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

Authors: Green, Timothy; Dunn, Gale; Erskine, Robert - Rob; SALAS, J. - COLORADO STATE UNIVERSITY; Ahuja, Lajpat

Submitted to: Vadose Zone Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/16/2008
Publication Date: 5/1/2009
Citation: Green, T.R., Dunn, G.H., Erskine, R.H., Salas, J.D., Ahuja, L.R. 2009. Fractal Analyses of Steady Infiltration and Terrain on an Undulating Agricultural Field. Vadose Zone Journal. 8(2)310-320.

Interpretive Summary: Fractal scaling behaviors have been observed across a range of scales in systems, where interacting factors cause nested spatial structures. Here, we focused on agricultural landscape positions to field scales, where surface water infiltration affects spatial patterns of soil water, nutrients, and plant development and crop yield. The field site in northeastern Colorado, USA comprises undulating agricultural terrain cropped with dryland winter wheat under conventional tillage. Field experiments included 150 steady infiltration measurements taken at ten landscape positions. At each landscape position, steady infiltration was measured at 15 locations distributed randomly within an area of 30-m by 30-m. Data were analyzed for simple scaling behavior by fitting power-law variograms and estimating a Hurst exponent (H) at each landscape position and at different scales across the field. Steady infiltration displayed some behaviors similar to terrain attributes using dense and sparsely sampled data, indicating that the observed spatial scaling of infiltration was not solely due to the clustering of measurements at discrete landscape positions. These results are intended to shed new light on research needed to address spatial variability of soil hydraulic properties and interactions between land areas when modeling infiltration, runoff, and plant water use under different climates and land management strategies.

Technical Abstract: Fractal scaling behaviors have been observed in systems where interacting factors cause nested spatial structures. Surface water infiltration affects spatial patterns of soil water, nutrients, and plant development and crop yield. Here, we explored simple fractal scaling of quasi-steady infiltration rates, emphasizing apparent changes in scaling behavior with domain size. Single-ring (0.30-m diameter) infiltration measurements (150 total) were taken at ten landscape positions (30-m by 30-m or approximately 0.1 ha) across a field (approximately 100 ha). The field site in northeastern Colorado, USA comprises undulating agricultural terrain cropped with dryland winter wheat under conventional tillage. At each landscape position, infiltration was measured in fifteen rings distributed randomly in nested patterns. Data were analyzed for simple scaling behavior by fitting power-law variograms and estimating a Hurst exponent (H) at each landscape position and over different scales across the field. Values of H changed with the maximum lag distance (hmax), peaking near H = 0.8 at approximately 200 m, which represents a typical hillslope length. Spatial persistence was not observed at long length scales, as H approached 0.14 for hmax > 600 m. Infiltration scaling displayed behaviors similar to terrain attributes using dense and sparsely sampled data, indicating that the observed spatial scaling of infiltration was not solely due to the clustering of measurements. These results shed new light on research needed to address spatial variability of soil hydraulic properties and interactions between land areas when modeling infiltration, runoff, and plant water use under different climates and land management strategies.