Incorporating multiple observational uncertainties in water quality model calibration

The presence of error in water quality and hydrologic variables can significantly impair the calibration of water quality models. Precise and reliable identification of observational errors can have a significant impact on improving model parameter estimation. This study develops the Bayesian error analysis with reordering (BEAR) method to accommodate multiple sources of observational errors in the calibration of a water quality model. It realizes this goal by sampling the errors for input and output data from their respective error distributions and reordering them with inferred ranks via the secant method. This approach is demonstrated in the case of total suspended solids (TSS) simulated via a conceptual water quality model. Based on case studies using synthetic data, the new algorithm successfully quantifies one source of observational error when the error model of another source of observational error can be estimated accurately in advance. The results of a real case study also illustrate that considering observational errors in both model inputs and outputs, rather than in just the inputs or outputs, can improve the parameter calibration and error characterization. The improvements depend on the precision of the prior information for the error model. The application of this new algorithm in TSS simulation can be an example to understand how the BEAR algorithm works in other water quality models. The core idea of the BEAR algorithm is flexible and can be extended to the calibration of other environmental models.

Automated summary

This study introduces the BEAR method for handling multiple sources of observational errors in water quality models to accurately estimate model parameters, which has been shown to successfully quantify sources of observational errors. Considering observational errors in both model inputs and outputs, rather than just inputs or outputs, can improve parameter calibration and error characterization.