Performance of Weibull and linear semi-logarithmic models in simulating Escherichia coli inactivation in waters

Authors: STOCKER, MATTHEW - University Of Maryland; Pachepsky, Yakov; Shelton, Daniel

Submitted to: Journal of Environmental Quality
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/27/2014
Publication Date: 9/9/2014
Citation: Stocker, M., Pachepsky, Y.A., Shelton, D.R. 2014. Performance of Weibull and linear semi-logarithmic models in simulating Escherichia coli inactivation in waters. Journal of Environmental Quality. 43(5):1559-1565.

Interpretive Summary: Microbial quality of irrigation, recreation, aquacultural, and many other types of water are impacted by various factors, including rates of bacterial die-off. It was suggested more than 100 years ago that bacteria concentrations decrease exponentially with time during die-off; this hypothesis is still used in the majority of watershed-scale water quality models. However, there are recent reports that this simple exponential dependence may not be sufficient to accurately explain the bacterial die-off in waters. Unlike the exponential model, the Weibull model allows for variable rates of die-off with time, which may be either faster or slower than the exponential rate. The objective of this work was to compare the accuracy of the exponential model vs. Weibull model in simulationing die-off of the indicator bacterium, Escherichia coli, in various types of natural untreated waters. We found the Weibull model to be much more efficient than the exponential model in simulating bacterial die-off. Using a large database of published experimental data, we found that the Weibull model outperformed the exponential model in 98% of cases, and was two times (or more) accurate in 40% of cases. Results of this work are expected to be useful in modeling-based microbial water quality management, in that deviations in die-off from the exponential model can be factored into modeling assessments to improve accuracy of the modeling results.

Technical Abstract: Modeling of pathogen and indicator microorganism inactivation is a necessary component of microbial water quality forecast and management recommendations. The linear semilogarithmic model is commonly used to simulate the dependencies of bacteria concentration in waters over time. There have been indications that assumption of the semilogarithmic linearity may be not accurate enough in natural waters. The objective of this work was to compare performance of the linear semilogarithmic model and the two-parametric Weibull inactivation models in simulating survival of indicator organism Escherichia coli in various types of surface waters with the data from representative database of 167 laboratory experiments. The Weibull model was preferred in more than 99% of all cases when the root-mean squared errors and Nash-Sutcliffe statistics, respectively, were compared. Comparison of corrected Akaike statistic AICc values gave the preference to the Weibull model in only 35% of cases. The lesser preference by AICc was caused by (a) small number of experimental points on some inactivation curves, (b) closeness of the shape parameter of the Weibull equation to one, and, consequently, reduction of the Weibull model to the linear semilogarithmic one, and (c) presence of piece-wise loglinear inactivation dynamic that could be well described by neither of two models compared. Based on AICc test, the Weibull model was favored in agricultural, lake, and pristine waters whereas the linear semilogarithmic model was preferred in groundwater, wastewater, rivers, and marine waters. The scale parameter of the Weibull model exhibited the Arrhenius-type dependence on temperature. Overall, the existing E. coli inactivation data indicate that the application of the Weibull model can improve predictive capabilities of microbial water quality modeling.