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United States Department of Agriculture

Agricultural Research Service

Research Project: WATER QUALITY IMPROVEMENT FROM MANAGEMENT PRACTICES IN AGRICULTURAL WATERSHEDS Title: Rational polynomial functions for modeling E. coli and bromide breakthrough

Authors
item Meek, David -
item Hoang, Chi -
item Malone, Robert
item Kanwar, Ramesh -
item Fox, Garey -
item Guzman, Jorge -
item Shipitalo, Martin

Submitted to: Transactions of the ASABE
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 18, 2012
Publication Date: September 1, 2012
Citation: Meek, D.W., Hoang, C., Malone, R.W., Kanwar, R., Fox, G., Guzman, J., Shipitalo, M.J. 2012. Rational polynomial functions for modeling E. coli and bromide breakthrough. Transactions of the ASABE. 55:1821-1826.

Interpretive Summary: Analysis of bacteria concentrations and transport to tile drainage systems through cracks and worm holes (preferential flow) following irrigation or rainfall events are important when assessing the risk of contamination. Complex, process-based, models of microbial organism transport through preferential flow have been developed. Less complex (empirical) models have been used to study chemical transport (e.g., nitrate) under agricultural systems and can have advantages to process-based modeling such as fewer or easier to determine input parameters and easier determination of model uncertainty such as confidence intervals associated with the peak concentration and its time of occurrance. However, use of empirical models to investigate microbial transport such as E. coli is rare in the literature. Also, the selection of empirical models for chemical transport from field or laboratory data is generally an arbitrary choice and often considers only conventional choices such as lognormal distributions. Here we evaluate four rational polynomial functions (a ratio of two polynomials) for modeling bromide and E. coli data from a single event from a tile drained field located near Nashua, IA. A simple rational polynomial accounts for 92% of the variation in E. coli concentration over time. A related equation known as the Gunary Model accounts for 93% of the bromide concentration over time. In comparison, the more commonly assumed lognormal distribution accounts for 78% and 68% of the variation in E. coli and bromide concentrations over time. In both the E. coli and bromide sets, the chosen models clearly tracked the data better than the lognormal distribution. This research will help agricultural and environmental scientists more easily analyze microbial transport through soil, which will facilitate the design of more effective systems that protect the environment.

Technical Abstract: Fecal bacteria peak concentrations and breakthrough times through preferential flow to tile drainage systems following irrigation or rainfall events are important when assessing the risk of contamination. Process-based, convective-dispersive modeling of microbial organism transport through preferential flow has been conducted. Empirical modeling has been used to study solute transport (e.g., nitrate) under agricultural systems and can have advantages to process-based modeling such as fewer or easier to determine parameters and easier determination of confidence intervals. However, use of empirical models to investigate microbial transport such as E. coli is rare in the literature. Also, the selection of time response curves to empirically model simple, right skewed, single breakthrough events from field or laboratory data is generally an arbitrary choice and often considers only conventional distribution-shaped response curves such as lognormal distributions. Here we evaluate four rational polynomial functions for modeling bromide and E. coli data from a single breakthrough event from a tile drained field located near Nashua, IA. Bromide and liquid swine manure was applied to a subsurface drained plot. Artificial rainfall was then applied and subsurface drainage water samples were collected for E. coli quantification and bromide concentrations over a 24-hr sampling period. Nonlinear iteratively re-weighted least squares regression procedures were used to model the breakthrough data. The maximum event value, its time of occurrence, and the event total were estimated from the parameters for each model. Selection of the best model is based on multiple performance criteria. A simple rational polynomial with a linear factor in the numerator and quadratic in the denominator was the overall best choice to model the E. coli data (R²=0.92). A related fractional order form of it also known as the Gunary Model was the best choice for the bromide data (R²=0.93). In comparison, the more commonly assumed lognormal distribution described 78% of the variation in E. coli data and 68% of the variation in bromide data with an error mean square 3.0 to 4.6 times larger than each selected rational polynomial model. In both the E. coli and bromide sets, the chosen models clearly tracked the data better than the lognormal distribution.

Last Modified: 4/23/2014
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