Cosmic-ray neutron probes are widely used to monitor environmental water content near the surface. The method averages over tens of hectares and is unrivaled in serving representative data for agriculture and hydrological models at the hectometer scale. Recent experiments, however, indicate that the sensor response to environmental heterogeneity is not fully understood. Knowledge of the support volume is a prerequisite for the proper interpretation and validation of hydrogeophysical data. In a previous study, several physical simplifications have been introduced into a neutron transport model in order to derive the characteristics of the cosmic-ray probe's footprint. We utilize a refined source and energy spectrum for cosmic-ray neutrons and simulate their response to a variety of environmental conditions. Results indicate that the method is particularly sensitive to soil moisture in the first tens of meters around the probe, whereas the radial weights are changing dynamically with ambient water. The footprint radius ranges from 130 to 240 m depending on air humidity, soil moisture, and vegetation. The moisture-dependent penetration depth of 15 to 83 cm decreases exponentially with distance to the sensor. However, the footprint circle remains almost isotropic in complex terrain with nearby rivers, roads or hill slopes. Our findings suggest that a dynamically weighted average of point measurements is essential for accurate calibration and validation. The new insights will have important impact on signal interpretation, sensor installation, data interpolation from mobile surveys, and the choice of appropriate resolutions for data assimilation into hydrological models.

Multicompartment and multiscale long‐term observation and research are important prerequisites to tackling the scientific challenges resulting from climate and global change. Long‐term monitoring programs are cost intensive and require high analytical standards, however, and the gain of knowledge often requires longer observation times. Nevertheless, several environmental research networks have been established in recent years, focusing on the impact of climate and land use change on terrestrial ecosystems. From 2008 onward, a network of Terrestrial Environmental Observatories (TERENO) has been established in Germany as an interdisciplinary research program that aims to observe and explore the long‐term ecological, social, and economic impacts of global change at the regional level. State‐of‐the‐art methods from the field of environmental monitoring, geophysics, and remote sensing will be used to record and analyze states and fluxes for different environmental compartments from groundwater through the vadose zone, surface water, and biosphere, up to the lower atmosphere.

Abstract. In the last few years the method of cosmic-ray neutron sensing (CRNS) has gained popularity among hydrologists, physicists, and land-surface modelers. The sensor provides continuous soil moisture data, averaged over several hectares and tens of decimeters in depth. However, the signal still may contain unidentified features of hydrological processes, and many calibration datasets are often required in order to find reliable relations between neutron intensity and water dynamics. Recent insights into environmental neutrons accurately described the spatial sensitivity of the sensor and thus allowed one to quantify the contribution of individual sample locations to the CRNS signal. Consequently, data points of calibration and validation datasets are suggested to be averaged using a more physically based weighting approach. In this work, a revised sensitivity function is used to calculate weighted averages of point data. The function is different from the simple exponential convention by the extraordinary sensitivity to the first few meters around the probe, and by dependencies on air pressure, air humidity, soil moisture, and vegetation. The approach is extensively tested at six distinct monitoring sites: two sites with multiple calibration datasets and four sites with continuous time series datasets. In all cases, the revised averaging method improved the performance of the CRNS products. The revised approach further helped to reveal hidden hydrological processes which otherwise remained unexplained in the data or were lost in the process of overcalibration. The presented weighting approach increases the overall accuracy of CRNS products and will have an impact on all their applications in agriculture, hydrology, and modeling.

[1] Hydraulic tomography is a method to identify the three-dimensional spatial distribution of hydraulic properties in the subsurface. We propose a tomographic approach providing the inversion of travel times of hydraulic or pneumatic tests conducted in a tomographic array. The inversion is based on the relation between the peak time of a recorded transient pressure curve and the diffusivity of the investigated system. The development of a transformation factor enables the inversion of further travel times besides the peak time of a transient curve. As the early travel times of the curve are mainly related to preferential flow features while the inversion based on late travel times are reflecting an integral behavior, it can be assumed that the different inversion results reflect the properties of the overall system. By comparing the different reconstructions the system interpretation therefore becomes more comprehensive and reliable. Furthermore, the similarity of the proposed hydraulic tomographic approach to seismic travel time tomography allows us to apply the inversion algorithms which are used for seismic tomography. We therefore apply the method of staggered grids, which enables to refine the grid resulting in a higher nominal resolution, to data from a set of interference tests arranged in a tomographic array. The tests were conducted in an unsaturated fractured sandstone cylinder in the laboratory. The three-dimensional reconstructions of the diffusivity distribution are found to be highly reliable and robust. In particular, the mapped fracture of the sandstone cylinder coincides with our reconstructed diffusivity distribution.

[1] Spatial variations in hydraulic conductivity (K) provide critical controls on solute transport in the subsurface. Recently, new direct-push tools were developed for highresolution characterization of K variations in unconsolidated settings. These tools were applied to obtain 58 profiles (vertical resolution of 1.5 cm) from the heavily studied macrodispersion experiment (MADE) site. We compare the data from these 58 profiles with those from the 67 flowmeter profiles that have served as the primary basis for characterizing the heterogeneous aquifer at the site. Overall, the patterns of variation displayed by the two data sets are quite similar, in terms of both large-scale structure and autocorrelation characteristics. The direct-push K values are, on average, roughly a factor of 5 lower than the flowmeter values. This discrepancy appears to be attributable, at least in part, to opposite biases between the two methods, with the current versions of the direct-push tools underestimating K in the highly permeable upper portions of the aquifer and the flowmeter overestimating K in the less permeable lower portions. The vertically averaged K values from a series of direct-push profiles in the vicinity of two pumping tests at the site are consistent with the K estimates from those tests, providing evidence that the direct-push estimates are of a reasonable magnitude. The results of this field demonstration show that direct-push profiling has the potential to characterize highly heterogeneous aquifers with a speed and resolution that has not previously been possible.

A tomographical method is presented that allows the reconstruction of the structure of soil layers between two boreholes. If the soil is water saturated, the transient field equation for pore water pressure S(x) delta tu(x,t)- Del .(k(x) Del u(x,t))=Q can be used to reconstruct the soil structure from its permeability k(x). The transient potential field u(x, t) is controlled by hydraulic dipoles (point source and point sink). The positions of source and sink are varied over both boreholes. Pore water pressure observations are used as data for the inverse problem. Uniqueness problems are discussed. The forward problem is discretized in a FE algorithm, the inverse problem solved by a standard output least-squares method.

Spreading of conservative solutes in groundwater due to aquifer heterogeneity is quantified by the macrodispersivity, which was found to be scale dependent. It increases with travel distance, stabilizing eventually at a constant value. However, the question of its asymptotic behavior at very large scale is still a matter of debate. It was surmised in the literature that macrodispersivity scales up following a unique scaling law. Attempts to define such a law were made by fitting a regression line in the log‐log representation of an ensemble of macrodispersivities from multiple experiments. The functional relationships differ among the authors, based on the choice of data. Our study revisits the data basis, used for inferring unique scaling, through a detailed analysis of literature marcodispersivities. In addition, values were collected from the most recent tracer tests reported in the literature. We specified a system of criteria for reliability and reevaluated the reliability of the reported values. The final collection of reliable estimates of macrodispersivity does not support a unique scaling law relationship. On the contrary, our results indicate, that the field data can be explained as a collection of macrodispersivities of aquifers with varying degree of heterogeneity where each exhibits its own constant asymptotic value. Our investigation concludes that transport, and particularly the macrodispersivity, is formation‐specific, and that modeling of transport cannot be relegated to a unique scaling law. Instead, transport requires characterization of aquifer properties, e.g., spatial distribution of hydraulic conductivity, and the use of adequate models.

Abstract. According to Dooge (1986) intermediate-scale catchments are systems of organized complexity, being too organized and yet too small to be characterized on a statistical/conceptual basis, but too large and too heterogeneous to be characterized in a deterministic manner. A key requirement for building structurally adequate models precisely for this intermediate scale is a better understanding of how different forms of spatial organization affect storage and release of water and energy. Here, we propose that a combination of the concept of hydrological response units (HRUs) and thermodynamics offers several helpful and partly novel perspectives for gaining this improved understanding. Our key idea is to define functional similarity based on similarity of the terrestrial controls of gradients and resistance terms controlling the land surface energy balance, rainfall runoff transformation, and groundwater storage and release. This might imply that functional similarity with respect to these specific forms of water release emerges at different scales, namely the small field scale, the hillslope, and the catchment scale. We thus propose three different types of "functional units" -specialized HRUs, so to speak -which behave similarly with respect to one specific form of water release and with a characteristic extent equal to one of those three scale levels. We furthermore discuss an experimental strategy based on exemplary learning and replicate experiments to identify and delineate these functional units, and as a promising strategy for characterizing the interplay and organization of water and energy fluxes across scales. We believe the thermodynamic perspective to be well suited to unmask equifinality as inherent in the equations governing water, momentum, and energy fluxes: this is because several combinations of gradients and resistance terms yield the same mass or energy flux and the terrestrial controls of gradients and resistance terms are largely independent. We propose that structurally adequate models at this scale should consequently disentangle driving gradients and resistance terms, because this optionally allows Published by Copernicus Publications on behalf of the European Geosciences Union. E. Zehe et al.: HESS Opinions: Thermodynamic reinterpretation of the HRU conceptequifinality to be partly reduced by including available observations, e.g., on driving gradients. Most importantly, the thermodynamic perspective yields an energy-centered perspective on rainfall-runoff transformation and evapotranspiration, including fundamental limits for energy fluxes associated with these processes. This might additionally reduce equifinality and opens up opportunities for testing thermodynamic optimality principles within independent predictions of rainfall-runoff or land surface energy exchange. This is pivotal to finding out whether or not spatial organization in catchments is in accordance with a fundamental organizing principle.