Efficient Estimation of the Number of Water Retention Curves Required for Applying a Scaling Technique to the Forest Soil

For the numerical simulation of rainwater infiltration in forest slope, information on the water retention curve (WRC), which shows spatial variability due to forest ecosystem and weathered granite in natural forest soils, is required. A scaling approach using three parameters of the LN model has been developed to simplify the spatial variability in the WRCs of forest slope of the soil under geomorphological process. This approach showed that we required spatial data set in scaling parameter, effective porosity, e, and each average value of remaining two parameters (the matric pressure head corresponding to the median pore radius, m, and the width of the pore-size distribution, ) which were defined as reference parameters. In this study, we estimated the minimum number of WRCs required to determine the reference parameters effectively. For this purpose, 77 WRCs of core samples were collected from whole 25 m forest slope, and we randomly sampled WRCs using a Monte Carlo simulation. The effect of scaling (EOS) increased with the sample size, and the increase became small at a sample size of approximately 20. We could explain 78% (EOS = 0.78) of spatial variability in the WRCs at the 95% confidence level by using the reference parameters derived from 8 samples. In addition, we performed stratified sampling to reduce the number of WRCs required. As a result, the sampling scheme, which considers the variability in only slope direction, was the most advantageous. This result indicated that the geomorphological process, which produces spatial variability in the reference parameters of forested slopes, is an important factor to effectively determine reference parameters. This paper concluded that scaling approach enables us to reduce the required number of samples for WRCs.