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Cosmic-ray neutron sensing (CRNS) allows for the estimation of root-zone soil water content (SWC) at the scale of several hectares. In this paper, we present the data recorded by a dense CRNS network operated from 2019 to 2022 at an agricultural research site in Marquardt, Germany – the first multi-year CRNS cluster. Consisting, at its core, of eight permanently installed CRNS sensors, the cluster was supplemented by a wealth of complementary measurements: data from seven additional temporary CRNS sensors, partly co-located with the permanent ones; 27 SWC profiles (mostly permanent); two groundwater observation wells; meteorological records; and Global Navigation Satellite System reflectometry (GNSS-R). Complementary to these continuous measurements, numerous campaign-based activities provided data by mobile CRNS roving, hyperspectral imagery via UASs, intensive manual sampling of soil properties (SWC, bulk density, organic matter, texture, soil hydraulic properties), and observations of biomass and snow (cover, depth, and density). The unique temporal coverage of 3 years entails a broad spectrum of hydro-meteorological conditions, including exceptional drought periods and extreme rainfall but also episodes of snow coverage, as well as a dedicated irrigation experiment. Apart from serving to advance CRNS-related retrieval methods, this data set is expected to be useful for various disciplines, for example, soil and groundwater hydrology, agriculture, or remote sensing. Hence, we show exemplary features of the data set in order to highlight the potential for such subsequent studies.

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The understanding of neutron transport by Monte Carlo simulations led to major advancements towards precise interpretation of measurements. URANOS (Ultra Rapid Neutron-Only Simulation) is a free software package which has been developed in the last few years in cooperation with particle physics and environmental sciences, specifically for the purposes of cosmic-ray neutron sensing (CRNS). Its versatile user interface and input/output scheme tailored for CRNS applications offers hydrologists straightforward access to model individual scenarios and to directly perform advanced neutron transport calculations. The geometry can be modeled layer-wise, whereas in each layer a voxel geometry is extruded using a two-dimensional map from pixel images representing predefined materials and allowing for the construction of objects on the basis of pixel graphics without a three-dimensional editor. It furthermore features predefined cosmic-ray neutron spectra and detector configurations and also allows for a replication of important site characteristics of study areas – from a small pond to the catchment scale. The simulation thereby gives precise answers to questions like from which location do neutrons originate? How do they propagate to the sensor? What is the neutron's response to certain environmental changes? In recent years, URANOS has been successfully employed by a number of studies, for example, to calculate the cosmic-ray neutron footprint, signals in complex geometries like mobile applications on roads, urban environments and snow patterns.

This paper presents a new theoretical approach to estimate the contribution of distant areas to the measurement signal of cosmic-ray neutron detectors for snow and soil moisture monitoring. The algorithm is based on the local neutron production and the transport mechanism, given by the neutron–moisture relationship and the radial intensity function, respectively. The purely analytical approach has been validated with physics-based neutron transport simulations for heterogeneous soil moisture patterns, exemplary landscape features, and remote fields at a distance. We found that the method provides good approximations of simulated signal contributions in patchy soils with typical deviations of less than 1 %. Moreover, implications of this concept have been investigated for the neutron–moisture relationship, where the signal contribution of an area has the potential to explain deviating shapes of this curve that are often reported in the literature. Finally, the method has been used to develop a new practical footprint definition to express whether or not a distant area's soil moisture change is actually detectable in terms of measurement precision. The presented concepts answer long-lasting questions about the influence of distant landscape structures in the integral footprint of the sensor without the need for computationally expensive simulations. The new insights are highly relevant to support signal interpretation, data harmonization, and sensor calibration and will be particularly useful for sensors positioned in complex terrain or on agriculturally managed sites.

Cosmic-ray neutron sensing (CRNS) allows for the estimation of root-zone soil water content (SWC) at the scale of several hectares. In this paper, we present the data recorded by a dense CRNS network operated from 2019 to 2022 at an agricultural research site in Marquardt, Germany – the first multi-year CRNS cluster. Consisting, at its core, of eight permanently installed CRNS sensors, the cluster was supplemented by a wealth of complementary measurements: data from seven additional temporary CRNS sensors, partly co-located with the permanent ones; 27 SWC profiles (mostly permanent); two groundwater observation wells; meteorological records; and Global Navigation Satellite System reflectometry (GNSS-R). Complementary to these continuous measurements, numerous campaign-based activities provided data by mobile CRNS roving, hyperspectral imagery via UASs, intensive manual sampling of soil properties (SWC, bulk density, organic matter, texture, soil hydraulic properties), and observations of biomass and snow (cover, depth, and density). The unique temporal coverage of 3 years entails a broad spectrum of hydro-meteorological conditions, including exceptional drought periods and extreme rainfall but also episodes of snow coverage, as well as a dedicated irrigation experiment. Apart from serving to advance CRNS-related retrieval methods, this data set is expected to be useful for various disciplines, for example, soil and groundwater hydrology, agriculture, or remote sensing. Hence, we show exemplary features of the data set in order to highlight the potential for such subsequent studies.

Above-ground cosmic-ray neutron sensing (CRNS) allows for the non-invasive estimation of the field-scale soil moisture content in the upper decimetres of the soil. However, large parts of the deeper vadose zone remain outside of its observational window. Retrieving soil moisture information from these deeper layers requires extrapolation, modelling or other methods, all of which come with methodological challenges. Against this background, we investigate CRNS for downhole soil moisture measurements in deeper layers of the vadose zone. To render calibration with in situ soil moisture measurements unnecessary, we rescaled neutron intensities observed below the terrain surface with intensities measured above a waterbody. An experimental set-up with a CRNS sensor deployed at different depths of up to 10 m below the surface in a groundwater observation well combined with particle transport simulations revealed the response of downhole thermal neutron intensities to changes in the soil moisture content at the depth of the downhole neutron detector as well as in the layers above it. The simulation results suggest that the sensitive measurement radius of several decimetres, which depends on soil moisture and soil bulk density, exceeds that of a standard active neutron probe (which is only about 30 cm). We derived transfer functions to estimate downhole neutron signals from soil moisture information, and we describe approaches for using these transfer functions in an inverse way to derive soil moisture from the observed neutron signals. The in situ neutron and soil moisture observations confirm the applicability of these functions and prove the concept of passive downhole soil moisture estimation, even at larger depths, using cosmic-ray neutron sensing.

Cosmic-ray neutron sensing (CRNS) is a non-invasive tool for measuring hydrogen pools such as soil moisture, snow or vegetation. The intrinsic integration over a radial hectare-scale footprint is a clear advantage for averaging out small-scale heterogeneity, but on the other hand the data may become hard to interpret in complex terrain with patchy land use. This study presents a directional shielding approach to prevent neutrons from certain angles from being counted while counting neutrons entering the detector from other angles and explores its potential to gain a sharper horizontal view on the surrounding soil moisture distribution. Using the Monte Carlo code URANOS (Ultra Rapid Neutron-Only Simulation), we modelled the effect of additional polyethylene shields on the horizontal field of view and assessed its impact on the epithermal count rate, propagated uncertainties and aggregation time. The results demonstrate that directional CRNS measurements are strongly dominated by isotropic neutron transport, which dilutes the signal of the targeted direction especially from the far field. For typical count rates of customary CRNS stations, directional shielding of half-spaces could not lead to acceptable precision at a daily time resolution. However, the mere statistical distinction of two rates should be feasible.

Investigations of neutron transport through air and soil by Monte Carlo simulations led to major advancements towards a precise interpretation of measurements, especially they improved the understanding of the cosmic-ray neutron footprint. Up to now, the conversion of soil moisture to a detectable neutron count rate relies mainly on the equation presented by Desilets et al. (2010). While in general a hyperbolic expression can be derived from theoretical considerations, their empiric parameterisation needs to be revised for two reasons. Firstly, a rigorous mathematical treatment reveals that the values of the four parameters are ambiguous because their values are not independent. We find a 3-parameter equation with unambiguous values of the parameters which is equivalent in any other respect to the 4-parameter equation. Secondly, high-resolution Monte-Carlo simulations revealed a systematic deviation of the count rate to soil moisture relation especially for extremely dry conditions as well as very humid conditions. That is a hint, that a smaller contribution to the intensity was forgotten or not adequately treated by the conventional approach. Investigating the above-ground neutron flux by a broadly based Monte-Carlo simulation campaign revealed a more detailed understanding of different contributions to this signal, especially targeting air humidity corrections. The packages MCNP and URANOS were used to derive a function able to describe the respective dependencies including the effect of different hydrogen pools and the detector-specific response function. The new relationship has been tested at two exemplary measurement sites and its remarkable performance allows for a promising prospect of more comprehensive data quality in the future.

Cosmic-ray neutron sensing (CRNS) allows for non-invasive soil moisture estimations at the field scale. The derivation of soil moisture generally relies on secondary cosmic-ray neutrons in the epithermal to fast energy ranges. Most approaches and processing techniques for observed neutron intensities are based on the assumption of homogeneous site conditions or of soil moisture patterns with correlation lengths shorter than the measurement footprint of the neutron detector. However, in view of the non-linear relationship between neutron intensities and soil moisture, it is questionable whether these assumptions are applicable. In this study, we investigated how a non-uniform soil moisture distribution within the footprint impacts the CRNS soil moisture estimation and how the combined use of epithermal and thermal neutrons can be advantageous in this case. Thermal neutrons have lower energies and a substantially smaller measurement footprint around the sensor than epithermal neutrons. Analyses using the URANOS (Ultra RApid Neutron-Only Simulation) Monte Carlo simulations to investigate the measurement footprint dynamics at a study site in northeastern Germany revealed that the thermal footprint mainly covers mineral soils in the near-field to the sensor while the epithermal footprint also covers large areas with organic soils. We found that either combining the observed thermal and epithermal neutron intensities by a rescaling method developed in this study or adjusting all parameters of the transfer function leads to an improved calibration against the reference soil moisture measurements in the near-field compared to the standard approach and using epithermal neutrons alone. We also found that the relationship between thermal and epithermal neutrons provided an indicator for footprint heterogeneity. We, therefore, suggest that the combined use of thermal and epithermal neutrons offers the potential of a spatial disaggregation of the measurement footprint in terms o

Monitoring soil moisture is still a challenge: it varies strongly in space and time and at various scales while conventional sensors typically suffer from small spatial support. With a sensor footprint up to several hectares, cosmic-ray neutron sensing (CRNS) is a modern technology to address that challenge. So far, the CRNS method has typically been applied with single sensors or in sparse national-scale networks. This study presents, for the first time, a dense network of 24 CRNS stations that covered, from May to July 2019, an area of just 1 km(2): the pre-Alpine Rott headwater catchment in Southern Germany, which is characterized by strong soil moisture gradients in a heterogeneous landscape with forests and grasslands. With substantially overlapping sensor footprints, this network was designed to study root-zone soil moisture dynamics at the catchment scale. The observations of the dense CRNS network were complemented by extensive measurements that allow users to study soil moisture variability at various spatial scales: roving (mobile) CRNS units, remotely sensed thermal images from unmanned areal systems (UASs), permanent and temporary wireless sensor networks, profile probes, and comprehensive manual soil sampling. Since neutron counts are also affected by hydrogen pools other than soil moisture, vegetation biomass was monitored in forest and grassland patches, as well as meteorological variables; discharge and groundwater tables were recorded to support hydrological modeling experiments. As a result, we provide a unique and comprehensive data set to several research communities: to those who investigate the retrieval of soil moisture from cosmic-ray neutron sensing, to those who study the variability of soil moisture at different spatiotemporal scales, and to those who intend to better understand the role of rootzone soil moisture dynamics in the context of catchment and groundwater hydrology, as well as land-atmosphere exchange processes. The data set is a

Cosmic‐ray neutron sensing (CRNS) is a promising non‐invasive technique to estimate snow water equivalent (SWE) over large areas. In contrast to preliminary studies focusing on shallow snow conditions (SWE 130 mm), more recently the method was shown experimentally to be sensitive also to deeper snowpacks providing the basis for its use at mountain experimental sites. However, hysteretic neutron response has been observed for complex snow cover including patchy snow‐free areas. In the present study we aimed to understand and support the experimental findings using a comprehensive neutron modeling approach. Several simulations have been set up in order to disentangle the effect on the signal of different land surface characteristics and to reproduce multiple observations during periods of snow melt and accumulation. To represent the actual land surface heterogeneity and the complex snow cover, the model used data from terrestrial laser scanning. The results show that the model was able to accurately reproduce the CRNS signal and particularly the hysteresis effect during accumulation and melting periods. Moreover, the sensor footprint was found to be anisotropic and affected by the spatial distribution of liquid water and snow as well as by the topography of the nearby mountains. Under fully snow‐covered conditions the CRNS is able to accurately estimate SWE without prior knowledge about snow density profiles or other spatial anomalies. These results provide new insights into the characteristics of the detected neutron signal in complex terrain and support the use of CRNS for long‐term snow monitoring in high elevated mountain environments.

Irrigation is essential for maintaining food production in water-scarce regions. The irrigation need depends on the water content of the soil, which we measured with the novel technique of cosmic-ray neutron sensing (CRNS). The potential of the CRNS technique for drip irrigation scheduling was explored in this study for the Picassent site near Valencia, Spain. To support the experimental evidence, the neutron transport simulation URANOS was used to simulate the effect of drip irrigation on the neutron counts. The overall soil water content (SWC) in the CRNS footprint was characterized with a root mean square error <0.03 cm3/cm3, but the experimental dataset indicated methodological limitations to detect drip water input. Both experimental data and simulation results suggest that the large-area neutron response to drip irrigation is insignificant in our specific case using a standard CRNS probe. Because of the small area of irrigated patches and short irrigation time, the limited SWC changes due to drip irrigation were not visible from the measured neutron intensity changes. Our study shows that CRNS modeling can be used to assess the suitability of the CRNS technique for certain applications. While the standard CRNS probe was not able to detect small-scale drip irrigation patterns, the method might be applicable for larger irrigated areas, in drier regions, and for longer and more intense irrigation periods. Since statistical noise is the main limitation of the CRNS measurement, the capability of the instrument could be improved in future studies by larger and more efficient neutron detectors.

Cosmic-Ray Neutron Sensing (CRNS) is a novel technique for determining environmental water content by measuring albedo neutrons in the epithermal to fast energy range with moderated neutron detectors. We have investigated the response function of stationary and mobile neutron detectors typically used for environmental research in order to improve the model accuracy for neutron transport studies. Monte Carlo simulations have been performed in order to analyze the detection probability in terms of energy-dependent response and angular sensitivity for different variants of CRNS detectors and converter gases. Our results reveal the sensor’s response to neutron energies from 0.1 eV to 106 eV and highest sensitivity to vertical fluxes. The detector efficiency shows good agreement with reference data from the structurally similar Bonner Spheres. The relative probability of neutrons contributing to the overall integrated signal is especially important in regions with non-uniform albedo fluxes, such as complex terrain or heterogeneous distribution of hydrogen pools

Neutron monitors on the Earth’s surface are usually used to track the dynamics of incoming cosmic-ray neutrons of high energy under the assumption that local environmental conditions do not influence the highly shielded flux. Oppositely, in a recently established research field the local dynamics of environmental water is monitored by detecting low-energy cosmic-ray neutrons. Water in soil, air, snow and vegetation determines the amount of ground albedo neutrons in the sensitive energy range from 1 eV to 100 keV. Plenty of small neutron detectors have been installed on natural or agricultural sites all around the world Climate research, hydrologic models and irrigation management rely on these measurements, which represent area-average water content within tens of hectares due to the fast diffusion of neutrons in air. A major issue is the modulation of the neutron flux by the dynamics of incoming cosmic-ray neutrons. Conventionally,independent data from neutron monitors are consulted to serve as a reference for the correction of the local detectors. However, the performance of this comparative correction approach is unreliable, because it does not account for geographical displacement, different energy windows of the detectors, or potential influence of atmospheric conditions on the referenced neutron monitor. In addition, neutron monitor stations are sparse on Earth, and occasionally signals from different locations appear to be significantly inconsistent. The presentation shows how ground albedo neutrons from cosmic-rays are used in environmental research and emphasizes the need for a reliable correction for the incoming flux.

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.