Multi-objective calibration of a reservoir water quality model in aggregation and non-dominated sorting approaches

Numerical water quality models are developed to predict contaminant fate and transport in receiving waters such as reservoirs and lakes. They can be helpful tools for water resource management. The objective of this study is to calibrate a water quality model which was set up to simulate the water quality conditions of Pepacton Reservoir, Downsville, New York, USA, using an aggregation hybrid genetic algorithm (AHGA) and a non-dominated sorting hybrid genetic algorithm (NSHGA). Both AHGA and NSHGA use a hybrid genetic algorithm (HGA) as optimization engines but are different in fitness assignment. In the AHGA, a weighted sum of scaled simulation errors is designed as an overall objective function to measure the fitness of solutions (i.e., parameter values). In the NSHGA, a method based on non-dominated sorting and Euclidean distances is proposed to calculate the dummy fitness of solutions. In addition, this study also compares the AHGA and the NSHGA. The purpose of this comparison is to determine whether the objective function values (i.e., simulation errors) and simulated results obtained by the AHGA and the NSHGA are significantly different from each other. The results show that the objective function values from the two HGAs are good compromises between all objective functions, and the calibrated model results match the observed data reasonably well and are comparable to other studies, supporting and justifying the use of multi-objective calibration.

[1]  J. R. Romero,et al.  One- and three-dimensional biogeochemical simulations of two differing reservoirs , 2004 .

[2]  Anne Ng,et al.  Selection of genetic algorithm operators for river water quality model calibration , 2003 .

[3]  Aysegul Aksoy,et al.  Calibration and Verification of QUAL2E Using Genetic Algorithm Optimization , 2007 .

[4]  Carlos E. Ruiz,et al.  Using spatially distributed parameters and multi‐response objective functions to solve parameterization of complex applications of semi‐distributed hydrological models , 2008 .

[5]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[6]  Martin T. Auer,et al.  Development and Testing of a Nutrient-Phytoplankto Model for Cannonsville Reservoir , 1998 .

[7]  Francisco J. Rueda,et al.  Propagation of uncertainty in ecological models of reservoirs: From physical to population dynamic predictions , 2012 .

[8]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[9]  Scott A. Wells,et al.  CE-QUAL-W2: A Two-dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 3.5 , 2006 .

[10]  Heinz G. Stefan,et al.  Propagation of uncertainty due to variable meteorological forcing in lake temperature models , 1992 .

[11]  Donald C. Pierson,et al.  Identifying parameter sensitivity in a water quality model of a reservoir , 2012 .

[12]  Avi Ostfeld,et al.  A hybrid genetic—instance based learning algorithm for CE-QUAL-W2 calibration , 2005 .

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

[14]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

[15]  Raymond M. Wright,et al.  Dissolved oxygen modeling of the Blackstone River (northeastern United States) , 1998 .

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

[17]  John Doherty,et al.  Efficient accommodation of local minima in watershed model calibration , 2006 .

[18]  D. McKinney,et al.  Genetic algorithm solution of groundwater management models , 1994 .

[19]  A. van Griensven,et al.  Integral water quality modelling of catchments. , 2001, Water science and technology : a journal of the International Association on Water Pollution Research.

[20]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

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

[22]  Eligius M. T. Hendrix,et al.  A method for robust calibration of ecological models under different types of uncertainty , 1994 .

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

[24]  Patrick M. Reed,et al.  When are multiobjective calibration trade‐offs in hydrologic models meaningful? , 2012 .

[25]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2004 .

[26]  Arturo A. Keller,et al.  Uncertainty assessment in watershed‐scale water quality modeling and management: 2. Management objectives constrained analysis of uncertainty (MOCAU) , 2007 .

[27]  Jeffrey G. Arnold,et al.  Automatic calibration of a distributed catchment model , 2001 .

[28]  Francisco J. Rueda,et al.  A calibration strategy for dynamic succession models including several phytoplankton groups , 2011, Environ. Model. Softw..

[29]  J. Doherty,et al.  A hybrid regularized inversion methodology for highly parameterized environmental models , 2005 .

[30]  Francisco J. Rueda,et al.  Pathways of river nutrients towards the euphotic zone in a deep-reservoir of small size: Uncertainty analysis , 2007 .

[31]  Arturo A. Keller,et al.  Uncertainty assessment in watershed‐scale water quality modeling and management: 1. Framework and application of generalized likelihood uncertainty estimation (GLUE) approach , 2007 .

[32]  Matthew R. Hipsey,et al.  Implementation of ecological modeling as an effective management and investigation tool: Lake Kinneret as a case study , 2009 .

[33]  Jakobus E. van Zyl,et al.  Operational Optimization of Water Distribution Systems using a Hybrid Genetic Algorithm , 2004 .

[34]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[35]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

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

[37]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[38]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[39]  Dennis Trolle,et al.  Predicting the effects of reduced external nitrogen loading on the nitrogen dynamics and ecological state of deep Lake Ravn, Denmark, using the DYRESM–CAEDYM model , 2008 .

[40]  Emmet M. Owens,et al.  Development and Testing of One-Dimensional Hydrothermal Models of Cannonsville Reservoir , 1998 .

[41]  Michael Rode,et al.  Multi-objective calibration and fuzzy preference selection of a distributed hydrological model , 2008, Environ. Model. Softw..

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

[43]  Michael Rode,et al.  Multi-objective calibration of a river water quality model—Information content of calibration data , 2007 .

[44]  Rui Zou,et al.  Robust Water Quality Model Calibration Using an Alternating Fitness Genetic Algorithm , 2004 .

[45]  David P. Hamilton,et al.  Predicting the effects of climate change on trophic status of three morphologically varying lakes: Implications for lake restoration and management , 2011, Environ. Model. Softw..

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

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

[48]  C. Ancey,et al.  An exact solution for ideal dam‐break floods on steep slopes , 2008 .

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

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

[51]  Donald C. Pierson,et al.  MODELING THE HYDROCHEMISTRY OF THE CANNONSVILLE WATERSHED WITH GENERALIZED WATERSHED LOADING FUNCTIONS (GWLF) 1 , 2002 .

[52]  Donald C. Pierson,et al.  Weather driven influences on phytoplankton succession in a shallow lake during contrasting years: Application of PROTBAS , 2007 .

[53]  K. Lindenschmidt,et al.  Structural uncertainty in a river water quality modelling system , 2007 .

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

[55]  Mark H. Houck,et al.  Automated Calibration and Use of Stream‐Quality Simulation Model , 1990 .

[56]  G. Mahinthakumar,et al.  Hybrid Genetic Algorithm—Local Search Methods for Solving Groundwater Source Identification Inverse Problems , 2005 .

[57]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[58]  Tammo S. Steenhuis,et al.  Incorporating variable source area hydrology into a curve‐number‐based watershed model , 2007 .

[59]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[60]  Y. T. Huang,et al.  A Hybrid Perturbation and Morris Approach for Identifying Sensitive Parameters in Surface Water Quality Models , 2008 .

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

[62]  C. Larson,et al.  Water Quality Modeling of Upper Mississippi River and Lake Pepin , 1995 .

[63]  Lei Liu,et al.  Multiobjective Water Quality Model Calibration Using a Hybrid Genetic Algorithm and Neural Network–Based Approach , 2010 .

[64]  George B. Arhonditsis,et al.  Eutrophication model for Lake Washington (USA) Part II-model calibration and system dynamics analysis , 2005 .

[65]  P. Reichert,et al.  Linking statistical bias description to multiobjective model calibration , 2012 .

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

[67]  A. Mulligan,et al.  Genetic Algorithms for Calibrating Water Quality Models , 1998 .

[68]  Amy B. Chan Hilton,et al.  Groundwater Remediation Design under Uncertainty Using Genetic Algorithms , 2005 .

[69]  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.

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

[71]  Donald R. F. Harleman,et al.  Hydrothermal Analysis of Lakes and Reservoirs , 1982 .

[72]  Q. J. Wang.  The Genetic Algorithm and Its Application to Calibrating Conceptual Rainfall-Runoff Models , 1991 .

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

[74]  Liang-Cheng Chang,et al.  Dynamic Optimal Groundwater Management with Inclusion of Fixed Costs , 2002 .

[75]  David E. Goldberg,et al.  Adaptive Hybrid Genetic Algorithm for Groundwater Remediation Design , 2005 .