Assessment of the different sources of uncertainty in a SWAT model of the River Senne (Belgium)

Although rainfall input uncertainties are widely identified as being a key factor in hydrological models, the rainfall uncertainty is typically not included in the parameter identification and model output uncertainty analysis of complex distributed models such as SWAT and in maritime climate zones. This paper presents a methodology to assess the uncertainty of semi-distributed hydrological models by including, in addition to a list of model parameters, additional unknown factors in the calibration algorithm to account for the rainfall uncertainty (using multiplication factors for each separately identified rainfall event) and for the heteroscedastic nature of the errors of the stream flow. We used the Differential Evolution Adaptive Metropolis algorithm (DREAM(zs)) to infer the parameter posterior distributions and the output uncertainties of a SWAT model of the River Senne (Belgium). Explicitly considering heteroscedasticity and rainfall uncertainty leads to more realistic parameter values, better representation of water balance components and prediction uncertainty intervals. Adapted a method to incorporate rainfall uncertainty in distributed hydrologic models.Considered different sources of uncertainty in semi-distributed hydrologic model.Assessed impacts of different sources of uncertainty on model parameter estimations.Accounting for different sources of uncertainty leads to more realistic parameter values.Explicitly treating different uncertainty sources improves water balance representation.

[1]  Jasper A. Vrugt,et al.  Significant variation in vegetation characteristics and dynamics from ecohydrological optimality of net carbon profit , 2009 .

[2]  Peter A. Vanrolleghem,et al.  Uncertainty in the environmental modelling process - A framework and guidance , 2007, Environ. Model. Softw..

[3]  W. Green Studies in soil physics : I. The flow of air and water through soils , 1911 .

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

[5]  B. Bates,et al.  A Markov Chain Monte Carlo Scheme for parameter estimation and inference in conceptual rainfall‐runoff modeling , 2001 .

[6]  S. Sorooshian,et al.  Stochastic parameter estimation procedures for hydrologie rainfall‐runoff models: Correlated and heteroscedastic error cases , 1980 .

[7]  Xiuying Wang,et al.  A framework for propagation of uncertainty contributed by parameterization, input data, model structure, and calibration/validation data in watershed modeling , 2014, Environ. Model. Softw..

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

[9]  John R. Williams,et al.  Flood Routing With Variable Travel Time or Variable Storage Coefficients , 1969 .

[10]  S. Sorooshian,et al.  Evaluation of Maximum Likelihood Parameter estimation techniques for conceptual rainfall‐runoff models: Influence of calibration data variability and length on model credibility , 1983 .

[11]  Willy Bauwens,et al.  Sobol' sensitivity analysis of a complex environmental model , 2011, Environ. Model. Softw..

[12]  Jasper A. Vrugt,et al.  Semi-distributed parameter optimization and uncertainty assessment for large-scale streamflow simulation using global optimization / Optimisation de paramètres semi-distribués et évaluation de l'incertitude pour la simulation de débits à grande échelle par l'utilisation d'une optimisation globale , 2008 .

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

[14]  Alessio Domeneghetti,et al.  Assessing rating-curve uncertainty and its effects on hydraulic model calibration , 2012 .

[15]  Michael Herbst,et al.  UvA-DARE ( Digital Academic Repository ) Inverse modelling of in situ soil water dynamics : investigating the effect of different prior distributions of the soil hydraulic parameters , 2011 .

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

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

[18]  Q. Kang,et al.  Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality , 2010 .

[19]  Willy Bauwens,et al.  Multi-variable sensitivity and identifiability analysis for a complex environmental model in view of integrated water quantity and water quality modeling. , 2012, Water science and technology : a journal of the International Association on Water Pollution Research.

[20]  Qi Zhang,et al.  Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model , 2010 .

[21]  András Bárdossy,et al.  Generic error model for calibration and uncertainty estimation of hydrological models , 2008 .

[22]  W. Green,et al.  Studies on Soil Phyics. , 1911, The Journal of Agricultural Science.

[23]  D. Higdon,et al.  Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling , 2009 .

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

[25]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[26]  Martyn P. Clark,et al.  Multi‐objective calibration of forecast ensembles using Bayesian model averaging , 2006 .

[27]  George H. Hargreaves,et al.  Agricultural Benefits for Senegal River Basin , 1985 .

[28]  A van Griensven,et al.  Sensitivity analysis and auto-calibration of an integral dynamic model for river water quality. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[29]  Raghavan Srinivasan,et al.  SWAT: Model Use, Calibration, and Validation , 2012 .

[30]  Jasper A. Vrugt,et al.  High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM(ZS) and high‐performance computing , 2012 .

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

[32]  Keming Yu,et al.  Bayesian Mode Regression , 2012, 1208.0579.

[33]  K. Beven,et al.  Bayesian Estimation of Uncertainty in Runoff Prediction and the Value of Data: An Application of the GLUE Approach , 1996 .

[34]  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 .

[35]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

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

[37]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[38]  V. T. Chow Open-channel hydraulics , 1959 .

[39]  Henrik Madsen,et al.  Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov chain Monte Carlo sampling , 2006 .

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

[41]  Bruce A. Robinson,et al.  Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging , 2007 .

[42]  Jimmy R. Williams,et al.  Continuous-time water and sediment-routing model for large basins , 1995 .

[43]  Cajo J. F. ter Braak,et al.  A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces , 2006, Stat. Comput..

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

[45]  Impacts of Uncertain Flow Data on Rainfall-Runoff Model Calibration and Discharge Predictions in a Mobile-Bed River. Paper Number H43D-1030 , 2008 .

[46]  Curtis L. Larson,et al.  Modeling infiltration during a steady rain , 1973 .

[47]  C. Priestley,et al.  On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters , 1972 .

[48]  George Kuczera,et al.  Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation , 2011 .

[49]  Cajo J. F. ter Braak,et al.  Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? , 2009 .

[50]  Jeffrey G. Arnold,et al.  Soil and Water Assessment Tool Theoretical Documentation Version 2009 , 2011 .

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

[52]  Alain Dassargues,et al.  Assessment of conceptual model uncertainty for the regional aquifer Pampa del Tamarugal – North Chile , 2009 .

[53]  A. Griensven,et al.  Integrated Water Quality Modelling of the River Zenne (Belgium) Using OpenMI , 2014 .

[54]  Eric Laloy,et al.  Mass conservative three‐dimensional water tracer distribution from Markov chain Monte Carlo inversion of time‐lapse ground‐penetrating radar data , 2012 .

[55]  Johan Alexander Huisman,et al.  Bayesian model averaging using particle filtering and Gaussian mixture modeling: Theory, concepts, and simulation experiments , 2012 .

[56]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

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

[58]  John R. Williams,et al.  LARGE AREA HYDROLOGIC MODELING AND ASSESSMENT PART I: MODEL DEVELOPMENT 1 , 1998 .

[59]  J. Monteith Evaporation and environment. , 1965, Symposia of the Society for Experimental Biology.

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

[61]  Budiman Minasny,et al.  Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation , 2011 .

[62]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[63]  Eric Laloy,et al.  Parameter optimization and uncertainty analysis for plot-scale continuous modeling of runoff using a formal Bayesian approach. , 2010 .

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

[65]  David D. Bosch,et al.  PROBLEMS AND POTENTIAL OF AUTOCALIBRATING A HYDROLOGIC MODEL , 2005 .

[66]  Jasper A. Vrugt,et al.  Hydrologic data assimilation using particle Markov chain Monte Carlo simulation: Theory, concepts and applications (online first) , 2012 .

[67]  R. Strawderman,et al.  Bayesian estimation of input parameters of a nitrogen cycle model applied to a forested reference watershed, Hubbard Brook Watershed Six , 2005 .

[68]  W. Bouten,et al.  Towards reduced uncertainty in catchment nitrogen modelling: quantifying the effect of field observation uncertainty on model calibration , 2004 .

[69]  K. Abbaspour,et al.  Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT , 2007 .

[70]  Mark Thyer,et al.  Goulburn River experimental catchment data set , 2007 .

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

[72]  Martin Volk,et al.  Using precipitation data ensemble for uncertainty analysis in SWAT streamflow simulation , 2012 .

[73]  Patrick Willems,et al.  A time series tool to support the multi-criteria performance evaluation of rainfall-runoff models , 2009, Environ. Model. Softw..

[74]  J. Vrugt,et al.  Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models , 2010 .

[75]  George Kuczera,et al.  Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors , 2010 .

[76]  R. Srinivasan,et al.  A global sensitivity analysis tool for the parameters of multi-variable catchment models , 2006 .

[77]  Steven A. Margulis,et al.  Characterizing parameter sensitivity and uncertainty for a snow model across hydroclimatic regimes , 2011 .

[78]  Jing Yang,et al.  Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China , 2008 .