Investigation of changes in fractal dimension and accuracy of fractal models of soil particle size distribution in the Imamzadeh Ebrahim sub-watershed, Guilan

Soil particle size distribution (PSD) is one of the most important soil characteristics. Various fractal equations have been proposed for better description of this characteristic in recent decades. This study aimed to investigate the changes in fractal dimensions of PSD calculated with different equations in the Imamzadeh Ebrahim sub-watershed, Guilan province. To conduct this research, 93 soil samples were collected from different parts of the sub-watershed with different land use, soil erosion and vegetation covers. The PSD of the samples was measured. Three fractal models of Bird, Perrier-Bird, and Tyler-Wheatcraft were fitted to the data. The results showed that the Perrier-Bird and Bird models had less root mean square error (RMSE) than the Tyler-Wheatcraft model (RMSE was 8.3 for the Perrier-Bird and Bird models, while it was 29.3 for the Tyler-Wheatcraft model). The value of fractal dimension obtained from Bird model (2.73) was lower than the other two models (the fractal dimensions were 2.94 and 2.95 for Perrier-Bird and Tyler-Wheatcraft, respectively). The results of this study demonstrated that the fractal models showed different accuracy and precision under various lands. According to result, fractal dimension of all three models had a positive nonlinear relationship with clay while showing a negative linear relationship with sand. In general, it can be concluded that PSD and therefore the fractal dimension of PSD are function of soil type, vegetation cover and land use, and two-parameter models are more accurate to describe soil PSD due to their higher flexibility.