The relationship between surface fractal dimension and soil water content at permanent wilting point

Permanent wilting point (PWP) is an important soil water parameter available from the soil water retention curve. Soil water content held at 1500 kPa determines plant survival or death. Recently, the application of fractal geometry concepts has been widely used for modeling soil and its hydraulic properties (e.g. soil water retention curve and unsaturated hydraulic conductivity). The objective of this study was to investigate the relationship between surface fractal dimension (Ds) and soil water content held at permanent wilting point, θPWP For this purpose, we used five datasets corresponding to Puckett et al. [Puckett, W.E., Dane, J.H., Hajek, B.F., 1985. Physical and mineralogical data to determine soil hydraulic properties. Soil Sci. Soc. Am. J. 49, 831–836], UNSODA [Leij, F.J., Alves, W.J., van Genuchten, M.T.h., Williams, J.R., 1996. Unsaturated Soil Hydraulic Database, UNSODA 1.0 user's manual. Rep. EPA/600/R96/095. USEPA, Ada, OK], GRIZZLY [Haverkamp, R., Zammit, C., Boubkraoui, F., Rajkai, K., Arrúe, J. L., Keckmann, N., 1997. GRIZZLY, Grenoble soil catalogue: Soil survey of field data and description of particle-size, soil water retention and hydraulic conductivity functions. Laboratoire d'Etude des Transferts en Hydrologie et en Environnement. Grenoble, France], Huang et al. [Huang, G., Zhang, R., Huang, Q., 2006. Modeling soil water retention curve with a fractal method. Pedosphere 16, 137–146], and Fooladmand [Fooladmand, H.R., 2007. Measurement of soil specific surface area and its relation to some soil physico-chemical properties. Ph.D. Thesis. Department of Irrigation. Science and Research Unit of Islamis Azad University, Tehran]. This yielded a total of 172 soil samples. The results showed that Ds was positively related to both θPWP and clay content. The Ds versus θPWP and Ds versus clay content relationships were well fitted by logarithmic functions (goodness of fit R2 = 0.97 and R2 = 0.88, respectively). Soil quality index (S-index) and Ds were also significantly correlated (R = 0.911). The water film retained at 1500 kPa (PWP) delineates the complex geometrical structure of the pore–solid interface which could be determined by the relative amount and orientation of clay particles.