Quantifying input uncertainty in the calibration of water quality models: reordering errors via the secant method

Abstract

Abstract. Uncertainty in input can significantly impair parameter estimation in water quality modeling, necessitating the accurate quantification of input errors. However, decomposing the input error from the model residual error is still challenging. This study develops a new algorithm, referred to as the Bayesian Error Analysis with Reordering (BEAR), to address this problem. The basic approach requires sampling errors from a pre-estimated error distribution and then reordering them with their inferred ranks via the secant method. This approach is demonstrated in the case of total suspended solids (TSSs) simulation via a conceptual water quality model. Based on case studies using synthetic data, the BEAR method successfully improves the input error identification and parameter estimation by introducing the error rank estimation and the error position reordering. The results of a real case study demonstrate that, even with the presence of model structural error and output data error, the BEAR method can approximate the true input and bring a better model fit through an effective input modification. However, its effectiveness depends on the accuracy and selection of the input error model. The application of the BEAR method in TSS simulation can be extended to other water quality models.