On the Use of Linearized Langmuir Equations

TLDR: In this paper, the authors examined the limitations of using linearized Langmuir equations by fitting P sorption data collected on eight different soils with four linearized versions of the LLE and compared goodness-of-fit measures and fitted parameter values with those obtained with the nonlinear LLE.

Abstract: One of the most commonly used models for describing solute sorption to soils is the Langmuir model. Because the Langmuir model is nonlinear, fitting the model to sorption data requires that the model be solved iteratively using an optimization program. To avoid the use of optimization programs, a linearized version of the Langmuir model is often used so that model parameters can be obtained by linear regression. Although the linear and nonlinear Langmuir equations are mathematically equivalent, there are several limitations to using linearized Langmuir equations. We examined the limitations of using linearized Langmuir equations by fitting P sorption data collected on eight different soils with four linearized versions of the Langmuir equation and comparing goodness-of-fit measures and fitted parameter values with those obtained with the nonlinear Langmuir equation. We then fit the sorption data with two modified versions of the Langmuir model and assessed whether the fits were statistically superior to the original Langmuir equation. Our results demonstrate that the use of linearized Langmuir equations needlessly limits the ability to model sorption data with good accuracy. To encourage the testing of additional nonlinear sorption models, we have made available an easily used Microsoft Excel spreadsheet (ars.usda.gov/msa/awmru/ bolster/Sorption_spreadsheets) capable of generating best-fit parameters and their standard errors and confidence intervals, correlations between fitted parameters, and goodness-of-fit measures. The results of our study should promote more critical evaluation of model fits to sorption data and encourage the testing of more sophisticated sorption models.