Models for Estimating Soil Particle‐Size Distributions

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.

The best mathematical models describing particle size distribution of soils

“…According to Fig. 7d, it was found that the fits of PSD models declined with increasing sand content (Hwang et al 2002). On this basis, it can be noted that model performance deteriorated as the sand proportion of soils increased.…”

“…Tested five log-normal models for 71 soils from New Zealand Hwang et al (2002) Evaluated fitting ability at 7 models on 1387 Korean soil samples Hwang (2004) Studied the effect of soil texture of 1387 Korean soil samples on the performance of nine different PSD models Lima and Silva (2007) Conducted a study on PSD of suspended sediments in river water Bah et al (2009) Compared the fitting ability of seven PSD models to data of 55 fine-textured soil samples from New South Wales in Australia Bagarello et al (2009) Evaluated the ability of the hyperbolic and Fredlund models to fit 243 soils Shangguan (2012) Investigated ten PSD models for the conversion of soil texture classification from ISSS and Katschineski to FAO/USDA system for soils from china Botula et al (2013) Evaluated the performance of 18 PSD models for 1412 soils from Central Africa which had humid tropics Weipeng et al (2015) Studied critical evaluation of PSD models of 1013 soil samples from different regions of china Bayat et al (2015) Investigated fitting capability of PSD models on the 713 PSD experimental data of the UNSODA database…”

“…a All soil samples, b clay texture group, c loamy texture group, d sandy texture group and each texture group, separately). It must note that in majority of past researches, (Hwang et al 2002;Hwang 2004;Vipulanandan and Ozgurel 2009), Fredlund model was reported as the best model for PSD description. In our study, acceptable fitting of Fredlund model on measured data was seen, too.…”

“…Iterative nonlinear regression was used to find the values of fitting parameters, so that, the best fitting would be determined between PSD models and measured data (Hwang et al 2002;Bah et al 2009). For this purpose, SOLVER routine operator of the Microsoft Excel software was applied (Wraith and Or 1998).…”

“…So, the most accurate model should be selected for each texture category. Hwang et al (2002) reported that Gompertz model had the best fit on sandy and sandy loam soils. That is similar to our result.…”