Abstract. The ensemble Kalman filter (EnKF) is a popular data assimilation method in soil hydrology. In this context, it is used to estimate states and parameters simultaneously. Due to unrepresented model errors and a limited ensemble size, state and parameter uncertainties can become too small during assimilation. Inflation methods are capable of increasing state uncertainties, but typically struggle with soil hydrologic applications. We propose a multiplicative inflation method specifically designed for the needs in soil hydrology. It employs a Kalman filter within the EnKF to estimate inflation factors based on the difference between measurements and mean forecast state within the EnKF. We demonstrate its capabilities on a small soil hydrologic test case. The method is capable of adjusting inflation factors to spatiotemporally varying model errors. It successfully transfers the inflation to parameters in the augmented state, which leads to an improved estimation.

Abstract. The representation of soil water movement exposes uncertainties in all model components. We assess the key uncertainties for the specific hydraulic situation of a 1-D soil profile with TDR (time domain reflectometry)-measured water contents. The uncertainties addressed are initial condition, soil hydraulic parameters, small-scale heterogeneity, upper boundary condition, and the local equilibrium assumption by the Richards equation. We employ an ensemble Kalman filter (EnKF) with an augmented state to represent and estimate all key uncertainties, except for the intermittent violation of the local equilibrium assumption. For the latter, we introduce a closed-eye EnKF to bridge the gap. Due to an iterative approach, the EnKF was capable of estimating soil parameters, Miller scaling factors and upper boundary condition based on TDR measurements during a single rain event.The introduced closed-eye period ensured constant parameters, suggesting that they resemble the believed true material properties. This closed-eye period improves predictions during periods when the local equilibrium assumption is met, but requires a description of the dynamics during local nonequilibrium phases to be able to predict them. Such a description remains an open challenge. Finally, for the given representation our results show the necessity of including smallscale heterogeneity. A simplified representation with Miller scaling already yielded a satisfactory description.

Abstract. The ensemble Kalman filter (EnKF) is a popular data assimilation method in soil hydrology. In this context, it is used to estimate states and parameters simultaneously. Due to unrepresented model errors and a limited ensemble size, state and parameter uncertainties can become too small during assimilation. Inflation methods are capable of increasing state uncertainties, but typically struggle with soil hydrologic applications. We propose a multiplicative inflation method specifically designed for the needs in soil hydrology. It employs a Kalman filter within the EnKF to estimate inflation factors based on the difference between measurements and mean forecast state within the EnKF. We demonstrate its capabilities on a small soil hydrologic test case. The method is capable of adjusting inflation factors to spatiotemporally varying model errors. It successfully transfers the inflation to parameters in the augmented state, which leads to an improved estimation.

The description of soil water movement at the field scale requires soil hydraulic material properties. These cannot be measured directly and exhibit an intrinsic multiscale heterogeneity. The estimation of soil hydraulic properties through inverse modeling or data assimilation requires measurements of the state of the system. However, these measurements are typically scarce and do not resolve soil heterogeneity leading to effective material properties with limited predictive capabilities. In a synthetic study at the scale of soil profiles, we explore the possibility to estimate an effective reduced one-dimensional representation based on only four local water content measurements in a vertical profile located in one-and two-dimensional heterogeneous media. We allow the effective material properties to deviate locally to consider the impact of the small-scale heterogeneity on the water content measurements. In the synthetic experiments, the estimated reduced one-dimensional representations predict soil water content and fluxes sufficiently well but can fail to predict the accurate timing and magnitude of infiltration fronts. Cumulative fluxes below the water content measurements were predicted correctly even on short time scales, if evaporation was estimated accurately. However, this proved to be challenging if the local evaporation fluxes above the measurement profile deviated strongly from the average evaporation fluxes of the heterogeneous medium. The one-dimensional estimation leads to soil hydraulic parameters describing effective material properties that differ from the true material properties to compensate the missing representation of heterogeneity and two-dimensional flow.