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United States Department of Agriculture

Agricultural Research Service

Title: FRACTAL-BASED SCALING AND SCALE-INVARIANT DISPERSION OF PEAK CONCENTRATIONS OF CROP PROTECTION CHEMICALS IN RIVERS

Authors
item Gustafson, David - MONSANTO COMPANY
item Carr, Katherine - MONSANTO COMPANY
item Green, Timothy
item Gustin, Christophe - MONSANTO COMPANY
item Jones, Russell - BAYER CROP SCIENCE
item Richards, R. - HEIDELBERG COLLEGE

Submitted to: Environmental Science and Technology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: January 15, 2004
Publication Date: June 1, 2004
Citation: Gustafson, D.I., Carr, K.H., Green, T.R., Gustin, C., Jones, R.L., Richards, R.P. 2004. Fractal-based scaling and scale-invariant dispersion of peak concentrations of crop protection chemicals in rivers. Environmental Science and Technology. Vol. 38, No. 11, June 2004. pages 2995-3003.

Interpretive Summary: A new regulatory approach is needed to characterize peak pesticide concentrations in surface waters over a range of watershed scales. Methods now in use rely upon idealized edge-of-field scenarios that ignore scaling effects. Although some watershed-scale models have been developed, none is used for regulatory modeling at the watershed scale, where nearly all exposure to both humans and aquatic organisms actually occurs. The theory of fractal geometry offers a method for addressing this regulatory need. One fractal characteristic is a simple power-law relationship in which log-log plots of maximum daily concentrations as a function of watershed area tend to be linear with a negative slope. We demonstrate that the extrapolation of such plots down to smaller watersheds agrees with edge-of-field concentrations predicted using the Pesticide Root Zone Model (PRZM), but only when the modeling results are properly adjusted for use intensity within the watershed. We also define a second useful property, 'scale-invariant dispersion,' in which concentrations are well described by a single equation, regardless of scale. Both of these findings make it possible to incorporate the effect of watershed scale directly into regulatory assessments.

Technical Abstract: A new regulatory approach is needed to characterize peak pesticide concentrations in surface waters over a range of watershed scales. Methods now in use rely upon idealized edge-of-field scenarios that ignore scaling effects. Although some watershed-scale models have been developed, none is used for regulatory modeling at the watershed scale, where nearly all exposure to both humans and aquatic organisms actually occurs. The theory of fractal geometry offers a method for addressing this regulatory need. Mandelbrot described rivers as 'space-filling curves,' a class of fractal objects implying two useful properties we exploit in this work. The first is a simple power-law relationship in which log-log plots of maximum daily concentrations as a function of watershed area tend to be linear with a negative slope. We demonstrate that the extrapolation of such plots down to smaller watersheds agrees with edge-of-field concentrations predicted using the Pesticide Root Zone Model (PRZM), but only when the modeling results are properly adjusted for use intensity within the watershed. We also define a second useful property, 'scale-invariant dispersion,' in which concentrations are well described by a single analytical solution to the convective-dispersion equation, regardless of scale. Both of these findings make it possible to incorporate the effect of watershed scale directly into regulatory assessments.

Last Modified: 7/25/2014
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