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Adaptive Hybrid EnKF-OI for State-Parameters Estimation in Contaminant Transport ModelsMohamad E. Gharamti, Johan Valstar, Ibrahim Hoteit

European Geoscience Union (EGU), Vienna, 2014Parameter Estimation, Inverse Modeling and Data Assimilation in Subsurface HydrologyMonday May 1st, 2014 1OutlineProblem ObjectivesDual Ensemble Kalman FilteringHybrid EnKF-OINumerical ExampleConclusion

KAUST King Abdullah University of Science and Technology2Problem: Groundwater Contamination 3

Rotterdam port Industrial region

Groundwater flow: Pressure

Groundwater contamination: Well data

Transport SimulationObjectives KAUST King Abdullah University of Science and Technology4Subsurface models: highly complex, expensive to run, nonlinearSources of uncertainties: Omitted physics, uncertain parameters, inputs and initial conditions, numerical errors Goal: Predict, analyze and quantify uncertainties of the subsurface state and parameters Available Information: Imperfect models and sparse observationsTools: Ensemble Kalman filtering (EnKF), Optimal interpolation (OI)4Dual Ensemble Kalman Filtering5Compute the probability density function of state and parameters given available observations:

Distributions: EstimatesUncertainties EnKF Limitations & HybridKAUST King Abdullah University of Science and Technology6Accuracy of the EnKF background covariance is mainly limited by: (1) small ensembles and (2) Model deficiencies

Rank deficiency, Spurious correlations, Underestimated background

Relax on OI/3D-Var static background to the flow-dependent EnKF covariance:

with weighting factor

Adaptive Hybrid EnKF-OIKAUST King Abdullah University of Science and Technology7On top of the state, use the hybrid idea for the parameters. Introduce background state-parameters cross-correlations:

Propose to optimize the weighting factors: Maximize the gain between the forecast and analysis statistics !

Reduce ensemble sampling errors,

Implement with small ensemblesConceptual Contaminant Transport Example8

Need to estimate: Dynamic contaminant concentration,Spatially-variable sorption rate (adsorption) coefficientsNumerical Results - I9

Numerical Results - IIKAUST King Abdullah University of Science and Technology10

Numerical Results - IIIKAUST King Abdullah University of Science and Technology11

Numerical Results - IV

Around 70% reduction in the ensemble size !!Numerical Results - VKAUST King Abdullah University of Science and Technology13

Conclusion We introduced an adaptive hybrid EnKF-OI scheme for state-parameters estimation for subsurface modelsThis scheme complements the sample ensemble covariance of the EnKF with a prescribed background covariance from an OI to limit the standard EnKF issues of rank deficiency and sampling errors Adaptive EnKF-OI was found more efficient than the EnKF providing more accurate concentration and sorption estimatesExperimental results suggest that around 70% smaller ensembles might be enough to get accurate system distributionsKAUST King Abdullah University of Science and Technology14THANK YOU !!!

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