Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques

Abstract

[1] Estimated parameter distributions in groundwater models may contain significant uncertainties because of data insufficiency. Therefore, adaptive uncertainty reduction strategies are needed to continuously improve model accuracy by fusing new observations. In recent years, various ensemble Kalman filters have been introduced as viable tools for updating high-dimensional model parameters. However, their usefulness is largely limited by the inherent assumption of Gaussian error statistics. Hydraulic conductivity distributions in alluvial aquifers, for example, are usually non-Gaussian as a result of complex depositional and diagenetic processes. In this study, we combine an ensemble Kalman filter with grid-based localization and a Gaussian mixture model (GMM) clustering techniques for updating high-dimensional, multimodal parameter distributions via dynamic data assimilation. We introduce innovative strategies (e.g., block updating and dimension reduction) to effectively reduce the computational costs associated with these modified ensemble Kalman filter schemes. The developed data assimilation schemes are demonstrated numerically for identifying the multimodal heterogeneous hydraulic conductivity distributions in a binary facies alluvial aquifer. Our results show that localization and GMM clustering are very promising techniques for assimilating high-dimensional, multimodal parameter distributions, and they outperform the corresponding global ensemble Kalman filter analysis scheme in all scenarios considered.

Bridging the ensemble Kalman and particle filters

“…To relax the Gaussian assumption, two paradigms are predominant: mixture filters that approximate the forecast distribution as a mixture of Gaussian distributions (Bengtsson et al, 2003;Sun et al, 2009;Dovera & Della Rossa, 2011;Stordal et al, 2011;Hoteit et al, 2012;Rezaie & Eidsvik, 2012;Frei & Künsch, 2013), and sequential importance samplers that use the ensemble Kalman filter as a proposal distribution (Mandel & Beezley, 2009;Papadakis et al, 2010). In this article, we introduce an update scheme that blends these: a Gaussian mixture proposal obtained from an ensemble Kalman filter update based on a tempered likelihood is corrected by a particle filter update.…”

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

“…EnKF algorithms are limited to Gaussian system as they rely on the first two moments of the ensemble statistics. Several studies were carried out to extend EnKF to handle non-Gaussian estimation problems (Bengtsson et al, 2003;Smith, 2007;Sun et al, 2009a;Zhou et al, 2011).…”

Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

“…In a Monte Carlo framework, heterogeneity of hydrogeologic properties is commonly characterized by the following two steps: (i) on the basis of a limited amount of direct measurements (i.e., hard data), multiple representations of aquifer properties are generated by means of the geostatistical techniques such as sequential Gaussian simulation (Deutsch and Journel, 1998), sequential indicator simulation (Gómez-Hernández and Srivastava, 1990), multiplepoint geostatistical approach (Strebelle, 2002;Mariethoz et al, 2010b) or other related methods; and then (ii) on the basis of indirect measurements such as piezometric head and concentration data, inverse modeling is utilized to reduce the uncertainty by integrating these data to better characterize the spatial variability of hydrogeologic properties (e.g. for an overview see Yeh, 1986;McLaughlin and Townley, 1996;Zimmerman et al, 1998;Carrera et al, 2005;Zhou et al, 2012b).…”

“…The EnKF is increasingly studied in hydrogeology as well as in petroleum engineering (e.g. Wen and Chen, 2005;Chen and Zhang, 2006;Hendricks Franssen and Kinzelbach, 2008;Sun et al, 2009;Nowak, 2009;Nan and Wu, 2010;Li et al, 2012b). The attractive characteristics of the EnKF are: (i) the efficiency in computation (e.g.…”

“…Hence, extending the EnKF to deal with non-Gaussian state vectors would facilitate more extensive applications. Sun et al (2009) and Zhou et al (2011Zhou et al ( , 2012c, developed variants of the EnKF which are better accommodated to handle non-Gaussianity of parameter distributions. Sun et al (2009) resort to couple the EnKF with a Gaussian mixture model to update the parameters of a multi-modal distribution by assimilating head data.…”