Monday, November 13, 2006

Assessing the Accuracy of Linearized Langmuir Equations.

Carl Bolster, USDA-ARS, 230 Bennett Ln, Bowling Green, KY 42104

One of the most commonly used models for describing phosphorus (P) sorption to soils is the Langmuir model. Because the Langmuir model is nonlinear it must be solved iteratively using an optimization program. Alternatively, a linearized version of the Langmuir model can be used so that model parameters can be obtained using linear regression; however, the transformation of data required for linearization can lead to misleading results. Although concerns have been raised in the past regarding the use of linearized equations, this practice is still commonly used today for describing P sorption to soils. The goal of this research was to investigate more fully the impact of linearization of the Langmuir equation on the accuracy of fitted parameter values and assessments of goodness of fit. Three different linearized versions of the Langmuir model were fit to sorption data collected on three western Kentucky soils and fitted parameters and goodness-of-fit measures were compared with results from the nonlinear equation. Both linear and nonlinear equations were also fit to two sets of synthetic sorption data. Results show that the use of the most commonly used Langmuir linearization can give erroneously high goodness-of-fit measures due to inherent self-correlation created during data transformation. Numerical simulations showed that the most accurate Langmuir equation will depend on the error structure of the measurements. Results of this study will allow researchers to make more informed decisions when applying the Langmuir model to their sorption data.