Investigating the Ability of Fractal Models to Estimate Retention Curve to Improve Water and Soil Resources Management

Document Type : Original Research Paper


1 Assistant Professor, Islamic Azad University, Science and Research Branch, Tehran, Iran.

2 Professor, Department of Irrigation and Drainage, Tarbiat Modares University, Tehran, Iran.

3 Professor, Department of Soil Science, Islamic Azad University, Science and Research Branch, Tehran, Iran.


Soil water retention curve is among the most important properties needed for many soil and water management purposes. Due to high spatial and temporal variability in soils, its direct measurement is rather difficult, time consuming and expensive. Consequently, it would be more feasible to estimate it by using some indirect mathematical methods. The objectives of this investigation are to (1) determine the fractal dimension of the soil retention curve by fitting fractal models to the measurements and (2) investigate the relationship between the fractal dimension and other physical/textural/hydraulic parameters such assoil particle fractions of clay, silt, and sand in large scale. For this purpose, 190 soil samples with broad range of textures from four large agricultural areas were collected, and their particle size distribution, bulk density, organic carbon, salinity, pH, and retention curves were measured. To evaluate the performance of examined fractal models, three statistical parameters including RMSE, RMSD and R2 were used. Results indicated that the fractal dimension has an inverse relationship with soil texture; the finer the soil texture, the greater the fractal dimension. The lowest and greatest fractal dimensions of the Tyler-Wheatcraft model in loamy sand and clay textures were obtained to be 2.38 and 2.74, respectively. These were significant at 1% level based on the Duncan’s multiple range tests. Results further showed that the most accuracy of estimating retention curve in different soil textures by using van Genuchten, Brooks-Corey, and Tyler-Wheatcraft with normalized errors average obtained were 0.06, 1.09, and 3.27, respectively. Furthermore, the obtained R2 values were ranged from 0.88 to 0.99 for Tyler-Wheatcraft and van Genuchten models, respectively. Compares to Brooks-Corey model, the van Genuchten retention model provided better accuracy in estimating retention curve for different soil textures.


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