Describing the soil physical characteristics of soil samples with cubical splines

The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations’ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interaction between the soil moisture retention and the hydraulic conductivity relationship, some data sets yield a fit that seems not to be optimal. So the search for alternatives started. We ended with the cubical spline approximation of the soil physical characteristics. Software was developed to fit the spline-based curves to sets of measured data. Five different objective functions are tested and their results are compared for four different data sets. It is shown that the well-known least-square approximation does not always perform best. The distance between the measured points and the fitted curve, as can be evaluated numerically in a simple way, appears to yield good fits when applied as a criterion in the optimization procedure. Despite an increase in computational effort, this method is recommended over the least square method.