Our network consists of 26 stations installed across the Italian Alps (Fig. 1), equipped with CRNS probes developed by Finapp SpA. The elevation range of the network covers almost 1500 m between the lowest and the highest stations, namely Lisser (1422 ma.s.l.) and Mosso (2901 ma.s.l.). Each sensor was integrated into already existing automated weather stations (AWSs) or, if the AWS framework could not host it, in the immediate proximity. A summary of the main features of each site (e.g. name, coordinates, elevation, number of manual SWE samples, and series length) is given in Table S1 in the Supplement. The AWSs employing the CRNS probes are managed by various institutions: the Regional Environmental Protection Agencies (ARPAs) of Veneto and Piemonte, the Office for Hydrology and Dams of the Autonomous Province of Bolzano, the University of Torino, and the Polytechnic University of Torino. The sensors are based on Lithium-doped ZnS(Ag) scintillators capable of detecting and discriminating neutrons and muons (Gianessi et al., 2024). The measurement of the local muon flux allows for an accurate site-specific correction of the neutron flux without the need of relying on a network of public observatories (Stevanato et al., 2022), which is the standard practice for CRNS technology (McJannets and Desilets, 2023).

A CRNS setup for SWE measurement includes a detector buried flush to ground and another detector mounted on a mast, above the snow surface. The measurement footprint for this setup has a radius of approximately 20 m, a feature that allows its SWE estimates to be directly compared with point-scale manual samples.

At 13 sites of the network, SWE is also manually measured following two different procedures: (i) measuring the density of a single vertical core that spans the entire snowpack from the top to the ground (Berni and Giancanelli, 1966), or (ii) density measurements of multiple horizontal cores obtained from the homogenous layers present in the snowpack. In the first case, the single vertical core is weighted to derive snow bulk density and SWE. Each vertical core was taken with an Enel Valtecne EV2 corer which has an internal diameter of 6 cm and is composed by a modular setup of stainless-steel sections with a length of 50 cm each (López-Moreno et al., 2020b). The vertical coring process is repeated for at least three times for each sampling campaign, resulting in multiple SWE and bulk density values. Subsequently, those measures are averaged to obtain an estimate of the SWE. For our analysis we used these averaged values assuming they represent the (point-scale) amount of SWE at each site. In the case of horizontal coring, each core is taken with a cylinder with a volume of 0.5 dm3(i.e. length of 18 cm and diameter of 6 cm), then the core is weighted with an analogic or digital scale. If there are layers with thickness lower than the diameter of the corer, the layer density is estimated following the results of Valt et al. (2012). The measurements and, crucially, the layers identification are carried out by expert researchers and technicians who have been extensively trained by the Italian Association for Snow and Avalanches (AINEVA). The sum of the SWE computed from each core (e.g. each layer) is assumed to be the SWE of the whole snowpack. It was assessed that the differences between the two methods are within 5 % (Valt, 2018) as it has been reported in existing literature focused on snow resources of our area of study (e.g. Colombo et al., 2022; Guyennon et al., 2019). In most of the cases, the direct SWE monitoring practices pre-dates the installation of CRNS probes and the measurements were not initially meant to be used for performance assessment on this technology. This fact, in combination with the inherent spatial heterogeneity of the snowpack, could hinder the capability of such measurements of being fully representative of the actual SWE at the AWSs. This criticality descends from the absence of a defined standard for taking SWE measurements meant specifically for CRNS validation. To address this matter, we compared the snow depth (HS) measured at the AWSs with the values obtained from manual measurements. For our analysis, we discarded direct SWE measurements taken where the HS differed from the corresponding AWS value by more than 20 % for deep snowpack (i.e. HS≥1 m) or more than 20 cm for shallow snowpack (i.e. HS<1 m).

Each sensor retrieves raw particle counts that are integrated on a 1-h time window. The neutron count rate measured by the ground detector represents the main signal, while the muon count rate measured by the mast detector provides the incoming flux reference. To correct the raw neutron and muon counts (i.e. Nraw and μraw), we adopted an atmospheric pressure correction from onsite atmospheric pressure measurements (p), recorded by the barometer embedded in each probe, and applied it to obtain the atmospheric pressure corrected count rates (Napc and μapc) following Eqs. (1a) and (1b): 1aNapc=Nraw⋅exp⁡βNp-pref,1bμapc=μraw⋅exp⁡βμp-pref,

Where βN and βμ are the barometric coefficients for the neutrons and muons respectively. While pref is the reference pressure at each site elevation (H, in meters) derived, according to the standard hydrostatic atmospheric equation (Wallace and Hobbs, 2006), as Eq. (2): 2pref=1013.25hPa⋅exp⁡-H8006m

Both βN and βμ values used in this study were provided by the manufacturer: βN is fixed at 0.0076 hPa-1, while βμ scales with the site elevation as described in the empirically derived Eq. (3): 3βμ=0.019×0.007H10000m

The atmospheric pressure correction is a crucial step in CRNS application as the number of cosmic ray particles reaching the ground is strongly influenced by the number of particles present in the air column they cross (i.e. the atmospheric thickness), which scales with the atmospheric pressure. The choice of pref is arbitrary and the literature presents various instances of values fixed a priori (e.g. the standard sea level pressure of 1013.25 hPa in Bogena et al., 2022; or 1000 hPa in Jitnikovitch et al., 2021) or obtained as the median or average pressure value over a selected period of time (e.g. Gianessi et al., 2024; Gugerli et al., 2019, 2022; Stevanato et al., 2022). The rationale behind the adoption of Eq. (2) lies in the fact that the network is intended to allow for near real-time snowpack monitoring starting from the probe's installation. Therefore, the choice fell on an a priori value that could still maintain the representativeness of each site's expected average atmospheric pressure.

While performing these processing steps, we discarded data that fell under at least one of the following criteria: (i) integration time lower than 500 s; (ii) null value of either air pressure, neutron counts, or muon counts.

For each site, we took the baseline (pressure corrected) neutron and muon count rates (Nref and μref) during a period characterised by the following features: (i) minimum length of 24 h, (ii) stable signal (i.e. without probe's reboots, outliers, or evident trends that overcome the random fluctuations), and (iii) absence of snow cover. Nref varies greatly from each site due to its dependence from elevation, soil composition, and morphology. At every station of the network, Nref and μref are assessed at the beginning of each season and their values are updated if needed.

Subsequently, to obtain the corrected neutron count (N) we applied to the pressure corrected neutron count rate (Napc) a site-specific incoming correction factor given by the ratio between μ0 and the atmospheric pressure corrected muon count (μapc) as proposed by Stevanato et al. (2022) and illustrated in Eq. (4): 4N=Napcμrefμapc

It is therefore possible to compute the normalised neutron count rate (Nr) according to Eq. (5): 5Nr=NNref

Then, we computed SWE adopting the widely used formula (e.g. Pokhrel et al., 2024; Jitnikovitch et al., 2021; Gugerli et al., 2019; Howat et al., 2018) reported in Eq. (6): 6SWE=-10Λlog⁡Nr

Where the attenuation length (expressed in cm-1) Λ is Eq. (7): Λ=1Λmax+1Λmin-1Λmax7×1-exp⁡a1-Nra2-a3

We assessed the parameters of Eq. (7) through a calibration process that leveraged 35 direct SWE measurements taken from six sites in the Veneto region (Eastern Alps) between December 2023 and March 2024 (Fig. S2 in the Supplement). To avoid over-parameterisation, we kept fixed the values of parameters Λmax, a2, and a3. These values were taken from Gugerli et al. (2019) due to the spatial proximity of our respective study areas (the Italian and Swiss Alps). The calibration was performed on the two free parameters Λmin and a2. This first instance of an interpolation common to multiple sites suggested the possibility of adopting a shared parameterisation across the Italian CRNS network and prompted the study presented in this work.

We obtained (including the 35 used for the calibration) a total of 154 SWE values between the 2023–2024 and the 2024–2025 snow seasons. These measurements are assumed to be representative of the on-site SWE daily average. Therefore, to compare the coring data with the CRNS neutron count rates, we averaged the hourly values of Nr over a 24 h time span. The calibration dataset was used to define the parameters of Eq. (7) that constitute the core of the network-wide parameterisation. Then, we compared the remaining daily Nr values (i.e. the validation dataset) with the direct SWE measurements at each site. In addition, we computed the mean absolute percentage error (MAPE) to identify site-specific sensible deviations from the theoretical parameterisation. Two stations (namely Mosso and Sestriere) presented MAPEs higher than 50 % limited to the data of the 2023–24 snow season. Their sensors were installed when the snow cover was already formed. This fact prevented the standard assessment of Nref, which had to be approximated. The efforts to define a posteriori normalisation value are ongoing, but outside the scope of this work. However, this occurrence remarks that the installation of CRNS probes needs to be performed in absence of snow cover, at least when adopting a network-wide parameterisation. To avoid biases, we decided to not consider for the next steps of the analysis the 2023–2024 data of the two stations.

After these evaluations, we converted the Nr data to average daily SWE (SWECRNS) according to the presented formula. For each day and site where a reference manual SWE value was available, we identified and coupled with it the correspondent SWECRNS. In total, we leveraged for our analysis 146 d of coupled manual and SWECRNS (e.g. 35 for calibration and 111 for validation). The validation dataset (Fig. S2) is divided as: (i) manual samples from the same sites chosen for the calibration, and (ii) manual samples from the 7 additional monitored sites of the network. Following the methodology adopted by Egli et al. (2009), we computed a least squares fit of the data according to the Eq. (8): 8SWECRNS=α⋅SWEmanual,

We also determined the standard error (SE) of α along with the root mean square error (RMSE) of the SWECRNS against the manual measurements. This procedure allows us to identify the systematic bias of SWE evaluation by observing how much the value of α approaches 1 (e.g. with α=1 the evaluation is theoretically unbiased). On the other hand, SE gives a measure of how much the data are scattered along the predictive line, with the RMSE constituting an average error that can be associated to the estimated SWE values.

Finally, to address the possibility to extend our considerations to unmonitored sites (i.e. the remaining 13 sites of the network where manual SWE samplings were not available), we evaluated the correlation (r) between their SWECRNS series. For each of the 78 possible pairings of unmonitored and monitored stations, we computed the correlation coefficient between their Nr and SWECRNS time series, considering only periods where the reference AWS data showed presence of snow on the ground (i.e. HS>0 cm). We assigned the obtained correlations to different classes based on the vertical and horizontal distances between each pair of stations and computed the average correlation for each class. The chosen divisions for the vertical distances are 250, 500, 750, 1000, and 1500 m; while for the horizontal distances we chose 25, 50, 100, 200, and 500 km. We defined these divisions based on the spatial distribution of the network's sites and pursuing two goals: (i) minimize the number of void classes, and (ii) avoid classes containing only one couple of stations to make its average correlation informative. The identification of variables that influence the similarity of SWE patterns is crucial in the effort of overcoming site-specific validation. Monitored sites could act as accuracy proxy for unmonitored locations with which they exhibit high correlation. For this reason, we averaged the resulting r values among subsets depending on the horizontal and vertical distances between each couple of monitored-unmonitored sites to assess the impact of these two variables on the SWE pattern.

The direct SWE measurements used for the analysis range from the minimum value of 20 mm recorded at Larici site on 11 December 2024 to the maximum of 897 mm recorded at Ornella site on 4 April 2024. The median of the manually measured values is 199 mm, while for their SWECRNS counterparts it is 160 mm. The two series retain extremely similar distributions with interquartile ranges (IQRs) 87–335 mm for the manual and 76–334 mm for the SWECRNS (Fig. S3).

The values of the parameters Λmax, Λmin, a1, a2, and a3 are 114, 21 cm, 0.41, 0.082, and 1.117, respectively. Figure 2 represents the daily averaged Nr values plotted against the direct SWE measurements for the calibration (Fig. 2a) and validation (Fig. 2b and c) dataset. The adopted parameterisation of the theoretical SWE curve appears to depict well the data distribution. R2 values obtained for the calibration, validation at sites of calibration, and validation at additional sites are 0.95, 0.87, and 0.65 respectively.

Figure 2d–f presents the results of the linear regressions. The values of α suggests that the parameterization adopted does not introduce any sensible bias, as in each of the three instances of linear regression the slope is close to the ideal value 1. The SEs, which have values similar to the highest presented by Egli et al. (2009), reflect that the data are scattered along the prediction fit. We attribute this feature to two main causes: (i) the data come from different sites inherently different from one another, and (ii) the possible representativity errors introduced by the manual measurements that, we stress again, were not originally intended for this kind of performance assessment. Even considering these potentially hindering factors, the RMSE computed over the whole series is 84 mm. This result can be considered as a benchmark value when taking into account the error associated with this novel network-wide approach to CRNS parameterisation. Remarkably, both the slope and the SE obtained for the validation subset at the sites used for calibration (Fig. 2e) appear to perform better than the calibration subset (Fig. 2d). Nevertheless, RMSEs sensibly increase across the three subsets from 34 mm of the calibration subset to the 130 mm of the validation subset in the 7 additional sites. The latter subset shows also an α further from 1 (1.084) and a higher SE (0.1441).

Among the 146 analysed data, in 82 cases (22 in the calibration dataset, 60 in the validation) CRNS estimates were lower compared to the manual SWE measurements. The medians of the underestimated and overestimated manual SWE values are 168 and 209 mm, respectively. In fact, it appears that higher SWE values are more likely to be overestimated by CRNS probes. However, this result could be biased by the relative scarcity of high SWE measurements available. Indeed, more than 70 % of the manual SWE data used for our analysis have values lower than 300 mm.

To better address the site sensitivity of our network approach, we looked at the distribution of selected statistical parameters computed separately for each site. The mean absolute errors (MAEs) emerging from the comparison between SWECRNS data and the manual measurements have an average value of 70 mm, while the average of the site specific RMSEs is 82 mm. However, the MAE and, in a lesser way, the RMSE distributions are skewed towards lower values. In fact, the median MAE and RMSE are 47 and 67 mm. These values are comparable with the errors associated with manual SWE measurements, that increase with SWE (e.g. Gugerli et al., 2019) and can be assumed to be in the range 20–50 mm for most of the values in our dataset. Focusing on the distribution of MAPEs for each site, its average and median values are 32 % and 29 %, respectively. These values are more than double compared to the maximum percentage error of ±13 % found by Gugerli et al. (2019). However, that study involved only measurements performed by CRNS probes installed on a glacier, which cancels out possible error contributions from the underlying soil water content (Wallbank et al., 2021).

The relatively high percentage error constitutes the trade-off linked to the choice of applying the same parameterisation to every site of the network. The same choice is intended to expand the spatial coverage of continuous SWE dataset including sites that cannot be subjected to direct measurements campaigns every season due to their inaccessibility. Indeed, the only comparable European CRNS network adopts as standard procedure the seasonal recalibration through manual SWE sampling of each sensor installed (Gottardi et al., 2013). This approach, although it may yield better overall estimations in already monitored sites, limits the number of locations available for installation of CRNS probes. In any case, if needed for site specific studies, any of the SWECRNS dataset used for our analysis could be improved with the implementation of an ad hoc parameterisation defined using the available manual SWE data.

The correlation coefficients computed between the SWECRNS from unmonitored and monitored sites (Fig. 3a) appear to be influenced by the vertical distances (i.e. the elevation difference) with the average r (Fig. 3c) monotonically decreasing from a maximum of 0.87 when the distance delta is in the range 0–250 m to a minimum of 0.41 in the range 1–1.5 km. On the other hand, horizontal distances (Fig. 3d) do not seem to affect the correlation between sites. In fact, although the maximum r of 0.76 is related to the horizontal distance range 0–50 km, the minimum value of 0.67 is observed in the range 50–100 km. Unmonitored stations data are highly correlated (average r=0.98) with monitored sites with a vertical and horizontal distance lesser than 250 m and 50 km respectively. Thus, statistical behaviour of unmonitored sites, including an estimate of accuracy and representativeness of SWE measurements, can be inferred from neighbouring monitored sites in that range. An analogous analysis conducted on the Nr time series instead of the SWECRNS ones showed similar results (Fig. 3b). As it was the case for SWECRNS, the average correlation decreases monotonically with vertical distances (Fig. 3e), ranging from a maximum value of 0.83 to a minimum of 0.19. As the horizontal distance varies, the average r for the Nr time series (Fig. 3f) yields the highest value (0.78) for the 0–25 km class and the lowest (0.49) for the 200–500 km class. In absence of monitored sites meeting those characteristics, a comparison with stations at similar elevations should still yield reasonable estimates. Overall, this approach can be adopted to extend the application of CRNS to inaccessible locations further extending the spatial coverage of continuous SWE data while avoiding the necessity of an unfeasible site-specific validation.

The conversion of raw particles counts into SWE values depends heavily on the choice of the adopted parameters, which are the object of Sect. 2.3, and is subject to the biases that any parameterisation process introduces. In this work, we built upon what was presented in existing literature while trying to preserve the near real-time monitoring capability of the network, which demands solutions that are ready to use and representative of each site's features.

Nevertheless, we acknowledge the limitations introduced by three main factors: (i) the adoption of a single βN for a wide elevation range, (ii) the choice of correcting the incoming neutron fluxes with muons, and (iii) the inherent variability of snowpack characteristics even at such small scales combined with the uncertainty on the footprint of CRNS probes, which may have introduced some biases in the performance evaluation of the network against manual SWE samples.

One of the main features of the network is its unprecedented elevation range. However, recent work by Davies et al. (2026), who focused on CRNS applications for soil moisture, showed that the barometric coefficient may depend sensibly on elevation. In this work, for βN we adopted the widely accepted (e.g. Bogena et al., 2022) value of 0.0076 hPa-1. Therefore, further studies shall focus on assessing the effect of an elevation dependent barometric coefficient leveraging the ∼1.5 km range offered by this network.

The most common way to perform an incoming flux correction relies on leveraging data from the nearest cosmic neutron observatory (e.g. Gugerli et al., 2019; Jitnikovitch et al., 2021). However, the CRNS probes of the network are installed with the native feature of a site-specific incoming flux correction based on muon fluxes (Eq. 4) as presented by Stevanato et al. (2022). This characteristic allows to perform a correction based solely on site-specific fluxes, although depending on a different kind of particles (i.e. the muons) which are correlated with neutrons. Nevertheless, future studies may focus on a comparison between the widely adopted correction based on neutron observatory data and the site-specific one which relies on muon fluxes.

The CRNS probes of the network retain a relatively small footprint whose radius has an upper limit of ∼20 m and is inversely proportional to the SWE. Yet, even at such scales snowpack variability plays an important role. In fact, López-Moreno et al. (2013) showed that in Alpine environments snow depth and, to a lesser extent, its density can sensibly vary for point scale measurements taken at distances of few meters thus affecting the error associated with SWE estimates. For this reason, we decided to perform comparison of manual SWE data taken where HS was comparable with the one measured by the corresponding AWS as it has been discussed in Sect. 2.2. Still, future works shall focus on the investigation how the snowpack variability affects the footprint of this CRNS setup as it has been done by Schattan et al. (2017), who focused on the above-ground CRNS assessing a footprint radius of ∼200 m although with a saturation SWE value of 500–600 mm which renders that setup unapplicable for our study purposes.