Benjamin Renard

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

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.

Regional methods for trend detection: Assessing field significance and regional consistency

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.

Flood frequency analysis using historical data: accounting for random and systematic errors.

Abstract Flood frequency analysis based on a set of systematic data and a set of historical floods is applied to several Mediterranean catchments. After identification and collection of data on historical floods, several hydraulic models were constructed to account for geomorphological changes. Recent and historical rating curves were constructed and applied to reconstruct flood discharge series, together with their uncertainty. This uncertainty stems from two types of error: (a) random errors related to the water-level readings; and (b) systematic errors related to over- or under-estimation of the rating curve. A Bayesian frequency analysis is performed to take both sources of uncertainty into account. It is shown that the uncertainty affecting discharges should be carefully evaluated and taken into account in the flood frequency analysis, as it can increase the quantiles confidence interval. The quantiles are found to be consistent with those obtained with empirical methods, for two out of four of the catchments. Citation Neppel, L., Renard, B., Lang, M., Ayral, P.-A., Coeur, D., Gaume, E., Jacob, N., Payrastre, O., Pobanz, K. & Vinet, F. (2010) Flood frequency analysis using historical data: accounting for random and systematic errors. Hydrol. Sci. J. 55(2), 192–208.

There are no hydrological monsters, just models and observations with large uncertainties!

Abstract Catchments that do not behave in the way the hydrologist expects, expose the frailties of hydrological science, particularly its unduly simplistic treatment of input and model uncertainty. A conceptual rainfall–runoff model represents a highly simplified hypothesis of the transformation of rainfall into runoff. Sub-grid variability and mis-specification of processes introduce an irreducible model error, about which little is currently known. In addition, hydrological observation systems are far from perfect, with the principal catchment forcing (rainfall) often subject to large sampling errors. When ignored or treated simplistically, these errors develop into monsters that destroy our ability to model certain catchments. In this paper, these monsters are tackled using Bayesian Total Error Analysis, a framework that accounts for user-specified sources of error and yields quantitative insights into how prior knowledge of these uncertainties affects our ability to infer models and use them for predictive purposes. A case study involving a catchment with an apparent water balance anomaly (a hydrological monstrosity!) illustrates these concepts. It is found that, in the absence of additional information, the rainfall–runoff record is insufficient to explain this anomaly – it could be due to a large export of groundwater, systematic overestimation of catchment rainfall of the order of 40%, or a conspiracy of these factors. There is “no free lunch” in hydrology. The rainfall–runoff record on its own is insufficient to decompose the different sources of uncertainty affecting calibration, testing and prediction, and hydrological monstrosities will persist until additional independent knowledge of uncertainties is obtained. Citation Kuczera, G., Renard, B., Thyer, M. & Kavetski, D. (2010) There are no hydrological monsters, just models and observations with large uncertainties! Hydrol. Sci. J. 55(6), 980–991.

Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis

Abstract This paper illustrates the importance of taking into account the potential errors in discharge estimation in the assessment of extreme floods. First, a summary of the main difficulties encountered in extrapolating rating curves for flood discharge is provided. Then a sensitivity analysis is carried out using a hydraulic modelling approach, applied to eight Mediterranean catchments, and yielding an envelope curve for the stage–discharge relationship, Q(H). To assess the influence of errors in the flood discharge on the uncertainty in estimating extreme floods, a Bayesian framework including a multiplicative error on the rating curve was applied. Its application on two catchments for which historical data are available for the period (1741–2004) shows that ignoring the rating curve errors may lead to an unduly optimistic reduction in the final uncertainty in estimation of flood discharge quantiles. Moreover, the quantile values are also affected by taking into account the rating curve errors. Citation Lang, M., Pobanz, K., Renard, B., Renouf, E. & Sauquet, E. (2010) Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis. Hydrol. Sci. J. 55(6), 883–898.

Bayesian Methods for Non-stationary Extreme Value Analysis

Non-stationary models for extremes have attracted significant attention in recent years. These models require adapted estimation methods. Bayesian inference offers an attractive framework to estimate non-stationary models and, importantly, to quantify estimation and predictive uncertainties.

Regional frequency analysis conditioned on large‐scale atmospheric or oceanic fields

Many studies report that hydrologic regimes are modulated by large-scale modes of climate variability such as the El Nino Southern Oscillation (ENSO) or the North Atlantic Oscillation (NAO). Climate-informed frequency analysis models have therefore been proposed to condition the distribution of hydrologic variables on climate indices. However, standard climate indices may be poor predictors in some regions. This paper therefore describes a regional frequency analysis framework that conditions the distribution of hydrologic variables directly on atmospheric or oceanic fields, as opposed to predefined climate indices. This framework is based on a two-level probabilistic model describing both climate and hydrologic data. The climate data set (predictor) is typically a time series of atmospheric of oceanic fields defined on a grid over some area, while the hydrologic data set (predictand) is typically a regional data set of station data (e.g., annual average flow at several gauging stations). A Bayesian estimation framework is used, so that a natural quantification of uncertainties affecting hydrologic predictions is available. A case study aimed at predicting the number of autumn flood events in 16 catchments located in Mediterranean France using geopotential heights at 500 hPa over the North-Atlantic region is presented. The temporal variability of hydrologic data is shown to be associated with a particular spatial pattern in the geopotential heights. A cross-validation experiment indicates that the resulting probabilistic climate-informed predictions are skillful: their reliability is acceptable and they are much sharper than predictions based on standard climate indices and baseline predictions that ignore climate information.

The open source RFortran library for accessing R from Fortran, with applications in environmental modelling

The open source RFortran library is introduced as a convenient tool for accessing the functionality and packages of the R programming language from Fortran programs. It significantly enhances Fortran programming by providing a set of easy-to-use functions that enable access to Rs very rapidly growing statistical, numerical and visualization capabilities, and support a richer and more interactive model development, debugging and analysis setup. RFortran differs from current approaches that require calling Fortran Dynamic link libraries (DLL) from R, and instead enables the Fortran program to transfer data to/from R and invoke R-based procedures via the R command interpreter. More generally, RFortran obviates the need to re-organize Fortran code into DLLs callable from R, or to re-write existing R packages in Fortran, or to jointly compile their Fortran code with the R language itself. Code snippets illustrate the basic transfer of data and commmands to and from R using RFortran, while two case studies discuss its advantages and limitations in realistic environmental modelling applications. These case studies include the generation of automated and interactive inference diagnostics in hydrological model calibration, and the integration of R statistical packages into a Fortran-based numerical quadrature code for joint probability analysis of coastal flooding using numerical hydraulic models. Currently, RFortran uses the Component Object Model (COM) interface for data/command transfer and is supported on the Microsoft Windows operating system and the Intel and Compaq Visual Fortran compilers. Extending its support to other operating systems and compilers is planned for the future. We hope that RFortran expedites method and software development for scientists and engineers with primary programming expertise in Fortran, but who wish to take advantage of Rs extensive statistical, mathematical and visualization packages by calling them from their Fortran code. Further information can be found at www.rfortran.org.

The ENSO–Precipitation Teleconnection and Its Modulation by the Interdecadal Pacific Oscillation

This study evaluates the role of the interdecadal Pacific oscillation (IPO) in modulating the El Nino?Southern Oscillation (ENSO)-precipitation relationship. The standard IPO index is described together with several alternatives that were derived using a low-frequency ENSO filter, demonstrating that an equivalent IPO index can be obtained as a low-frequency version of ENSO. Several statistical artifacts that arise from using a combination of raw and smoothed ENSO indices in modeling the ENSO?precipitation teleconnection are then described. These artifacts include the potentially spurious identification of low-frequency variability in a response variable resulting from the use of smoothed predictors and the potentially spurious modulation of a predictor-response relationship by the low-frequency version of the predictor under model misspecification. The role of the IPO index in modulating the ENSO?precipitation relationship is evaluated using a global gridded precipitation dataset, based on three alternative statistical models: stratified, linear, and piecewise linear. In general, the information brought by the IPO index, beyond that already contained in the Nino-3.4 index, is limited and not statistically significant. An exception is in northeastern Australia using annual precipitation data, and only for the linear model. Stratification by the IPO index induces a nonlinear ENSO?precipitation relationship, suggesting that the apparent modulation by the IPO is likely to be spurious and attributable to the combination of sample stratification and model misspecification. Caution is therefore required when using smoothed climate indices to model or explain low-frequency variability in precipitation. This study evaluates the role of the interdecadal Pacific oscillation (IPO) in modulating the El Nino-Southern Oscillation (ENSO)-precipitation relationship. The standard IPO index is described together with several alternatives that were derived using a low-frequency ENSO filter, demonstrating that an equivalent IPO index can be obtained as a low-frequency version of ENSO. Several statistical artifacts that arise from using a combination of raw and smoothed ENSO indices in modeling the ENSO?precipitation teleconnection are then described. These artifacts include the potentially spurious identification of low-frequency variability in a response variable resulting from the use of smoothed predictors and the potentially spurious modulation of a predictor-response relationship by the low-frequency version of the predictor under model misspecification. The role of the IPO index in modulating the ENSO?precipitation relationship is evaluated using a global gridded precipitation dataset, based on three alternative statistical models: stratified, linear, and piecewise linear. In general, the information brought by the IPO index, beyond that already contained in the Nino-3.4 index, is limited and not statistically significant. An exception is in northeastern Australia using annual precipitation data, and only for the linear model. Stratification by the IPO index induces a nonlinear ENSO-precipitation relationship, suggesting that the apparent modulation by the IPO is likely to be spurious and attributable to the combination of sample stratification and model misspecification. Caution is therefore required when using smoothed climate indices to model or explain low-frequency variability in precipitation.

Bayesian analysis of stage-fall-discharge rating curves and their uncertainties

Stage-fall-discharge (SFD) rating curves are traditionally used to compute streamflow records at sites where the energy slope of the flow is variable due to variable backwater effects. We introduce a model with hydraulically interpretable parameters for estimating SFD rating curves and their uncertainties. Conventional power functions for channel and section controls are used. The transition to a backwater-affected channel control is computed based on a continuity condition, solved either analytically or numerically. The practical use of the method is demonstrated with two real twin-gauge stations, the Rh\^one River at Valence, France, and the Guthusbekken stream at station 0003