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United States Department of Agriculture

Agricultural Research Service

Title: Preliminary Fractal Analysis of Crop Yield and Experimental Design for Modeling Space-Time Variability under Dryland Agriculture

Authors
item Green, Timothy
item Nachabe, M - UNIV OF SOUTH FLORIDA
item Ahuja, Lajpat
item Murphy, Michael
item Shaffer, Marvin

Submitted to: Annual Hydrology Days Conference Proceedings
Publication Type: Proceedings
Publication Acceptance Date: March 1, 1999
Publication Date: N/A

Interpretive Summary: Landscape variability associated with topographic relief affects the variability of crop yields in space and time. Furthermore, soil physical properties, fertility and moisture status are all associated with landscape topography and are known to affect yield patterns. Yet, landscape processes and their interactions are not well quantified over a range of scales. The efarm or field management unit is an intermediate scale to which we may extend our knowledge gained from plot and watershed studies. In this paper, we present fractal analyses of crop yield for one year of winter wheat in northeastern Colorado. Crop yield over a quarter section varied substantially with a variance of 320 bu2/ac2. The self-affine ("simple scaling") fractal described the spatial variability fairly well with a fractal dimension of 1.79 (two other fields had dimensions of 1.80 and 1.82). This indicates that new sources of variability contribute to the variation in yield at different, nested scales. Knowledge of this fractal geometry makes it possible to scale the yield variation within the range of analysis. Further analysis of variance indicated that surveyed soil series did not explain more than 15% of the total variance in yield, while the specific contributing area explained 60% of the yield variation. Ongoing collection of soil-water data on the same field is designed to further our understanding of water movement and to gain a quantitative, process-based understanding of space-time variabilities. There remains a need for improved linkages between plot, landscape, and watershed fluxes of water and materials affecting microenvironments and crop yields. This should lead to a stronger scientific basis for transferring information between sites and across scales.

Technical Abstract: Landscape variability associated with topographic relief affects the variability of crop yields in space and time. Furthermore, soil physical properties, fertility and moisture status are all associated with landscape topography and are known to affect yield patterns. Yet, landscape processes and their interactions are not well quantified over a range of scales. The efarm or field management unit is an intermediate scale to which we may extend our knowledge gained from plot and watershed studies. In this paper, we present fractal analyses of crop yield for one year of winter wheat in northeastern Colorado. Crop yield over a quarter section varied substantially with a variance of 320 bu2/ac2. The self-affine ("simple scaling") fractal described the spatial variability fairly well with a fractal dimension of 1.79 (two other fields had dimensions of 1.80 and 1.82). This indicates that new sources of variability contribute to the variation in yield at different, nested scales. Knowledge of this fractal geometry makes it possible to scale the yield variation within the range of analysis. Further analysis of variance indicated that surveyed soil series did not explain more than 15% of the total variance in yield, while the specific contributing area explained 60% of the yield variation. Ongoing collection of soil-water data on the same field is designed to further our understanding of water movement and to gain a quantitative, process-based understanding of space-time variabilities. There remains a need for improved linkages between plot, landscape, and watershed fluxes of water and materials affecting microenvironments and crop yields. This should lead to a stronger scientific basis for transferring information between sites and across scales.

Last Modified: 7/22/2014