Scrutinizing Parameter Consistency and Predictive Uncertainty in Rainfall-Runoff Models Using Bayesian Total Error Analysis

The lack of a robust framework for quantifying the uncertainty in the parameters and predictions of conceptual rainfall runoff (CRR) models remains a key challenge for hydrological science. The Bayesian total error analysis (BATEA) provides a systematic approach to hypothesize, infer and evaluate probability models describing input, output and model structural error. This paper compares the ability of BATEA and standard calibration approaches (standard least squares (SLS) and weighted least squares (WLS)) to address two key requirements of uncertainty assessment: (i) reliable quantification of predictive uncertainty and (ii) reliable estimation of parameter uncertainty. The case study was challenging due to the semi-arid climate, ephemeral responses and high rainfall gradients in the catchment. The post-calibration diagnostics suggest that BATEA provided a considerable improvement over SLS/WLS in terms of satisfying the assumed probability models. This was also confirmed using a novel quantile-based diagnostic for assessing whether the total predictive uncertainty is consistent with the observations. Parameter consistency and reliability was evaluated by comparing parameter estimates obtained for the same CRR model with same catchment runoff, but with different rainfall gauges and time periods. BATEA provided more consistent, albeit more uncertain, parameter estimates than SLS/WLS. The implication for CRR parameter regionalization is that the WLS/SLS-derived parameter estimates can be highly dependent on the choice of rainfall data and calibration period, which may obscure the relationship between CRR parameters and catchment attributes. In contrast, BATEA has the potential to remove this obstacle to regionalization.