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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: A Convenient Spreadsheet Method for Fitting the Nonlinear Langmuir Equation to Sorption Data

Author
item Bolster, Carl

Submitted to: Internet Web Page
Publication Type: Other
Publication Acceptance Date: February 1, 2007
Publication Date: February 1, 2007
Repository URL: http://www.ars.usda.gov/pandp/docs.htm?docid=14971
Citation: Bolster, C.H. 2007. A convenient spreadsheet method for fitting the nonlinear langmuir equation to sorption data. Internet Web Page.

Interpretive Summary: The Langmuir model is commonly used model for describing solute and metal sorption to soils. This model can be fit to data using nonlinear regression or, alternatively, a linearized version of the model can be fit to the data using linear regression. Although linearized versions of the Langmuir equation are mathematically equivalent to the nonlinear equation, the transformation of data required for linearization can result in modifications of error structure, introduction of error into the independent variable, and alteration of the weight placed on each data point often times leading to differences in fitted parameter values between linear and nonlinear versions of the Langmuir model. In addition, research has shown that the use of linearized Langmuir equations needlessly limits the ability to accurately model sorption data with more sophisticated sorption models. Because the use of linearized Langmuir equations is largely due to the ease of using linear regression, we make available an easy-to-use Microsoft Excel spreadsheet capable of fitting nonlinear sorption equations to isotherm data. The spreadsheet generates best-fit parameters, parameter uncertainties, parameter correlations, and goodness-of-fit measures. The accuracy of the spreadsheet has been thoroughly tested by comparing model fits and parameter estimates with a more sophisticated software package (SAS).The spreadsheet can be downloaded at http://ars.usda.gov/msa/awmru/bolster/Sorption_spreadsheets

Technical Abstract: The Langmuir model is commonly used model for describing solute and metal sorption to soils. This model can be fit to data using nonlinear regression or, alternatively, a linearized version of the model can be fit to the data using linear regression. Although linearized versions of the Langmuir equation are mathematically equivalent to the nonlinear equation, the transformation of data required for linearization can result in modifications of error structure, introduction of error into the independent variable, and alteration of the weight placed on each data point often times leading to differences in fitted parameter values between linear and nonlinear versions of the Langmuir model. In addition, research has shown that the use of linearized Langmuir equations needlessly limits the ability to accurately model sorption data with more sophisticated sorption models. Because the use of linearized Langmuir equations is largely due to the ease of using linear regression, we make available an easy-to-use Microsoft Excel spreadsheet capable of fitting nonlinear sorption equations to isotherm data. The spreadsheet generates best-fit parameters, parameter uncertainties, parameter correlations, and goodness-of-fit measures. The accuracy of the spreadsheet has been thoroughly tested by comparing model fits and parameter estimates with a more sophisticated software package (SAS).The spreadsheet can be downloaded at http://ars.usda.gov/msa/awmru/bolster/Sorption_spreadsheets

Last Modified: 4/19/2014
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