Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field

Abstract

A localized ensemble Kalman filter (EnKF) method is developed to assimilate transient flow data to calibrate a heterogeneous conductivity field. To update conductivity value at a point in a study domain, instead of assimilating all the measurements in the study domain, only limited measurement data in an area around the point are used for the conductivity updating in the localized EnKF method. The localized EnKF is proposed to solve the problems of the filter divergence usually existing in a data assimilation method without localization. The developed method is applied, in a synthetical two dimensional case, to calibrate a heterogeneous conductivity field by assimilating transient hydraulic head data. The simulations by the data assimilation with and without localized EnKF are compared. The study results indicate that the hydraulic conductivity field can be updated efficiently by the localized EnKF, while it cannot be by the EnKF. The covariance inflation and localization are found to solve the problem of the filter divergence efficiently. In comparison with the EnKF method without localization, the localized EnKF method needs smaller ensemble size to achieve stabilized results. The simulation results by the localized EnKF method are much more sensitive to conductivity correlation length than to the localization radius. The developed localized EnKF method provides an approach to improve EnKF method in conductivity calibration.

A partial ensemble Kalman filtering approach to enable use of range limited observations

“…Nonetheless, the EnKF has proven very successful for non-linear models within a wide range of applications such as oceanography, meteorology, oil reservoir modelling, groundwater modelling, hydrology, etc. (Keppenne and Rienecker, 2002;Lee et al, 2012;Naevdal et al, 2003;Olume, 2006;Tong et al, 2012) and must be regarded as one of the most versatile DA methods available.…”

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilationand Indicator Geostatistics With Level‐Set Transformation

“…We chose ensemble sizes of 300 and 600 for the 2D and 3D test cases, respectively, which were tested to be sufficient. The filter inbreeding might also be alleviated by better sampling design (Evensen, 2004), covariance inflation (Hendricks Franssen & Kinzelbach, 2008), and localization (Tong et al, 2012), all of which could be incorporated into our framework. The reconditioning step we introduced in this study, similar to the resampling step used by Nejadi et al (2015) to maintain the diversity of ensemble members, could also alleviate the filter inbreeding problem.…”

Data Assimilation in Density‐Dependent Subsurface Flows via Localized Iterative Ensemble Kalman Filter

“…Inflation and multiensemble configuration (Houtekamer & Mitchell, 2001) could mitigate this issue to some extent. Localization techniques, including covariance and/or domain localization, could also be used to dampen long-range spurious correlations (e.g., Evensen, 2003;Nan & Wu, 2011;Tong et al, 2012). Covariance localization is typically performed by the Schur product of a smoothing function with the regularized error covariance matrix (Nan & Wu, 2011).…”