Stochastic estimation of the distribution of soil water repellency on the soil surface in a humid-temperate forest

Soil water repellency (SWR) increases surface runoff and preferential flows. Thus, quantitative evaluation of SWR distribution is necessary to understand water movements. Because the variability of SWR distribution makes it difficult to measure directly, we developed a method for estimating an SWR distribution index, defined as the areal fraction of surface soil showing SWR (SWRarea). The theoretical basis of the method is as follows: (1) SWRarea is equivalent to the probability that a position on the soil surface is drier than the critical water content (CWC); SWR is present (droplets absorbed in >10 s) when the soil surface is drier than the CWC and absent when it is wetter. (2) CWC and soil moisture content (theta) are normally distributed independent variables. (3) Thus, based on probability theory, the cumulative normal distribution of theta - CWC (f(x)) can be obtained from the distributions of CWC and theta, and f(0), the cumulative probability that theta - CWC < 0, gives the SWRarea. To investigate whether the method gives reasonable results, we repeatedly measured theta at 0-5 cm depth and determined the water repellency of the soil surface at multiple points in fixed plots with different soils and topography in a humid-temperate forest. We then calculated the CWC from the observed theta-SWR relationship at each point. We tested the normality of the CWC and theta distributions and the correlation between CWC and theta. Then, we determined f(x) from the CWC and theta distributions and estimated the SWRarea on each measurement day. Although CWC and theta were both normally distributed, in many cases they were correlated. Nevertheless, the CWC-theta dependency had little effect on the estimation error, and f(x) explained 69% of the SWRarea variability. Our findings show that a stochastic approach is useful for estimating SWRarea.

Automated summary

The study developed a method for estimating soil water repellency distribution by using a stochastic approach, finding that despite the correlation between critical water content and soil moisture content, it had little effect on estimation errors. The method explained 69% of the variability in SWR area, demonstrating its usefulness in estimating SWR distribution.