Fractal Models of Soil Water Retention: How Good are They?.
Daniel Gimenez1, Roberto R. Filgueira2, Sung Won Yoon1, and Hyen Chung Chun1. (1) Rutgers University, Department of Environmental Sciences, 14 College Farm Rd., New Brunswick, NJ 08901-8551, (2) Facultad de Ciencias Agrarias y Forestales-Universidad Nacional de La Plata, Calles 60 y 119, La Plata, Argentina
Fractal models of soil structure have been used to derive models of soil hydraulic properties, which can potentially explain links among soil morphology and soil function. An alternative to these models is to fit widely tested functions to data and optimize their parameters. The disadvantage of the latter approach is that it does not contribute to our understanding of the soil system. Fractal models of soil water retention were proposed more than fifteen years ago and tested by fitting models to data and verifying that the value of the fitting parameter (i.e., a fractal dimension) was within theoretical bounds. Although important as a first step, this approach is not sufficient to fully test the theory. The various proposed fractal models of water retention assume fractal properties of pore-, and/or particle-size distribution, and mass distribution within soil aggregates. The objectives of this work were to: 1) measure water retention properties, particle size distribution, and pore structure from two dimensional images, 2) test models of soil structure by comparing fractal dimensions of soil structure (as measured under objective 1) with equivalent fractal dimensions obtained by fitting the models to measured water retention. We sampled aggregates from the A horizon of three soils, each under two contrasting management situations (wooded and cultivated). Water retained by soil aggregates when equilibrated at pressure potentials of -0.1, -0.3, -1, -3, -10, -30, -100, -300, and -1000 kPa were measured on ten replicates, i.e., water retentions were constructed from a minimum of 90 independent measurements. About 70 aggregates covering a range from 0.05 to 6 cm3 were used to define a mass-volume relationship. Volume was measured on individual air-dry aggregates using a volume displacement technique in two non-mixing liquids. Particle size distribution was measured with the pipette method and by X-ray diffraction. Six impregnated aggregates in each of three aggregate size classes (with approximate volumes of 0.05, 2, and 6 cm3) were used to generate binary images of pore structure. There was limited agreement between the fractal dimensions of mass obtained directly from the mass-diameter relationships and those obtained from the water retention curves with three related fractal models, and between fractal dimensions from pore- (water retention data) and particle-size distributions. Our results suggest that a single fractal dimension may not be enough to capture the complexity of soil structure. This is particularly true in agricultural soils. New approaches to modeling soil structure and related hydraulic properties will be discussed, with an emphasis on simplicity and applicability.