One decade of multi-objective calibration approaches in hydrological modelling: a review

Abstract One decade after the first publications on multi-objective calibration of hydrological models, we summarize the experience gained so far by underlining the key perspectives offered by such approaches to improve parameter identification. After reviewing the fundamentals of vector optimization theory and the algorithmic issues, we link the multi-criteria calibration approach with the concepts of uncertainty and equifinality. Specifically, the multi-criteria framework enables recognition and handling of errors and uncertainties, and detection of prominent behavioural solutions with acceptable trade-offs. Particularly in models of complex parameterization, a multi-objective approach becomes essential for improving the identifiability of parameters and augmenting the information contained in calibration by means of both multi-response measurements and empirical metrics (“soft” data), which account for the hydrological expertise. Based on the literature review, we also provide alternative techniques for dealing with conflicting and non-commeasurable criteria, and hybrid strategies to utilize the information gained towards identifying promising compromise solutions that ensure consistent and reliable calibrations. Citation Efstratiadis, A. & Koutsoyiannis, D. (2010) One decade of multi-objective calibration approaches in hydrological modelling: a review. Hydrol. Sci. J. 55(1), 58–78.

[1]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[2]  S. Sorooshian,et al.  Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system , 2004, Journal of Hydrology.

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

[4]  Günter Blöschl,et al.  Uncertainty and multiple objective calibration in regional water balance modelling: case study in 320 Austrian catchments , 2007 .

[5]  Jeffrey G. Arnold,et al.  Formulation of a hybrid calibration approach for a physically based distributed model with NEXRAD data input , 2004 .

[6]  J. Refsgaard.  Parameterisation, calibration and validation of distributed hydrological models , 1997 .

[7]  Remegio Confesor,et al.  Automatic Calibration of Hydrologic Models With Multi‐Objective Evolutionary Algorithm and Pareto Optimization 1 , 2007 .

[8]  K. Beven,et al.  Shenandoah Watershed Study: Calibration of a Topography‐Based, Variable Contributing Area Hydrological Model to a Small Forested Catchment , 1985 .

[9]  Henrik Madsen,et al.  Comparison of different automated strategies for calibration of rainfall-runoff models , 2002 .

[10]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[11]  Soroosh Sorooshian,et al.  Multi-objective global optimization for hydrologic models , 1998 .

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

[13]  Henrik Madsen,et al.  Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling , 2008 .

[14]  M. H. Diskin,et al.  A procedure for the selection of objective functions for hydrologic simulation models , 1977 .

[15]  Jeffrey J. McDonnell,et al.  On the dialog between experimentalist and modeler in catchment hydrology: Use of soft data for multicriteria model calibration , 2002 .

[16]  Keith Beven,et al.  Multi-objective conditioning of a simple SVAT model. , 1999 .

[17]  Ezio Todini,et al.  Comment on: ‘On undermining the science?’ by Keith Beven , 2007 .

[18]  George Kuczera,et al.  The quest for more powerful validation of conceptual catchment models , 1997 .

[19]  Demetris Koutsoyiannis,et al.  Fitting Hydrological Models on Multiple Responses Using the Multiobjective Evolutionary Annealing-Simplex Approach , 2009 .

[20]  Stein Beldring,et al.  Multi-criteria validation of a precipitation–runoff model , 2002 .

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

[22]  S. Sorooshian,et al.  Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data , 1996 .

[23]  J. Seibert.  Multi-criteria calibration of a conceptual runoff model using a genetic algorithm , 2000 .

[24]  J. E. Freera,et al.  Constraining dynamic TOPMODEL responses for imprecise water table information using fuzzy rule based performance measures , 2004 .

[25]  Kolbjørn Engeland,et al.  Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique , 2005 .

[26]  Misgana K. Muleta,et al.  Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model , 2005 .

[27]  S. Ranjithan,et al.  Using genetic algorithms to solve a multiple objective groundwater pollution containment problem , 1994 .

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

[29]  Keith Beven,et al.  Changing ideas in hydrology — The case of physically-based models , 1989 .

[30]  Keith Beven,et al.  Multi-period and multi-criteria model conditioning to reduce prediction uncertainty in an application of TOPMODEL within the GLUE framework , 2007 .

[31]  F. Pappenberger,et al.  Ignorance is bliss: Or seven reasons not to use uncertainty analysis , 2006 .

[32]  Carlos A. Coello Coello,et al.  Recent Trends in Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[33]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[34]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[35]  Weng Tat Chan,et al.  Derivation of Pareto front with genetic algorithm and neural network , 2001 .

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

[37]  Keith Beven,et al.  Using internal catchment information to reduce the uncertainty of discharge and baseflow predictions , 2007 .

[38]  Etienne Leblois,et al.  Multi-objective regional modelling , 2006 .

[39]  K. Bevenb,et al.  Use of spatially distributed water table observations to constrain uncertainty in a rainfall – runoff model , 1998 .

[40]  Carlos A. Coello Coello,et al.  A Micro-Genetic Algorithm for Multiobjective Optimization , 2001, EMO.

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

[42]  Bellie Sivakumar,et al.  Undermining the science or undermining Nature? , 2008 .

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

[44]  Stuart Hamilton.  Just say NO to equifinality , 2007 .

[45]  J. Harlin.  Development of a Process Oriented Calibration Scheme for the HBV Hydrological Model , 1991 .

[46]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[47]  D KnowlesJoshua,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000 .

[48]  J. Eheart,et al.  Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem , 1995 .

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

[50]  Chuntian Cheng,et al.  Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure , 2006 .

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

[52]  Keith Beven,et al.  A comparison of non-linear least square and GLUE for model calibration and uncertainty estimation for pesticide transport in soils , 2006 .

[53]  John W. Nicklow,et al.  Multi-objective automatic calibration of SWAT using NSGA-II , 2007 .

[54]  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 .

[55]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[56]  George Kuczera,et al.  Assessment of hydrologic parameter uncertainty and the worth of multiresponse data , 1998 .

[57]  Gerrit Schoups,et al.  Multi-objective calibration of a surface water-groundwater flow model in an irrigated agricultural region: Yaqui Valley, Sonora, Mexico , 2005 .

[58]  Hoshin Vijai Gupta,et al.  Model identification for hydrological forecasting under uncertainty , 2005 .

[59]  Anthony J. Jakeman,et al.  Performance of conceptual rainfall‐runoff models in low‐yielding ephemeral catchments , 1997 .

[60]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[61]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[62]  Keith Beven,et al.  On constraining TOPMODEL hydrograph simulations using partial saturated area information , 2002 .

[63]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[64]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[65]  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 .

[66]  Henrik Madsen,et al.  Incorporating multiple observations for distributed hydrologic model calibration : An approach using a multi-objective evolutionary algorithm and clustering , 2008 .

[67]  Keith Beven,et al.  Prophecy, reality and uncertainty in distributed hydrological modelling , 1993 .

[68]  Patrick Willems,et al.  Parameter estimation in semi‐distributed hydrological catchment modelling using a multi‐criteria objective function , 2007 .

[69]  Henrik Madsen,et al.  Concepts of Hydrologic Modeling , 2006 .

[70]  Demetris Koutsoyiannis,et al.  HYDROGEIOS: a semi-distributed GIS-based hydrological model for modified river basins , 2007 .

[71]  Pao-Shan Yu,et al.  Fuzzy multi-objective function for rainfall-runoff model calibration , 2000 .

[72]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[73]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

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

[75]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

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

[77]  J. Doherty,et al.  The cost of uniqueness in groundwater model calibration , 2006 .

[78]  Yong Tang,et al.  Parallelization strategies for rapid and robust evolutionary multiobjective optimization in water resources applications , 2007 .

[79]  S. Sorooshian,et al.  Uniqueness and observability of conceptual rainfall‐runoff model parameters: The percolation process examined , 1983 .

[80]  Keith Beven,et al.  Multi-objective parameter conditioning of a three-source wheat canopy model , 2004 .

[81]  Henrik Madsen,et al.  Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. , 2000 .

[82]  Roger Moussa,et al.  Comparison of different multi-objective calibration criteria using a conceptual rainfall-runoff model of flood events. , 2007 .

[83]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[84]  Chuntian Cheng,et al.  Multiple criteria rainfall–runoff model calibration using a parallel genetic algorithm in a cluster of computers / Calage multi-critères en modélisation pluie–débit par un algorithme génétique parallèle mis en œuvre par une grappe d'ordinateurs , 2005 .

[85]  R. Hunt,et al.  Are Models Too Simple? Arguments for Increased Parameterization , 2007, Ground water.

[86]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods , 2000 .

[87]  David E. Goldberg,et al.  Simplifying multiobjective optimization: An automated design methodology for the nondominated sorted genetic algorithm‐II , 2003 .

[88]  Keith Beven,et al.  Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving dam safety assessment in a large basin in the Czech Republic , 2004 .

[89]  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 .

[90]  Chuntian Cheng,et al.  Combining a fuzzy optimal model with a genetic algorithm to solve multi-objective rainfall–runoff model calibration , 2002 .

[91]  Dragan Savic,et al.  WATER NETWORK REHABILITATION WITH STRUCTURED MESSY GENETIC ALGORITHM , 1997 .

[92]  Harald Kunstmann,et al.  Inverse distributed hydrological modelling of Alpine catchments , 2005 .

[93]  Patrick M. Reed,et al.  How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration , 2005 .

[94]  Thibault Mathevet,et al.  What is really undermining hydrologic science today? , 2007 .

[95]  K. Beven.  Rainfall-Runoff Modelling: The Primer , 2012 .

[96]  Demetris Koutsoyiannis,et al.  Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows / Calage d’un modèle semi-distribué pour la simulation conjointe d’écoulements superficiels et souterrains , 2004 .

[97]  Hubert H. G. Savenije,et al.  Soft combination of local models in a multi-objective framework , 2007 .

[98]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[99]  N. J. DE VOS,et al.  Multi-objective performance comparison of an artificial neural network and a conceptual rainfall—runoff model , 2007 .

[100]  L. Jain,et al.  Evolutionary multiobjective optimization : theoretical advances and applications , 2005 .

[101]  John Doherty,et al.  Comparison of hydrologic calibration of HSPF using automatic and manual methods , 2007 .

[102]  Demetris Koutsoyiannis,et al.  On the practical use of multiobjective optimisation in hydrological model calibration , 2009 .

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

[104]  Wesley W. Wallender,et al.  Multi-criteria optimization of a regional spatially-distributed subsurface water flow model , 2005 .

[105]  J. D. Schaffer,et al.  Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition) , 1984 .

[106]  Luis A. Bastidas,et al.  Multicriteria parameter estimation for models of stream chemical composition , 2002 .

[107]  Jeffrey Horn,et al.  Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA) , 2002 .

[108]  H. Madsen,et al.  Multiobjective calibration with Pareto preference ordering: An application to rainfall‐runoff model calibration , 2005 .

[109]  E. Todini.  Hydrological catchment modelling: past, present and future , 2007 .

[110]  S. Uhlenbrook,et al.  Prediction uncertainty of conceptual rainfall-runoff models caused by problems in identifying model parameters and structure , 1999 .

[111]  Henrik Madsen,et al.  Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives , 2003 .

[112]  David R. Dawdy,et al.  Mathematical Models of Catchment Behavior , 1965 .

[113]  S. Sorooshian,et al.  Effective and efficient algorithm for multiobjective optimization of hydrologic models , 2003 .

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

[115]  Florian Pappenberger,et al.  Grasping the unavoidable subjectivity in calibration of flood inundation models: A vulnerability weighted approach , 2007 .

[116]  Hubert H. G. Savenije,et al.  A comparison of alternative multiobjective calibration strategies for hydrological modeling , 2007 .

[117]  Nanée Chahinian,et al.  Distributed hydrological modelling of a Mediterranean mountainous catchment – Model construction and multi-site validation , 2007 .

[118]  A. Jakeman,et al.  How much complexity is warranted in a rainfall‐runoff model? , 1993 .

[119]  C. Perrin,et al.  Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments , 2001 .

[120]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

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