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

Abstract

Parameter estimation in variable‐density groundwater flow systems is confronted with challenges of strong nonlinearity and heavy computational burden. Relying on a variant of the Henry problem, we evaluate the performance of a domain localization scheme of the iterative ensemble Kalman filter in the framework of data assimilation settings for variable‐density groundwater flows in a seawater intrusion scenario. The performance of the approach is compared against (a) the corresponding domain localization scheme of the ensemble Kalman filter in its standard formulation as well as (b) a covariance localization scheme of the latter. The equivalent freshwater head, hf, and salinity, Sa, are set as the target state variables. The randomly heterogeneous field of equivalent freshwater hydraulic conductivity, Kf, is considered as the system parameter field. Density‐independent and density‐driven flow settings are considered to evaluate the assimilation results using various methods and data. When only hf data are assimilated, all tested approaches perform generally well and a localization scheme embedded in the iterative ensemble Kalman filter appears to consistently outperform the domain localized version of the standard ensemble Kalman filter (EnKF) in a density‐driven scenario; Dirichlet boundary conditions tend to show a more pronounced negative effect on estimating Kf for density‐independent than for density‐dependent flow conditions; hf data are more informative in a density‐dependent than in a density‐independent setting. The sole use of Sa information does not yield satisfactory updates of hf for the covariance localization scheme of the standard EnKF, while the sole use of hf does. The domain localization scheme leads to difficulties in the attainment of global filter convergence when only Sa data are used. A covariance localization scheme associated with a standard EnKF can significantly alleviate this issue.

Deep Autoregressive Neural Networks for High‐Dimensional Inverse Problems in Groundwater Contaminant Source Identification

“…However, its applicability toward high‐dimensional problems is computationally prohibitive as a large number of model evaluations are often required to obtain converged solutions (Chaudhuri et al, ; Keller et al, ; Zhang et al, ). As relatively faster alternatives to the Markov chain Monte Carlo methods, ensemble‐based data assimilation algorithms such as ensemble Kalman filter (EnKF; Evensen, ) and ensemble smoother (ES; van Leeuwen & Evensen, ) have been widely used in groundwater hydrology to solve the inverse problem (e.g., Chang et al, ; Chaudhuri et al, ; Chen & Zhang, ; Elsheikh et al, ; Emerick & Reynolds, , ; Ju et al, ; Keller et al, ; Li et al, ; Sun et al, , ; White, ; Xia et al, ; Xu & Gómez‐Hernández, ; Zhang et al, ; Zhou et al, ). Similar to the Markov chain Monte Carlo methods, the ensemble‐based data assimilation algorithms can provide simultaneously estimations of the parameter values and of the associated uncertainty, which enables further uncertainty analysis on predictions.…”

Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

“…A stark example is given by groundwater related scenarios, where soil parameters, such as porosity and hydraulic conductivity, are frequently conceptualized as spatial random fields. In this context, MC methods play a significant role in dealing with uncertainty quantification [4][5][6], uncertainty reduction (e.g., in the framework of data assimilation techniques, such as the ensemble Kalman filter and/or smoother [7][8][9][10]), and variance-or momentbased global sensitivity analyses [11][12][13][14][15]. Implementation of MC relies on performing multiple forward simulations of the selected forward FSM upon using a collection of independent realizations of the uncertain model parameters.…”

“…Constant head conditions are set at the right and left sides, no-flow boundaries being set at the top and bottom. The five exemplary locations selected for the illustration of the results correspond to points (a) with coordinates (2, 1), (b) with coordinates (6, 3), (c) with coordinates (10, 5), (d) with coordinates(14,7), and (e) with coordinates(18,9).The color scale refers to values of a selected realization of log-transmissivity.…”

Data assimilation with multiple types of observation boreholes via ensemble Kalman filter embedded within stochastic moment equations

“…Recent studies include the work of Xia et al (2018), who tackle conductivity estimation in a two-dimensional variabledensity flow setting using a localized IEnKF to balance central processing unit (CPU) time and estimation accuracy. Bauser et al (2018) develop an adaptive covariance inflation method for the EnKF to reduce the negative effect of spurious correlations and illustrate an application of the method in a soil hydrology field context.…”

“…In this broad framework, it is noted that the accuracy of parameter estimation for a given environmental system is jointly determined by the ability of the mathematical model to describe the system of interest (Sakov et al, 2018;Alfonzo and Oliver, 2019;Luo, 2019;Evensen, 2019), the ability of the used assimilation algorithm (Emerick and Reynolds, 2013;Bocquet and Sakov, 2014) as well as by the quantity and quality of available observations (Zha et al, 2019;Xia et al, 2018 and references therein).…”