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

By Mark A. Thyer, Benjamin Renard, Dmitri Kavetski, George A. Kuczera, S. Franks, S. Srikanthan. 2009

394 citations recorded by the source corpus.

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.

Subfields: Global and Planetary Change, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/364cc26b82323f114aba5b7ef0c1176f79160879

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In Global and Planetary Change

In Water Science and Technology

Citations in the corpus

Improving probabilistic prediction of daily streamflow by identifying Pareto optimal approaches for modeling heteroscedastic residual errors (2017, methodology): “For example, high rainfalls and streamflows are typically subject to larger predictive uncertainty than low rainfalls and streamflows [e.g., Villarini and Krajewski, 2008; Thyer et al., 2009].”
Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments (2010, background): “In the specific areas of input data uncertainty and model structural uncertainty, a wealth of recent research from the University of Newcastle research group [e.g., Kavetski et al., 2006; Renard et al., 2010; Thyer et al., 2009] has indicated the importance of addressing these components for improve”
A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors (2010, methodology): “Such violations have been reported in other rainfall‐runoff studies as well [e.g., Kuczera, 1983; Feyen et al., 2007; Thyer et al., 2009].”
A log‐sinh transformation for data normalization and variance stabilization (2012, neutral): “Various heteroscedastic error models have been proposed for hydrological applications [e.g., Schoups and Vrugt, 2010; Thyer et al., 2009].”
Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors (2010, methodology): “[110] 2. Evaluate the predictive distribution (PD) of the observed runoff during the validation period (see Thyer et al. [2009] for details).”
Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction (2010, methodology): “[38] The adaptive MCMC strategy used in this study is described by Thyer et al. [2009] .”
Hydrological uncertainty processor based on a copula function (2018, methodology): “Using the guide presented in Thyer et al. (2009) to assess the results, it is clear that the overall performances of all predictive QQ plots are acceptable.”
Comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and heteroscedasticity (2014, methodology): “In this study, reliability is assessed graphically using predictive quantile-quantile (PQQ) plots [Laio and Tamea, 2007; Thyer et al., 2009] and quantified numerically using the metric pReliab½~QkQ presented in Appendix B.”
Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm (2011, background): “[15] It is worth mentioning that inappropriate modeling of the noise term may cause biased estimation of model parameters and underestimation of the uncertainty [Neuman, 2003; Thyer et al., 2009].”
A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites (2009, background): “This PIT uniform probability plot (termed predictive QQ plot by Thyer et al. [2009]) is useful for indicating whether the forecast probability distributions are predicting too high or too low, or too wide or narrow [Laio and Tamea, 2007; Thyer et al., 2009].”
Toward diagnostic model calibration and evaluation: Approximate Bayesian computation (2013, neutral): “…and Beven, 2009], the Bayesian Total Error Analysis framework of Kavetski and coworkers [Kavetski et al., 2006a, 2006b; Kuczera et al., 2006; Thyer et al., 2009; Renard et al., 2011], the Simultaneous Optimization and Data Assimilation, DiffeRential Evolution Adaptive Metropolis (DREAM),…”