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LeastSquares Analysis of Phosphorus Soil Sorption Data with Weighting from Variance Function Estimation: A Statistical Case for the Freundlich Isotherm
 Author:
 Tellinghuisen, Joel, Bolster, Carl H.
 Source:
 Environmental science & technology 2010 v.44 no.13 pp. 5029
 ISSN:
 15205851
 Subject:
 phosphorus, sorption, soil, models, sorption isotherms, statistical analysis, least squares, data analysis, equations, estimation, soil analysis, nutrient availability
 Abstract:
 Phosphorus soil sorption data are typically fitted to simple isotherms for the purpose of compactly summarizing experimental results and extrapolating beyond the range of measurements. Here, the question of which of the commonly preferred modelsLangmuir and Freundlichis better, is addressed using weighted leastsquares, with weights obtained by variance function analysis of replicate data. Proper weighting in this case requires attention to a special problemthat the dependent variable S is not measured, rather is calculated from the measured equilibrium concentration C. The latter is commonly taken as the independent variable but is subject to experimental error, violating a fundamental leastsquares assumption. This problem is handled through an effective variance treatment. When the data are fitted to the Langmuir, Freundlich, and Temkin isotherms, only the Freundlich model yields a statistically adequate x2 value, and then only when S is taken to include labile residual P (S0) estimated from isotopeexchange experiments. The Freundlich model also yields good estimates of S0 when this is treated as an adjustable parameter rather than a known quantityof relevance to studies in which S0 is not measured. By contrast, neglect of weights and labile P can lead to a mistaken preference for the Langmuir model.
 Agid:
 44386
 Handle:
 10113/44386

http://dx.doi.org/10.1021/es100535b