Submitted to: Journal of Environmental Quality
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: March 10, 2008
Publication Date: September 1, 2008
Repository URL: http://hdl.handle.net/10113/19093
Citation: Bolster, C.H. 2008. Revisiting a Statistical Shortcoming When Fitting the Langmuir Model to Sorption Data. Journal of Environmental Quality. Vol. 37 p. 1986-1992 Interpretive Summary: Soil sorption parameters are often obtained by fitting the Langmuir model to sorption isotherm data using nonlinear regression. This approach, however, violates several assumptions inherent within nonlinear regression. In this study I look at these assumptions and offer an alternative approach for solving the Langmuir equation which does not suffer from these statistical limitations. The new approach was tested on phosphorus sorption data and was found to provide better model fits and generally more precise parameter estimates than the original Langmuir model.
Technical Abstract: The Langmuir model is commonly used for describing sorption behavior of reactive solutes to surfaces. Fitting the Langmuir model to sorption data requires either the use of nonlinear regression or, alternatively, linear regression using one of the linearized versions of the model. Statistical limitations to using linear regression for fitting the Langmuir model to sorption data are well documented; however, what is not as well known is that statistical problems also exist when using nonlinear regression for fitting the Langmuir model. In this short communication I briefly discuss the statistical limitations inherent in using nonlinear regression for fitting the Langmuir model to sorption data and test a modified Langmuir equation which does not suffer from these same statistical limitations. Phosphorus sorption data were fit with both the traditional and modified version of the Langmuir equation and model fits and parameter uncertainties between the two models were compared. For the soils tested in this study the modified Langmuir equation provided better overall fits and generally more precise parameter estimates than the original Langmuir equation indicating that this approach is a more statistically valid way of obtaining sorption parameters with the Langmuir model.