AN IMPROVED FRACTAL EQUATION FOR THE SOIL-WATER RETENTION CURVE

The water retention curve, theta(psi), is important for predicting soi l physical properties and processes. Until recently, equations for the theta(psi) were empirical. Advances in fractal geometry have led to t he derivation of physical models for the theta(psi). However, both exi sting fractal equations have only two parameters and thus are relative ly inflexible. We derived a new three-parameter fractal model for the theta(psi). This equation was fitted to 36 theta(psi)'s fora silt loam soil with a wide range of structural conditions. The new equation fit ted these data much better than the existing equations, The parameters of the new equation, psi(a), psi(d), and D, are physical entities, co rresponding to the air-entry value, tension draining the smallest pore s, and fractal dimension, respectively. Estimates of the psi(a), psi(d ), and D were physically reasonable, with median values of 2.9 x 10(-1 ) kPa, 1.6 x 10(4) kPa, and 2.87, respectively. In contrast, the exist ing equations yielded anomalous estimates of either psi(a) or D. The n ew equation was able to fit theta(psi) for a variety of porous media, including sandstone, glass beads, sands, sieved soil, and undisturbed soils ranging from very fine sandy loam to heavy clay. The psi(a) and psi(d) were more sensitive to structural and textural variation than D . The new equation represents an improvement over existing models in t erms of both goodness of fit and the physical significance of its para meters.