H. Hardelauf

Temporal Stability of Soil Water Contents: A Review of Data and Analyses

Temporal stability (TS) of soil water content (SWC) has been observed throughout a wide range of spatial and temporal scales. Yet, the evidence with respect to the controlling factors on TS SWC remains contradictory or nonexistent. The objective of this work was to develop the first comprehensive review of methodologies to evaluate TS SWC and to present and analyze an inventory of published data. Statistical analysis of mean relative difference (MRD) data and associated standard deviations (SDRD) from 157 graphs in 37 publications showed a trend for the standard deviation of MRD (SDMRD) to increase with scale, as expected. The MRD followed generally the Gaussian distribution with R 2 ranging from 0.841 to 0.998. No relationship between SDMRD and R 2 was observed. The smallest R 2 values were mostly found for negatively skewed and platykurtic MRD distributions. A new statistical model for temporally stable SWC fields was proposed. The analysis of the published data on seven measurement-, terrain-, and climate-related potentially controlling factors of TS SWC suggested intertwined effects of controlling factors rather than single dominant factors. This calls for a focused research effort on the interactions and effects of measurement design, topography, soil, vegetation and climate on TS SWC. Research avenues are proposed which will lead to a better understanding of the TS phenomenon and ultimately to the identification of the underlying mechanisms.

Spatiotemporal relations between water budget components and soil water content in a forested tributary catchment

We examined 3 years of measured daily values of all major water budget components (precipitation P, potential evapotranspiration PET, actual evapotranspiration ET, and runoff R) and volumetric soil water content θ of a small, forested catchment located in the west of Germany. The spatial distribution of θ was determined from a wireless sensor network of 109 points with 3 measurement depths each; ET was calculated from eddy-covariance tower measurements. The water budget was dominantly energy limited, with ET amounting to approximately 90% of PET, and a runoff ratio R/P of 56%. P, ET, and R closed the long-term water budget with a residual of 2% of precipitation. On the daily time scale, the residual of the water budget was larger than on the annual time scale, and explained to a moderate extent by θ (R2 = 0.40). Wavelet analysis revealed subweekly time scales, presumably dominated by unaccounted fast-turnover storage terms such as interception, as a major source of uncertainty in water balance closure. At weekly resolution, soil water content explained more than half (R2 = 0.62) of the residual. By means of combined empirical orthogonal function and cluster analysis, two slightly different spatial patterns of θ could be identified that were associated with mean θ values below and above 0.35 cm3/cm3, respectively. The timing of these patterns as well as the varying coherence between PET, ET, and soil water content responded to changes in water availability, including a moderate response to the European drought in spring 2011.

Short Note: On preconditioning for a parallel solution of the Richards equation

In this paper, we present a class of preconditioning methods for a parallel solution of the three-dimensional Richards equation. The preconditioning methods Jacobi scaling, block-Jacobi, incomplete lower-upper, incomplete Cholesky and algebraic multigrid were applied in combination with a parallel conjugate gradient solver and tested for robustness and convergence using two model scenarios. The first scenario was an infiltration into initially dry, sandy soil discretised in 500,000 nodes. The second scenario comprised spatially distributed soil properties using 275,706 numerical nodes and atmospheric boundary conditions. Computational results showed a high efficiency of the nonlinear parallel solution procedure for both scenarios using up to 64 processors. Using 32 processors for the first scenario reduced the wall clock time to slightly more than 1% of the single processor run. For scenario 2 the use of 64 processors reduces the wall clock time to slightly more than 20% of the 8 processors wall clock time. The difference in the efficiency of the various preconditioning methods is moderate but not negligible. The use of the multigrid preconditioning algorithm is recommended, since on average it performed best for both scenarios.

Quantitative Imaging of 3D Solute Transport Using 2D Time‐Lapse ERT: A Synthetic Feasibility Study

Time-lapse electrical resistance tomography (ERT) has proven significant potential to monitor solute plumes in the subsurface. However, the ultimate value of ERT for quantitative imaging of solute transport, for example in heterogeneous aquifers, is still under dispute. Here, difficulties may be expected to arise particularly from the fact that ERT data acquisition and interpretation is often limited to 2D image planes, while aquifers are generally characterized by a 3D structure involving considerable variability of flow and transport properties. The potential of time-lapse ERT in such a situation is investigated by means of a synthetic tracer experiment. For this purpose, 3D solute transport in a heterogeneous hydraulic conductivity field, characterized by an exponential covariance function, is simulated. Assuming that solute concentration is linearly related to electrical conductivity, the spatiotemporal evolution of the tracer plume is imaged in a transect spanned by a set of fictive boreholes using 2D time-lapse ERT. Although the 3D process is imaged using a 2D inversion approach, the recovered electrical conductivity distributions coincide well with the input distributions. The obtained images are interpreted as concentration maps and then analyzed in terms of transport properties. By adopting a stream-tube model, an equivalent advection velocity and longitudinal dispersivity can be quantified for each pixel in the ERT image plane. The recovered equivalent advection velocities exhibit fair agreement with those obtained from the original model. The results of the synthetic study demonstrate that quantitative imaging of 3D solute transport by means of time-lapse ERT is feasible. Importantly, systematic errors associated with the 2D representation of a 3D model are found to play an insignificant role concerning the quantification of transport properties, justifying the use of simple 2D imaging, for instance if equipment, time, and/or budget is limited.

Global Random Walk Simulations of Diffusion

Random walk methods are suitable to build up convergent solutions for reaction-diffusion problems and were successfully applied to simulations of transport processes in a random environment. The disadvantage is that, for realistic cases, these methods become time and memory expensive. To increase the computation speed and to reduce the required memory, we derived a “global random walk” method in which the particles at a given site of the grid are simultaneously scattered following the binomial Bernoulli repartition. It was found that the computation time is reduced three orders of magnitude with respect to individual random walk methods. Moreover, by suitable “microscopic balance” boundary conditions, we obtained good simulations of transport in unbounded domains, using normal size grids. The global random walk improves the statistical quality of simulations for diffusion processes in random fields. The method was tested by comparisons with analytical and finite difference solutions as well as with concentrations measured in “column experiments”, used in laboratory study of soils’ hydrogeological and chemical properties.