The High Resolution Deterministic Prediction System (HRDPS) produced by the Meteorological Service of Canada provides a 2.5 km gridded hourly forecast of atmospheric variables for most of Canada . Atmospheric variables are computed for each pixel at a reference elevation provided by the underlying 2.5 km resolution digital elevation model. This study is based on a grid of 70 HRDPS prediction cells overlying the study area and including the following variables: TA, RH, VW, DW, PSUM, ISWR, and ILWR. First, using the 20 m Canadian Digital Elevation Model (CDEM), we transformed each HRDPS cell data into a virtual weather station. To do so, each cell's centroid coordinates were recomputed, minimizing the hypotenuse distance between each underlying CDEM pixel centroid and the HRDPS centroid, in an 800 m radius around the original HRDPS centroid. Then, TA, RH, PSUM, and ILWR were parameterized to correct for the model's biases and account for the elevation discrepancy between the HRDPS cell elevation and the new centroid CDEM elevation. VW was parameterized to account for the topography underlying the 2.5 km resolution grid unresolved by HRDPS.

Based on all weather stations in the park, the bias in air temperature has a nonlinear relationship with the elevation difference between the station elevation and the original HRDPS cell elevation over the 2018–2020 period. We generated a training set by randomly selecting 75 % of this dataset uniformly across elevations, and the remaining 25 % served as validation set. The data were transposed into logarithmic space to perform a linear regression. The resulting logarithmic fit was then applied over the TA dataset when the elevation difference between the virtual weather station and its overlying HRDPS cell was over 100 m. 1TAp=TAhrdps+ln⁡(-0.012ΔE+6.89)if |ΔE|>100TAhrdpsotherwise  Here ΔE corresponds to the elevation difference between the CDEM cell and the HRDPS cell, TAp is the parameterized air temperature, and TAhrdps is the raw HRDPS air temperature.

RH was corrected by first converting relative humidity to dew point temperature, as described in . This dew point temperature was then adjusted using the logarithmic fit presented above and converted back to relative humidity.

Snowfall was first parameterized using an elevation lapse-rate correction. This lapse rate was computed by performing a simple linear regression of precipitation as a function of elevation. We used a dataset of 4 weeks of manual SWE measurements on four conventional HN24 precipitation boards placed between 1330 and 1920 m at Mount Fidelity, all placed in flat and open areas sheltered from the wind. 2PSUMp=PSUMhrdps+0.0011×ΔE×PSUMhrdps Finally, the HRDPS ILWR was downscaled using the lapse-rate correction as highlighted by , and VW was downscaled to the 20 m CDEM resolution at each new centroid position using the sky view factor approach .

These virtual weather stations were then spatially interpolated on a 100 m grid via MeteoIO using the CDEM grid resampled to 100 m. TA was spatialized using a simple lapse rate computed from the AWS data and inverse distance weighting (IDW). RH, VW, and DW were spatialized using the MicroMet algorithms described in . To spatialize precipitation, we used topographic parameters and prevailing winds to alter the precipitation field to account for wind snow redistribution . Incoming shortwaves were spatialized considering terrain shading, slopes, and reflections from neighboring cells. Finally, ILWR was spatialized using IDW. All the spatial interpolation algorithms mentioned above are a part of the MeteoIO library, which is integrated into the Alpine3D model.

Alpine3D is a spatially distributed 3D model, which allows running the vertical 1D snow model SNOWPACK over an area while taking into account the spatial processes affecting the input atmospheric variables, such as terrain shadowing . SNOWPACK is a detailed multi-layer thermodynamic finite-element model of snow microstructure and metamorphism. In this model, the snow microstructure is represented by four main variables: grain size, bond size, dendricity, and sphericity for each snow layer. In addition, the model simulates several metrics of interest when monitoring the evolution of the snowpack, such as height of snow, SWE, density, optical grain size, or snow temperature . To do so, the model is fed with three text files describing the weather parameters on the time domain of the simulation, the initial state of the soil layers on which the snow is going to develop (and initial snow layers if relevant), and finally the configuration of the simulation. Alpine3D uses a DEM and a land-use layer to properly initiate each SNOWPACK cell. Depending on the land-use category each cell falls into, canopy information is provided for forested cells to represent snow interception and forest snow processes. The model was run at Rogers Pass on the same 100 m grid described above, over an area of 18 km × 16 km (288 km2) centered on the Highway 1 corridor for winters 2018–2019 and 2019–2020. The snowdrift scheme was turned off, and we generated outputs for three reference stations: Fidelity, Hermit, and Abbott. To assess the spatial variability capacity of the subgridding framework, the model was run on the whole simulation domain, and we also generated outputs at six points within the same cell for intra-cell variability assessment. The specific cell was chosen because it is the only cell in the simulation domain that features a north and south slope with elevations ranging from below the treeline to the alpine on both aspects. No glacier is present in the area. Table  summarizes the topographic characteristics for the chosen intra-cell spatial variability points.

To compare with snow simulations driven by the raw HRDPS and the subgridding framework, we performed SNOWPACK simulations driven with AWS data at Fidelity, Hermit, and Abbott stations. We filtered weather station data to remove outliers; data gaps smaller than 6 h were linearly interpolated, while larger gaps were filled using parameterized HRDPS data. Note that Abbott station is located in a thunderstorm-prone area. Hence, the station is shut down all summer and is only turned back on mid-October. Parameterized HRDPS data were again used to fill in this gap. Moreover, SR50 snow depth measurements at Fidelity and Abbott stations were compared against each snow simulation approach.

The numerical weather forecast subgridding quality was statistically assessed using three well-known criteria: bias, mean absolute error (MAE), and Spearman R correlation coefficient. These indicators allowed respectively quantifying the systematic difference between the models and the ground-truth measurements at the AWSs, the prediction accuracy, and the strength of the association between modeled variables and the ground truth. To smooth small time lags between modeled meteorological events and measurements at the AWSs, we averaged the meteorological time series over 2 h time steps, and reaccumulated precipitation over the same period.

Dynamic time warping (DTW) is an algorithm developed to measure the similarity between two sequences. In a nutshell, DTW computes the optimal match between two signals while allowing for an elasticity in time (or space, in the case of snow profiles). It first resamples the two sequences on 1D grids of the same elemental size and length. Then, a local cost matrix D is built, summarizing the distance between every elemental pair. From there, an accumulated cost matrix G is built by computing the accumulated cost to iterate from one element of D to the next one, respecting a predefined constraint set. The optimal alignment is found by minimizing the alignment accumulated cost.

Although originally designed for speech recognition , DTW is extensively used in time series analysis, and it has recently received increased interest in the snow community . In the snow science community, DTW has only been used so far in an avalanche forecasting perspective, focusing on aligning standard snow parameters (e.g., grain type, hardness, liquid water content). In this study, we present a new development to the open-source DTW snow profile alignment package written by , allowing aligning snow profiles on remote-sensing-oriented snow parameters, namely layer density and optical grain size (OGS), two key parameters in snow radiative transfer modeling. To do so, an alternative cost function was added to compute the local cost matrix D. 3Di,j=wddd(qid,rjd)+wogsdogs(qiogs,rjogs), where wd and wogs are averaging weights respectively applied to density and OGS (wd+wogs=1), rnk denotes the nth element of the reference profile R, and qnk denotes the nth element of the query profile Q. Finally, dd() and dogs() correspond to the distance function for density and OGS respectively, which is simply the absolute difference between the two elements, normalized over the entire vertical profile.

The space elasticity in the alignment algorithm allows us to find the best match for a layer of the query profile in the same depth range in the reference profile. The algorithm constraints define the amount of elasticity allowed, i.e., the warping window definition and the local slope constraint. These constraints are essential to keep the algorithm from degenerating and from generating irrelevant alignments. However, HRDPS tends to underestimate precipitation in mountain environments . Hence, profiles generated from atmospheric models and ground truth profiles can significantly diverge in HS. Physically matching layers are then too far apart, according to the algorithm's constraints, preventing the algorithm from generating relevant matches. Therefore, we artificially inflated profiles modeled using NWP, each layer being multiplied by the height ratio with the station profile. This allowed us to rely solely on snow microstructure parameters for the alignment, assessing only the microstructure representation. The generated aligned (or warped) profile was then used to compute a mean bias for density and OGS with respect to the ground truth. As precipitation is usually underestimated by HRDPS, HS should be underestimated as well, which should impact the overburden pressure on basal layers. A small negative bias on density might result with regards to AWS-driven SNOWPACK runs, depending on the amount of missing snow. For OGS, the temperature gradient in this region is low and metamorphism mainly happens through gravitational settling, leading to little variability in OGS in the snowpack . As a result, we do not expect much impact of the inflation approach on this microstructure parameter, as the main discrepancies should come from offsets in rain-on-snow modeling and melt/percolation events. Height of snow was compared to the station's SR50 measurements when available, and the Nash–Sutcliffe model efficiency coefficient allowed us to assess the SWE modeling quality using HRDPS and subgridded HRDPS data versus the station runs over the two seasons. For more details on the DTW implementation used in this paper, see .

Figure  summarizes the performances of the subgridding framework (denoted as SGF in the figures) applied to the 2018–2019 and 2019–2020 HRDPS time series. The SGF delivers a mixed performance for TA in 2018–2019. The HRDPS model shows a 1.8 °C negative bias at Abbott, which is reduced by 1.2 °C when using the subgridding framework. However, the negative bias increases by 0.6 °C at the Fidelity station and increases very slightly at the Hermit station (< 0.1 °C). On the other hand, the mean absolute error (MAE) and the Spearman R coefficient slightly increase for most of the validation stations. TA shows a very strong correlation with station measures (R>0.8).

Relative humidity subgridding yields good performances as the HRDPS model bias and MAE are reduced by 1 % to 6 % at all sites. The bias is constant at Fidelity station, as is the MAE at Abbott. The Spearman correlation coefficient also slightly increases at Hermit and Fidelity stations and only slightly decreases at Abbott. Finally, modeled RH shows a strong correlation with station values (0.6<R<0.8).

Overall, the SGF performs best at subgridding VW. HRDPS is constantly overestimating wind speed by 1.5 cm s-1. This bias is considerably reduced to 0.25 m s-1 on average, and MAE is reduced by around 1 m s-1. However, the correlation with station values is overall weak (0.2<R<0.4), and the subgridding workflow seems to have even weakened this correlation, except for Hermit station, which shows a negligible correlation (R<0.2).

Finally, subgridding shows a good performance for PSUM as well. In agreement with the literature, the bias in modeled precipitation shows a general lack of precipitation in the HRDPS model and ranged from 0.05 to 0.2 mm. For 2018–2019, MAE values range between 0.25 and 0.35 mm. With the subgridding, bias and MAE decrease at Abbott and slightly increase at Hermit, and bias decreases at Fidelity, while the MAE remains constant. Correlation with station values is moderate at Abbott and Hermit (0.4<R<0.6) and strong at Fidelity (0.6<R<0.8). Finally, subgridding slightly improves the correlation with AWS measurements at the former sites and stayed constant at the latter.

The 2019–2020 season yields very similar results to those for 2018–2019; the bias and MAE are corrected on the same scale, and the Spearman R coefficient is in the same range for each variable. The only notable difference is that the PSUM bias at Abbott is positive for this season, meaning that HRDPS overestimated precipitation, which is highly unusual. As a result, the SGF introduces even more precipitation bias (+0.07 mm).

Figures and summarize the subgridding framework performances for the seasons 2018–2019 and 2019–2020. From here, snow simulations are denoted as SGF-SNOWPACK, HRDPS-SNOWPACK, and AWS-SNOWPACK when driven respectively by subgridded atmospheric parameters from the SGF, raw HRDPS forecasts, and AWS measurements. For 2018–2019, the snowpack similarity behaves identically at every site and for both HRDPS-SNOWPACK and SGF-SNOWPACK. The season begins with average similarity values (around 0.5), and then it plummets to low values in mid-October (<0.5) before improving to higher levels of similarity in November and for the rest of the season (0.6 < sim < 0.8). In general, HRDPS-SNOWPACK tends to have a closer similarity to AWS-SNOWPACK early in the season. SGF-SNOWPACK tends to score higher similarities than HRDPS-SNOWPACK in the mid-season before converging back with HRDPS-SNOWPACK in the spring. For the 2019–2020 season, similarity is again highly variable around 0.5 at Abbott and Hermit for both HRDPS-SNOWPACK and SGF-SNOWPACK. The early season at Fidelity shows very low similarities for SGF-SNOWPACK and HRDPS-SNOWPACK. Then, starting in November, the similarities stabilize and slowly rise throughout the season to 0.8 at every site. Again, SGF-SNOWPACK shows a higher similarity than HRDPS-SNOWPACK during the mid-winter period at Abbott and Hermit. HRDPS-SNOWPACK reaches the same level of similarity by early spring or the end of the winter. At Abbott, HRDPS-SNOWPACK and SGF-SNOWPACK similarities are very close, though the former shows more fluctuations during most of the winter and early spring. The average similarity for all sites and seasons is 0.8 for SGF-SNOWPACK and 0.75 for the HRDPS-SNOWPACK. Overall, SGF-SNOWPACK increased snowpack similarity by 7 % at Abbott, by 2 % at Hermit, and by 6 % at Fidelity with respect to HRDPS-SNOWPACK and when compared against AWS-SNOWPACK. The mean error in OGS shows a similar behavior at every site in 2018–2019 for both approaches. The error peaks and fluctuates strongly in the early season for both approaches and then stabilizes around mid-November. Considering the high variability in the fall for both seasons (September to November included), the first 3 months were considered a spin-up phase for the model to initiate a proper snowpack. Hence, the numerical analysis of the results was carried out starting on the first of December. Both HRDPS-SNOWPACK and SGF-SNOWPACK are slightly overestimating OGS with respect to AWS-SNOWPACK, but overall, the proposed method allows the bias to be decreased by 0.04 mm at Fidelity. However, OGS bias remains constant at Abbott and Hermit in the same period. The same pattern repeats for the 2019–2020 season at all sites, where SGF-SNOWPACK decreases on average the OGS bias by 0.07 mm at Fidelity and 0.09 mm at Hermit. The bias in OGS remains unchanged at Abbott once again that season.

Similarly to OGS, in 2018–2019, the mean error in density shows higher values in the early season and stronger fluctuations for both HRDPS-SNOWPACK and SGF-SNOWPACK. Variations tend to stabilize by mid-November, and the error increases again towards the end of the season. Again, the numerical analysis was performed from the first of December until the end of the simulation for both seasons. Generally, HRDPS-SNOWPACK seems to underestimate snow density. SGF-SNOWPACK brought density 3.17 kg m-3 closer to AWS-SNOWPACK at Abbot and 6.79 kg m-3 closer at Fidelity for the 2018–2019 season. However, in the same period at Hermit, the density bias increases by 1.71 kg m-3 on average. In 2019–2020, the density bias decreases on average by 4.65 kg m-3 at Fidelity and by 3.62 kg m-3 at Hermit. However, the density bias increases by 0.9 kg m-3 over the same period at Abbott.

Finally, SGF-SNOWPACK mean error in modeled HS is 35 cm in 2018–2019 (20 cm improvement when compared to HRDPS-SNOWPACK) and 29 cm in 2019–2020 (29 cm improvement) when compared with the SR50 measurement at Fidelity. For reference, the modeled HS with AWS-SNOWPACK shows a mean error of 8 cm in 2018–2019 and of 14 cm in 2019–2020. However, SGF-SNOWPACK seems to degrade the quality of the HS modeling regarding HRDPS-SNOWPACK when compared to the SR50 at Abbot station, overestimating HS for each season. Yet, the AWS-SNOWPACK run at Abbott shows a high discrepancy with the SR50 measurements as well, overestimating HS (especially in 2018–2019). Finally, HS remains relatively unchanged at Hermit for 2018–2019 as the framework does not bring a substantial improvement when compared to the AWS-SNOWPACK-modeled HS.

SWE modeling is considerably improved at all stations except at Abbott in 2019–2020 (Fig. ) when compared to AWS-SNOWPACK. Table summarizes the Nash–Sutcliffe efficiency coefficient (NSE) values at each site and for each season. On average, SGF-SNOWPACK improves the SWE NSE by 13 %, up to 57 % at Hermit in 2019–2020.

Figure summarizes the main atmospheric parameter values for the six spatial variability sites, averaged per month (and accumulated for precipitation). First, as a direct consequence of the applied lapse rate for TA downscaling and spatialization, the general rule of thumb that TA should get colder with elevation is respected. However, the selected point on the north aspect is 100 m lower than the south aspect point, and as a result, the figure shows slightly warmer temperatures consistently throughout the season on the north aspect. Second, the aspect gradient is respected with lower incoming shortwave radiation and slightly lower temperatures in the north aspects. Moreover, wind direction is mostly coming from the south and southwest. South slopes are thus more exposed to the wind and north aspects are more sheltered. This is reflected by wind speed values being higher in the south aspects, especially in the alpine region. Wind-generated snow redistribution is accounted for, leeward slopes getting more snow than windward slopes. Finally, the altitudinal precipitation rate gradient is also respected by the subgridding framework, with precipitation rates getting higher with elevation. This atmospheric parameter variability is then propagated to the modeled snowpacks (Fig. ). Again, the altitudinal gradient in HS is present, with a deeper snowpack from below the treeline to the alpine region. Moreover, the melt onset date is a few days earlier on the south aspect than on the north aspect, and water is percolating faster and deeper in the snowpack on the south aspects.

Season 2019–2020 results for spatial variability appear in Appendix A, Figs.  and . The subgridding framework creates the same altitudinal and aspect gradients, with more precipitation overall, milder temperatures, and stronger wind speeds on average.

Figure shows the evolution of simulated SWE averaged by elevation band and aspect. The elevation gradient is well represented over all four quadrants. In the east and west aspects, which face dominant winds in the area, the high alpine elevation is showing SWE equal to or lower than that in the alpine elevation band. This reflects the effect of wind on ridges, modeled in the SGF as an alteration of the PSUM field with wind speed and terrain features. Figure  shows the variability in the modeled SWE within each HRDPS cell over the simulation domain. The top plot shows the variability in the early season (19 November 2018), and the bottom plot shows the variability at the end of the season when the snowpack is at its peak (4 March 2019). Each cell shows a wide spread of SWE values, which indicates that the subgridding of weather parameters is very effective in bringing spatial variability within each cell.