Sigmoidal Water Retention Function with Improved Behavior in Dry and Wet Soils

A popular parameterized soil water retention curve (SWRC) has a hydraulic conductivity curve associated with it that can have an infinite slope at saturation. The problem was eliminated before by giving the SWRC a non–zero air–entry value. This improved version still has an asymptote at the dry end, which limits its usefulness for dry conditions and causes its integral to diverge for commonly occurring parameter values. We therefore joined the parameterizations' sigmoid mid–section to a logarithmic dry section ending at zero water content for a finite matric potential, as was done previously for a power–law type SWRC. We selected five SWRC parameterizations that had been proven to produce unproblematic near–saturation conductivities and fitted these and our new curve to data from 21 soils. The logarithmic dry branch gave more realistic extrapolations into the dry end of both the retention and the conductivity curves than an asymptotic dry branch. We tested the original curve, its first improvement, and our second improvement by feeding them into a numerical model that calculated evapotranspiration and deep drainage for nine combinations of soils and climates. The new curve was more robust than the other two. The new curve was better able to produce a conductivity curve with a substantial drop during the early stages of drying than the earlier improvement. It therefore generated smaller amounts of more evenly distributed deep drainage compared to the spiked response to rainfall produced by the earlier improvement.