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United States Department of Agriculture

Agricultural Research Service

Research Project: Efficient Management and Use of Animal Manure to Protect Human Health and Environmental Quality

Location: Food Animal Environmental Systems Research

Title: A statistical case against the use of the Langmuir model for describing P sorption data

item Bolster, Carl
item Tellinghuisen, Joel

Submitted to: ASA-CSSA-SSSA Annual Meeting Abstracts
Publication Type: Abstract Only
Publication Acceptance Date: 4/19/2012
Publication Date: 10/24/2012
Citation: Bolster, C.H., Tellinghuisen, J. 2012. A statistical case against the use of the Langmuir model for describing P sorption data. ASA-CSSA-SSSA Annual Meeting Abstracts. Abstract.

Interpretive Summary:

Technical Abstract: 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 data. 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 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 fitted 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.

Last Modified: 06/22/2017
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