Validation of the reanalysis wave field

The ERA-Interim reanalysis is a global atmospheric, wave and ice data assimilation system beginning in 1979 and continuing in near real-time13. The spatial resolution of the wave model in the Arctic Ocean is around 110 km in longitude and 110 km in latitude, with wave spectra available for 24 directions and 30 frequencies. The relatively coarse grid resolution prevents the resolution of the fine-scale structure of the ice edge in the Arctic Ocean. While the recent reanalysis assimilates significant-wave-height data from an altimeter on the Jason-2 satellite, its orbital inclination of 66.038° precludes measurement of Arctic Ocean waves, implying the Artic wave field of the ERA-Interim reanalysis system is essentially lacking any data assimilation in recent years. Since ERS-1/2 were assimilated from Aug. 1991 to Jul. 2003, and ENVISAT from Jul. 2003 to Aug. 2012, 1991 and 2011 marks the transition between assimilation free and assimilated periods, which could be critical in the trend analysis. The sea-surface temperature (SST) and the ice concentration data assimilation systems have utilized the Operational Sea Surface Temperature and Sea-Ice Analysis (OSTIA) data in recent years. As Dee et al.13 report that the surface wind speed depends strongly on the SST and extent of the ice coverage in the polar region, uncertainties in the OSTIA sea-ice cover and SST affect the magnitude of the surface wind speed. Therefore, without data assimilation, the accuracy of the ERA-interim wave field remains uncertain.

The ERA-Interim wave field in the Chukchi and Beaufort Seas, interpolated on the wind and wave collocated 0.75 degrees regular grid, was validated by a 2016 wave observation campaign by The University of Tokyo. During the Mirai cruise (MR16-06) of the Japan Agency for Marine-Earth Science and Technology from 22 August to 5 October 2016, two drifting-type wave buoys (WII: Waves In Ice buoys) were deployed off Point Barrow on 10 September. The two buoys remained within an area of a few hundred square kilometres, and successfully collected wave data before contact was lost with both on 2 November 2016. The tracks of the two buoys, which are indicated by red and green trajectories in Fig. 1, remained in close proximity to one another until 19 September when a storm separated the buoys by approximately 50 km, before further separating during the 18 October storm by 250 km to 300 km.

Figure 1 (a) Buoy trajectories, sea-ice concentration (colour shading) and sea-level pressure (SLP) (contours) on 22 October 2016. The region bounded by the orange line indicates the area analyzed here. (b) An enlarged image of the buoy trajectories with the sea-ice concentration (colour shading) and SLP (contours) on 22 October 2016. (c) An enlarged image of the buoy trajectories with the significant wave height (colour shading) and SLP (contours) on 22 October 2016. The SLP, H s and sea-ice concentration are from ERA-Interim reanalysis data. The Grid Analysis and Display System (GrADS) version 2.0.2 (http://cola.gmu.edu/grads/) was used to create the maps in this figure. Full size image

The ERA-Interim H s at the buoy locations compares well with the observations (Fig. 2). Since the spatial resolution is coarse and time intervals are sparse, the nearest-neighbour interpolation was applied to the ERA-Interim data. The correlation coefficient between the ERA-Interim data and observed H s is 0.91 for both buoys, but 0.78 and 0.76 between the mean wave periods of the ERA-Interim data and the observations for buoys 1 and 2, respectively. While the timings of the storm events are well reproduced, the magnitudes of H s are slightly under-predicted during October. The reproducibility of mean wave period is not as good as that of significant wave height, and the differences between ERA-Interim mean wave period and observed energy period, T 0,−1 tend to be larger for smaller wave heights. The error metrics are summarized in Table S1. A similar comparison was made with measurements obtained with the Surface Wave Instrument Float with Tracking (SWIFT) buoy in 201411, which was deployed by the University of Washington and measured wave heights from 27 July to 28 September 2014 in the Chukchi and Beaufort Seas, to find a correlation coefficient with ERA-Interim data of 0.91, which is the same as for our 2016 observations.

Figure 2 The ERA-interim wave field (○) together with (a) the significant wave height of buoy 1 (red ●), (b) the significant wave height of buoy 2 (green ●), (c) the mean wave period of buoy 1 (red ●), and (d) the mean wave period of buoy 2 (green ●). Full size image

Large wave events were observed, for example, on 19 September, when buoys 1 and 2 recorded a H s of 4.86 m and 4.63 m, respectively, which is comparable to the highest wave directly observed in this region by Thomson et al.8. During this time, an Arctic cyclone developed off Point Barrow (Fig. S1)14 to the north of the buoy locations. As the location of the large wave height was recorded south of the cyclone centre, which is relatively widespread, the largest significant wave height in this region may even have been larger than the buoy observation. The H s of the ERA-Interim data and the buoys agree quite well during this storm. However, during the October 22 storm (Fig. 1), when buoy 2 recorded a significant wave height of 4.7 m, the reanalysis fails to reproduce the observed wave height. For both the 19 September and 22 October storms, the pressure minimums were located to the north of the buoys, and, therefore, the wind direction was predominantly from the west (Fig. 3). The wind speeds were relatively high during both storms at around 16 m/s and 13 m/s, respectively. Compared with the 19 September condition, the area of the ice-free waters on 22 October has substantially reduced. However, the cause of the difference of the observed and reanalysis H s for the October event is not because of the coarse resolution of ERA-Interim. The reproducibility of the October event did not improve with a 16 km high-resolution modeling that was conducted in a related study, and the reason for the discrepancy is likely the lack of accuracy of the wind. Distinct from the storm event observed during the Sikuliaq cruise in 2015 which was associated with a high-pressure system and an Easterly wind, both the September and the October events in 2016 were associated with an Arctic Cyclone. The wind was blowing from the west, and the sea ice extended south into the west of the Chukchi sea. However, the effective fetch was not limited by the sea ice in the upwind direction as the scale of the storm was comparable to the open water in the Chukchi and the Beaufort Seas (Fig. 1).

Figure 3 ERA-Interim data at the locations of buoys 1 (red) and 2 (green) for (a) 10-m wind speed, (b) 10-m wind direction, and (c) sea-level pressure. Full size image

The trend of the expected largest significant wave height in the ice-free waters

The wave, wind and ice fields are analyzed within a domain including the Laptev, East Siberian, Chukchi and Beaufort Seas (96.75 E to 113.25 W and 68.25 N to 81.75 N), which is the area bounded by the orange line in Fig. 1. The area of ice-free water in the domain varies during the summer season and enlarges over the analyzed 38 years. Note that ERA-Interim treats any area with a sea ice cover over 30% as without waves and the rest with ice cover less than 30% as ice-free. In the rest of this paper, we will consider grid-points where the wave parameter is undefined as areas covered with ice. The domain was chosen such that the boundary is either land or ice, even during the largest retreat of sea ice in 2012, except for the Bering Strait. The percentage of the ice-free water area to the total area of the domain including land and ice, ρ, is equivalent to the ratio of the number of the ERA-Interim grid points in the completely ice-free water and the total number of grid points in the domain area; \({\rho }\approx \frac{{N}_{icefree}}{{N}_{total}}\). Thus, this index ρ is related to the number of ice-free data points N in the domain (see equation 1). The 6-h significant wave height and wind speed at 10 m in August, September, and October are analyzed.

The August, September, and October monthly areal averages of H s and U 10 are calculated, along with the 38-year trends. The August, September and October climatological values of H s are 0.85 ± 0.11 m, 1.07 ± 0.12 m and 1.26 ± 0.17 m, respectively. The highest mean wave height and greatest variability occur in October. In Table 1, the linear trend of the mean H s and the scaling parameter of the Weibull fit are shown. On average, the linear trend of H s is around 5 mm/year, and that of the scaling parameter of the Weibull distribution is of the same magnitude. The linear trend of the scaling parameter \({c}_{{H}_{s}}\) is about half that estimated by Thomson et al.10 which is based on 23-year reanalysis data. The difference of the data length may account for this difference implying the acceleration of the increasing trend of the average wave height in the Arctic Ocean. We can state that since 1979, the average H s has increased by about 20%, corresponding to 0.15 m in August, 0.19 m in September, and 0.20 m in October. The estimate falls within the range of the increasing trend, 0.3–0.8%/year, detected by Wang et al.6. The wind speed over the ice-free waters, however, does not show any noticeable trend (Table 1). The August and September U 10 decreases by about 0.06 m/s and 0.12 m/s, respectively, and increases by about 0.17 m/s in October over the 38 years investigated, which amount to only a few percent of the climatological wind speeds of 6.0 m/s in August, 6.6 m/s in September, and 7.1 m/s in October. An independent study by Wang et al.6 also detects no statistically significant trend of the areal mean wind speed.

Table 1 Linear trends of the mean values and the scaling parameter \({c}_{{H}_{s}}\) of the Weibull fit to H s , and the linear trend of the mean values of the wind speed U 10 . Full size table

On the contrary, the maximum H s in the ice-free water has clearly an increasing trend, where Fig. 4a shows the expectation of the maximum H s in the ice-free water according to equation (3). The inter-annual variation is large as inferred from the scatter of the annual \(E[{H}_{s}^{max}]\) (green circles, blue squares, and red triangles) along the linear trends (green, blue and red lines) for August, September and October, respectively. The increasing trend is largest in October (Table 2), with an increase of almost 30% since 1979, which is more than a 70 cm increase from H s ≈ 2 m. For the other months, the increase is around 20% or 40 cm from 1979 to 2016. The robustness of the trend was tested using the homogenization tool, and was confirmed that the mixture of the assimilated and assimilation-free periods did not affect the detected trend estimate, see Fig. S215,16. As the ice starts to melt in July and August, the area of the ice-free water E[ρ] was little more than 10% in the 1980s (Fig. 4c); September had a similar percentage of ice-free water. However, in October, the area reduced to less than 10%. The area of ice-free water gradually started to increase in the 1990s and 2000s, when the percentage of ice-free water in September increased to around 30%, and then rapidly increased in the 2010s, reaching around 60% in 2012, which is the largest ice retreat to date. The correlation coefficient between the area of the ice-free water E[ρ] and the annual \(E[{H}_{s}^{max}]\) is 0.56 for August and September, and 0.68 for October. Therefore, to a certain extent, the long-term trend of the increase of the maximum significant wave height can be explained by the increase in the area of the ice-free water.

Figure 4 (a) The annual \(E[{H}_{s}^{max}]\) are plotted for August ( ), September ( ) and October ( ) from 1979 to 2016. The linear trends are indicated by green (August), blue (September) and red lines (October); (b) The annual E[U 10 ] and trend lines, with nomenclature the same as (a); (c) The annual E[ρ]. The solid lines indicate the change of ρ from August to October. Full size image

Table 2 Linear trends of the maximum values of H s and U 10 . Full size table

A possible reason for the enhancement in wave height as the area of open water expands is the increase in the effective fetch F11 on which the significant wave height depends following

$$(\frac{g{H}_{s}}{{U}_{10}^{2}})\propto {(\frac{gF}{{U}_{10}^{2}})}^{\alpha },$$ (4)

where α is typically around 1/2. Hence, the growth of the significant wave height depends on both the fetch F and the wind speed. While the retreat of sea ice during summer may enhance the strength of Arctic cyclones as a result of the thermal contrast between the ocean and atmosphere17, the extent is not yet evident to which the wind speeds over the ice-free water are enhanced. The ERA-Interim wind speed at 10-m altitude over the ice-free water is shown in Fig. 4b. The grid points of winds over ice are detected from the undefined values of the collocated wave height, and are excluded. The annual \(E[{U}_{10}^{max}]\) varies similarly to the annual \(E[{H}_{s}^{max}]\), where the greatest positive trend is found for October (Table 2). For August and September, the \(E[{U}_{10}^{max}]\) increased by around 70 cm/s from 1979 to 2016, while the October \(E[{U}_{10}^{max}]\) increased by around 2.3 m/s, which accounts for the increase of the expected maximum wind speed in the ice-free waters from 12 m/s to 14.2 m/s in October. Moreover, the inter-annual variation seems to follow a similar change between \(E[{H}_{s}^{max}]\) and \(E[{U}_{10}^{max}]\). Indeed, extremely high correlations of 0.92 for August, 0.89 for September and 0.94 for October are detected. In contrast, the correlation between E[ρ] and \(E[{U}_{10}^{max}]\) is 0.39 for August, 0.42 for September, and 0.77 for October, and hence are relatively lower. It is, therefore, puzzling that while the wind speed seems to affect the significant wave height directly in the ice-free waters, it itself is not affected as much as one would have conjectured by the enlarged area of the ice-free waters.

Possible causes of the increase in the maximum wave height: how does the wind speed intensify?

To further clarify the cause of the positive trend of the maximum significant wave height in the Arctic Ocean, a partial correlation analysis was conducted. As depicted in Fig. 4, the inter-annual variation is the dominant signal of the \(E[{H}_{s}^{max}]\) and \(E[{U}_{10}^{max}]\). A 7-year moving average is used as a low-pass filter to separate the low from the high frequency components,

$$E[{H}_{s}^{max}]=\,\langle E[{H}_{s}^{max}]\rangle +\,(E[{H}_{s}^{max}])^{\prime} $$ (5)

$$E[{U}_{10}^{max}]=\,\langle E[{U}_{10}^{max}]\rangle +(E[{U}_{10}^{max}])^{\prime} $$ (6)

$$E[\rho ]=\langle E[\rho ]\rangle +(E[\rho ])^{\prime} ,$$ (7)

where the low-pass filter is denoted by <> and the high-pass filter by ()′. The partial correlations are applied to the low-pass filtered \(\langle E[{H}_{s}^{max}]\rangle \), \(\langle E[{U}_{10}^{max}]\rangle \) and 〈E[ρ]〉, and high-pass filtered \((E[{H}_{s}^{max}])^{\prime} \), \((E[{U}_{10}^{max}])^{\prime} \) and (E[ρ])′ (Table 3).

Table 3 Partial correlations among high-pass-filtered expected-area maxima of wave height \((E[{H}_{s}^{max}])^{\prime} \) , wind speed \((E[{U}_{10}^{max}])^{\prime} \) , and the ice-free water area (E[ρ])′ (left column), and low-pass-filtered expected-area maxima of wave height \(\langle E[{H}_{s}^{max}]\rangle \) , wind speed \(\langle E[{U}_{10}^{max}]\rangle \) , and ice-free water area 〈E[ρ]〉 (right column). Full size table

High partial correlations are found between the low-pass filtered wave height and wind speed, \(\langle E[{H}_{s}^{max}]\rangle \) and \(\langle E[{U}_{10}^{max}]\rangle \), excluding the influence of 〈E[ρ]〉, and amount to 0.95 for August, 0.92 for September and 0.95 for October. Conversely, the partial correlations between ice-free water area 〈E[ρ]〉 and \(\langle E[{H}_{s}^{max}]\rangle \) or \(\langle E[{U}_{10}^{max}]\rangle \) are much smaller, and may even take a negative value. Therefore, the long-term positive trend of the maximum wave height \(\langle E[{H}_{s}^{max}]\rangle \) is closely related to the long-term positive trend of the maximum wind speed over the ice-free waters \(\langle E[{U}_{10}^{max}]\rangle \) angle, but less so to the ice-free water area 〈E[ρ]〉.

While the correlation between the high-pass filtered wave height \((E[{H}_{s}^{max}])^{\prime} \) and wind speed \((E[{U}_{10}^{max}])^{\prime} \) (0.78 for August, 0.68 for September, 0.87 for October) is not as high as that of the low-pass filtered data, it is much more pronounced than the correlation between the high-pass filtered ice-free area (E[ρ])′ and the wave height \((E[{H}_{s}^{max}])^{\prime} \) (<0.1). Therefore, while the inter-annual variation of the significant wave height is not directly correlated with the inter-annual variation of the ice coverage in the Arctic Ocean, \((E[{U}_{10}^{max}])^{\prime} \) is correlated well with (E[ρ])′ in September, but relatively weakly in other months. In summary, the correlation of interannual variation of the maximum wind speed \((E[{U}_{10}^{max}])^{\prime} \) and the maximum wave height \((E[{H}_{s}^{max}])^{\prime} \) is reasonably large, but other correlations do not show a systematic tendency.

Overall, the partial correlation analysis reveals that the area-maximum significant wave height in the Arctic ice-free waters is not directly influenced by the ice coverage for both long-term and inter-annual variations, but is strongly affected by the maximum wind speed in the ice-free water area. Whether this is related to the change in storm intensity in the past several decades is discussed below.