The first set of simulation scenarios focussed on the effect of variation in soil chemical composition. URANOS allows adding selected chemical elements to the standard soil. For this study we added C, K, Mn, Na, Ti and Gd to the standard soil. Here, we chose the average 90 %-quantile (Q0.9) for top and subsoil as well as the overall average of these elements reported in the Geochemical Atlas of Europe . In addition, we simulated 6 setups by adding 0.001 g cm⁻³ of one element (C, K, Mn, Na and Ti) to the standard soil. Adding chemical elements to the standard soil in URANOS is designed for trace amounts up to 0.001 g cm⁻³. For adding larger amounts as reported in , we rescaled the bulk density of the soil in the simulation scenarios to maintain the same amount of solid soil material in the model domain. An overview of all soil chemistry scenarios can be found in Table .

The second set of simulation setups involved the simulation of different amounts of above-ground biomass. Therefore, we added plant gas layers of different heights and densities below and above the detector layer within the model domain. The plant gas in URANOS (≥v1.0) consists of air plus a defined amount of C (14 %), O (72 %) and H (14 %) in kg m⁻³ representing biomass . Hence, biomass water equivalents (BWE, in kg m⁻² or mm) can be estimated from wet biomass (BM, in kg m⁻²) by multiplication with a conversion factor of 0.86. The use of homogeneous material layers to represent biomass in neutron transport models has been shown by to be sufficient for epithermal neutrons and is therefore adapted for this study. An overview of all biomass scenarios can be found in Table .

The last two sets of homogeneous simulation setups involved the variation of soil bulk density compared to the 1.43 g cm⁻³ of the standard soil and the addition of water layers on top of the soil to mimic snow and ponding water. For the soil bulk density scenarios, the bulk density was either changed in the entire soil column or as a more realistic gradual linear increase in soil bulk density from the surface to 30 cm depth in 5 cm increments. An overview can be found in Table . For the water-layer setups, an additional subset of different water layers above a soil with 0.04 cm³ cm⁻³ and an above-ground BWE of 33.9 kg m⁻² was simulated, in order to investigate the impact of above-ground biomass on the response to snow and ponding water.

The response of a bare and moderated detector signal relative to the simulated intensity at a soil moisture content of 0.01 cm³ cm⁻³ in the individual setup (Tab. –) is shown in Fig.  and relative to the individual average intensity in Fig.  for the homogeneous simulation setups. It can be seen that in all simulation setups, both the moderated and bare detector respond to changes in soil moisture. However, the bare detector response is less steep compared to the moderated detector and thus exhibits a lower signal-to-noise ratio, making it less favourable for the estimation of soil moisture, which is in line with simulation results from previous studies e.g.,. As shown in Fig. a and b, the bare detector signal response to changes in soil moisture reveals a higher variability between simulation scenarios with different soil chemical compositions compared to the moderated detector with a 25 mm HDPE shielding. As a consequence, differences in soil chemical composition alter the response of the bare detector to changes in soil moisture while the moderated detector is much less affected. Although these results are in line with findings from previous studies e.g.,, it should be noted that the total amount of additional chemical elements added to the standard soil in the simulation scenarios partly exceeds the trace amounts (0.001 g cm⁻³) for which the respective URANOS functionality was designed and, hence, these results come with additional uncertainty.

In this study, we not only derived detector response functions for a bare and a standard moderated detector with a HDPE shielding of 25 mm thickness but also for a HDPE thickness ranging from 5 to 40 mm in order to investigate the impact of soil chemistry depending on the thickness of the HDPE shielding. The results are shown in Fig. . The average range of relative simulated values per moderator thickness over all simulation setups including different soil chemical composition serves as an indicator for chemistry dependence (Fig. a). It can be seen that soil chemistry sensitivity decreases exponentially with increasing thickness of the HDPE moderator detector. A shielding with 5 and 10 mm HDPE already reduces the dependence by 45 % and 69 %, respectively, compared to the reduction of 80 % for 25 mm. For thicker HDPE shieldings, the reduction is comparably small. As shown in Fig. b for the standard soil and compared to a bare detector, the reduction of simulated neutron intensities with increasing soil moisture becomes larger with increasing moderator thickness. The strongest decrease with soil moisture is simulated for a moderated detector with a HDPE shielding of 20 mm, indicating that a slightly thinner moderator may also be used for estimating soil moisture with CRNS. However, due to different detector surface areas and volumes caused by the different moderator sizes as well as individual DRF, different average absolute neutron intensities can be expected. This leads to different levels of statistical uncertainty and such considerations should be included in the detector design e.g.,.

For changes in above-ground wet biomass, both the moderated and bare detector responses to soil moisture changes deviate from the scenario without above-ground biomass (Fig. c–d). Hence, in contrast to differences in soil chemistry, biomass changes not only change the absolute neutron intensities observed by bare and moderated detectors but also the response to soil moisture changes. Here, it can be seen, that the bare detector response to soil moisture increases with increasing biomass below the detector while the response of the moderated detector decreases (Fig. d). However, the response of both detectors does not change monotonically if biomass changes occur above the detector (Fig. c). While the bare detector response becomes generally steeper with increasing biomass, the steepness increases with 1 m biomass added but then decreases slightly with more biomass added until it increases again for the scenario with highest biomass. The response of the moderated detector to changes in soil moisture becomes smaller up to the scenario with 1 m below and 8.5 m biomass above the detector. The response then increases again with increasing biomass. The point where this response changes its behaviour is consistent with the maximum intensity of the bare detector response with increasing biomass (Fig. a) underlining a complex behaviour of both, moderated and bare detector signals with changes in both biomass and soil moisture at vegetated observation sites. Despite this non-monotonic behaviour, the presented results also reveal that in many vegetated setups like a forest, the responses of a bare and moderated detector to changes in soil moisture generally tend to become more similar than under conditions with little or no vegetation (see also Fig. c).

Different soil bulk densities also change the response to soil moisture for moderated and bare detectors with a somewhat stronger effect on the bare detector (Fig. e). Nevertheless, in this case, the direction of the effect is similar leading to an general increase in the response with decreasing soil bulk density over the scenarios with uniform bulk density in the soil column and increasing bulk density from the surface down to 30 cm depth. This is in line with what has been reported for epithermal neutrons in previous studies e.g., and recently introduced transfer functions to convert soil moisture to neutron intensities and vice versa include a scaling approach to account for the effect of different bulk densities . A water layer on top of the soil surface, representing ponding water or a layer of snow, leads to a decreased response of the moderated detector signal to changes in soil moisture below the water layer (Fig. f). The water layer also affects the bare detector signal, although here this trend is not monotonic. Compared to a scenario without water layer, the decrease in neutron intensity with increasing soil moisture becomes stronger with a thin water layer of 1 and 2.5 cm. Then, with a water depth of 10 cm, the response decreases and becomes smaller than that without a water layer. This illustrates that although a moderation optimum in absolute neutron intensities occurring in the thermal energy range and under very dry soil conditions may not be visible in the bare detector signal due to the contribution of epithermal neutrons, other moderation optimum features can still be present under specific environmental conditions. This makes the interpretation of observed bare detector signals more complicated than those observed with moderated detectors.

While different transfer functions to derive soil moisture from moderated detector signals have been introduced in the last 15 years , a transfer function for the bare detector is currently lacking, largely because of the decreased response to soil moisture changes and because the higher complexity and variability of the bare detector response to changes in soil moisture hampers the development of a generalised transfer function. However, mathematically characterising the response of bare detector signals to changes in soil moisture is a prerequisite for a future exploration of potential applications of bare detectors for environmental monitoring, e.g. for estimating uncertainties of biomass products from bare detector signals which originate from underlying soil moisture dependencies. Based on the homogeneous simulation scenarios listed in Tables –, we found that the change in the bare detector signal with soil moisture relative to the intensity observed above a freshwater surface (e.g., a lake) where θtotal=∞ is well represented by the same hyperbolic relationship: 1I=p1+p2θtotalp1+θtotal⋅p3, where 2I=NphiNphiwater, and 3θtotal=θSM+θSOM+θLW.

Solved for θtotal, Eq. () becomes: 4θtotal=p1-Ip3p1Ip3-p2=p1p3-II-p2p3.

In Eq. (), Nphi is the observed bare detector intensity corrected for variations in air pressure, high-energy cosmic radiation and absolute air humidity. Note that the correction for absolute air humidity variations for neutrons observed with a bare detector is different to those measured with a moderated detector as simulated in and supported by empirical evidence given in and . Nphiwater is the intensity of the same detector above a freshwater surface. In Eq. (), the total soil water content θtotal in cm³ cm⁻³ is the sum of the soil moisture content θSM, the water equivalent of soil organic matter θSOM and the amount of lattice water θLW. The fitted shape-giving parameters p1…3 show a distinct variability between the simulation setups which resembles the changing relationship between the bare detector signal and soil moisture depending on soil chemistry, above-ground biomass, bulk density and water layers on the soil surface. Individually fitted for all setups listed in Tables , , using non-linear least squares, the parameter p1 ranges from 0.06623 to 0.2712 (average = 0.1655, median = 0.1936), p2 ranges from 0.2676 to 0.6473 (average = 0.3718, median = 0.3594) and p3 ranges from 1.638 to 6.267 (average = 3.166, median = 2.767). The fitted parameters for each individual scenario can be found in Table . The variability in fitted parameters indicates a change of the relationship between neutron intensity and soil moisture depending on the environment.

For the simulation setup with standard soil chemistry and standard bulk density (1.43 g cm⁻³) but without biomass or water layer, the fitted parameters p1…3 become 0.1936, 0.3639 and 2.733, respectively. If this standard parameter set is used for Eq. () in conjunction with replacing θtotal by θtotal′=θtotal⋅(1.43gcm-3/ρsoil) to account for differences in actual bulk density ρsoil and simulated standard bulk density see e.g., and Nphiwater is calibrated for each setup, the fits shown in Fig.  can be derived. Larger deviations become apparent for some soil chemistry, biomass and water layer setups which is also reflected by the RMSE values shown in Table . All RMSE values derived with the standard parameter set (RMSEcalibrated) are considerably higher compared to individually fitted parameters (RMSEindividual). Especially, water layers on top of the soil and increasing biomass cause increasing RMSE values. This again underlines a change of the relationship between the neutron intensity of bare detectors and soil moisture. However, given that variations of the relationship between neutron intensity and soil moisture can also be observed for epithermal neutron signals from moderated detectors (see e.g., Fig. d and f), the fit with the standard parameter set may be considered acceptable over a range of environmental conditions. Acknowledging that deviations remain and that further research on transfer functions for bare detector intensities is required, this shows that the same shape-giving parameters in Eq. () may be used as a first model to predict local neutron intensities of bare detectors if calibrated to the local conditions using reference soil moisture measurements in cm³ cm⁻³. It should be noted that this calibrated intensity above water (Nphiwater) then represents a mere calibration parameter which compensates for local site characteristics such as soil chemistry and above-ground biomass. Hence, if these influences have not been otherwise corrected for, the calibrated Nphiwater is not directly comparable with the intensity measured with the same detector above water. This also applies for existing transfer functions developed for pure epithermal neutrons and neutrons measured with moderated detectors. A correction of observed neutron intensities for, e.g., total biomass and its temporal changes, would improve the comparability between the measured and locally calibrated intensity above water of the same neutron detector and is discussed in Sect. .

It should further be noted that found a dependence of the response to soil moisture with absolute air humidity for neutrons measured with moderated detectors. Even though the humidity dependence for bare detector signals is likely to be reduced , it may still have an impact on derived neutron intensities and soil moisture estimates from bare detector signals. Applying existing correction approaches for variations in air humidity developed for neutron intensities from bare detectors e.g., in conjunction with Eqs. ()–() may therefore only be seen as a first-order approximation and remains to be tested against measured data in future studies.

Figure a shows the response of the bare and moderated detector signals to increasing biomass below and above the detector (maximum vegetation height of 40 m above ground) under different soil moisture conditions. For all simulated soil moisture conditions, the response changes with increasing biomass but the overall trends are somewhat different. For biomass above and below the detector (Fig. a), moderated detector intensities continuously decrease with increasing biomass. On the contrary, bare detector intensities increase up to a biomass water equivalent of around 8 mm, and then decrease for higher values. These simulation results support findings from and who observed an increase in neutrons observed with the moderated detector after a forest clear-cut. At the same time, this clear-cut caused a decrease of neutrons from the bare detector . For biomass water equivalents with changes below the virtual detector only (Fig. b), the bare and moderated detector signal changes are highly similar and inversely linearly correlated. Compared to the case of biomass above and below the detector (Fig. b vs. a), the response of a moderated detector is very similar whereas bare detector response is strongly reduced in the case of biomass confined below the detector. This supports conclusions drawn by from experimental data suggesting the use of bare detector signals to directly correct moderated detector signals for changes in biomass. However, the simulation results of this study suggest that the applicability of this approach is limited to biomass changes that occur below the neutron detector.

In general, findings from this simulation-based study are in line with conceptual ideas and experimental findings in and : above-ground BWE increases intensities measured by the bare detector through an increased slowing-down (moderation) of epithermal neutrons and thereby reduces moderated detector intensities. Although small and only occurring during higher simulated soil moisture contents, an increase in moderated detector intensities is visible between the simulation scenario with wet biomass 1 m below as well as 1 m below and 1 m above the detector (Fig. a) which further supports the conclusions from that tall vegetation growing at the installation height of the detector increases neutron intensities measured by the moderated detector but once it overgrows the detector, moderated intensities start to decrease again. This increase in moderated intensities is much smaller compared to the maximum reached by the bare detector signal with the latter being reached at higher amounts of biomass.

The reduction in moderated neutron intensities with increasing BWE in the majority of scenarios shown in Fig. a and b is visibly higher compared to what has been derived empirically in . Being one of the accepted approaches to correct epithermal neutron intensities from moderated detectors for changes in BWE, the Baatz correction factor CBWE can be calculated as follows, where BWE is in units of mm: 5CBWE=(1-(β⋅BWE))-1 In their empirical work, found β to be 0.005 which is less than half of the average value of 0.013 derived from the neutron transport simulations in this work, which is well in line with findings from empirical studies . Values of β of -0.005, 0.011 and 0.015 have been reported by and derived values between 0.006 and 0.017 with an average β of 0.011. Furthermore, the simulation results shed further light on potential reasons for the differences between the empirically derived values. As empirically shown in and simulated in this study, vegetation growing at the height of the detector can influence the relationship between BWE and neutron intensity. At the same time, different soil moisture states may result in different estimates of β due to a dependence of the response to changing BWE on soil moisture (Fig. a and b) which also includes a non-linearity in the relationship. For correcting the inverse behaviour of thermal neutron signals from bare detectors, β in Eq. () becomes -0.0055 if only biomass changes below the detector are considered (Fig. b), while β reaches -0.14 if BWE below and above the detector up to 8.17 mm are taken into account (Fig. a, fit not shown). Due to biomass being implemented with a constant height of 1 m below the detector in the simulation setups of this study, the influence of increasing vegetation height below the detector in addition to a higher biomass density cannot be assessed. For the bare detector with an overall higher sensitivity to above-ground biomass, a change of vegetation height below the detector could lead to a stronger signal response than suggested by the results shown in Fig. b. It should be noted here that vegetation is implemented as a homogeneous plant gas layer, which poses a further limitation. In fact, show different neutron responses and that a homogeneous vegetation layer well represents epithermal neutron observations while more complex vegetation structures best fit thermal neutron observations. Hence, additional research on the joint influences of biomass, vegetation height and geometries as well as soil moisture on bare detector signals, rather than thermal neutron intensities, is required to further explore their usability in biomass estimation and monitoring.

Given the non-linearity in the relationship between epithermal neutron signals from moderated detectors found in this study, the recently introduced UTS (parameter set MCNP drf) by is used to include the non-linear effect of BWE on soil moisture estimates as follows: 6Npi=ND⋅p1+p2θtotal′p1+θtotal′⋅p3+p4h+BWE⋅p9+p5h2+e-p6θtotal′p7+p8h+BWE⋅p10+BWE2⋅p11, where 7θtotal′=θSM+θSOM+θLW⋅1.43gcm-3ρsoil

This modified UTS predicts the neutron intensity based on total soil water content and absolute air humidity and therefore, the predicted neutron intensity represents the intensity corrected for variations in atmospheric pressure and incoming primary neutron flux Npi. The parameter ND represents the average neutron intensity of the same neutron detector under the boundary conditions defined in the neutron transport simulations for deriving the UTS. θtotal is the total water content in cm³ cm⁻³ comprising soil moisture content θSM, soil moisture equivalent from soil organic matter θS0M and lattice water content θLW which is then scaled by the local soil bulk density at the study site ρsoil . The shape-giving parameters p1…8 have been derived by while p9…11=(1.907,4.0180,-0.1425) have been derived from the simulations in this study. The BWE is the above-ground biomass water equivalent in kg m⁻² (or mm) and Eq. () may be used with BWE values ≤40 kg m⁻². Note that p9…11 are only valid in conjunction with p1…8= (0.0280, 0.254, 1.094, -0.0088, 0.0001150, 3.537, 0.139, -0.00140). A comparison of the different biomass correction approaches can be found in Fig. . Compared to no biomass correction or the original approach after , an improved representation of the simulated moderated neutron intensities can be achieved by using the UTS if the adjusted coefficient of 0.013 mm⁻¹ BWE is used in Eq. () or by using the modified UTS (Eq. ). While these results confirm findings of previous studies that an adjustment of the original β derived by may be necessary, a thorough assessment of the modified UTS in Eq. () with integrated correction for BWE is beyond the scope of this study. Nevertheless, from a practical point of view, the findings from this study suggest that Eq. (5) with a β of 0.013 instead of 0.005 mm⁻¹ BWE should be used for correcting neutron signals from moderated detectors for variations in above-ground biomass.

For water layers on the soil surface (Fig. c), a moderation optimum for bare detector intensities can be found between a water layer thickness of 1 and 2.5 cm which is in line with findings from e.g., for thermal neutrons. In addition, showed in measured data that bare detector intensities increase for thin snow layers but decrease for thicker snow layers. In contrast, intensities measured with moderated detectors always decreased with snow height. The simulation scenarios in this study representing all above-surface water as a liquid water layer support these observations. Although this has been done in previous studies e.g.,, representing snow as a water layer remains a simplification which does not fully account for the lower density of snow. For example, similar to layers of biomass, snow layers with heights approaching or exceeding the height of the detector are likely to lead to a different response despite containing the same amount of a water layer with lower height. Therefore, the results of the simulations conducted in the scope of this study are only valid for snow layers of heights up to approx. 30 cm (at a snow density of 0.3 g cm⁻³).

For bare detector signals, the neutron intensity increase for thin water layers depends on the soil moisture content with a stronger increase being visible for low soil moisture contents. Furthermore, additional simulation results for a soil moisture content of 0.04 cm³ cm⁻³ show that the response of a moderated and a bare detector to water layers above the soil changes when above-ground biomass is added to the simulation setup (Fig. ). The moderation optimum in the bare detector signal becomes smaller and also the moderated detector signal responds less to changes in water layer thickness. Hence, for estimating snow heights and water equivalents by utilising the different response of bare and moderated detector signals one may need to include the site-specific amount of above-ground biomass as well as other hydrogen pools such as soil organic matter present in addition to soil moisture. This is supported by measured data from a CRNS observation in north-eastern Germany (site Serrahn, ) shown in the appendix (Fig. ). The site is located in a forest and during periods with estimated maximum snow heights of ≈15 cm no distinct increase of the bare detector signal is visible. Yet, the small size of the dataset and missing information of measured snow water equivalents need to be considered when interpreting the observation data shown. This underlines the need for further research using field measurements such as the study by at sites with different amounts of BWE and average soil moisture and to evaluate findings from simulation-based studies.

At very dry sites without dense vegetation cover and if only the top few centimetres of the soil are getting wetted during small rainfall events, this distinct vertical heterogeneity of soil moisture may act similar to a thin water (or snow) layer on top of the soil surface. This explains observed neutron intensities shown in Fig.  from an observation site in northern Australia (Oak Valley, ) where bare detector intensities increase during small but not during larger rainfall events in periods with low soil moisture, while moderated detector intensities show a decrease in all cases. On the one hand, this needs to be considered when using e.g., Eqs. ()–() to derive soil moisture from neutrons observed with bare detectors. On the other hand, this suggests that bare detector signals could be used to derive information on the vertical distribution of soil moisture during dry periods. However, the visibility of a bare detector signal increase due to a vertically heterogeneous wetting of the soil or thin layers of water and snow on the soil surface also depends on the temporal aggregation and smoothing of observed neutron intensities as well as simultaneously changing soil moisture contents underneath a water (or snow) layer.

In this study, the footprint radius R86 and footprint depth D86 are calculated as the 86 %-quantile of distances to the point of first soil contact of all detected neutrons in the model domain and their maximum depth in the model domain, respectively. R86 and D86 for the different, homogeneous simulation scenarios using the detector response function are shown in Figs.  and . The values lie in a comparable range to what has been stated in . For a moderated detector and over all scenarios, the derived average R86 is 154 m (median =168 m) if a detector response function is applied and weighted quantiles are calculated, or 163 m (median =178 m) using the energy window approach (not shown). Similarly, an average D86 of 33 cm (median =29 cm) and 31 cm (median =27 cm) can be derived, respectively, which shows that the impact of the moderated detector response function on the derived sensitive footprint is rather small. Similarly, for the bare detector, the average R86 is 135 m (median =145 m) using the detector response function and 130 m (median =141 m) for the energy window approach, respectively. On average, R86 of the bare detector is 12.5 % and 19.8 % smaller than that of a moderated detector, depending on if a detector response function is applied to evaluate the neutron transport simulations or if the simplified energy window thresholds are used. In contrast to a smaller R86, the D86 of a bare detector is on average 34 % and 43 % deeper with values of 44 cm (median =38 cm) and 45 cm (median =39 cm), respectively. These results indicate that the use of DRF is important for simulating the response of neutron intensities to changes in e.g., soil moisture but might be less important for determining R86 and D86 based on the point of first soil contact and maximum depth, respectively. Interestingly, changes in BWE amounts strongly affected R86 and, in the scenarios with high BWE (Fig. c), the measurement radius of bare and moderated detectors reached values of less than 30 m, with slightly larger values for the bare compared to the moderated detector. For epithermal neutrons, similar findings have been described by . Although the implementation of vegetation is rather simplified in these setups, the results may be a first indicator that the footprint at densely vegetated measurement sites such as forests could be much smaller than the range of 100–200 m currently accepted in the community.

Although the slightly smaller footprint radius but larger footprint depth of the bare detector is in line with simulation-based findings from , the derived radius and depth strongly depend on how the footprints are calculated from neutron transport simulations. This has been underlined by who show the differences if the point of first soil contact or the point of thermalisation are used to calculate the sensitive depth and radius of thermal neutrons. If the latter is used, R86 and D86 are less dependent on soil moisture, R86 is relatively constant between 40 and 50 m and D86 is slightly smaller compared to epithermal neutrons. These calculated values are similar to those reported by who used the same definition to estimate the sensitive footprint for thermal neutrons from neutron transport simulations.

In order to shed more light on how to estimate the footprint radius and depth for bare detector signals, we conducted additional and non-homogeneous simulation setups. First, we conducted a vertically expanding soil setup to gain more information on the sensitive depth (Fig. a). In Fig. , it can be seen that the signals of a bare and moderated detector increase when more water is replaced with soil. This occurs for both simulated soil moisture contents. The threshold at which the simulated intensity changes less than 1 % to the previous scenario is reached later for the bare detector compared to the moderated detector. Also, a dependence of this threshold on soil moisture content can be observed. Without previous assumptions on how to calculate the footprint depth, these simulation-based results confirm findings from that neutron signals observed with a bare detector have a larger measurement depth compared to moderated detector signals. Thus, for both moderated and bare detectors, the use of a DRF and of the maximum depth reached by all detected neutrons should be applied when calculating D86 from neutron transport simulations.

A similar simulation experiment was conducted for R86 (Fig. b). Here, an expanding soil island with different soil moisture contents was simulated to investigate the signal response of a bare and a moderated detector. In contrast to the vertically expanding soil thickness scenarios used to investigate D86, the 1 %-threshold is reached earlier for the bare detector compared to the moderated detector and a dependence on soil water content is also seen here (Fig. ). This again confirms findings by that the same definition (i.e., point of first soil contact) should be used with DRFs to estimate the footprints of bare and moderated detector signals. It also underlines that the results shown in Figs.  and provide reasonable estimates of the measurement radius and depth of bare and moderated detectors under various environmental conditions.

Due to the distinct difference in response between bare and moderated detector signals to changes in above-ground BWE, we also set up horizontally heterogeneous simulation scenarios with an expanding clearing of vegetation instead of an expanding soil island in a water-filled model domain (Fig. c). Figure  shows the results for two setups with higher (panel a) and lower (panel b) vegetation height and BWE. It is apparent that the bare and moderated detector signals behave differently in these scenarios, and that such difference is larger when soil moisture is lower (Fig. a). In general, the moderated detector intensities increase continuously with increasing distance to vegetation and the response is stronger with higher vegetation. The bare detector intensities, instead, decrease rapidly up to around 40–50 m distance before a rather constant behaviour up to 100 m distance and a later increase. The increase beyond 100 m is similar to that of the moderated neutron intensities. This behaviour is seen for both simulated soil moisture contents in the forest setup (Fig. a) but only for the lower simulated soil moisture of 0.04 cm³ cm⁻³ when less vegetation is present (Fig. b). These bare detector responses are different compared to those of an expanding soil island (shown in Fig. ). Also, they indicate that a large fraction of the difference between moderated and bare detector signal responses shown in Fig.  is likely to arise from the first ≈50 m around the neutron detector. This is also the distance in which detected neutrons reach thermal energies prior to reaching the virtual detector . As a consequence, the weighting functions derived by for neutrons in the thermal energy range, could be used to describe the sub-footprint of the bare detector in which sensitivity to BWE, snow water equivalents and soil chemistry is highest. Nevertheless, if BWE changes occur in distances ⪆50 m and beyond, the response of bare detector signals to changes in BWE will be different to what is shown in Fig.  and can be expected to become more similar to the response of moderated detector signals. When taken to real-world measurements, these findings suggest that bare detectors may only be used to monitor BWE changes up to the 40–50 m distance of thermalisation found by and . Beyond such distance and especially if BWE changes are non-homogeneous in space, monitoring of BWE with bare detectors may not be possible. This can also be expected to hold true for non-homogeneous distributions of snow water equivalents around the instrument with an increase in bare but a decrease in moderated intensities when snow is located within ≈50 m radius, only.

The larger footprint radius and deeper measurement depth of the bare detector also has practical implications when reference soil moisture information are weighted for calibrating neutron-to-soil moisture transfer functions using observation data. Although the first set of weighting functions developed by can be expected to be valid for the thermal part of the life of a detected neutron only, it may pose a valuable tool for describing the soil moisture sensitivity of bare detectors in their near-field (≈50 m) radius where their signals are also most sensitive to e.g., changes in BWE. However, following the results of the present study, these first weighting functions are not sufficient to describe the entire footprint of bare detector signals in terms of soil moisture sensitivity. As a consequence, a set of weighting functions similar to those developed in and for epithermal neutrons are required which include the entire life of a detected thermal neutron as well as a different sensitivity to BWE and absolute air humidity. Different soil chemical compositions may also need to be considered. Despite the average differences in R86 and D86 between neutrons from moderated detectors and neutrons from bare detectors, a much larger horizontal footprint radius than derived by as well as a stronger soil moisture dependency was found in this study. This is further amplified by the use of detector response functions instead of selected energy windows. Therefore, using the same weighting functions developed by for epithermal neutrons also for thermal neutrons and thus, bare detectors may be a more suitable first-order approach to represent the entire sensitive footprint. Nevertheless, designated weighting approaches for neutrons from bare detectors remain an important knowledge gap and should be investigated in future studies to further increase the applicability of bare detector signals in the scope of CRNS.