Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters

We combined water activity meters and fractal modeling to facilitate rapid, physically based characterization of the soil water retention curve. Desorption data (6 points per sample) were collected in the tension (h) range 2.0 × 10² to 1.5 × 10⁵ kPa using the gravimetric method to measure water content (w) and water activity meters to measure h. Thirty-two disturbed samples from a long-term nitrogen fertilization and tillage comparison study on a silt loam soil were analyzed. A new form of an established fractal equation was derived: w = ah^D-3 - ρ_w/ρ _s, where a is a compound parameter including the bulk density (ρ_b) and air entry tension (h_a), D is the mass fractal dimension, ρ_w is the density of water, and ρ_s is the particle density. This model was fitted to the measured water retention curves by nonlinear regression analysis. The a and D parameters were estimated, while ρ_w and ρ_s were fixed at 1.00 and 2.65 Mg m^-3, respectively. Convergence was always achieved and the equation fitted the data extremely well; residual sums of squares ranged from 1.2 × 10^-6 to 6.7 × 10^-5, with a median value of 2.2 × 10^-5. Estimates of a (0.62-0.74) and D (2.948-2.963) were physically reasonable, and sensitive to soil management practices. The a parameter increased, r = 0.80 (P < 0.01), (signifying decreasing ρ_b and/or h_a) whereas D decreased, r = -0.75 (P < 0.01), (signifying more rapid capillary drainage) with increasing soil carbon content. Additional research is needed to test this approach on other soil types, and to assess the influence of soil disturbance and variations in ρ₅ on the model's performance.