Bayesian model averaging assessment on groundwater management under model structure uncertainty

This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the “1,500-foot” sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used.

[1]  Jesús Carrera,et al.  Optimal design of measures to correct seawater intrusion , 2006 .

[2]  Yunjung Hyun,et al.  Model Identification Criteria for Inverse Estimation of Hydraulic Parameters , 1998 .

[3]  S. Gorelick,et al.  Optimal groundwater quality management under parameter uncertainty , 1987 .

[4]  S. P. Neuman,et al.  Estimation of aquifer parameters under transient and steady-state conditions: 2 , 1986 .

[5]  L Foglia,et al.  Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods , 2007, Ground water.

[6]  S. Gorelick,et al.  Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design , 1989 .

[7]  Domenico A Baú,et al.  Optimal design of pump-and-treat systems under uncertain hydraulic conductivity and plume distribution. , 2008, Journal of contaminant hydrology.

[8]  F. Tsai,et al.  Geophysical data integration, stochastic simulation and significance analysis of groundwater responses using ANOVA in the Chicot Aquifer system, Louisiana, USA , 2008 .

[9]  George Christakos,et al.  Boundary condition sensitivity analysis of the stochastic flow equation , 1996 .

[10]  Paul P. Wang,et al.  MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User's Guide , 1999 .

[11]  Ahmed E. Hassan,et al.  Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis , 2008 .

[12]  S. Gorelick.  A review of distributed parameter groundwater management modeling methods , 1983 .

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

[14]  Cass T. Miller,et al.  Optimal design for problems involving flow and transport phenomena in saturated subsurface systems , 2002 .

[15]  Mustafa M. Aral,et al.  Multi-objective optimization of pumping rates and well placement in coastal aquifers , 2004 .

[16]  Steven M. Gorelick,et al.  Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas , 2005 .

[17]  David Russo,et al.  Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties , 1988 .

[18]  Peter Bayer,et al.  Optimization of concentration control by evolution strategies: Formulation, application, and assessment of remedial solutions , 2007 .

[19]  Xiaobao Li,et al.  Multiple Parameterization for Hydraulic Conductivity Identification , 2008, Ground water.

[20]  Hamid R. Nemati,et al.  Groundwater quality management under uncertainty: stochastic programming approaches and the value of information , 1992 .

[21]  Marco Bittelli.  Conceptual Models of Flow and Transport in the Fractured Vadose Zone. , 2002 .

[22]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[23]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 3. Application to Synthetic and Field Data , 1986 .

[24]  C. Shoemaker,et al.  DYNAMIC OPTIMAL CONTROL OF IN-SITU BIOREMEDIATION OF GROUND WATER , 1998 .

[25]  Frank T.-C. Tsai,et al.  Enhancing random heterogeneity representation by mixing the kriging method with the zonation structure , 2006 .

[26]  Abhishek Singh,et al.  Uncertainty‐based multiobjective optimization of groundwater remediation design , 2003 .

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

[28]  N. Chan.  Robustness of the multiple realization method for stochastic hydraulic aquifer management , 1993 .

[29]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information , 1986 .

[30]  David W. Watkins,et al.  Finding Robust Solutions to Water Resources Problems , 1997 .

[31]  Xiaobao Li,et al.  Bayesian model averaging on hydraulic conductivity estimation and groundwater head prediction , 2008 .

[32]  A. Mahesha,et al.  Control of Seawater Intrusion through Injection-Extraction Well System , 1996 .

[33]  Yeou-Koung Tung,et al.  Groundwater Management by Chance‐Constrained Model , 1986 .

[34]  David Anderson,et al.  Multimodel Ranking and Inference in Ground Water Modeling , 2004, Ground water.

[35]  Manoutchehr Heidari,et al.  Applications of Optimal Hydraulic Control to Ground-Water Systems , 1994 .

[36]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[37]  D. Carroll.  Chemical laser modeling with genetic algorithms , 1996 .

[38]  Christine A. Shoemaker,et al.  Efficient prediction uncertainty approximation in the calibration of environmental simulation models , 2008 .

[39]  Aris P. Georgakakos,et al.  Stochastic Control of Groundwater Systems , 1991 .

[40]  Keith Beven,et al.  Uncertainty assessment of a process-based integrated catchment model of phosphorus , 2009 .

[41]  Clayton V. Deutsch,et al.  Calculation of Uncertainty in the Variogram , 2002 .

[42]  B. Wagner.  Recent advances in simulation-optimization groundwater management modeling (95RG00394) , 1995 .

[43]  D. Madigan,et al.  Bayesian model averaging and model selection for markov equivalence classes of acyclic digraphs , 1996 .

[44]  A. Mantoglou.  Estimation of heterogeneous aquifer parameters from piezometric data using ridge functions and neural networks , 2003 .

[45]  Keith Beven,et al.  Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: Conditioning on head observations , 2001 .

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

[47]  David Draper,et al.  Assessment and Propagation of Model Uncertainty , 2011 .

[48]  Stochastic delineation of capture zones: classical versus Bayesian approach , 2003 .

[49]  William W.-G. Yeh,et al.  Systems Analysis in Ground-Water Planning and Management , 1992 .

[50]  Arlen W. Harbaugh,et al.  MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process , 2000 .

[51]  Frank T.-C. Tsai,et al.  Characterization and identification of aquifer heterogeneity with generalized parameterization and Bayesian estimation , 2004 .

[52]  Frank T.-C. Tsai,et al.  Bayesian model averaging for groundwater head prediction and uncertainty analysis using multimodel and multimethod , 2009 .

[53]  David E. Goldberg,et al.  Risk‐based in situ bioremediation design using a noisy genetic algorithm , 2000 .

[54]  J. Guan,et al.  Optimal remediation with well locations and pumping rates selected as continuous decision variables , 1999 .

[55]  J. Eheart,et al.  Neural network-based screening for groundwater reclamation under uncertainty , 1993 .

[56]  P. A. Hsieh,et al.  Documentation of a computer program to simulate horizontal-flow barriers using the U.S. Geological Survey's modular three-dimensional finite-difference ground-water flow model , 1993 .

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

[58]  Ming Ye,et al.  Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff , 2003 .

[59]  Nak-Youl Ko,et al.  Convergence of deterministic and stochastic approaches in optimal remediation design of a contaminated aquifer , 2009 .

[60]  J. Peirce,et al.  Identification of Hydraulic Conductivity Structure in Sand and Gravel Aquifers: Cape Cod Data Set , 1996 .

[61]  J. Hanor,et al.  Spatial Variations in Subsurface Pore Fluid Properties in a Portion of Southeast Louisiana: Implications for Regional Fluid Flow and Solute Transport , 1990 .

[62]  J. Eheart,et al.  Aquifer remediation design under uncertainty using a new chance constrained programming technique , 1993 .

[63]  Michael D. Dettinger,et al.  First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development , 1981 .

[64]  Coupled Semivariogram Uncertainty of Hydrogeological and Geophysical Data on Capture Zone Uncertainty Analysis , 2008 .

[65]  Eric G. Reichard,et al.  Assessment of Regional Management Strategies for Controlling Seawater Intrusion , 2005 .

[66]  P. Bayer,et al.  Evolutionary algorithms for the optimization of advective control of contaminated aquifer zones , 2004 .

[67]  L. Feyen,et al.  Reliable groundwater management in hydroecologically sensitive areas , 2004 .

[68]  M. Person,et al.  Faults as conduit‐barrier systems to fluid flow in siliciclastic sedimentary aquifers , 2006 .

[69]  Frank T.-C. Tsai,et al.  Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window , 2008 .

[70]  Richard C. Peralta,et al.  Optimal design of aquifer cleanup systems under uncertainty using a neural network and a genetic algorithm , 1999 .

[71]  Mustafa M. Aral,et al.  Genetic Algorithm for Constrained Optimization Models and Its Application in Groundwater Resources Management , 2008 .