A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

[1]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[2]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[3]  A. N. Tikhonov,et al.  REGULARIZATION OF INCORRECTLY POSED PROBLEMS , 1963 .

[4]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[5]  C. G. Broyden Quasi-Newton methods and their application to function minimisation , 1967 .

[6]  H. Akaike A new look at the statistical model identification , 1974 .

[7]  Donald R. Smith Variational methods in optimization , 1974 .

[8]  Hirotugu Akaike,et al.  On entropy maximization principle , 1977 .

[9]  J. Ware,et al.  Applications of Statistics , 1978 .

[10]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[11]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[12]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[13]  E. Hannan The Estimation of the Order of an ARMA Process , 1980 .

[14]  Franklin W. Schwartz,et al.  mass transport: 2. Analysis of uncertainty in prediction , 1981 .

[15]  Philip E. Gill,et al.  Practical optimization , 1981 .

[16]  Rangasami L. Kashyap,et al.  Optimal Choice of AR and MA Parts in Autoregressive Moving Average Models , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  L. Lake,et al.  A new approach to shale management in field scale simulation models , 1982 .

[18]  S. P. Neuman,et al.  Effects of kriging and inverse modeling on conditional simulation of the Avra Valley Aquifer in southern Arizona , 1982 .

[19]  E. G. Vomvoris,et al.  A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one‐dimensional simulations , 1983 .

[20]  M. Boucher,et al.  Interpretation of Interference Tests in a Well Field Using Geostatistical Techniques to Fit the Permeability Distribution in a Reservoir Model , 1984 .

[21]  L. Lake,et al.  A New Approach to Shale Management in Field-Scale Models , 1984 .

[22]  J. C. Ramírez,et al.  Estimation of aquifer parameters under transient and steady-state conditions , 1984 .

[23]  L. Townley,et al.  Computationally Efficient Algorithms for Parameter Estimation and Uncertainty Propagation in Numerical Models of Groundwater Flow , 1985 .

[24]  G. Dagan Stochastic Modeling of Groundwater Flow by Unconditional and Conditional Probabilities: The Inverse Problem , 1985 .

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

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

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

[28]  W. Yeh Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[29]  D. F. Watson,et al.  The distinction between probabilistic prediction and statistical decision-making , 1986 .

[30]  M. Th. van Genuchten,et al.  Parameter estimation for unsaturated flow and transport models — A review , 1987 .

[31]  R. Fletcher Practical Methods of Optimization , 1988 .

[32]  Y. Rubin Stochastic modeling of macrodispersion in heterogeneous porous media , 1990 .

[33]  J. Jaime Gómez-Hernández,et al.  ISIM3D: and ANSI-C three-dimensional multiple indicator conditional simulation program , 1990 .

[34]  Yoram Rubin,et al.  Prediction of tracer plume migration in disordered porous media by the method of conditional probabilities , 1991 .

[35]  Dan Rosbjerg,et al.  A Comparison of Four Inverse Approaches to Groundwater Flow and Transport Parameter Identification , 1991 .

[36]  J. Carrera,et al.  On geostatistical formulations of the groundwater flow inverse problem , 1991 .

[37]  William W.-G. Yeh,et al.  A stochastic inverse solution for transient groundwater flow: Parameter identification and reliability analysis , 1992 .

[38]  A. Bennett Inverse Methods in Physical Oceanography , 1992 .

[39]  A. Lavenue,et al.  Application of a coupled adjoint sensitivity and kriging approach to calibrate a groundwater flow model , 1992 .

[40]  J. Gómez-Hernández,et al.  Joint Sequential Simulation of MultiGaussian Fields , 1993 .

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

[42]  Shlomo P. Neuman,et al.  Erratum: ``Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation'' [Water Resources Research, 29(2), 341-364 (1993)] , 1993 .

[43]  S. P. Neuman,et al.  Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal , 1993 .

[44]  R. M. Srivastava,et al.  Multivariate Geostatistics: Beyond Bivariate Moments , 1993 .

[45]  G. Evensen Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[46]  M. Marietta,et al.  Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments , 1995 .

[47]  Minghui Jin,et al.  AN ITERATIVE STOCHASTIC INVERSE METHOD: CONDITIONAL EFFECTIVE TRANSMISSIVITY AND HYDRAULIC HEAD FIELDS , 1995 .

[48]  M. G. Marietta,et al.  Pilot Point Methodology for Automated Calibration of an Ensemble of Conditionally Simulated Transmissivity Fields: 2. Application , 1995 .

[49]  P. Kitanidis Quasi‐Linear Geostatistical Theory for Inversing , 1995 .

[50]  D. McLaughlin,et al.  A Reassessment of the Groundwater Inverse Problem , 1996 .

[51]  E. Poeter,et al.  Inverse Models: A Necessary Next Step in Ground‐Water Modeling , 1997 .

[52]  D. Oliver,et al.  Markov chain Monte Carlo methods for conditioning a permeability field to pressure data , 1997 .

[53]  A. Sahuquillo,et al.  Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory , 1997 .

[54]  G. Fogg,et al.  Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains , 1997 .

[55]  Edzer Pebesma,et al.  GSTAT: a program for geostatistical modelling, prediction and simulation , 1998 .

[56]  Andrés Sahuquillo,et al.  Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric head data—3. Application to the Culebra formation at the Waste Isolation Pilot Plan (WIPP), New Mexico, USA , 1998 .

[57]  G. Evensen,et al.  Analysis Scheme in the Ensemble Kalman Filter , 1998 .

[58]  J. Gómez-Hernández,et al.  To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology , 1998 .

[59]  D. A. Zimmerman,et al.  A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow , 1998 .

[60]  W. J. Shuttleworth,et al.  Parameter estimation of a land surface scheme using multicriteria methods , 1999 .

[61]  Alberto Guadagnini,et al.  Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 2. Computational examples , 1999 .

[62]  G. Marsily,et al.  Regards sur 40 ans de problèmes inverses en hydrogéologie , 1999 .

[63]  Alberto Guadagnini,et al.  Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 1. Theory and computational approach , 1999 .

[64]  Andrés Sahuquillo,et al.  Joint simulation of transmissivity and storativity fields conditional to steady-state and transient hydraulic head data , 1999 .

[65]  J. Gómez-Hernández,et al.  Simulation of Non-Gaussian Transmissivity Fields Honoring Piezometric Data and Integrating Soft and Secondary Information , 1999 .

[66]  M.I.M. Bakr A Stochastic Inverse-Management Approach to Groundwater Quality Problems , 2000 .

[67]  T. Ulrych,et al.  A full‐Bayesian approach to the groundwater inverse problem for steady state flow , 2000 .

[68]  R. L. Cooley An analysis of the pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields , 2000 .

[69]  Mary C. Hill,et al.  Comment on RamaRao et al. [1995] and LaVenue et al. [1995] , 2000 .

[70]  Production Data Integration in Sand/Shale Reservoirs Using Sequential Self-Calibration and GeoMorphing: A Comparison , 2000 .

[71]  J. Jaime Gómez-Hernández,et al.  Stochastic analysis of flow response in a three-dimensional fractured rock mass block $ , 2001 .

[72]  Joseph F. Atkinson,et al.  Groundwater Flow And Quality Modeling , 2001 .

[73]  Ghislain de Marsily,et al.  Three‐dimensional interference test interpretation in a fractured aquifer using the Pilot Point Inverse Method , 2001 .

[74]  L. Hu,et al.  Gradual deformation and iterative calibration of truncated Gaussian simulations , 2001, Petroleum Geoscience.

[75]  You‐Kuan Zhang Stochastic Methods for Flow in Porous Media: Coping with Uncertainties , 2001 .

[76]  S. P. Neuman,et al.  Three‐dimensional numerical inversion of pneumatic cross‐hole tests in unsaturated fractured tuff: 2. Equivalent parameters, high‐resolution stochastic imaging and scale effects , 2001 .

[77]  Jesús Carrera,et al.  Geostatistical Inversion of Cross‐Hole Pumping Tests for Identifying Preferential Flow Channels Within a Shear Zone , 2001 .

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

[79]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[80]  J. J. Gómez-Hernández,et al.  3D inverse modelling of groundwater flow at a fractured site using a stochastic continuum model with multiple statistical populations , 2002 .

[81]  Uncertainty estimation of well catchments in heterogeneous aquifers , 2002 .

[82]  Jef Caers,et al.  Geostatistical History Matching Under Training-Image Based Geological Model Constraints , 2002 .

[83]  Alberto Guadagnini,et al.  Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion , 2003 .

[84]  Andrés Sahuquillo,et al.  Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data , 2003 .

[85]  John Doherty,et al.  Ground Water Model Calibration Using Pilot Points and Regularization , 2003, Ground water.

[86]  Jef Caers,et al.  History Matching Under Training-Image-Based Geological Model Constraints , 2003 .

[87]  M. Bakr,et al.  Stochastic groundwater quality management: Role of spatial variability and conditioning , 2003 .

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

[89]  Sigurd Ivar Aanonsen,et al.  Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter , 2005 .

[90]  J. Carrera,et al.  Geostatistical inversion of coupled problems: dealing with computational burden and different types of data , 2003 .

[91]  Johan Valstar,et al.  A representer‐based inverse method for groundwater flow and transport applications , 2004 .

[92]  W. Nowak,et al.  A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing , 2004 .

[93]  Wolfgang Kinzelbach,et al.  Semianalytical uncertainty estimation of well catchments: Conditioning by head and transmissivity data , 2004 .

[94]  Adrian P. Butler,et al.  Worth of head data in well-capture zone design: deterministic and stochastic analysis , 2004 .

[95]  Harrie-Jan Hendricks Franssen,et al.  Joint estimation of transmissivities and recharges—application: stochastic characterization of well capture zones , 2004 .

[96]  S. Finsterle,et al.  Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements , 2004 .

[97]  P. Renard,et al.  Dealing with spatial heterogeneity , 2005 .

[98]  Geir Nævdal,et al.  Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter , 2005 .

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

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

[101]  Andres Alcolea,et al.  Inverse problem in hydrogeology , 2005 .

[102]  Arnold W. Heemink,et al.  Inverse modeling of groundwater flow using model reduction , 2005 .

[103]  Yan Chen,et al.  Data assimilation for transient flow in geologic formations via ensemble Kalman filter , 2006 .

[104]  Andres Alcolea,et al.  Pilot points method incorporating prior information for solving the groundwater flow inverse problem , 2006 .

[105]  Andres Alcolea,et al.  Inversion of heterogeneous parabolic-type equations using the pilot points method , 2006 .

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

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

[108]  Alberto Guadagnini,et al.  Assessment of uncertainty associated with the estimation of well catchments by moment equations , 2006 .

[109]  J. Valstar,et al.  Inverse modeling of multimodal conductivity distributions , 2006 .

[110]  J. Caers,et al.  The Probability Perturbation Method: A New Look at Bayesian Inverse Modeling , 2006 .

[111]  S. P. Neuman,et al.  Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media , 2006 .

[112]  A. Tarantola Popper, Bayes and the inverse problem , 2006 .

[113]  H. Ngodock,et al.  The Representer Method, the Ensemble Kalman Filter and the Ensemble Kalman Smoother: A Comparison Study Using a Nonlinear Reduced Gravity Ocean Model , 2006 .

[114]  I. Bateman,et al.  Scope sensitivity in households' willingness to pay for maintained and improved water supplies in a developing world urban area: Investigating the influence of baseline supply quality and income distribution upon stated preferences in Mexico City , 2006 .

[115]  Henrik Madsen,et al.  Calibration framework for a Kalman filter applied to a groundwater model , 2006 .

[116]  Bernard Bourbiaux,et al.  History Matching of a Stochastic Model of Field-Scale Fractures: Methodology and Case Study , 2007 .

[117]  Yuqiong Liu,et al.  Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework , 2007 .

[118]  H. Ngodock,et al.  Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model , 2007 .

[119]  J. Carrera,et al.  Inverse Modeling of Coastal Aquifers Using Tidal Response and Hydraulic Tests , 2007, Ground water.

[120]  Robert N. Miller,et al.  Representer‐based variational data assimilation in a nonlinear model of nearshore circulation , 2007 .

[121]  Arnold W. Heemink,et al.  Application of the representer method for parameter estimation in numerical reservoir models , 2007 .

[122]  Philippe Renard,et al.  Stochastic Hydrogeology: What Professionals Really Need? , 2007, Ground water.

[123]  J. Carrera,et al.  Estimation of Recharge from Floods in Disconnected Stream‐Aquifer Systems , 2007, Ground water.

[124]  S. P. Neuman,et al.  On model selection criteria in multimodel analysis , 2007 .

[125]  Harrie-Jan Hendricks Franssen,et al.  Equally likely inverse solutions to a groundwater flow problem including pattern information from remote sensing images , 2008 .

[126]  J. Caers,et al.  Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization , 2008 .

[127]  John Doherty,et al.  Predictive error dependencies when using pilot points and singular value decomposition in groundwater model calibration , 2008 .

[128]  P. Renard,et al.  Issues in characterizing heterogeneity and connectivity in non-multiGaussian media , 2008 .

[129]  Andres Alcolea,et al.  Regularized pilot points method for reproducing the effect of small scale variability : Application to simulations of contaminant transport , 2008 .

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

[131]  W. Kinzelbach,et al.  Real‐time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem , 2008 .

[132]  L. Hu,et al.  Extended Probability Perturbation Method for Calibrating Stochastic Reservoir Models , 2008 .

[133]  L. Y. Hu,et al.  Multiple‐point geostatistics for modeling subsurface heterogeneity: A comprehensive review , 2008 .

[134]  Dongxiao Zhang,et al.  Investigation of flow and transport processes at the MADE site using ensemble Kalman filter , 2008 .

[135]  Philippe Renard,et al.  Reducing the impact of a desalination plant using stochastic modeling and optimization techniques , 2009 .

[136]  J. Gómez-Hernández,et al.  Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method. , 2009 .