Quantifying input uncertainty in the calibration of water qualitymodels: reshuffling errors via the secant method

Abstract. Uncertainty in inputs can significantly impair parameter estimation in water quality modeling, necessitating accurate quantification of input errors. However, decomposing input error from model residual error is still challenging. This study develops a new algorithm, referred to as Bayesian error analysis with reshuffling (BEAR), to address this problem. The basic approach requires sampling errors from a pre-estimated error distribution and then reshuffling them with their inferred ranks via the secant method. This approach is demonstrated in the case of total suspended solids (TSS) simulation via a conceptual water quality model. Based on case studies using synthetic data, the BEAR method successfully isolates the input error and parameter error. 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 is limited by the assumption that the input uncertainty should be dominant and that the prior information of the input error model can be estimated. The application of the BEAR method in TSS simulation is effective for understanding a range of water quality conditions and the further developed algorithm can be extended to other water quality predictions.