Models for Estimating Soil Particle-Size Distributions
01 Jul 2002-Soil Science Society of America Journal (John Wiley & Sons, Ltd)-Vol. 66, Iss: 4, pp 1143-1150
TL;DR: In this article, the authors evaluated the ability of seven models (i.e., five lognormal models, the Gompertz model, and the Fredlund model) to fit PSD data sets from a wide range of soil textures.
Abstract: An accurate mathematical representation of particle-size distributions (PSDs) is required to estimate soil hydraulic properties or to compare texture measurements from different classification systems. The objective of this study was to evaluate the ability of seven models (i.e., five lognormal models, the Gompertz model, and the Fredlund model) to fit PSD data sets from a wide range of soil textures. Special attention was given to the effect of texture on model performance. Several criteria were used to determine the optimum model with the least number of fitting parameters when other conditions are equal. The Fredlund model with four parameters showed the best performance with the majority of soils studied, even when three criteria that impose a penalty for additional fitting parameters were used. Especially, the relative performance of the Fredlund model in regard to other models increased with increase of clay content. Among all soil classes, the lognormal models with two or three parameters showed better fits for silty clay, silty clay loam, and silt loam soils, and worse fit for sandy clay loam soil.
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Cites background from "Models for Estimating Soil Particle..."
...For example, Hwang et al. (2002) found that only about half of the USDA texture triangle can be adequately described by a bimodal Gaussian model, and that the suitability of different PSD models appears to be influenced by soil textural classes and/or by the soil clay content....
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...Hwang et al. (2002) pointed out that all of silty clay, silty clay loam, and silt loam among the USDA texture triangle could be properly modelled with lognormal PSDs; but more complex distributions were required for sandy clay loam, sandy clay, and much of the clay region....
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TL;DR: In this article, the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects is studied, and a particular configuration that is very commonly seen can arise in a simple way.
Abstract: I study the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects. I show that a particular configuration that is very commonly seen can arise in a simple way. I give a formula by means of which the risk incurred by the “minimum CP ” rule can be estimated.
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