Analysis of spatial variability of soil water retention using the cumulative distribution function matching

The importance of modeling dependencies of spatial variability of soil water content on soil matric potential grows due to the proliferation of ensemble modeling, data assimilations, and other soil water modeling applications. The objective of this work was to investigate conversions between cumulative distribution functions of water contents at different matric potentials. In total, 80 samples were taken in the nodes of the grid to measure soil water retention using sand and sand-kaolin capillarimeters at absolute values of soil matric potential of 0.001, 0.003, 0.010, 0.020, and 0.050 MPa, and with the water vapor desorption method at 3, 21, 39, 82, and 142 MPa. The probabilities of distributions of both non-transformed and log-transformed soil water contents being normal appeared to be larger than 0.05 in most cases. Using the probit function to represent the observed variability allowed us to match cumulative probability distributions at different soil water potentials. Slopes of dependencies of probits on non-transformed and log-transformed water contents had one-parametric linear dependencies on the logarithms of the absolute value of soil matric potential in capillary and adsorptive potential ranges.