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International audience; This study identified and analysed the sources of error in runoff estimation via rating curves. This was undertaken by applying the BATEA framework to the rating curve model used to transform river stage to runoff for the Mahurangi catchment a heavily instrumented experimental catchment in New Zealand. The systematic errors due to rating curve uncertainty were the dominant source of uncertainty. This rating curve uncertainty is due to a limited number of uncertain runoff gaugings. The contribution of the random error component was small. This contradicts the common assumption of random runoff measurement error used in hydrological model calibration. The impact of rating curve uncertainty was incorporated into hydrological model calibration for the hourly Mahurangi data using the BATEA framework. Comparing these results to the typical standard least squares approach (with fixed rating curve) illustrated that incorporating rating curve uncertainty improved the reliability of the hydrological model predictions and caused a shift in the parameter distributions. These results have implications for hydrological model calibration. Runoff data are typically assumed to be observed but rating curve uncertainty induces significant systematic runoff errors which can have a significant impact on hydrological model predictions.

International audience; The quantification of uncertainties in hydrological predictions is a key step in improving the reliability and usefulness of flood forecasts. In this study, we investigate the impact of uncertainty from streamflow data used in flood forecasting models for real-time updating of hydrological ensemble predictions. The GRP hydrological forecasting model, a lumped rainfall-runoff model, is used over a selected number of catchments in France, for which gaugings and rating curves are available. Rating curve uncertainty is estimated for each catchment using a Bayesian approach. In the first step, the uncertainty in individual gaugings is quantified. It depends on the gauging method (e.g. velocity-area method, tracer dilution, ADCP, surface velocity measurements, etc.) and the operational characteristics of the gauging (e.g. spatial sampling of velocity and depth throughout the cross-section, unsteadiness of the flow, etc.). These uncertain gaugings are then used to estimate the rating curve and related uncertainties, using hydraulics-based priors on the rating curve coefficients. In the second step, the GRP model is used to produce streamflow forecast series. The model uses the last observed discharge and its related uncertainty to update the state of the routing reservoir at the time of forecasting. Errors in streamflow data are considered jointly with errors in precipitation forecasts. For the latter, the hydrological model is driven by the 10-day ECMWF deterministic and ensemble (51 members) precipitation forecasts for a period of about 3.5 years (March 2005 to September 2008). Ensemble streamflow predictions are evaluated against observed discharges (and judged in terms of bias, reliability, spread, ability to detect exceedances of critical discharges or water levels in advance, etc.) and as a function of forecast lead-time and warning thresholds. The results obtained by enabling/disabling the treatment of streamflow uncertainty are then compared and discussed, contributing to a better understanding of the role of streamflow errors in the total predictive uncertainty.

International audience

International audience; Calibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by the sampling and measurement uncertainty in the observed input/output data and by the structural error of the model conceptualisation. The Bayesian Total Error Analysis methodology (BATEA) provides the opportunity to directly and comprehensively address these sources of uncertainty. BATEA is based on Bayesian hierarchical methods and uses explicit error models for input/output data and structural errors. However, previous studies demonstrated that simultaneous inference on forcing (e.g. rainfall) and structural errors requires strong prior knowledge of the error mechanisms (e.g., statistical properties of rainfall errors). This paper investigates methods to derive informative prior knowledge on data (input/output) errors. A geostatistical approach is used to estimate the sampling error made in approximating the areal rainfall by averaging point-values from a raingauge network. The geostatistical model generates an ensemble of rainfall fields conditioned on gauged values (conditional simulation). This ensemble is treated as a distribution of the true areal rainfall over the catchment and used as a prior in the BATEA framework. Prior knowledge on runoff errors is derived from a statistical analysis of the gaugings used to derive the rating curve. A comparative case study is then carried out, by comparing several inference schemes (full BATEA, ignoring input errors, ignoring structural errors, ignoring both input/structural errors). Results show that: (i) the inclusion of prior knowledge on rainfall accuracy allows simultaneous estimation of input and structural errors, whereas in the absence of such information the inference is ill-posed; (ii) accounting for all sources of errors leads to a more reliable estimation of predictive uncertainty. These findings demonstrate the key role played by priors on data (rainfall/runoff) accuracy, since they control the well-posedness of the inference and allow decomposing predictive uncertainty into its contributing sources. This paves the way for a meaningful analysis of structural errors affecting hydrologic models, thus enabling meaningful model comparison and improvement.

International audience; Hydrological modeling has traditionally suffered from a variety of errors including input-output data errors, structural errors in the model conceptualization and, finally, numerical errors in the model implementation. These errors have distinctly different origins, behavior and require specialized treatment. Following a brief theoretical review, we present a number of case studies where these errors are identified and treated. First, we demonstrate the occurrence of numerical errors when the model equations are solved using unreliable techniques. Remarkably, the hydrological community has allowed such errors to arise and persist despite the weaknesses of these techniques being well known for decades in the applied mathematics literature, and despite far more robust techniques being widely available. Second, we demonstrate the use of statistical techniques to get useful insights into rainfall and runoff data errors. When exploited within a Bayesian inference, these data insights can be used to estimate structural errors. Third, we demonstrate a methodology for characterizing structural errors using stochastic parameters, and flexible model structures. The case studies move us another step closer towards the elusive goal of reliably understanding and treating the distinct sources of error afflicting hydrological models. Benefits for improved scientific hypothesis-testing and more reliable operational predictions are discussed.

International audience; Confronted with frequently poor model performance, rainfall-runoff modellers have in the past blamed a plethora of sources of uncertainty, including rainfall and runoff errors, non-Gaussianities, model nonlinearities, parameter uncertainty, and just about everything else from Pandorra's box. Moreover, recent work has suggested astonishing numerical artifacts may arise from poor model numerics and confound the Hydrologist. There is a growing recognition that maintaining the lumped nebulous conspiracy of these errors is impeding progress in terms of understanding and, when possible, reducing predictive errors and gaining insights into catchment dynamics. In this study, we take the hydrological bull by its horns and begin disentangling individual sources of error. First, we outline robust and efficient error-control methods that ensure adequate numerical accuracy. We then demonstrate that the formidable interaction between data and structural errors, irresolvable in the absence of independent knowledge of data accuracy, can be tackled using geostatistical analysis of rainfall gauge networks and rating curve data. Structural model deficiencies can then begin being identified using flexible model configurations, paving the way for meaningful model comparison and improvement. Importantly, informative diagnostic measures are available for each component of the analysis. This paper surveys several recent developments along these research directions, summarized in a series of real-data case studies, and indicates areas of future interest.

International audience; Efforts to improve hydrological predictions are often thwarted by several sources of error, including (i) data uncertainty, e.g, input (rainfall) errors and output (runoff) errors; and (ii) structural uncertainty in the hydrological model. The Bayesian total error analysis methodology was introduced to overcome these challenges and provides a framework which can explicitly account for each source of error. While several studies have shown that accounting for rainfall error notably improves hydrological predictions, the runoff error models used are based on unduly simplistic assumptions (e.g 10% random error). This study will use streamflow rating curve data to develop probabilistic model of streamflow measurement error prior to the calibration of the hydrological model. Several diagnostic tools aiding the runoff error model development are presented. Different types of runoff error models (with both random and systematic errors) are developed using the rating curve data. These runoff error models are incorporated into hydrological model calibration using the BATEA methodology and a comparative analysis of the calibration results (predictive time series, model parameters and state variables) is presented, thoroughly scrutinizing its assumptions and comparing them to commonly error model assumptions. Several catchment case studies are compared to evaluate the benefits under diverse hydrological regimes. The implications for improving hydrological predictions via disentangling structural errors from data errors is discussed.

International audience; Calibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by the sampling and measurement uncertainty in the forcing/response data and by the structural error of the model conceptualisation. These errors significantly affect the calibration procedure, leading to biased estimates of CRR model parameters and unreliable assessment of predictive uncertainty. The Bayesian Total Error Analysis methodology (BATEA) provides the opportunity to directly and comprehensively address these sources of uncertainty. BATEA is built on Bayesian hierarchical methods, constructing explicit error models for forcing/response data and structural errors. This communication provides a general presentation of such error models, and studies their identifiability using two synthetic data sets. The first synthetic data set is affected by forcing and response errors, but encompasses no structural errors. In this case, BATEA is able to retrieve the actual errors corrupting the input data, resulting in unbiased parameter estimates and reliable predictive uncertainty quantification. In a second, more realistic, case study, the synthetic data set also encompasses structural errors. Results show that when these structural errors are ignored by BATEA, the estimated errors in input data overestimate the actual errors. Moreover, identifiability issues arise when both input and structural errors are to be estimated from the data. These results illustrate the difficulty in identifying the different sources of errors affecting the calibration procedure. This is likely to be due to the insufficient information content of the data to identify several distinct error processes. A possibility to overcome this limitation is to introduce in the calibration procedure additional sources of information (e.g. radar data providing a rough estimate of the rainfall errors due to spatial averaging).

International audience; Meaningful characterization of uncertainties affecting conceptual rainfall-runoff (CRR) models remains a challenging research area in the hydrological community. Numerous methods aimed at quantifying the uncertainty in hydrologic predictions have been proposed over the last decades. In most cases, the outcome of such methods takes the form of a predictive interval, computed from a predictive distribution. Regardless of the method used to derive it, it is important to notice that the predictive distribution results from the assumptions made during the inference. Consequently, unsupported assumptions may lead to inadequate predictive distributions, i.e. under- or over-estimated uncertainties. It follows that the estimated predictive distribution must be thoroughly scrutinized (validated); as discussed by Hall et al. [2007] Without validation, calibration is worthless, and so is uncertainty estimation. The aim of this communication is to study diagnostic tools aimed at assessing the reliability of uncertainty estimates. From a methodological point of view, this requires diagnostic approaches that compare a time-varying distribution (the predictive distribution at all times t) to a time series of observations. This is a much more stringent test than validation methods currently used in hydrology, which simply compare two time series (observations and optimal simulations). Indeed, standard goodness-of-fit assessments (e.g. using the Nash-Sutcliff statistic) can not check if the predictive distribution is consistent with the observed data.

International audience; The development of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall runoff (CRR) models remains a key challenge in hydrology. For practical purposes, reliable and robust characterization of predictive uncertainty is important for comparing the impact of management options on key variables of interest (e.g. reservoir yield, meeting low flow criteria for ecological purposes). For research purposes, robust identification of the sources of uncertainty is essential for understanding how to reduce predictive uncertainty, and thereby enhance model predictions. Both these tasks are recognized as a major challenge for hydrological modelling science. It is generally recognized that CRR modelling is affected by three main sources of uncertainty: (i) input uncertainty, e.g., measurement and sampling errors in the estimates of areal rainfall; (ii) output uncertainty, e.g., rating curve errors affecting runoff estimates; and (iii) structural uncertainty (sometimes referred to as model uncertainty), arising from lumped and simplified representation of hydrological processes in CRR models. Various approaches in the literature have aimed to quantify the individual contributions of input, output and structural uncertainties to the total predictive uncertainty. The beneficial impact of quantifying input errors on CRR parameter estimates and the reliability of model predictions has been established and techniques for evaluating model structural errors have begun to appear. However, almost all these studies make assumptions regarding the output (runoff measurement) errors. This study evaluated whether there is any beneficial impact in utilizing rating curve data to fit a runoff measurement error model. This was undertaken by incorporating this fitted output error (OE) model into the Bayesian total error analysis (BATEA) methodology. BATEA provides a comprehensive framework to hypothesize, infer and evaluate probability models describing input, output and model structural error. BATEA was used to calibrate the GR4J model to the ephemeral Horton catchment. To evaluate the impact of the fitted OE model the calibration results were compared to two other OE models; one representing a commonly assumed OE model and the other representing a conservative overestimate of the OE model. The estimated predictive uncertainty was more consistent with the observed runoff data for the fitted OE model than the assumed OE (which systemically under predicted the observed runoff) and the conservative OE (which overestimated the predictive uncertainty). This result was consistent in model calibration and validation. This illustrates for this case study there was beneficial impact in incorporating a fitted OE model. Comparison of the posterior distributions of parameters showed that the different OE model produced significantly different parameter estimates. This has implications for regionalizing parameters estimations to produce predictions in ungauged basins. Comparison of the estimated input/structural errors also showed substantial differences for different OE. This suggests an interdependency between the error sources, where reliable estimates of input/structural errors will be dependent on reliable estimates of the output error.

International audience; Calibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by the sampling and measurement uncertainty in the observed input/output data and by the structural error of the model conceptualisation. The Bayesian Total Error Analysis methodology (BATEA) provides the opportunity to directly and comprehensively address these sources of uncertainty. BATEA is based on Bayesian hierarchical methods and uses explicit error models for input/output data and structural errors. Previous studies demonstrated that simultaneous inference on forcing (e.g. rainfall) and structural errors requires strong prior knowledge of the error mechanisms (e.g., statistical properties of rainfall errors).This paper investigates a geostatistical approach to estimate the sampling error made in approximating the areal rainfall by averaging point-values from a raingauge network. The geostatistical model generates an ensemble of rainfall fields conditioned on gauged values. This ensemble is treated as a distribution of the true areal rainfall over the catchment and used as a prior in the BATEA framework. A case study shows that the inclusion of such prior knowledge allows simultaneous estimation of input and structural errors, whereas in the absence of such information the inference is ill-posed.

International audience; Confronted with poor model performance, the Hydrologist has blamed data errors, non-Gaussianities, model nonlinearities, parameter uncertainty, and just about everything else from Pandorra's box. Moreover, recent work has suggested astonishing numerical artefacts may arise from poor model implementation. Yet progress in hydrology requires reducing predictive errors and disentangling individual sources of uncertainty. How can this be accomplished? First, robust and efficient numerical methods are needed to avoid unnecessary artefacts. Second, the formidable interaction between data and structural errors, irresolvable in the absence of independent knowledge, can be approached using statistical analysis of rain- and stream- gauge networks. Structural errors, the key unresolved challenge, can then be explored using flexible model configurations, paving the way for more stringent hypothesis-testing. Importantly, informative diagnostic measures are available for each component of the analysis. This paper surveys several recent developments along these research directions and indicates areas of ongoing and future interest.