1. Adaptive Hybrid EnKF-OI for State- Parameters Estimation in Contaminant Transport Models Mohamad E. Gharamti, Johan Valstar, Ibrahim Hoteit European Geoscience Union (EGU), Vienna, 2014 Parameter Estimation, Inverse Modeling and Data Assimilation in Subsurface Hydrology Monday – May 1 st, 2014

2. Outline o Problem o Objectives o Dual Ensemble Kalman Filtering o Hybrid EnKF-OI o Numerical Example o Conclusion KAUST King Abdullah University of Science and Technology2

3. Problem: Groundwater Contamination 3 Rotterdam port “Industrial region” Groundwater flow: Pressure Groundwater contamination: Well data Transport Simulation

4. Objectives KAUST King Abdullah University of Science and Technology4 Subsurface models: highly complex, expensive to run, nonlinear Sources of uncertainties: Omitted physics, uncertain parameters, inputs and initial conditions, numerical errors … o Goal: Predict, analyze and quantify uncertainties of the subsurface state and parameters o Available Information: Imperfect models and sparse observations o Tools: Ensemble Kalman filtering (EnKF), Optimal interpolation (OI)

5. Dual Ensemble Kalman Filtering 5 o Compute the probability density function of state and parameters given available observations: Distributions:  Estimates  Uncertainties

6. EnKF Limitations & Hybrid KAUST King Abdullah University of Science and Technology6 o Accuracy 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

7. Adaptive Hybrid EnKF-OI KAUST King Abdullah University of Science and Technology7 o On top of the state, use the hybrid idea for the parameters. Introduce background state-parameters cross-correlations: o Propose to optimize the weighting factors: Maximize the gain between the forecast and analysis statistics ! -Reduce ensemble sampling errors, -Implement with small ensembles

8. Conceptual Contaminant Transport Example 8 Need to estimate: -Dynamic contaminant concentration, -Spatially-variable sorption rate (adsorption) coefficients

9. Numerical Results - I 9

10. Numerical Results - II KAUST King Abdullah University of Science and Technology10

11. Numerical Results - III KAUST King Abdullah University of Science and Technology11

12. Numerical Results - IV Around 70% reduction in the ensemble size !!

13. Numerical Results - V KAUST King Abdullah University of Science and Technology13

14. Conclusion o We introduced an adaptive hybrid EnKF-OI scheme for state-parameters estimation for subsurface models o This 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 o Adaptive EnKF-OI was found more efficient than the EnKF providing more accurate concentration and sorption estimates o Experimental results suggest that around 70% smaller ensembles might be enough to get accurate system distributions KAUST King Abdullah University of Science and Technology14

15. THANK YOU !!! KAUST King Abdullah University of Science and Technology15