Mohamad El Gharamti

Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF

AbstractThe stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of the observational error covariance, which is often the case in real oceanic and atmospheric data assimilation applications. This work introduces an efficient serial scheme to mitigate the impact of observations’ perturbations sampling in the analysis step of the EnKF, which should provide more accurate ensemble estimates of the analysis error covariance matrices. The new scheme is simple to implement within the serial EnKF algorithm, requiring only the approximation of the EnKF sample forecast error covariance matrix by a matrix with one rank less. The new EnKF scheme is implemented and tested with the Lorenz-96 model. Results from numerical experiments are conducted to compare its performance with the E...

Constraining a compositional flow model with flow‐chemical data using an ensemble‐based Kalman filter

Isothermal compositional flow models require coupling transient compressible flows and advective transport systems of various chemical species in subsurface porous media. Building such numerical models is quite challenging and may be subject to many sources of uncertainties because of possible incomplete representation of some geological parameters that characterize the systems processes. Advanced data assimilation methods, such as the ensemble Kalman filter (EnKF), can be used to calibrate these models by incorporating available data. In this work, we consider the problem of estimating reservoir permeability using information about phase pressure as well as the chemical properties of fluid components. We carry out state-parameter estimation experiments using joint and dual updating schemes in the context of the EnKF with a two-dimensional single-phase compositional flow model (CFM). Quantitative and statistical analyses are performed to evaluate and compare the performance of the assimilation schemes. Our results indicate that including chemical composition data significantly enhances the accuracy of the permeability estimates. In addition, composition data provide more information to estimate system states and parameters than do standard pressure data. The dual state-parameter estimation scheme provides about 10% more accurate permeability estimates on average than the joint scheme when implemented with the same ensemble members, at the cost of twice more forward model integrations. At similar computational cost, the dual approach becomes only beneficial after using large enough ensembles.

Enhanced Adaptive Inflation Algorithm for Ensemble Filters

AbstractSpatially and temporally varying adaptive inflation algorithms have been developed to combat the loss of variance during the forecast due to various model and sampling errors. The adaptive Bayesian scheme of Anderson uses available observations to update the Gaussian inflation distribution assigned for every state variable. The likelihood function of the inflation is computed using model-minus-data innovation statistics. A number of enhancements for this inflation scheme are proposed. To prevent excessive deflation, an inverse gamma distribution for the prior inflation is considered. A non-Gaussian distribution offers a flexible framework for the inflation variance to evolve during the update. The innovations are assumed random variables, and a correction term is added to the mode of the likelihood distribution such that the observed inflation is slightly larger. This modification improves the stability of the adaptive scheme by limiting the occurrence of negative and physically intolerable inflat...

A One-Step-Ahead Smoothing-Based Joint Ensemble Kalman Filter for State-Parameter Estimation of Hydrological Models

The ensemble Kalman filter (EnKF) recursively integrates field data into simulation models to obtain a better characterization of the model’s state and parameters. These are generally estimated following a state-parameters joint augmentation strategy. In this study, we introduce a new smoothing-based joint EnKF scheme, in which we introduce a one-step-ahead smoothing of the state before updating the parameters. Numerical experiments are performed with a two-dimensional synthetic subsurface contaminant transport model. The improved performance of the proposed joint EnKF scheme compared to the standard joint EnKF compensates for the modest increase in the computational cost.

A Greedy Approach for Placement of Subsurface Aquifer Wells in an Ensemble Filtering Framework

Optimizing wells placement may help in better understanding subsurface solute transport and detecting contaminant plumes. In this work, we use the ensemble Kalman filter (EnKF) as a data assimilation tool and propose a greedy observational design algorithm to optimally select aquifer wells locations for updating the prior contaminant ensemble. The algorithm is greedy in the sense that it operates sequentially, without taking into account expected future gains. The selection criteria is based on maximizing the information gain that the EnKF carries during the update of the prior uncertainties. We test the efficiency of this algorithm in a synthetic aquifer system where a contaminant plume is set to migrate over a 30 years period across a heterogenous domain.