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United States Department of Agriculture

Agricultural Research Service

Title: Fractal-Based, Scale-Dependent Models for Characterizing Peak Concentrations of Crop Protection Chemicals in Surface Waters

Authors
item Gustafson, D - MONSANTO
item Carr, K - MONSANTO
item Gustin, C - MONSANTO
item GREEN, TIMOTHY
item Jones, R - AVENTIS
item Richards, R - HEIDELBERG COLLEGE

Submitted to: Internationl Congress on Chemistry of Crop Production
Publication Type: Abstract Only
Publication Acceptance Date: May 7, 2002
Publication Date: July 1, 2002
Citation: Gustafson, D.I., Carr, K.H., Gustin, C., Green, T.R., Jones, R.L., Richards, R.P. 2002. Fractal-based, scale-dependent models for characterizing peak concentrations of crop protection chemicals in surface waters. Internationl Congress on Chemistry of Crop Production. July 1,2002.

Interpretive Summary: There is a clear regulatory need for a new approach to characterize peak pesticide concentrations in surface waters at a wide range of length scales. Current assessment methods in the United States rely upon highly idealized "reasonable worst case" scenarios such as the so-called "standard farm pond" (for ecological assessments) or the "index reservoir" (for drinking water assessments), both of which ignore all potential scaling effects, such as spatial variability in rainfall, spatial variation in land use patterns, varying physical properties of the watershed, and many of the fate processes that attenuate chemical residues as they are transported from treated field boundaries to the receiving water body. No generally accepted approach is currently available for "scaling up" such assessments to larger watersheds, which constitute the vast majority of actual exposures. The relatively recent mathematical discoveries of fractal geometry offer a possible answer to this regulatory need. Numerous researchers have made the fundamental observation that rivers can be considered as "space filling curves" as described by Mandelbrot and others. In addition, spatial rainfall patterns are themselves fractals of a different kind. The resultant interaction of spatially variable rainfall patterns onto fractal river basins produces scale-dependent phenomena that should be governed by the same type of power-law relationships shown to describe other natural processes. This paper seeks to explore the validity and utility of such an approach for describing peak concentrations of crop protection chemicals at a range of length scales from individual fields to continental sized watersheds. Datasets from the United States Geological Survey, the Acetochlor Registration Partnership, and the Heidelberg Water Quality Laboratory are used to demonstrate that log-log plots of peak concentrations as a function of watershed size are linear with a negative slope. The slope is compound-dependent, with more mobile and persistent pesticides having shallower slopes. The implications for regulatory modeling assessments are discussed.

Technical Abstract: There is a clear regulatory need for a new approach to characterize peak pesticide concentrations in surface waters at a wide range of length scales. Current assessment methods in the United States rely upon highly idealized "reasonable worst case" scenarios such as the so-called "standard farm pond" (for ecological assessments) or the "index reservoir" (for drinking water assessments), both of which ignore all potential scaling effects, such as spatial variability in rainfall, spatial variation in land use patterns, varying physical properties of the watershed, and many of the fate processes that attenuate chemical residues as they are transported from treated field boundaries to the receiving water body. No generally accepted approach is currently available for "scaling up" such assessments to larger watersheds, which constitute the vast majority of actual exposures. The relatively recent mathematical discoveries of fractal geometry offer a possible answer to this regulatory need. Numerous researchers have made the fundamental observation that rivers can be considered as "space filling curves" as described by Mandelbrot and others. In addition, spatial rainfall patterns are themselves fractals of a different kind. The resultant interaction of spatially variable rainfall patterns onto fractal river basins produces scale-dependent phenomena that should be governed by the same type of power-law relationships shown to describe other natural processes. This paper seeks to explore the validity and utility of such an approach for describing peak concentrations of crop protection chemicals at a range of length scales from individual fields to continental sized watersheds. Datasets from the United States Geological Survey, the Acetochlor Registration Partnership, and the Heidelberg Water Quality Laboratory are used to demonstrate that log-log plots of peak concentrations as a function of watershed size are linear with a negative slope. The slope is compound-dependent, with more mobile and persistent pesticides having shallower slopes. The implications for regulatory modeling assessments are discussed.

Last Modified: 7/28/2014
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