Fractal Analyses of Steady Infiltration and Terrain on an Undulating Agricultural Field

Abstract

Analysis of spatially distributed quasi‐steady infiltration measurements is important because of the effects of infiltration capacity on spatial patterns of soil water, nutrients, and plant development and production. We explored fractal models of quasi‐steady infiltration rates, emphasizing apparent changes in scaling exponents with domain size. Quasi‐steady infiltration rates were measured using single‐ring (0.30‐m‐diameter) constant‐head infiltrometers at 150 locations over 10 landscape positions (30 by 30 m, or approximately 0.1 ha) across a field (approximately 100 ha). At each landscape position, 15 rings were distributed randomly in nested patterns. The field in northeastern Colorado comprises undulating agricultural terrain cropped with dryland winter wheat (Triticum aestivum L.) under conventional tillage. Data were analyzed for multifractal and monofractal behavior. A monofractal model fit the infiltration data best, while terrain attributes other than elevation deviated from monofractals to different degrees. The Hurst exponent (H) was estimated by fitting power‐law variograms at different scales across the field. Values of H changed with the maximum lag distance, peaking near H = 0.9 at approximately 200 m, which represents a typical hillslope length. Spatial persistence in steady infiltration was not observed at long distances (>300 m). Using dense and sparsely sampled terrain attributes as proxy data indicated that the observed spatial scaling of infiltration was not solely due to the clustering of infiltration measurements. These results shed new light on research needed to address spatial variability of soil hydraulic properties, with implications for hillslope process interactions between land areas when modeling distributed infiltration, runoff and run‐on, and plant water use.