CLASSIC requires the following seven meteorological forcings: incoming short- and long-wave radiation, near-surface air temperature, wind speed, specific humidity, total precipitation rate (and optionally snowfall rate), and air pressure. Both total precipitation and snowfall rates were prescribed at all sites to minimize uncertainties related to snow accumulation. The quality-controlled and standardized SnowMIP data are used, which combine meteorological forcings and snow measurements such as snow depth, snow water equivalent, albedo, surface and soil temperatures, depending on sites . Additionally, three Arctic sites are considered in this study: Bylot Island , Umiujaq TUNDRA , and Trail Valley Creek (Fig. ). The boreal SnowMIP sites (Old Aspen, Old Black Spruce, and Old Jack Pine) are excluded from our study because of the uncertainties due to snow canopy processes, which are out of the scope of this work. All sites are described in Table . More information about site initialization and variables is available Tables S1–S3 in the Supplement.

The relative humidity at Umiujaq and TVC was converted to specific humidity as an input for CLASSIC (see Sect. S2). The data from Umiujaq FOREST were not used because of the uncertainties related to snow trapping by tall vegetation (tall shrubs and black spruce) . At the Umiujaq TUNDRA, soil data are available separately for the shrub and lichen subareas but were averaged here, as the snow measurements and meteorological forcing are based on a single location between the two subareas. To best match the observations, the plant functional type at this site was prescribed in the model as 50 % broadleaf deciduous cold shrub (Betula glandulosa) and 50 % bare soil, as lichen is not currently represented as a plant functional type in CLASSIC (Table S1). At all Arctic sites, a fibric peat layer was prescribed in the uppermost soil layer (top 10 cm) to partially alleviate the absence of explicit lichen and moss representations in CLASSIC and to mimic the insulating properties of the lichen or moss layers present at these sites. This imperfect solution is further discussed in Sect. . The thickness of the peat layer (10 cm) was set to best match the observed amplitude of summer soil temperatures and soil water content (not shown). When needed, the simulated soil variables (soil temperature and soil water content) were linearly interpolated to the first observational measurement depth greater than or equal to 5 cm (corresponding to the center of the first model soil layer) for comparison with observations.

At TVC, the dataset used in was not publicly available at the time of this study; therefore, we relied on the forcing data from , which span a two-year period and include precipitation corrected for gauge undercatch following . As only total precipitation was provided, rainfall and snowfall rates were estimated using the suggested temperature threshold of 1 °C from . This temperature-based rain–snow partitioning may introduce uncertainties, especially for mixed-phase events or precipitation occurring near the threshold temperature e.g.,. The station location itself may act as a local snow accumulation zone, leading to measured snow depths that are likely larger than those representative of the surrounding tundra (Brampton Dakin and Georgina Woolley, personal communication, 2023). Despite the prior gauge-undercatch correction, the initial simulated snow depth was too low and the snow density was underestimated relative to snow-pit measurements. We therefore adjusted the snowfall rate in to match the snow depth at peak snow accumulation in our simulations including our new Arctic snow model developments (corresponding to a scaling of the snowfall rates by a factor of two; Fig. S1a–d in the Supplement blue and green lines in Sect. S3), which will be further discussed in Sect. . The updated dataset used in is expected to provide improved forcing data and may help resolve these snowfall rate uncertainties in future studies.

The precipitation at Umiujaq was measured only from 2016 onward, and ERA5 data are used prior to that . Therefore, only the period after 2016 is considered for the model evaluation. The albedo at the Arctic sites can be retrieved from the incoming and outgoing shortwave radiation measurements. However, due to frost-related issues with the instruments, some data are inaccurate and gap-filled, often leading to unrealistic values; therefore, the simulated albedo will not be assessed against observations at those sites. All data provided are quality-controlled and use snowfall wind undercatch corrections . Further in-depth discussion on the measurement uncertainties is addressed in Sect. . The snow depth time series at all sites are shown in Fig. .

This study introduces three snow model physics improvements: (1) a correction of the computation of the thermal conductivity at the top of the first soil layer (Sect. ), (2) a revised computation of the bottom snow temperature (Sect. ), and (3) the addition of a windless exchange coefficient within the sensible heat flux calculation (Sect. ). Furthermore, three Arctic-specific snowpack adaptations are proposed: (1) the inclusion of blowing-snow sublimation losses (Sect. ), (2) a revised compaction scheme (Sect. ), and (3) a modification of the snow thermal conductivity parameterization (Sect. ). All details about the code implementation are available in Sect. S4.

This study uses CLASSIC v1.8 in a 1D point-scale configuration. In practice, strictly point-scale simulations are somewhat idealized, given that the meteorological forcing data and validation measurements cover different areas around the stations, and the spatial footprint of each sensor varies. We therefore prescribed soil properties, vegetation cover, and other site characteristics to be as representative as possible of the area surrounding the measurement sensors. CLASSIC point-scale simulations are treated similarly to single-grid-cell simulations, allowing fractional vegetation cover and separate surface energy and water balances over different subareas, including snow-covered and snow-free fractions. The snow cover fraction parameterization was kept active and follows a linear relationship between 0 and 10 cm snow depth, as further discussed in Sect. . However, the presence of snow at the scale of a snow depth sensor is effectively binary; consequently, this introduces uncertainties when comparing model outputs with point-based measurements, particularly during shallow or patchy snow conditions and in wind-affected environments where snow redistribution can generate strong small-scale variability in snow depth. Scanning laser measurements could help improve the spatial representativeness of snow depth observations in future studies e.g.,. To limit these effects, evaluation metrics were computed only when observed snow depth exceeded 10 cm (Sect. ), and further discussion about the uncertainties related to point-scale simulations is covered in Sect. .

The meteorological forcings at all sites described in Sect.  were used to force the model and were linearly interpolated from 1 h to the chosen 30 min model physics time step. CLASSIC requires full-year forcing files; therefore, the forcing data were extended at both the beginning and end of the time series by replicating the first and last available full years over any missing periods, and analyses were carried out only on the available data period. All the forcing files were provided in local time or were converted to local time. Uncertainties related to the meteorological forcing can also affect the simulations, particularly at Arctic sites where precipitation, radiation, and near-surface meteorological measurements are more prone to errors due to wind undercatch, frost, polar night conditions, and data gap filling; these uncertainties are further discussed in Sect. .

The soil texture (sand, clay, and organic matter content) was prescribed based on site information when available (Tables  and S2) and complemented with the global gridded dataset SoilGrids250m version 1 when needed. Soil permeable depth and soil color index were prescribed with the nearest grid cell of the gridded dataset from and . The PFTs were prescribed with site information (Tables  and S1). The proportions of C₃ and C₄ grasses were derived from . The model was run with the biogeochemistry component (CTEM) enabled, allowing vegetation to evolve dynamically and CO₂ fluxes to be simulated. The methane and nitrogen cycle, fire, competition, and dynamic tiling options were not activated (the default options in the current CLASSIC version). The CO₂ forcing was derived from . Further information is available in Sect. S1 of the Supplement.

A first spin-up phase was performed at all sites over 100 to 300 years by looping over the forcing files (with an accelerated carbon pool storage – spinfast parameter set to 10) until reaching the equilibrium in the carbon pools. A final spin-up phase was performed over the same duration with the spinfast parameter set to 1 to ensure the conservation of carbon (see Sect. S6 for further details on the spin-up procedure). During the spin-up phases, the CO₂ concentration was held constant at the value corresponding to the first year of the meteorological forcing file specific to each station; then, for the runs, the CO₂ concentration evolved on an annual basis, following the values from .

Table  presents the set of experiments conducted at the SnowMIP and Arctic sites, designed to sequentially test the improvements and modifications introduced above in the CLASSIC snowpack scheme (Sect.  and ).

Model skill is evaluated using observed manual and automatic snow depth and SWE, snow albedo (excluding Arctic sites; see Sect. ), surface temperature, soil temperature in the upper soil layers (1–30 cm, depending on the site), and snow cover duration (SCD), which is derived as the number of days within a snow season (September to August) with snow depth exceeding 10 cm. Table S3 lists the measurements available at each site. To avoid uncertainties arising from patchy snow in both the model and observations, the metrics are computed for snow depth greater than 10 cm. In addition, observed snow albedo values are constrained to be between 0.4 and 0.9, and snow surface temperature to be less than or equal to 0 °C, to ensure that they remain within a realistic physical range and to avoid potential artifacts or errors from observational measurements. Observed albedo may still be influenced by protruding vegetation, especially during shallow snow conditions, despite the 10 cm snow depth threshold. However, albedo measurements are available mainly at sites with short or mowed grass, alpine tundra, or little vegetation cover, making them broadly comparable to the simulated snow albedo. Remaining uncertainties may instead arise from limitations in the representation of vegetation in CLASSIC, including possible overestimation of simulated vegetation height and the absence of vegetation bending, as further discussed in Sect. . For the soil temperatures, the first soil layer measurement at a depth greater than or equal to 5 cm is used for comparison with the model.

The following mean bias (MB), normalized mean bias (NMB), root-mean-square error (RMSE), and normalized RMSE (NRMSE) are used for each site: 16MB=1d∑t=1dMt-Ot,17NMB=MBσO,18RMSE=1d∑t=1dMt-Ot2,19NRMSE=RMSEσO, where Mt and Ot denote the daily modeled and in situ observed values at time t, d is the number of days available within the analysis period for each variable and site, and σO is the standard deviation of the daily observed values over the corresponding period. An NRMSE greater than 1 indicates poorer RMSE-based performance than using the observed temporal mean as a constant predictor. The normalized RMSE and MB allow for better comparison among sites and variables.

In addition, we define an overall score over all sites and variables as follows: 20Score=1∑i=1nmi∑i=1n∑j=1miσO,ij-RMSEijσO,ij, where n is the number of variables, mi is the number of available sites for each variable i, RMSE_ij is the root-mean-square error for the variable i at site j, and σO,ij is the standard deviation of the corresponding observations. The score is equal to 1 when the model perfectly matches the observations, equal to 0 when the RMSE equals the observational standard deviation, and becomes negative when the RMSE exceeds the observational variability. Each variable enumerated before is counted (snow depth, SWE, snow albedo, surface temperature, soil temperatures, and SCD). The snow depth and SWE include both the automatic and manual measurements, giving slightly more weight to those variables.

Pearson correlation coefficients were also computed as a complementary diagnostic to assess the temporal agreement between simulated and observed daily time series. These values should be interpreted with caution, as daily simulated time series are not expected to exactly follow the observations, especially for snow depth at Arctic sites where wind-driven redistribution can cause local snow depth changes that are not directly related to precipitation events. Therefore, correlations are used only as an additional diagnostic and are not included in the overall score. All metric values are reported in Sect. S11.

The snow model physics developments (Sect. ) were mainly carried out independently of each other, guided by physical considerations and evaluated against available observations, without aiming to optimize scores or overall model performance. The snow Arctic adaptations (Sect. ) were developed upon the physics developments by testing various formulations with manual iteration and exploration of the parameter space. All sites except TVC were used in this process in order to preserve TVC as an independent validation site – and given the substantial uncertainties associated with the snowfall rates at this site (see Sect. ). Nevertheless, we also propose an adjusted version that includes TVC (experiment ALL_TVC; Table ), motivated by the distinct behavior observed at this site and the limited number of available Arctic sites (see details below).

This study presents only the optimal solutions, although additional combinations of parameters and parameterizations were tested (not shown). The key tuning process was focused on the dry maximum snow density (Eq. ). The following spaces of parameters were tested: 0.5<d0<2 with increments of 0.1 m, 0.5<σ<1 with increments of 0.1 m, 1<U0<5 with increments of 0.1 m s⁻¹ and the maximum constant of 430 (Eqs.  and ) was tested between 400 and 450 kg m⁻³ with increments of 5 kg m⁻³. The threshold wind speed at which wind-induced compaction is triggered was tested as U0 (independently). Modifications to the constant 700 kg m⁻³ in the wet maximum snow density Eq. () were tested but did not yield any enhancements; therefore, this value was left unchanged. Note that snow density can exceed this value through melting and refreezing processes, but the snowpack will not undergo further compaction.

The overall score presented in Eq. () was used as the most objective metric to tune those parameters across all sites and variables, but when similar scores occurred (difference lower than 0.1), further investigation was carried out at individual sites to choose the most physically-based option (considering consistency between the simulated snow depth, soil temperatures, and snow density), and/or we favored best performances at the Arctic sites (Bylot and Umiujaq) because of their underrepresentation. Even though the simulations and results are presented stepwise, we calibrated the effects of the three Arctic model enhancements by systematically testing each possibility back and forth to ensure consistent tuning.

TVC was excluded from the tuning process and only added in the ALL_TVC experiment by adjusting the U0 parameter in Eq. () – by exploring the same parameter space described above – to get the best score at all sites (including TVC), but without redoing the whole tuning process mentioned above. Despite the large uncertainties associated with TVC (snowfall rates, limited number of years, etc.), this approach allows us to provide a range of possible values for the U0 parameter. Furthermore, given the limited number of Arctic sites currently available and the uncertainties inherent to Arctic environments (such as drifting snow, frost on sensors, and snowfall rate measurements), this allows us to retain a parameter to fine-tune for future spatial simulations.

Overall, the default version of CLASSIC (DEF) reasonably reproduces the seasonal evolution of snow depth and most variables at the SnowMIP sites (see Sect.  for the site-specific details). The main biases occur at the Arctic sites, where simulated snow depth is overestimated by about 10–20 cm – a large relative bias given the thin Arctic snowpacks – and winter soil temperatures by about 5–10 °C (Fig. jj, oo, tt, nn, ss, and xx). This suggests that the simulated Arctic snowpack is too insulating, mainly because the default compaction scheme produces bulk snow densities that are too low for thin, wind-exposed Arctic snowpacks, resulting in snowpacks that are too deep for a given snow mass.

The main improvement for the Arctic sites is the revised snow compaction scheme (Sect. ). By allowing thin, wind-exposed snowpacks to reach higher maximum dry-snow densities while having little effect on deeper snowpacks or under weak-wind conditions, this scheme produces simulated bulk snow densities more consistent with Arctic observations. At Bylot, for example, the snow depth bias decreases from about 7.5 cm to nearly zero, while simulated bulk snow density approaches the observed values of about 300 kg m⁻³ (further details are presented in Sect. ). This denser and thinner snowpack reduces excessive soil insulation and improves simulated snow, bottom snow, and soil temperatures, with the mean temperature bias at Bylot decreasing from about 10 to 5 °C between the PHYS and COMPAC experiments (which is further enhanced in the CL11 experiment detailed below). Similar improvements are found at TVC, whereas the impact on most SnowMIP sites remains limited, as intended. Lastly, blowing-snow sublimation losses have a smaller impact than the revised compaction scheme but still affect some sites, as further discussed in Sect. .

On the other hand, the physics improvements (Sect. ) provide further physical consistency in the snowpack thermal regime and allow the Arctic developments to be built on a more robust basis. The original bottom snow temperature formulation in the DEF experiment tended to overestimate the simulated snow temperature and underestimate the bottom snow temperature, thereby inducing excessive heat storage within the snowpack and biasing temperature gradients at the snow–atmosphere and snow–soil interfaces (see Sect.  for further details). The revised bottom snow temperature formulation addresses these deficiencies. For example, at Col de Porte, the vertically-averaged snow temperature bias decreases from 0.8 to 0.3 °C and the bottom snow temperature bias from -0.4 to -0.1 °C (e.g., Fig. g–j). These new developments do not necessarily improve the performance of all variables and can even degrade simulated soil temperatures when applied alone. However, they are essential for representing the snowpack thermal regime more consistently and for avoiding bias compensation.

The use of the snow thermal conductivity parameterization of (Sect. ), in combination with the Arctic developments (CL11), further improves simulated snow, bottom snow, and soil temperatures. This suggests that the previous snow thermal conductivity parameterization partly compensated for the bottom snow temperature bias. For example, at Bylot, the winter soil temperature bias increases from 6.8 °C in the DEF experiment to 9.6 °C in the PHYS experiment before decreasing to 0.9 °C in the CL11 experiment (Fig. m).

Finally, the addition of the windless exchange coefficient in the formulation of turbulent fluxes (Sect. ) has a more targeted effect. It substantially improves simulated snow surface temperatures at the SnowMIP sites, reducing the average RMSE from 3.4 to 1.5 °C and the mean bias from -2.2 to -0.3 °C (Figs. k and k), while having limited effects on snow depth, SWE, and soil temperatures. More detailed results are presented below.

Figures  and  show the RMSE and mean bias for each variable and site and their normalized values (i.e., divided by the standard deviation of the observations) to better compare between the different sites with varying amplitudes. The following subsections provide a more quantitative assessment of the incremental model developments for each variable, complementing the more qualitative analysis of the seasonal cycles presented in Sect. . Section  then summarizes the overall model performance using the aggregated scores, while Sect.  presents Pearson correlation coefficients as a complementary diagnostic of temporal agreement between simulated and observed daily time series.

Pearson correlation coefficients were computed as an additional diagnostic of the temporal agreement between simulated and observed daily time series and are reported in Table S8. Daily simulated and observed variations are not necessarily expected to be strongly correlated, especially at Arctic sites where wind-driven snow redistribution can produce local snow depth changes not directly related to the precipitation forcing. Correlations are therefore used only as complementary information and did not inform the model development or the ranking of the experiments.

Overall, the correlations support the main conclusions drawn from the RMSE, bias, and score analyses. For automatic snow depth, correlations are generally high at the SnowMIP sites, with values mostly between 0.84 and 0.94 depending on the site and experiment. Lower correlations are found at the Arctic sites, ranging from about 0.49 to 0.78, particularly at Bylot. This is consistent with the stronger influence of local wind-driven snow redistribution in Arctic environments, which can cause point-scale snow depth variations that are not directly related to precipitation events and are not explicitly represented in the 1D simulations. At the SnowMIP sites, the new model developments do not substantially modify the snow depth correlation patterns compared to the DEF experiment, whereas slight improvements are found at some Arctic sites, especially Umiujaq and TVC, where correlations increase from about 0.73 in DEF to 0.77 and 0.78, respectively, after the implementation of the new compaction (COMPAC) and thermal conductivity schemes (CL11) at both sites.

The SWE correlations are also generally high, with values mostly above 0.8 for manual measurements and above 0.9 where automatic SWE measurements are available. Albedo correlations are more moderate, around 0.7 at most sites, with lower values at Sapporo, likely reflecting processes not represented in the model, such as light-absorbing particle deposition, as already discussed. Surface temperature correlations are high at most sites, generally exceeding 0.9, while soil temperature correlations vary more strongly among sites, from about 0.5 to 0.97. Lower soil temperature correlations are found at some sites where soil temperatures remain close to the zero-curtain or where small differences in the timing of snow accumulation, melt, or soil freezing can strongly affect temporal agreement (e.g., at Senator Beck, Sodankylä, and Weissfluhjoch). At TVC, the soil temperature correlation substantially improves from 0.76 in the DEF experiment to 0.97 in the CL11 and ALL_TVC experiments, consistent with the improved representation of snow insulation and soil thermal conditions.

The evaluation metrics and aggregated scores were used as diagnostic tools to compare experiments across sites and variables, but they were not intended as formal statistical rankings. No significance tests were applied to differences in metrics or scores, given the diversity of variables, site conditions, observational uncertainties (not always characterized or available), and temporal autocorrelation in the errors. The model developments were instead primarily guided by identified physical limitations and by the consistency of the simulated responses across snow depth, SWE, snow density, snow thermal properties, and soil temperature.

For instance, we first identified that simulated bulk snow densities were consistently too low compared to available snow pit observations at Arctic sites, with underestimations exceeding 50 kg m⁻³ in some cases (Sect. ; Fig. c and d). This bias was physically consistent with the overestimation of snow depth by about 10–20 cm and winter soil temperatures by about 5–10 °C in the DEF experiment at Arctic sites (Sect. ; Fig. jj, nn, oo, ss, tt, and xx). Together, these biases suggest that the default snowpack was too insulating, mainly because the original CLASSIC maximum dry-snow density was too low for thin, wind-exposed Arctic snowpacks and because enhanced wind-induced compaction was not explicitly represented. Although low-density depth hoar can partly counterbalance the formation of dense wind slabs in terms of bulk density, the available observations still indicate that CLASSIC underestimated bulk snow density. The revised compaction scheme therefore consistently increases snow density, reduces snow depth, and decreases soil temperatures through a reduced insulating effect and an increased density-dependent snow thermal conductivity. For example, at the Arctic sites, including TVC, the mean snow depth bias decreases from 12.0 to -1.0 cm between the DEF and COMPAC experiments, while the associated warm soil temperature bias decreases from 4.6 to 3.1 °C (Fig. a and m; blue empty circles). Nevertheless, persistent soil temperature overestimation remained even when simulated snow depth and snow density became more consistent with observations, suggesting that snow thermal conductivity was still underestimated. Using the parameterization instead of the default formulation improves this aspect and provides a more physically based estimate of snow thermal conductivity, as further discussed below.

These improvements related to the compaction scheme did not substantially impact the SWE, which is driven by other processes such as precipitation forcing, sublimation losses, and snow redistribution. Indeed, snow depth and density errors can persist even when SWE biases are reduced, highlighting the importance of evaluating snow compaction processes and complementary snowpack variables in addition to SWE alone e.g.,. The blowing-snow sublimation parameterization has only a limited effect at most sites, reducing snow depth by about 2–4 cm, mainly at Umiujaq, TVC, and Senator Beck (Sect. ), and therefore cannot, by itself, explain the initial soil temperature bias. Only the combination of the blowing snow sublimation losses parameterization with the new compaction scheme and snow thermal conductivity can provide consistent improvements in the model for snow depth, SWE, snow densities, and soil temperatures.

The improvements related to snow compaction must also be interpreted together with the full snow–soil thermal regime, including the revised bottom snow temperature formulation (Sect. ) and the snow thermal conductivity parameterization (Sect. ). These developments also illustrate why scores alone are not sufficient for interpreting model performance and how compensating errors can mask process-level deficiencies e.g.,. Indeed, the revised bottom snow temperature formulation was motivated by a physical inconsistency identified from snow temperature observations at Col de Porte and theoretical estimates at Bylot (Figs. g–j and ). It reduces the vertically averaged snow temperature bias at Col de Porte from 0.8 to 0.3 °C and the bottom snow temperature bias from -0.4 to -0.1 °C, and decreases the theoretical bottom snow temperature RMSE at Bylot from 4.2 to 0.9 °C. However, when applied without the updated snow thermal conductivity parameterization, it amplifies soil temperature biases at the Arctic sites (Sect. ; Fig. m). For instance, at Bylot, the snow temperature bias decreases from 10.6 to 9.0 °C, while the 5 cm soil temperature bias increases from 6.8 to 9.6 °C between the DEF and PHYS experiments (Fig. ).

Indeed, in the original formulation, the bottom snow temperature (Eq. ) was too strongly influenced by the bulk snow temperature, which tended to underestimate the temperature at the snow–soil interface. This produced an overly strong temperature gradient between the soil and the base of the snowpack, thereby resulting in an excessive conductive heat flux from the soil into the snowpack. As a result, part of the soil heat was artificially transferred into the snow layer, contributing to warm snow temperature biases while partly compensating for the warm soil temperature bias. This behavior highlights a second deficiency of the original configuration: the thermal conductivity of the snowpack was too low, limiting the transfer of heat through the snowpack toward the atmosphere. This interpretation is physically consistent with the fact that the parameterization is based on needle-probe measurements, which have since been shown to tend to underestimate snow thermal conductivity when used with standard, uncorrected protocols e.g.,.

By increasing snow thermal conductivity, the parameterization enhances heat transfer through the snowpack and allows excess soil heat to be more efficiently dissipated to the atmosphere. At Bylot, along with the other model developments, especially the revised compaction scheme, the parameterization led to a consistent improvement in the snow–soil thermal regime. The snow temperature bias decreases from 10.6 °C in the DEF experiment to 3.6 °C in the CL11 experiment. Similarly, the bottom snow temperature bias decreases from 6.7 to 1.5 °C, and the soil temperature bias decreases from 6.8 to 0.9 °C (Fig. ). Similar improvements are observed at TVC and Umiujaq, where the final configurations also reduce soil temperature biases relative to the DEF experiment (Figs.  and ). These simultaneous improvements in snow temperature, bottom snow temperature, and soil temperature support the interpretation that the final configuration reduces previous bias compensations and provides a more physically consistent representation of heat transfer through the Arctic snowpack.

By contrast, changes in snow albedo and surface temperature are less directly coupled in this study. No albedo-specific development was introduced, and the effects of light-absorbing particles on snow albedo are not represented; consequently, albedo RMSE remains nearly unchanged across experiments, with average values around 0.07–0.08 at the SnowMIP sites (Sect. ; Fig. i and j). The improvement in surface temperature is mainly caused by the windless exchange coefficient, which reduces excessive surface cooling under stable atmospheric conditions, especially at night, and decreases, at SnowMIP sites, the mean surface temperature RMSE from 3.41 to 1.51 °C and the mean bias from -2.20 to -0.25 °C (Figs. k and k). Because this correction acts primarily on turbulent heat exchange under stable conditions, it is not expected to produce systematic albedo improvements. However, by modifying the snow surface energy balance, it can contribute to slightly earlier melt at some sites, such as Col de Porte, Reynolds Mountain East, and Swamp Angel (Sect. ; Fig. ). This indicates that the windless exchange coefficient is useful for reducing a clear surface temperature bias, but may remain a simplified solution that requires further investigation in future work.

In summary, the different developments are physically linked and need to be interpreted as a combined adjustment of the snow–soil system rather than as independent improvements of individual metrics. The revised compaction scheme first reduces biases in snow depth and snow density, limiting the risk of compensating thermal errors with an unrealistic snowpack structure. The revised bottom snow temperature formulation then corrects the thermal state at the snow–soil interface and improves snow and bottom snow temperatures, but also reveals the need for a more conductive snowpack to avoid excessive heat retention in the soil. Finally, the thermal conductivity parameterization increases heat transfer through the snowpack and improves the consistency between snow, bottom snow, and soil temperatures. This sequence explains why some intermediate experiments may degrade specific metrics, while the final combination of developments improves model performance in a physically consistent way, especially at Arctic sites, without degrading the overall performance at the SnowMIP sites. The model developments were therefore primarily driven by identified physical limitations rather than by maximizing the aggregated score. The scores and normalized metrics provided a practical way to compare experiments across variables and sites and to constrain plausible parameter ranges, especially for the wind-dependent compaction parameters, but the final interpretation relies on whether the changes are consistent with the expected physical relationships among snow mass, density, insulation, heat transfer, and soil temperature. This is why the CL11 and ALL_TVC configurations should be viewed as physically plausible final configurations with slightly different trade-offs among variables and Arctic sites, rather than as a strictly ranked pair of solutions. The remaining uncertainties in forcing data, observations, and unresolved processes are discussed in the following sections.

The discrepancies in simulated snow depth with respect to observations at Senator Beck and Swamp Angel (Fig. k and p) could be due to the lack of representation of wind-driven snow redistribution in the model. Indeed, Senator Beck is located at 3714 m a.s.l. in an alpine tundra with thin soils and exposed bedrock, subject to strong winds that favor snow erosion, whereas Swamp Angel is located in a sheltered meadow surrounded by subalpine forest at 3371 m a.s.l., lower down in the same watershed. Therefore, Swamp Angel could trap part of the wind-redistributed snow during wind events (not reflected in the snowfall measurements), leading to higher observed snow depths than simulated, while wind-driven snow erosion at Senator Beck – not accounted for in the model – could lead to an overestimation of simulated snow depth at this site. Alternatively, the current snow compaction scheme could not be adapted to the conditions at these sites. Further investigation would be needed to unravel this uncertainty, especially since most models underestimate the simulated SWE at Swamp Angel their Fig. 2.

The early melt at Weissfluhjoch (Fig. ee) could be due to the lack of representation of the effects of LAPs on snow albedo in our simulations. Indeed, the model uses a single time constant for the albedo decay for dry snow and cannot capture differences in albedo decay due to differences in LAP deposition. For example, snow albedo tends to be overestimated during the ablation period at Col de Porte, Senator Beck, Swamp Angel, and Sapporo (Fig. c, m, r, and w), which are all known to be affected by LAPs . show that the snow albedo can be reduced by up to 0.18 during the ablation period at Sapporo due to the deposition of LAPs on the snow surface, which corresponds to the discrepancies between the simulated and observed snow albedo in our simulations (Fig. w). At Weissfluhjoch, the simulated albedo is closer to observations during the ablation period, suggesting that this site is likely less subject to LAPs. However, because the CLASSIC snow scheme was calibrated to fit sites, including Col de Porte unpublished manuscript, 2001, it indirectly takes into account the LAPs, which could partly explain the good performance at the Col de Porte and early melt at Weissfluhjoch. Alternatively, this early melt at Weissfluhjoch could result from an underestimated simulated albedo during the accumulation period (Fig. gg), leading to excessive absorption of solar radiation and, in turn, a warmer snowpack, which could trigger an earlier onset of melt. Further investigation will be needed by including LAPs and/or adapting the albedo scheme to distinguish the contribution of these respective phenomena to those discrepancies, especially since early melt is also observed at other sites (discussed in other sections below). Future developments could therefore target a more explicit representation of snow albedo evolution, including snow aging, grain-size effects, and light-absorbing particles, following both the theoretical basis of snow radiative transfer e.g., and recent land-surface-model applications e.g.,.

A key limitation of this study is the use of point-scale simulations at Arctic sites, where snow processes are strongly influenced by spatial heterogeneity e.g.,. Arctic environments are subjected to harsh conditions, including strong winds that induce significant snow drifting and sublimation losses, which are difficult to quantify. As a result, simulated snow depth is not necessarily correlated with observed precipitation (e.g., strong snowstorms can erode an entire snowfall event). For instance, on 12 April 2018, conducted 172 distributed snow depth measurements within a 100 m radius of the Umiujaq TUNDRA site. Observed snow depths ranged from 50 to 210 cm, with a mean value of 109 cm, which is within 8 cm of the value measured by the automatic station on the same day (117 cm). This suggests that we can reasonably assume the station is representative of the surrounding snow depth, although it demonstrates the intrinsic spatial heterogeneity of snow characteristics in these environments. Large-scale LSMs such as CLASSIC are designed to represent processes at grid-cell scales of tens to hundreds of kilometers. Consequently, our simulations are not intended to reproduce the exact snowpack evolution at a specific site affected by wind-driven redistribution, but rather to capture its key characteristics over multiple snow seasons.

Enabling or deactivating SCF parameterizations is also a thorny question for point-scale simulations. and advise deactivating the SCF parameterizations in the ESM-SnowMIP exercise, as they assume that snow cover is either present or absent in site simulations. Indeed, SCF parameterizations are generally designed to represent large-scale spatial heterogeneities e.g.,. However, time-lapse camera observations at Arctic sites (e.g., Bylot and Umiujaq) reveal small-scale spatial variability at meter or sub-meter scales, driven by microtopography, vegetation, and surface roughness, particularly during the ablation period or at the onset of the snow season. In addition, the presence of instruments themselves can locally enhance melt around the measurement station e.g.,their Fig. 3. Such small-scale snow cover heterogeneities can affect the surface energy budget, soil temperatures, and measurements of upward long- and shortwave radiation, whose instruments have larger spatial footprints than automatic snow depth sensors, thereby influencing the measured albedo, for example. A 10 cm snow depth threshold is usually applied – excluding periods with shallow snow cover – to limit those uncertainties in point-scale snow studies; however, it is not obvious whether considering a complete snow cover for point-scale simulations is always relevant. Further investigation should be conducted at specific sites, including with cameras, to clarify this issue. Estimating the average snow depth and SCF around a station could help develop site-dependent SCF parameterizations, which could alternatively be inferred indirectly from albedo measurements using known snow and snow-free albedo values at those sites e.g.,their Eq. 54.

In CLASSIC, the model imposes a minimum snow depth of 10 cm – when snow is present – over the snow-covered subfraction of the grid cell to ensure numerical stability of the time-stepping scheme. Consequently, the snow cover parameterization cannot be deactivated without compromising numerical stability at snow depths below 10 cm. We tested minimum snow depth thresholds ranging from 5 to 20 cm at a subset of sites where such experiments could be performed without compromising numerical stability. These tests showed limited impacts on simulated soil temperatures, except during occasional periods characterized by strong temperature gradients between the soil and the atmosphere, combined with thin snowpacks. Overall, these effects were transient and smaller than those associated with the new snow model developments (not shown); however, they may still affect model tuning parameters. Furthermore, the choice of SCF parameterization e.g., is expected to exert a stronger influence in spatial simulations and will be investigated in future studies using the new snow model developments.

The vertical energy and water fluxes are modeled separately in CLASSIC for the four subareas in each grid cell: vegetated and bare soil surfaces, each with and without snow cover. However, at each model time step, all variables of each subarea are averaged together. Therefore, the separate energy budgets of each subarea do not persist over time. This assumption is particularly critical for snow because the presence or absence of snow cover strongly modifies the surface energy balance (e.g., albedo, insulation, and latent heat exchanges). Averaging the subareas may artificially smooth sharp contrasts between snow-covered and snow-free fractions, which can in turn affect simulated snow accumulation and melt rates. Further investigation could assess whether this assumption is realistic and at which spatial scales it applies.

Furthermore, the current hypothesis of quadratic temperature profiles within the snowpack could reach some limitations. On the one hand, it allows for an indirect representation of multilayer heat transfer within the snowpack, which may be more realistic than a simple linear profile in a single-layer snow model. On the other hand, it is known that snowpack temperature profiles may be more complex e.g.,their Fig. 1. For instance, cold temperatures accumulated during the night can persist in the mid-upper layers of the snowpack, while the surface warms during the day and the bottom remains relatively warm due to ground heat flux, resulting in a temperature profile that deviates from a simple quadratic curve. Therefore, when the surface and soil temperatures simulated by CLASSIC both approach 0 °C, the modeled average snowpack temperature will also approach 0 °C, whereas in reality the bulk snowpack could still be colder. Despite its good overall performance, this may be a limitation of the single-layer CLASSIC snowpack and could be one of the causes of the early melt observed at a few sites, especially at the Arctic ones (e.g., Figs. , , and a).

Some limitations in the representation of bulk snow properties may also arise from the use of a single-layer snow model. As shown in Sect. , the simulated bulk snow thermal conductivity in the CL11 experiment is overestimated at Bylot and TVC by about 0.1 W m⁻¹ K⁻¹ relative to observations (Figs. e and f and  c). Generally, estimating an effective snow thermal conductivity from the mean snow density can be misleading in a single-layer framework. Indeed, the relationship between density and thermal conductivity is nonlinear e.g.,, and thermal resistances (i.e., layer thickness divided by thermal conductivity) – not conductivities – combine in series in vertically stratified snowpacks. As a result, applying a density-dependent snow thermal conductivity parameterization to the mean snow density cannot reproduce the equivalent conductivity of a multilayer snowpack. An idealized two-layer sensitivity analysis presented in Sect. S12 indicates that the bulk approximation underestimates the integrated thermal resistance by approximately 7, 26, and 48 % for moderate, strong, and very strong stratification (represented by depth-hoar/wind-slab density pairs of 250/350, 200/400, and 150/450 kg m⁻³, respectively). This limitation could partly explain why the model reproduces observed snow density reasonably well while still deviating from observed snow thermal conductivity. Heated-needle-probe measurements are also known to underestimate snow thermal conductivity because of contact-resistance effects and assumptions inherent to the heating method , potentially contributing to the model–observation differences. In addition, the limited number of point measurements may not adequately capture the vertical snow stratigraphy needed to estimate an effective bulk conductivity.

The improved performance of the CL11 experiment should therefore be interpreted within the context of the CLASSIC single-layer framework rather than as evidence that the parameterization is universally more appropriate for Arctic snowpacks. Under the assumptions of the sensitivity analysis (Sect. S12), explicitly representing the stratified layers using the same density–conductivity relationship would reduce the effective snowpack conductance relative to that obtained in the successful bulk CL11 experiment. Reproducing this bulk conductance would therefore likely require layer-scale conductivities at least as high as, and potentially higher than, those predicted by the parameterization. This result is directionally more consistent with the higher conductivities predicted by than with the lower values predicted by , although it does not establish the universal validity of either relationship for natural Arctic depth hoar. Conversely, the better performance obtained with the parameterization in some previous Arctic studies can also partly reflect compensating biases when snow depth and/or density remain inadequately represented, as a lower conductivity can compensate for a snowpack that is too thin or too dense without improving its overall physical representation e.g.,. Our sequential evaluation, in which snow depth and bulk density were improved before modifying thermal conductivity, was specifically designed to mitigate this risk. More generally, density alone is insufficient to characterize snow thermal conductivity, which also depends strongly on snow microstructure. This limitation is particularly important for depth hoar, whose pronounced anisotropy and evolving grain and bond structure can produce substantially different thermal conductivities at similar densities e.g.,. Further evaluation using vertically resolved conductivity measurements, multilayer snow models, and microtomographic measurements of representative natural Arctic depth-hoar samples is therefore needed. Future parameterizations could incorporate microstructural descriptors, such as anisotropy or grain and bond geometry, in addition to density e.g.,. In addition, future CLASSIC developments could diagnose an internal density profile within the single prognostic snow layer, similarly to the quadratic temperature profile already used in the model, or implement a fully multilayer snow scheme.

Despite the model improvements, persistent warm biases remain in the simulated snowpack and snow surface temperatures at some Arctic sites (e.g., at Bylot; Fig. c–j), which may contribute to an early onset of melt. A first possible explanation is related to the treatment of meltwater refreezing in CLASSIC: meltwater can refreeze entirely within the snowpack if the available heat sink is sufficient, thereby releasing latent heat and warming the snowpack. However, in reality, preferential flow pathways may allow some of the meltwater to reach the soil without fully refreezing, even when the snowpack heat sink would be sufficient to refreeze it. This effect may be particularly important in Arctic environments, where the formation of depth hoar at the base of the snowpack can enhance water drainage due to its larger grain size e.g.,. Alternatively, the simulated early melt at Arctic sites may also arise from uncertainties in the forcing datasets, especially in spring when radiative sensors are often affected by frost e.g.,, or from limitations of the albedo scheme, since light-absorbing particles are not represented (as discussed for the Weissfluhjoch site in Sect. ). Furthermore, warm biases may arise from radiative heating of near-surface air temperature sensors under high incoming and reflected shortwave radiation combined with weak wind conditions, which can lead to air temperature overestimations of several degrees Celsius e.g., – conditions that could occur at Bylot given its relatively low wind speeds e.g.,. A sensitivity test applying a radiation-dependent correction to spring air temperatures could help assess its contribution to the simulated early melt e.g.,.

Ultimately, the new wind-dependent compaction scheme could be further refined using additional datasets in future work. The most sensitive parameters in Eq. () are U0 and the wind speed threshold triggering enhanced wind compaction. In this study, the latter was fixed at 2.5 m s⁻¹, while a range of U0 values between 2.5 and 3.5 m s⁻¹ was explored. Additional Arctic sites and improved forcing data would help reassess these values and better constrain the center (d0=0.8 m) and width (σ=1.0 m) of the Gaussian function controlling wind-enhanced compaction. More generally, better constraining fresh snow density, maximum snow density, and compaction rates will likely require dedicated experimental and field studies – such as wind tunnel experiments e.g., and targeted in situ observations – to jointly inform and disentangle the effects of snowfall properties, wind redistribution, and mechanical compaction in Arctic snowpacks. In addition, both the fixed wind threshold used for enhanced compaction and the temperature-only threshold used for blowing-snow sublimation (Eq. ) could be refined by accounting for additional controls on surface-snow erodibility, such as snow density and microstructural properties e.g.,.

Large uncertainties can also arise from forcing and observation data. Indeed, Arctic field sites often face extreme conditions, including prolonged polar nights and harsh weather, which can impact sensor reliability and data collection, especially due to frost and solid precipitation wind undercatch e.g.. The remote nature of these sites also makes it difficult to perform regular maintenance and verification of instruments. Therefore, the measurements can have many gaps, which are often filled with data from nearby stations and/or reanalysis products. For example, at Bylot, the Geonor 200 measurements are complemented with data from nearby Geonor gauge stations at Pond Inlet (84.1 km to the southeast) and Cape Liverpool 79.5 km to the northeast;, which adds further uncertainties. An alternative precipitation gap-filling method was tested at Bylot , resulting in significant differences in simulated snow depth and soil temperatures, reaching up to 10 cm and a few degrees, respectively, within a few years (not shown). Although those differences were, on average, of lower magnitude than the impact of our model developments, they could affect parameter optimization.

At TVC, large uncertainties arise because the station itself may act as a local snow accumulation zone (Brampton Dakin, personal communication, 2023), further complicating the interpretation of snow depth measurements. In addition, the site lacks direct snowfall measurements and, although the precipitation forcing had already been corrected for gauge undercatch following , it remained inconsistent with the simulated snowpack evolution, as discussed in Sect. . In particular, the initial simulated snow depth is too low, and snow density is underestimated relative to snow pit measurements (Fig. S1a–c; DEF (1xSnowf), blue line in the Sect. S3). To address this, we doubled the snowfall rates (Sect. ) to obtain more realistic simulated snow depth, density, and soil temperature values in better agreement with observations when using our new model developments (Fig. S1a–c; ALL_TVC (2xSnowf), green line). This additional empirical adjustment introduces uncertainties into the analysis and may bias the tuning applied at TVC in the ALL_TVC experiment. Residual discrepancies may arise from precipitation-phase partitioning, remaining measurement uncertainties, local snow trapping, and wind-driven snow redistribution, which cannot be resolved by a gauge-undercatch correction alone. A wind-dependent adjustment representing lateral snow transport and local deposition, conceptually similar to that proposed by , could be explored as an alternative to the uniform snowfall scaling. However, because snow drifting can occur even in the absence of precipitation, it remains challenging to determine which correction approach is most accurate. In this context, the forthcoming 32-year dataset at TVC will be particularly valuable for better constraining these model developments and ascertaining whether the two snow seasons currently available from are representative, or whether snow redistribution processes compensate over longer time scales.

Using CLASSIC enables the simulation of carbon fluxes and dynamically evolving vegetation. However, simulated vegetation height can differ from observations at specific sites. For example, at Col de Porte, grass is regularly mowed , which is not represented in the model and leads to overestimated vegetation height, affecting simulated albedo when vegetation is not yet fully buried by snow (Figs.  and S3c). In addition, CLASSIC does not account for vegetation bending under snow load e.g.,, further increasing uncertainty in the representation of vegetation height. As a result, simulated surface albedos (Fig. S3, third column in Sect. S7) differ substantially from observations, particularly at the beginning of the snow season at Col de Porte, Senator Beck, and Swamp Angel, with underestimations exceeding 0.2 (Fig. S3c, m, and r). This bias is partly related to unrealistic vegetation heights, which can reach 50 cm to 1 m in the model, even at Arctic sites, where the vegetation is in reality dominated by short grasses, mosses, and lichens. Sensitivity tests comparing bare-ground and grass configurations showed only minor impacts on snowpack evolution in these offline simulations, despite noticeable albedo differences during transition periods (not shown). However, such effects are expected to be more pronounced in land–atmosphere coupled simulations, where albedo biases can feed back on surface energy fluxes, near-surface temperatures, and snow evolution and will become increasingly important in a changing climate, inducing Arctic greening .

Uncertainties in simulated soil temperatures at Arctic sites may also partly arise from the thermal bridge effect associated with shrubs, which is not represented in CLASSIC. This effect can enhance heat exchange between the atmosphere and the ground and reduce soil temperatures by up to 4 °C during cold spells compared to shrub-free areas . Its absence in the model could therefore contribute to the limited improvement and remaining warm biases in simulated soil temperatures at Umiujaq TUNDRA, where broadleaf deciduous cold shrubs are present (e.g., Fig. ss). Consistent with this interpretation, reported that simulated soil temperatures in shrub-dominated environments were generally slightly warmer in winter and slightly cooler in summer than observations (their Fig. 1). However, this effect may yet be weak at Umiujaq TUNDRA, as shrubs are short relative to snow depth, largely bent under the snow, and characterized by very small branch diameters, all of which strongly limit the efficiency of thermal bridging. Uncertainties may also stem from the pedotransfer functions used in CLASSIC , which are calibrated over a broad range of soil types and may perform poorly for extreme cases e.g., nearly pure sand;. Such limitations can affect the estimation of key soil properties, such as soil moisture at saturation, and consequently influence simulated soil water content and soil temperatures.

Using a peat layer to compensate for the absence of explicit moss and lichen representation at Arctic sites (Sect. ) also highlights important model limitations. Mosses and lichens exhibit distinct behaviors in terms of water drainage, heat transfer, and carbon fluxes , which are not fully captured by this simplified approach. This may introduce additional uncertainties in our simulations, even if its impact appears limited in winter and mainly leads to improved summer albedo, soil temperatures, and soil moisture (not shown). However, remaining biases in simulated volumetric water content persist (Fig. S4 in Sect. S8) and may still affect winter soil temperatures, particularly during zero-curtain periods when excess liquid water delays soil freezing. Previous studies that explicitly implemented mosses in land surface models, such as JSBACH and JULES, reported notable improvements, particularly for permafrost dynamics .

Additional analyses of Arctic carbon budgets are presented in Sect. S9. They show that improved simulation of winter soil temperatures can substantially affect modeled net ecosystem exchange (NEE), particularly by reducing winter CO₂ emissions at sites with the largest soil temperature biases (e.g., Bylot and TVC). In these cases, lower winter soil temperatures reduce heterotrophic respiration and shift the annual carbon balance toward weaker sources or net sinks (Fig. S5a and c in Sect. S9). In contrast, changes in NEE at Umiujaq are limited, consistent with the smaller soil temperature differences simulated at this site (Fig. S5b). While simulated NEE amplitudes remain smaller than observed (Fig. S6), large uncertainties in winter flux measurements and limitations in Arctic vegetation representation complicate a direct evaluation. Overall, these results highlight the strong coupling between snow processes, soil thermal regimes, and Arctic carbon fluxes and emphasize the need to improve the representation of Arctic snowpacks and their interactions with vegetation – such as vegetation bending, thermal bridging in shrubs, and explicit moss and lichen plant functional types – particularly in the context of ongoing Arctic shrubification and greening, to achieve more consistent simulations of energy, water, and carbon budgets in Arctic environments e.g.,.

Another source of uncertainty arises from the lack of detailed information on soil composition and measurement locations at some sites (e.g., soil temperature sensors and snow pits), which hampers accurate simulation of snow–soil interactions. This is particularly relevant at TVC, where hummock and inter-hummock zones can exhibit markedly different thermal properties (Brampton Dakin, personal communication, 2023). More broadly, the absence of standardized, homogenized Arctic snow datasets comparable to those of SnowMIP remains a major challenge for Arctic snow model evaluation and intercomparison. Expanded and more comprehensive observations – including snow temperature, snow thermal conductivity, and camera-based monitoring – are also needed to better constrain and evaluate snow processes in Arctic environments.