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  • View in gallery

    Climatological seasonal-mean vertically integrated eddy kinetic energy (contours; ×105 J m−2) bandpass-filtered for (a) <2 days, (b) 2–10 days, and (c) >10 days. Contour spacing is 5 × 105 J m−2. Cyclone track density per season (DJF) per 2° box in 1980–2016 is shown in shading in (b).

  • View in gallery

    Climatological (a) seasonal-mean and (b) seasonal-maximum Hs (shading) and mean wave and wind directions (red and black vectors, respectively) for DJF 1980–2016 (FULL). Colored dots correspond to buoy sites used in further analysis.

  • View in gallery

    Snapshots of Hs simulated by the decomposed wind fields (a) SUBS, (b) SYNOP, (c) LF, and (d) full forcing FULL at 1200 UTC 30 Dec 2000.

  • View in gallery

    Climatological seasonal-mean Hs (in DJF 1980–2016) and directions forced by decomposed wind fields: Hs and θ from (a) SUBS, (b) SYNOP, and (c) LF simulations and their difference with full forcing simulations: (d) (SUBSFULL), (e) (SYNOPFULL), and (f) (LFFULL).

  • View in gallery

    Climatological seasonal-maximum Hs (DJF, 1980–2016) forced by decomposed wind fields: Hs from the (a) SUBS, (b) SYNOP, and (c) LF simulations and their difference from full forcing simulations: (d) (SUBSFULL), (e) (SYNOPFULL), and (f) (LFFULL).

  • View in gallery

    Histograms of wave heights from SUBS, SYNOP, LF, and FULL wave model simulations on the (a) eastern and (b) western margins of the North Atlantic sited in blue dots in Fig. 2a.

  • View in gallery

    Difference between sum of wave heights simulated by decomposed forcing and waves simulated by full forcing [i.e., (SUBS + SYNOP + LF) − (FULL)]. The dashed line corresponds to zero.

  • View in gallery

    Ratio between (top) mean and (bottom) maximum significant wave heights from simulations with decomposed forcing and reference simulations: (a),(d) (SUBS)/(FULL) × 100%, (b),(e) (SYNOP)/(FULL) × 100%, and (c),(f) (LF)/(FULL) × 100%.

  • View in gallery

    Ratio between standard deviations of significant wave heights from simulations with decomposed forcing and reference simulations: (a) , (b) , and (c) .

  • View in gallery

    The canonical spatial patterns of eddy kinetic energy, wave heights, and wave directions for the (a) first and (b) second canonical modes for [EKESYNOP and θ] and [EKESYNOP and Hs], and the same for the (c) first and (d) second canonical modes for [EKELF and θ] and [EKELF and Hs]. Solid (dashed) lines indicate positive (negative) values of EKE canonical spatial patterns from CCA for [EKE and Hs]. Vectors indicate canonical patterns for wave direction (θ). Red (blue) shading represents positive (negative) values of canonical patterns for wave heights (Hs). Dots are positioned at the locations of maximum (blue) and minimum (purple) values of Hs canonical pattern from the CCA for [EKELF and Hs]. See text for more details regarding this plot.

  • View in gallery

    Normalized occurrence anomalies of DJF Hs at locations where Hs variability is maximal in the (b),(c) first and (e),(f) second CCA modes for [EKELF and Hs]. Locations are 2° × 2° boxes centered on markers in Figs. 10c and 10d and labeled there by corresponding subplots in this figure. (a),(d) Years are ranked according to the first two principal components, respectively. Black circles show values for the 95th percentile of Hs.

  • View in gallery

    Taylor diagram for Hs in reference model simulation (FULL) in comparison to NDBC buoys in DJF 2010.

  • View in gallery

    Spatial distribution of first leading EOFs of seasonal mean storm track (defined as bandpass-filtered vertically integrated EKE) for (a),(b) synoptic variability of EKE (2–10 days), (c),(d) low-frequency variability of EKE (>10 days), and (e),(f) significant wave height and mean wave direction.

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Ocean Wind Wave Climate Responses to Wintertime North Atlantic Atmospheric Transient Eddies and Low-Frequency Flow

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  • 1 Shirshov Institute of Oceanology, Russian Academy of Sciences, and Lomonosov Moscow State University, Moscow, Russian Federation
  • | 2 Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russian Federation
  • | 3 Shirshov Institute of Oceanology, Russian Academy of Sciences, and Lomonosov Moscow State University, Moscow, Russian Federation
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Abstract

Atmospheric transient eddies and low-frequency flow contributions to the ocean surface wave climate in the North Atlantic during boreal winter are investigated (1980–2016). We conduct a set of numerical simulations with a spectral wave model (WAVEWATCH III) forced by decomposed wind fields derived from the ERA-Interim reanalysis (0.7° horizontal resolution). Synoptic-scale processes (2–10-day bandpassed winds) are found to have the largest impact on the formation of wind waves in the western midlatitudes of the North Atlantic along the North American and western Greenland coasts. The eastern North Atlantic is found to be influenced by the combination of low-frequency forcing (>10-day bandpassed winds) and synoptic processes, contributing up to 60% and 30% of the mean wave heights, respectively. Midlatitude storm track variability is found to have a direct relationship with wave height variability along the eastern and western margins of the North Atlantic, implying an association between cyclogenesis over the North American eastern seaboard and wave height anomalies in the eastern North Atlantic. A change in wave height regimes defined using canonical correlation analysis is reflected in changes to their wave height distribution shapes. The results highlight the important role of transient eddies for the ocean surface wave climatology in the midlatitudes of the eastern North Atlantic both locally and through association with cyclone formation in the western part of the basin. These conclusions are presented and discussed particularly within the context of long-term storm track shifts projected as a possible response to climate warming over the coming century.

Denotes content that is immediately available upon publication as open access.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Margarita Markina, markina@sail.msk.ru

Abstract

Atmospheric transient eddies and low-frequency flow contributions to the ocean surface wave climate in the North Atlantic during boreal winter are investigated (1980–2016). We conduct a set of numerical simulations with a spectral wave model (WAVEWATCH III) forced by decomposed wind fields derived from the ERA-Interim reanalysis (0.7° horizontal resolution). Synoptic-scale processes (2–10-day bandpassed winds) are found to have the largest impact on the formation of wind waves in the western midlatitudes of the North Atlantic along the North American and western Greenland coasts. The eastern North Atlantic is found to be influenced by the combination of low-frequency forcing (>10-day bandpassed winds) and synoptic processes, contributing up to 60% and 30% of the mean wave heights, respectively. Midlatitude storm track variability is found to have a direct relationship with wave height variability along the eastern and western margins of the North Atlantic, implying an association between cyclogenesis over the North American eastern seaboard and wave height anomalies in the eastern North Atlantic. A change in wave height regimes defined using canonical correlation analysis is reflected in changes to their wave height distribution shapes. The results highlight the important role of transient eddies for the ocean surface wave climatology in the midlatitudes of the eastern North Atlantic both locally and through association with cyclone formation in the western part of the basin. These conclusions are presented and discussed particularly within the context of long-term storm track shifts projected as a possible response to climate warming over the coming century.

Denotes content that is immediately available upon publication as open access.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Margarita Markina, markina@sail.msk.ru

1. Introduction

Ocean surface wind waves, also known as surface gravity waves, influence upper-ocean turbulence and mixing (Babanin 2006; Babanin et al. 2009), heat and momentum air–sea fluxes (Komen et al. 1994; Veron et al. 2008; Sullivan and McWilliams 2002; Högström et al. 2009), the production of atmospheric aerosols via bubbles and sea spray (de Leeuw et al. 2011; Babanin 2011; Andreas et al. 2015), sea ice formation and breaking (Thomson and Rogers 2014; Kohout et al. 2014), and ice shelf disintegration (Massom et al. 2018). Due to these numerous interactions with the atmospheric boundary layer, cryosphere, and upper-ocean dynamics, ocean surface wave processes are becoming increasingly recognized as fundamental to climate over a range of spatial and temporal scales (e.g., Cavaleri et al. 2012; Fan and Griffies 2014; Babanin et al. 2012; D’Asaro 2014; Qiao et al. 2016; Walsh et al. 2017; Fan et al. 2009; Aijaz et al. 2017; Stoney et al. 2018). In practical terms, information about extreme waves is also critical for planning marine operations and the design of offshore marine infrastructure (Cardone et al. 2015). Ocean surface waves bear the signature of synoptic-scale atmospheric dynamics (e.g., Gulev and Grigorieva 2006; Semedo et al. 2015; Martínez-Asensio et al. 2016) and can transmit it over large spatial scales (Ardhuin et al. 2009; Delpey et al. 2010; Snodgrass et al. 1966). In this respect, wind waves are an important indicator of climate variability and the intensity of synoptic and mesoscale atmospheric processes.

This is particularly true in the North Atlantic, which is characterized by high-magnitude and strong variability in wind wave activity, especially throughout boreal winter (Gulev et al. 2003; Semedo et al. 2008; Hanley et al. 2010; Semedo et al. 2011). This is the direct result of midlatitude baroclinicity in general and, more specifically, the vigorous flow that comprises the regional atmospheric storm track and eddy-driven jet. Many authors have demonstrated a statistical association between the interannual variability in wind wave climate and time-averaged atmospheric characteristics, such as interannual fluctuations in the large-scale meridional pressure gradient referred to as the North Atlantic Oscillation (NAO; Bacon and Carter 1993; Carretero et al. 1998; Gulev and Hasse 1999; Wang and Swail 2001; Woolf et al. 2002; Wang et al. 2004; Camus et al. 2014). There is a great deal of discussion regarding storm track variability and so-called poleward deflection (e.g., Tamarin-Brodsky and Kaspi 2017; Booth et al. 2017), which has been found in some but not all reanalyses (Tilinina et al. 2013) as well as some model simulations corresponding to warming climate scenarios (Pinto et al. 2007; Fan et al. 2013; Woollings et al. 2012). Uncertainties in local storm track and eddy-driven jet changes propagate into projections of wave climate and limit our ability to have confidence in these diverse projections (Hemer et al. 2013; Fan et al. 2014; Khon et al. 2014).

Differences in wave climate in the tropics and middle and high latitudes are associated with the differences in dominant atmospheric circulations. In the tropics, summer wave heights are strongly impacted by changes in the intensity and frequency of tropical cyclones (e.g., Teague et al. 2007; Phibbs and Toumi 2014). These cyclones are generally expected to become relatively sparser but more intense and a change in their zonal and meridional distributions over the coming century is also expected to occur (e.g., Bender et al. 2010; Knutson et al. 2013; Studholme and Gulev 2018). At subpolar and polar latitudes, both winter and summer increases in seasonal mean and maximum waves have been identified over the last 36 years (Waseda et al. 2018) and are projected to continue into the coming century (Casas-Prat et al. 2018). These regime changes are expected to result from a set of complex wave responses to both wind and sea ice forcings acting simultaneously (Khon et al. 2014).

In the midlatitudes, wind wave climate is associated with storm track activity (Lozano and Swail 2002). A poleward shift in the midlatitude storm track is one of the most widely discussed features in the observational records (Bender et al. 2012) and numerical model simulations of future climate warming (Woollings et al. 2012; Bengtsson et al. 2006; Mbengue and Schneider 2017). This can be mostly understood as a response to an alteration of the tropospheric meridional temperature gradient and associated vertical shear. In addition, a poleward shift of the jet stream is observed (Woollings and Blackburn 2012), as well as a strengthening and poleward (and upward) shift in transient kinetic energy and momentum flux (Lorenz and DeWeaver 2007). Yin (2005) found that midlatitude westerlies also demonstrated a poleward shift. Ensemble mean model projections demonstrate evidence for increasing storm track activity in the eastern North Atlantic, amounting to a 5%–8% increase in baroclinic wave activity by the end of the twenty-first century (Ulbrich et al. 2008, 2013). However, a considerable spread among models is found (Harvey et al. 2012; Zappa et al. 2013a).

Wind wave climate variability in the midlatitudes is strongly associated with extratropical cyclonic activity via changes in wind speeds. In turn, atmospheric transient eddies may demonstrate different patterns of interannual variability from the mean winds and pressure gradients, especially locally (e.g., Gulev et al. 2002). The response of the wind wave climate to atmospheric forcing is quite complex since waves in the open ocean are a composition of locally generated wind sea and remotely generated swell (Young et al. 2011). Thus, wind wave climate reflects local trends in wind speed and the frequency and intensity of atmospheric processes integrated over larger scales. Quantifying the responses of wind wave climate to the varying impacts of different spatial and temporal scales of atmospheric motions presents a considerable challenge. In this respect, numerical wind wave modeling represents an effective tool for the simulation of wave characteristics as a function of varying atmospheric forcings.

Here, our aim is to derive insights into how variability in atmospheric dynamical processes of different length scales affects wave climate. As a case study, we conduct and analyze a suite of numerical experiments during boreal winter in the North Atlantic. Ultimately, improved understanding here may help to constrain and better understand uncertainties in wave climate projections. This paper is organized as follows: Section 2 gives model details, datasets, and the analysis methodology. Section 3 examines the responses of the simulated wind waves to decomposed atmospheric forcing. Section 4 discusses the link between wave climate and atmospheric interannual variability at different scales. Section 5 provides a brief discussion of the potential uncertainties as well as avenues for future work. The conclusions are presented in section 6.

2. Numerical simulations

a. Wave model and experiment design

The simulations in this study were conducted with version 5.16 of the third-generation spectral wave model WAVEWATCH III (WW3 herein; WAVEWATCH III Development Group 2016) for the North Atlantic from 0° to 80°N and 90°W to 15°E. For this domain, the influence of swell originating from south of the equator is considered to be negligible and is thus ignored (e.g., Alves 2006). We use the ST4 parameterization for wave energy input and dissipation (Ardhuin et al. 2010) and the Discrete Interaction Approximation (DIA) scheme for nonlinear wave interactions (Hasselmann and Hasselmann 1985). The model integration time step is 15 min. The simulations were performed for the boreal winter season [December–February (DJF)] over the period 1980–2016. Individual model runs are initiated two weeks in advance (i.e., mid-November) to account for the model spinup. This initialization period is discarded from further calculations. The model settings described above have been used in a number of wave climate studies (e.g., Chawla et al. 2013; Rascle and Ardhuin 2013; Markina et al. 2018).

Each seasonal experiment was run at 0.7° spatial resolution and forced by 10-m winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) dataset (Dee et al. 2011). ERA-Interim is the demonstrably optimal reanalysis dataset to use for interannual studies of wave climate due to its relative consistency over the record period in comparison to alternative products (Stopa and Cheung 2014). The ice source term package (IC0; Tolman 2003) used in our WW3 configuration assumes the exponential attenuation of waves in partially sea ice–covered regions given by 12-hourly sea ice concentrations from the ERA-Interim reanalysis. Grid points are defined as partially covered when sea ice concentrations are between 25% and 75%. Grid points with sea ice concentrations below 25% are treated as open water, while those above 75% are assumed to have zero wave energy, and the boundary conditions along the ice edges are considered the same as those for shore lines.

Throughout this manuscript, we use the notation FULL to refer to the results of the experiment forced by the original ERA-Interim winds. The FULL simulation serves as the reference model run. In three further experiments, the wind forcing was decomposed into three components corresponding to short-term subsynoptic variability (0–2 days), hereafter referred to as SUBS; synoptic-scale variability (defined here as 2–10 days; e.g., Hoskins and Hodges 2002), hereafter referred to as SYNOP; and low-frequency variability (more than 10 days), hereafter referred to as LF. A similar decomposition was previously used by Ayrault et al. (1995), Gulev et al. (2002), and Foussard et al. (2019). The wind field decomposition was performed using a bandpass Lanczos filter (Lanczos 1956; Duchon 1979), which was effectively used earlier by Gulev et al. (2002).

b. Diagnostics

We concentrate on significant wave height Hs and mean wave direction θ, which are derived from the spectral model solution at grid points that are free from sea ice for the entire period covered by the model integrations. In the analysis of covariability between wave climate and atmospheric variability (section 4), we discuss mean and extreme characteristics (95th percentile). The maximum values of Hs discussed in section 3 are used as proxies for the upper bound of the simulated wave heights (e.g., Caires and Sterl 2005; Janssen 2015), which are defined as seasonal-maximum values averaged over the period 1980–2016 (DJF).

As an Eulerian measure of the intensity of atmospheric dynamical processes over a range of scales we use vertically integrated eddy kinetic energy (EKE) (Lorenz 1955; Orlanski and Katzfey 1991) computed from <2, 2–10, and >10 day bandpass filtered 6-hourly wind fields (Blackmon 1976; Blackmon et al. 1977; Hoskins and Hodges 2002; Schneider et al. 2015; Woollings et al. 2016). The expression for EKE is given by
e1
where u′ and υ′ represent the bandpass filtered zonal and meridional components of wind speed, respectively; p represents pressure (the vertical coordinate); and g represents acceleration due to gravity. We use bandpass filtering to isolate atmospheric transient eddies since there is a risk of inadvertently including stationary eddies in more rudimentary eddy identification schemes (e.g., Mbengue et al. 2018). The remaining <2-day and >10-day bandpassed flows act as high-frequency (i.e., subsynoptic processes) and low-frequency modes of atmospheric forcing. The integral is evaluated between 800 and 200 hPa to capture dynamical processes in the free troposphere (e.g., Mbengue et al. 2018). Since we are particularly interested in midlatitude baroclinicity, a collection of potential metrics exist that could be used for this purpose. In particular, in addition to the vertically integrated EKE, near-surface eddy meridional heat fluxes () and upper-tropospheric eddy momentum flux convergence () are both viable candidates as measures of the baroclinic eddy life cycle (e.g., Chang et al. 2002; Mbengue and Schneider 2013). Since we are interested in atmospheric dynamical processes more generally, EKE is the logical candidate for the present analysis.

Figure 1 shows climatological EKE for different bandpassed ranges computed according to Eq. (1) and the mean cyclone track density during the winter season (DJF) from 1980 to 2016 (Fig. 1b). The maximum values of EKE in the synoptic range (~5.2 × 105 J m−2) are located to the east of Newfoundland and are associated with the region of intensive cyclogenesis and development in the North Atlantic. The highest-frequency mode (i.e., SUBS) of EKE (Fig. 1a) demonstrates a spatial structure very similar to its synoptic-scale counterpart, although with half the magnitude. By the nature of the bandpass procedure, bundled in with true subsynoptic dynamical processes, SUBS filtering may also contain a small number of synoptic-scale processes, such as fast propagating cyclones (e.g., Rudeva and Gulev 2011). The low-frequency filtering of EKE (Fig. 1c) has the largest magnitudes (up to ~30 × 105 J m−2) and this is an order of magnitude larger than EKE for the other components. The maximum values coincide at similar locations as in SUBS and SYNOP, but LF also reveals an additional second maximum in the eastern subtropics. This EKE pattern (i.e., an Eulerian measure of the storm track) is highly consistent with the pattern for cyclone counts (i.e., a Lagrangian measure of storm track density) in the North Atlantic, which is also shown in Fig. 1b. Lagrangian statistics have been derived from ERA-Interim storm tracks provided by K. Hodges at the University of Reading, as used in Roberts et al. (2014), based on a methodology described in Hoskins and Hodges (2002) and Hodges (1995). These storm tracks exhibit high consistency with the cyclone track climatologies available from other numerical tracking algorithms applied to ERA-Interim (Neu et al. 2013; Rudeva and Gulev 2011; Tilinina et al. 2013). There is a strong correspondence between the Eulerian and Lagrangian characterizations of the storm track in this particular region that is critical for wave formation (Gulev and Grigorieva 2006). The Lagrangian tracking algorithm also appears to pick up a second local maxima off the southeastern coast of Greenland, which is presumably either large polar lows (Stoll et al. 2018) or cyclones associated with the Greenland tip jets (Våge et al. 2009) that are not seen in the climatological EKE.

Fig. 1.
Fig. 1.

Climatological seasonal-mean vertically integrated eddy kinetic energy (contours; ×105 J m−2) bandpass-filtered for (a) <2 days, (b) 2–10 days, and (c) >10 days. Contour spacing is 5 × 105 J m−2. Cyclone track density per season (DJF) per 2° box in 1980–2016 is shown in shading in (b).

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

3. Wave climate responses to different scale atmospheric dynamical processes

a. Climatologies

The climatological seasonal-mean and seasonal-maximum distributions of wave heights and directions (DJF; 1980–2016) from the reference simulation (Fig. 2) show a maximum Hs of ~4.7 m in the northeastern sector of the North Atlantic, which is consistent with voluntary observing ship (VOS) observation climatologies (Gulev and Hasse 1998; Gulev et al. 2003), satellite data (Zieger et al. 2009; Young et al. 2017), and the ERA-Interim wave reanalysis (Dee et al. 2011). The pattern correlation with the ERA-Interim wave reanalysis is 0.97 for all winters (not shown), and the control experiment corresponds well with the U.S. National Data Buoy Center (NDBC) data in coastal areas (an example for 2010 is shown in Fig. A1 in appendix A). The seasonal-mean Hs is largest in an area displaced northeastward from the maximum storm track activity in the western North Atlantic (Fig. 2a). This pattern is generally consistent with the mean direction and spatial scales of swell propagation that contributes largely to the total significant wave heights in this region (Chen et al. 2002; Semedo et al. 2011). In areas with the most intensive wind wave formation, such as the western tropics and midlatitudes, the dominant wave direction (shown with red vectors) is more aligned with the mean wind direction (black vectors) than that over the rest of the domain.

Fig. 2.
Fig. 2.

Climatological (a) seasonal-mean and (b) seasonal-maximum Hs (shading) and mean wave and wind directions (red and black vectors, respectively) for DJF 1980–2016 (FULL). Colored dots correspond to buoy sites used in further analysis.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

The spatial structure of the seasonal-maximum Hs (Fig. 2b) reveals a pattern qualitatively similar to the one observed for the mean values (Fig. 2a), although with a noisier structure. There are several areas with maximum significant wave heights up to 15.9 m in the eastern midlatitudes, and there is a local peak in the Labrador Sea, with values up to 14 m. The observed spatial pattern reflects, to a certain degree, the influence of synoptic-scale atmospheric structures on the formation of wave height extremes.

Figure 3 shows model snapshots at 1200 UTC 30 December 2000 as obtained by the four aforementioned experiments (i.e., FULL, SUBS, SYNOP, and LF). This figure demonstrates how the simulated wave structures are superimposed and related to a corresponding simulation with full forcing at any given time. The smoothest and most intense wind forcing field (LF) is reflected in large-scale wave patterns (Fig. 3c), while the synoptic-scale (SYNOP) and subsynoptic-scale (SUBS) processes in the atmosphere influence the surface ocean at shorter spatial scales (Figs. 3a,b). The reference simulation with full wind forcing (FULL; Fig. 3d) superimposes the combined effect of low- and high-frequency atmospheric forcing, as would be expected.

Fig. 3.
Fig. 3.

Snapshots of Hs simulated by the decomposed wind fields (a) SUBS, (b) SYNOP, (c) LF, and (d) full forcing FULL at 1200 UTC 30 Dec 2000.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

The climatological seasonal-mean Hs and θ distributions for all four simulations forced by the decomposed wind fields are presented in Fig. 4. The synoptic-scale processes, which are predominantly associated with cyclonic activity, are resolved into a spatial pattern with Hs magnitudes being maximal (up to 2 m) in the midlatitudes of the North Atlantic (Fig. 4b). Subsynoptic-scale processes, in general, have the largest impact in the same areas as those in the SYNOP experiment, while inducing waves that are twice as small (Fig. 4a). Low-frequency forcing dominates the wave distribution in the tropics (i.e., following the persistent, steady flow of the easterly trade winds; Fig. 4f), with Hs values up to 2.5 m in the western tropical Atlantic (Fig. 4c). In addition, the LF component has a large impact over the eastern North Atlantic in the midlatitudes in areas that have the largest wave heights in the reference model run (Fig. 2), with mean Hs up to 3 m. Therefore, the area of highest climatological Hs (Fig. 2), while mostly dominated by LF, is also influenced by SUBS and SYNOP processes, whose contributions are nonnegligible.

Fig. 4.
Fig. 4.

Climatological seasonal-mean Hs (in DJF 1980–2016) and directions forced by decomposed wind fields: Hs and θ from (a) SUBS, (b) SYNOP, and (c) LF simulations and their difference with full forcing simulations: (d) (SUBSFULL), (e) (SYNOPFULL), and (f) (LFFULL).

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

Both the SUBS and SYNOP simulations demonstrate an almost purely divergent structure in θ emanating out from where the storm track intensity is maximal, which reflects the largely cyclonic origin of the momentum flux (i.e. surface stresses; Fig. 1 and Figs. 4a,b). The differences between these simulations and the control experiment (Figs. 4d,e) reveal strong negative deviations everywhere, with the largest differences along the eastern North Atlantic. These spatial characteristics reveal the association between waves driven by synoptic and subsynoptic processes and areas where the storm track is most active. These characteristics also emphasize the dominant role of low-frequency atmospheric flow in forcing wind waves in the eastern North Atlantic midlatitudes.

Figure 5 shows the responses of the wave height maxima to different atmospheric forcings in the same manner as Fig. 4 for does for the mean values. The patterns of maximum Hs in the SUBS, SYNOP, and LF experiments are noisier in comparison to those for the mean values (Fig. 4). The highest waves are identified in the Labrador Sea (in SYNOP) and the Irminger Sea along the eastern coast of Greenland (in LF). These signatures are not present in the distribution of the mean Hs (Fig. 4). The magnitudes of the maximum wave heights for all simulations with decomposed forcings are comparable (8, 9.6, and 8 m for SUBS, SYNOP, and LF, respectively). Physically, this means that atmospheric motion across the entire range of temporal scales, from subsynoptic and synoptic transient eddies to lower-frequency oscillations, may have an influence of equal magnitude upon the ocean surface wave climate. The largest difference between the decomposed and reference simulations is observed in SUBS since this component initially has the lowest magnitudes of atmospheric forcing, which is reflected in the lowest values of the simulated Hs and amounts up to 16.5 m near the northern coast of the British Isles (Fig. 5d). For the SYNOP and LF experiments, the differences compared with FULL are up to 10 m (Figs. 5e,f) and are observed over the northeastern North Atlantic.

Fig. 5.
Fig. 5.

Climatological seasonal-maximum Hs (DJF, 1980–2016) forced by decomposed wind fields: Hs from the (a) SUBS, (b) SYNOP, and (c) LF simulations and their difference from full forcing simulations: (d) (SUBSFULL), (e) (SYNOPFULL), and (f) (LFFULL).

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

The similar magnitudes of the maximal Hs across the SUBS, SYNOP, and LF simulations imply that the respective probability density distributions for Hs have very different shapes. To illustrate these regional connections among different scales of atmospheric variability with wind wave heights, Fig. 6 shows histograms for Hs at the sites indicated by blue dots in Fig. 2a. Stronger midlatitude transient eddy activity (i.e., an intensified storm track) leads to increased waves along the North American eastern seaboard, while it contributes less to waves along the European coast since they are highly affected by low-frequency atmospheric forcing (LF). Note also that transient eddies contribute mostly to low-magnitude waves along the eastern margin of the basin up to 4 m near the coast of the British Isles (while the full range of Hs expands up to 10 m). Along the western margin, cyclonic activity contributes to very large values over the entire spectrum of the ocean surface wave distribution.

Fig. 6.
Fig. 6.

Histograms of wave heights from SUBS, SYNOP, LF, and FULL wave model simulations on the (a) eastern and (b) western margins of the North Atlantic sited in blue dots in Fig. 2a.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

b. Consideration of inherent nonlinearity: Aggregated decomposed-forcing climates compared to full-forced climate

We note that the magnitudes of Hs in the FULL simulations are close but not exactly equal to the algebraic sum of the magnitudes of Hs in the simulations separately forced by the decomposed wind flow (i.e., FULLSUBS + SYNOP + LF). This result follows from the invocation of nonlinear processes in air–sea momentum fluxes, wave growth, and wave interactions. Moreover, the Lanczos filtering used for the wind forcing decomposition, while quite effective, may allow for the minor transfer of variance between the defined ranges (the so-called aliasing effect). Here, the aggregated sum of such aliasing in all filtered forcings corresponds to less than 1% of the total wind field over the majority of the domain. In the very deep tropics along the eastern boundaries, where climatological winds are <3 m s−1, such aliasing is maximal but even there this is less than 4% of the total forcing. Furthermore, these regions are confined and contribute very little to the overall wave climate. Therefore, the aliasing effect is negligible to the conclusions of this study.

The values for misalignment between FULL and (SUBS + SYNOP + LF) (Fig. 7) vary from −90% to 58%, with the average estimate being approximately −8.5%. The mean total difference between the algebraic sum of the simulations forced by decomposed wind fields and the magnitude of Hs in FULL is moderately negative, while there are high-magnitude positive values found along the North American coast. Atmospheric and surface wave processes responsible for this pattern over the western margin of the basin vary depending on latitude. In the tropics, this pattern most likely results from the relatively smooth and consistent trade winds retained in LF. In contrast, in the midlatitudes running up the eastern seaboard of the North American continent, this offshore pattern is presumably dominated by transient eddies in the atmosphere in SUBS and SYNOP because the influence of LF is relatively weak in this region, as discussed above (e.g., Fig. 6a and the corresponding discussion).

Fig. 7.
Fig. 7.

Difference between sum of wave heights simulated by decomposed forcing and waves simulated by full forcing [i.e., (SUBS + SYNOP + LF) − (FULL)]. The dashed line corresponds to zero.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

Moderately negative values of the differences are widespread around the eastern margin of the basin, which can presumably be explained by the wave growth resulting from the combination of numerous atmospheric processes operating simultaneously over a range of spatial and temporal scales (Fig. 3). The wave growth process is nonlinear (e.g., Miles 1957; Cavaleri and Malanotte-Rizzoli 1981) and, thus, an underestimation of the wave heights resulting from (SUBS + SYNOP + LF) relative to those revealed by the FULL experiment seems to be quite reasonable at the eastern midlatitudes. In the eastern tropics and equatorial region, the difference is strongly negative and, given generally low Hs magnitudes here (less than 1 m in the climatological seasonal mean; Fig. 2a), this difference is presumably associated with the persistent momentum flux in the LF simulations, which leads to the formation of higher waves relative to the FULL experiment. The same is true for the Gulf of Mexico.

To summarize the role of different forcing components in forming mean and maximum Hs, we consider the ratios between wave heights in the experiments with decomposed forcing and those in the reference experiment (FULL) for both the mean and maximum Hs (Fig. 8). For the maximum Hs, this ratio is further considered as a proxy for the upper bound of the observed contributions at different scales of the atmospheric dynamical processes to the wind wave climatology. Since the sum of the fractions is not equal to unity over most of the area, this diagnostic complements the analysis of the differences between the full and decomposed-forcing simulations presented above (Figs. 4d–f and 5d–f).

Fig. 8.
Fig. 8.

Ratio between (top) mean and (bottom) maximum significant wave heights from simulations with decomposed forcing and reference simulations: (a),(d) (SUBS)/(FULL) × 100%, (b),(e) (SYNOP)/(FULL) × 100%, and (c),(f) (LF)/(FULL) × 100%.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

c. Relative contributions to actual wave climate provided by atmospheric dynamical processes of different scales

As mentioned above, the area with the maximum seasonal-mean Hs in the northeastern North Atlantic is influenced by all three components of wind forcing (up to 70%, 30%, and 20% in the LF, SYNOP, and SUBS simulations, respectively). However, if we consider the seasonal-maximum values of Hs, LF accounts for up to 60%, with SYNOP and SUBS contributing 50% and 40%, respectively. The area with the highest impact of synoptic-scale atmospheric variability is located near the North American coast and in the Labrador Sea. The waves forced by synoptic-scale winds can be up to 80% of the mean and up to 90% of the maximum significant wave heights (Figs. 8b,e). At the same time, this area is affected by low-frequency atmospheric variability to a lesser extent (Figs. 8c,f): the LF simulation shows that waves have a general eastward direction (consistent with winds in LF), which thereby, does not provide favorable conditions for fetch along the North American coast. Subsynoptic-scale atmospheric processes do not significantly contribute to the mean wave characteristics (Fig. 8a), while they have a profound impact on the maximum waves (Fig. 8d) over the main North Atlantic storm track area (Fig. 1), particularly along the North American coast in the Gulf Stream region. The ratios for the wind fields are qualitatively similar (not shown), emphasizing the dominant role of low-frequency flow in the tropics and synoptic- and subsynoptic-scale processes in the midlatitudes.

To quantify the degree to which the different components contribute to the total variability in wave heights, we analyze the ratio between the standard deviations in each experiment relative to the control simulation. The largest values are observed in the LF simulation (Fig. 9c), where (Hs) has approximately the same magnitude as that in the FULL simulation, which reflects the dominant role that LF forcing plays in wave formation in the tropics and semienclosed basins.

Fig. 9.
Fig. 9.

Ratio between standard deviations of significant wave heights from simulations with decomposed forcing and reference simulations: (a) , (b) , and (c) .

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

In the midlatitude open ocean the majority of the total variability in Hs is defined by a combination of synoptic-scale and low-frequency forcings, with differing impacts along the eastern and western margins. The variability observed in the LF simulations accounts for up to 100% of the total variability in Hs along the British Isles, while along the North American coast the major agent is the synoptic-scale forcing (up to 70% of the total variability; Fig. 9b). Wave heights from the SUBS simulation demonstrate maximum variability compared to those in the control experiment in the semi-enclosed basins of the North Sea, the Mediterranean Sea, the Gulf of Mexico, and the Gulf of Guinea. The SUBS simulation also produces a local maximum along the North American coast. Given that the upper bound of the contribution to the mean wave climate from the SUBS scales is very low relative to that of SYNOP and LF (Figs. 8a–c) and that its contributions are homogenous in the North Atlantic (Fig. 9a), we neglect this dynamical length scale from further analysis and concentrate on the response of wind wave climate to synoptic and low-frequency modes of atmospheric forcing.

4. Linking wave climate and atmospheric interannual variability at different scales

To study the large-scale atmospheric flow patterns invoking specific wind wave responses, we use synoptic (2–10 day) and low-frequency (>10 day) filtered vertically integrated EKE (hereafter EKESYNOP and EKELF, respectively; Figs. 1b,c) as proxies for the intensity of atmospheric dynamical processes with the largest impacts on wave height dynamics in the North Atlantic. We explore the covariability of these characteristics with the mean Hs and θ from the simulations with full forcing (i.e., EKESYNOP vs Hs and θ; EKELF vs Hs and θ). For this purpose, we applied canonical correlation analysis (CCA; von Storch and Zwiers 1999) to the detrended seasonal (DJF) time series of EKE and wave characteristics. The first five empirical orthogonal functions (EOFs) were used for the CCA, and cumulatively they capture between 75.3% and 87.2% of the total variance for different variables. (Figure B1 shows the first two EOFs for EKESYNOP and EKELF with Hs and θ; for details, see appendix B.) The CCA was applied to the following pairs of parameters: [EKESYNOP and Hs], [EKESYNOP and θ] (where the first and second CCA modes are presented in Figs. 10a and 10b, respectively), F10 [EKELF and Hs], and [EKELF and θ] (where the first and second CCA modes are presented in Figs. 10c and 10d, respectively). Since the CCA for EKE with both θ and Hs demonstrate very similar spatial patterns (not shown), we present only EKE from the CCA for [EKE and Hs] (Fig. 10).

Fig. 10.
Fig. 10.

The canonical spatial patterns of eddy kinetic energy, wave heights, and wave directions for the (a) first and (b) second canonical modes for [EKESYNOP and θ] and [EKESYNOP and Hs], and the same for the (c) first and (d) second canonical modes for [EKELF and θ] and [EKELF and Hs]. Solid (dashed) lines indicate positive (negative) values of EKE canonical spatial patterns from CCA for [EKE and Hs]. Vectors indicate canonical patterns for wave direction (θ). Red (blue) shading represents positive (negative) values of canonical patterns for wave heights (Hs). Dots are positioned at the locations of maximum (blue) and minimum (purple) values of Hs canonical pattern from the CCA for [EKELF and Hs]. See text for more details regarding this plot.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

The correlation coefficients between the first two modes of wave heights, θ and EKE (synoptic and low-frequency), are presented in Table 1. The correlation for the lead canonical pair is 0.90 for EKESYNOP (Fig. 10a) and 0.95 for EKELF (Fig. 10c). The obtained spatial patterns for EKESYNOP are consistent with the results of Lozano and Swail (2002). Interestingly, the absolute loadings of Hs are maximal at similar locations in the canonical patterns for both EKESYNOP and EKELF.

Table 1.

Canonical correlation coefficients for the first two canonical pairs of wave heights and wave direction and synoptic and low-frequency modes of EKE.

Table 1.

The first canonical pairs for both EKESYNOP and EKELF imply that the ocean surface wave height anomalies in the northeastern North Atlantic (i.e., the Norwegian and North Seas) and the wave height anomalies of opposite sign in the eastern North Atlantic are associated, which implies the meridional displacement of the storm track (Figs. 10a,c). The major difference in the spatial structures of these canonical patterns between synoptic and low-frequency variability is that the maximal loadings are strongly shifted across the basin eastward in EKESYNOP relative to EKELF. In general, the low-frequency flow demonstrates a much more zonal pattern than its synoptic counterpart. This result is also true for the second canonical pattern discussed below.

Unlike the similar first modes, the second canonical patterns for EKESYNOP and EKELF diverge from each other (Figs. 10b,d). The pattern for the synoptic atmospheric flow (Fig. 10b) is presumably associated with the storm track intensity, which indicates areas with positive EKESYNOP loading in the storm track region in the eastern part of the North Atlantic associated with negative Hs loading in the same region. The region of negative EKESYNOP anomalies near the North American coast is characterized by weaker loading by nearly an order of magnitude less than the aforementioned region of positive anomalies of EKESYNOP and is associated with wave height tendencies of the opposite sign. Positive wave anomalies in the western and central North Atlantic (south of Iceland) are closely associated with cyclone formation on the eastern margin of the basin. Therefore, storm track activity in the western North Atlantic is profoundly connected to wind wave anomalies in the eastern North Atlantic.

The second canonical pattern of EKELF (Figs. 10d) indicates the strengthening of the zonal flow, which is reflected in the lower wave heights at eastern North Atlantic midlatitudes. In this way, lower wave heights at North Atlantic eastern midlatitudes can be considered either as a result of suppressed storm track activity (Fig. 10b) or a more intensive zonal flow in low-frequency mode (Fig. 10d). The CCA for the 95th percentile of Hs (not shown) reveals a very similar spatial pattern to that observed for the mean values; hence, the above discussion is also applicable to extreme waves.

The patterns for the mean wave direction (θ) demonstrate a strong association with those observed for transient eddies and low-frequency flows (Fig. 10, shown in vectors). Larger values of EKE are associated with eastward wave propagation, whereas lower EKE values are associated with westward wave propagation. Interestingly, the pattern for wave direction is much more consistent with atmospheric variability, while wave heights demonstrate the eastward displacement of maximum loadings relative to EKE.

Finally, to examine the specific responses of wave heights in areas with the largest association with the synoptic and low-frequency bands of the storm track, we discuss the normalized occurrence anomalies of Hs. Figures 11b, 11c, 11e, and 11f correspond to 2° boxes, centered at sites indicated by purple and blue dots in Figs. 10c and 10d, respectively (annotated with letters corresponding to the subplots in Fig. 11). These sites are objectively identified as the locations where the CCA pattern for Hs is minimal (Figs. 11b,e) and maximal (Figs. 11c,f) in the first (Figs. 11b,c) and second (Figs. 11e,f) canonical modes, respectively. To visualize changes to the wave distribution depending on the state [i.e., value of the principal component (PC)] of the particular mode of variability (i.e., the CCA mode), we sort years as a function of their rank in the first and second PC time series from the Hs EOFs. The values of the PCs themselves are shown in Figs. 11a and 11d.

Fig. 11.
Fig. 11.

Normalized occurrence anomalies of DJF Hs at locations where Hs variability is maximal in the (b),(c) first and (e),(f) second CCA modes for [EKELF and Hs]. Locations are 2° × 2° boxes centered on markers in Figs. 10c and 10d and labeled there by corresponding subplots in this figure. (a),(d) Years are ranked according to the first two principal components, respectively. Black circles show values for the 95th percentile of Hs.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

During the years with the lowest values of the first PC for Hs (i.e., 2010, 2001, 1996, 2013, 1982, and 2011), an increase in the occurrence of high waves is observed in the eastern part of the North Atlantic (Fig. 11c). Concurrently, a decrease in the occurrence of high waves is observed in the northeastern North Atlantic (Fig. 11b). The opposite pattern is observed during years with the highest values of the first PC (i.e., 1993, 1989, 1981, 2015, and 2012) in the northeastern part of the North Atlantic (Fig. 11b), where waves become higher in magnitude. Correspondingly, in the eastern North Atlantic (Fig. 11c), a negative anomaly in the number of high waves is observed.

For PC2, the pattern is quite noisy for the central North Atlantic (Fig. 11f), whereas in the northeastern North Atlantic (Fig. 11e) the pattern is close to that observed for PC1 (Fig. 11b). During years with the highest values of PC2 (i.e., 2014, 1990, 1994, 1995, and 2016), higher than normal waves are observed, whereas when moving toward the lowest values of PC2 we see a clear change in the wave height distribution toward lower values.

When considering extreme waves, changes in the 95th percentile of Hs are essentially consistent with the changes in wave distribution, as observed in the occurrence anomalies (Figs. 11b,c,e,f). The changes are subtler in the 95th percentile values, which change by only a few meters over the entire range of the PCs. Meanwhile, the maximum wave heights are heavily dependent on the sampling variability; therefore, they may not necessarily correspond to changes in the wave distribution. For example, this conclusion is true for 1990 (Fig. 11b), 1998 (Fig. 11c), and 2008 (Fig. 11e).

5. Discussion

Considering potential uncertainties in our results, it should be noted that all potential errors and misrepresentations inherent in surface winds are transmitted into wave models (Cavaleri 2009) because wind-driven momentum flux to the surface ocean is the only energetic source for wind wave growth. As such, important issues exist related to deriving a vertical wind profile in the atmospheric surface layer. These profiles are typically derived from Monin–Obukhov similarity theory (Obukhov 1946; Monin and Obukhov 1954), which is semiempirical and can be implemented in various flavors through the choice of stability classification and similarity functions. Small but nonnegligible diversity among such interpretations exists in models and reanalysis products (Jiménez et al. 2012).

Uncertainties in reanalysis surface winds may also include the impacts of inhomogeneities in data assimilation. An additional source of uncertainty is associated with the interpolation of atmospheric forcing characteristics between the model time steps, which is particularly relevant in the highly turbulent atmospheric boundary layer. In these experiments, atmospheric surface winds are linearly interpolated from 6-hourly ERA-Interim winds to the integration time step of the spectral wave model (15 min in this study). In this way, higher-resolution atmospheric forcing can provide a more reliable forcing for wave models because any local boundary layer particularities, as well as atmospheric transient eddies, can significantly alter in structure and location over the course of 6 h (e.g., Held and Hoskins 1985).

Additional nuances arise from the nonconstant nature of the drag coefficient CD. In the model, CD differences due to temperature are neglected, and only variations with wind velocity are used for its determination. We estimate that the effective (i.e., time-mean and domain-mean) wind speed in FULL is 6.9 m s−1, while the analogous values in the filtered forcings are 1.6, 3.0, and 5.1 m s−1 for SUBS, SYNOP, and LF, respectively. The corresponding effective CD × 103 values are, therefore, 1.0 (FULL), 0.9 (SUBS), 0.7 (SYNOP), and 0.8 (LF) (Edson et al. 2013). Further examination of this issue is beyond the scope of this study since here we focus on the atmospheric dynamical controls of wave climate rather than the absolute veracity in the representation of air–sea interaction itself. All potential uncertainties and issues discussed above do not limit the effectiveness of the conclusions we draw given the nature of this study.

Here, we have analyzed the large-scale atmospheric flow configurations driving wave climate responses. We do not account for the decomposition into wind sea and swell separately. Gulev and Grigorieva (2006) found that wind sea demonstrates the strongest association with the local wind speed, while swell is most sensitive to the variation in cyclone frequency. In this way, the analysis of the interannual variability in wave climate and the identified remote responses in the near-coastal areas require consideration, specifically in the context of potentially different signals of these characteristics.

The analysis concept presented here provides an interesting avenue for the study of diversity in wind wave climate projections (e.g., Hemer et al. 2013; Fan et al. 2014; Wang et al. 2014; Aarnes et al. 2017). The NAO is projected to tend toward its positive phase in the upcoming century (e.g., Fan et al. 2013), which may be partially linked to high-confidence Arctic sea ice loss projections (Screen 2017). Thus, the local storm track and eddy-driven jet will likely experience corresponding perturbations (Ulbrich et al. 2013; Zappa et al. 2013b). We note this here since synoptic-scale atmospheric processes have been shown to play an important role in the distribution of mean and extreme waves, particularly along the North American coast.

A considerable question remains of how well global climate models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) represent the behavior of individual atmospheric transient eddies. For example, the majority of global climate models demonstrate a reasonable number of extratropical cyclones; however, in most of them, the storm track is found to be either too zonally oriented or displaced southward in the central North Atlantic (Zappa et al. 2013a). CMIP5 global climate models also tend to underestimate cyclone intensity, specifically in the winter season (e.g., Zappa et al. 2013a). The magnitude of changes in storm track intensity in the Northern Hemisphere is the largest in the eastern North Atlantic and exceeds half of the interannual variability. This result is found in up to 40% of CMIP5 models (Harvey et al. 2012) but, again, there is no consensus between models for areas with maximum Hs to the south of Iceland. This spread in uncertainties, which are all of atmospheric origin, resoundingly influences projections of wave climate, particularly in storm track influenced areas, such as the North Atlantic (Hemer et al. 2013). In this way, understanding the differential effect of atmospheric flow decomposed into different length scales on ocean surface waves can contribute a new perspective in understanding projections of future wind wave climate.

Ocean surface waves have been demonstrated to contribute to extreme water level events in coastal areas (Vitousek et al. 2017; Rueda et al. 2017; Vousdoukas et al. 2018; Melet et al. 2018). These works note specifically that the contributions of surface waves to sea level rise and associated events are both largely unconstrained and, for the most part, poorly appreciated. Given this, it is particularly relevant to observe regional responses of wave climate to variability in extratropical storm track activity.

6. Conclusions

We analyzed the different responses of the ocean surface wind wave field in the North Atlantic to atmospheric dynamical processes of various scales in boreal winter. For this purpose, we performed a suite of numerical experiments conducted with a spectral wave model forced by bandpass filtered winds. We, thus, decomposed atmospheric forcings into subsynoptic (<2 days), synoptic (2–10 days), and low-frequency (>10 days) components and specifically resolved the responses of wave climate to each of these individually.

The region of the seasonal-maximum wave height in the North Atlantic is displaced northeastward of the area with the most vigorous tropospheric flow (measured here by vertically integrated EKE). The subsynoptic and synoptic-scale atmospheric forcings are found to have the largest impacts upon wind waves along the North American coastline and in the Labrador Sea (up to 70% of the total Hs). Meanwhile, in the midlatitudes, where the mean wintertime Hs is ~4.7 m, waves are generated by simultaneous contributions from both atmospheric synoptic-scale variability (i.e., transient atmospheric eddies) and lower-frequency atmospheric forcing, such as prevailing westerlies. Subsynoptic-scale variability does not significantly contribute to the seasonal-mean wind wave characteristics but does have a considerable impact on the seasonal-maximum wave heights. This result is particularly true along the North American coastline and over the Gulf Stream region.

In subsequent analysis of responses to interannual atmospheric variability, we have concentrated on the influences of synoptic-scale transient eddies and low-frequency flow since they are found to have the largest effects on both the absolute wave heights and interannual variability. Wind waves in the eastern midlatitudes of the North Atlantic are strongly influenced by low-frequency atmospheric forcing, with only a low estimated upper bound for the contribution from synoptic-scale variability (~30%). Synoptic-scale processes in the western Atlantic are critical for modulating wind wave variability in the eastern midlatitudes. In this way, the reduction in wave heights along the European coast is likely associated with situations when weakening cyclone activity is observed over the North American eastern seaboard and more intensive zonal flow is observed within the low-frequency mode. At the same time, the meridional displacement of atmospheric transient eddies and low-frequency flow is associated with corresponding wave height anomalies. This relationship is also found to be reflected in the occurrence of anomalies in significant wave height distributions at sites along the eastern North Atlantic boundary. The change in the wave regime, which is well captured by the leading PCs of Hs, reflects a change in the ocean surface wave distribution and corresponding variability in extreme waves.

Acknowledgments

We are grateful to the three anonymous reviewers for extremely useful comments, which helped very much to improve the manuscript. We thank Cheikh Mbengue for the useful discussion, particularly regarding the Eulerian characterization of a storm track. We thank Kevin Hodges for providing the data on cyclone trajectories and very much appreciate his comments on the first versions of the manuscript. We thank Yulia Zyulyaeva for her methodological insights. We also thank Alexander Babanin and Bernard Barnier for more general discussions on the first manuscript versions. This work is the IORAS contribution to the ST-ASS-0149-2018-0001. This work was funded by Grant 17-77-20112 from the Russian Science Foundation (cyclone activity analysis) and Agreement 14.W0331.006 with the Ministry of Education and Science (analysis of forcing fields). WAVEWATCH III is available courtesy of the National Oceanic and Atmospheric Administration (NOAA). We thank the ECMWF for releasing their data to the public. These model experiments were conducted using the Lomonosov supercomputer at Moscow State University.

APPENDIX A

Validation of Reference Simulations

The main body of the paper claims a good agreement between the model results and the ERA-Interim reanalysis (section 2a) and mentions that the model configuration has been widely used in wave climate studies. However, as discussed above, coastal areas are particularly difficult to model with high accuracy, and models are known to underestimate higher-magnitude waves in particular (Stopa and Cheung 2014). Figure A1 shows the validation against buoy data from the National Data Buoy Center (NDBC; http://www.ndbc.noaa.gov/) along the U.S. eastern seaboard and demonstrates a mean Pearson correlation coefficient of 0.92 (varying from 0.9 to 0.95). In view of the arguments presented above, model results are considered to be reliable for the analysis conducted in this study.

Fig. A1.
Fig. A1.

Taylor diagram for Hs in reference model simulation (FULL) in comparison to NDBC buoys in DJF 2010.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

APPENDIX B

EKE and Significant Wave Height EOFs

Figure B1 shows the EOFs for the seasonal-mean EKESYNOP and EKELF, Hs, and . The synoptic and low-frequency modes of the EKE reveal similar patterns with Hs, with a significant portion of the total variance being contained within the first two EOFs. The first mode contains 40.6% and 31.5% of the variability in EKELF and EKESYNOP, respectively, and 43% of the variability in significant wave height. The second EOF corresponds to 26.2% and 17.9% of the variability in EKELF and EKESYNOP, respectively, and 30.7% of the variability in Hs, with smaller values for the subsequent modes. Regarding wave direction, the first EOF accounts for 29.5% and the second EOF accounts for 14.5% of the variability in . The correlation coefficient between the first PCs of Hs and EKE is 0.78 for the EKE synoptic mode and 0.92 for the EKE low-frequency mode (p value < 0.00001 in both cases), which confirms the link between these two characteristics.

Fig. B1.
Fig. B1.

Spatial distribution of first leading EOFs of seasonal mean storm track (defined as bandpass-filtered vertically integrated EKE) for (a),(b) synoptic variability of EKE (2–10 days), (c),(d) low-frequency variability of EKE (>10 days), and (e),(f) significant wave height and mean wave direction.

Citation: Journal of Climate 32, 17; 10.1175/JCLI-D-18-0595.1

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