Scaling properties of topographic indices and crop yield: Multifractal and joint multifractal approaches

Abstract

Topography controls soil water distribution in semiarid environments where water is the major growth-limiting factor. Identification of the topographic index that best represents the spatial variability and scaling properties of crop yield is important for precision farming. Our objective was to characterize the scaling properties of four topographic indices [relative elevation (RE), wetness index (WI), upslope length (USL), and curvature (CR)] and their relationships to wheat (Triticum aestivum L.) grain yield and biomass using multifractal and joint multifractal approaches. Wheat grain yield and terrain data were collected at 6-m intervals along a 576-m-long transect on a nonlevel landscape with dominant soil type of Aridic Ustoll, under the semiarid environment of Saskatchewan, Canada. Results indicated that CR and RE had a fractal type of scaling only for a narrow range of moment orders. Wetness index showed a monofractal scaling with fractal dimension of 0.98; whereas yield, biomass, and USL showed a multifractal scaling. Joint multifractal analyses showed a high correlation coefficient between the scaling indices of grain yield and USL (r = 0.93). Wetness index appeared to be effective as a yield covariate only at low slope areas and depressions where it has similar scaling to that of USL. Results from this study suggested that USL was the hest indicator of grain yield and biomass at any scale. The implication for precision farming is that USL can be used as a guideline for varying production inputs such as fertilizer as well as for yield prediction.