Identifying input and output data errors in the calibration of a water quality model using Bayesian error analysis with reordering (BEAR) method

Abstract

The presence of errors in water quality and hydrologic variables can significantly impair the calibration of water quality models. To enhance the estimation of model parameters, it is important to accurately identify data errors during the calibration process. However, this task is challenging due to the complex interactions between model parameter uncertainty and data uncertainty. Existing methods for incorporating data uncertainty in model calibration have limitations, such as high-dimensional computation or the inability to handle stochastic errors. To address these challenges, a novel method called Bayesian Error Analysis with Reordering (BEAR) has been developed. Given that the data uncertainty arises from the data itself and is independent of the model calibration or simulation, the cumulative distribution function (CDF) of the data error can be estimated ahead and regarded as the prior information of Bayesian inference. Then the values of data error series only depend on their ranks in the CDF. BEAR method transforms the values of data error series into their ranks in the CDF. This transformation enables the effective identification of input and/or output data errors in water quality calibration. The innovation of the BEAR method can be attributed to several key aspects: 1) Modification of the secant method to handle the non-linear transformation from input to output, ensuring the correspondence between the rank of input data error and the residual error of the model. 2) Decomposition of model simulations to calculate the delay between each input and its corresponding output. 3) Utilization of the Autoregressive model to account for the correlation of residual errors. 4) Selection of an appropriate updating logic to minimize the compensation effects among multiple sources of data uncertainty. Overall, the BEAR method demonstrates flexibility and adaptability to various environmental modelling scenarios, making it a valuable tool for improving model specification under conditions of data uncertainty.