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This study considers the assimilation problem of subsurface contaminants at\udthe port of Rotterdam in the Netherlands. It involves the estimation of\udsolute concentrations and biodegradation rates of four different chlorinated\udsolvents. We focus on assessing the efficiency of an adaptive hybrid ensemble\udKalman filter and optimal interpolation (EnKF-OI) and the exact second-order\udsampling formulation (EnKFESOS) for mitigating the undersampling\udof the estimation and observation errors covariances, respectively. A\udmulti-dimensional and multi-species reactive transport model is coupled to\udsimulate the migration of contaminants within a Pleistocene aquifer layer\udlocated around 25 m below mean sea level. The biodegradation chain of\udchlorinated hydrocarbons starting from tetrachloroethene and ending with\udvinyl chloride is modeled under anaerobic environmental conditions for 5\uddecades. Yearly pseudo-concentration data are used to condition the forecast\udconcentration and degradation rates in the presence of model and\udobservational errors. Assimilation results demonstrate the robustness of the\udhybrid EnKF-OI, for accurately calibrating the uncertain biodegradation\udrates. When implemented serially, the adaptive hybrid EnKF-OI scheme\udefficiently adjusts the weights of the involved covariances for each\udindividual measurement. The EnKFESOS is shown to maintain the\udparameter ensemble spread much better leading to more robust estimates of the\udstates and parameters. On average, a well tuned hybrid EnKF-OI and the\udEnKFESOS respectively suggest around 48 and 21 % improved\udconcentration estimates, as well as around 70 and 23 % improved anaerobic\uddegradation rates, over the standard EnKF. Incorporating large uncertainties\udin the flow model degrades the accuracy of the estimates of all schemes.\udGiven that the performance of the hybrid EnKF-OI depends on the quality of\udthe background statistics, satisfactory results were obtained only when the\uduncertainty imposed on the background information is relatively moderate

hydrology and earth system sciences

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