In the previous section, all components and parameterizations that constitute the system of equations for blowing snow were described in detail. In this section, details of the numerical algorithm to solve Eq. () in CRYOWRF are explained. The designing of the numerical solver was guided (and, in some ways, constrained) by WRF's overall software framework in general and, in particular, the implementation of microphysics schemes. It was noted earlier that Eq. () is quite similar to equations for hydrometeors such as cloud ice, and thus, this approach is, in many ways, justified by the solvers for those species. As described earlier, the prognostic equations of qbs and Nbs are of the advection–diffusion type, with additional terms for sedimentation and phase change. Describing the algorithm in terms of the mass mixing ratio qbs suffices, since it is similar for Nbs.

The equation for qbs is spatially discretized to cell centres of the Arakawa C grid, which are referred to as mass points in WRF's terminology. These are the same grid points at which various prognostic scalars such as temperature, moisture and other hydrometeors are defined. The vertical discretization is illustrated in Fig. . As shown in this figure, there is an additional fine-resolution mesh uniquely for the blowing snow variables between the surface and the first WRF mass point level. The additional fine mesh (FM) is required because the blowing snow variables have extremely large gradients in the vertical, compared to other scalars (e.g. temperature), because of the impact of sedimentation. In mesoscale models such as WRF, the first model level above the surface, ΔzWRF, is ∼O (10 m), which is far too coarse to capture the sharp gradients near the surface. The fine mesh has a mesh size, ΔzFM is ∼O (1 m), with the first FM level fixed to 50 cm above the surface. The number of levels in the fine mesh can be chosen at runtime and remains fixed during the simulation. Typically, 8 to 10 levels are sufficient to capture the near-surface gradients. Values for WRF's prognostic variables are diagnosed for points on the fine mesh using either the stability-corrected log laws (u, v, T, q) or a simple linear interpolation (w and Kbs). The implementation of the FM in CRYOWRF is inspired by SURFEX . In SURFEX, there is a prognostic, multi-layer surface layer scheme called CANOPY , whereas in the current version of CRYOWRF, the values of the atmospheric variables are only interpolated onto the fine mesh.

To follow WRF's existing framework to solve for hydrometeors, we begin by reformulating Eq. () as follows: 20∂qbs∂t=∂qbs∂tm+s+∂qbs∂tp+∂qbs∂tadvec, where the three terms (from left to right) on the right-hand side of the above equation are contributions from turbulent mixing and sedimentation (m+s), phase change (p), and advection (advec), respectively. They are stated as follows: 21a∂qbs∂tm+s=-Kbs∂2qbs∂xi2δi3+∂∂xiqbsVqδi321b∂qbs∂tp=Sq21c∂qbs∂tadvec=-ui∂qbs∂xi.

Equation () is solved in a semi-implicit fashion (fully implicit for turbulent mixing and explicit for sedimentation), using second-order finite differencing, resulting in a tridiagonal matrix that is solved using the well-known Thomas algorithm. The semi-implicit matrix-based solver is required to make the solver numerically stable and able to deal with the fine resolution of the fine mesh and the relatively coarse resolution of WRF's native mesh in the same matrix. Immediately after, Eq. () is solved in an explicit fashion for both the fine mesh and WRF's native mesh together. The heat and mass transfer quantities in the region of the fine mesh are added as correction terms to the first WRF level to ensure conservation of mass and energy. Equation () is solved using WRF's existing advection routines for scalars, similar to how hydrometeors are advected. The possible advection algorithms in WRF range from finite difference schemes of different orders, and positive definite schemes to weighted essentially non-oscillatory (WENO)-type schemes, etc. Temporal integration of Eq. () is done using second- or third-order Runge–Kutta. The numerical algorithms for the advection of blowing snow quantities is, at present, constrained to be the same as that for other scalars.

Finally, the mass balance at the surface due to precipitation and snow transport, Δmsfc (kg m-2 s-1), is computed as follows: 22aΔmsfc=P+∫0∞∂qbs∂tm+sρairdz+∇HQsalt,where,22b∇H=1s∂uWRF∂x+∂vWRF∂y,s=uWRF2+vWRF2. The first term on the right-hand side of the above equation is precipitation (P). The second term is the vertically integrated left-hand side of Eq. () and represents the contribution of snow transport, specifically snow suspension. The final term, the horizontal divergence of saltation flux Qsalt, is the contribution of saltation to the surface mass balance. It is computed using the horizontal wind components at the first level of WRF uWRF,vWRF above the surface. The above formulation for surface mass balance is similar to that implemented in Alpine3D .

The first case study is a 1-year (July 2010–July 2011) simulation for the entire continent of Antarctica using CRYOWRF. The chosen simulation set-up is standard for mass balance calculations in Antarctica and comparable with the most common models of RACMO and MAR e.g.. The intention of this case study is to demonstrate the accuracy of the CRYOWRF model along with showcasing the kind of information now available directly from CRYOWRF, particularly with respect to the snow cover. This, and the following case studies, also serves as tutorials to ease the adoption of CRYOWRF for interested researchers.

The simulation is performed over a single domain with a horizontal resolution of 27 km, covering the domain shown in Fig. . The domain encompasses the entire continent along with a substantial portion of the surrounding Southern Ocean. Static data (topography and land use) are from the 1 km resolution Reference Elevation Model of Antarctica dataset REMA; and the AntarcticaLC2000 land use data , respectively, and were prepared as WRF input by . The model is initialized and forced at the lateral boundaries by ERA5 reanalysis data . The parameterizations used are RRTMG (Rapid Radiative Transfer Model; shortwave and longwave radiation), Kain–Fritsch (KF; convection), a modified version of the Morrison scheme that improves representation of secondary ice production (microphysics; ), and MYNN (Mellor–Yamada–Nakanishi–Niino; boundary layer scheme). The simulation is nudged against ERA5 for wind speeds in the zonal and meridional direction in the top 20 levels of the atmosphere. A total of 64 atmospheric levels are simulated with the topmost pressure level set at 10 kPa (approximately 15 km a.s.l. – above sea level). The lowest layer is on average 8 m a.g.l. (above ground level), and there are 22 layers within the first 1 km above the surface.

The land surface model (LSM) is the SNOWPACK model. The snow cover is initialized using data from Utrecht University's Firn Densification Model (FDM; ), forced by RACMO 2.3 , which provides vertical profiles for snow layer thickness, density, and temperature, along with grain radius for the entire continent. Pixel-wise ASCII files are created from the FDM data (which is in netcdf format). The simulation is initialized for only the top 20 m of the snowpack. Snow cover modelling requires parameterizations for many different processes. To calculate albedo, we used the model developed by and implemented in SNOWPACK by . The new snow density is fixed to 300 kg m-3, and the water transport through a snow column is done using the bucket approach. Snow–atmosphere exchange of mass and energy is calculated using the Holtslag surface layer model . The snow surface roughness is fixed at 0.002 m. The minimum thickness of a snow layer is set to 0.001 m. This is indeed quite a small value and was chosen as such to simply demonstrate CRYOWRF's ability to model snowpacks at such extreme resolutions. The blowing snow model was active with an eight-layer fine mesh between the surface and the first mass point of WRF. The resolution of the fine mesh extended between 0.5 m (closest to the surface) and 1.5 m.

Results of this simulation are compared to weather station measurements from 14 stations spread throughout the continent (mostly along the coast and marked in red in Fig. ). Station data are taken from several databases. A summary is given in Table . No thorough quality checks were performed for the station data for this study. Data gaps are commonly occurring. Some stations provide no information about relative humidity (Mizuho), pressure (D-17), and wind direction (D-17). In addition to a verification with AWSs data, figures of the surface mass balance components and snow profiles showcasing the capabilities of the entire CRYOWRF framework (including diagnostics) are presented in the following section.

Figure  shows scatterplots comparing the measurements (on the horizontal axes) with CRYOWRF outputs (on the vertical axes) for the four standard meteorological variables of surface pressure, potential temperature, and relative humidity (with respect to ice) at 2 m above surface and wind speed at 10 m above surface. For comparison, results from a simulation with Noah-MP as the LSM are also shown. The best correlation is found for surface pressure (r=0.90) and the worst correlation for relative humidity (r=0.31), with CRYOWRF outperforming or being similar to Noah-MP for each of the variables. Though, admittedly, the improvements over Noah-MP are minor, except for relative humidity.

The South Pole was chosen to present an example of direct comparison of time series between CRYOWRF, Noah-MP, and measurements. These are shown in Fig. . In addition to time series, a comparison of the probability density functions (PDFs) for the entire time series is shown in adjoining figures on the right for each row. In addition to the four variables presented earlier, wind direction time series are shown as well. It is clear that CRYOWRF follows the measurements reasonably well. Additionally, CRYOWRF performs better than Noah-MP with lower mean absolute errors (mae), for each variable. The best improvement is found for potential temperature and relatively humidity. The same conclusions can be drawn from the PDF plots. For example, the PDFs of CRYOWRF and measurements of potential temperature have much overlap in comparison to that with Noah-MP, which has a significant warm bias. The improvement in CRYOWRF with respect to Noah-MP could be due to a multitude of reasons. A recent study by , for example, attributed the warm bias in Noah-MP to low albedo. Another reasoning, for example, could be that CRYOWRF includes the effect of blowing snow sublimation, which has a cooling effect on the atmosphere. Finally, measurements, especially of variables such as relative humidity at extremely low temperatures, are known to be unreliable. However, all this is mere speculation, and a deeper analysis would be necessary to explain these differences, which is beyond the scope of this study. At the very least, Figs.  and show that CRYOWRF produces comparable results to Noah-MP out of the box.

One major reason for performing simulations such as in this case study is to calculate components of the surface mass balance (SMB). The polar surface mass balance is of critical importance in understanding the implications of global warming on sea level rise. CRYOWRF outputs these quantities as two-dimensional fields directly as a part of the standard output via its specially implemented diagnostics package. An example of the surface mass balance output during this case study is shown in Fig. . Since the simulation period is of only 1 year, it is not possible to quantitatively compare the results presented in this figure with those published in the literature, which are typically calculated over climate timescales of at least 30 years. In fact, given the interannual variability in SMB patterns, particularly at the coast (due to phenomena such as atmospheric rivers), it is likely that the numbers from 1 year, as shown in Fig. , may be different from long-term averages. However, qualitatively, the spatial patterns for each of the different terms matches quite well (for example, ). For example, precipitation is dominant in west Antarctica and the peninsula, while in east Antarctica, it is limited to the coasts, with strong gradients along the topographic contours. It is interesting to see melt–refreeze dynamics being dominant in the Ross and Ronne ice shelves. Sublimation (or vapour deposition) patterns reveal the importance of this mechanism on the coastline, while identifying locations in the interior of the continent where vapour deposition is actually a net positive term in the surface mass balance.

A notable feature of CRYOWRF is its ability to run atmospheric simulations with highly (vertically) resolved snowpacks. This allows an accurate representation of thin subsurface ice layers with a thickness of the order of a few millimetres that have significant impact on snow hydrology at larger scales . In Fig. , the evolution of the snowpack at the Casey station (66.4058∘ S, 110.8043∘ E) on the eastern Antarctic coastline is represented by the density, temperature, and liquid water content (LWC) profiles. For this location, based on the local mass and thermal forcing, SNOWPACK converges to 130 snow layers. As can be seen in the density profiles, thin layers of high-density snow (or ice) layers can be found within the top 1 m of the snowpack. These layers are mostly less than 1 cm thick and are between layers of (in some cases, considerably) lower density. The top 1 m of the snowpack is also thermally active, with significant cooling/warming at the diurnal and seasonal scale, relative to subsurface temperature fluctuations. The exceptional period is between the middle of December till the middle of February when significant melt occurs, reducing by nearly 0.5 m of snow. The meltwater percolates through the snowpack up to a depth of 1 m, resulting in isothermal melting point temperatures at the beginning of February. The meltwater percolation is clearly seen in the LWC profiles, where significant meltwater is found to remain in a localized region at the depth of 1 m until the middle of February.

The second case study simulates the formation of an hydraulic jump at the coast surrounding the Dumont d'Urville (DDU) station between 8 and 11 August 2017. The hydraulic jump occurs when a well-developed, high-velocity katabatic flow draining off the sloped ice sheet of Antarctica reaches the coast. The high-velocity outflow experiences an abrupt and rapid transition due to changes in topographic and surface conditions, thereby transitioning to a hydraulic jump. The hydraulic jump itself further triggers gravity waves. A remarkable manifestation of the hydraulic jump, given the right surface conditions, is the large-scale entrainment and convergence of blowing snow particles within the hydraulic jump. This can result in the formation of 100–1000 m high, highly localized walls of snow in the air in an otherwise cloud-free sky.

The case study is directly inspired by the recent work of , who present a detailed analysis on the genesis, dynamics, and implications of the hydraulic jumps and the corresponding gravity waves in the region in proximity of DDU. Their study used (standard) WRF as the principal tool and showed that capturing this phenomenon in simulations is only possible with high-resolution domains with resolutions higher that 3 km at the very least.

This case study serves as a perfect example to highlight the capabilities of CRYOWRF both from a physical modelling and a technical perspective. CRYOWRF, due to its non-hydrostatic atmospheric core can indeed simulate such a phenomenon, in direct contrast with the pre-eminent mesoscale models for polar research, namely RACMO and MAR. From a technical perspective, performing such a simulation necessarily requires a nested domain approach. As mentioned earlier, CRYOWRF is compatible with the nesting capability of WRF. Finally, unlike , who used standard WRF, CRYOWRF includes the blowing snow model, which allows for studying the impact of hydraulic jump formation on blowing snow dynamics and simulating the formation of the aforementioned snow walls for the first time.

The simulation set-up is as follows: a three-domain simulation is performed, having horizontal resolutions of 12 km (d01), 4 km (d02), and 1 km (d03) for the three domains. All the domains are centred on DDU, with the Adélie Land coastline approximately passing diagonally across the domains. The domain locations and extents are shown in Fig. . The nesting is of a one-way nature, i.e. the inner, higher-resolution domain is forced at the lateral boundaries by the outer, coarser domain, while there is no upscaling of the inner domain data to nudge the outer domain. The outermost domain (d01) has exactly the same set-up as that in the previous case study (apart from the resolution), i.e. the same static data and physical parameterizations are used, and ERA5 is used to force the simulations. The two inner domains also have the same set-up as the outer domain, with the exception that the convection parameterization is switched off. The blowing snow model is active in all three domains. The three domains have 69 vertical levels in the atmosphere, with top-level pressure fixed at 5 kPa (approximately 18 km a.s.l.). Similar to the previous set-up, the lowest layer is on average 8 m a.g.l., and there are 22 layers within the first 1 km above the surface.

The simulation starts with only the outermost domain first, with the inner domains activated successively. The snow profile at each of the pixels is initialized using *.sno files generated from a restart (wrfrst) file from a coarse-resolution simulation, similar to that in case study Ia. The starting times for the three domains are the 8 August 2017 at 00:00 and 06:00 UTC and 9 August 2017 at 00:00 h for the three domains, respectively. The simulation of all three domains continues until 11 August 2017. Increasing resolution implies decreasing time steps. The three domains used time steps of 45, 15, and 5 s, respectively. The LSM (SNOWPACK) uses a time step of 900 s in each of the three domains, using the built-in capability of CRYOWRF to call the LSM module with flexible time steps. Using a lower time step for the LSM is justified, since the phenomenon we are interested in simulating is a purely mechanical one and not particularly dependent of the near-surface heat fluxes, thermal snow–atmosphere interaction, and certainly not the surface and subsurface thermodynamics.

In the following section, two illustrations of model output are shown where the hydraulic jump and the excited gravity waves, along with its effect on blowing snow, can be seen. Differences between the domains on account of the resolution are also highlighted.

As reported by , using station measurements, there is a relatively quiescent period before the 9 August 2017, with stable wind speed, wind direction, and air temperature recorded at DDU. The situation dramatically changes on the 9 August when the katabatic flow rapidly strengthens, and very high wind speeds are reported at DDU in the first half of 10 August. At 12:00 UTC on 10 August, there is a sudden drop in the wind speed, following which the wind becomes gusty but on average remains slower than the previous day. showed that the abrupt deceleration of the katabatic flow is due to excitation of gravity waves and the enhanced friction induced.

These trends are reproduced by CRYOWRF and shown in Fig. , where the simulated time series of wind speed, direction, and temperature at the DDU station are plotted. It is interesting to note the differences in the trends shown by the three nested domains with different resolutions, particularly for wind speeds and direction. The coarse-resolution domain 1 (12 km resolution) follows the trends mentioned earlier, but the rate of wind acceleration and its abrupt slowdown are significantly less pronounced than the finer-resolution nests, which match each other quite well. Differences between the two inner nests emerge in the case of wind direction, where the flow in domain 3 shows significant oscillations in flow direction in the period before and after 12:00 UTC on 10 August. The flow direction resolved at 12 km resolution in domain 1 remains relatively fixed, on the other hand. The air temperature, initially quite stable on 8 August experiences a rapid decrease that coincides with the change in wind direction and an acceleration of wind speeds. This decrease continues until the middle of 9 August, followed by a warming trend. Interestingly, both the inner, higher-resolution domains are slightly warmer during the katabatic phase and at the onset of the gravity wave excitation, where temperature oscillations can be observed. These plots perfectly highlight the need for CRYOWRF's high-resolution capability because the intensity of the katabatic jet, its sharp transition into a hydraulic jump, can only be resolved by increasing the resolution from 12 to 4 km. The further phenomenon of gravity wave excitation is only possible by increasing the resolution even further to 1 km .

The impact of the flow transitions on blowing snow dynamics are illustrated in the following two figures. Figures  and both show the blowing snow mixing ratio qbs (kg kg-1) on 10 August 2017 at 12:00 UTC, for each of the three domains. This time period was chosen as the onset of gravity waves occurs close to this time (based on Fig. ). Blowing snow at 1500 m a.g.l. is shown in Fig. , with DDU marked on the map (red triangle) along with the coastline (black line) for reference. In all three domains, there is a boundary delineating the regions with and without blowing snow. The boundary is precisely the location of the hydraulic jump. The effect of the model resolution is also clearly apparent. In the coarsest domain (domain 1; Fig. a), particle concentrations are lower and more uniformly spread. Increasing the resolution from 12 to 4 km, the concentration values increase, while at the same time, the part of the domain where blowing snow particles exist at this height shrinks to a smaller area as compared to the outer domain. Finally, in the innermost 1 km resolution domain, there is a clear imprint of wave-like fluctuations on the blowing snow concentration field. Vertical cross sections of the blowing snow mixing ratio are extracted at the dashed red line passing through DDU and are shown in Fig. . Additionally, potential temperature isotherms for values between 260 and 290 K are shown to indicate the presence of gravity waves. Similar to the previous figure, the flow in each of the three domains shows the characteristic hydraulic jump approximately 25 km inland from the coast. As expected, increasing the resolution results in a sharper localization of the jump location. Further inland from the coast, a thin region with high concentration of blowing snow particles can be observed. These particles are entrained into the hydraulic jump and are mixed up to much greater altitude off the coast. High concentrations are found even at 2000 m a.s.l. Only the innermost 1 km resolution nest exhibits signs of gravity wave excitation, as evidenced by the wavy perturbations to the isotherms, and particularly those for 270 and 280 K. Correspondingly, spatial patterns of the blowing snow mixing ratio matches the envelopes of the wave trains at different altitudes quite well. A video that shows the dynamics of the blowing snow mass mixing ratio for the entire simulation period is provided as Video M1 in the Supplement. This video shows the impact of the acceleration of the katabatic flow on blowing snow dynamics, the formation of the hydraulic jump, and the excitation of the gravity waves in the innermost 1 km domain.

This case study requires further detailed verification and analysis, even though, qualitatively, it reproduces satellite and visual observations of snow walls reported at DDU (see , for more data sources). More pertinent for the scope of this article is that this case study showcases an example of how CRYOWRF can contribute to enquiries in coupled snow–atmosphere interaction in polar regions that necessarily require high resolution. Extensive blowing snow clouds, with particles regularly reaching as high as 500 m above the surface, have been observed in satellite measurements that have not yet been accurately simulated by models. High-resolution simulations of the sort presented in this case study may be useful in matching or explaining the satellite measurements and analyses of .

This case study showcases the ability of CRYOWRF to simulate alpine snowpacks in complex topography. It highlights the ability of CRYOWRF (on account of its WRF-based atmospheric core) to perform extremely high-resolution, LES-scale snow–atmosphere coupled simulations in addition to mesoscale flows using the same modelling framework. Due to the differences in spatial and temporal scales relevant for alpine meteorology, as compared to polar meteorology, different snow physics parameterizations with higher precision are required for simulating alpine snowpacks compared to polar snowpacks. For example, this case study uses a different albedo parameterization than the previous, polar-based simulations. Meltwater dynamics, new snow density parameterization, and snow–soil interaction are additional examples of processes that are more crucial in alpine environments as opposed to polar regions. This case study thus provides an additional template for interested future users of CRYOWRF in terms of name list settings for SNOWPACK and WRF, which is more suitable for alpine environments.

In terms of novelty, the most interesting meteorological feature of this case study is the simulation of blowing snow in the Alps. While blowing snow in the Alps received significant attention in the cryospheric community from the surface mass balance and avalanche forecasting perspective, its impact on different atmospheric components such as cloud dynamics or local radiative balance are unknown. There is evidence of potential feedback loops between blowing snow and cloud formation . However, to the best of our knowledge, it has not been explored numerically.

The simulation consists of two domains, with the larger domain at a spatial resolution of 1.25 km, covering an area of 225 km2, and the inner nest with a spatial resolution of 250 m, covering an area of 60 km2. The outer domain covers a significant portion of eastern Switzerland and the adjoining parts of Austria and Italy, with the alpine arc passing roughly across the middle of the outer domain. The alpine town of Davos is located in the southwestern quadrant of the inner domain, offset by less that 5 km from the domain centre. The location of the domains and the complex topography over which the simulation is conducted are shown in Fig. . A total of 90 atmospheric levels are simulated, with the top-level pressure imposed at 15 kPa (approximately 11 km a.s.l). The lowest layer is 20 m a.g.l, with a total of 10 layers below 1000 m a.g.l.

The simulations performed are similar to those by in that they are driven by hourly analyses fields of the operational COSMO model (COSMO refers to COSMO-1 in this study). Underlying topography and land use are from the Aster 1 s digital elevation model and the Coordination of Information on the Environment (CORINE) dataset , respectively, prepared as WRF input as in . The difference is the use of CRYOWRF in this case study as opposed to standard WRF by . The boundary scheme in both domains is the Shin–Hong scale-aware scheme , which is applicable for resolutions as high as 250 m. This is a unique scheme in the WRF physics suite that is able to represent subgrid-scale mixing in the grey zone that exists between mesoscale flow O (1 km) and turbulent flow O (10–100 m). RRTMG is used for the parameterization of radiative effects both for short and longwave radiation, while the Thompson microphysics scheme is used to account for clouds. At the relatively high resolutions used in this case study, no convection scheme is required.

As mentioned earlier, using SNOWPACK as the LSM requires per pixel *.sno files for initializing the snowpacks at each pixel. In this case study, snow profiles are generated using snow height and snow density information from the single-layer data available in COSMO analysis fields and using 30 snow layers. The temperature of the layers is calculated via linear interpolation between the surface temperature and the underlying soil temperature, again using data from the COSMO fields. The initial grain diameter is arbitrarily chosen to be 300 µm, with bond diameters of 75 µm for all layers. The main difference between this case study and those presented earlier is that the underlying soil column is accounted for as well, with an additional 10 soil layers for each pixel. This is possible using SNOWPACK's existing capability for solving for both the soil and snow columns and is crucial for using CRYOWRF for simulating seasonal snow covers and over regions with partial snow coverage.

The above simulation was performed for a period of 36 h, beginning on 11 March 2019 at 00:00 UTC for the inner, high-resolution domain. This period is coincident with a period with high wind speeds recorded on alpine ridges surrounding Davos. Furthermore, the wind direction is from the northwest, blowing across the inner simulation domain, such that many of the ridges simulated in the region are nearly perpendicular to the dominant, large-scale flow direction. After allowing for an extensive period for the spin-up of the model, results are analysed only for the period between 18:00 UTC on 11 March 2019 and 12:00 UTC on 12 March 2019.

To set the meteorological context of the case study, wind speed and temperature simulated by CRYOWRF at two locations, the upper, Weissfluhjoch station (denoted as WFJ; 46.833323∘ N/9.806371∘ E; altitude of 2691 m a.s.l.) and at Davos (denoted as DAV; 46.802128∘ N/9.833477∘ E; altitude of 1594 m a.s.l.) in the valley (is shown in Fig. ). Two variants of the simulation, with and without blowing snow sublimation, were performed to assess the impact of enhanced heat and mass transfer between the particles and the atmosphere. The wind speed within the valley is reasonably stable and moderate, with values of approximately 7.5 m s-1. On the other hand, at high altitudes, the wind is significantly faster at 18:00 UTC, reaching speeds as high as 20 m s-1 at WFJ. The wind speed at WFJ decelerates from this high value but remains significantly higher than those in the valley until 04:00 UTC on 12 March. As expected, the air temperature is lower at WFJ than at DAV initially, and the higher-altitude regions experience significant warming on 12 March 2019.

Figures  and present surface maps of various diagnostic quantities relevant for blowing snow dynamics calculated in the innermost, 250 m resolution domain. In Fig. a, patterns of cumulative erosion and deposition during the course of the simulation are shown. It is instructive to compare the regions of extensive blowing snow erosion and deposition with the topography in Fig. c. The most active areas for snow transport are the ridges perpendicular to the flow as expected. It can be observed further that erosion occurs mostly on the windward side of the ridges, with zones of deposition found immediately on the leeward side, which is in agreement with earlier model assessments and measurements in the area . On the other hand, there is not much blowing snow activity in the valleys. Note that, qualitatively, there seems to be more erosion than deposition. This could be explained by Fig. b, which presents vertically integrated mass loss (or gain) of blowing snow due to sublimation (or deposition). There are regions with extensive sublimation of blowing snow that are coincident with regions of high snow erosion, which is in partial contradiction to earlier model results and needs further investigation. Interestingly, there is a significant zone of sublimation found along the windward edge of the Engadine valley system east of Davos. Furthermore, the vapour mass transfer between blowing snow and the atmosphere is spatially quite heterogeneous, with vapour deposition being the dominant mass transfer in many regions, particularly in the centre of the domain. The map of vapour mass transfer quantities and sign seems to suggest that the currently established paradigm of blowing snow largely undergoing sublimation may be too simplistic and may be valid only in terms of spatial and temporal averages with significant underlying heterogeneity in both rates and directions (transport of water from particles to air, and vice versa).

Figure  illustrates the horizontal variations in surface friction velocity (Fig. a) and blowing snow mixing ratio in the saltation layer (Fig. b) at 00:00 UTC on 12 March 2019. As expected in regions with complex topography, there is significant heterogeneity in surface shear stress. Saltation mixing ratio is a diagnostic quantity that is linked to the surface friction velocity and the state of the cohesion of the snowpack's surface through complex, nonlinear relationships (see Sect. ). Recall that the saltation mixing ratio acts as the boundary condition for blowing snow equations for snow in suspension. High values of saltation mixing ratios are found in regions of topographic prominence such as ridges and the high-altitude region in the centre of the domain. However, there is no saltation occurrence in the lower-lying parts of the domain. This is not only due to lower wind speeds but also due to the fact that the cohesion is higher at low altitudes due to warmer air temperatures.

Saltation occurs very close to the surface, within a height of centimetres. However, snow in suspension, though many orders of magnitude lower in concentration, undergoes long-range transport, both horizontally and vertically. In classical boundary layer meteorology, transport in the horizontal and the vertical is driven mostly by advection and turbulent mixing, respectively. However, in alpine regions, the interplay between complex topography and atmospheric stability results in a wide range of complex flow types, such as orographic waves, rotors, katabatic and anabatic winds, etc. Such motions can be significant sources of vertical advection of blowing snow. These features are also active in preferential deposition of precipitating snow . Enhanced vertical displacement of blowing snow particles further increases their propensity for horizontal transport due to higher wind speeds aloft.

An illustration of the complexity of blowing snow clouds is shown in Fig. , which shows the blowing snow mass and number mixing ratios (Fig. a and b, respectively) along a vertical cross section located at the dashed red line shown in Fig. c. While blowing snow quantities are not significant from a surface mass balance perspective, they are relevant from a microphysics perspective. From this point of view, blowing snow particles can be found even 1000 m above the surface and at some locations with values of the order of 0.01 kg kg-1. While it is not well known at the moment whether blowing snow particles trigger any microphysics feedback processes, for example, acting as seeders for cloud formation, CRYOWRF can be used for further research in this direction. The final subplot in Fig.  shows the mean particle radius, which is a diagnostic variable from the blowing snow module. There is qualitatively a trend of decreasing radii with height, even though there are significant variations from this. There are cases, for example, where even 100 µm particles are found at significant altitudes above the surface. A video that shows the dynamics of the blowing snow mixing ratios for the entire simulation period is provided as Video M2 in the Supplement.

There is an important caveat to values of blowing snow presented in this case study (apart from the lack of verification with field measurements). As described in the previous section, the snowpack was initialized using single-layer snow information from COSMO-1 analysis fields. Surface grain diameters and cohesion between the grains were arbitrarily chosen. For very short simulations, as in this case study, the initial conditions of the snowpack can play a critical role in modulating the simulation results. The ideal way of initializing the snowpack would be by first running Alpine3D (the spatially distributed version of SNOWPACK) forced by meteorological or even COSMO-1 analyses fields for the domain of interest and initializing the snowpacks within CRYOWRF from the outputs of Alpine3D. This would provide a reasonably correct state of snowpacks at the start of the simulation. Such a workflow would be followed in dedicated studies focused on the verification of CRYOWRF for alpine simulations.