[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] 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] This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data-based probability models describing uncertainties in rainfall and runoff data and incorporating them into the Bayesian total error analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall-runoff model GR4J is presented. It exploits a calibration period where dense rain gauge data are available to characterize the uncertainty in the catchment average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill-posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff, and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.

Risk assessment requires a description of the probabilistic properties of hydrological variables. In a number of cases, this description is made on a single variable, whereas most hydrological events are intrinsically multivariate. In this context, copulas have recently received attention in order to derive a multivariate frequency analysis. After a reminder of the general results in the field of multivariate extreme value theory, the paper gives a description of a very simple copula, the Gaussian copula. Four case studies demonstrate its usefulness in the contexts of field significance determination, regional risk analysis, Discharge-Duration-Frequency (QdF) models with design hydrograph derivation and regional frequency analysis. The limitations and potential errors related to this statistical tool are also highlighted.

Discharge time series in rivers and streams are usually based on simple stage-discharge relations calibrated using a set of direct stage-discharge measurements called gaugings. Bayesian inference recently emerged as a most promising framework to build such hydrometric rating curves accurately and to estimate the associated uncertainty. In addition to providing the rigorous statistical framework necessary to uncertainty analysis, the main advantage of the Bayesian analysis of rating curves arises from the quantitative assessment of (i) the hydraulic controls that govern the stage-discharge relation, and of (ii) the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions. In this paper, we introduce the BaRatin method for the Bayesian analysis of stationary rating curves and we apply it to three typical cases of hydrometric stations with contrasted flow conditions and variable abundance of hydraulic knowledge and gauging data. The results exemplify that the thorough analysis of hydraulic controls and the quantification of gauging uncertainties are required to obtain reliable and physically sound results.

[1] This paper describes regional methods for assessing field significance and regional consistency for trend detection in hydrological extremes. Four procedures for assessing field significance are compared on the basis of Monte Carlo simulations. Then three regional tests, based on a regional variable, on the regional average Mann-Kendall test, and a new semiparametric approach, are tested. The latter was found to be the most adequate to detect consistent changes within homogeneous hydro-climatic regions. Finally, these procedures are applied to France, using daily discharge data arising from 195 gauging stations. No generalized change was found at the national scale on the basis of the field significance assessment of at-site results. Hydro-climatic regions were then defined, and the semiparametric procedure applied. Most of the regions showed no consistent change, but three exceptions were found: in the northeast flood peaks were found to increase, in the Pyrenees high and low flows showed decreasing trends, and in the Alps, earlier snowmelt-related floods were detected, along with less severe drought and increasing runoff due to glacier melting. The trend affecting floods in the northeast was compared to changes in rainfall, using rainfall-runoff simulation. The results showed flood trends consistent with the observed rainfall.

Concern over the potential impact of anthropogenic climate change on flooding has led to a proliferation of studies examining past flood trends. Many studies have analysed annual-maximum flow trends but few have quantified changes in major (25-100 year return period) floods, i.e. those that have the greatest societal impacts. Existing major-flood studies used a limited number of very large catchments affected to varying degrees by alterations such as reservoirs and urbanisation. In the current study, trends in majorflood occurrence from 1961 to 2010 and from 1931 to 2010 were assessed using a very large dataset (>1200 gauges) of diverse catchments from North America and Europe; only minimally altered catchments were used, to focus on climate-driven changes rather than changes due to catchment alterations. Trend testing of major floods was based on counting the number of exceedances of a given flood threshold within a group of gauges. Evidence for significant trends varied between groups of gauges that were defined by catchment size, location, climate, flood threshold and period of record, indicating that generalizations about flood trends across large domains or a diversity of catchment types are ungrounded. Overall, the number of significant trends in major-flood occurrence across North America and Europe was approximately the number expected due to chance alone. Changes over time in the occurrence of major floods were dominated by multidecadal variability rather than by long-term trends. There were more than three times as many significant relationships between major-flood occurrence and the Atlantic Multidecadal Oscillation than significant long-term trends.

This study explores the relationship between low flows and large scale climate variability in France. To this aim, a national low flow reference network of near-natural catchments, consisting of 236 gauging stations, was set up. A subset of 220 daily streamflow records for the period 1968-2008 was used to detect trends in a number of severity and timing drought indices. In addition to testing temporal trends, correlations with four climate indices were also evaluated: the North Atlantic Oscillation (NAO), the Atlantic Multidecadal Oscillation (AMO) and the frequency of two Weather Patterns corresponding to circulation types associated to wet (WP2) and dry (WP8) conditions over France. Due to their specific dynamics, NAO and WPs were also analyzed seasonally. Results show a consistent increase of drought severity in southern France.