[1] Meaningful quantification of data and structural uncertainties in conceptual rainfallrunoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill-posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill-posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall-runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.

[1] Parameter estimation in rainfall-runoff models is affected by uncertainties in the measured input/output data (typically, rainfall and runoff, respectively), as well as model error. Despite advances in data collection and model construction, we expect input uncertainty to be particularly significant (because of the high spatial and temporal variability of precipitation) and to remain considerable in the foreseeable future. Ignoring this uncertainty compromises hydrological modeling, potentially yielding biased and misleading results. This paper develops a Bayesian total error analysis methodology for hydrological models that allows (indeed, requires) the modeler to directly and transparently incorporate, test, and refine existing understanding of all sources of data uncertainty in a specific application, including both rainfall and runoff uncertainties. The methodology employs additional (latent) variables to filter out the input corruption given the model hypothesis and the observed data. In this study, the input uncertainty is assumed to be multiplicative Gaussian and independent for each storm, but the general framework allows alternative uncertainty models. Several ways of incorporating vague prior knowledge of input corruption are discussed, contrasting Gaussian and inverse gamma assumptions; the latter method avoids degeneracies in the objective function. Although the general methodology is computationally intensive because of the additional latent variables, a range of modern numerical methods, particularly Monte Carlo analysis combined with fast Newton-type optimization methods and Hessian-based covariance analysis, can be employed to obtain practical solutions.

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[1] 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.Citation: Thyer, M., B. Renard, D. Kavetski, G. Kuczera, S. W. Franks, and S. Srikanthan (2009), Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis, Water Resour. Res.,

[1] Recent research has highlighted the persistence of multi-decadal epochs of enhanced/reduced flood risk across New South Wales (NSW), Australia. Recent climatological studies have also revealed multi-decadal variability in the modulation of the magnitude of El Niño/Southern Oscillation (ENSO) impacts. In this paper, the variability of flood risk across NSW is analysed with respect to the observed modulation of ENSO event magnitude. This is achieved through the use of a simple index of regional flood risk. The results indicate that cold ENSO events (La Niña) are the dominant drivers of elevated flood risk. An analysis of multidecadal modulation of flood risk is achieved using the interdecadal Pacific Oscillation (IPO) index. The analysis reveals that IPO modulation of ENSO events leads to multi-decadal epochs of elevated flood risk, however this modulation appears to affect not only the magnitude of individual ENSO events, but also the frequency of their occurrence. This dual modulation of ENSO processes has the effect of reducing and elevating flood risk on multi-decadal timescales. These results have marked implications for achieving robust flood frequency analysis as well as providing a strong example of the role of natural climate variability.