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Related Experiment Video

Updated: Apr 18, 2026

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

M D Stocker, Y A Pachepsky, D R Shelton

    Journal of Environmental Quality
    |January 21, 2015
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    The Weibull model significantly outperforms the linear semi-logarithmic model for predicting microbial inactivation in water, enhancing water quality forecasting. This microbial inactivation modeling improves water management recommendations.

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    Area of Science:

    • Environmental microbiology
    • Water quality modeling
    • Microbial inactivation kinetics

    Background:

    • Accurate modeling of indicator microorganism inactivation is crucial for microbial water quality forecasting and management.
    • The linear semi-logarithmic (LSL) model is widely used but may lack accuracy in diverse water types.
    • Alternative inactivation models are needed to improve predictive capabilities.

    Purpose of the Study:

    • To compare the performance of the two-parametric Weibull model against the LSL model for microbial inactivation.
    • To evaluate model performance across various water types using a comprehensive database of laboratory experiments.

    Main Methods:

    • Comparative analysis of LSL and Weibull inactivation models using 167 laboratory experiments.
    • Performance evaluation based on root mean squared errors, Nash-Sutcliffe statistics, and corrected Akaike information criterion (AICc).
    • Assessment of model fit across different water matrices including agricultural, lake, pristine, groundwater, wastewater, river, and marine waters.

    Main Results:

    • The Weibull model was statistically preferred in over 99% of cases based on root mean squared errors and Nash-Sutcliffe statistics.
    • AICc-based comparisons favored the Weibull model in 35% of cases, influenced by data sparsity, Weibull shape parameter values, and piecewise inactivation dynamics.
    • Model preference varied by water type: Weibull for agricultural, lake, and pristine waters; LSL for groundwater, wastewater, rivers, and marine waters.

    Conclusions:

    • The Weibull model demonstrates superior performance for predicting microbial inactivation in various water types compared to the LSL model.
    • The decimal reduction time parameter in both models shows temperature dependence, following an Arrhenius-type relationship.
    • Implementing the Weibull model can significantly enhance the predictive accuracy of microbial water quality models.