Two criteria were applied in selecting the datasets. First, since this study aims to investigate the influence of ice age and SIT on SND distributions, it requires coincident in-situ measurements of SND and SIT from diverse ice types. We therefore selected field campaigns spanning a range of ice ages, surface roughness conditions, flooding states, and seasons, while maintaining a balance among sampling sites. Campaigns with well-established contextual knowledge of meteorological events and local ice conditions were prioritized to support the interpretation of the observations. Second, this study aims to analyse the temporal evolution of the SND distribution, which requires time-series observations of snow and ice properties at approximately weekly intervals. Characterizing snow and ice on this timescale is essential to capture snow accumulation and redistribution processes associated with ice growth and meteorological events .

Based on the above criteria, the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) 2019–2020 dataset was selected as the primary dataset because it spans a wide range of ice types and provides time-series in-situ measurements along repeated transects. The MOSAiC dataset includes four typical ice types: SYI and FYI from winter to spring, newly-formed smooth FYI in winter, and SYI in summer. Beyond MOSAiC, additional datasets were selected to capture two critical snow and ice conditions that are not represented in MOSAiC. First, to better account for the effects of thick snow on sea ice prone to flooding, we included data from the Norwegian Young Sea ICE Expedition 2015 (N-ICE2015) and the Weddell Sea (2013) campaigns. Second, the Lincoln Sea (2017) campaign was included to represent a distinct rough MYI type, enabling a more comprehensive assessment of SND distributions across different ice ages. We note that only three transects were acquired over newly-formed smooth FYI from the MOSAiC (i.e. Runway), as this site was disrupted by ice motion . To improve sampling for this ice type, we included the Resolute Bay (2025) dataset, which represents smooth FYI covered by a thin snow layer comparable to that on the MOSAiC Runway. Although co-located SIT measurements were not available for Resolute Bay, field drilling indicated similar ice conditions (see Table ). The geolocations of the selected test sites are shown in Fig. . Table  summarizes the ice type, season, mean, median, and standard deviation of both SIT and SND, and the number of transects, providing an overview of snow and ice properties of the selected test sites.

In all campaigns, SND measurements were carried out using automated snow-depth probes (magnaprobes) equipped with a data logger and GPS . The device has a maximum measurement depth of 1.2 m, with an estimated accuracy of ∼3 mm . In the Lincoln Sea, MOSAiC, and Weddell Sea campaigns, total thickness (snow + ice thickness) was sampled using a ground-based electromagnetic (EM) induction sounding system (GEM-2, Geophex Ltd.) operating at multiple frequencies . During the N-ICE2015 campaign, total thickness was measured with portable EM instruments (EM31 and EM31SH, Geonics Ltd.) mounted on a sledge . The precision of the EM measurements is approximately 0.1 m on level ice up to 4 m thick. The accuracy decreases on rough and deformed ice, and the EM instrument can underestimate the ridge thickness by up to 50 % . For all datasets, SND and total thickness measurements were acquired along the same tracks.

All datasets had previously been corrected for sea ice drift following the procedures described in , , , . Co-location between magnaprobe and EM measurements was performed using nearest-neighbour interpolation. The co-location mismatch arises from the spacing between the magnoprobe and EM measurements, which is around 1–5 m . Given that our analyses in the following sections are based on values averaged along the transect rather than on individual measurements, the metre-scale mismatch is unlikely to influence the results. The SIT was then calculated as the co-located total thickness minus SND. Examples of the co-located SND and SIT along the transects are shown in Fig. .

Figure  shows an overview of the statistical distributions of SND and SIT measurements for each test site. Each test site comprises several sampling transects, and the corresponding violin plots for individual transects are provided in the Supplement (Figs. S1–S3).

This section introduces four statistical distributions for fitting the observed SND samples: normal, log-normal, gamma, and skew. For a normal distribution with mean μg and standard deviation σg, the PDF is given by 1N(x;μg,σg)=12πσg2e-(x-μg)22σg2 The PDF of the log-normal distribution follows : 2LG(x;μl,σl)=1xσl2πe-(ln⁡(x)-μl)22σl2 where μl and σl are the location and scale parameters in the logarithmic space, respectively. The mean and variance are e(μl+σl2/2) and e2μl+σl2eσl2-1, respectively.

The PDF of the gamma distribution is defined as : 3Ga(x;ag,θ)=1Γ(ag)θagxag-1e-x/θ where ag>0 is the shape parameter and θ>0 is the scale parameter. Γ(⋅) is the gamma function.

The PDF of the skew distribution with standard deviation σs is given as : 4S(σs;ω,as,ξ)=1ω2π1+erfasx2e-(x2/2),x=σs-ξω where ω is the scaling parameter, as is the shape parameter, ξ is the location parameter, and erf(⋅) is the error function.

The four PDFs are used to fit the observed SND distributions. For each transect, the PDF parameters for each distribution are estimated using maximum likelihood estimation (MLE) . Considering that each transect has hundreds of samples, overfitting of MLE can be negligible. Figure a shows an example transect from MOSAiC Nloop (14 November 2019), where the histogram of the observed SND is shown as a step-line plot, while the fitted distributions are displayed in different colours.

The goodness of fit is assessed using a quantile-quantile (Q-Q) plot, which compares the quantiles of the observed SND values with those of the fitted distributions . If the fitted distribution accurately represents the data, the points in the Q-Q plot should be along the 1:1 line. Deviations from this line indicate discrepancies between the observed and fitted distributions. To quantify the goodness of fit, we calculate the root-mean-square error (RMSE) between the observed and fitted quantiles : 5RMSE=1n∑i=1nQobs,i-Qfit,i2 where Qobs,i and Qfit,i are the ith quantiles of the observed and fitted distributions (Fig. b–e), respectively, and n is the total number of quantile points considered. A lower RMSE indicates a better fit. In contrast to the histogram, which is sensitive to arbitrary binning choice, the Q-Q plot enables a direct quantile–quantile comparison between the observed and theoretical distribution. Consequently, the RMSE derived from the Q-Q plot is not affected by binning, providing a more objective basis for evaluating model performance.

Spatial variability in SND is controlled by factors such as local precipitation, wind redistribution, ice topography, and the amount of snow already accumulated in pre-existing bedforms that can be reworked by wind . A variogram provides a measure of the spatial continuity of snow cover and how it varies with distance and orientation on sea ice . A variogram can be computed by relating the semi-variance γ(h) to the lag distance : 6γ(h)=12NΣi=1N(xi-xi+h)2 where xi and xi+h are the sample values (measured SND) at the location i and i+h respectively. N denotes the number of observations at a specific lag distance h.

In this study, the semi-variogram analysis employs the Matheron estimator with an exponential model and incorporates a non-zero nugget effect, using a bin width of 3 m. The non-zero nugget reflects either measurement error or spatial variability occurring at scales smaller than the 3 m bin size . Note that the bin width is set to 3 m based on the median spacing of the magnaprobe measurements. This choice ensures sufficient point pairs per bin while resolving spatial variability up to the sill. A constant bin width of 3 m enables a consistent comparison of variogram parameters across sites. We adopt the exponential model to fit the semi-variogram, as it provides a good balance between simplicity and accuracy. Data screening and data quality are essential for semi-variogram analyses. In this study, measurements with distances greater than 10 m are excluded, as they correspond to periods when the magnaprobe was moved between sampling locations. In addition, measurements with snow depths <1 cm or equal to 120 cm (the operational limits of the magnaprobe) were removed.

Figure  presents the semi-variogram of SND measurements collected from MOSAiC Sloop transect on 14 November 2019, as an example. The fitted exponential model approaches the sill, and the effective range corresponds to the lag distance where the modeled semi-variance reaches 95 % of the sill value. In the following, this effective range is referred to as the correlation length. The snow correlation length is the distance over which the SND remains spatially correlated; beyond this scale, the measurements become effectively independent. The correlation length provides a statistical measure of spatial continuity. Larger correlation lengths can be associated with prominent surface features, such as ridges and snow dunes, which can extend up to tens of meters . The estimated correlation length can be influenced by the spacing of the magnaprobe measurements. Finer sampling intervals allow the semi-variogram to resolve small-scale snow bedforms , whereas coarser spacing may miss these features and instead primarily capture broader-scale snow structures, leading to a longer apparent correlation length. showed that a characteristic scale of around 10 m is associated with the formation of snow dunes, whereas a second scale, between 30 and 100 m, likely reflects interactions among dunes, such as merging, calving, and lateral linking.

To examine the relationship between SND and SIT for different ice types, we calculated the mean (μSND) and standard deviation (σSND) of SND, as well as the mean SIT (μSIT) for each transect at each site, as shown in Fig. . A clear linear relationship is observed between μSND and μSIT for FYI. This can be explained by the concurrent increase in SND and SIT during the ice thermodynamic growth season. In contrast, no significant linear relationship is observed for SYI and MYI. For these ice types, SIT is no longer controlled primarily by ongoing thermodynamic growth, as they tend to approach a quasi-equilibrium thickness. At the same time, the overlying snow has a longer residence time and is therefore increasingly modified by post-depositional processes such as wind-driven redistribution and the influence of surface roughness, rather than by concurrent snow accumulation alone.

Since CV is defined as the ratio of σSND to μSND, a linear relationship is expected : 7σSND=CV×μSND which suggests that σSND can be estimated when μSND is known.

Figure a shows the relationship between σSND and μSND for all sites. The results do not show a dependence of CV on μSIT, suggesting a constant value of CV across different ice types. A linear fit between σSND and μSND in Fig. b gives CV=0.5. The CV can be used to estimate SND variability from its mean value, as obtained from snow modelling . Most of the Lincoln Sea samples lie above the fitted line, indicating enhanced SND variability which can be linked to observed ice rafting events and significantly deformed surfaces. In contrast, samples from N-ICE2015 and the Weddell Sea (MYI) fall below the fitted line, with lower CV values than the other sites. Interestingly, these two sites experienced flooding . Flooding wets the basal snow layer, promoting wet-snow settling and densification that reduce the mean SND . Although flooding reduces mean SND, it is also associated with a lower-than-expected variability, leading to a reduced CV.

The reduced SND variability at flooded sites may arise from two physical mechanisms. First, because overburden stress increases with SND, thicker snow can undergo greater compaction once wet , leading to a greater reduction in SND than thinner snow and thus reducing spatial SND variability. reported the lowest brine wicking in the lowest-density layer, while the denser layers tended to exhibit higher wicking heights. A plausible explanation is that smaller capillaries in denser basal snow increase capillary suction, enhancing upward brine infiltration and increasing the volume of snow that becomes slush and subsequently freezes into snow ice. If snow-ice formation is more extensive in initially thicker snow, this could amplify net snow-thickness loss there and further suppress spatial SND variability. Second, snow may become more cohesive and mechanically stronger after flooding, making it less susceptible to wind-driven redistribution. In winter, upward conductive heat flux from the ocean warms the ice–snow interface, increasing the temperature gradient across the snow (for a given air temperature) and also raising the snow's mean temperature. Since sintering accelerates at higher temperatures , snow warmed by basal flooding sinters faster, thus increasing cohesion and making the snow less susceptible to wind redistribution and thus reducing SND variability. The difference in CV between flooded and non-flooded sites suggests that flooding can imprint a measurable signature in the SND distribution. The above proposed mechanisms still require validation through sufficient in-situ SND and SIT measurements at flooded sites.

This subsection investigates (1) temporal variability based on the MOSAiC datasets; (2) the dependence of PDF fitting performance on ice age and SIT across all test sites. Following the method introduced in Sect. , the observed SND values for each transect across the test sites are fitted using the four probability distributions: normal, log-normal, gamma, and skew. The corresponding RMSE values derived from Q-Q plots are calculated to identify the most appropriate distribution for each sub-kilometre-scale transect (summarized in Table ). To capture the levels of deformation, we define the SIT range (ΔSIT) as the difference between the 95th and 5th percentiles of SIT for each transect.

The correlation length of SND for each transect at all test sites was estimated using the method in Sect. . Note that four transects, namely the MOSAiC Nloop transect on 27 February 2020, MOSAiC Summer transect on 27 June 2020, and Lincoln Sea transects 4 and 5, were excluded because their semi-variograms do not reach a constant semi-variance value, preventing accurate estimation of the sill and effective range (i.e. correlation length). This occurs because semi-variogram analysis can fail to detect slope-change points at large length scales due to undulations in the variogram introduced by local non-stationarities . In such cases, the effective range cannot be robustly estimated from the semi-variogram, and more advanced approaches such as multifractal temporally weighted detrended fluctuation analysis are required .

The correlation lengths of the transects within each site are shown in Fig. . We observe that thicker ice is associated with a larger mean correlation length. The mean correlation length and mean SIT of each site are plotted as blue and red lines, respectively, showing a high correlation of 0.92. In general, the mean correlation length for FYI is 39±25 m (mean ± standard deviation). For smooth and thin snow-covered SYI in summer (MOSAiC Summer), it increases to 54±28 m, while snow-covered SYI and MYI in the non-summer season (i.e. excluding MOSAiC Summer) exhibit the longest correlation length, averaging 72±25 m.

For FYI, the correlation lengths vary between 10–80 m, as shown in Fig. . The range is consistent with observations from undeformed FYI where the 10 m length scale is associated with wind-driven dune formation . On larger scales (30–100 m), the governing processes may involve interactions between individual dunes, such as their gradual movement, merging, or dispersal over time. Specifically, for the three sites (Weddell Sea, MOSAiC Runway, and Resolute Bay) covered by thin ice with μSIT<1.2m, the mean correlation length is approximately 14±8 and 19±8m for FYI in the Weddell Sea and Resolute Bay, respectively. For MOSAiC Runway (FYI), the mean correlation length is 32±18m. For MOSAiC Sloop, where FYI is growing with μSIT of 1.4m, the mean correlation length is 46±26m, with greater variability than other FYI possibly due to the broader range of SIT.

For SYI and MYI, the SIT values for the Weddell Sea and N-ICE2015 are ∼1.5m, similar to the MOSAiC Sloop. The mean correlation lengths are approximately 45±17m, consistent with those observed for MOSAiC Sloop. reported that snow-surface correlation lengths vary from 3 to 70m, averaging 13–23 m, based on observations from FYI and MYI in the Bellingshausen, Amundsen, and Ross Seas. In this study, the correlation lengths derived from two FYI floes and one MYI floe from the Weddell Sea are 8, 20, and 40 m, respectively, with a mean value of 23m, which agrees well with the observations from .

For SYI and MYI thicker than 2m, including MOSAiC Summer, Lincoln Sea, and MOSAiC Nloop, the correlation length shows larger mean values and greater variation compared to others. The mean correlation lengths are 75±24m for the MOSAiC Nloop and 82±21m for the Lincoln Sea. For MOSAiC Summer, the mean correlation length is 54±28m, less than that of the Lincoln Sea, despite a similar mean SIT. This can result from the very thin snow layer (μSND=0.07m) during the melting season, where the surface was smooth and therefore exhibits reduced spatial correlation.

The positive correlation between correlation length and SIT can be explained by the physical processes that shape the snow surface features. Small correlation lengths are likely associated with the spatial scale of individual snow dunes , beyond which SND at one location provides little information about that at another. In contrast, on rougher MYI, larger correlation lengths are expected, as prominent surface features, such as hummocks and ridges, affect snow accumulation over broader spatial scales. The surface topography of FYI (MOSAiC Sloop) and SYI (MOSAiC Nloop) captured by ALS is provided in Fig. S5, visualizing that SYI exhibits more pronounced surface features than FYI, which likely results in larger correlation lengths.

To investigate the temporal changes of the spatial heterogeneity of snow cover, we analyse time-series variograms from the MOSAiC Nloop and Sloop sites. For MOSAiC Nloop, we observed a consistent increase in correlation length between 30 January and 27 February 2020, following snowfall and drifting-snow events that began on 30 January and 18 February 2020 (Fig. ). A major drifting snow event occurred on 24–25 February 2020, coinciding with the largest correlation length observed on 27 February 2020, indicating a snow correlation length exceeding 150m. Slight increases in snow correlation length were also observed on 26 December 2019, 24 April 2020, and 7 May 2020, coinciding with snowfall or drifting snow events. One possible process is that, during significant snowfall or drifting snow events, the valleys between the snow dunes become filled , leading to larger and more continuous snow structures, represented by increasing correlation lengths. This infill alters the pattern of the SND distribution and influences subsequent snow redistribution processes. For MOSAiC Sloop, although the changes in snow correlation length are less pronounced than those at MOSAiC Nloop, there is a steady increase from around 28 to 60m during the drifting snow event from 20 February to 20 March 2020. These results suggest that drifting snow events have a greater impact on increasing snow correlation length over rougher ice (MOSAiC Nloop) compared to smoother ice (MOSAiC Sloop).

evaluated the skew distribution using SND transects spanning FYI to MYI. This study extends previous analyses by further investigating the effects of SIT and meteorological events on SND distribution. showed that the skew distribution provides the best fit for SND over MYI, which is consistent with our results (Fig. e and g), with two exceptions. First, during summer, when the snow cover is very thin (mean 7 cm) over SYI (Fig. h and i), the log-normal distribution performs best. Second, during the early stage of snow accumulation over the MOSAiC Nloop (Fig. a), prior to wind-driven redistribution, the log-normal again provides the best fit. These two exceptions complement the findings of and demonstrate that meteorological events and seasonality are essential in regulating SND distribution. Note that in these two cases, the improvement in the log-normal over skew distribution is modest (≈20 %–25 %), calculated from Table  using (RMSEskew-RMSElog-normal)/RMSEskew. However, the skew significantly outperforms the log-normal by ≈60 %–80 % in other SYI and MYI cases. In particular, large RMSE values of log-normal are observed for MOSAiC Nloop after 30 January 2020 in Fig. a and the Lincoln Sea and N-ICE2015 in Fig. . Hence, although the log-normal distribution performs best in these two exceptions, the skew distribution exhibits greater stability and is less sensitive to extreme deviations from the observed SND distributions. For practical applications, the skew distribution therefore provides a more robust representation of SND distribution over regions containing mixed ice types or lacking a priori knowledge of ice type.

quantified the CV of the snow in MYI. We extend the analysis to include FYI and obtained an overall CV of 0.50. The value reported by (CV = 0.42) falls within the 95 % prediction interval of our empirical fit (Fig. b), indicating consistency across the datasets. Additionally, we demonstrate that CV shows no dependence on SIT, suggesting that the linear relation (Eq. ) to estimate sub-grid or footprint-scale SND variability from mean SND can be applied across a range of SIT conditions. We also observe that flooding can reduce CV, revealing that flooding can imprint a measurable signature on the SND distribution.

used GEM on the floe-scale (400 m × 400 m) and GEM inside the terrestrial laser scanning (TLS) field (80 m × 80 m) to characterise spatial variability in SND and SIT. This study uses GEM floe-scale data because the 400 m × 400 m coverage can represent an individual floe and is consistent with the spatial scale across other test sites. reported SND and total thickness (snow + ice) for each floe (503, 506, and 517) using both datasets. The violin plots (Figs.  and S3) summarize SND and SIT for FYI (503 and 506) and MYI (517) which are consistent with . Beyond this, we further explored the PDF that best fits the SND distributions related to ice age and SIT (Figs. 10–11).

Using MOSAiC time-series data, this study analysed the weekly evolution of SND statistics, providing new insights for the snow community. reported a strong correlation between mean SND and ice age (in days), suggesting that it is not sufficient to know only whether the ice is FYI; we must also know the age of FYI (in days or weeks). We examine how the best-fitting statistical distribution of SND evolves using weekly MOSAiC measurements (Fig. ). For the Sloop (FYI) during the growing season, we observe a clear shift in the SND distribution from log-normal to gamma/skew as SIT continues to increase. These results not only reinforce the hypothesis that ice age strongly controls snow evolution , but also provide new quantitative insights into the temporal variability of snow layers. Furthermore, indicated that topography and wind redistribution are two main factors controlling the spatial variability of SND and its correlation length. Our results support the role of wind redistribution: drifting snow events increase correlation length (Fig. ), consistent with the growth of snow-dune size . We also examine the influence of surface topography on SND distributions using ALS data for MOSAiC Nloop and Sloop (Fig. S5). However, no pronounced snow-topographic features were observed from December 2019 to February 2020, spanning the period before and after the transition in the best-fitting PDFs. Previous studies suggest a dependence of the correlation length on ice types . The findings of this study are consistent with this dependence on ice types and further suggest a clear relationship between correlation length and SIT (Fig. ).

Sea ice models within coupled climate models are key tools for quantifying high-latitude climate variability and supporting seasonal sea ice prediction . Because even 1 km configurations cannot explicitly resolve the strong sub-grid heterogeneity of SIT and associated processes, most models represent thickness variability using an ice thickness distribution (ITD) framework . In practice, the ITD is discretized into a finite number of thickness categories. A proper selection of the number of categories is essential to ensure a meaningful simulation of key sea ice variables, such as the ice volume . In addition to the ITD, snow parameterizations are a key source of uncertainty and control in sea ice models. showed that spatial variability in SND strongly modulates conductive heat flux, winter ice growth, and the timing and magnitude of surface melt, through its control on insulation, surface temperature, and radiative processes. evaluated two snow representations: one in which the SND is independent of the underlying SIT, and another in which the snow is distributed proportionally to the ITD. Their results indicate that the latter approach improves the simulation of thermodynamic ice growth during the ice-formation period. therefore emphasized the need for large-scale field observations to establish representative and robust statistical relationships between snow and sea ice. Our results provide new quantitative insights into this perspective. Specifically, Fig.  demonstrates that SND distributions exhibit a clear dependence on SIT for FYI, which can be used to evaluate and refine category-specific snow parameterizations in models. Moreover, our findings on SND distributions across ice ages and SIT values can be incorporated into ITD frameworks to better represent the statistical coupling between snow and ice, thereby improving simulations of thermodynamic ice growth during the ice-formation period. As a simplified alternative, a skew distribution can serve as a robust candidate when assuming a single universal distribution for the snow field across the ITD categories.

To derive SIT from satellite altimetry, freeboard measurements must be combined with SND information. However, the horizontal resolution of snow depth products (25–100 km) is much coarser than that of along-track freeboard measurements (15 m–2 km) , creating a scale mismatch that necessitates parameterized representations of sub-grid snow redistribution within altimeter footprints. Previous approaches have introduced empirical redistribution functions based primarily on freeboard , with coefficients derived from airborne observations during Operation IceBridge . The findings of this article highlight that ice age, in addition to freeboard, can be a potentially important factor to consider in the empirical snow-redistribution functions for laser-altimetry-based SIT retrieval.

Because SIT retrieval from altimetry depends explicitly on SND through hydrostatic equilibrium, SND variability within the footprint directly propagates into SIT retrieval uncertainty. Given a large-scale mean SND, the standard deviation of SND can be inferred using the CV (Fig. ). The statistical distribution of SND derived in this study provides a more comprehensive representation of sub-grid SND variability. Specifically, the most appropriate distribution (e.g. log-normal or skew) can be selected according to the ice age and SIT. For a log-normal distribution, which is defined by two parameters, the mean and standard deviation are sufficient to determine the distribution parameters and reconstruct the fitted PDF. The skew distribution requires three parameters, namely mean, standard deviation, and the skewness (as given in this study). Once the PDF is fitted, additional SND statistics, including modal values and percentiles, can be derived. From a satellite perspective, the modal SND is particularly relevant because it is the most frequently occurring SND within a satellite footprint and can be associated with the dominant surface condition. These statistics provide a more complete characterization of sub-grid snow variability and can be propagated to quantify uncertainty in SIT retrieval at sub-kilometre scale.

A limitation of this study is the regional datasets. The analysis in this article is based on the selected test sites rather than on unified pan-Arctic and -Antarctic datasets. Nevertheless, the sites were carefully chosen to span various snow and ice types and each contains thousands of samples, ensuring statistically robust analysis. However, SND distributions can be sensitive to many local factors such as ice topography, snowfall, wind redistribution, flooding, and melt processes. Consequently, extending these findings to the hemispheric scale requires thorough evaluation using large and comprehensive datasets. Despite this limitation, the regional cases analysed here, supported by high-quality in-situ measurements, provide new insights into how SND distributions depend on ice types and thicknesses at the sub-kilometre scale. To assess the regional representativeness of the findings of this study, we summarize the dominant climatic and ice-type characteristics captured at each test site in the following.

The MOSAiC Nloop and Lincoln Sea datasets represent the thick (μSIT>2.5m) and deformed SYI and MYI conditions. The consistent PDF-fitting performance between Nloop and the Lincoln Sea supports the conclusion that the SND distribution depends on ice age. Therefore, these results are most applicable to thick and deformed SYI and MYI types. The N-ICE2015 dataset, combined with observations from the Weddell Sea (MYI) during austral winter, represents conditions of substantial snow loading (μSND>0.5m) and susceptibility to flooding. These sites are particularly relevant for characterizing SND distributions under heavy snow accumulation and snow–ice formation processes. The MOSAiC Sloop reflects a growing FYI evolving from newly-formed ice to fully developed FYI, with SIT increasing from <1 to ∼2 m between October and May. These observations are most representative of the evolution of snow over growing FYI, from initial formation through full development to the pre-melt season. The MOSAiC Runway and Resolute Bay datasets represent relatively level FYI with thin and smooth snow cover. Among all sites, they exhibit the lowest mean SND and standard deviation and are therefore most representative of newly-formed snow over young ice. The MOSAiC Summer represents SYI that persists into summer with a shallow snow layer (∼7 cm). This case demonstrates that, despite the same ice type (SYI), SND distributions can differ substantially between winter and summer. These observations are most applicable to thin snow-covered SYI during the melt season.

Another limitation concerns the measurement accuracy of SND and SIT obtained from the magnaprobe and EM instruments. The magnaprobe has a precision of 3 mm. Given that the typical mean SND within each transect is several to tens of centimetres, 3 mm is small relative to the SND measurements. In the analyses, we use μSND computed from all samples along each transect rather than an individual sample, which further reduces the influence of measurement uncertainty. Each transect contains hundreds of samples, ensuring that the inferred PDFs are statistically robust; therefore measurement error from a single sample has a negligible effect on the overall distribution shape. When evaluating the fitting performance, the differences in RMSE between two PDFs less than 3 mm are considered comparable (Table 2), consistent with the instrumental precision of the magnaprobe. The precision of the EM measurements is approximately 0.1 m on level ice. Similarly, we use μSIT calculated by averaging all samples along each transect, rather than individual measurements, thus reducing the influence of measurement uncertainty on the reported SIT-dependent relationship. The μSIT is used primarily for mean-SIT binning, so the influence of measurement uncertainty on the results is expected to be limited.

This study examines the influence of ice age, SIT, and meteorological conditions on the most appropriate PDF to describe SND observations. In the context of practical applications, we recommend the following considerations for characterizing sub-kilometre SND distributions:

The ice age should be explicitly considered. Ice age represents the effective snow residence time on a given ice floe and therefore controls the degree of snow accumulation and wind redistribution. SND distributions vary with ice age: newly accumulated snow on younger ice (often FYI) is typically well described by a log-normal distribution, whereas progressive wind redistribution, compaction, and drift processes reshape the distribution toward a skew shape. Consequently, snow over older and thicker ice (often SYI and MYI), where the snow has a longer residence time, is generally better characterised by a skew distribution.