Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

[1] Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff 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]  K. Beven,et al.  On constraining the predictions of a distributed model: The incorporation of fuzzy estimates of saturated areas into the calibration process , 1998 .

[2]  B. Carlin,et al.  Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models. , 2000, Statistics in medicine.

[3]  Soroosh Sorooshian,et al.  Dual state-parameter estimation of hydrological models using ensemble Kalman filter , 2005 .

[4]  Asgeir Petersen-Øverleir,et al.  Bayesian methods for estimating multi-segment discharge rating curves , 2009 .

[5]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[6]  I. Rodríguez‐Iturbe,et al.  Random Functions and Hydrology , 1984 .

[7]  Jim W. Hall,et al.  On not undermining the science: coherence, validation and expertise. Discussion of Invited Commentary by Keith Beven Hydrological Processes, 20, 3141–3146 (2006) , 2007 .

[8]  Dmitri Kavetski,et al.  Assessing the impact of mixing assumptions on the estimation of streamwater mean residence time , 2010 .

[9]  Breanndán Ó Nualláin,et al.  Parameter optimisation and uncertainty assessment for large-scale streamflow simulation with the LISFLOOD model , 2007 .

[10]  Peter C. Young,et al.  Data-based mechanistic modelling of environmental, ecological, economic and engineering systems. , 1998 .

[11]  Peter Reichert,et al.  Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland) , 2007 .

[12]  Roman Krzysztofowicz,et al.  Bayesian system for probabilistic river stage forecasting , 2002 .

[13]  S. Sorooshian,et al.  Multi-model ensemble hydrologic prediction using Bayesian model averaging , 2007 .

[14]  Soroosh Sorooshian,et al.  A framework for development and application of hydrological models , 2001, Hydrology and Earth System Sciences.

[15]  Michel Lang,et al.  Flood frequency analysis using historical data: accounting for random and systematic errors , 2010 .

[16]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[17]  Keith Beven,et al.  So just why would a modeller choose to be incoherent , 2008 .

[18]  George Kuczera,et al.  Calibration of conceptual hydrological models revisited: 2. Improving optimisation and analysis , 2006 .

[19]  D. Kavetski,et al.  Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterising model error using storm-dependent parameters , 2006 .

[20]  Heikki Haario,et al.  Componentwise adaptation for high dimensional MCMC , 2005, Comput. Stat..

[21]  M. Trosset,et al.  Bayesian recursive parameter estimation for hydrologic models , 2001 .

[22]  Stefania Tamea,et al.  Verification tools for probabilistic forecasts of continuous hydrological variables , 2006 .

[23]  J. Hadamard.  Sur les problemes aux derive espartielles et leur signification physique , 1902 .

[24]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[25]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 2. Application , 2006 .

[26]  A. Montanari,et al.  Uncertainty in river discharge observations: a quantitative analysis , 2009 .

[27]  John Doherty,et al.  Efficient nonlinear predictive error variance for highly parameterized models , 2006 .

[28]  Michael Goldstein,et al.  Reified Bayesian modelling and inference for physical systems , 2009 .

[29]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory , 2006 .

[30]  Peter C. Young,et al.  DATA-BASED MECHANISTIC MODELLING OF ENVIRONMENTAL SYSTEMS , 2001 .

[31]  Jery R. Stedinger,et al.  Appraisal of the generalized likelihood uncertainty estimation (GLUE) method , 2008 .

[32]  George Kuczera,et al.  Bayesian total error analysis for hydrologic models: Markov chain Monte Carlo methods to evaluate the posterior distribution , 2007 .

[33]  George Kuczera,et al.  Comment on “An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction” by Newsha K. Ajami et al. , 2009 .

[34]  Peter Reichert,et al.  Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters , 2009 .

[35]  George Kuczera,et al.  Characterizing Errors in Areal Rainfall Estimates: Application to Uncertainty Quantification and Decomposition in Hydrologic Modelling , 2009 .

[36]  R. T. Clarke,et al.  The use of Bayesian methods for fitting rating curves, with case studies , 2005 .

[37]  Francesco Dottori,et al.  A dynamic rating curve approach to indirect discharge measurement , 2009 .

[38]  David Huard,et al.  Calibration of hydrological model GR2M using Bayesian uncertainty analysis , 2008 .

[39]  Alberto Montanari,et al.  What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology , 2007 .

[40]  George Kuczera,et al.  Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm , 1998 .

[41]  George Kuczera,et al.  Semidistributed hydrological modeling: A “saturation path” perspective on TOPMODEL and VIC , 2003 .

[42]  Amilcar Soares,et al.  Stochastic environmental research risk assessment , 2007 .

[43]  George Kuczera,et al.  Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis , 2009 .

[44]  A. Brath,et al.  A stochastic approach for assessing the uncertainty of rainfall‐runoff simulations , 2004 .

[45]  Jeroen P. van der Sluijs,et al.  A framework for dealing with uncertainty due to model structure error , 2004 .

[46]  F. Atger,et al.  The Skill of Ensemble Prediction Systems , 1999 .

[47]  C. Perrin,et al.  Improvement of a parsimonious model for streamflow simulation , 2003 .

[48]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[49]  A. Gelfand,et al.  Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models , 1999 .

[50]  Thibault Mathevet,et al.  Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models , 2006 .

[51]  Lucy Marshall,et al.  Towards dynamic catchment modelling: a Bayesian hierarchical mixtures of experts framework , 2007 .

[52]  P. Mantovan,et al.  Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology , 2006 .

[53]  Teresa Alpuim,et al.  Spatiotemporal models in the estimation of area precipitation , 2005 .

[54]  George Kuczera,et al.  Effect of rainfall errors on accuracy of design flood estimates , 1992 .

[55]  H. Gupta,et al.  Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation , 2009 .

[56]  Hubert H. G. Savenije,et al.  Learning from model improvement: On the contribution of complementary data to process understanding , 2008 .

[57]  J. Stedinger,et al.  Appraisal of the generalized likelihood uncertainty estimation (GLUE) method , 2008 .

[58]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[59]  Asaad Y. Shamseldin,et al.  Development of a possibilistic method for the evaluation of predictive uncertainty in rainfall‐runoff modeling , 2007 .