Parameter estimation for sorption isotherms
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Parameter estimation for sorption isotherms is a very important practice in groundwater modeling. Both linear and nonlinear regression has been extensively used to obtain isotherm parameters for hydrophobic organic compounds (HOCs). However, there are several limitations with the traditional regression approaches, including: (1) incorrect objective functions, (2) unclear error structures, (3) convergence to local minima, (4) lack of statistical tools for the multi-model ranking, and (5) inadequate placement of observation points in experimental design. To improve the practice of isotherm estimation, this dissertation developed two modified objective functions, investigated several weighting schemes, adapted a robust software package (IsoFit) to avoid local minima, applied various regression statistics for model ranking, and explored different experimental design strategies. Two sets of extensive numerical experiments were conducted to evaluate the new methods, including re-calibration of thirteen datasets from three published studies and isotherm fitting of synthetic datasets. Key results from the numerical experiments include: (1) Eleven candidate isotherms were applied in the fitting of literature data, and the Polanyi-partition isotherm was observed to have the strongest support for describing HOCs sorption from both mechanistic and statistical standpoints. (2) It appeared that many of the published isotherm parameters were local minima, highlighting the need for a robust solver (such as IsoFit). (3) For data weighting schemes, the standard deviation of sorbed concentration ( q ), as computed by error propagation via the isotherm mass balance equation, was the best approximation to the "true" standard deviation, and is therefore recommended for use in data weighting. (4) For isotherm fitting methods, the one-variable and the two-variable objective functions based on the aforementioned weighting scheme gave the best results from among several candidate methods. (5) In numerical experiments using synthetic datasets, increasing the number and concentration range of the isotherm data points generally improved the accuracy of the parameter estimation process. In addition, logarithmic and hybrid distributions of data points across the aqueous concentration axis resulted in more accurate parameter estimation than evenly-spaced data.