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Estimating Natural Attenuation Rate Constants Using a Fuzzy Framework

Fuzzy set theoretic approaches provide convenient tools to quantify subjective information and characterize the decision‐maker's preferences with minimal data. The estimation of natural attenuation and degradation rates, using the method of Buschek and Alcantar (1995), while pragmatic, is subject to significant imprecision due to mathematical simplifications and site complexities. In this paper, two fuzzy approaches, namely fuzzy arithmetic and fuzzy regression, are used to characterize the variability in the estimated degradation and attenuation rates. The variability in the input parameters can be characterized using membership functions that characterize the decision‐maker's perception of likely values. The choice of the membership function for critical inputs is seen to affect the variability in the estimated outputs. Similarly, the decision‐maker's belief related to the compatibility of the steady‐state model to represent the observed plume behavior at the site can also be quantified using a compatibility criterion. Sensitivity studies carried out using the fuzzy‐based estimation methodology are extremely useful to assess how differences in the decision‐makers’preferences will affect the estimated rate constants and associated variability. As such, the proposed methodology is of high value during negotiations related to monitored natural attenuation.