ALBERT

Description: This study evaluated three algorithms of the iterative ensemble Kalman filter (EnKF). They are Confirming EnKF, Restart EnKF, and modified Restart EnKF developed to resolve the inconsistency problem (i.e., updated model parameters and state variables do not follow the Richards equation) in vadose zone data assimilation due to model nonlinearity. While Confirming and Restart EnKF were adapted from literature, modified Restart EnKF was developed in this study to reduce computational costs by calculating only the mean simulation, not all the ensemble realizations, from time t = 0. A total of 11 cases were designed to investigate the performance of EnKF, Confirming EnKF, Restart EnKF, and modified Restart EnKF with different types and spatial configurations of observations (pressure head and water content) and different values of observation error variance, initial guess of ensemble mean and variance, ensemble size, and damping factor. The numerical study showed that Confirming EnKF produced considerable inconsistency for the nonlinear unsaturated flow problem, which differs from the apparent consensus opinion that Confirming EnKF can resolve the inconsistency problem. In contrast, Restart EnKF and its modification can resolve the inconsistency problem. Restart EnKF and its modification outperformed EnKF and Confirming EnKF in the various cases considered in this study. It ws also found that combining different types of observations can achieve better assimilation results, which is useful for monitoring network design.

Description: In vadose zone modeling, parameter estimates and model predictions are inherently uncertain, regardless of quality and quantity of data used in model-data fusion. Accurate quantification of the uncertainty is necessary to design future data collection for improving the predictive capability of models. This study is focused on evaluating predictive performance of two commonly used methods of uncertainty quantification: nonlinear regression and Bayesian methods. The former quantifies predictive uncertainty using the regression confidence interval (RCI), whereas the latter uses the Bayesian credible interval (BCI); neither RCI nor BCI includes measurement errors. When measurement errors are considered, the counterparts of RCI and BCI are regression prediction interval (RPI) and Bayesian prediction interval (BPI), respectively. The predictive performance is examined through a cross-validation study of two-phase flow modeling, and predictive logscore is used as the performance measure. The linear and nonlinear RCI and RPI are evaluated using UCODE_2005. The nonlinear RCI performs better than the linear RCI, and the nonlinear RPI outperforms the linear RPI. The Bayesian intervals are calculated using Markov Chain Monte Carlo (MCMC) techniques implemented with the differential evolution adaptive metropolis (DREAM) algorithm. The BCI/BPI obtained from DREAM has better predictive performance than the linear and nonlinear RCI/RPI. Different from observations in other studies, it is found that estimating nonlinear RCI/RPI is not computationally more efficient than estimating BCI/BPI in this case with low-dimensional parameter space and a large number of predictions. MCMC methods are thus more appealing than nonlinear regression methods for uncertainty quantification in vadose zone modeling.