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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 Unit

Title: Limitations to Using Linearized Langmuir Equations

Author
item Bolster, Carl

Submitted to: SERA-IEG 17 Bulletin
Publication Type: Abstract Only
Publication Acceptance Date: June 12, 2007
Publication Date: June 13, 2007
Repository URL: http:////ars.usda.gov/msa/awmru/bolster/Sorptionspreadsheets
Citation: Bolster, C.H. Limitations to Using Linearized Langmuir Equations. SERA-IEG 17 Bulletin.

Technical 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. First, the transformation of data required for linearization can lead to statistical differences between the linear and nonlinear equations. Second, the ease of using linearized Langmuir equations may discourage critical evaluation of model fits. And finally, relying solely on linearized equations for describing sorption data prevents the testing of more sophisticated models which cannot be linearized. We examined the limitations of using linearized Langmuir equations by fitting phosphorus (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. Although the nonlinear Langmuir equation did provide slightly different parameter estimates than did the four linearized versions of the Langmuir equation, these differences were minor when compared to the improvement in fit obtained with the modified Langmuir equations. 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 make available an easily used Microsoft® ExcelTM spreadsheet (http://ars.usda.gov/msa/awmru/bolster/Sorption_spreadsheets) capable of generating best-fit parameters, standard errors of the parameters, confidence intervals for the parameters, 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.

Last Modified: 10/1/2014
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