Quantifying input error in hydrologic modeling using the Bayesian error analysis with reordering (BEAR) approach

Abstract

Input error in hydrologic models, mainly arising from observed precipitation, can impair model calibration. Precise and reliable identification of input error is important for improved model parameter estimation. However, limited information about the nature of the error and the memory of the hydrologic system make it challenging to disentangle input error from the total residual error. Based on a Sequential Monte Carlo sampling algorithm, Bayesian error analysis with reordering (BEAR) method is developed to quantify the unknown input error series by sampling errors from an assumed error distribution and reordering them with inferred error ranks via the secant method, rather than estimating their values directly. The results of a synthetic case and a real case using the hydrologic models GR4J and HYMOD show several benefits of this new approach: 1) the reordering strategy via the secant method can significantly improve the efficiency and accuracy of input error quantification, and consequently promote the parameter estimation; 2) an autoregressive model can address the persistence of hydrologic residual errors in calibration; 3) the lag-time between the forcing data and the corresponding response can be explicitly acknowledged when the system exhibits a delayed response. This developed BEAR algorithm can be extended to other environmental modeling studies with correlated or/and delayed responses although its ability is limited by the impacts of model structural error and the output observational error.