Scrutinizing parameter consistency and predictive uncertainty in rainfall-runoff models using Bayesian total error analysis

摘要

The lack of a robust framework for quantifying the uncertainty in the parameters andpredictions of conceptual rainfall runoff (CRR) models remains a key challenge forhydrological science. The Bayesian total error analysis (BATEA) provides a systematicapproach to hypothesize, infer and evaluate probability models describing input, outputand model structural error. This paper compares the ability of BATEA and standardcalibration approaches (standard least squares (SLS) and weighted least squares (WLS))to address two key requirements of uncertainty assessment: (i) reliable quantification ofpredictive uncertainty and (ii) reliable estimation of parameter uncertainty. The casestudy was challenging due to the semi-arid climate, ephemeral responses and highrainfall gradients in the catchment. The post-calibration diagnostics suggest that BATEAprovided a considerable improvement over SLS/WLS in terms of satisfying the assumedprobability models. This was also confirmed using a novel quantile-based diagnostic forassessing whether the total predictive uncertainty is consistent with the observations.Parameter consistency and reliability was evaluated by comparing parameter estimatesobtained for the same CRR model with same catchment runoff, but with differentrainfall gauges and time periods. BATEA provided more consistent, albeit moreuncertain, parameter estimates than SLS/WLS. The implication for CRR parameterregionalization is that the WLS/SLS-derived parameter estimates can be highlydependent on the choice of rainfall data and calibration period, which may obscure therelationship between CRR parameters and catchment attributes. In contrast, BATEA hasthe potential to remove this obstacle to regionalization.