Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers

Correspondence Liangping Li, Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA. Email: Liangping.Li@sdsmt.edu Abstract Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation data. The ensemble Kalman filter (EnKF), a real-time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES, and the iterative ES using a synthetic example in groundwater modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling.

[1]  Domenico Baù,et al.  Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation , 2012 .

[2]  Alberto Guadagnini,et al.  Data assimilation and parameter estimation via ensemble Kalman filter coupled with stochastic moment equations of transient groundwater flow , 2013 .

[3]  Haibin Chang,et al.  Surrogate model based iterative ensemble smoother for subsurface flow data assimilation , 2017 .

[4]  Harrie-Jan Hendricks Franssen,et al.  Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems , 2009 .

[5]  Domenico Baù,et al.  Ensemble smoother assimilation of hydraulic head and return flow data to estimate hydraulic conductivity distribution , 2010 .

[6]  L. Hu.  Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models , 2000 .

[7]  Harrie-Jan Hendricks Franssen,et al.  Joint assimilation of piezometric heads and groundwater temperatures for improved modeling of river‐aquifer interactions , 2013 .

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

[9]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[10]  Glenn E. Hammond,et al.  Application of ensemble‐based data assimilation techniques for aquifer characterization using tracer data at Hanford 300 area , 2013 .

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

[12]  Liang Xue,et al.  A multimodel data assimilation framework via the ensemble Kalman filter , 2014 .

[13]  J. Gómez-Hernández,et al.  Joint identification of contaminant source location, initial release time, and initial solute concentration in an aquifer via ensemble Kalman filtering , 2016 .

[14]  Jan-Arild Skjervheim,et al.  An Ensemble Smoother for Assisted History Matching , 2011, ANSS 2011.

[15]  Bill X. Hu,et al.  Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field , 2012, Stochastic Environmental Research and Risk Assessment.

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

[17]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[18]  John Doherty,et al.  MODFLOW-2000, the U.S. Geological Survey modular ground-water model -- Documentation of MOD-PREDICT for predictions, prediction sensitivity analysis, and evaluation of uncertainty , 2003 .

[19]  Albert C. Reynolds,et al.  Ensemble smoother with multiple data assimilation , 2013, Comput. Geosci..

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

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

[22]  Tongchao Nan,et al.  Groundwater parameter estimation using the ensemble Kalman filter with localization , 2011 .

[23]  Liangping Li,et al.  An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering , 2011 .

[24]  Ibrahim Hoteit,et al.  Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering , 2013 .

[25]  O. Cirpka,et al.  Joint inference of groundwater–recharge and hydraulic–conductivity fields from head data using the ensemble Kalman filter , 2015 .

[26]  G. Evensen,et al.  Data assimilation and inverse methods in terms of a probabilistic formulation , 1996 .

[27]  Harrie-Jan Hendricks Franssen,et al.  Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling , 2012 .

[28]  Xian-Huan Wen,et al.  Real-Time Reservoir Model Updating Using Ensemble Kalman Filter , 2005 .

[29]  Harrie-Jan Hendricks Franssen,et al.  Operational real‐time modeling with ensemble Kalman filter of variably saturated subsurface flow including stream‐aquifer interaction and parameter updating , 2011 .

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

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

[32]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[33]  Bill X. Hu,et al.  Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source , 2009 .

[34]  Wolfgang Nowak,et al.  Parameter Estimation by Ensemble Kalman Filters with Transformed Data , 2010 .

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

[36]  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 .

[37]  Domenico Baù,et al.  Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother , 2011 .

[38]  Harrie-Jan Hendricks Franssen,et al.  Jointly Mapping Hydraulic Conductivity and Porosity by Assimilating Concentration Data via Ensemble Kalman Filter , 2012 .

[39]  D. Oliver,et al.  Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother , 2011, Mathematical Geosciences.

[40]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

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

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

[43]  H. H. Franssen,et al.  A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments , 2009 .

[44]  Domenico Baù,et al.  Estimating spatially-variable rate constants of denitrification in irrigated agricultural groundwater systems using an Ensemble Smoother , 2012 .

[45]  Liangping Li,et al.  Inverse methods in hydrogeology: Evolution and recent trends , 2014 .

[46]  Alexander Y. Sun,et al.  Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data , 2009 .

[47]  R. Bilonick.  An Introduction to Applied Geostatistics , 1989 .