The icing model output was further processed to allow a comprehensive evaluation of the changes in icing climate from multiple perspectives. The results can be divided into two categories: (1) results calculated for 50 m above ground to investigate icing on power lines, and (2) results calculated for multiple lower tropospheric heights (50–400 m) relevant for wind energy production. The altitude of 50 m was chosen for power lines as it was the lowest height above ground level where HCLIM output data were available. Table  lists the evaluated parameters and details the domains and heights they were analyzed at. In addition, we focused only on the months when freezing temperatures are common in northern Europe (October to April) in our analysis, following the example of .

Figure  displays the specific areas referenced in Table , while supplementary information on the areas, including the relief information, are shown in Table . Each area is named according to the municipality or one of the municipalities they fall under. In areas 1–5, which were selected to coincide with existing or planned wind parks, results were calculated for all heights. For power line perspective, separate areas were selected (areas 6–7) and in these regions only results at 50 m height were considered. In areas 6–7, the maximum of all the grid points in the area was determined for each time step, and additional parameters were derived from that, including annual mean and maximum ice masses and icing episode durations. An icing episode is defined as the number of days the ice cover thickness stays over 2 mm. This limit is based on earlier research relating to corona losses caused by icing. In addition, when calculating the annual average of icing hours for the entire Fennoscandian area, 2 mm was used as the threshold for defining an icing hour.

For areas 1–5, extreme values of ice mass were calculated by taking the 99th quantile of the 20-year periods. The 99th quantile was first determined for each grid point in the area, after which the regional maximum, average and minimum values were calculated. To obtain these values, it was assumed that the climate is similar over a 20-year period; similar assumptions were made with the whole domain when comparing the changes across three distinct time periods. The icing hours and episode durations were calculated from the average ice mass of the grid points in the area. After obtaining the average ice mass, it was checked how often this regional average value fulfills specific icing conditions (adjusted due to the model's time resolution of 3 h) which gives the total sum of icing hours annually. If the regional average fulfills the icing condition for at least eight time steps, an icing episode is recognised, and its duration is counted in days. Here, it is also essential to emphasize that the definitions for an icing hour and an icing episode are different for areas 1–5 and 6–7. In areas 1–5, the presence of at least 10 g m⁻¹ of ice in the model cylinder is used as the definition for an icing hour. This threshold applies to the icing conditions of a wind turbine .

After computing the icing model with HCLIM data, issues considering the lower boundary of sea surface temperatures (SST) and sea ice concentrations in HCLIM data over multiple areas of the Baltic Sea for both GCMs were found. The errors were clear during winter (December–February) and reflected in the surface temperatures and precipitation fields in the same areas. Through discussion with NorCP data providers , we were informed that the error should have little influence on the land output, as also indicated by previously published studies based on the same data ; thus, results are shown only for land areas.

Without a proper ensemble, where the mean of the ensemble members can be used to differentiate a climate change signal, other practises need to be considered to reduce the effect of natural climate variability in the results. We used spatial averaging for the change signals of mean and maximum ice mass and mean icing hours, where the value in a grid point is assessed by averaging the values from the neighbouring 3 × 3 grid points, following for example and . This helps to reduce the noisiness of the point-wise change estimates, although, at the same time, some of the high-resolution details of the data are lost.

Statistical significance of the icing trends are tested using a standard two-sample t test with a 0.1 confidence level, originally. We adjust this confidence level by calculating a false discovery rate for each set of significance tests by following . Performing multiple statistical tests simultaneously, as is done with grid point data, can result in many of the grid points falsely being reported as significant. With the false discovery rate, this phenomenon is taken into account.

For the entire study area, changes in both the ice mass and the hours of ice over the standard cylinder are presented for the height of 50 m. Figure  illustrates the projected relative changes in the mean and annual maximum ice masses. A generally decreasing trend in mean ice masses is evident in Fig. a by the end-of-century according to both setups and HCLIM with GFDL-CM3 projects widely a statistically significant decrease already by mid-century. In HCLIM with EC-EARTH, the signals are less robust in mid-century with most of the FDR-adjusted decrease projected in southern Norway, the Scandinavian mountains and locally over central Finland and Sweden and southern parts of the domain. Over northern Lapland, northern Norway and Kola-Peninsula, HCLIM with EC-EARTH simulates locally a 30–50, even close to an 80 %–100 % increase during mid-century. However, the trend is only significant by the 0.1 confidence level. Overall, the signals projected by HCLIM with EC-EARTH in the northern parts of the domain are not statistically significant, while some of the projected decrease (about 30 %–60 %) in HCLIM with GFDL-CM3 are. With some of the very strong decrease seen especially in HCLIM with GFDL-CM3 in the end-of-century, it should be noted that the simulated mean loads in these regions are low to begin with, resulting in a small absolute change, as seen in Fig. a.

There is greater variability in the results for maximum ice masses. Figure b depicts the relative change in annual maximum ice masses (absolute changes are seen in Fig. b). With the maxima, a statistically significant increasing signal persists until end-of-century in northern Lapland, northern Norway and Kola-Peninsula in HCLIM with EC-EARTH. A similar trend is present in HCLIM with GFDL-CM3 in mid-century. The increasing trend is more pronounced for EC-EARTH, where the increase is greater than 50 % in northern Lapland and Norway for both time spans; in GFDL-CM3, the increasing trend is limited only to Kola-Peninsula by end-of-century. In other areas where increase is projected, mostly elsewhere over northern Fennoscandia or the Scandinavian mountains, the increase is not statistically significant or only significant by the 0.1 confidence level. FDR-limited significant decreasing trends are rare in HCLIM with EC-EARTH in mid-century and located mostly in western Norway (20 %–50 %); in end-of-century significant decreasing trends become more widespread and seen around the study region. According to HCLIM with GFDL-CM3, FDR-limited significant trends are projected in many parts of the southern and central parts of the domain already in mid-century and more widely by end-of-century. A clear example of differences with the projections is over western Finland, where a decreasing trend is pronounced in HCLIM with GFDL-CM3 both in mid-century and in end-of-century (50 %–100 %); the trend is also evident for absolute values (locally above -0.1 kg m⁻¹ in Fig. b).

Beyond the actual ice masses accumulated on structures, the duration of the presence of ice is crucial; hence, changes in icing hours were examined. Here, as explained in Sect. , an icing hour is described as an hour with an ice cover thickness of ≥ 2 mm in the model cylinder. Figure  visualizes the relative change in annual mean icing hours in the Fennoscandian area. A significant decreasing trend is prevalent in most of the study area, with a more substantial decrease in GFDL-CM3-based outputs; in southern and central Finland, a decrease of 80 %–100 % is projected by the end-of-century. For absolute changes in icing hours (Fig. ), the largest changes are in northern parts of Finland, central and northern Sweden, and the Scandinavian mountains, where a decrease of 500–1000 h annually (20–40 d) is projected for the mid-century and close to 1000 h or even more for the end-of-century (40 d or more). This corresponds to a 10 %–50 % decrease in the mid-century; by the end-of-century, a 60 %–80 % decrease is simulated over central Sweden and southern Lapland, while northern Lapland is expected to see a 40 %–60 % decrease. Locally, some of the weakest decreasing trends in the northern and eastern parts of the domain are not statistically significant. Additionally, none of the localized increasing trends are statistically significant.

To study changes in icing conditions in more detail, various areas were selected for further analysis. This section presents results related to ice masses, thicknesses, and icing episode durations at 50 m from two areas presented in Fig. ; one in eastern Finland (6: Kontiolahti) and the second in northernmost Finland (7: Utsjoki). Both areas cover 66 grid points in total and they are situated in relatively low terrain (average altitudes of 110 m in Kontiolahti and 245 m in Utsjoki, Table ). Additionally, in Sect.  we have outlined the methods and definitions used to derive the parameters applied here, such as an icing episode.

For Kontiolahti, results are presented in Fig. a–b, while Fig. c–d show the same for Utsjoki. In box plots (Fig. a and c), the evolution of regional maximum ice masses are visualized with both the annual mean and the annual maximum shown for the regional maximum of the grid points. In Kontiolahti, a decreasing trend is noticeable as the median values show a decrease across time periods with both configurations. The extremes of the distributions (whiskers) also show decreasing trend. Moreover, according to the GFDL-CM3 boundary model, the maxima of the mean distribution become smaller than the median value in the historical period for both locations; this is mostly supported by HCLIM with EC-EARTH, however, there are outliers in both locations.

With Utsjoki, the results exhibit greater variability. GFDL-CM3 shows a decrease in the median values and interquartile range across the time periods, while EC-EARTH projects slight increase in the mid-century turning towards decreasing in the end-of-century. Smallest mean values (whiskers) are projected in both models in the end-of-century period, while the largest mean values (if excluding outliers) are shown for mid-century. Generally, the mean values are smaller in EC-EARTH than in GFDL-CM3 in Utsjoki, while the situation is somewhat opposite in Kontiolahti.

While decreasing trends can be distinguished in Kontiolahti for annual means, the signal is less clear with annual maxima. The median values decrease slightly when comparing future periods with the historical period. Between future periods, the trend is neutral. In end-of-century, there is indication of increased variability caused by a decrease in the minima of the distributions. In Utsjoki, both model configurations show an increase in mid-century and, for EC-EARTH, the maxima of the distributions increase until the end-of-century. Thus, while mean ice masses are expected to mostly decrease (as discussed in Sect. ), the potential for larger ice masses remains.

Changes in the relationship between the maximum thickness of the ice cover during an icing episode and the duration of such an episode are depicted for both model configurations in Fig. b and d. There are some regional differences in the scatter plots; for Kontiolahti (Fig. b), a shift toward shorter episodes and thinner ice covers is expected, while in Utsjoki, thick covers persist even with decreasing episode lengths (Fig. d). In Kontiolahti, icing episode lengths of 0–40 d are most common with a maximum thickness of 3–15 mm, with the largest thicknesses of 20–35 mm occurring when icing episode lengths exceed 20 d. HCLIM with EC-EARTH suggests slightly more potential for thicker covers (10–35 mm) and longer episodes (over 40 d) than HCLIM with GFDL-CM3. In Utsjoki, maximum thicknesses are generally around 40–60 mm across boundary models and time periods. In mid-century, there is indication of an increased chance of thicknesses of more than 60 mm in HCLIM with GFDL-CM3.

In this section, results from all the five output heights (50, 100, 200, 300, and 400 m) are investigated in the case study area of Kauhajoki located in western Finland along with four additional areas around Fennoscandia. These areas correspond to areas 1–5 presented in Fig. , and they coincide with existing or planned wind park locations. All areas cover 42 grid points in total, and while areas 1–3 are in relatively low terrain (average altitudes above sea level in HCLIM data are under 200 m), areas 4–5 are situated in higher terrain with average altitudes of around 550–600 m, with the highest simulated altitude in area 4 (922 m, Table ). Consequently, here an icing hour is described differently from Sect.  to better align with wind power standards (≥ 10 g m⁻¹ of ice present in the cylinder). However, an important factor here is to note that the model output was calculated for a cylinder of diameter of 3 cm, which is more suited for transmission lines than for wind turbines.

For Kauhajoki, yearly icing hours at heights 50–400 m are presented in Fig. , with distributions presented for each time period. It is evident that the number of icing hours decreases with time at each height and for both boundary models. For HCLIM with GFDL-CM3 (Fig. b), at upper heights of 200–400 m, the mean icing hour values in the mid-century period align with or are smaller than the minimum values in the historical period, while at the end-of-century, the simulated maximum hours align with or are smaller than the minimum values in history. With EC-EARTH (Fig. a), the distributions in future periods cover a wider spectrum, although with a similar decreasing trend. At lower heights of 50–100 m, there are individual years with more than 1000 h of significant ice present in the historical period, but none forecasted for the end-of-century. If we compare the heights of 300 and 100 m, the mid-century mean in 300 m is greater than the historical mean in 100 m for both configurations; an interesting point to consider, as wind turbine heights have increased with time. A similar plot of the distributions of icing episode durations is presented in Fig. ; the decrease in durations for this location is strongest in HCLIM with GFDL-CM3.

In Table , results for Kauhajoki can be found in numerical format, including the maximum and minimum icing hours for each height and time period. In addition, the maximum icing episode length (when averaged over the area) and the range of the 99th quantile of ice masses (maximum-average-minimum in the area) for each period are presented. As noted before, with icing hours and icing episodes, the trend is towards decreasing amounts; according to HCLIM (GFDL-CM3), in the future, a year without icing could occur even at 400 m height in Kauhajoki. Also notable is the decrease in the maximum icing episode lengths; from 50–100 d to around 5–35 d by the end-of-century depending on the boundary model and height. For the ice masses, the signal is also decreasing, and with HCLIM (GFDL-CM3), the average 99th quantile is 0.1 kg m⁻¹ even at 400 m by the end-of-century.

In Tables –, results are collected from additional study areas. For Pello (area 3 in northwestern Finland, Table ), results indicate mixed signals for the 99th quantile ice mass at the height of 50 m with decreasing trends from 100 m upwards (from highest values of 1–3 kg m⁻¹ in the area in the historical period to 0.4–2 kg m⁻¹ in future periods). For the rest of the areas, trends in both ice masses and icing durations are decreasing. In area 2 (Haapajärvi, Table ), by the end-of-century, the 99th quantiles become dominantly smaller than 1 kg m⁻¹ across both models and all heights, while the maximum episode durations change from 70–175 d to around 15–50 d. For area 4 (around Narvik, Norway; Table ), the maxima of the 99th quantile ice masses range from 20 to 40 kg m⁻¹ in history and from 7 to 20 kg m⁻¹ at the end-of-century across heights and both model configurations. For Rutan (area 5 in central Sweden, Table ), maximum durations decrease from over 100 d to under 100 d starting from mid-century, while the 99th quantile loads are reduced by more than half in HCLIM with GFDL-CM3 (less with EC-EARTH).

Ice formation takes place at freezing temperatures; therefore, it is important to consider how often freezing conditions occur. The critical threshold temperature between icing and melting in the rime ice model is set to 0 °C, above which water remains liquid or the existing ice melts. In reality, this can vary depending on the type of icing and other meteorological conditions, such as the presence of ice nucleation particles . In contrast, at sufficiently low temperatures, around and lower than -20 °C, ice accumulation from supercooled liquid droplets is limited, as the air can only hold a small amount of liquid water .

Exploring changes in the occurrence of the critical temperature threshold is important, as it dictates the effect of temperature on icing. In Fig. a, the mean temperatures of a typical icing season (October–April) at 50 m are shown for the historical period and the two future periods (2041–2060, 2081–2100). The boundary model in the upper panel is EC-EARTH, and in the lower panel, GFDL-CM3. It is evident that the mean temperature in the historical period is widely below 0 °C from the northern to central parts of the domain. By the end-of-century, the mean temperature is projected to be below zero only in northern Lapland and over Scandinavian mountains corresponding to the strongly warming emission scenario RCP 8.5.

An important factor to consider is how much time is spent under freezing conditions even in a highly warming future. Figure b shows the average hours spent below 0 °C at the height of 50 m in historical and future periods. The time spent in freezing conditions decreases everywhere in the domain. Excluding southern Sweden and some of the coastal regions in Norway, Fennoscandia experiences around 4–7 months of freezing temperatures in the historical period. For the mid-century, this drops down to 2–6 months, except for mountainous regions. However, for the end-of-century, southern and central Fennoscandia fall under an average of 0–2 months, northern parts to 2–4 months, and the highest altitudes on average to 4–6 months of freezing temperatures. Some areas in the southern part of the domain, such as the south-western coast of Finland, southernmost Sweden, coastal regions of Norway and Baltic states, and Denmark, may experience close to zero months of freezing conditions at the end-of-century.

The effect of the strong warming is especially present in the mean changes (ice mass and icing hours), for which widespread decreases are projected already in mid-century. For the mean parameters, the icing across the whole winter season counts, and if the winter period becomes noticeably short, this will be reflected in the mean parameters. As an exception, the northernmost areas can experience, in the mid-century, a long enough cold season but with less time spent in very cold temperatures, so that local increase is projected. With ice mass maxima, a similar effect is present. For the largest ice buildups, consecutive time in freezing temperatures is needed. In the northernmost areas, the projected future icing episodes are still long enough for significant ice buildup to occur, while the episodes themselves will happen in warmer and moister conditions. This allows for larger masses than in the historical period.

The amount of cloud liquid water content in the atmosphere defines how much ice is possible to accumulate from in-cloud icing if other meteorological conditions are favorable. The function of wind in relation to atmospheric icing is then to transport liquid droplets to the surface of an object where ice may form. If the wind speed is high, transportation is more efficient compared to situations with calmer winds. The icing model used in this study assumes a freely rotating cylinder, thus, wind direction is not considered.

The relative change in the mean CLWC values at the model height of 50 m can be seen in Fig. a, while the relative changes in mean wind speed are shown in Fig. b. An increasing trend (dominating red colors) is present in most of Fennoscandia for both mid-century and end-of-century for cloud liquid water content, applying particularly for HCLIM with EC-EARTH. With mean wind speed, only minor changes are predicted, at least in HCLIM with EC-EARTH; HCLIM (GFDL-CM3) projects increase of about 10 %–15 % in cold season wind speeds in the southern parts of the domain in end-of-century. Oppositely, GFDL-CM3 simulates there a slight decreasing trend in mean CLWC, by the end-of-century also in most of the Finnish and Swedish coastal areas. In EC-EARTH, a similar pattern is present on the western coast of Norway, while HCLIM with GFDL-CM3 predicts mostly an increasing trend. The absolute changes in the mean CLWC are shown in Fig. a and for wind speeds in Fig. b. The strongest absolute increase in mean CLWC can be seen at higher altitudes, with an increase of 0.02 g m⁻³, while the absolute increase in mean wind speed in GFDL-CM3 is around 0.5–1 m s⁻¹.

This widely increasing trend in CLWC aligns with a warming climate, as warmer air can hold more moisture and, thus, liquid water in an atmospheric layer. However, mostly decreasing icing trends are projected for northern Europe, which indicates that in most areas, the loss of time spent under freezing temperatures dominates the effect on icing. Temperature's dominating effect is supported by the changes in wind speed, as either little change (HCLIM with EC-EARTH) or slight increase (HCLIM with GFDL-CM3) is projected. In northernmost areas, the strong increase in mean CLWC can help to obtain larger maxima. In western and southern parts of Finland and southern Sweden, however, the slightly decreasing trend in CLWC in HCLIM with GFDL-CM3 can add to the projected stronger warming and explain the robust decreasing signal in annual ice mass maxima in these regions in HCLIM with GFDL-CM3.