The HIRHAM RCM is based on the dynamics of the High Resolution Limited Area Model HIRLAM; and the physical parameterizations of the atmospheric general circulation model ECHAM . We utilize here version 5, which combines HIRLAM model release 7.0 with ECHAM model release 5.2.02 . HIRHAM5 has been applied to various Arctic studies recently, e.g.,.

HIRHAM5 is run at a horizontal resolution of 0.25∘ (about 27 km) on a rotated latitude–longitude grid with the North Pole on the geographical Equator at 0∘ E and with 40 vertical levels. The altitude ranges from about 10 m above the surface up to 10 hPa, and the lowermost 1 km is represented by 10 levels. In this study, the daily snowfall rate constructed from the 3-hourly output is used for the observation-to-model approach. On the other hand, the 3-hourly output of the thermodynamic state and the mass mixing ratios of cloud ice, cloud liquid, snow, and rain are used to calculate synthetic reflectivities in the model-to-observation approach. While cloud ice and liquid mixing ratios are prognostic variables in the model, snow and rain are diagnostic variables.

We apply at every time step a grid point nudging, i.e., dynamical relaxation (sometimes also called indiscriminate nudging or grid relaxation), which was originally developed for data assimilation . We have chosen a parameter value corresponding to 1 % nudging. This ensures constrainment of the simulated large-scale flow to the driving ERA-Interim reanalysis. For an evaluation of HIRHAM5 snowfall using observations, the simulations must stay reasonably close to the real development of the synoptic weather situation, allowing us to separate dynamical from microphysical effects. Due to the nudging, the large-scale snowfall patterns are expected to correspond with reasonable accuracy to the observations, as is demonstrated in a snowfall case study for 7 March 2010 in Figs.  and . The location of the precipitation system and its vertical extent are rather similar in HIRHAM5 and CloudSat observations. Therefore, it is assumed that the differences between the modeled snowfall and observations are to a lesser degree related to the simulated large-scale flow but are mostly caused by the ECHAM5 boundary layer and microphysical parameterization employed in HIRHAM5 and observational uncertainties.

Unless specified, HIRHAM5 uses the modified Tompkins cloud scheme throughout the whole paper. However, to study the effect of different cloud cover schemes, we have also run the model for the studied period with two other schemes: the original Tompkins and Sundqvist cloud schemes. The Sundqvist scheme is based on relative humidity; i.e., a critical threshold of relative humidity controls the cloud cover formation. The threshold decreases exponentially from 90 % near the surface to 70 % at higher altitudes. The Tompkins scheme is a prognostic statistical cloud scheme. The subgrid-scale variability of total atmospheric water content is specified by a probability density function in terms of the beta distribution. The higher-order moments of the beta distribution, namely, variance and skewness, are included and linked to subgrid-scale processes like turbulence, convection and microphysics. Fractional cloud cover is computed as an integral over the supersaturation part of the actual beta distribution. The Tompkins scheme includes adjustable parameters, which determine the shape of the beta distribution and microphysical processes (e.g., the aggregation rate – the efficiency of snow formation by aggregation of cloud ice particles).  found that a parameter tuning of the cloud ice threshold controlling the efficiency of the Bergeron–Findeisen process, combined with a scheme extension which allows negatively skewed beta distributions, is most suitable for Arctic cloud simulations. They showed that this modified Tompkins scheme significantly reduces Arctic cloud cover, in better agreement with CloudSat/CALIPSO observations. The more efficient Bergeron–Findeisen process decreases (increases) the cloud water (ice) content.

ERA-Interim is a global atmospheric reanalysis produced by the ECMWF . It was widely used as a reference, covering the period from 1 January 1979 onward until 31 August 2019, and was replaced by the ERA5 reanalysis, also available from 1 January 1979 onward. The system includes a four-dimensional variational analysis (4D-Var) with a 12 h analysis window. The spatial resolution of the data set is approximately 80 km (T255 spectral) on 60 levels in the vertical from the surface up to 0.1 hPa . To improve and constrain the forecast, surface, radio-sounding, and airborne observations as well as satellite measurements are assimilated into ERA-Interim . However, CloudSat observations are not applied, nor are the direct precipitation observations from any source. The cloud microphysics scheme utilized in ERA-Interim is based on , representing clouds in terms of two prognostic variables. One variable is for cloud fraction and the other one for total cloud condensate, which in turn is divided into separate liquid and ice categories diagnostically according to temperature . ERA-Interim is used here as lateral forcing as well as for the nudging for the HIRHAM5 simulations. Comparing both HIRHAM5 and ERA-Interim surface snowfall rates with CloudSat retrievals allows us to assess the influence of HIRHAM5 cloud and precipitation treatment. Mean snowfall rate for ERA-Interim is calculated from the monthly accumulation from the twice-daily values. Note that HIRHAM5 simulations were carried out before the release of ERA5.

CloudSat is part of the NASA A-Train constellation in a sun-synchronous orbit with an inclination of 98.2∘. Therefore, it provides nearly global coverage, reaching 82.5∘ from south to north by a 16 d repeat cycle. The onboard Cloud Profiling Radar (CPR) operates at 94 GHz, providing observations of the vertical distribution of clouds and light precipitation with the vertical resolution (bin) of 240 m . Its footprint is 1.4 km across and 2.5 km along track. The minimum detectable reflectivity is dependent on, e.g., cloud cover, seasonal changes in temperature, surface type, and atmospheric attenuation, typically varying by ∼ 1 dB over the globe in the range from −30.9 to −29.9 dBZ , and the measurement uncertainties related to noise range from 3 dBZ for a reflectivity of -30 dBZ to about 0.1 dBZ for reflectivities above -10 dBZ . Due to the relatively high frequency, the CPR signal can suffer from attenuation of atmospheric gases, e.g., of water vapor and oxygen. In addition, significant attenuation is also caused by the hydrometeors, and the measurements may be affected by the multiple scattering effects .

Here, we use two CloudSat products, the measured radar reflectivity vertical profile 2B-GEOPROF and the snow profile product 2C-SNOW-PROFILE . Version 5 (R05) is used for both products. 2B-GEOPROF includes the observed reflectivity corrected with the MODIS (Moderate-Resolution Imaging Spectroradiometer) cloud mask product . The measured reflectivity may be attenuated, which is not compensated in the product itself. Hence, in model-to-observation comparison, the attenuation due to atmospheric gases and hydrometeors is included in the reflectivity computations (Sect. ). The 2C-SNOW-PROFILE product includes estimates of particle size distribution and snowfall rate retrieved from the observed radar reflectivity applying ancillary meteorological information of ECMWF-AUX and a priori information of snow microphysical and scattering properties . In the 2C-SNOW-PROFILE product, the precipitation presence and phase at the surface are primarily examined from an additional 2C-PRECIP-COLUMN product and secondarily defined from the 2B-GEOPROF near-surface reflectivity values with the cloud mask correction and temperatures from ECMWF-AUX, for each radar profile within the retrieval algorithm. The snowfall is indicated, and a snowfall rate is retrieved if the assessed melted fraction of precipitation is lower than 10 %.

The retrieval of the snowfall rate (S) from the measured reflectivity (Z) is a significant source of uncertainty when applying radar measurements to estimate snowfall rates, e.g., . Hence, in the 2C-SNOW-PROFILE product, the snow retrieval is not based on a single pair of parameter values of the Z–S relation but is optimized by minimizing a cost function which represents differences between simulated and observed reflectivities and also differences between estimated and a priori values of the snow microphysical properties . found that adoptable Z–S parameterizations considering the local microphysical conditions provide better performance than a method with the static Z–S relationship. Thus, we are confident in using the output of the 2C-SNOW-PROFILE product as the ground truth while acknowledging the relevant unreliability stemming from the uncertainties in observed reflectivities, the used retrieval parameters and their a priori assumptions . The product has shown good detectability of light snow (snow water equivalent less than 1 mm h-1) but limited ability to retrieve at the higher end of snowfall intensity distribution (>1 mm h-1) when compared to the weather-radar-estimated surface snowfall rate . The relative uncertainty of the product increases with complex topography and higher frequency of mixed-phase precipitation .

As mentioned in Sect. , due to clutter contamination, the CPR cannot reliably measure reflectivity near the surface, resulting in the blind zone. The magnitude and vertical extent of the enhanced reflectivity values relating to back-scattered power from the surfaces vary depending on surface characteristics such as topography, roughness and material . In the 2C-SNOW-PROFILE product, the blind zone is determined as the two (four) bins above the bin containing the surface over the ocean (land) and the next highest bin; i.e., an altitude of ∼ 750 m (1250 m) over the ocean (land) is considered for the snowfall retrieval . Therefore, shallow precipitation or evaporation below this height might lead to a deviation from the true near-surface snowfall rate. The resulting underestimation (sometimes also overestimation) of snowfall rate due to a 1000 m blind zone has been found to be rather small for Svalbard but higher at the Belgian Princess Elisabeth station in East Antarctica .

One of the important updates in the R05 product version is the use of an improved DEM (digital elevation model) for the estimation of the surface height, and this should affect especially Greenland, which has steeply varying terrain. With R05, the number of observations suspected of being contaminated by ground clutter should have decreased . When applying the 2C-SNOW-PROFILE product, we have determined the surface snowfall rate from the snow profile data utilizing quality flagging of the snow retrieval status, following the example shown in and . The retrieval status is represented for each profile by an 8-bit array, and an activated bit provides information about the retrieval performance . We have utilized only those profiles which have the zeroth and first bit field activated, indicating that a snow layer is detected in the profile and that snow is indicated at the surface. Additionally, if the third bit field is activated, meaning a large vertical gradient in snowfall rate between the near-surface bin and the bin immediately above is seen, the surface snowfall rate is determined from the second-lowest bin instead of the lowest near-surface bin. Such a strong gradient can be caused by surface clutter or by the presence of shallow precipitation. In the latter case, we underestimate the surface snowfall rate. However, the other two possible reasons, the mentioned ground clutter contamination or the partial melting, can produce a significant error into the estimated surface snowfall rate. pointed out that the third bit field was mainly activated on the edges of the fjords over the eastern coast of Greenland and on the peaks of the Prince Charles Mountains expected to have clutter issues. Although orographic precipitation can also produce large snowfall gradients, in this case these flagged observations should cover larger areas along the ridges and coastline which were not observed by .

PAMTRA is a model framework to forward-simulate passive and active microwave radiation through the cloudy atmosphere for upward- and downward-looking geometries. It can calculate polarized brightness temperatures and the full radar Doppler spectrum and its moments. PAMTRA requires input that describes the atmospheric state, including hydrometeor contents and characteristics, instrument specifications, and the observation geometry.

In this study, the atmospheric state from HIRHAM5 was used to calculate the two-way gaseous attenuation of the radar beam using the gas absorption model by including modifications of the water vapor continuum absorption and the line width modification of the 22.235 GHz H2O line . To calculate the absorption/emission and scattering properties of hydrometeors, the hydrometeor mixing ratios have been converted to particle size distributions following the microphysical assumptions of HIRHAM5 (Appendix ). For each size, the back-scattering and extinction cross sections are calculated and used for simulation of the radar reflectivity. For cloud liquid and rain particles, which can be assumed to be spherical, the Lorentz–Mie method is used, and the refractive index of water is defined according to . Cloud ice and snow particles have more complex structures than droplets or raindrops, and the spheroidal or spherical approximations do not provide realistic scattering characteristics at 94 GHz . Hence, for these particles, the self-similar Rayleigh–Gans approximation SSRGA; is utilized, and the coefficients needed to describe the ice particle properties for the scattering computations are derived as in . The refractive index of ice is taken from . From extinction and backscatter cross sections, both the attenuated (by gases and hydrometeors) and unattenuated reflectivities have been calculated.

Multiple scattering may affect the observations at 94 GHz and can be approximately 1 dB in snowfall with reflectivity values greater than 10–15 dBZ but are not considered in these computations. PAMTRA includes a set of different options to describe particle size distributions from monodisperse, several functions and fully resolved distributions. To be consistent with the microphysical scheme of the atmospheric model or the in situ measurements that provide the input, PAMTRA implements the same assumptions for the particle size distributions and particle properties (Appendix ).

HIRHAM5 model grid points and CloudSat CPR observations differ in space and time. These sampling differences need to be considered by spatial and temporal re-sampling in order to guarantee a fair comparison. The used sampling grid is an equal 1∘ × 1∘ grid. As stated in , the CloudSat overpass occurring every couple of days is not representative for describing individual snowstorm variability in a certain specific location. However, with a large enough sampling grid, CloudSat can on average produce a reliable climatology.

Within the observation-to-model approach for each sampling grid point, one daily value is retained, taken as a mean of all the values of the CloudSat overpasses over the grid area and similarly for the HIRHAM5-modeled values. In case there are no CloudSat observations in the specific grid point, the daily value is excluded from the 4-year analysis, also from the model. Due to the CloudSat orbit, the grid points are observed at different preferable times of day, which is investigated in the model-to-observation approach (see below).

As the analysis is performed on the 1∘ × 1∘ grid, the number of model grid points per sampling grid cell decreases with latitude due to the meridian convergence (Fig. ). Due to its orbit, the number of CloudSat measurements increases with latitude (, therein Fig. 1). Therefore, for both data sets the frequency of occurrence per grid point is calculated and taken into account within statistical intercomparisons. When constructing joint histograms of temperature and reflectivity, so-called contoured frequency by temperature diagrams (CFTDs), the normalization is performed firstly by the number of samples in each grid point and secondly by the total sum of hits. In addition, the temporal sampling difference is considered by using the respective model output for each region closely coinciding with the times of the CloudSat overpasses. The stated model times for each region are shown in Table .

For the model-to-observation intercomparison, we also need to consider the different vertical sampling, i.e., equal spacing by CloudSat and a vertically stretched grid by HIRHAM5. Here, we defined the height bins as having a 250 m size below 1 km, a 500 m size between 1 and 4 km and a 750 m size between 4 and 10 km. The temperature bins are equally sized (2 K) between -70 and -10 ∘C. In our analysis, we have restricted the temperatures to below -10 ∘C to exclude any effect of melting and melting layer from the statistical analyses of modeled and observed reflectivities. The temperature values for the PAMTRA-modeled reflectivities are taken from HIRHAM5 itself, and for the CloudSat observations, temperatures are obtained from ECMWF-AUX . The sensitivity of the CPR is approximately -28 dBZ, so the binning for reflectivities is carried out with 2 dBZ between -28.0 and 20 dBZ in the comparisons between modeled and measured reflectivity values. However, model-only analysis includes a wider range of values to demonstrate the small reflectivity values produced by cloud ice from the model, with more discussion in the results (Sect. ).

To better identify reasons for potential deviations between observations and HIRHAM5, we also composite snowfall maps for different distinguishable weather regimes and evaluate the model output to observations in each regime separately as performed in . Separating the daily modeled and observed snowfall rates according to an external parameter allows us to identify possible systematic model biases related to synoptic processes. In this study, we chose to investigate regimes of large-scale atmospheric circulation classified by strength, direction and vorticity of the geostrophic wind. We selected two sub-regions of the northern North Atlantic around Svalbard (Fig. d) covering the latitude band of 70–81∘ N. The eastern (40–10∘ E) and western (20∘ W–10∘ E) regions are considered such that the eastern region is directly north of Scandinavia and includes Svalbard, while the western region avoids land regions and is placed between Greenland and Svalbard. Both areas are characterized by high synoptic variability with frequent cyclone passages. The regime classification was performed with ERA-Interim 6-hourly 850 hPa geopotential height and shear vorticity for the studied period with the methodology of Jenkinson–Collison . The geopotential at 850 hPa is used to avoid topographic and boundary layer effects. The Jenkinson–Collision method is an automatic classification scheme , where the geostrophic wind speed and vorticity at high/low central pressure are assessed in horizontally and isotropically arranged grid points and, based on threshold values, are set to eight exclusionary directional classes according to compass points (N, NE, E, SE, S, SW, W and NW) and two vorticity circulation regimes (cyclonic, C, and anticyclonic, AC) .

The daily regime classification of the two sub-regions (western/eastern) is specified with the cost733class software package of the COST Action framework , and the occurrence of each regime for both sub-regions is determined. Clearly, the northerly, southerly and both vorticity classes are by far the most frequent, with occurrences of 16 % (25 %), 12 % (10 %), 31 % (38 %) and 34 % (32 %), respectively, for the eastern (western) sub-region. To simplify the analysis, the less frequent NE (6 % (7 %)) and NW (9 % (6 %)) were added to the northern regime, typically representing situations when cold Arctic air masses move southward. Similarly, SW (7 % (10 %)) and SE (8 % (3 %)) were added to the southern cluster, which is a typical situation for warm air intrusions into the Arctic. Finally, we divided the modeled and observed daily mean snowfall rates to these four regimes and calculated the contribution to the yearly mean snowfall rate to each regime separately.

Two distinct regions of high (>500 mm yr-1) average annual snowfall in the Arctic, namely, the southeastern coast of Greenland and the Atlantic storm track, are detected by both HIRHAM5 and CloudSat (Fig. ). These are mostly related to cyclones which bring the heaviest snowfall during the snow accumulation season (September–May) in the regions of East Greenland, the Barents Sea, and the Kara Sea, which are the dominant regions of the extreme cyclone occurrence. Typically 20–40 events per one winter season take place . The cyclone activity is much stronger in the Arctic Atlantic than in the Pacific; i.e., cyclone snowfall accounts for approximately 80 % of the total snowfall in these Atlantic regions, while cyclones account for only circa 50 % of total snowfall in the Pacific region . Additionally, lee cyclogenesis is important for precipitation production over southern and eastern Greenland , whereas so-called Icelandic cyclones traveling further east are not favorable for precipitation over Greenland . This highlights the importance of the nudging in HIRHAM5 that leads to a good representation of cyclone-associated snowfall as depicted in Fig. . The lowest snowfall rates in both HIRHAM5 and CloudSat are located in the Beaufort Sea, the Canadian Archipelago, the central Greenland Ice Sheet, and eastern Siberia, with less than 100 mm yr-1.

Across the whole Arctic, the area-weighted domain average of the HIRHAM5 annual snowfall rate shows nearly perfect agreement with the CloudSat-based product, with 213 (214) mm yr-1 for HIRHAM5 (CloudSat). This value is also very similar to , who derived 211 mm yr-1 as the CloudSat mean annual snowfall rate over the whole Arctic area when all profiles were included but a rate of 183 mm yr-1 when only profiles passing rigorous quality control were retained. Note that the studied area is different between these two studies. CloudSat and HIRHAM5 agree much better with each other than they do with ERA-Interim, which shows an annual area-weighted average Arctic snowfall rate of only 117 mm yr-1 in our study area (Fig. ).

When looking at the frequency distribution of the annual mean snowfall rates over all grid points, a rather similar distribution with the highest occurrence of snowfall rates around 150 mm yr-1 is apparent for HIRHAM5 and CloudSat (Fig. a). As a minor difference, HIRHAM5 shows more often rates between 100 and 300 mm yr-1, whereas CloudSat has a tendency to higher extremes. The reasons for this could be the finer resolution of CloudSat-resolving local precipitation hotspots or clutter contamination. In contrast to HIRHAM5 and CloudSat, the coarser-scale ERA-Interim reanalysis has a much narrower frequency distribution, and its distribution has a maximum at only 100 mm yr-1. This demonstrates that, although HIRHAM5 is driven by ERA-Interim, snowfall is determined by its physical parameterizations, and these lead to an improved representation of snowfall.

We have proven that the chosen refined sampling has only minor effects on the results. That is, the difference in mean yearly snowfall rate between the model values coinciding with CloudSat observations and model-only values (Fig. d) is on average small over the whole Arctic region. For 92 % of grid points the difference is less than 20 %. When the coinciding sampling with CloudSat is applied, the modeled yearly snowfall rate is closer to CloudSat observations (the mean difference reduces from 2.2 to 0.7 mm yr-1).

Given the overall good agreement, we now look at spatial differences in the annual snowfall rate across the whole Arctic (Fig. c). Note that the observations by CloudSat are generally in line with the results of and . Though model and observations show similar spatial distributions, distinct spatial differences occur (Fig. c), and, e.g., root-mean square error in the yearly surface snowfall rates is high, at 148 mm yr-1 between HIRHAM5 and CloudSat and at 175 mm yr-1 between ERA-Interim and CloudSat. First, HIRHAM5 seems to consistently produce overly high orographic precipitation than is detected by CloudSat over the coastal mountains, e.g., in Greenland, Norway, Svalbard, Novaya Zemlya and the Putorana Plateau in Siberia. Therefore, this will also be investigated via the model-to-observation approach (Sect. ), which allows a closer look at the vertical structure. Second, while in many areas differences seem to be of a random nature and can be attributed to the poor sampling by CloudSat, two larger areas with systematic differences also occur, namely, an underestimation of HIRHAM5 along the North Atlantic storm track, the Kara Sea, Baffin Bay and the Bering Strait and an overestimation of HIRHAM5 over Greenland.

The North Atlantic storm track region sticks out as the largest area of a systematic underestimation of HIRHAM5 (Fig. c). The underestimation is particularly strong southwest of Svalbard: the observed values are in between 500 and 1000 mm yr-1 here. In contrast, the model provides values of 400–700 mm yr-1 across this region. However, when studying the uncertainty in the CloudSat climatology in more detail, identified the Arctic North Atlantic region as having relatively large uncertainty, mainly due to a high frequency of possible mixed precipitation. In this respect it is important to look at the monthly resolved snowfall distribution (Appendix , Fig.  for HIRHAM5, Fig.  for differences). From September on, the region of the highest snowfall in the North Atlantic moves more and more south with decreasing temperatures until its southern maximum extent in February/March. Interestingly, the highest model underestimation above 50 % (Fig. ) over the Atlantic does not occur during the time of the strongest snowfall (January to March) but rather at the beginning of the snow season from September to November. This is reasonably in agreement with , who indicated an underestimated occurrence of deep cyclones in these months. Interestingly, this model underestimation seems to be coincident with the sea-ice-free areas of the North Atlantic and also Baffin Bay, as deduced from satellite data (Fig. ) . However, this is only a qualitative interpretation and requires more detailed examination in future studies. A clear statement whether and to what extent the HIRHAM5 underestimation in that region is related to model deficits or CloudSat uncertainty cannot be given yet.

While for the region of southern Greenland a pronounced seasonal cycle in snowfall is evident, likely related to cyclone activity, this is not the case for the northern Greenland region (Fig. ). A noticeable feature is the strong overestimation of the modeled snowfall rates over the Greenland Ice Sheet and the coastal mountainous regions in the southern part, as stated already in the yearly surface snowfall results (Fig. ) (e.g., in the Greenland region with a median difference of 2.6 mm month-1 for the model to show higher values calculated over the whole year). However, it should be noted that total precipitation in North Greenland is rather low, and a high relative overestimation is not related to high snowfall rates. The annual distribution of the snowfall is similar to the detailed snowfall climatology from CloudSat over the Greenland Ice Sheet shown in , even though the magnitude is overestimated by the HIRHAM5 model.

In general, the seasonal course of the snowfall rate for the different regions is well represented in HIRHAM5 as compared to CloudSat (Fig. ). During the summer months, the model consistently overestimates the snowfall rates; however, the rates are also small in all regions, typically around 10 mm month-1 or less, except in Greenland, between 10 and 20 mm month-1. Again, the clear overestimation of the model is most visible during fall, especially in the lower-latitude band of the Kara Sea and Greenland regions. The North Atlantic (and the southern Chuckchi Sea) winter season sticks out as the only one where CloudSat shows higher snowfall rates than HIRHAM5. As discussed before, here too retrieval problems related to mixed-phase precipitation might occur, making it difficult to judge whether the model or the observations show deficits. The same also holds for effects of the blind zone, which therefore calls for an extended intercomparison in the observation space.

The model's underestimation of the annual snowfall rate distribution in the North Atlantic and the Kara Sea (Fig. c) is not visible in the region-wide averaged rates (Fig. ), except in the winter season for the North Atlantic region. The reason lies in the averaging across the region. The model's overestimation over orographic and coastal areas (e.g., over the Scandinavian coast, Svalbard and Novaya Zemlya) masks the model's underestimation over the oceanic regions. To expand our study, we zoom into two distinct regions in the North Atlantic corridor for defining the CWT regimes introduced in Sect. .

Because the strongest underestimation of HIRHAM5 surface snowfall rate is seen in the North Atlantic, we selected two smaller sub-regions (depicted in Fig. d) for the regime assessment with CWTs, namely, N, S, C and AC flow. The four different CWT regimes reveal consistently different snowfall distributions for both sub-regions (Fig. , Fig. ). Both the HIRHAM5-modeled and CloudSat-observed surface snowfall patterns agree well, which can be explained by the nudging of HIRHAM5. Region-wide snowfall is brought in both sub-regions by cyclones which transport heat and moisture into the Arctic, and accordingly the C regime brings most of the snowfall for the region.

In the eastern sub-regions, during anticyclonic conditions (regime AC), a clear snowfall maximum northwest of Svalbard appears to decrease to the south and east in both HIRHAM5 and CloudSat. With the southerly flow the highest snowfall accumulation appears in the northern part of the region, generally above 76∘ N. During northerly flow, CloudSat shows that the majority of snow falls in the region southeast of Svalbard (Fig. ), which is sensible, as this is a few hundred kilometers downwind of the ice edge, and convection needs time to fully develop when the cold air flows over the relatively warm ocean. For this CWT regime, HIRHAM5 shows nearly a factor of 2 underestimation in the maximum snowfall rates in the southeast of Svalbard, also seen in the mean snowfall rates in Fig. . Similar characteristics can be found for the western sub-region (Fig. ). As both these sub-regions relate to the area of the largest underestimation southwest of Svalbard in the annual snowfall rate (Fig. ), the poor representation of snowfall associated with northerly flow might be responsible for the overall HIRHAM5 underestimation. The northerly flow has a significant occurrence of 31 % / 38 % for the eastern/western sub-region and is often associated with marine cold air outbreaks (MCAOs). MCAOs lead to organized convection when cold air flows over the relatively warm ocean, a phenomenon which many models struggle to represent . The effect of underestimation during northerly flow might be partly compensated by cyclones which are associated with a higher snowfall rate in HIRHAM5 than in CloudSat.

To investigate the differences in the vertical reflectivity structure between the different regions, we focus on the winter season (DJF), which covers snowfall rates of approximately 30 % over all seasons. Furthermore, we reduce problems related to mixed-phase conditions as temperatures are generally low. The other seasons are shown in Appendix . We follow , who build CFTDs instead of the often-used geometrical height, as this allows a better focus on the temperature-dependent cloud processes. CloudSat observations show the typical bi-modal structure in the CFTDs (Fig. ) in nearly all regions with frequent occurrence of an ice cloud mode with low reflectivities around -20 dBZ at low temperatures of around -50 ∘C and a second mode associated with snow with reflectivities around 0 dBZ and temperatures warmer than -30 ∘C. Note that a minimum threshold of -15 dBZ is often utilized for identifying snowfall in the 2C-SNOW-PROFILE product .

As the transition from ice clouds to snow is seamless, a clear occurrence of a maximum following a linear slope from low reflectivities at cold temperatures to high reflectivities at warm temperatures is found in CloudSat observations (red line depicted in Fig. ). This transition also reflects different snow growth processes, the depositional growth starting from around -50 ∘C and the dendritic growth zone at approximately -15 ∘C, leading typically through aggregation to enhanced snowfall rates. Also, different snowfall types such as shallow cumuliform and deeper nimbostratus snowfall events are associated with different CFTDs, as demonstrated by . Therefore, when averaging over larger regions and seasons, this linear pattern becomes dominant, as, for example, in the global CloudSat CFTD by . Clearly this behavior cannot be seen in the HIRHAM5 simulations. Hardly any reflectivities in regions colder than -35 ∘C are produced, indicating a problem with ice clouds which will be addressed in more detail in the next subsection.

Due to the lower occurrence (<0.1 %) of cold temperature reflectivities, reflectivities at warmer temperatures are relatively more frequent in HIRHAM5 than in CloudSat observations, with occurrences of >0.8 % for HIRHAM5 and with occurrences of between 0.6 % and 0.8 % for CloudSat. However, HIRHAM5 is able to reproduce regional differences seen by CloudSat correctly. Enhanced reflectivity related to the snow mode (-10 and 5 dBZ) occurs at the warmest temperature in the North Atlantic (around -10 ∘C) in both observations and model, similarly to slightly warmer temperatures in the Kara Sea region. In the Chukchi Sea, occurrences (0.4 %–0.8 %) are confined to a narrow temperature range between -20 and -35 ∘C, while in the Laptev Sea the distribution broadens to colder temperatures again in both observations and simulations. In the Chukchi Sea, HIRHAM5 can also reproduce the increased reflectivity occurrence (0.6 %) around -20 ∘C in the lower-latitude region compared to the higher-latitude region. The strongest difference between the observed and simulated CFTDs is visible for Greenland, where the simulations show reflectivities at much warmer temperatures (-20 to -10 ∘C) and higher reflectivities (0–10 dBZ), consistent with the overestimation in snowfall rate by HIRHAM5 discussed before.

We also checked the effect of attenuation in the simulations by comparing the attenuated reflectivity values to the non-attenuated values. The attenuated CFTDs are 5.1 % closer to the observed CFTDs and, generally, even with attenuation considered, the model sees higher reflectivities at warmer temperatures, except in the case of Greenland, where the observed occurrences of higher reflectivities are higher than the simulated ones. Additionally, the effect of using the modeled values concurrent with the expected CloudSat overpasses (Fig.  and Table ) with respect to all modeled values is examined. Typically, differences show a random geographical distribution, in particular in regions where occurrences are low. The overall improvement in agreement is 0.8 % for the observed reflectivity values when only concurrent model values are used. Thus, the exact matching is considered insignificant except for times with little snow, such as in summer in some regions.

Because CFTDs average over different surfaces (ocean, sea ice, and land), we now investigate the vertical reflectivity structure for a latitude band of 72–73∘ N (circle indicated in Fig. c), again for the winter season. Figure  shows the seasonal mean reflectivity cross section along the latitude circle together with the mean surface snowfall rate to emphasize the reasons for strong snowfall in southeastern Greenland and across the North Atlantic Ocean. The importance of orography is clearly evident. HIRHAM5 shows orographic effects with reflectivity enhancement reaching mid-tropospheric levels at both coasts of Greenland and over the Baffin mountains and Novaya Zemlya. These structures are even more obvious in the differences from CloudSat, where HIRHAM5 shows strong overestimations (spikes) for nearly all grid points associated with strong orographic slopes. The strong vertical extent of these reflectivity signatures in HIRHAM5 is not visible in the observations and led us to conclude that this is a model deficit.

Looking at the CloudSat observations, the effect of ground clutter which causes a deeper blind zone over land (up to 1200 m) is most visible for Greenland and Baffin Island (with elevations up to 2000 m). Clutter filtering might cause the possible model overestimation over Greenland in winter (Fig. ), which has also been found by for the Arctic-wide average. Consistent with the CFTDs, reflectivities of more than -20 dBZ can be found in much higher (colder) parts of the atmosphere by CloudSat than in HIRHAM5, which will be investigated next.

The simulated reflectivities can provide additional insight into the contributing portions of different hydrometeors to the total reflectivity. At first, we look at the HIRHAM5 control run employing the modified Tompkins scheme. Again for winter, we show the reflectivity by different hydrometeor types along the latitude belt in Fig. a. Snow particles clearly contribute the most to the simulated reflectivity for all heights and also throughout all the seasons. Even in summer (not shown), when the snow particles manifest higher in altitude to the reflectivity, their contribution to reflectivity dominates over that of rain particles. The highest reflectivity values due to rain particles are concentrated in the North Atlantic region (20∘ W–10∘ E), and some higher values are also modeled in the East Siberian Sea (150–180∘ E) and the Beaufort Sea (150–130∘ W). Cloud ice produces reflectivities over the full troposphere; however, these are rather low, in particular in the higher troposphere. This likely originates from the threshold of ice particle radius to be monodisperse of 40 µm (see Appendix ), which results in very low reflectivity values. In contrast, the smallest radius of a particle in the snow class is 0.1 mm, and, thus, snow always produces significant snow reflectivity.

Even in winter, cloud liquid water is present within the lowest 4 km and produces significant reflectivities close to the surface over the North Atlantic. During the summer months, their contribution is more widely distributed to the studied latitude ring and is higher in altitude (not shown), as is to be expected. The presence of low-level clouds and rain over the North Atlantic points to the difficulties in both (i) retrieving snowfall in mixed-phase conditions and (ii) simulating reflectivity, as melting might produce complex particles which are not taken into account in the forward simulation.

In addition to the control run with the modified Tompkins scheme, two more runs with different cloud microphysical schemes, i.e., the original Tompkins and Sundqvist schemes, are performed, and their results are compared (Fig. b). For all the schemes, the overall total mean reflectivity profile compared to the CloudSat-observed reflectivity profile is close to similar. The mean reflectivity difference from CloudSat varies between seasons and schemes, but generally the mean difference ranges between 0.3 % and 2.3 %, and no clear statement can be made as to which of the schemes in general would be closest to reproducing the total reflectivity values compared to observations.

However, there are distinct dissimilarities between the schemes when the contributions to reflectivity by different hydrometeors are examined (Fig. ). The original Tompkins scheme seems to produce more cloud liquid particles than the modified Tompkins or Sundqvist scheme, similarly to stated in , connected to the enabled more enhanced Bergeron–Findeisen process and thus associated with an increase in cloud ice particles. The finding of  is limited over sea ice areas only, and this is not obvious from our analysis here over a lower-latitude band (72–73∘ N) from these model runs. Another difference is that the Sundqvist scheme produces rain particles, though small amounts, reaching high levels of the atmosphere, which is not the case with either of the Tompkins schemes. The notable dissimilarity between the schemes is the contribution of cloud ice and snow particles to reflectivity. As both Tompkins schemes seem to have a high fraction of snow particles, especially at the lower altitudes, the Sundqvist scheme tends to have higher fractions of cloud ice particles contributing even at the lower altitudes. The abovementioned scheme differences seem to be seasonally independent; i.e., similar features can be seen not only during winter, as shown in Fig. . While we do not go into more detail here, it is clear that the model-to-observation approach allows us to investigate the relative performance of different schemes. The next step would be to identify regimes, such as those based on temperature that show especially high differences between the cloud schemes, and subsequently compare observations and different model simulations for these regimes.