On the efficiency of the hybrid and the exact second-order sampling formulations of the EnKF: a reality-inspired 3-D test case for estimating biodegradation rates of chlorinated hydrocarbons at the port of Rotterdam

Abstract. This study considers the assimilation problem of subsurface contaminants at the port of Rotterdam in the Netherlands. It involves the estimation of solute concentrations and biodegradation rates of four different chlorinated solvents. We focus on assessing the efficiency of an adaptive hybrid ensemble Kalman filter and optimal interpolation (EnKF-OI) and the exact second-order sampling formulation (EnKF_ESOS) for mitigating the undersampling of the estimation and observation errors covariances, respectively. A multi-dimensional and multi-species reactive transport model is coupled to simulate the migration of contaminants within a Pleistocene aquifer layer located around 25 m below mean sea level. The biodegradation chain of chlorinated hydrocarbons starting from tetrachloroethene and ending with vinyl chloride is modeled under anaerobic environmental conditions for 5 decades. Yearly pseudo-concentration data are used to condition the forecast concentration and degradation rates in the presence of model and observational errors. Assimilation results demonstrate the robustness of the hybrid EnKF-OI, for accurately calibrating the uncertain biodegradation rates. When implemented serially, the adaptive hybrid EnKF-OI scheme efficiently adjusts the weights of the involved covariances for each individual measurement. The EnKF_ESOS is shown to maintain the parameter ensemble spread much better leading to more robust estimates of the states and parameters. On average, a well tuned hybrid EnKF-OI and the EnKF_ESOS respectively suggest around 48 and 21 % improved concentration estimates, as well as around 70 and 23 % improved anaerobic degradation rates, over the standard EnKF. Incorporating large uncertainties in the flow model degrades the accuracy of the estimates of all schemes. Given that the performance of the hybrid EnKF-OI depends on the quality of the background statistics, satisfactory results were obtained only when the uncertainty imposed on the background information is relatively moderate.