Performance of Weibull and Linear Semi-logarithmic Models in Simulating Inactivation in Waters

Modeling inactivation of indicator microorganisms is a necessary component of microbial water quality forecast and management recommendations. The linear semi-logarithmic (LSL) model is commonly used to simulate the dependencies of bacterial concentrations in waters on time. There were indications that assumption of the semi-logarithmic linearity may not be accurate enough in waters. The objective of this work was to compare performance of the LSL and the two-parametric Weibull inactivation models with data on survival of indicator organism in various types of water from a representative database of 167 laboratory experiments. The Weibull model was preferred in >99% of all cases when the root mean squared errors and Nash-Sutcliffe statistics were compared. Comparison of corrected Akaike statistic values gave the preference to the Weibull model in only 35% of cases. This was caused by (i) a small number of experimental points on some inactivation curves, (ii) closeness of the shape parameter of the Weibull equation to one, and (iii) piecewise log-linear inactivation dynamic that could be well described by neither of the two models compared. Based on the Akaike test, the Weibull model was favored in agricultural, lake, and pristine waters, whereas the LSL model was preferred for groundwater, wastewater, rivers, and marine waters. The decimal reduction time parameter of both the LSL and Weibull models exhibited an Arrhenius-type dependence on temperature. Overall, the existing inactivation data indicate that the application of the Weibull model can improve the predictive capabilities of microbial water quality modeling.