Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis

TLDR

Conceptual rainfall‑runoff models lack a robust framework for quantifying parametric and predictive uncertainty, a gap addressed by the Bayesian total error analysis (BATEA) methodology, which integrates input, output, and structural error probability models. This study evaluates whether BATEA, compared to standard least squares (SLS) and weighted least squares (WLS), can reliably quantify predictive uncertainty and estimate parameter uncertainty. The authors calibrate the lumped GR4J model to a catchment with episodic responses and steep rainfall gradients, applying BATEA, SLS, and WLS to assess uncertainty. BATEA better satisfies its probability model assumptions than SLS/WLS, produces consistent but more uncertain parameter estimates that aid regionalization, yet still overestimates predictive uncertainty—especially during validation—likely because inferred rainfall errors compensate for simplified structural error treatment.

Abstract

The lack of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall‐runoff (CRR) models remains a key challenge in hydrology. The Bayesian total error analysis (BATEA) methodology provides a comprehensive framework to hypothesize, infer, and evaluate probability models describing input, output, and model structural error. This paper assesses 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: (1) reliable quantification of predictive uncertainty and (2) reliable estimation of parameter uncertainty. The case study presents a challenging calibration of the lumped GR4J model to a catchment with ephemeral responses and large rainfall gradients. Postcalibration diagnostics, including checks of predictive distributions using quantile‐quantile analysis, suggest that while still far from perfect, BATEA satisfied its assumed probability models better than SLS and WLS. In addition, WLS/SLS parameter estimates were highly dependent on the selected rain gauge and calibration period. This will obscure potential relationships between CRR parameters and catchment attributes and prevent the development of meaningful regional relationships. Conversely, BATEA provided consistent, albeit more uncertain, parameter estimates and thus overcomes one of the obstacles to parameter regionalization. However, significant departures from the calibration assumptions remained even in BATEA, e.g., systematic overestimation of predictive uncertainty, especially in validation. This is likely due to the inferred rainfall errors compensating for simplified treatment of model structural error.