models proposed by Burdine (1953) and Alexander and Skaggs (1986), which assume a bundle of parallel capillaries with tortuous flow paths, and two more sophisticated models based on statistical cut-and-random-rejoin approaches, namely those proposed by Childs and Collis-George (1950) and the aforementioned model of Mualem (1976a). To examine how the choice of the WRC parameterization affects the adequacy of different capillary bundle models, we utilized four different capillary saturation models in combination with each of the conductivity prediction models, resulting in 16 SHP model schemes. All schemes were calibrated using 12 carefully selected data sets that provided water retention and hydraulic conductivity data over a wide saturation range. Subsequently, the calibrated models were tested and rated by their ability to predict the hydraulic conductivity of 23 independent data sets of soils with varying textures. The statistical cut-and-random-rejoin models, particularly the Mualem (1976a) model, outperformed the simpler capillary bundle models in terms of predictive accuracy. This was independent of the specific WRC model used. Our findings suggest that the widespread use of the Mualem model is justified.