A multimodel data assimilation framework via the ensemble Kalman filter

Abstract

The ensemble Kalman filter (EnKF) is a widely used data assimilation method that has the capacity to sequentially update system parameters and states as new observations become available. One noticeable feature of the EnKF is that it not only can provide real-time updates of model parameters and state variables, but also can give the uncertainty associated with them in each assimilation step. The natural system is open and complex, rendering it prone to multiple interpretations and mathematical descriptions. In this paper, a multimodel data assimilation method is proposed by embedding the EnKF into the Bayesian model averaging framework to account for the uncertainty stemming from the model itself. An illustrative example, considering both hydrogeological and groundwater flow uncertainties, is employed to demonstrate the proposed multimodel data assimilation approach via the EnKF. Results show that statistical bias and uncertainty underestimation can occur when the data assimilation process relies on a single postulated model. The posterior model weight can adjust itself dynamically in time according to its consistency with observations. The performances of log conductivity estimation and head prediction are compared to the standard EnKF method based on the postulated single model and the proposed multimodel EnKF method. Comparisons show that the multimodel EnKF performs better in terms of statistical measures, such as log score and coverage, when sufficient observations have been assimilated in this case.

Identification of hydrological model parameter variation using ensemble Kalman filter

“…It is applicable to a variety of nonlinear problems (Evensen, 2003;Weerts and El Serafy, 2006) and has been widely applied to hydrological models (Abaza et al, 2014;DeChant and Moradkhani, 2014;Delijani et al, 2014;Samuel et al, 2014;Tamura et al, 2014;Xue and Zhang, Deng et al, 2015). Furthermore, the EnKF has been successfully used in time-invariant parameter estimations for hydrological models (Moradkhani et al, 2005;Wang et al, 2009;Zhang, 2010, 2013).…”

Towards Improving the Efficiency of Bayesian Model Averaging Analysis for Flow in Porous Media via the Probabilistic Collocation Method

“…The zero-mean unconditional reference field of log hydraulic conductivity was generated using modified sequential Gaussian simulation code [41]. The reference variogram model used to generate the reference random field of log hydraulic conductivity was selected as the truncated power variogram model with Gaussian modes (TpvG) [32,49]:…”

“…As an alternative, Bayesian model averaging (BMA) is considered to be a rigorous Bayesian analysis framework that can account for the model uncertainty [28,29]. BMA and its maximum likelihood version have been used widely in hydrogeological research [21,[30][31][32][33][34]. GLUE and BMA were integrated together by [35] in order to make GLUE more coherent with the Bayesian analysis framework.…”

Characterization of Aquifer Multiscale Properties by Generating Random Fractal Field with Truncated Power Variogram Model Using Karhunen–Loève Expansion

“…It renders two types of truncated power variogram: truncated power variogram with exponential modes (TpvE) and truncated power variogram with Gaussian modes (TpvG). We have modified the GSLIB code to incorporate these truncated power variogram models to generate random fractal field, both unconditional and conditional, using sequential Gaussian simulation method [22]. Other methods can also generate random fractal field, such as the spectral methods [23] and fractal method [24].…”