Climatology of sea‐effect snow in Finland

Convective sea‐effect snowfall, in the form of snowbands, is observed over the northern Baltic Sea annually. Quasi‐stationary snowbands may last up to several days over the sea and, depending on the wind direction, move towards the coast. This study provides climatology of spatial and temporal occurrence of snowbands in Finland for a 48‐year period (1973–2020). We used a set of detection criteria together with ERA5 reanalysis at off‐shore areas and FMIClimGrid gridded observational data for on‐shore areas to find the days favouring snowband formation. Only those snowband days (SBD) when snow reached the Finnish coastal mainland were considered. The total annual number of SBDs in Finland varied from 6 to 40 with an average of 16. SBDs were detected most frequently over the Gulf of Bothnia near the western coast of the country. The largest increase in snow depth (SDI) during an SBD (67 cm/day) also took place on the western coast, although the long‐term mean of SDI (3–5 cm/day) was highest over the southern coast. Throughout the country, November and December showed the highest frequency of SBDs. However, between the periods 1973–1996 and 1997–2020, the seasonal cycle of SBDs shifted 1 month forward from late autumn to mid‐winter as the decrease in the number of SBDs during December as well as the increase during January and February were statistically significant in Finland. In northern Baltic Sea, long‐term increases in monthly means of sea surface temperature (SST) and air temperature at the atmospheric level of 850 hPa (T850) were in line with the decadal changes in the occurrence of SBDs. The increasing trend in SST favours the formation of snowbands but in late autumn the probability for snowband formation decreased because even larger increases in T850 resulted in diminishing differences between SST and T850.


| INTRODUCTION
Sea-effect snowfall is convective precipitation triggered by cold air moving over warm bodies of water. Snowfall associated with convective bands can be considerable, but the affected downwind area may remain narrow, ranging from a few to 50 km in width. Therefore, snowbands can unexpectedly change the local weather situation. Depending on the wind direction, excess sea-effect snowfall may hit the shores of the Baltic Sea, as experienced in Merikarvia in Finland in January 2016 (73 cm of new snow, Olsson et al., 2017Olsson et al., , 2018, Danish island of Bornholm in December 2010 (150 cm) and in Gävle andOskarshamn in Sweden in December 1998 (130 cm, Jeworrek et al., 2017;SMHI, 2013) and January 1985 (90 cm, Andersson and Nilsson, 1990;SMHI, 2013), respectively.
Snow is no stranger to Finland during wintertime. Although Finnish society has learned to cope with cold weather and snow, persistent snowfall and massive snow loads can hamper the traffic and cause damage to hall roofs and power lines. Snowy winters can affect problems for snow removal logistics as the places to dump the snow might run out near residential districts (Keskinen, 2012), as happened, for example, in the current winter in Finland (YLE, 2022. Low road surface friction together with poor visibility due to snowfall increases the accident risk especially in areas with large traffic amounts (Juga, 2010). Several hundred vehicles were involved in the crashes in the Helsinki metropolitan area during snowband episodes in January 2006, February 2007 (5-10 cm/day of snow, Juga, 2010) and February 2012 (5-10 cm/day of snow, Juga et al., 2014). More recently, several traffic accidents occurred when heavy snowbands hit the west coast of Finland on the 24-25 December 2021. The largest amount of snow, 41 cm (27.8 mm as liquid), fell on the 24th of December in Vaasa and on the 25th of December in Turku, 20 cm (13 mm).
The most important forcing mechanism to inflate convective snowfall is the vertical temperature difference between ice-free sea surface and overlaying air mass (Niziol, 1987). The larger the temperature difference the larger the surface heat and moisture fluxes from the sea into the atmosphere. Without the surface fluxes, convergence of air streams and organized precipitation fail to develop (Norris et al., 2013). Vertical temperature difference between sea surface and 850 hPa atmospheric level should exceed 13 C, roughly corresponding the dry adiabatic lapse rate (9.8 C/km), to destabilize the cold air mass and to develop sea-effect convection (Markowski and Richardson, 2010). Other forcing mechanisms resulting in large surface heat fluxes are strong winds that is, ambient wind speed over 10 m/s (dynamical forcing), and in case of calm winds large sea-land temperature difference causing land breeze (diabatic forcing) (Laird and Kristovich, 2004). In addition, Suursaar and Meitern (2021) brought forth the enhancing effect of winter upwelling in the Gulf of Finland to sea-effect snow. Winter upwelling can locally increase the ice-free fetch and the SST, and consequently, contribute to atmospheric instability by increasing the vertical temperature difference (Suursaar and Meitern, 2021).
Furthermore, frictional convergence and forced lifting, caused by the differences in roughness between land and sea, can initiate or intensify onshore convection (Andersson and Nilsson, 1990). The effect of orographic lifting and coastal convergence depends on wind direction and the spatial differences are large. Although Finnish coast is only gently sloping, sea-effect precipitation is intensified by orographic lifting especially in southern coast of Finland (Solantie and Pirinen, 2006).
Usually, the snowfall reaches only 20 km inland as cold land does not provide the necessary surface fluxes to sustain snowbands (Andersson and Nilsson, 1990). A concave shape of the coastline with offshore winds has a profound effect in generating convergence lines (Mazon et al., 2015). Orography and friction differences between land and sea affect the location, timing and morphology of the precipitation but not the occurrence of snowbands (Norris et al., 2013). The processes affecting the formation of snowbands are complex including composites of wind speed and direction, open water area, horizontal and vertical temperature differences and shape of the coastline which makes it computationally expensive to study when long time series are considered.
Climate models to be able to resolve convective snowband cells should have a high horizontal resolution, 5 km or less. Given the small scale of these phenomena, forecasting the location, timing and intensity of sea-effect snow is still challenging even for convection permitting weather forecast models (Fujisaki-Manome et al., 2022). Especially, heavy precipitation in output data of coarse (resolution typically > 25 km) climate models or reanalysis tend to be underestimated (Médus et al., 2022). Instead, the favourable synoptic conditions and known characteristics associated with these convective phenomena can be detected also based on coarser data. When a set of propitious conditions to produce sea-effect snowfall is met the day can be regarded as favourable for snowband formation. Criteria for seven atmospheric variables have been previously shown to be able to detect the days favouring snowbands along the Swedish east coast (Jeworrek et al., 2017) and on Finnish coastal areas  with regional climate model data.
Many case studies of snowbands in Finland have been performed (Juga, 2010;Niemelä, 2012;Savijärvi, 2012;Juga et al., 2014;Mazon et al., 2015;Olsson et al., 2017Olsson et al., , 2018 but long-term statistics of past events do not exist for Finland. Statistics of a short time period (years 2000-2010) have been studied in Finland  and the east coast of Sweden (Jeworrek et al., 2017). In these studies, the mean annual number of days favouring snowband formation was 3 and 11, respectively. Nevertheless, due to the large interannual and decadal climate variations the 11-year period is too short for climatological purposes.
Climatology of extreme snowfall cases (>20 cm/2 day) on the Polish Baltic Sea coast for 1981-2020 revealed that most of those cases resulted from sea-effect snowfall (Bednorz et al., 2022). In addition, occurrence of atmospheric parameters favouring snowband formation in the east coast of Sweden have been studied from 1970 to 2099 with the aid of a coupled regional atmosphere-ice-ocean model RCA4-NEMO (Dieterich et al., 2020). Their preliminary results suggested that due to increasing air temperature, the number of snowband days will decrease, and the seasonal maximum of snowband occurrence will shift from November to December and January. Because Dieterich et al. (2020) included only northerly to easterly winds, their results for the future are not straight applicable to Finland (due to its coastline facing an opposite direction compared to that of Sweden) but they give good guidelines on what could be expected in the future. Overall, little is known about potential changes of snowband events in the Baltic Sea during the past and upcoming decades .
We used ERA5 reanalysis to study the climatology of sea-effect snowfall along the Finnish coastline for 1973-2020. The main objective of the current work was to study the spatial frequency of the sea-effect snow and to find the onshore regions most affected by them. The detection of sea-effect snow (Section 2.3) was done by utilizing the same thresholds as tested previously by Olsson et al. (2020). Our previous case studies have suggested that the frequency and spatial distribution of the seaeffect snow over the Finnish sea areas can be studied with the aid of ERA5 but the accumulated snowfall over land remained too low in comparison to observations (Olsson et al., 2018). Thus, the favourable days were detected using ERA5 data over sea areas (Section 2.1) but the daily snowfall accumulation over land, approximated by the snow depth change between two subsequent days, was studied from observations (FMIClimGrid, Section 2.2). Only days when snow fell over the Finnish coastal mainland were considered. The main results show the spatial and temporal statistics of the occurrence of the snowbands (Sections 3.1 and 3.3) as well as the daily snow depth increase in different areas (Section 3.2). Finally, we examine the distinct features behind the detected snowband days (Section 3.4) and explore longterm changes in air and sea temperature to understand how they might affect the seasonal cycle of the snowband occurrence (Section 3.5) during the 48-year study period.

| DATA AND METHODS
ERA5 reanalysis (Section 2.1) and FMIClimGrid gridded observational data (Section 2.2) were used together to assess the spatiotemporal characteristics of the snowbands in Finland. Days favouring the snowband formation on surrounding sea-areas of the country ( Figure 1) were detected from ERA5 reanalysis for 1973-2020. To consider a day to be favourable for snowband formation, seven criteria for meteorological variables in ERA5 had to be fulfilled. Thereafter, a final, the eight criterion was applied to daily snow depth in FMIClimGrid (Section 2.3).
In addition to these data sets, specialist assessments were used to narrate typical synoptic weather situations during snowband days in Finland (Section 3.4). Moreover, weather radar images were used to present the example cases (Section 3.4) and to check some detected events with large snow accumulation or early autumn or late spring occurrence. FMI's radar composite figures are available from 1998 and with better quality from September 2006 onwards.

| ERA5
ERA5 is the fifth generation of the European Centre for Medium-Range Weather Forecast (ECMWF) atmospheric reanalysis of the global climate and weather . ERA5 data is available from 1950 onwards near real time.
Reanalysis combines model data with observations from across the world into a globally complete and consistent dataset providing a best estimate of the state of the atmosphere. The improvement of reanalysis products compared to traditional observational data comes with the continuous data coverage over sea and land areas as well as up to atmospheric levels.
ERA5 provides hourly estimates of atmospheric and surface parameters necessary for sea-effect snowfall analysis. These are air temperature at 850 hPa level (T850), wind direction at pressure levels 975 hPa, 900 hPa and 700 hPa, 10 m wind speed, sea surface temperature (SST), precipitation amount and type, and boundary layer height (BLH), all at a resolution of about 31 km (0.25 ) worldwide. Hourly data on pressure levels (Hersbach et al., 2018a;Bell et al., 2020a) and on single levels (Hersbach et al., 2018b;Bell et al., 2020b) from 1973 to 2020 was downloaded from the Climate Data Store (CDS, cds.climate.copernicus.eu).
Daily SST is a crucial variable for sea-effect snowfall studies. We found that for the northern Baltic Sea, only climatological seasonal variation was available in ERA5 until 1972. Thus, the selected time period for this study could be extended to start only from the year 1973.

| FMIClimGrid
The FMIClimGrid is a daily gridded climate dataset based on weather observations at meteorological stations in Finland and the neighbouring countries (i.e., Sweden, Norway, Russia and Estonia) (Aalto et al., 2016). It covers land areas in Finland for 1961-2020 with spatial resolution of 10 km. The dataset consists of 10 climate variables from which daily snow depth was used here to study the accumulation of snow on the land areas. FMIClimGrid includes also daily precipitation data, but it was not utilized because it does not contain information of the form of the precipitation.
A kriging interpolation method was used for the gridding procedure (Matheron, 1963;Goovaerts, 1999). The effects of the geographical location of the weather stations, topography and water bodies (sea-and lakeeffects) were considered in the interpolation routine used by Aalto et al. (2016). The uncertainties in the dataset were related to spatiotemporal inconsistencies in the station network, the incomplete sample of background data used as external predictors, inhomogeneity in the observation data and the sensitivity of the interpolation model parameters. The gridded dataset may not catch all the small variations and thus the largest snow accumulations may be smoothed compared to station observations.

| Sea-effect snow detection
We were only interested in days when snowbands reached the Finnish mainland as these are the events that can cause problems to the Finnish society. Thus, Finland's shoreline was separated into five regions (S, SW, W, NW and N) according to the direction the shore is facing (Figure 1). The favourable wind directions to bring snowfall onshore in these areas are listed below. When the whole Finnish coastline from S to N is addressed, an abbreviation FI is used. The five regions vary in surface-area and thus the number of detected seaeffect snowfall days is not comparable between regions.
Altogether, eight criteria were used to detect snowband days in Finland. The seven criteria applied to ERA5 to detect days favouring sea-effect snowfall formation in offshore areas ( Figure 1). Similar criteria have been previously utilized by Jeworrek et al. (2017) and Olsson et al. (2020).
• difference between sea surface temperature (SST) and air temperature at 850 hPa (T850) larger than 13 C, • SST above 0 C, • boundary layer height (BLH) over 1,000 m, • daily snowfall amount at least 1.5 mm (water equivalent), • 10 m wind speed stronger than 7 m/s, • wind shear between 700 hPa and 975 hPa less than 60 and • wind direction at 900 hPa towards the Finnish coast (depending on study area, discussed below). The ranges for wind direction were South ( Because we were interested only in cases when the snow fell over land areas, the detected days favouring sea-effect snowfall were checked from FMIClimGrid data which led to the final and eighth criterion: • daily accumulated snow depth had to increase at least 2 cm over land somewhere on an onshore study area ( Figure 1).
The daily snow increase criterion for gridded data was selected to discard the lightest snowfall cases but still be high enough to include known snowband episodes with approximately 5 cm/day snow accumulation (based on station gauge measurements).
Days when all these criteria were fulfilled somewhere in the study area are called snowband days (SBD) hereafter.

| Analysing Sea-effect snow variables
The definitions of the analysed variables are as follows: • Snowband day (SBD) is a day fulfilling all eight criteria of the sea-effect snow detection method (Section 2.3). • SBD season is the time of year (from September to May) when SBD was detected. SBD season can vary in the five regions. • Snow depth increase (SDI, cm/day) is the accumulated snow depth during a detected SBD, calculated from the difference between the day in question and the next day in gridded observational FMIClimGrid snow depth data. • Daily maximum SDI (SDImax) is the maximum SDI somewhere in an onshore study region ( Figure 1) during a detected SBD. • Monthly mean of SDImax is the mean calculated from values of SDImax in an onshore study region ( Figure 1). • A snowband episode (SBE) was calculated from consecutive SBDs. This was done separately for five regions as well as for the whole FI. In FI, consecutive days were accumulated if snowbands were detected from at least one of the five regions. Detected snowbands could occur, for example, in NW in 1 day, in NW and W in the following day, and in SW the day after that. In that case, the length of SBE would be 3 days in FI, 2 days NW and 1 day in W and SW.
Mann-Kendall rank correlation and its p-value on a two-sided test were used to find out if the positive or negative correlation with time was statistically significant (p < .05). It was also used to find out if there was any correlation between SDImax and variables used in the SBD detection method.
To study the possible changes in SBDs and SDImax, the time period was analysed over two shorter periods (1973-1996 and 1997-2020). The significance (p < .05) of the change between the periods was assessed for the winter period (September to May) and each month separately using one-sided Mann-Whitney-test.

| Snowband days
Snowband days (SBDs) were detected every year in 1973-2020 in FI but their frequency varied distinctly from year to year and between different areas. The total annual number of SBDs in FI varied from 6 to 40 with a 48-year average of 16 days (Table 1). The SBDs were most frequent in the W with on average 7 days per year. In S, SW and NW, the mean annual number of SBDs was five and in N, one.
As snowbands are typically narrow, the related snowfall does not necessarily cover the whole study area during a single detected SBDs and thus, there were distinct differences in the spatial distribution also inside the study areas. In W, the most active area was located off the western coast of Finland, over the sea-area in front of Rauma ( Figure 1). This area received, on average, at least three SBDs annually. In SW, the most active area was located further away to the open sea southwest of the coastline with at least two SBDs annually. In S, NW and N areas, the favourable conditions were distributed more evenly along the sea-areas and no location stood out with a distinctly higher frequency.
The temporal change in the annual number of SBDs along FI was not statistically significant during the period 1973-2020, although there seemed to have been a decreasing rather than an increasing tendency (not shown). The same applies also to five separate regions.
The most favourable months to produce sea-effect snowfall in FI were November (in N and NW, Figure 2, Figure S1) and December (in W, SW and S). That said, the number of SBDs in November and December decreased in FI from 1973-1996 to 1997-2020 (statistically significant during December). In contrast, the number of SBDs in January and February increased at a statistically significant level in FI.
In northern areas, N and NW, the SBDs occurred mostly on the autumn side of the year, the maximum occurring in November ( Figure 2). But during 1997-2020, the mid-winter has become more important as SBD decreased statistically significantly in November in both areas. Simultaneously, SBDs increased during February (statistically significant) in NW.
Also in W, the number of SBDs decreased during the most active month, December (significant), and had an increasing tendency during January to March (not significant). Thus, the annual cycle appears to have changed in W as January has taken the place as the most active month to produce SBDs during 1997-2020 ( Figure 2). In S the changes were not so clear, the monthly number of SBDs decreased in December (significant) and increased in February (significant) but the seasonal cycle remained the same from 1973-1996 to 1997-2020. In SW, no statistically significant changes were detected.
The seasonal cycle for the SBDs remained the same in FI with the maximum occurring during December.
Nevertheless, the decrease during December and increase during January and February shifted the focus more towards mid-winter from late autumn. Seasonal cycle for monthly maximum of SBDs shifted 1 month further in winter in NW and W, but remained the same in N, SW and S. Overall, the increase during the spring side of the winter was smaller than the decrease in the number of SBDs in autumn.

| Daily snow depth increase
The long-term mean of the daily snow depth increase (SDI) during the SBDs, as calculated from the FMIClim-Grid separately for each onshore study region, varied from 2-3 cm/day in NW to 3-5 cm/day in S (Figure 3). Although the annual number of SBDs was largest in W ( Figure 1 and Table 1), the daily mean SDI was smaller there than in S. The detection criteria were applied to each study region, ignoring the fact that distinct snowbands or largescale snowfall may have occurred also elsewhere during the same day. For example, when snowbands were detected in N, snow accumulated also in SW and S (Figure 3). This may be explained by the fact that lowpressure areas with large scale precipitation are typically brought to Finland by southerly and southwesterly winds. However, in case of snowbands in S, intense snowfall was unlikely in other regions (see Section 3.4). During SBDs in SW the most intensive snowfall tended to drift ashore in S (Figures 3 and 4) instead of SW. Figure 4 shows the spatial distribution of days with at least 10 cm/day SDI during the detected SBDs in 1973-2020. SDIs of at least 10 cm/day were detected most frequently in S where almost the whole coastline has experienced such large SDI on more than ten SBDs. Hot spots included a small area near Merikarvia in W and area district east of SW (in S) where SDI exceeded 10 cm/day during 15 days and over 20 days, respectively. In S, NW and N, SDI exceeded 10 cm/day most often in November and December and in SW and W in December and January (not shown). This goes well along with the seasonal cycle of SBDs in these areas (Figure 2) as also the maximum frequency of SBDs occurred in the same months. We also studied the difference between the periods 1973-1996 and 1997-2020 for mean (Figure 3) or days exceeding 10 cm/day SDI ( Figure 4) and generally found no clear signals of change (not shown).
Our finding that the daily mean SDI (Figure 3) and the number of days with at least 10 cm/day SDI (Figure 4) are largest in S, may be explained by Figure 5a which shows that the share of SBDs with large SDI is greater in S than in the other areas. SBDs with excessive SDI (≥20 cm/day) were not an annual event in separate regions, but they still occasionally occurred in all areas, most often in S (Figure 5b-f), during November and December (not shown). Also in W, NW and N, most of these events occurred during November and December and in SW during December and January.
The largest SDI varied from 25 to 67 cm/day during the SBDs (Table 1, Figure 5b-f). The maximum and the second highest SDI, based on the gridded data set, have occurred in W. In S the maximum SDI was 35 cm/day, in SW 36 cm/day, in NW 31 cm/day and in N 25 cm/day.
Among the five regions, the highest annual value of the SDImax occurred most often in S with the largest SDI during 35% of winters. W reached almost the same with 31% of winters. Altogether, the monthly mean of SDImax was largest in S (>8 cm/day).
The interannual and annual variation in SDImax were large and no clear changes from 1973-1996 to 1997-2020 were generally found. No distinct differences F I G U R E 3 Observed daily mean snow depth increase (cm/day) onshore during the detected snowband days of the period 1973-2020 according to FMIClimGrid. The onshore study regions corresponding to the offshore study regions in Figure 1  between calendar months were found for monthly mean SDImax in November to March ( Figure 6). In September, April and May only scant SBDs occurred (totally 16 days in FI during 1973-2020), but in such cases in April or May more than 6 cm of snow was typically accumulated. There were slight indications of decreasing tendency of SDI during November and December and increasing tendency from January to April in FI, but only in February was the increase statistically significant (Figure 6). In separate regions, SDImax in December decreased statistically significantly (p = .01) in N and SW alone.

| Temporal duration
To study the temporal characteristics of the SBDs the days were grouped into snowband episodes (SBE) according to their duration on consecutive days. In FI, consecutive days were accumulated if snowbands were detected from at least one of the five regions. Duration of SBEs ranged from 1 day to even 9 consecutive days in FI (Table 2). Typically, snowbands lasted only 1 day (or less in practice, see Section 3.4). These short lived 1-day snowbands corresponded to 60% of all SBEs in FI. 2-day SBEs corresponded 25%, 3-day SBEs 7% and 4-day SBEs 4% of all SBEs. SBEs lasting 5-9 days, altogether, corresponded only 4% of all SBEs. All 5-day to 9-day SBEs were detected between November and January. The longest 9-day SBE was detected during December 1996 in SW, W and NW.

| Typical atmospheric conditions
Typical atmospheric conditions associated with the detected SBDs were studied. The mean of the daily maximum vertical temperature difference, calculated from hourly values, between sea surface and the 850 hPa level in the atmosphere varied from 15.5 C in N to 17.1 C in NW (Table 3). The mean of the maximum SST during SBDs varied from 3.9 C in W to 4.8 C in S. The mean of the minimum daily T850 varied between −13.1 C in NW and −11.6 C in N. The mean of the maximum BLH varied from 1,250 m in N to 1,430 m in NW. The relatively low resolution of ERA5 smooths out the most extreme values and the results should thus be considered with caution.
The medians of the wind direction and 10 m wind speed during the SBDs were studied instead of the maximum or the mean because the wind fields might vary considerably for 1 day. On average, the median 10 m wind speed was slightly above 10 m/s (Table 3) with a maximum of medians below 20 m/s in all areas. The median wind direction in N was southwesterly (217 ), in NW and W northwesterly (334 and 294 , respectively), in SW southerly (194 ) and in S southeasterly (158 ).
Kendall rank correlation and its p-value on a two-sided test was used to find out if there was any correlation between daily maximum SDI and variables presented above in Table 3. Only in S was the daily maximum SDI positively correlated with BLH (p = .02) and 10 m wind speed (p = .04). Otherwise, the variability of daily maximum SDI was so large that no clear correlation with other variables could be found. In the five regions, the daily maximum SDI remained below 10 cm/day during 69-83% of the detected SBDs (Table 1) and these SDI values could occur in many kinds of atmospheric conditions that still fulfilled the criteria presented in Section 2.3.
Examples of synoptic weather situations and weather radar maps during SBDs in the five different Finnish coastal areas are shown in Figures 7 and 8, respectively. The examples, selected by an operational meteorologist, represent relatively recent past, which enables us to present similar weather maps and weather radar images for all five episodes. Weather situations favouring snowband formation in these episodes as well as different regions in Finland are described below: 1. NORTH, NORTHWEST, WEST, SOUTHWEST: A strong low-pressure area moving over Northern Scandinavia to the east and a cold air outbreak from the northwest arrives in Finland (Figure 7a,b, Figure S2). In this situation, stronger snow showers will develop over the Gulf of Bothnia and move towards the southeast. Usually, the event does not last very long (less than 6 hr), because the centre of low pressure normally will move further east, and the wind direction veers to the north so the snow showers will stay over the sea. However, in the northwestern part (if no sea ice) and in the Åland Island (see Figure 1) snow showers can last longer. 2. WEST, SOUTHWEST, SOUTH: A very cold air mass and a weak low-pressure area over Finland. In this situation a minor low can arrive from the northwest (Norwegian Sea) to the Gulf of Bothnia and move slowly along sea areas to the Gulf of Finland (Figure 7c, Figure S2). This could lead to a rather large area of snow showers, which moves from the west coast to southwestern parts of Finland and further to the south coast. Snowfall could last from 6 to 12 hr and its intensity can be very strong (more than 2 mm/h, measured in liquid precipitation). 3. NORTH, SOUTHWEST, SOUTH: A cold air mass and a high-pressure area over the Baltics and Russia. In this situation, a centre of low pressure arrives from the west to Scandinavia and strengthens the southerly winds (Figure 7d, Figure S2). Cold air from the Baltics moves over the relatively warm Baltic Sea forming snow showers. If the high pressure is strong enough, the snowbands can last long over the same area. Usually, the event does not last very long because warmer air masses arrive from the west. 4. SOUTH: Cold air mass and a strong high pressure reaching to northern Finland from Russia and a low pressure is over the southern Baltic Sea (Figure 7e, Figure S2). Cold easterly to southeasterly flow over southern Finland and snow shower bands developing over the Gulf of Finland. At times, these snowbands Did the atmospheric values in these example cases hit the ranges given in Table 3? The 10 m wind speed in N (Figures 7a and 8a) and BLH in NW (Figures 7b and  8b) were slightly lower compared to Table 3. In W (Figures 7c and 8c), the minimum T850 was colder and the temperature difference larger than the mean range. In addition, the median wind direction and shear deviated from the given range. In SW (Figures 7d and  8d), the SST was colder and wind speed lower than the mean range. In S (Figures 7e and 8e), T850 was colder, temperature difference larger, BLH higher and wind direction slightly more easterly compared to the ranges in Table 3. Otherwise, the values were inside the mean ranges.

| Long-term changes in temperature variables
Temperatures in Finland are expected to rise with a larger increase during winter than summer (Ruosteenoja et al., 2016;Ruosteenoja and Jylhä, 2021). The difference between SST and air temperature at 850 hPa level (T850) is one of the main drivers to generate sea-effect snowfall. The larger the temperature difference the larger the possibility for snowband formation (Norris et al., 2013). The number of SBDs had a decreasing tendency in September-December and an increasing tendency in January-May in Finland (Figure 2). When trying to find out why this happened the most obvious variable to study was the vertical temperature difference. Instead of focusing only on the detected SBDs for which, by definition, the difference exceeds 13 C, monthly mean values of SST and T850 over the sea, together with their difference, were studied to address this question.
Increases in monthly mean SST from 1973SST from -1996SST from to 1997SST from -2020 (Figure 9a) ranged in FI from 0.3 C to 1.5 C with the largest increase in September and October (p < .05 in all months). Also, monthly mean T850 increased by 0.3 C to 2.0 C with the largest and statistically significant (p ≤ .02) increase in September, November and December. As a result, the monthly mean vertical temperature difference decreased statistically significantly in November-December (Figure 9b). In midwinter, from January to March, no distinct changes in T850 and in the vertical temperature difference were found.  Increasing SST during the SBD season is an indicator for decreases in the occurrence of sea-ice and could thereby favour snowband formation. Although the SST increased, the simultaneous decrease in the vertical temperature difference, I.e., the increasing hydrostatic stability, in November-December (Figure 9) might have hampered the formation of favourable temperature differences for snowbands in FI. On the other hand, the increase in SST in January-March together with no significant changes in T850 might have increased the F I G U R E 7 Weather maps of typical situations when sea-effect snowfall have been observed in Finland. The maps are based on weather observations at the given time. Meteorologist's analysis of the weather conditions is also included. Source: https://en.ilmatieteenlaitos.fi/ weather-in-europe [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 8 Weather radar images with precipitation phase (water/sleet/ snow) and precipitation intensity (weak/ moderate/heavy) on the same days as presented in Figure 7. Radar images from radar.fmi.fi [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 9 Monthly averages of SST and T850 ( C) over sea area in FI (a) as well as their difference (b) during 1973-1996 and 1997-2020 according to ERA5. A statistically significant change (p < .05) is marked with an asterisk for SST and for the temperature difference, and with a circumflex for T850 [Colour figure can be viewed at wileyonlinelibrary.com] possibility of favourable meteorological conditions to produce snowbands.
Another interesting question is the potential longterm change in the monthly number of days when the temperature difference between ice-free sea surface and 850 hPa atmospheric level exceeds 13 C somewhere over the study area during the cold season months (September to May). Although this temperature difference favours, in its part, the formation of convective precipitation, rainfall rather than snowfall may occur especially during early autumn. Nevertheless, the changes in the number of days exceeding this threshold indicate changes in favourable general conditions for convective precipitation over the sea.
On average during the cold season months of 1973-2020, temperature differences larger than 13 C were exceeded most often (13-18 days/month) between September and December in all regions. Due to the formation of sea ice cover in winter, the number of days having ice-free sea surface and a vertical temperature difference above the threshold decreased from November towards March. This was most evident in N, NW and S where there were only, on average, up to 7 such days during February and March in S and NW and none in N.
As one could expect based on monthly means (above, Figure 9) also the number of days exceeding 13 C threshold decreased during November and December towards 2020. This decrease was statistically significant in NW and N during November and in W and NW during December. Number of days exceeding the 13 C threshold had an increasing tendency towards 2020 between January and March in all areas and was statistically significant in S and N during January and in S, W and NW during March.

| DISCUSSION
Snowbands occur annually in northern Baltic Sea. In this research, we were interested only in those snowbands which would bring snowfall over Finnish land areas and thus affect the society and infrastructure. If also offshore snowbands had been used in this study, it would have overestimated the probability of influential incidents. The 2 cm threshold used for daily onshore SDI removed 14-23% of those SBDs detected offshore fulfilled the first seven criteria (Section 2.3).
Many snowband studies are based on case studies and known snowband events (Juga, 2010;Niemelä, 2012;Savijärvi, 2012;Juga et al., 2014;Mazon et al., 2015;Olsson et al., 2017Olsson et al., , 2018. In the present work, we have studied the climatology of SBDs in Finland in 1973-2020. To be able to cover decades-long time series in hourly and daily time resolution, detection algorithms are necessary to save human working hours. SBDs were detected in this study utilizing a set of criteria for atmospheric variables favouring sea-effect snowfall formation. Because the detection is performed on grid-by-grid basis and does not consider spatial coverage of the grids that fulfil the criteria of the algorithm, large-scale snowfall is not excluded. Thus, in addition to isolated convective seaeffect snowfall bands, the detected cases may include convective mesoscale structures in low-pressure related large-scale snowfall (for further discussion, see Saarikivi, 1989).
We did not aim to separate or classify the detected SBDs according to their detailed formation mechanisms or orientation. For example, if the wind direction changes during the day, a single or several adjacent long shoreparallel snowbands may deform to multiple bands perpendicular to shore (like in February 2012 in S, see Section 1). Or the precipitation might start as large-scale rain but evolve to intense snowbands when colder air masses are flown over the area (as in November 2012 in S, not shown).
The current results of most SBDs occurring in November and December agree with previous snowband studies by Jeworrek et al. (2017) and Olsson et al. (2020). Their findings for a 11-year period (2000-2011) showed on average 3 SBDs in Finland  and 11 in east coast of Sweden (Jeworrek et al., 2017). The smaller number of SBDs in the previous studies, compared to the current annual average of 16 SBDs, is presumably related to differences in model data resolutions. In Jeworrek et al. (2017) and Olsson et al. (2020) SST was provided by ERA-40 (resolution of 125 km) to regional climate model RCA4. Jeworrek et al. (2017) performed sensitivity studies with different RCA4 model setups. They concluded that coarse ERA-40 data provided colder SST compared to higher resolution data which had a direct impact on heat fluxes and convective development. Also, the precipitation totals were smaller in coarse simulations. Cold bias in SST (Jeworrek et al., 2017) could explain the fewer SBDs in Olsson et al. (2020) compared to our current results. Although the total number of SBDs was smaller in the above-mentioned studies the seasonal cycle was similar to our results. In addition, most SBDs were detected over western coast of Finland and the largest mean SDI in southern coast of Finland as in Olsson et al. (2020).
Dieterich et al. (2020), studied the changing climatic conditions in the northern Baltic Sea and how those affect the statistics of snowbands. They found that the most days with moderate atmospheric conditions for convective snowbands occurred in November during 1970-1999 but shifted to December already in the near future, 2020-2049. Similar shift from late autumn towards midwinter is seen in our current results with ERA5 and FMIClimGrid data.
Recent study by Bednorz et al. (2022) produced climatology of extreme cases of sea-effect snowfall on the southern Baltic Sea coast. They found out that temperature difference between SST and T850 was over 15 C when snowfall accumulated at least 20 cm/2 day of new snow. In our study, the mean of maximum vertical temperature difference during SBDs were over 15 C in all five study regions but no statistically significant correlation between vertical temperature difference and SDI were found.
Three well-known snowband episodes (SBEs), 2-5 February 2012 (Juga et al., 2014;Mazon et al., 2015), 15-22 January 2006 (Juga, 2010;Mazon et al., 2015) and 8 February 2007 (Juga, 2010) were selected as example cases to bring forth some issues in the detection method. We were able to detect the SBEs in 2006 and 2012 although the SBEs were shorter than presented by Mazon et al. (2015) presumably due to differences in study methods. Unlike Mazon et al. (2015), we did not include those SBDs to our analysis when the snowband remained over the sea. In contrast, 8 February 2007, discussed by Juga (2010), was not detected from ERA5 data with this method. Factors hampering the detection of this SBD were too low precipitation amount and BLH in ERA5 compared to criteria required. It is possible that the detection method also failed to detect some other SBDs due to too low resolution or other deficiencies in ERA5.
The snow depth observations in coastal areas, utilized in FMIClimGrid, pose another source of uncertainty. Observing snow depth and snowfall in convective band situations is difficult due to wind and snow drifting (Andersson and Nilsson, 1990). Strong winds may cause snow to pile up on the measuring point or remove it from there, affecting thus the accuracy of the measurement. In the precipitation measurements, strong winds may prevent snow from falling into the rain gauge. Because the FMIClimGrid includes only daily snow depth observations and the time scales of convective snowbands may vary from hours to days, all the snowpack changes in FMIClimGrid on detected days are not necessarily related to convective snowbands. Some snow might also have accumulated from large-scale snowfall that may be moving over the study region during the SBD before or after the passage of the snowbands. The depth of the snowpack in centimetres is also strongly influenced by the air temperature. Depending on the temperature, the accumulated snow might melt or pack before the snow depth is measured. It is also possible that a narrow snowband can simply hit between scant measuring stations. Despite these uncertainties, the data sources that we have utilized in this research are the best available information for studying convective snowbands in decades-long time scales.
Finally, the detection method of snowbands is briefly discussed. The criteria for atmospheric parameters used in the detection method may in general need some adjustment which depend on the spatial resolution and other features of data sources used. For example, snowfall amounts during an hour (>0.5 mm/h) and a day (>1.5 mm/day) were used as criteria by Jeworrek et al. (2017) but we found the hourly snowfall limit to be too high for ERA5 and hence applied the daily threshold only. Furthermore, because open sea is vital for the formation of snowbands, we used SST (>0 C) instead of 2 m air temperature as a criterion, thereby ensuring that the sea would be ice-free. Indeed, we found that, during SBDs, the mean of daily maximum SST was well above 0 C, between 3.9 C and 4.8 C (Table 3). For wind shear, Jeworrek et al. (2017) used two alternative criterion, strong (<30 ) and weak (<60 ). We applied the weaker of them but found that at least most of the SBDs would have also fulfilled the strong one (Table 3).
In addition to the quality and resolution of the data, the appropriateness of the criteria utilized inevitably influence the number of detected SBDs and thereby the accuracy of the snowband climatology in Finland. Some real SBDs may have remained undetected, in addition to 8 February 2007 (Juga, 2010), but on the other hand, the criteria may have been too loose in some other cases. Despite these uncertainties, the detection method is a great tool for climatological purposes. It provides long time series of SBDs where only the length of the used dataset is the restricting factor. Moreover, this detection method offers the possibility for more detailed case studies as one can select favourable dates from the detected set of SBDs.

| CONCLUSIONS
The spatiotemporal statistics of the occurrence of the seaeffect snow as well as the accumulated snow depth were assessed in different regions along the Finnish coast during a 48-year period . Finland's shoreline was separated into five regions (S, SW, W, NW and N) according to the direction the shore is facing. On average, 16 snowband days (SBDs) were detected annually somewhere in Finland. SBDs occurred most often in W with, on average, 7 days every winter. In S, SW and NW, snowbands occurred during 5 days and in N for 1 day annually. The annual number of SBDs did not show any statistically significant trend due to strong variation between years.
During the whole 48-year period, the frequency of SBDs was largest in November and December, with on average 4 and 6 days annually, respectively. That said, the number of SBDs decreased towards the present day in December and increased in January and February. These changes in the monthly number of SBDs also affected the seasonal cycle of the snowband days. During 1997-2020, the maximum frequency of SBDs shifted more towards December and January. The seasonal cycle of SBDs was slightly different in separate regions with maximum frequency occurring earlier in the north than in the southwest.
The snow depth increase (SDI) during SBDs was typically moderate, with largest daily mean SDI in S (3-5 cm/day) and smallest in NW (2-3 cm/day). The single largest SDI was observed in W (67 cm/day) but the number of days with SDI over 10 cm/day was largest in S. Annual SDImax of over 10 cm/day occurred more often than every second year in S and W but SDImax over 20 cm/day occurred approximately every third year in S and every fifth year in W. The SDI revealed large variations between years, with statistically significant increase in monthly mean SDImax in FI in February from 1973-1996 to 1997-2020. This paper contributes to the knowledge base of sea-effect snow in the northern Baltic Sea region. We have clarified how frequently SBDs have occurred during the past five decades. Estimates for snowband occurrence are of interest for example for the transport infrastructure agencies maintaining the road network and the railways, winter street maintenance in coastal cities as well as for coastal nuclear power plants. Based on simple physical reasoning alone it is difficult to assess whether the warming climate will increase or decrease snowband frequency and magnitude in the future. Currently, the results indicate a seasonal shift towards mid-winter during the past five decades. Further studies are needed to access the snowband frequency in the future as well as the possible impacts of seasonal shift of snowband occurrence on snow accumulation.