Wave climate and storm activity in the Kara sea 1 2

Recurrence of extreme wind waves in the Kara Sea strongly influences the Arctic climate change. The 9 paper presents the analysis of wave climate and storm activity in the Kara Sea based on the results of numerical modeling. A 10 third-generation wave model WaveWatchIII is used to reconstruct wind wave fields on an unstructured grid with a spatial 11 resolution of 15–20 km for the period from 1979 to 2017. 12 The mean and maximum wave heights, wavelengths and periods are calculated. The maximum significant wave 13 height (SWH) for the whole period amounts to 9.9 m. The average long-term SWH for the ice-free period does not exceed 1.3 14 m. The seasonal variability of the wave parameters is analyzed. 15 The interannual variability of storm waves recurrence with different thresholds (from 3 to 7 m) was calculated. A 16 significant linear trend shows an increase in the storm wave frequency for the period from 1979 to 2017. A double growth in 17 the reccurence was observed for cases with an SWH more than 3‒5 m from 1979 to 2017. The local maximum of the storm 18 waves more than 3‒4 m was observed in 1995, and the minimum in 1998. The maximum value (four cases) of the number of 19 storms with an SWH threshold 7 m is registered in 2016. The frequency of wind speeds and ice conditions contributing to the 20 storm waves formation were analyzed. It is shown that trends in the storm activity of the Kara Sea are primarily regulated by 21 the ice. If the ice cover decreases in the southern part of the sea that leads to the increase of the number of events only with 22 SWH threshold more than 3‒4 m. If in the entire sea the ice cover decreases that leads already to increase of the extreme 23 storms. The frequency of strong and long-term winds has high interannual variability and a weak positive trend. 24 The analysis of distribution functions of the storm events with an SWH more than 3 m was carried out. Six different 25 sectors of the Kara Sea were analyzed to reveal spatial differences. A comparison of the different distribution laws showed 26 that the Pareto distribution is in the best agreement with the data. Up to 99% of the points are described by this distribution. 27 However, the extreme events with an SWH more than 6‒7 m deviate from the distribution, and their probability is 28 approximately twice as less as that predicted by the Pareto distribution. Presumably, this deviation is caused by the combined 29 impact of rare wind speed frequencies and anomalies of the sea ice conditions. 30 31

More detailed description of the model configuration, the main features of the experiments with the unstructured mesh 126 is presented in (Myslenkov et al., 2018;Myslenkov et al., 2019). Wind and sea ice concentration data for the wave modeling 127 were taken from the NCEP/CFSR reanalysis (1979-2010) with a spatial resolution ~ 0.3° (Saha et al., 2010) and NCEP/CFSv2 128 reanalysis (2011-2017) with a resolution ~ 0.2° (Saha et al., 2014), temporal resolution is 1 hour. 129 As a result, we got the wind wave fields for every three hours from 1979 to 2017 (total 39 years). The model results 131 include the SWH (average value from 1/3 of the highest waves), the wave propagation direction, the mean wave period (WP) 132 Tm02 and mean wave length (WL). Also, the wave heights of 1% and 3% probability of exceedance were used for the data 133 analysis. These values were calculated as 1.51SWH and 1.32SWH, respectively (Coastal Egineering, 1995). The maximum 134 and long-term SWH were calculated based on these data. When the Kara Sea was ice covered the wave parameters were equal 135 to zero in model results. The mean long-term characteristics were performed for the ice-free period when the wave parameters 136 were nonzero. 137 138

Recurrence of the storm waves 139
The storm activity analysis was held according to the Peak Over Threshold (POT) method, which is widely used (De 140 Leo et al., 2020;Menéndez et al., 2008). This method was previously used for the Barents Sea (Myslenkov et al., 2019). The 141 number of storm waves with different SWH from 3 to 7 m was calculated for each year in the Kara Sea or within the sea sector. 142 The calculation procedure includes the following steps: if at least one node in the investigated sea area has the SWH exceeding 143 a threshold, then such event is attributed to the storm case with waves more than this threshold. This event continues until the 144 SWH will not be less than the threshold at all nodes of the investigated area. Further, if the threshold is exceeded in one of the 145 nodes again, then this event is added to the following case. A period of 9 hours at least should pass between two storm cases 146 for eliminating the possible errors. This technique has an inaccuracy associated with storms running in a row or from different 147 directions at the same time. However, such cases are rare. The proposed algorithm works correctly, it was validated by a visual 148 analysis conducted for several years. 149 The 3 m threshold was chosen as the 99% percentile of the entire studied period (1979-2017 in 3-hour interval) for 150 the points in the central part of the sea (including the ice-covered periods) or as the 95% percentile for the ice-free period. 151 There could be different criteria for the 95th percentile for regions of the Kara Sea. However, the aim of this research is deep 152 analysis of the extreme events with the SWH exceeding 3 m for any points of the Kara Sea. 153   The general features of the wave climate in the Kara Sea are discussed in this chapter. 175 The distribution of the maximum SWH and mean long-term SWH for the Kara Sea for the modeling period  2017) is shown in Fig. 5, a-d. The mean long-term SWHs are about 1.1-1.3 m (Fig. 5a) in the ice-free period. The maximum 177 mean SWH is 1.3 m and observed in the northern part of the Kara sea. This area is associated with the influence of storms 178 coming from the Barents Sea in the ice-free period. Formally the maximum SWH during the whole period reaches 9.9 m and 179 is observed in the northern part of the sea, at the border with the Barents Sea (Fig. 5b). However, the wave conditions of this 180 area are largely determined by the Barents Sea and this area belong to the Kara Sea because of the formal border. In the central 181 part of the Kara Sea, the SWH maximum is 9.4 m and it is observed off the western coast of the Yamal Peninsula (Fig. 5b). 182 The maximum wave height of a 3% probability is 12.4 m (Fig. 5, c), and a 1% probability is 14.3 m (  According to long-term mean SWH fields and to maximum SWH values, at least we can reveal two large regions 195 with particular spatio-temporal patterns of wave conditions, in the Kara Sea. The first one is the northern part which is often 196 occupied by the ice. It is affected by storms from the Barents Sea in the ice-free periods. The second region is the southwestern 197 part of the sea (Fig. 5-6). This region has longer ice-free period and wave generation occur without the influence of the Barents 198 Sea. It should be pointed that in the north-eastern part of the Kara Sea the influence of storms from the Barents Sea should be 199 expected, but, due to the high probability of the ice presence (> 0.8) in this region, the wave height is significantly lower than 200 in other parts of the sea. 201 The next step of our research was seasonal analysis of the SWH maximum for four periods: December-January-202   (Fig. 8a). The Kara Sea is free from ice in this period for a short time and in small areas. There is only one local SWH 210 maximum (8.1 m) in the southern part of the sea in June-August (Fig. 7b). During this period, wind speed is usually less than 211 https://doi.org/10.5194/nhess-2020-198 Preprint. Discussion started: 7 July 2020 c Author(s) 2020. CC BY 4.0 License.
in November-December therefore, severe storms are very rare despite the long ice-free period. Several SWH maxima are 212 observed in September-November, including the 9.4 m height in the central part of the sea (Fig. 7c). This maximum is an 213 absolute multi-year maximum for the central Kara Sea (Fig. 5b). Ice occurs only in the northern Kara Sea in this period (Fig.  214 8c). The strongest winds are observed in December -February. Most of the Kara Sea is ice-covered and the generation and 215 propagation of wind waves are limited. However, severe storms from the Barents Sea pass to the northern Kara Sea during 216 short ice-free periods. The absolute SWH maximum (9.9 m) for the entire sea was recorded was recorded there (Fig. 7a). The The mean and maximum values of the average wave period and average wavelength are presented below. The long-220 term mean WP is 3.5 s (Fig. 9a). Such small WP is due to the long ice period and as consequence wave fetch is short. Mean 221 WP corresponds to the mean long-term SWH of 1 -1. The analysis of the ice concentration variability in the Kara Sea was performed to explain the interannual variability 247 of the storminess. The graphs of ice probability for two points in the Kara Sea is presented in Figure 11. Ice probability is the 248 ratio of number of days with observed ice to the duration of the whole year. The points were selected in the central and 249 southern parts of the Kara Sea to demonstrate the difference of the ice conditions. There is a significant negative trend in the 250 variability of ice cover. Ice probability is approximately twice as less from 1979 to 2017. This trend is observed at both points. 251 It can be assumed that ice cover decreases in the whole sea. This fact has been detected by various researchers previously 252 This minimum probably led to an increase of the number of storms with SWH ≥ 3 and 4 m (Fig. 10). But in 1995 ice cover 256 reduction was observed only in the southern Kara, not in the whole sea, that's why such reduction does not cause extreme 257 storms (≥5 m). The maximum ice cover was observed in 1998-1999 and amounted to 0.8 in both points. It led to the storminess 258 weakening (Fig. 10). The ice probability minima were observed in 2012 and 2016 in T1 and T2. These minima coincide with 259 a significant increase in number of storms (including storms with SWH ≥7 m) that was observed exactly in these years. 260 Climate changes in storm wind conditions may be associated with changes in the ice conditions in the Kara Sea, 284 however, this analysis is already beyond the scope of our research and requires more detailed study. It is a challenge task for 285 future research. 286 287

Probability analysis of storm waves in different sectors of the Kara Sea. 288
Based on the analysis of the mean long-term and seasonal variability of the wave heights, the Kara Sea was divided 289 into several sectors with different wave conditions. In these areas, several zones of maximum waves are observed in different 290 periods of the year (Fig. 7a-d). This segmentation allows to analyze extreme storms in detail. 291

Figure 13 292
A catalog of storms with SWH more than 3 m was formed for each sector shown in Fig. 10. The POT method was 293 used to create the catalog, and a threshold of 3 m was chosen as the 95th percentile for the sample for the ice-free period. In 294 this catalog, each member of the series is a separate storm event. It is necessary condition for the independence of the members 295 of the series according to the method of "independent storms" (Cook, 1982). The length of the data series is sufficient for The storm data series for each of the 6 sectors were approximated by various distribution functions. A comparison of the 298 functions with the empirical data showed that the best approximations for the storm recurrence was the Pareto distribution 299 300 where ℎ is the threshold value.  is the distribution parameter easily determined by the least square. For this purpose, formula
(3) 303 If the empirical values on the diagram are located along a straight line in the logarithmic coordinates, this means that 304 the empirical distribution corresponds to the Pareto distribution. The quantitative correspondence of the empirical and the 305 theoretical distribution is established by using known statistical criteria. 306 Pareto distribution for all sectors is shown in Fig. 14. About 99% of the points are described by the Pareto distribution 307 with parameters Hth = 3 m and γ = 4.8 and a determination coefficient of R 2 = 0.98 in sector 6. This approximation is used as 308 base distribution. The Kolmogorov-Smirnov test also shows that the Pareto distribution is quite well. A similar pattern of 309 distribution functions is observed for all six sectors. 310

Figure 14 311
The average value of γ is equal to 4.6 (varying from 4.2 to 5.0 for different sectors). The proximity of the parameters 312 in the Pareto distribution indicates that the extrema are generated in all sectors with a similar law. Thus, the wave generation 313 with an SWH more than 3 m is determined by the same mechanism. The basis of the hypothesis is the series of extrema 314 determined by the same law of probability distribution. A similar analysis is given in (Taleb, 2010). All extreme events are 315 called "swans", while the maximum and the largest rare events are "black swans". However, there are very rare cases when 316 the empirical distribution deviates and exceeds the base distribution in the large values area. These unique events are called 317 "dragons" (Sornette, 2009). The extreme values of SWH greater than 8 m observed in 2, 4, 5 sectors. 318 In our case, several extreme values that deviate from the base distribution were detected in each sector due to the 319 analysis of the distribution functions. The direction is common to these deviations -the points always deviate upward (Fig.  320   14). Therefore, these events are "dragons". A similar principle was used for freak wave detection (Buhler, 2007) and in 321 studying wind speed extremes (Kislov and Matveeva, 2016;Kislov and Platonov, 2019;Platonov and Kislov, 2019 ). Unique 322 extrema "dragons" falling out of the base distribution and have a different distribution law and, probably, a different genesis. 323 It is very important that the probability of extreme events based on a theoretical function, in our case, the Pareto 324 distribution. For example, the data of sector 6 (East coast of Novaya Zemlya) (Fig. 14) shows an SWH equal to 6.7 m (logarithm 325 1.9)almost the last value that still lies on the base Pareto distribution. This value repeated through 47 sample elements 326 (( ℎ ) ) on average. However, storms with such SWH occurs about a 100 times in reality (Fig. 14), twice as much as it was 327 planned by the Pareto approximation. A similar situation is reflected for the other sectors in the "dragons" zone. Use of base 328 distribution in this zone leads to incorrect probability calculation results. This fundamental result demonstrates the source of 329 systematic errors in evaluating the recurrence of extreme wave heights, which are especially relevant in applied and forecast 330 tasks. 331 The probability of "dragons" doesn't match the base distribution. In the Kara Sea, the occurrence of storms with high 332 waves depends on several factors simultaneously: primarily on the wind speed, direction, and duration of the wind, secondly 333 on the ice conditions (fetch limit) or the influence of the Barents Sea (for 4-th sector). The number of storms with SWH more 334 than 3-4 m is closely related to wind speed and wind duration as it was shown in chapter 3.2, but the repeatability of storms 335 with SWH more than 6-8 m requires the simultaneous combination of small ice cover and extreme wind conditions. Thus, the 336 division of the empirical distribution function between "black swans" and "dragons" occurs when the influence of small ice 337 cover (and consequently more long fetch) is observed besides the wind forcing. Since wind and ice conditions are considered 338 as approximately independent events, their joint probability is much lower than the probability of rare wind events. 339 https://doi.org/10.5194/nhess-2020-198 Preprint. Discussion started: 7 July 2020 c Author(s) 2020. CC BY 4.0 License. Extreme events with any (even very large) wave height can occur according to the base distribution function, formally. 340 However, the empirical function for the "dragons" is nonlinear and goes to a certain plateau; it was shown in the logarithmic 341 graphs. The  values (starting with some values of H) begin to increase rapidly. Thus, there is a certain natural limit observed 342 for extreme events. "Dragons" have a limitation for maxima wave height that differs from the base distribution. The basic 343 distribution ends in the range of SWH values 6.5-8 m in different sectors. Such differences are associated with the definition 344 of freak waves in the article (Buhler, 2007). Freak waves are unique anomalous individual waves that do not correspond to the 345 general distribution. In our case, we have a similar picture on the synoptic scale, where specific storms with a certain SWH 346 maximum defined as "dragons". 347 Figure 15 shows the graph of "dragons" passing by year in each of the six sectors. This graph was analyzed for the 348 possible impact of climate change on the "dragon" recurrence. "Dragons" occurred in sectors 1 and 5 only after 1997-2000, 349 when the increased recurrence was registered for the entire Kara Sea. A higher recurrence of "dragons" was registered in years 350 when there were simultaneous peaks of wind recurrence and small sea ice cover (see Fig. 13). 351 The combined analysis of the storm activity, the recurrence of strong winds, and the ice probability was carried out. 369 The high recurrence of strong winds and the absence of sea ice lead to increase of storm number with SWH 3-4 m in the 370 southern Kara Sea. When the sea ice probability decreases for the whole sea and recurrence of strong winds is high 371 simultaneously, then the number of extreme storms (SWH more than 5-7 m) increases. 372 There is an obvious positive trend of the storm activity in the Kara Sea and a positive linear trend of the weaker storm 373 recurrence (SWH more than 3-4 m) for 1979 -2017. Linear trend of the severe storm recurrence (SWH more than 5-7 m) is 374 positive but statistically insignificant because such events are rare. This trend is mainly caused by a reduced sea ice cover over 375 the past 40 years, the trend in recurrence of storm wind conditions is not significant. 376 The Kara Sea was divided for six sectors with different wave conditions due to the analysis of the mean long-term 377 and seasonal variability of wave heights. 378 The probability analysis for the six sectors of the Kara Sea was provided. Different approximations were compared 379 with the empirical distribution, the best approximation for the storm recurrence was the Pareto distribution. The proximity of 380 the parameters in the Pareto distribution indicates that the extrema generation occurs in the same way for all sectors. 381 https://doi.org/10.5194/nhess-2020-198 Preprint. Discussion started: 7 July 2020 c Author(s) 2020. CC BY 4.0 License.
Analysis of the distribution functions for each of the sectors showed that several extreme events ("dragons") deviate 382 upward from the base Pareto distribution. Thus, the division of the empirical distribution function between "black swans" and 383 "dragons" occurs when the influence of small ice cover (and consequently more long fetch) is observed besides the wind 384 forcing. "Dragons" occurred in sectors 1 and 5 only after 2000, when the increased recurrence was registered for the entire 385 Kara Sea. A higher recurrence of "dragons" was registered in years when there were simultaneous peaks of wind recurrence 386 and small sea ice cover. On a time scale of 40 years, we see climatic changes in increasing the recurrence of such extreme 387 events as "dragons". 388 There are some questions of the quality assessment of the wave model for extremely high waves, but unfortunately, 389 we do not have full-scale direct measurement data in the Kara Sea, and satellite data also need verification and are not accurate.