NORA10EI: A revised regional atmosphere‐wave hindcast for the North Sea, the Norwegian Sea and the Barents Sea

NORA10EI, a new atmosphere and wave hindcast for the Norwegian Sea, the North Sea and the Barents Sea is presented. The hindcast uses ERA‐Interim as initial and boundary conditions and covers the period 1979–2017. The earlier NORA10 hindcast used ERA‐40 as initial and boundary conditions before September 2002 and operational analyses from the European Centre for Medium‐Range Weather Forecasts (ECMWF) in the continuation. This change in initial and boundary conditions may lead to non‐stationarities in bias and random errors, and it is a question of some concern whether this also leads to spurious trends. We investigate this by comparing the two hindcasts. We find only minor differences in the statistics of means and upper percentiles, but somewhat larger differences in the extremes (100‐year return values) of significant wave height and 10‐m winds. Generally, NORA10EI outperforms NORA10 in the ERA‐40 period (before September 2002) since ERA‐Interim outperforms ERA‐40. Conversely, NORA10 outperforms NORA10EI after 2006, since the operational ECMWF analyses here outperform ERA‐Interim. Years 2002–2006 is a transition period with minor differences between the NORA10 and NORA10EI where the resolution of ERA‐Interim is lower than that of the ECMWF analyses, but its physics are from a more recent model (2006). An important finding is that the regional hindcasts appear quite insensitive to changes in the host reanalysis with no statistically significant differences in mean and upper percentile trends of wind speed and wave height. A comparison of four polar low cases confirms that using ERA‐Interim as host reanalysis yields a slightly better representation of evolution and intensity of polar lows than NORA10 in the ERA‐40 period and the opposite after 2006.

without the need for an expensive data assimilation system. Several high-quality regional hindcasts have been generated in recent years (e.g., the studies by Gaslikova and Weisse, 2006;Günther, 2007 andvon Storch, 2010 for the North Sea and the NORA10 hindcast by Reistad et al., 2011 to be investigated here). As waves are entirely forced by the wind, these studies perform well without assimilation of wave observations. Wave hindcasts are useful since the regional wave climate requires relatively high resolution to resolve topographical features that modify the wind field and obstruct the wave field. A number of regional (e.g., Bromirski et al., 2013;Izaguirre et al., 2013;Appendini et al., 2014;Semedo et al., 2015), basin-scale (Wang et al., 2012) and global (Semedo et al., 2011;Aarnes et al., 2015;Meucci et al., 2019) studies on wave climate variability and trends from hindcasts and reanalyses have recently been presented. Common to all of them is that they take their boundary conditions from global reanalyses.
The first global reanalyses were the ERA-15 reanalysis (Gibson et al., 1997) developed at the European Centre for Medium-Range Weather Forecasts (ECMWF) and the 40-year reanalysis (since extended) developed at the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) (Kalnay et al., 1996). These were followed a few years later by the first coupled atmosphere-wave reanalysis, ERA-40 (Uppala et al., 2005), developed at ECMWF.
After ERA-40 came a series of global atmospheric reanalyses, most notably the Japanese Reanalysis (JRA-25, Onogi et al., 2007), the Climate and Forecast Reanalysis (CFSR, Saha et al., 2010), the Modern Era Reanalysis (MERRA, Rienecker et al., 2011), ERA-Interim (Dee et al., 2011), and the updated version of CFSR (CFSv2, Saha et al., 2014). Recently, century-long reanalyses have been produced at lower resolution, notably the 20th-century reanalysis, covering the period from 1871 to present (Compo et al., 2011) and ERA20C, covering the period 1900-2010 (Hersbach et al., 2015;Poli et al., 2016). The latter was recently accompanied by CERA20C, a coupled atmosphere-ocean low-resolution reanalysis (Buizza et al., 2018;. ERA-Interim is continually updated but is not extended back beyond 1979. Compared with ERA-40, ERA-Interim has an improved hydrological cycle and better stratospheric circulation. Furthermore, in situ observations and satellite data are handled by four-dimensional variational data assimilation whereas ERA-40 employed a three-dimensional (3D) variational assimilation scheme (Dee et al., 2011). Although now being replaced by the new modern-era reanalysis ERA-5 , ERA-Interim is still used extensively.
NORA10 (Reistad et al., 2011) is a regional atmosphere and wave hindcast which employs ERA-40 on the boundaries and as initial conditions for the atmosphere, and spectra from a coarser wave model forced with ERA-40 winds for the wave field. NORA10 originally covered the same period as ERA-40, September 1957to September 2002, but has since been extended to present time using operational analyses as boundary and initial conditions (Aarnes et al., 2012). (This extension is referred to as the second period of NORA10). Although of high quality, this inconsistency in the boundary forcing has led to concerns about the stationarity of the statistical properties of the hindcast archive since model upgrades have inevitably led to improvements and thus a reduction of bias and random error in the boundary and initial conditions. The question of whether the intensity of storm systems has been affected by these gradual changes to the forcing is of particular interest. This would show up as spurious trends which could also be interpreted as a climate change signal and compromises extreme value estimation (Aarnes et al., 2015). This question of how sensitive a regional hindcast is to its host analysis is of wider scientific interest, as reanalyses are often found to yield spurious trends due to increasing amounts of observations (of improving quality), see Aarnes et al. (2015) and Meucci et al. (2019).
In order to explore the stationarity issue, we have applied ERA-Interim on the boundaries of the NORA10 model domain and run the atmospheric model for the period 1979-2017. ERA-Interim was the best reanalysis available at the start of the NORA10EI production, and it is comparable in quality to the ECMWF analyses used for the early second period of the NORA10 hindcast. The same wave model as was used for NORA10 was employed to produce wave fields for the period, where an outer wave model forced by ERA-Interim winds provided spectral wave boundary conditions to the inner model. With other things kept constant, we will thus investigate whether the change from ERA-40 to ECMWF analyses on the boundaries has led to spurious trends in mean and upper percentiles of the wind and wave field of NORA10. This paper is organized as follows. A description of the new NORA10EI hindcast is presented in Section 2. A presentation of the general performance of NORA10EI follows in Section 3. Section 4 investigates median and upper percentiles of the wind speed at offshore windmeasuring stations. Section 5 assesses the performance of the wave model fields against offshore wave-measuring stations. The trends in wind speed are investigated in Section 6 and spatial wind patterns are presented in Section 7. A comparison of extreme value estimates from NORA10 and NORA10EI is presented in Section 8. The total impact of the transition to operational analyses on NORA10 is discussed in Section 9 and the conclusions are summarized in Section 10. A short description of the usage of the offshore observations related to Section 4 is given in Appendix A1. Four polar low cases are presented in Appendix A2 ( Figures A1-A8) where the relative merit of NORA10 v NORA10EI is considered, and the method used in trend analysis in Section 6 is presented in Appendix A3.

| MODEL SETUP
This hindcast study has deliberately been set up on the same model domain and with a configuration which closely matches that of NORA10. This is because we aim to investigate the sensitivity of a regional hindcast to host analysis forcing, and to what extent NORA10 is affected by the change in forcing data in 2002 where the transition from ERA-40 to ECMWF analyses takes place. The only exception to this is that the wind input to the wave model is hourly instead of 3 hr. This is not expected to have a major impact on the performance, except to give a slightly better representation of the upper percentiles.
The NORA10 atmosphere and wave hindcast (Reistad et al., 2011) was based on an atmospheric downscaling of the global ERA-40 reanalysis (Uppala et al., 2005). The wave model was set up in a nested configuration where ERA-40 10-m winds were used to force a 50-km resolution wave model covering the North Atlantic which provided boundary conditions for a 10-km wave model (see Breivik et al., 2009 for details on the nesting scheme).
The NORA10EI atmospheric downscaling uses ERA-Interim as boundary and initial conditions but is otherwise, identical to NORA10. The HIgh-Resolution Limited Area Model (HIRLAM, see Unden et al., 2002) is run in four 9-hr forecast sequences every day. HIRLAM is initialized by a blending of the ERA-Interim reanalysis and the previous HIRLAM forecast, valid at the start time of the forecast. This allows small scale structures to develop freely in the forecast while the large-scale structures are being controlled by the largescale forcing Yang (2005).
The model domain is a rotated spherical grid with the south pole positioned at 22 S, 40 W (see Figure 1). The domain is 248 × 400 grid points with 0.1 resolution. The vertical is resolved by 40 hybrid levels with variable spacing. Near the surface, the vertical coordinate closely follows the terrain and it gradually transforms with height toward a pressure coordinate at the top of the domain. The model equations are solved by a semi-implicit, semi-Lagrangian two-time level integration scheme and the time step is 240 s (Unden et al., 2002). Sequences of 10-m wind fields from +3 to +8 hr lead time exhibit the lowest biases and random errors and were therefore chosen for the wave model forcing as well as the model-observation comparison presented in the following sections.
No changes were made to the wave model physics or the spectral or spatial resolution. The WAM Cycle 4 model physics is described by Günther et al. (1992); Komen et al. (1994). The ice coverage was updated every 10 days based on the ice concentration in the ERA-Interim reanalysis.
F I G U R E 1 Overview of the model domain with offshore and coastal stations. The domains used for trend analysis are coloured. The domains are numbered 1-4 from south to north The model grid orientation and resolution are identical to the atmospheric grid. The two-dimensional spectrum is discretized with 24 directional bins (15 resolution) and 25 logarithmically spaced frequency bins, ranging from 0.042 to 0.41 Hz in 10% increments.

| GENERAL PERFORMANCE OF NORA10EI
NORA10EI is compared against NORA10, the combined ERA-40 reanalysis/ECMWF analysis (hereafter referred to as EC), ERA-Interim and the more recent reanalysis ERA-5. Norwegian observations, retrieved from the climate database operated by the Norwegian Meteorological Institute, form the basis for the validation. 1 The observation locations are indicated in Figure 1, where the stations 1-8 are offshore and stations 9-21 are onshore. The offshore stations provide discontinuous measurements over the period investigated, 1979-2017, and will not be used in the performance appraisal. All the onshore stations have reliable and relatively continuous measurement series over this period where the requirement has been at least 60% coverage every month. Observations have been despiked by removing observations deviating by more than 20 mÁs −1 from the hindcasts or the reanalyses. All onshore stations are used in the assessment of the general performance of NORA10EI together with the two arctic stations, Jan Mayen and Hopen, which also meet the requirements.
The validation is based on a total of 753,403 wind measurements. Figure 2 compares the Weibull distribution (Zong, 2006) of these wind measurements against the Weibull distribution of the two hindcasts, NORA10EI, NORA10, and the three reanalyses, EC, ERA-Interim and ERA-5. All three reanalyses exhibit significant overestimation of the frequency of wind speed in the interval 3-10 mÁs −1 and an underestimation of wind speed above 11 mÁs −1 . The two hindcasts show the same pattern, but with less deviation from the observations. Most significant improvements from the reanalyses are seen for wind speeds between 4 and 5 mÁs −1 and for wind speeds higher than 11 mÁs −1 . Figure 3 shows the general performance of the two hindcasts, NORA10EI and NORA10 together with the reanalyses EC, ERA-Interim and ERA-5, expressed by mean error (bias), root mean square error (RMSE) and the correlation with observations (panels a, b, and c, respectively).
The time series of the mean error ( Figure 3a) shows that both the hindcasts and the host reanalyses primarily underestimate the wind speed, except for EC in the period 2006-2011. The hindcasts show shorter periods with weak positive mean errors, however, the negative mean errors dominate the time series. The underestimation in wind speed is considerably smaller for NORA10EI and NORA10 than for EC and ERA-5, but very close to ERA-Interim up to 2002. From 2007 and forwards, NORA10 is the best performing of the hindcasts and the reanalyses, if we ignore the EC for the years 2012 and 2013. The performances of NORA10 and NORA10EI are also more stable, with smaller changes in mean error from year to year compared with the reanalyses. (The range interval in mean error is less than 0.4 mÁs −1 for the hindcasts, equal to 0.4 mÁs −1 for ERA-5, 0.5 mÁs −1 for ERA-Interim and 1.2 mÁs −1 for the EC.) Before 2002, the underestimation is greatest in EC and smallest in NORA10EI. The transition from ERA-40 to ECMWF analysis in 2002 is clearly visible by the abrupt change from a strong underestimation of the wind speed before 2002 to a weak overestimation in the years 2006-2011. This change in mean error in the EC time series has only a small impact on the NORA10 mean error, but the impact of changing the forcing of NORA10 is sufficient to cause a shift in the performance level. While NORA10EI outperforms NORA10 before 2002, NORA10 marginally outperforms NORA10EI in the second period of NORA10 (the mean error is reported for the period 2002-2017 in Table 1). This trend is also found in the hindcasts and in ERA-5, however, the decrease is considerably weaker.  Table 2).
The time series of the correlation between the hindcasts and the observations and between the (a)

Correlation of 10 m Wind Speed
Year 0.65 0.70 0.75 0.80 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 F I G U R E 3 General model wind speed performance expressed by mean error (a), root mean square error (b) and the correlation to the observations (c). EC (light grey) represents ERA-40 up to September 2002 and ECMWF analyses thereafter reanalyses and the observations (Figure 3c) show that ERA-5 yields the highest correlation overall. However, ERA-5 is biased low in wind speed. NORA10EI is as expected surpassed by NORA10 in the last part of the period. EC outperforms ERA-Interim from 2006, as must be expected as it is built on the operational model version of the ECMWF Integrated Forecast System (IFS) that became operational in December 2006 (Cy31r2). Note, however, that EC analysis is very close in performance to ERA-Interim even in the period 2003-2006, as its resolution is about 40 km in 2002 and thus much higher than the resolution of ERA-Interim (79 km). Figure 3 and Tables 1-3 demonstrate the effect of increased resolution and improved model physics in the host analysis. In September 2002, the resolution of the host analysis to NORA10 was changed from approximately 125 km to about 40 km with the transition from ERA-40 to operational ECMWF analyses. The transition  Figure 4 shows the 50th (median), 95th and 99th percentiles of observed and modelled 10 m wind speed at offshore stations (stations 1-8 in Figure 1). The offshore wind stations are very scarce in the early period, with just Ekofisk in operation between period 1980 and 1989. Gullfaks-C started reporting in October 1989, followed by Sleipner and Draugen in 1994 and Heidrun in 1995. Norne and Troll-A started reporting in 1998 and Heimdal in 2005. Offshore stations typically observe winds at heights between 30 and 130 m. The observations are here reduced to 10 m height by using the NORSOK profile defined in Appendix A1.
EC exhibits a lower range (6.7-8.4 mÁs −1 ) for the median wind speed. The trend is also opposite to what is observed with the highest values in the last decade of the period, caused by the change from ERA-40 to operational EC analyses in 2002. ERA-Interim has somewhat higher values than EC (ranging from 6.9 to 8.8 mÁs −1 ) and is closer to the observations. The ERA-Interim trends are also similar to the observations, that is, the highest values during the first two decades and somewhat weaker winds during the last part of the period. ERA-5 displays a relatively similar range (7.0-8.6 mÁs −1 ).
The 95th percentile observed wind speed varies between 15.2 and 19.8 mÁs −1 . NORA10EI underestimates the 95th percentile (with a range 14.4-17.3 mÁs −1 ). The underestimation is quite strong in the beginning of the period but is strongly reduced from 1998, probably caused by increased confidence in the measuring data with the take in of NORNE and TROLL-A. NORA10 exhibits a slightly smaller range in 95th percentiles than NORA10EI, but the differences are very small. Among the reanalyses, ERA-Interim performs the best in terms of 95th percentile wind speed, closely followed by ERA-5. The 99th percentile observed wind speed ranges from 18.5 to 24.9 mÁs −1 . NORA10EI and NORA10 both fit the 99th percentile observations in the last part of the period, but underestimate in the first part of the period. The range of NORA10EI is 17.1-20.5 mÁs −1 and NORA10 displays almost exactly the same range. It is however a question of how credible the observed percentiles in the beginning of the period are, as there are very few observations in the first two decades (see Figure 5).
A general observation from inspection of Figure 3 is that the NORA10 mean error (panel a) and RMSE (panel b) exhibit a weak, decreasing trend, with NORA10 outperforming NORA10EI after 2006. This suggests a small spurious trend in wind speed for NORA10, but, as can be seen from Figure 4, the effect is rather weak.  5 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 F I G U R E 4 Offshore stations, 50th (a), 95th (b) and 99th (c) percentiles of 10-m wind speed (mÁs −1 ) Figure 6 shows the quantile-quantile (QQ) comparison of 10-m wind speed and the associated scatter plot based on the eight maritime stations 1-8 in Figure 1. It is clear that the wind speed distributions of NORA10EI and NORA10 are very similar and very close to the observed distribution with NORA10EI showing a slightly better match against the highest observed wind speeds. The slightly lower RMSE of NORA10EI is evident in the slightly smaller spread seen in Figure 6b), but the quantiles very nearly coincide.

| OFFSHORE WAVE MEASUREMENTS
The wave model fields have been compared against wave observations of significant wave height, H s , from a number of offshore platforms in Tables 4 and 5. The performance of NORA10EI is generally slightly better than for NORA10 before 2002, and slightly poorer after 2006, in agreement with the results presented above for the 10-m wind speed. This is illustrated in Figures 7 and 8. The differences are small, and the comparison with observations in generally good. There are no big differences between the two, but NORA10 (red) tends to yield slightly higher H s after 2006. This tendency is particularly evident in Figure 8 (Draugen field, location 6 in Figure 1), where the 99th percentile (panel b) deviates by as much as 5% toward the end of the period. Ekofisk in the central North Sea (location 1 in Figure 1) exhibits a similar, but weaker, pattern (Figure 7b). The main reason is the small increase in mean wind speed due to higher resolution in EC analyses compared to the early period which is forced with ERA-40, as seen in the trend analysis (Section 6).  1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

| TRENDS IN MARINE WIND CLIMATE
It is generally difficult to estimate trends from reanalyses as updates to the observation network can lead to spurious trends, even with no changes to the model setup or to the assimilation scheme. ERA-Interim is no exception, as Aarnes et al. (2015) demonstrated. It is however clear that the trends found in the downscaled hindcast are somewhat more robust than those of the reanalysis itself. This is because the impact of the assimilation scheme is significantly weakened when the reanalysis is employed as a host analysis providing boundary and initial conditions for short-range forecasts with no assimilation. We do not see strong evidence of spurious trends throughout the model period, but the mean error is slightly more stationary for NORA10EI than for NORA10 (see upper panel, Figure 3, where the wind speed bias for all qualitycontrolled stations is shown). The RMSE (panel b) is also more stationary for NORA10EI than NORA10, and the correlation (panel c) is significantly higher near the beginning of the period for NORA10EI compared to NORA10. These differences are however small and in the open ocean even smaller (see Figure 4). Figure 9 shows the median and the 95th and 99th percentiles 10-m wind speed from NORA10EI at four offshore domains (shown in Figure 1) with trends calculated using Sen's slope (see Appendix A3). Figure 9 shows that Domain 1 has typically the highest median wind speed, but among the lowest 99th percentile wind speeds. Domain 4 has typically the lowest values of both median and upper percentiles. Domain 2 has the strongest wind speeds with 19.6 mÁs −1 in mean of the 99th percentile wind speed compared to 19.3 mÁs −1 for Domain 3.

Trends of the 99th percentile wind speed at four offshore domains
Year m·s -1 17 18 19 20 21 22 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 F I G U R E 9 NORA10EI time series of the trend in 50th (a), 95th (b) and 99th (c) percentile 10 m wind speed at the four different offshore domains shown in Figure 1 Unsurprisingly, the transition from ERA-40 to EC analyses shows a relatively strong positive trend for all the domains and for all the three percentiles investigated, except for the 99th percentile trend for Domain 1. Finally, ERA-Interim shows uniformly negative trends.
The slightly stronger positive trends (and weaker negative trends) in NORA10 compared to NORA10EI are mainly caused by the change in boundary conditions from ERA-40 to ECMWF operational analyses in September 2002. Note that these trends are all weak and in fact not statistically significant. Interestingly, the relatively minor differences seen between NORA10 and NORA10EI demonstrate that the hindcasts are quite insensitive to resolution changes in the host analysis. This is also in accordance with Davis (2014) who showed that little error can be clearly ascribed to the lateral boundary conditions with a proper choice of domain. Figure 10 shows the mean wind speed in the two periods related to the two different forcing periods of NORA10, 1979NORA10, -2002NORA10, and 2002NORA10, -2017. The general picture shows decreasing wind speed from west to east between Iceland and Great Britain, and from north to south in the North sea and from south to north in the Norwegian Sea and the Greenland Sea. This pattern reflects the synopticscale picture with frequent low-pressure systems moving eastward over the Atlantic and weakening as the systems approach land and when they travel northward into the Barents Sea. This pattern is clearly visible in both periods. The mean wind speed ranges from 4 to 10 mÁs −1 over the ocean. Figure 10b) shows the difference between the two periods for NORA10EI and for NORA10. Except for the Arctic region, NORA10EI exhibits only minor differences between the two periods. NORA10 shows weakly T A B L E 6 A 10-m wind speed trend estimates based on Sen's slope and the statistically significant threshold increasing wind speed in large parts of the domain. Common to the two hindcasts is an increase in wind speed south and south-east of Iceland, and in the Greenland Sea. The difference in wind speed between the two periods also agrees quite well with the trend analysis performed in Section 6. Because of the lack of reliable longterm measurements for the Arctic, we will not focus on the Arctic area here. However, due to receding sea ice cover, we expect considerable changes in wind speed and waves in this area (Aarnes et al., 2017;Waseda et al., 2018;Morim et al., 2019). Figure 10c) shows the difference between NORA10EI and NORA10 in the first and the second period. In the first period, the wind speed is stronger in NORA10EI in the southern part of the In the second period, the two models are more equal and the differences are mostly limited to different inflow at the boundaries. NORA10 shows stronger inflow between 65 and 80

| SPATIAL WIND PATTERNS
N, but NORA10EI still has stronger wind speed over the sea ice north of 80 N. Figure 11 shows the 99th percentile wind speed. It is clear that the upper percentiles exhibit the same spatial pattern as the mean values in Figure 10, but with values ranging from 13 to above 20 mÁs −1 over the ocean. Figure 11b) shows the difference between the two periods for NORA10EI and for NORA10. While NORA10 showed an increase in mean wind speed over large parts of the ocean, which was not visible in NORA10EI, NORA10EI shows an increase up to 0.5 mÁs −1 offshore from western Norway. NORA10EI also shows an increase in wind speed over the northern part of Great Britain and a strong increase north of Svalbard. NORA10 shows the same pattern, however, with even stronger increase in wind speed in the southern part of the domain. Figure 11c) shows the difference between the 99th percentile of NORA10EI and NORA10 in the first and the second period. NORA10EI has higher 99th percentile wind speeds in the southern domain in the first period and weaker wind speeds than NORA10 in the second period, as can be expected based on the differences between their host analyses.

| EXTREME VALUE ESTIMATES OF WIND SPEED AND SIGNIFICANT WAVE HEIGHT
The comparison of trends in mean and upper percentile wind speed and significant wave height suggest that the differences are small, and that the impact of the transition in boundary forcing used in NORA10 has had negligible impact on the overall statistics. As a further test of this, we compare the return value estimates from annual maxima of wind speed and significant wave height in NORA10 and NORA10EI. The procedure follows that outlined by Aarnes et al. (2012) where a generalized extreme value (GEV) distribution is fitted to annual (block) maxima (see Coles, 2001, pp 45-51). The GEV distribution is an asymptotic limit F I G U R E 1 2 Map of 100 year return values of 10 m wind speed (upper panels) and significant wave height (lower panels). The NORA10 return value estimates are shown on the left (a) and (c) for the period 1979-2017. The corresponding estimates for NORA10EI are found on the right (b) and (d). The NORA10EI estimates are higher than the NORA10 estimates, particularly in wind speed (up to 5 mÁs −1 difference), and considerably less in significant wave height for a distribution of blocked maxima M n = max{X 1 , X 2 , …, X n }. Following Coles (2001), the cumulative distribution function (CDF) of the block maxima formed from a random sequence of independent variables can be written where σ n is the scale parameter, μ n is known as the location parameter, and ξ is the so-called shape parameter. The GEV distribution contains as special cases the Fréchet (ξ > 0), Gumbel (ξ = 0) and reversed Weibull (ξ < 0) distributions. In the following analysis, we use the Gumbel distribution, fitted using a maximum likelihood method (Coles, 2001). This has the desired effect of creating smoother spatial return value estimates than the full GEV, making it easier to compare the two datasets. Figure 12 contrasts the 100-year return value estimates for U 10 and H s . For consistency, the NORA10 estimates (a) and (c) are based on the same period as NORA10EI (b) and (d), that is, 1979-2017. It is clear that NORA10EI yield somewhat higher return values than NORA10, both for U 10 and H s , especially in the region south of Iceland and north-west of Scotland. Here, the 100-year return value for wind speed increase from 35 to 40 mÁs −1 between the Faroe islands and Scotland. This gives a slight increase in 100-year return estimates of the significant wave height from 22 to 24 m in the same region. Although these changes are not dramatic, it shows that using EC analysis to force NORA10 has not led to particularly high return estimates, rather the opposite. It is however important to note that the return values are based on just 29 years, which is considered a short period for extreme value analysis, and represents a much smaller data set than other recent extreme value estimates of wind speed and significant wave height (Breivik et al., 2013(Breivik et al., , 2014Meucci et al., 2018). This means that the impact of individual storms becomes large (Aarnes et al., 2012).

| DISCUSSION
This study was motivated by the question of nonstationarity in NORA10 at the changeover from using ERA-40 to using ECMWF analyses as initial and boundary conditions. The results show that the stationarity issue is of negligible importance, although we do see a decreasing bias and RMSE and increasing correlation with wind observations in the second part of NORA10 (Figure 3).
The maps in Figure 10 reveal a larger negative wind speed bias in NORA10 compared with NORA10EI in the first period  in the North Sea and the Norwegian Sea, but a better match in the second period (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017). This explains the weak positive trends in NORA10 which are not reproduced by NORA10EI. However, over most parts of the oceans, the two hindcasts show a large degree of similarity despite differences in boundary and initial conditions. Since the two hindcasts employ the same numerical weather prediction model at the identical horizontal and vertical resolutions, the only differences stem from the boundary and surface forcing.
The weak trends in wind speed in NORA10EI are in agreement with other studies for northwestern Europe and the North-eastern Atlantic (Ciavola et al., 2011;Cusack, 2013;Feser et al., 2015;Minola et al., 2016).

| CONCLUSIONS AND FURTHER WORK
The NORA10EI hindcast is generally found to be in close agreement with NORA10. This study, and the generation of the NORA10EI hindcast, was in part motivated by a need to test the impact of an abrupt change in the forcing fields in the NORA10 hindcast as it is extensively used for extreme value analysis and climatological studies of wind and wave height in the North Sea, the Norwegian Sea and the Barents Sea (Aarnes et al., 2012;Furevik and Haakenstad, 2012;Bruserud and Haver, 2016), but more generally to look for the impact of host analysis on regional hindcasts. We find a slight reduction in the mean wind speed trend compared with NORA10, and as expected the bias and RMSE are more stationary. This does not appear to have a major impact on the upper percentiles, although, and the two hindcasts are in close agreement with each other for the offshore locations analysed. The representation of polar lows was qualitatively found to be slightly better in NORA10EI in the period before September 2002 (the host reanalysis ERA-Interim is superior to ERA-40). The difference is again small, and it is clear that a better host model and higher resolution of the hindcast itself is required before a proper representation of polar lows can be expected. Improved reanalyses are now available, in particular the new ERA-5 , and work is now underway to assess the required resolution for the next generation hindcast archive. The AROME atmospheric model (Seity et al., 2011) is one candidate to be tested with nonhydrostatic physics and a resolution of the order of 3 km.  Figure A1 shows the track of the January 12, 2002 Barents Sea polar low and the NOAA image of the cloud signature. The polar low was first observed in position 74 N and 28 E. It moved south-east and dissolved after 15 hr hitting Novaya Zemlya. Figure A2 shows the evolution of the mean sea level pressure field in NORA10 and in NORA10EI and near-surface wind speed exceeding 14 mÁs −1 from NORA10EI. The polar low is well F I G U R E A 1 Track and NOAA-image of polar low January 12, 2002. Source: STARS database represented in NORA10EI. The cyclone has a mean sea level pressure of 980 hPa in the first-time step which decreases to 976 hPa after 13 hr. The maximum wind speed increases from 18 mÁs −1 in the first-time step to 24 mÁs −1 after 13 hr. NORA10 does not produce a cyclone until 5 hr later than observed and has a minimum mean F I G U R E A 2 Polar low case January 12, 2002. Mean sea level pressure from NORA10EI (black) and NORA10 (red) and wind speed exceeding 14 mÁs −1 from NORA10EI (blue) sea level pressure of 982 hPa. Maximum wind speed in NORA10 is 16 mÁs −1 . The conclusion from this polar low is that NORA10EI reproduces the polar low very well, while NORA10 shows a too late and too weak evolution.

ACKNOWLEDGMENTS
ERA-40 period: Polar low case 2 (March 9, 2002) Figure A3 shows the track of the March 9, 2002 Jan Mayen polar low and the NOAA-image of the cloud signature. The cloud image shows a characteristic commashaped pattern which suggests a typical wave cyclone near occlusion (Douglas et al., 1995) Figure A4 shows the evolution of the mean sea level pressure field in NORA10 and in NORA10EI together with the nearsurface wind speed exceeding 14 mÁs −1 from NORA10EI. The polar low occurs in the rear of a synoptic scale cyclone hitting Trøndelag at the time step when the polar low was first observed. The polar low is not a fully developed vortex in neither NORA10 nor NORA10EI in the first-time step, but shows up in NORA10EI as a cyclone 6 hr later than first observed and last for the rest of the observed period. NORA10 shows a polar low 8 hr later than first observed and this polar low does only last for 3 hr. According to these two situations, NORA10EI shows an improved representation of the polar lows compared to NORA10.
After ERA-40: Polar low case 3 (January 7, 2009) The third polar low investigated, occurred in the Barents Sea 7 January 2009 and lasted for 7 hr. SAR winds of above 25 mÁs −1 were observed in the Barents Sea and part of the coast of Finnmark. At Banak airport located sheltered in the innermost part of the Porsanger fjord, wind speed of 13 mÁs −1 and wind gust of 17 mÁs −1 were observed. Figure A5 shows the track of the polar low and the NOAA image of the cloud signature. Figure A6 shows the evolution of the mean sea level pressure field in NORA10 and in NORA10EI and near-surface wind speed exceeding 14 mÁs −1 from NORA10. The location of the polar low is the same in NORA10 and NORA10EI. The location fits quite well with the observed polar low, but is somewhat too far east of the observed one. The polar low is fully developed in NORA10 at 04:00 UTC and in NORA10EI 1 hr later. NORA10 shows a maximum wind speed of 26 mÁs −1 which last for the whole period of the polar low. This wind speed values fits the SAR observations. NORA10EI shows somewhat lower wind speed and reaches 26 mÁs −1 at just one-time step (2009-01-07 08:00).
After ERA-40: Polar low case 3 (7 January 2009) The fourth polar low appeared in the Norwegian Sea at 18:00 UTC 26 February 2009 and lasted until 11:00 UTC 27 February. The Stars database 3 describes the polar low F I G U R E A 3 Track and NOAA-image of polar low March 9, 2002. Source: STARS database as a classic version formed off the coast of Troms with a cold-air outbreak and a strong cold upper trough as precursors to the polar low. Southwest of the main low, a secondary, less intense centre formed. An inversion layer north east of the northern centre was broken by heating from air above the sea surface, intensifying the polar low. The low made landfall at the coast of the Nordland in northern Norway with a maximum observed wind speed of 23 mÁs −1 . Wind gusts up to 28 mÁs −1 were observed. Figure A7 shows the track of the polar low and the NOAA-image of the cloud signature. Figure A8 shows that a polar low off the coast of Troms in northern Norway with a minimum mean sea level pressure of 989 hPa is present in both NORA10 and NORA10EI. However, the low is more extensive in NORA10 compared to NORA10EI. NORA10 shows the overall deepest mean sea level pressure throughout the lifetime of the low. NORA10 wind speed reached 24 mÁs −1 at 02:00 UTC February 27, 2009, comparable, but slightly stronger than the NORA10EI wind speed (23 mÁs −1 ). The maximum wind speeds in the models occur offshore and becomes strongly weakened before landfall.
Although no firm conclusions can be drawn from these four case studies, it seems clear that the polar lows are better represented by NORA10EI in the period up to September 2002 when ERA-40 was used as boundary conditions for NORA10, and conversely that NORA10 captures the polar lows better in the period after August 2002.

Trend analysis
The non-parametric Mann-Kendall (Mann, 1945;Kendall, 1975) and Sen's (Theil, 1950;Sen, 1968) method were used in the trend analysis of the 50th, 95th and 99th percentile wind speed in Section 6. The Mann-Kendall trend test is a frequently used test for monotonic trend in a time series based on Kendall rank correlation. The Mann-Kendall test statistic or score S is calculated as where n is the length of the time series, x is the data values in the time series, and sgn is the sign function; The variance is calculated as where data having the same value in the sample, have been tied up in groups. m is the number of tied groups and t i is the number of ties of extent i. With the requirement of a sample size which is greater than 10, the standard normal test statistic Z s is computed as If Z s is positive, the trend is increasing and opposite, if Z s is negative the trend is decreasing. The trend test is done at significance level α = 0.1. Sen's slope is used to determine the strength of the trend, calculated as the median of the slopes in the time series,