In our investigation of the relationship between sLCCs and surface snowfall biases, we rely on satellite observations from CloudSat and CALIPSO for the comparison with ERA5 and CMIP6 models. Specifically, we use Release 5 (R05) versions of the 2B-CLDCLASS-LIDAR product for cloud-phase determination, the 2C-SNOW-PROFILE product for the surface snowfall rate estimation, and 2 m temperatures from the ECMWF-AUX dataset that contains ancillary ECMWF state variable data interpolated to each vertical radar bin (see Table ).

The 2B-CLDCLASS-LIDAR product utilizes the CALIOP lidar and the CPR on CloudSat and their different sensitivities to liquid droplets and ice crystals in order to retrieve the phase of a cloudy layer. The algorithm uses a temperature-dependent radar reflectivity threshold , the integrated attenuated lidar backscattering coefficient, and cloud-base and cloud-top temperatures from atmospheric reanalysis data to discriminate between ice, mixed, or liquid water clouds . In accordance with , we focus on the phase of the bottom cloud layer within the atmospheric column and neglect the cloud-phase quality flag, irrespective of the confidence level indicated. The rationale for the latter is the lidar's ability to robustly detect any liquid (liquid or mixed), and a low-confidence value for the phase determination could stem from the uncertainty in the distinction between purely liquid clouds and mixed-phase clouds. This is particularly true for the frequent structure of polar mixed-phase clouds with the liquid layer at cloud top .

To estimate the surface snowfall rate, we use the 2C-SNOW-PROFILE product , which is based on an optimal estimation algorithm to retrieve profiles of parameters of the snow size distribution. The optimal estimation uses the radar reflectivity profile of the snow layer, ancillary meteorological information, and assumptions about snow microphysical and scattering properties. As the CPR cannot reliably measure near-surface reflectivities due to ground clutter, the surface snowfall rate is estimated based on the lowest clutter-free radar bin . The truncation height of the snow profile due to ground clutter is surface-dependent two range bins above surface and over ocean (∼500m); four range bins over land and sea ice (∼1000m);.

We focus on the years 2007 to 2010 before CloudSat switched to daytime-only operations due to a battery malfunction. Furthermore, we exclude September 2008 and December 2009 due to insufficient CALIOP data and the CloudSat battery failure . We aggregate the profile-by-profile data to a horizontal grid with a resolution of 3.75°×1.9° for each month. Subsequently, we calculate the monthly fsLCC and fsnow, as described in Sect. .

The sea ice concentration (SIC) data used in this study are obtained from the Institute of Environmental Physics, University of Bremen. The data are derived using the ARTIST Sea Ice (ASI) algorithm developed by . The ASI retrieval method utilizes microwave radiometer data from the Advanced Microwave Scanning Radiometer for the Earth Observing System (EOS) instrument on the Aqua satellite and the Advanced Microwave Scanning Radiometer 2 instrument on the Global Change Observation Mission–Water (GCOM-W1) satellite. Both datasets were reprocessed in 2018 with the same parameters. To present the 20% SIC, a seasonal average of the SIC is calculated for the years 2007 to 2010 and then gridded onto the 3.75°×1.9° grid using bilinear interpolation.

The ERA5 reanalysis data employ the 4D-Var data assimilation of the ECMWF Integrated Forecast System. ERA5 incorporates an improved stratiform cloud and precipitation scheme, enhancing the representation of mixed-phase clouds compared to ERA-Interim and includes prognostic variables for both rain and snow . The meteorological values are output at a resolution of 0.25×0.25°.

In order to detect the presence of sLCCs in ERA5 data, specific criteria involving the 2 m temperature (T2m) threshold and liquid water path (LWP) threshold must be met (see Sect. ). However, it is worth noting that ERA5 does not readily provide LWP values. Therefore, we calculated the LWP using the total column cloud liquid water (tclw) and the total column rainwater (tcrw; expressed in kgm-2; Table ). We incorporate tcrw with the T2m threshold below 0°C as this threshold is used to exclude any rainwater below the melting layer. Using daily mean values of tclw and tcrw and applying the daily man temperature threshold, we can analyze the role of supercooled liquid water within clouds and the contribution of liquid water to the snowfall precipitation process in ERA5.

To calculate the fsnow, we rely on the mean snowfall rate variable (msr, Table ). The mean snowfall rate (expressed in units of kgm-2s-1) provides a combined measurement of both large-scale and convective snowfall. It is calculated as an average over 24 h. Here we use the ERA5 Climate Data Store tool to average all of the output variables into daily mean values based on hourly data . It is important to note that 2t, tclw, and tcrw (Table ) are reported as instantaneous values every hour, meaning that when they are averaged to obtain daily mean values, they may not accurately represent the actual daily mean values. Nevertheless, a non-zero model daily mean LWP means that there was an sLCC in the grid box at some point during the day. In contrast, the mean snowfall rate is reported as a temporal average and accurately represents the daily mean snowfall rate.

Our intermodel comparison relies on data from CMIP6, involving simulations from various modeling centers. Specifically, we focus on the “historical” simulations 1850–near-present;, selecting 10 models with daily mean outputs from different ensemble members, as outlined in Table . In most of the figures shown in this study, we present the CMIP6 multimodel mean.

In our analysis, we consider the following variables (Table ): the mass mixing ratio of cloud liquid water (clw) encompassing liquid water in both large-scale and convective clouds provided at each model level (in units of kgkg-1). Precipitating hydrometeors within the clw variable are included only if they affect the model's radiative transfer calculations. Near-surface air temperature (tas), reflecting the temperature at a height of 2 m above the surface (measured in K), and snowfall flux (prsn), representing precipitation in all forms of frozen water (expressed in kgm-2s-1) are also considered.

As none of the models listed in Table  directly provides LWP as a daily output variable, we derive LWP based on clw. To calculate the LWP, we interpolate the CMIP6 hybrid sigma pressure to isobaric pressure (Appendix ). The UKESM1-0-LL and HadGEM3-GC31-LL models provide values on orographic vertical coordinates. Consequently, for these models, we use the CMIP6 variable phalf (Table ) instead of calculating isobaric pressure levels. Subsequently, we utilize the hydrostatic equation to calculate the liquid water content for each vertical grid box. The liquid water content is then summed up over the vertical to obtain the LWP for each horizontal grid box (see Appendix ).

CMIP6 data are gathered from 2006 to 2009 as these years represent the closest available overlapping time range for all CMIP6 models (some models ended the simulations by December 2009 and are marked with an asterisk in Table ). The slight mismatch in the time range is of limited relevance as CMIP6 model simulations are not designed to reproduce the exact temporal evolution of past weather but instead generate their own internal variability (e.g., El Niño–Southern Oscillation (ENSO) cycles), so they should only be viewed as generally representative of the time period in question.

The instrument sensitivities of the CPR and CALIOP, as well as their different temporal and spatial sampling in contrast to the gridded ERA5 and CMIP6 data, require different metrics that ensure a like-for-like comparison to the extent possible. In the following, we describe the calculation of these metrics (fsLCC and fsnow) and call attention to differences between the satellite observations and ERA5 or CMIP6. For ERA5 and for CMIP6 models, we remap all models to the coarsest resolution of 3.75°×1.9°, which corresponds to the grid of IPSL-CM5A2-INCA (Table ), with a nominal resolution of approximately 500km. We use area-weighted averages for both the NH and SH to calculate spatial means.

Figure a–d present the seasonal variability in fsLCC observed by CloudSat–CALIPSO in the mid-to-high latitudes of the NH. Evident from the figure is a clear seasonal progression in the spatial distribution of fsLCC. In summer (June–August, JJA), fsLCC reaches its minimum spatial average, with non-negligible values primarily within the Arctic basin. In NH autumn (September–November, SON), fsLCC values increase significantly in the Arctic basin but also spread poleward to land areas at about 60°N. In boreal winter (December–February, DJF), maximum values shift away from the Arctic basin and are instead found over the ocean close to the average seasonal sea ice edge (Fig. a; red line).

The Greenland ice sheet (GRIS) is a region of particular interest for this study, as sLCCs have been proposed to accelerate GRIS surface melt , while snowfall represents the primary ice sheet growth mechanism. The GRIS, which is characterized by its high elevation and snow-covered surface, experiences numerous sLCCs during boreal summer and autumn due to sufficient moisture and temperatures below 0°C in the CloudSat–CALIPSO observations (Fig. c, d). However, during boreal winter and spring (March–May, MAM), the fsLCC is low (< 15 %) as the region becomes too dry and cold to support the formation of sLCCs. The seasonal cycle of the fsLCC as observed by CloudSat–CALIPSO is largely what would be expected from the combined seasonal influence of atmospheric circulation, moisture availability, and temperature conditions in the mid-to-high-latitudes in the NH.

Comparing the CloudSat–CALIPSO observations with ERA5 and the CMIP6 model mean, we generally observe that ERA5 and the CMIP6 models show a similar seasonal progression of fsLCC to that seen in the satellite observations. However, both ERA5 and the CMIP6 mean overestimate fsLCC to various extents during all seasons. The most significant discrepancy is observed during boreal spring, with area-weighted-averaged differences between CloudSat–CALIPSO and ERA5 and the CMIP6 model mean of -11% and -14%, respectively (Fig. f, j). Nevertheless, the spatial extent of areas with fsLCC amounts larger than 0% in CloudSat–CALIPSO is replicated well in ERA5 and the CMIP6 model mean (Fig. ). Although ERA5 and the CMIP6 models have remarkably similar spatial patterns of fsLCC, the CMIP6 model mean generally exhibits slightly larger area-weighted biases in the NH (6 %–14 %, Fig. i–l) than ERA5 (1 %–11 %, Fig. e–h) when compared to CloudSat–CALIPSO.

The fact that these discrepancies are about equally present in both ERA5 and the CMIP6 models provides valuable insights into their potential causes. They are most likely linked to the microphysical parameterizations of cloud processes that govern the cloud phase in ERA5 and CMIP6 models. It is reasonable to assume that the temperature in the ECMWF-AUX product used in CloudSat–CALIPSO is quite similar to the ERA5 daily mean as indicated by the seasonal mean 0°C isotherm in Figs.  and . However, ERA5 shows a slight variation in the 0°C isotherm line over central Europe during DJF compared to ECMWF-AUX (Fig. e). Furthermore, a comparison of the 2m temperature between ECMWF-AUX and ERA5 shows a latitudinal average difference of 0.24K±0.22K (Fig. ). Atmospheric circulation and overall cloud cover should be well constrained by the observations used in the ERA5 reanalysis. However, the cloud phase is not as evident in the identified biases. This finding will be discussed in greater depth in Sect. .

Unlike the NH mid-to-high latitudes, the SH does not experience significant seasonal variations in fsLCC, according to the CloudSat–CALIPSO observations (Fig. a–d). The fsLCC remains relatively constant across all seasons and is the highest in a band bounded by the Antarctic continent in the south and approximately the 60° parallel in the north, with values between 17 %–24 %. However, the area-weighted averages of fsLCC in the SH are generally higher than in the NH. The relatively constant fsLCC indicates that a more persistent cloud regime exists in the SH, with extensive sLCC cover present all year round. This is consistent with the previous literature reporting that the Southern Ocean is the region of the world with the most extensive mixed-phase cloud cover .

Like the GRIS, the Antarctic ice sheet has a low fsLCC amount, with the lowest frequency in austral winter (JJA; ≤15%). With its high elevations, the East Antarctic Ice Sheet exhibits a lower fsLCC amount than the flatter West Antarctic Ice Sheet during austral summer (DJF), autumn (MAM), and spring (SON). Just like the NH, the SH shows a reduced area of the fsLCC in austral summer (Fig. c) but with a larger extent towards lower latitudes (NH: > 70° N; SH: > 60° S). In all seasons, fsLCC activities are observed primarily southward of the Antarctic Circumpolar Current, which may be due to the presence of warm water that results in surface temperatures above the sLCC threshold (Fig. a–d).

In ERA5 and the CMIP6 model mean, there is a prominent gradient of sLCCs between the Southern Ocean and the Antarctic ice sheet, with fsLCC of up to 100% over the Southern Ocean and < 15 % over the Antarctic ice sheet. For the SH spatial mean, ERA5 and the CMIP6 model mean moderately overestimate fsLCC (1 %–8 %), with the CMIP6 model mean, in general, performing slightly better than ERA5 in comparison to CloudSat–CALIPSO (Fig. ).

The biases in ERA5 and the CMIP6 models regarding fsLCC, relative to CloudSat–CALIPSO, are further demonstrated through the area-weighted averages for each month in both hemispheres (Fig. ). For the area-weighted averages, we consider only the locations for which CloudSat–CALIPSO provided valid data (values between |45°–82°|). CMIP6 models generate a large spread of fsLCC, with both CloudSat–CALIPSO and ERA5 falling within the range of the model maximum and minimum values (green dots in Fig. ). Again, it is evident that ERA5 and the CMIP6 model mean have higher fsLCC than CloudSat–CALIPSO in the NH (Fig. a). The SH area-weighted averages show a better agreement between CloudSat–CALIPSO, ERA5, and the CMIP6 model mean than in the NH (Fig. b). The CMIP6 model mean underestimates fsLCC in comparison to CloudSat–CALIPSO during austral summer and autumn but overestimates during winter and spring, while ERA5 overestimates fsLCC to various degrees all year round in the SH.

Finally, to assess the model performance relative to CloudSat–CALIPSO for ERA5 and the individual CMIP6 models for fsLCC, we analyze the difference in the seasonal and spatial averages for each of the 11 models (Fig. ) for the NH and SH mid-to-high latitudes. The most significant discrepancy is seen in boreal winter and spring for AWI-ESM-1-1-LR, MPI-ESM1-2-LR, and IPSL-CM6A-LR with a negative difference > 15 % (Fig. a). In the NH, MPI-ESM1-2-LR is generally the model with the larger overestimation (> 15 %), despite a difference of < 10 % in boreal summer. IPSL-CM5A2-INCA has a low difference, < 5 %, in boreal summer, autumn, and winter. As previously highlighted, the difference values for fsLCC are lower in the SH (Fig. b), and none of the models stands out in terms of overall performance in either direction.

To assess the ability of ERA5 reanalysis and the CMIP6 models to represent snowfall processes, we compare the fsnow between them and the CloudSat–CALIPSO observations. Based on CloudSat–CALIPSO observations, NH sLCCs frequently produce snowfall, as can be seen by the non-zero values of fsnow in Fig. a–d. However, during boreal summer, the majority of sLCCs rarely produces snowfall, as shown by the relative increase in the areal extent of zero fsnow values (Fig. c). Notably, during boreal winter, spring, and autumn, the seasonal average fsnow is highest over open-ocean regions, such as the Greenland, Norwegian, and Barents seas (30 %–65 %), the Labrador Sea (40 %–80 %), and the Bering Sea (40 %–100 %; Fig. a, b, d). This is likely due to plentiful available moisture for snowfall to occur and is possibly linked to cold-air outbreaks CAOs;. CAOs arise when cold and dry air flows over warmer and moist sea surfaces. CAOs occur frequently in the North Atlantic in boreal winter and spring, and the clouds associated with them are predominantly sLCCs . While the influence of CAOs is also visible in the fsnow patterns across various seasons, with the exception of boreal summer, the fsnow values over land areas tend to be lower. Although it is possible that the higher minimum height bin of the radar used over land (∼1000m) may lead to the 2C-SNOW-PROFILE product missing some of the precipitation over land, the variability in the fsnow values in regions where similar cloud types are expected suggests that this land–sea contrast is likely a representative feature. This discrepancy can be attributed to the limited moisture content and shallower boundary layer over land during winter, resulting in lower fsnow compared to ocean areas where CAOs provide deeper moisture-rich clouds. Once clouds embedded in CAOs reach a certain distance from the sea ice, they frequently produce precipitation e.g.,. In contrast, during the winter months, northern Europe is often covered by non-precipitating supercooled stratus clouds . The models also show a lower fsnow over land, supporting the idea that the observed land–sea contrast is a genuine characteristic rather than an artifact of measurement techniques.

In contrast to the CloudSat–CALIPSO observations, both ERA5 and the CMIP6 model mean have much higher fsnow values (> 60 %), which are evenly distributed over the NH mid-to-high latitudes, without a significant seasonal variability. In regions where all three datasets have sLCCs, ERA5 and the CMIP6 model mean overestimate the fsnow by ∼50% (Fig. ). This indicates that ERA5 and the CMIP6 models produce snowfall much more frequently from sLCCs than observed. It is important to note that since fsnow accounts for the number of sLCCs, ERA5 and the CMIP6 models are too efficient at producing snowfall, regardless of the number of sLCCs that are simulated/assessed.

Regarding the SH mid-to-high latitudes, the CloudSat–CALIPSO observations show that there is no significant seasonal variation in fsnow, with spatially averaged values of ∼20% for all seasons (Fig. a–d). However, when comparing the results from ERA5 and the CMIP6 model mean with observations from CloudSat–CALIPSO, we find that similar to the NH, the simulated fsnow values are much higher than those observed (Fig. ). When only considering regions where CloudSat–CALIPSO observe fsnow (45–82° S), the area-weighted seasonal average of fsnow is approximately 60 %–70 % higher in ERA5 and the CMIP6 model mean (Fig. ). The high simulated values of fsnow in both the NH and SH indicate that ERA5 and the CMIP6 models produce snowfall far too frequently from sLCCs compared to the satellite observations. In fact, when sLCCs are present, snow is produced practically all of the time (between 70 % and 90 %). This bears resemblance to a well-established bias in ESMs, namely the persistent “perpetual drizzle” problem for warm liquid clouds .

To investigate the annual cycle of fsnow and the interannual variation between 2007 and 2010, we present the area-averaged data based on grid boxes in which CloudSat–CALIPSO is capable of making observations (|45°–82°|; Fig. ). CloudSat–CALIPSO displays a relatively clear seasonal cycle in fsnow in the NH but not in the SH. The difference in the fsnow between boreal summer months and the rest of the year in the NH is 15%, while the SH value is constant around 20% throughout the year. In contrast, ERA5 and the CMIP6 model mean display a more significant seasonal cycle, with a difference of 25% between boreal summer and winter months (Fig. a). Also, in the SH, there is more of a seasonal cycle evident for ERA5 and the CMIP6 model mean. Also worth noting is that ERA5 shows more pronounced interannual variability in both hemispheres of fsnow for a given month, meaning that the year-to-year fluctuations are larger than for CloudSat–CALIPSO and the CMIP6 model mean.

The comparison of the magnitude and model differences for fsnow in Fig.  indicates how well the individual ESMs represent the frequency of occurrence for snow and if the same models that perform well for fsLCC (Fig. ) do so for surface snowfall as well. Among the models, AWI-ESM-1-1-LR and MPI-ESM1-2-LR come closest to matching CloudSat–CALIPSO observations, but their fsnow values are still much too high (NH: ∼30%; SH: ∼45%; Fig. ). At the same time, IPSL-CM5A2-INCA deviates the most for fsnow in the NH and SH, having a negative difference of ∼65% and ∼75%, respectively. Interestingly, it appears that some models that perform well for fsLCC perform poorly for fsnow. This could be an indication that models that are able to simulate the right frequency of occurrence for sLCCs can do so because they are converting cloud condensate to snow too readily. In other words, the models may be getting the right answer for the wrong reason.

In the comparison by , the analysis was performed on a 6 h instantaneous model output to define the occurrence of LCCs in CESM-LE. As we compare ERA5 and CMIP6 models to CloudSat–CALIPSO, we only have daily means of LWP available. Thus, instead of four instantaneous values per day for a given model grid box, we use only one daily mean value of the LWP. In this way, we are comparing 30 daily values from ERA5 and CMIP6 models with thousands of CloudSat–CALIPSO profiles within each grid box to calculate fsLCC. Due to the 16 d repeat cycle of CloudSat–CALIPSO, we cannot perform the satellite analysis on a daily temporal resolution at the given spatial resolution of the models. While CMIP6 output is not available at a higher temporal resolution, for ERA5, we can actually test the sensitivity using an even higher time resolution than . We take the hourly outputs from ERA5 from July and November 2007 to 2010 and create monthly mean values. July and November are chosen as these are the months with the lowest and highest fsLCC in CloudSat–CALIPSO (Fig. a). We find that the fsLCC values emerging from ERA5 data are not very sensitive to the output frequency, as shown in Fig. d–e and i–j. The area-weighted difference between CloudSat–CALIPSO and ERA5 hourly values is negligible in July (1%) and ∼15% in the inner Arctic and reduces from 12% overestimation to 7% in November. However, the conclusion that ERA5 overestimates the fsLCC does not change by changing to a higher time resolution (Fig. ). While the sensitivity analysis for ERA5 data indicates that changes in output frequency do not significantly affect the results, the same conclusions cannot be directly extrapolated to CMIP6 models. However, based on our analysis, it is reasonable to assume that similar results could be observed for individual ESMs within CMIP6, although this cannot be confirmed.

conducted a similar analysis to that in this study by examining the frequency of Arctic LCCs and fsnow. They experimented with different LWP thresholds. Specifically, they used the 5 and 0.01gm-2 thresholds and based their LWP threshold of 5gm-2 on the approximate retrieval uncertainty in the LWP from ground-based microwave radiometer observations. We performed sensitivity tests in which we varied the threshold between 3, 5, 10, and 15gm-2 (Fig. ). While some of these values are unreasonably high, it is nevertheless useful to test how adjusting the LWP threshold value affects the identified bias between the observations and simulations. As expected, Figs.  and indicate that as the LWP threshold increases, the overestimation of fsLCC decreases in the NH and SH. However, unless we increase the LWP threshold in ERA5 and in the CMIP6 models to an unrealistically high value, the general findings and conclusions hold – ERA5 and the CMIP6 model mean still overestimate the occurrence of sLCCs in the study area in comparison to CloudSat–CALIPSO.

We find that ERA5 and CMIP6 overestimate the magnitude of fsLCC and fsnow in the mid-to-high latitudes of both hemispheres when compared to CloudSat–CALIPSO. In contrast, showed that the CESM-LE underestimates the fLCC by ∼17% and overestimates the fsnow by ∼57% in the Arctic. However, since we utilize a different metric (sLCC instead of LCC), there is no reason to expect the model biases to be identical. Nevertheless, in a further study by , it was shown that the LCC frequency in the newer CESM version is more aligned with the satellite observations, except for in the summer months, where it overestimates the LCC frequency.

Similarly, we generally observe that ERA5 and the CMIP6 mean overestimate the fsLCC to various extents during all seasons. These overestimations are likely linked to the microphysical parameterizations of cloud processes that govern the cloud phase. This finding aligns with , indicating that while newer model versions have advanced in representing LCC frequencies more accurately, they can still overestimate cloud occurrences, particularly in specific seasons. Precipitation in the new CESM version is more frequent but lighter overall compared to the previous version, which is similar to our findings, indicating that the models's sLCCs produce continuous snowfall, analogous to the “perpetual drizzle” problem .

Furthermore, while considered a single ESM, our study considers an ensemble of CMIP6 models. Nevertheless, the insights from provide a relevant context for our finding that ERA5 and the CMIP6 model mean produce sLCCs more frequently than observed in the NH and SH mid-to-high latitudes, especially over the sea ice and land, depending on the season (Figs.  and ). In these regions, not only is the frequency of occurrence of sLCCs too high, but the sLCCs are too efficient at producing snowfall in ERA5 and CMIP6 models (Figs.  and ). The latter finding is consistent with the findings of , who showed that LCCs produce snow too frequently in the CESM-LE model.

explained the overestimation of fsnow from LCC by exploring one potential microphysical pathway for removing supercooled cloud liquid – the WBF process. An overactive WBF process and the subsequent removal of cloud ice from the cloud through snow formation in ERA5 and CMIP6 models could also explain the large overestimation of fsLCC and fsnow in ERA5 and the CMIP6 model mean. ERA5 and the CMIP6 models may thus have more frequent but lighter snowfall events that lead to a higher fsnow, while maintaining the clouds for longer compared to the CloudSat–CALIPSO observations. However, for some ESMs, there is no explicit simulation of the WBF process but rather a simple temperature-dependent partitioning of cloud condensate into liquid and ice. For such crude parameterization schemes, the identified biases are inevitable, as clouds at a given mixed-phase temperature would always have some liquid present (hence a very high fsLCC) and at the same time always have ice available that could be converted to snow (hence a very high fsnow).

The difference in the simulated fsLCC and fsnow compared to CloudSat–CALIPSO in the NH and SH could, in theory, result from differences in surface conditions and/or weather patterns and thereby differences in moisture availability for the formation of sLCCs . However, the fact that very similar biases to those in the reanalysis are found in the CMIP6 models might suggest that surface conditions and weather patterns are not the main explanation for the identified biases. That being said, reanalysis products are known to be less reliable at high latitudes . We therefore cannot rule out differences in weather patterns as a partial cause of the biases discussed above but maintain that deficiencies in the model representation of cloud microphysics is the more likely culprit. The inclusion of both ERA5 and CMIP6 models in this analysis is thus beneficial as it helps highlight potential root causes of the identified biases, although it should be noted that individual CMIP6 models do not all show biases that match ERA5 (Figs.  and ). As stated above, we cannot entirely rule out a modest contribution to the biases from circulation differences, even for the reanalysis. For example, according to , all reanalysis products show lower precipitation amounts in the southern Ross Sea and Weddell Sea embayments near the ice shelves. They explain that this is due to persistent cold and dry katabatic wind blowing from the continent across the ice shelves and out over the sea ice, which is not beneficial for precipitation formation and not captured well by the reanalyses.

Under the assumption that the overall weather patterns and surface conditions are accurate in ERA5, the most plausible root causes of the biases in fsLCC and fsnow are linked to the microphysical parameterizations in the reanalysis and ESMs .

suggest that the difference in temperature and temperature threshold among various reanalysis microphysical products may explain the latitudinal inequality in the snowfall amount observed between CloudSat and the reanalysis products. But, here, no strong latitudinal dependence is observed in Fig.  as we investigate fsnow instead of the snowfall amount. The same principle should apply to ERA5 and the CMIP6 models as they rely on microphysical parameterizations. For the most part, the 0°C isotherm shown in Figs.  and supports our argument that the primary issue with the ERA5 and CMIP6 datasets lies not with the simulated temperature itself but with the representation of cloud properties and microphysics. This distinction highlights that the observed deviations in fsLCC and fsnow are driven more by inaccuracies in cloud simulation than by temperature discrepancies. Exceptions occur over central Europe during DJF between ECMWF-AUX, ERA5, and the CMIP6 ensemble mean (Fig. a, e, i). However, more notable is the difference in the CMIP6 ensemble mean over the central Arctic during summer (Fig. k), where simulated temperatures appear to be too cold. In this specific case, the cloud bias could stem from a temperature bias, suggesting a potential link between temperature inaccuracies and cloud simulation in the CMIP6 ensemble mean for this region and season. Figures  and show some models performing better than others for fsLCC and fsnow in comparison to CloudSat–CALIPSO. As discussed above, many models have a simple temperature-dependent cloud phase that would almost certainly cause them to overestimate the fsLCC and fsnow. A follow-up study will investigate the SLF by isotherms for mixed-phase clouds of several CMIP6 models. Figure  shows that some of the CMIP6 models have a more variable SLF in time and space (e.g., AWI-ESM-1-1-LR and MPI-ESM1-2-LR), which might be an indication that they could have more sophisticated microphysics and could, therefore, perform better in terms of sLCC and surface snowfall occurrence. However, it is not immediately clear which models use a purely temperature-dependent cloud-phase partitioning. From the interquartile range (IQR; Fig. ) CNRM-CM6-1, CNRM-ESM2-1, and IPSL-CM6A-LR are assumed to have a simple temperature-dependent cloud phase due to the smaller IQR of the temperature at various SLF. It is interesting to note that these models with the simpler temperature-dependent schemes are the most poorly performing models for fsnow (Fig. ).

studied the effect of changing the microphysical parameterization scheme from the traditional diagnostic scheme used in MIROC6, and participating in CMIP6, to a prognostic scheme. They found that the prognostic scheme improved cloud coverage and snowfall in the Arctic. In our study, MIROC6 is one of the models with the largest overestimation of fsLCC in the SH and the model with the smallest difference in boreal spring (Fig. ). Furthermore, MIROC6, with the diagnostic scheme used here, has a large negative difference in fsnow (45 %–60 %) that is independent of hemisphere and season (Fig. ). However, the MIROC6 with the prognostic parameterization scheme in produced light snowfall too frequently, which is in agreement with the results presented here, despite the use of a different microphysical scheme.

ERA5 and the CMIP6 model mean are not able to reproduce fsnow in comparison to CloudSat–CALIPSO. The overestimation in ERA5 could be related to the global average wet bias of up to 0.27mmd−1 in the ECMWF product used in ERA5 . If the modeled sLCCs are practically always snowing, then the sLCCs should have a shorter lifetime and subsequently have a lower fsLCC than observations suggest. However, ERA5 and the CMIP6 model mean seem to have sLCCs that produce a little bit of snow all the time and, at the same time, maintain the sLCCs in the atmosphere. This bias may be the sLCC's counterpart to the “perpetual drizzle problem” that has been identified in ESMs for warm liquid clouds .

An overestimation of the snowfall frequency can have significant effects on the Earth's radiative budget. The fact that the models seem to snow a little bit all the time instead of producing occasional heavy snowfall events, as well as periods with no snowfall, is therefore concerning. One implication is that fresh snow will be deposited too frequently on top of the snowpack, ice sheets, sea ice, and land surfaces, with consequences for the surface albedo. With time, the aging snow surfaces darken due to snow/ice metamorphism processes and the deposition of absorbing aerosols e.g.,. Continuous light snowfall in the model could thus lead to a simulated overestimation of the surface brightness, which in turn could limit sea ice melt in ESMs. Indeed, only ESMs that simulate excessive Arctic warming are able to reproduce the observed sea ice loss in recent decades .

The overestimations of fsLCC and fsnow could stem from how models handle cloud microphysical processes, particularly the WBF process and the partitioning of cloud condensates into the liquid and ice phases. Some identified biases in ESMs may be due to the specific parameterization schemes used in the models, which could rely on simple temperature-dependent cloud-phase partitioning. For example, models with a temperature-dependent cloud phase could simulate a fixed liquid fraction at a given temperature within the mixed-phase range, making it impossible for them to simulate an all-ice or all-liquid cloud in that range. Consequently, these models could tend to under- or overestimate the occurrence of sLCCs.

Interestingly, models with more sophisticated microphysics schemes (Figs.  and ) do not necessarily perform better (Figs.  and ). Larger biases in cloud phase can still occur, for example, if these models do not accurately represent INPs. This underscores how generational advancements and implementations of observational constraints can significantly influence the comparison and interpretation of cloud and precipitation patterns.

Continuing work should be performed on the comparison between ESMs, reanalysis, and observations at specific locations to better understand microphysical processes and their representation in ESMs and reanalysis data. Cloud microphysical scheme development should, therefore, focus on improving these processes in order to reduce cloud-phase and surface snowfall biases. More sophisticated schemes should be explored, and ensemble studies with varied microphysical model parameterizations can provide insights into how different parameterizations affect the representation of sLCCs and snowfall in climate simulations.

Ground and aircraft observations in connection with field campaigns at specific locations should, therefore, be increased, especially to improve our understanding of cloud phase, liquid and ice water content, and cloud-top temperatures in regions where sLCCs form. These field campaigns should also focus on the processes responsible for snowfall from these clouds.

Finally, as shown in the present study, satellite observations are an essential validation tool for assessing the representations of clouds and precipitation in ESMs. To ensure that future model generations are as accurate as possible, continuous improvements to satellite retrievals are required to further refine our understanding of cloud and snowfall properties, especially in high-latitude regions where limitations in the Sun angle and ground track are prevalent. The accurate representation of these cloud and snowfall processes in models, validated through enhanced satellite observations, is essential for reliable simulations of weather and climate. This accuracy is particularly important for making future predictions of the hydrological cycle, which are essential for understanding and mitigating the impacts of climate change.