Multi-objective calibration and fuzzy preference selection of a distributed hydrological model

Multi-objective evaluation of distributed hydrological models enables an analysis of prediction behaviour of individual sub-systems within a catchment. The aim of this paper is to demonstrate an application of multi-response, multisite calibration strategy for a distributed hydrological model, so that model limitations can be identified and subsequently improved. The study was carried out for calibration of flows from two gauging stations in a 152km^2 catchment in Elbe Basin in Germany. The multi-objective optimisation tool NSGA-II was used for the calibration of distributed hydrological modelling code WaSiM-ETH. A fuzzy set theory based methodology was formulated for selection of preferred solution from numerous Pareto solutions in four-dimensional space. The methodology consistently led to selection of the solution which is able to reasonably represent the magnitude and dynamics of streamflow hydrograph. For a reasonable simulation of water balance in the downstream gauge, overprediction of water balance in the upstream gauge was necessary. The analysis of precipitation-discharge data and geological conditions in the river channel support the possibility of flow reduction in the upstream gauge and increase in the downstream gauge. Due to this limitation in observation data, additional optimisation runs were carried out by explicitly considering the effect. This led to a significant improvement in the performance of the model. Therefore, the study provides an effective implementation of the multi-objective calibration strategy for a distributed hydrological model, which can be used for the analysis of different catchments using a combination of different objective functions.

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

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

[3]  Karl-Erich Lindenschmidt,et al.  Physically-based hydrological modelling for non-point dissolved phosphorus transport in small and medium-sized river basins / Modélisation hydrologique à bases physiques et du transport de phosphore dissous diffus en bassins versants de petite et moyenne tailles , 2004 .

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

[5]  Patrick M. Reed,et al.  A framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO) , 2007, Environ. Model. Softw..

[6]  Patrick M. Reed,et al.  Using interactive archives in evolutionary multiobjective optimization: A case study for long-term groundwater monitoring design , 2007, Environ. Model. Softw..

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

[8]  Pao-Shan Yu,et al.  Application of Fuzzy Multi-Objective Function on Reducing Groundwater Demand for Aquaculture in Land-Subsidence Areas , 2006 .

[9]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

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

[11]  Aravind Seshadri,et al.  A FAST ELITIST MULTIOBJECTIVE GENETIC ALGORITHM: NSGA-II , 2000 .

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

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

[14]  C. Konrad.  Location and timing of river-aquifer exchanges in six tributaries to the Columbia River in the Pacific Northwest of the United States , 2006 .

[15]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[16]  Dragan Savic,et al.  Incorporating spatial and temporal information for urban drainage model calibration: An approach using preference ordering genetic algorithm , 2006 .

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

[18]  S. Uhlenbrook,et al.  Multiscale calibration and validation of a conceptual rainfall-runoff model , 2000 .

[19]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[20]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[21]  Kalyanmoy Deb,et al.  Evolutionary Multi-Objective Optimization Without Additional Parameters , 2007, Parameter Setting in Evolutionary Algorithms.

[22]  D. Goldberg,et al.  A multiobjective approach to cost effective long-term groundwater monitoring using an elitist nondominated sorted genetic algorithm with historical data , 2001 .

[23]  F. Triska,et al.  Linking hyporheic flow and nitrogen cycling near the Willamette River: A large river in Oregon, USA , 2001 .

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

[25]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

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

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

[28]  Walter Boughton,et al.  Calibrations of a daily rainfall-runoff model with poor quality data , 2006, Environ. Model. Softw..

[29]  Rodger B. Grayson,et al.  Distributed parameter hydrologic modelling using vector elevation data: THALES and TAPES-C. , 1995 .

[30]  Göran Lindström,et al.  Multi‐variable parameter estimation to increase confidence in hydrological modelling , 2002 .

[31]  Guangtao Fu,et al.  Multiple objective optimal control of integrated urban wastewater systems , 2008, Environ. Model. Softw..

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

[33]  Karl-Erich Lindenschmidt,et al.  Distributed sediment and phosporus transport modeling on a medium sized catchment in central germany , 2001 .

[34]  K. Jensen,et al.  Distributed hydrological modelling of the Senegal River Basin — model construction and validation , 2001 .

[35]  D. Legates,et al.  Evaluating the use of “goodness‐of‐fit” Measures in hydrologic and hydroclimatic model validation , 1999 .

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

[37]  Taesoon Kim,et al.  Multireservoir system optimization in the Han River basin using multi‐objective genetic algorithms , 2006 .

[38]  Jörg Schulla,et al.  Hydrologische Modellierung von Flussgebieten zur Abschätzung der Folgen von Klimaänderungen , 1997 .

[39]  Dixon H. Landers,et al.  Transient storage and hyporheic flow along the Willamette River, Oregon: Field measurements and model estimates , 2001 .

[40]  Lucien Duckstein,et al.  Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems , 1995 .

[41]  Franz Nestmann,et al.  Analysis and propagation of uncertainties due to the stage–discharge relationship: a fuzzy set approach , 2007 .

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

[43]  Michael Rode,et al.  A hybrid deterministic-fuzzy rule based model for catchment scale nitrate dynamics , 2007 .

[44]  Francesc Gallart,et al.  Sensitivity analysis and multi‐response, multi‐criteria evaluation of a physically based distributed model , 2002 .