A Statistical Case Against the Use of the Langmuir Model for Describing P Sorption Data.

Sorption of P to soils is often investigated through batch experiments where sorption models are fit to the resultant sorption curve by least-squares regression. One of the most commonly used sorption models is the Langmuir model, a model which was originally developed for the study of gas sorption to surfaces. While theoretical arguments have been made against the use of this model for describing solute sorption data, the Langmuir model is still commonly used for describing P sorption to soils; in part because several linearized versions of the Langmuir model exist and thus sorption parameters can be easily obtained through linear regression. Furthermore, fitting the Langmuir model provides an estimate of the maximum sorption capacity of the soil, a parameter which has utility in P management planning. However, physically representative sorption parameter estimates will be obtained only when a suitable model is fit to the data. Here, we specifically address whether the Langmuir model is adequate for describing P sorption data by using weighted least-squares regression with weights obtained by variance function analysis of replicate data. Proper weighting in this case requires attention to a special problem - that the dependent variable is not measured but rather is calculated from the measured equilibrium concentration, commonly taken as the independent variable but subject to experimental error, violating a fundamental least-squares assumption. P sorption data collected on a variety of soils were fit with the Langmuir, Freundlich, and Temkin isotherms, with only the Freundlich model yielding statistically adequate chi-square values. Our results provide convincing statistical evidence that the Langmuir model is not the most appropriate model for describing P sorption to soils.