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Estimating Mass Fractal Dimension of Soil Using Artificial Neural Networks for Improved Prediction of Water Retention Curve

Ghanbarian-Alavijeh, Behzad1; Taghizadeh-Mehrjardi, Ruhollah2; Huang, Guanhua3

doi: 10.1097/SS.0b013e318266e99f
Technical Article

Abstract: Fractal geometry appears to be a useful tool to simulate a porous medium that can be quantified by scaling exponent(s), which is a fractal dimension(s). The objective of this study was to estimate the mass fractal dimension of the Rieu and Sposito (RS) model from readily available parameters, such as clay, silt, and sand contents; geometric mean diameter and geometric S.D. of soil particles; and total soil porosity by developing an artificial neural network (ANN) model. Two databases with a total of 190 soil samples of 12 soil texture classes were used to develop and validate the ANN model. To determine the mass fractal dimension, the RS model was fitted to measured soil-water retention data. A sensitivity analysis was also performed on the RS model parameters. The results of sensitivity analysis showed that the most sensitive parameter of the RS model is the mass fractal dimension, whereas this model is less sensitive to air entry value and soil porosity. We used the cross-validation technique, for example, repeated random splitting of the data set into subsets for the development and validation processes of the ANN model. To evaluate the developed ANN model, the estimated mass fractal dimension, measured soil porosity, and air entry value combined with the RS model were consequently used to determine soil-water content corresponding to each prescribed tension head. Results showed that the developed ANN model estimated the soil-water retention curve accurately.

1Department of Earth and Environmental Sciences, Wright State University, Dayton OH.

2Department of Soil Science Engineering, University of Tehran, Karaj, Iran.

3Department of Irrigation and Drainage, China Agricultural University, Beijing, China.

Address for correspondence: Behzad Ghanbarian-Alavijeh, Department of Earth and Environmental Sciences, Wright State University, 3540 Colonel Glenn Hwy., Dayton, OH 45435; E-mail:

Financial Disclosures/Conflicts of Interest: None reported.

Received February 10, 2012.

Accepted for publication June 25, 2012.

© 2012 Lippincott Williams & Wilkins, Inc.