Modelling soil water retention scaling. Comparison of a classical fractal model with a piecewise approach

Soil water retention curves are very important for modeling and predicting geohydrological processes. Fractal-based models seem to be appropriate theoretical frameworks for investigating this soil characteristics. Since soil water retention is sensitive to both structure and soil texture, it is difficult to see a unique value of fractal dimension as a physical descriptor of both soil conditions. The objectives of this work were to (i) present a piecewise fractal approach to approximate the soil water retention data, (ii) test the model with previously published and unpublished data sets, and (iii) compare its performance with a traditional surface fractal model. The goodness-of-fit of the piecewise model was excellent (R2>0.95). Almost all the soil water retention data (21 data sets in total) showed two fractal scaling regimes. The cutoff ranged from a minimum hc=10.889 kPa (Ariana silty clay loam soil) to a maximum hc=2951 kPa (Walla-Walla silt loam soil). The fractal dimension corresponding to the first domain ranged from D1p=2.59 to D1p=2.85, while those values corresponding to the second regime varied between D2p=2.72 and D2p=2.95. The fit of a classical surface fractal model rendered poor results in terms of goodness-of-fit parameters with a large dispersion of predicted water content values at low tensions. The presented piecewise approach could be consistent to some extent with the bimodal pore-size distributions usually observed in experimental studies.