Improved models of particle-size distribution: an illustration of model comparison techniques

Abstract

We investigated a relatively unexplored area of soil science: the fitting of parameterized models to particle-size distribution (a subject more thoroughly explored in sedimentology). Comparative fitting of different models requires the use of statistical indices enabling rational selection of an optimum model, i.e., a model that balances the improvement in fit often achieved by increasing the number of parameters, p, against model simplicity retained by minimizing p. Five models were tested on cumulative mass-size data for 71 texturally diverse New Zealand soils: a one-parameter (p = 1) Jaky model borrowed from geotechnics; the standard lognormal model (p = 2); two modified lognormal models (each with p = 3); and the bimodal lognormal model (p = 3). The Jaky and modified lognormal models have not previously been introduced into the soil science literature. Three statistical comparators were used: the coefficient of determination, R²; the F statistic; and the Cp statistic of Mallows. The bimodal model and one modified lognormal model (denoted ORL) best fit the data. The bimodal model gave a marginally better fit, but incorporates a sub-clay mode (untestable with the present data), so we adopted the ORL model as the physically best benchmark for comparison of other models. The simple Jaky one-parameter model gave a good fit to data for many of the soils, better than the standard lognormal model for 23 soils. The model comparison methods described have potential utility in other areas of soil science. The Cp statistic is advocated as the best statistic for model selection.