Bayesian Total Error Analysis for hydrologic models: Quantifying uncertainties arising from input, output and structural errors

Abstract

Rigorous quantification of the various sources of uncertainty arising during the calibration of conceptual rainfall-runoff (CRR) models remains a challenging task in hydrological modelling. The Bayesian Total Error Analysis methodology (BATEA) addresses this challenge using Bayesian hierarchical methods, constructing explicit statistical models of the sampling and measurement uncertainty in the forcing/response data and the structural error of the model conceptualization. This paper is a general presentation of the BATEA framework, along with its strengths and current limitations. The Bayesian hierarchical model arising from BATEA handling of error processes is first presented, and the resulting posterior distribution is derived. Guidelines for constructing robust error models are then provided: we describe BATEA pre-processing analyses, including the choice of parameters to be treated as latent variables and the identification of their temporal structure. Once inference has been performed, prediction limits can easily be computed, and the contribution of the various sources of errors to the overall predictive uncertainty can be estimated. Although BATEA offers a very general framework for incorporating error processes in the analysis of CRR models, its application is not straightforward as several issues –both practical and theoretical - still need to be tackled. They are presented in this paper, along with research directions for solving them. Lastly, a case study involving the calibration of a CRR model using various rain gauges is performed. This case study demonstrates the consistency of BATEA estimates of CRR parameters, as opposed to standard least square estimates, which are highly sensitive to the rain gauge used for calibration. This result offers interesting perspectives for parameter regionalization.