Joint multifractal analysis of crop yield and terrain slope

Quantifying the spatial variability of crop yields and yield-affecting factors are important issues in precision agriculture. Topography is frequently one of the most important factors affecting yields, and topographical data are much easier to obtain than time and labor-consuming measurements of soil properties. In this study, yield variability and the relationships between yields and terrain slopes were analyzed using theories of multifractal and joint multifractal measures. Corn (Zea mays L.) and soybean [Glycine max (L.) Merr.] yield data from 1994 to 1998 were collected via yield monitors from a central 6.6 ha section of an agricultural field in eastern Indiana. Slopes were derived from a field terrain map using a GIS. Multifractal analysis of yield and slope maps revealed that both yield and slope distributions were multifractal measures. Hence, joint multifractal analysis was applied to evaluate the effect of slope on crop-yield spatial variability. Joint multifractal analysis facilitated (i) the ability to differentiate between yield distributions corresponding to field locations with high and low slopes, and (ii) the ability to make inferences about slope distributions that affect grain yield the most. Multifractal analysis revealed that during four growing seasons with moderate and dry weather conditions, larger yields were observed at low slope locations while a wide range of yield values was observed at sites with moderate and high slopes. During the wet growing season, lower yields prevailed at locations with low slopes. Joint multifractal theory was useful for the study of yield/topography relationships and was an applicable tool for the analysis of spatially distributed data.