Estimating the Uncertainty of Hydrological Predictions through Data-Driven Resampling Techniques

AbstractEstimating the uncertainty of hydrological models remains a relevant challenge in applied hydrology, mostly because it is not easy to parameterize the complex structure of hydrological model errors. A nonparametric technique is proposed as an alternative to parametric error models to estimate the uncertainty of hydrological predictions. Within this approach, the above uncertainty is assumed to depend on input data uncertainty, parameter uncertainty and model error, where the latter aggregates all sources of uncertainty that are not considered explicitly. Errors of hydrological models are simulated by resampling from their past realizations using a nearest neighbor approach, therefore avoiding a formal description of their statistical properties. The approach is tested using synthetic data which refer to the case study located in Italy. The results are compared with those obtained using a formal statistical technique (meta-Gaussian approach) from the same case study. Our findings prove that the nea...

[1]  M. Hipsey,et al.  “Panta Rhei—Everything Flows”: Change in hydrology and society—The IAHS Scientific Decade 2013–2022 , 2013 .

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

[3]  Dmitri Kavetski,et al.  Pursuing the method of multiple working hypotheses for hydrological modeling , 2011 .

[4]  Francesca Pianosi,et al.  Dynamic modeling of predictive uncertainty by regression on absolute errors , 2012 .

[5]  Keith Beven,et al.  On red herrings and real herrings: disinformation and information in hydrological inference , 2011 .

[6]  W. Bastiaanssen,et al.  Constraining model parameters on remotely sensed evaporation: Justification for distribution in ungauged basins? , 2008 .

[7]  Alberto Montanari,et al.  Uncertainty of Hydrological Predictions , 2011 .

[8]  Ralf Sander PANTA RHEI – “EVERYTHING FLOWS”Renewable energy sculpture , 2016 .

[9]  Murugesu Sivapalan,et al.  ON THE REPRESENTATIVE ELEMENTARY AREA (REA) CONCEPT AND ITS UTILITY FOR DISTRIBUTED RAINFALL-RUNOFF MODELLING , 1995 .

[10]  Marilyn A. Brown,et al.  Machine learning approaches for estimating commercial building energy consumption , 2017 .

[11]  Dimitri Solomatine,et al.  A novel approach to parameter uncertainty analysis of hydrological models using neural networks , 2009 .

[12]  Florian Pappenberger,et al.  Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system , 2011 .

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

[14]  J. Vrugt,et al.  A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors , 2010 .

[15]  Andrew W. Moore,et al.  An Investigation of Practical Approximate Nearest Neighbor Algorithms , 2004, NIPS.

[16]  Maya R. Gupta,et al.  Weighted Nearest Neighbor Classifiers and First-order Error , 2009 .

[17]  J. Bertrand-Krajewski,et al.  Separately accounting for uncertainties in rainfall and runoff: Calibration of event‐based conceptual hydrological models in small urban catchments using Bayesian method , 2013 .

[18]  Bennett L. Fox Estimation and Simulation , 1978 .

[19]  R. Mantilla,et al.  Impact of radar‐rainfall error structure on estimated flood magnitude across scales: An investigation based on a parsimonious distributed hydrological model , 2012 .

[20]  Florian Pappenberger,et al.  Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions , 2010 .

[21]  Paul S. P. Cowpertwait,et al.  A generalized spatial-temporal model of rainfall based on a clustered point process , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[22]  Demetris Koutsoyiannis,et al.  Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods / Prévision du débit du Nil à moyen terme: une comparaison de méthodes stochastiques et déterministes , 2008 .

[23]  M. Clark,et al.  Probabilistic Quantitative Precipitation Estimation in Complex Terrain , 2005 .

[24]  Yasin Abbasi-Yadkori,et al.  Fast Approximate Nearest-Neighbor Search with k-Nearest Neighbor Graph , 2011, IJCAI.

[25]  Alberto Montanari,et al.  Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall‐runoff simulations , 2005 .

[26]  Jasper A. Vrugt,et al.  UvA-DARE ( Digital Academic Repository ) DREAM ( D ) : An adaptive Markov chain Monte Carlo simulation algorithm to solve discrete , noncontinuous , and combinatorial posterior parameter estimation problems , 2011 .

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

[28]  Jim Freer,et al.  Towards a limits of acceptability approach to the calibration of hydrological models : Extending observation error , 2009 .

[29]  George Kuczera,et al.  'Calibrate it twice': A simple resampling method for incorporating parameter uncertainty in stochastic data generation , 2009 .

[30]  John Langford,et al.  Cover trees for nearest neighbor , 2006, ICML.

[31]  A. Western,et al.  Characteristic space scales and timescales in hydrology , 2003 .

[32]  Jim Freer,et al.  Ensemble evaluation of hydrological model hypotheses , 2010 .

[33]  Hubert H. G. Savenije,et al.  On the calibration of hydrological models in ungauged basins: A framework for integrating hard and soft hydrological information , 2009 .

[34]  Ming Ye,et al.  Towards a comprehensive assessment of model structural adequacy , 2012 .

[35]  Martyn P. Clark,et al.  Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models , 2008 .

[36]  Keith Beven,et al.  Preferential flows and travel time distributions: defining adequate hypothesis tests for hydrological process models , 2010 .

[37]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[38]  P. Reichert,et al.  Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference , 2007 .

[39]  Demetris Koutsoyiannis,et al.  Hydrology and change , 2013 .

[40]  Keith Beven,et al.  Causal models as multiple working hypotheses about environmental processes , 2012 .

[41]  Armando Brath,et al.  Neural networks and non-parametric methods for improving real-time flood forecasting through conceptual hydrological models , 2002 .

[42]  Alberto Montanari,et al.  Inferring the flood frequency distribution for an ungauged basin using a spatially distributed rainfall-runoff model , 2008 .

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

[44]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[45]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[46]  Keith Beven,et al.  Concepts of Information Content and Likelihood in Parameter Calibration for Hydrological Simulation Models , 2014 .

[47]  H. McMillan Referee Interactive comment on “Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models” by A. E. Sikorska et al , 2012 .

[48]  Keith Beven,et al.  Comment on “Pursuing the method of multiple working hypotheses for hydrological modeling” by P. Clark et al. , 2012 .

[49]  M. Franchini Use of a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models , 1996 .

[50]  Alberto Montanari,et al.  Estimating the uncertainty of hydrological forecasts: A statistical approach , 2008 .

[51]  P. E. O'connell,et al.  River flow forecasting through conceptual models part III - The Ray catchment at Grendon Underwood , 1970 .

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

[53]  Keith Beven,et al.  Hydrological model calibration using a short period of observations , 2012 .

[54]  P. Kyriakidis,et al.  Effects of uncertain topographic input data on two‐dimensional flow modeling in a gravel‐bed river , 2011 .

[55]  Giuliano Di Baldassarre,et al.  Corrigendum to data errors and hydrological modelling: The role of model structure to propagate observation uncertainty [Advances in Water Resources 51 (2013) 498–505, DOI: 10.1016/j.advwatres.2012.09.007] , 2013 .

[56]  D. Boyle Multicriteria Calibration of Hydrologic Models , 2013 .

[57]  Hubert H. G. Savenije,et al.  Comparison of two model approaches in the Zambezi river basin with regard to model reliability and identifiability , 2005 .

[58]  Charles Obled,et al.  Uncertainty in flood forecasting: a French case study , 1994 .

[59]  M. Taqqu,et al.  Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation , 1997 .

[60]  Andreas Scheidegger,et al.  Considering rating curve uncertainty in water level predictions , 2013 .

[61]  Dmitri Kavetski,et al.  Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models , 2011 .

[62]  Jasper A Vrugt,et al.  Improved evolutionary optimization from genetically adaptive multimethod search , 2007, Proceedings of the National Academy of Sciences.

[63]  Armando Brath,et al.  Real-time flood forecasting via combined use of conceptual and stochastic models , 1999 .

[64]  Demetris Koutsoyiannis,et al.  A blueprint for process‐based modeling of uncertain hydrological systems , 2012 .

[65]  Andreas Scheidegger,et al.  Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models , 2011 .

[66]  Hoshin Vijai Gupta,et al.  Improving robustness of hydrologic parameter estimation by the use of moving block bootstrap resampling , 2010 .

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

[68]  S. Yakowitz,et al.  Rainfall-runoff forecasting methods, old and new , 1987 .

[69]  Hoshin Vijai Gupta,et al.  How Bayesian data assimilation can be used to estimate the mathematical structure of a model , 2010 .

[70]  Durga L. Shrestha,et al.  Machine learning approaches for estimation of prediction interval for the model output , 2006, Neural Networks.

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

[72]  Demetris Koutsoyiannis,et al.  A Blueprint for Process-Based Modeling of , 2012 .

[73]  Pablo A. Mendoza,et al.  Uncertainty in flood forecasting: A distributed modeling approach in a sparse data catchment , 2012 .

[74]  Karsten H. Jensen,et al.  Statistical analysis of the impact of radar rainfall uncertainties on water resources modeling , 2011 .

[75]  Giuliano Di Baldassarre,et al.  Data errors and hydrological modelling: The role of model structure to propagate observation uncertainty , 2013 .

[76]  S. Yakowitz,et al.  Nearest‐neighbor methods for nonparametric rainfall‐runoff forecasting , 1987 .

[77]  M. J. Hall,et al.  Rainfall-Runoff Modelling , 2004 .

[78]  S. P. Neuman,et al.  Maximum likelihood Bayesian averaging of uncertain model predictions , 2003 .

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

[80]  H. Gupta,et al.  Correcting the mathematical structure of a hydrological model via Bayesian data assimilation , 2011 .

[81]  Qingyun Duan,et al.  An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction , 2006 .

[82]  L. S. Pereira,et al.  Crop evapotranspiration : guidelines for computing crop water requirements , 1998 .