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Evaluation of Procedures for Aggregating Nonlinear Sulfate Adsorption Isotherm Data

NSI Technology Services Corp., USEPA Environmental Research Lab., Corvallis, OR 97333

* Corresponding author.

ABSTRACT

As part of a study to assess potential regional surface-water acidification in the southern Blue Ridge region of the USA, more than 700 individual soils were sampled from 35 watersheds and analyzed. Sulfate adsorption isotherms were generated for all mineral soil horizons. Subsequent use of these data in dynamic watershed chemistry models required aggregation of adsorption data to two or three isotherms (one per soil mineral horizon) per watershed. This study evaluated several techniques for aggregation of the nonlinear adsorption-isotherm data. The objective of the analysis was to identify a procedure for aggregation that would generate a function providing a representative weighted average of the SO^2-₄ adsorption partitioning coefficients (isotherm slopes) of several individual isotherms, and would do so over a range of dissolved SO^2-₄ concentrations. The most effective procedure involved a sequence of: (i) fitting isotherms for individual soils, (ii) computing values of adsorbed SO^2-₄ corresponding to several reference concentrations of dissolved SO^2-₄, (iii) computing weighted averages of adsorbed SO^2-₄ at each of the reference concentrations, and (iv) fitting a new isotherm to the set of weighted points. Two alternate procedures for aggregation, computation of weighted averages of the coefficients of isotherms fitted to data for individual soils, or fitting a single isotherm to the raw data points for several soils, gave highly variable results that were usually skewed to low estimates of slope. Although specific results of this analysis relate to aggregation of SO^2-₄-adsorption isotherms, the strengths and weaknesses of the various aggregations have significant implications for aggregation of data sets for other nonlinear functions and for subsequent use of data. Use of an inappropriate aggregation procedure can lead to erroneous estimates of the capacity, efficiency, or response time of the system being described or modeled, and is likely to result in ineffective or inefficient treatment to supply putative adsorbates to the solid phase or to remove pollutants from solution.

Received for publication July 11, 1990.