Data Assimilation with the Ensemble Kalman Filter using Integrated Subsurface Flow Models

Reliable estimates of the water availability and fluxes within the vadose zone and groundwater are important for numerous applications. Integrated numerical subsurface flow models can give comprehensive estimates of states and fluxes within both compartments (vadose zone and groundwater), accounting for two-way feedbacks between them. However, those estimates are highly uncertain. Using data assimilation (DA), one can reduce the forecast uncertainty of the numerical model by utilizing information obtained from measurements. The numerical model state is updated, determining its most likely value, given a certain observation. Despite what might be intuitively assumed, it is not necessarily the case in DA with integrated subsurface flow models that assimilating observations from one compartment improves estimates in the other one. In fact, updates often need to be limited to the respective compartment to avoid deteriorations by the DA due to spurious covariances. Considering the core idea of integrated modeling, there are incentives to work out strategies to i.) mitigate such deteriorations and ii.) utilize interactions between the subsurface compartments more extensively when conducting DA with such models.

We test DA strategies using the ensemble Kalman Filter, which is a common choice for data assimilation with subsurface flow models. We extract measurements from a numerical reference model that exhibits heterogeneous soil hydraulic parameter fields. We acknowledge that such heterogeneous structures are commonly not known in real catchments, so we use homogenized soil hydraulic parameters in the ensemble (forecast model). We conduct the experiments on the plot/hillslope scale but consider spatial averages of the estimates for transferability to larger spatial scales. The analyzed variables are the soil moisture near the land surface, the soil moisture within the root zone, groundwater recharge, and the groundwater table height. They are all highly relevant for applications and give a comprehensive overview of the whole subsurface.

Both soil moisture and groundwater table assimilation consistently improve estimates in their respective compartment but sometimes deteriorate estimates in the other compartment. We find both bias correction and vertical localization to be suitable measures to mitigate the deterioration of groundwater table height predictions by soil moisture assimilation. Estimates of groundwater recharge are generally deteriorated by the updates of DA since DA introduces artificial balancing fluxes between the compartments. Still, recharge estimates can be improved in a simulation without DA, which uses the states and soil hydraulic parameters estimated by DA. We find that applying information from the groundwater observations to both the groundwater and the deep vadose zone can dampen the artificial balancing fluxes between the compartments, which leads to improved estimates of the groundwater table height. Multivariate DA of both soil moisture and groundwater leads to similarly good estimates as univariate DA near the respective observations and better estimates between the observations (i.e., within the root zone).