Fractal description of the spatial and temporal variability of soil water content across an agricultural field

There is an increasing interest in quantifying the space-time variation of soil properties. This issue offers a unique set of problems that have been addressed using various methods. Here, the spatial and temporal scaling behavior of topsoil water content at the field scale was explored using the fractal approach. Results from fractal analysis were compared with those from other methods describing either spatial variability or temporal trends and stability of soil moisture. Time domain reflectometry probes were installed at the 0- to 20-cm depth in a clay loam soil under natural pasture in Ottawa, Ontario, Canada. Soil water content was measured 34 times at 164 points on a square grid with 10-m spacing. Mean soil water content and coefficients of variation showed significant negative linear relationship for both sampling dates (r = 0.783) and sampling points (r = 0.804). Both spatial and temporal data sets were characterized by a self-affine fractal Brownian motion model that requires two parameters, fractal dimension, D, and crossover length, l. For spatially sampled data sets at different times, D ranged from 2.589 to 2.910 and l ranged from 0.95 to 6.97 m. For temporal data sets measured on 10-m grid nodes, D was between 1.145 and 1.919 and l was from 0.069 to 9.40 days. Fractal analysis added information on the scale dependence of spatially and temporally sampled data sets, which is not taken into account by classical statistics. Also, interpretation of fractal parameters provided further insight when contrasted with temporal stability analysis. Fractal dimension and crossover length of temporal series showed spatial dependence, and ordinary kriging was used to map these two fractal parameters.