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. Unrepresented model errors influence the estimation of effective soil hydraulic material properties. As the required model complexity for a consistent description of the measurement data is application dependent and unknown a priori, we implemented a structural error analysis based on the inversion of increasingly complex models. We show that the method can indicate unrepresented model errors and quantify their effects on the resulting material properties. To this end, a complicated 2-D subsurface architecture (AS-SESS) was forced with a fluctuating groundwater table while time domain reflectometry (TDR) and hydraulic potential measurement devices monitored the hydraulic state. In this work, we analyze the quantitative effect of unrepresented (i) sensor position uncertainty, (ii) small scale-heterogeneity, and (iii) 2-D flow phenomena on estimated soil hydraulic material properties with a 1-D and a 2-D study. The results of these studies demonstrate three main points: (i) the fewer sensors are available per material, the larger is the effect of unrepresented model errors on the resulting material properties. (ii) The 1-D study yields biased parameters due to unrepresented lateral flow. (iii) Representing and estimating sensor positions as well as small-scale heterogeneity decreased the mean absolute error of the volumetric water content data by more than a factor of 2 to 0.004.
Abstract. High-resolution time-lapse ground-penetrating radar (GPR) observations of advancing and retreating water tables can yield a wealth of information about near-surface water content dynamics. In this study, we present and analyze a series of imbibition, drainage and infiltration experiments that have been carried out at our artificial ASSESS test site and observed with surface-based GPR. The test site features a complicated but known subsurface architecture constructed with three different kinds of sand. It allows the study of soil water dynamics with GPR under a wide range of different conditions. Here, we assess in particular (i) the feasibility of monitoring the dynamic shape of the capillary fringe reflection and (ii) the relative precision of monitoring soil water dynamics averaged over the whole vertical extent by evaluating the bottom reflection. The phenomenology of the GPR response of a dynamically changing capillary fringe is developed from a soil physical point of view. We then explain experimentally observed phenomena based on numerical simulations of both the water content dynamics and the expected GPR response.
Abstract. Quantitative knowledge of the subsurface material distribution and its effective soil hydraulic material properties is essential to predict soil water movement. Groundpenetrating radar (GPR) is a noninvasive and nondestructive geophysical measurement method that is suitable to monitor hydraulic processes. Previous studies showed that the GPR signal from a fluctuating groundwater table is sensitive to the soil water characteristic and the hydraulic conductivity function. In this work, we show that the GPR signal originating from both the subsurface architecture and the fluctuating groundwater table is suitable to estimate the position of layers within the subsurface architecture together with the associated effective soil hydraulic material properties with inversion methods. To that end, we parameterize the subsurface architecture, solve the Richards equation, convert the resulting water content to relative permittivity with the complex refractive index model (CRIM), and solve Maxwell's equations numerically. In order to analyze the GPR signal, we implemented a new heuristic algorithm that detects relevant signals in the radargram (events) and extracts the corresponding signal travel time and amplitude. This algorithm is applied to simulated as well as measured radargrams and the detected events are associated automatically. Using events instead of the full wave regularizes the inversion focussing on the relevant measurement signal. For optimization, we use a global-local approach with preconditioning. Starting from an ensemble of initial parameter sets drawn with a Latin hypercube algorithm, we sequentially couple a simulated annealing algorithm with a Levenberg-Marquardt algorithm. The method is applied to synthetic as well as measured data from the ASSESS test site. We show that the method yields reasonable estimates for the position of the layers as well as for the soil hydraulic material properties by comparing the results to references derived from ground truth data as well as from time domain reflectometry (TDR).
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 1D soil profile with TDR measured water contents. Addressed uncertainties 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 to estimate 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 non-equilibrium phases to be able to predict them. Such a description remains an open challenge. Finally, for the given representation our results show the necessity to include small scale heterogeneity. A simplified representation with Miller scaling already yielded a satisfactory description.
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