مقایسه مدل های توزیع لوگ-نرمال و گاما برای نمایش منحنی توزیع اندازه ذرات خاک

Abstract
In recent years, many researchers have attempted to estimate the soil hydraulic functions (e.g. soil moisture characteristics curve, and hydraulic conductivity function) using particle-size distribution (PSD) curve. In these studies, an accurate mathematical representation of PSD is required for fitting the observed data. So far, some mathematical models were developed with different limitations. The goodness of fit is directly related to the number of the model parameters. However, estimating the parameters for higher-parameter models which have no mathematical or physical significance is a problem. Among the current models, 2-parameter Log-normal distribution model with mathematical significant parameters has been considered as a basis for many studies. In this study, it is indicated that the 2-parameter Log-normal distribution model can not be very accurate for representation of the PSD for all of soil textural classes. As an alternative, 2-parameter Gamma distribution model is proposed for more accurate representation of the PSD that its two parameters also are mathematical significant and readily computable. These two models have been compared in fitting the observed PSD data of 461 soil samples from UNSODA soil database. Gamma distribution model indicated a pronounced improvement in representation of the PSD. Based on Coefficient of determination (R2), in 362 samples and based on RMSE, in 323 samples, Gamma distribution model showed a better representation of the PSD than Log-normal. To evaluate the significance of the difference between two models, a t-test was performed. The results showed that, at confidence level of 1%, the R2-values of the Gamma model are significantly greater than those of Log-normal model. Also, at confidence level of 5%, a significant difference between the RMSE-values of two models was shown. Therefore, 2-parameter Gamma distribution model is judged to be better than 2-parameter Log-normal model for representation of PSD.

Key words: Particle-size distribution (PSD), Log-normal distribution, Gamma distribution, UNSODA