Abstract

The seasonal structure of the wind sea and swell is analyzed from the existing 29-yr surface gravity wave climatology produced using a coupled atmosphere–wave model. The swell energy fraction analysis shows that swell dominates most of the World Ocean basins for all four seasons, and the Southern Ocean swells dominate swell in the global ocean. The swells are loosely correlated with the surface wind in the midlatitude storm region in both hemispheres, while their energy distribution and propagation direction do not show any relation with local winds and vary significantly with season because of nonlinear interactions. The same coupled system is then used to investigate the projected future change in wind-sea and swell climate through a time-slice simulation. Forcing of the coupled model was obtained by perturbing the model sea surface temperatures and sea ice with anomalies generated by representative Working Group on Coupled Modelling (WGCM) phase 3 of the Coupled Model Intercomparison Project (CMIP3) coupled models that use the IPCC Fourth Assessment Report (AR4) A1B scenario late in the twenty-first century. Robust responses found in the wind seas are associated with modified climate indices. A dipole pattern in the North Atlantic during the boreal winter is associated with more frequent occurrence of the positive North Atlantic Oscillation (NAO) phases under global warming, and the wind-sea energy increase in the Southern Ocean is associated with the continuous shift of the southern annular mode (SAM) toward its positive phase. Swell responses are less robust because of nonlinearity. The only consistent response in swells is the strong energy increase in the western Pacific and Indian Ocean sector of the Southern Ocean during the austral winter and autumn.

1. Introduction

Ocean surface gravity waves (OSGW) exist at the interface between the atmosphere and the ocean and account for more than half of the energy carried by all waves on the ocean surface, surpassing the contribution of tides, tsunamis, and coastal surges (Kinsman 1965). The OSGWs directly generated and affected by local winds are called wind seas. As they leave their generation zone, the wind seas become swells. Since swells can be very persistent with energy e-folding scales exceeding 20 000 km (Ardhuin et al. 2009), they can carry sizable wave energy across global oceans and impact offshore and coastal infrastructures. The International Energy Agency (2007) has estimated that approximately 8000–80 000 TWh yr−1 (cf. total world electricity production from all sources of 17 450 TWh yr−1) could be produced from the ocean via wave power.

Waves play a significant role in many physical processes at the air–sea interface, including the momentum, heat, and moisture fluxes (Li and Garrett 1997; Grachev and Fairall 2001; Hanley and Belcher 2008; Fan et al. 2009; Cavaleri et al. 2012). Transfer of momentum can occur both up and down in that swells can also interact with the airflow and create wave-driven winds (Harris 1966). In the presence of swells outrunning relatively weak winds the velocity spectra no longer have universal shapes, so the classical Monin–Obukhov similarity theory is not valid, and the stress may be near zero and sometimes negative (Drennan et al. 1999). Donelan et al. (1997) measured the air–sea momentum flux via eddy correlation off the coast of Virginia and found that swell aligned with the wind can deliver momentum to the atmosphere. Many cases of upward momentum flux (i.e., flux from ocean to atmosphere) have been observed in tropical Pacific, where calm to light winds are common in the presence of strong swells (Grachev and Fairall 2001).

Studies on the swell and wind-sea climatology have been conducted using satellite measurements (Chen et al. 2002; Young et al. 2011) and observations from voluntary observing ships (Gulev and Grigorieva 2006). These studies are limited by the length of satellite measurements and uncertainty in the separation between wind-sea and swell heights, which depend on human judgment and experience.

Semedo et al. (2011) constructed a global climatology of wind sea and swells through spectral partitioning using the 40-yr European Centre for Medium-Range Weather Forecast (ECMWF) Re-Analysis (ERA-40) wave reanalysis data produced by the ocean wave prediction model (WAM; WAMDI Group 1988; Komen et al. 1994) at 1.5° horizontal resolution in both latitude and longitude. They found the global wave field to be dominated by swell waves with the swell energy portion of total wave energy greater than 65% almost everywhere across the World Ocean (even in extratropical regions during winter). However, Caires et al. (2004) found the ERA-40 data to underestimate the significant wave height at wind speeds above 14 m s−1. One reason for the underestimate could be the rather coarse angular and frequency resolution (12 directions and 25 intrinsic frequencies) used in the WAM configured in ERA-40. With this resolution, the spectrum has a broad directional distribution, and low-frequency swells in the Pacific are not always well captured (Janssen 2004). Hemer et al. (2010) also pointed out that, as a consequence of the relatively coarse resolution of the atmospheric model and its limited ability to resolve storm systems, Southern Ocean wave heights are underestimated in ERA-40. For these reasons, Semedo et al. (2011) may have underestimated the energy in both the wind sea and swells.

Further studies have been conducted on dynamical and statistical global wave climate projections, with such studies focused on significant wave height and mean wave parameters (i.e., period and direction) (Wang and Swail 2006; Mori et al. 2010; Hemer et al. 2012; Fan et al. 2013; Hemer et al. 2013a). There is, however, no study that considers how swell and wind sea may be altered under conditions of anthropogenic climate change. The present study aims to contribute to this question of great importance for climate impacts, particularly near the coast.

Fan et al. (2012) have developed a global simulation system by coupling the operational wave model (WAVEWATCH III) developed at the National Centers for Environmental Prediction Environmental Modeling Center to the Geophysical Fluid Dynamics Laboratory (GFDL) High Resolution Atmospheric Model (HiRAM). They generated a 29-yr wave climatology at 0.5° horizontal resolution, and the wave spectra were discretized into 24 directions and 40 frequencies. This wave climatology was shown to be reliable through evaluations against National Data Buoy Center observations, satellite measurements, and ERA-40 reanalysis. In particular, the significant wave height low bias in ERA-40 was improved. The model wave fields also show strong response to the North Atlantic Oscillation in the North Atlantic and the Southern Oscillation index in the Pacific Ocean that are well connected with the atmospheric responses. Hanafin et al. (2012) show that WAVEWATCH III is capable of both reproducing the observed phenomenal sea states and accurately predicting the subsequent propagation for the swell field.

In the present study, we analyze the seasonal variations of the wind-sea and swell climatology using wave spectra data produced by Fan et al. (2012). We also investigate the wind-sea and swell climate change to the sea surface temperature (SST)/sea ice anomalies in the late twenty-first century through a time-slice climate change simulation using the Fan et al. (2012) coupled model.

The paper is presented in five sections. The model data and spectra partitioning method are described in section 2, and the wind-sea and swell seasonal climatology are presented in section 3. In section 4, we analyze the wind-sea and swell projections for the end of the twenty-first century, and then we offer a summary in section 5.

2. Model data and method

a. Simulated wind-sea and swell climatology

The 29-yr (1981–2009) Atmospheric Model Intercomparison Project (AMIP)-type simulation of wave climatology by Fan et al. (2012) is conducted using a coupled atmosphere–wave model developed at the National Oceanic and Atmospheric Administration (NOAA)/GFDL. Prescribed SSTs from the Hadley Centre Sea Ice and SST version 1.1 dataset (HadISST1.1; Rayner et al. 2003) are used as the lower boundary condition for the atmospheric model. In addition, well-mixed greenhouse gases, volcanic aerosols, and both tropospheric and stratospheric ozone vary from year to year, following the procedure used in the GFDL Coupled Model, version 2.1 (CM2.1), historical simulations in the phase 3 of the Coupled Model Intercomparison Project (CMIP3) database (Delworth et al. 2006).

Both the atmosphere and ocean surface gravity wave models are configured with 0.5° horizontal resolution, and the simulation outputs are saved every 6 h. The wave spectrum F(f, θ) at every grid point is discretized using 24 directions (θm, m = 1, … , 24) and 40 intrinsic (relative) frequencies extending from 0.0285 to 1.1726 Hz (wavelengths of 1.1–1920 m), with a logarithmic increment of f(n + 1) = 1.1f(n), where f(n) is the nth frequency. Because of the nature of the latitude–longitude grid that WAVEWATCH III uses, unless an extremely small time step is used, the model will generate a numerical instability at high latitudes. Thus, the global simulation domain is cut off at 72°N at the northern boundary. There is no cutoff at the southern boundary, which extends to Antarctica. At both the land–sea and ice–sea boundaries, wave action propagating toward land is assumed to be absorbed without reflection, and waves propagating away from the coast are assumed to have no energy at the coastline. Ocean waves can penetrate remarkable distances into ice fields and impact sea ice thermodynamics by breaking up ice floes and accelerating ice melting during the summer or by influencing sea ice growth and hence the morphology of the mature ice sheet during the winter (Squire 2007; Williams et al. 2013). Creating the cutoff at 72°N at the northern boundary will limit the interactions between waves and sea ice, which is not a feature available in this coupled model but are important research questions that need to be addressed with a more comprehensive model that includes waves and sea ice.

The method of Hanson and Phillips (2001) is used for spectra partitioning in WAVEWATCH III. A detailed partitioning implementation is described in Tracy et al. (2007). A wind-sea fraction W is introduced for the partitioning,

 
formula

where E is the total spectral energy,

 
formula

and Up is the component of the wind in the wave direction multiplied by the wave age factor Cmult,

 
formula

where U10 and θwind are the magnitude and direction of the 10-m wind, respectively. When Up is larger than the local wave phase velocity c, locally generated waves dominate the wave spectrum. Thus, E|Up>c represents the energy in the wind-sea part of the spectrum. The constant Cmult is set to be 1.7, which follows Tracy et al. (2007).

The wind-sea (swell) peak direction is defined as the mean direction in the frequency–wavenumber bin containing the peak frequency of the wind sea (swell) only. The global wave field is very complicated and the wave spectra can be broad and have several propagating directions. Determining which direction to use in this study is very important. We choose peak direction instead of mean direction because looking at the mean has the potential to confuse signals (particularly in the swell sector, which may have multiple peaks; e.g., consider the mean of two opposing swells). Thus, we choose to look at the characteristics of wind sea/swell that have the peak energy, with the dominant wave conditions being defined by wave frequencies with the most energy.

The 6-hourly U10, wind-sea and swell energy and peak direction, and the swell energy fraction (S = 1 − W) are averaged during the 29-yr period to produce the seasonal means. The seasons are defined as follows: boreal winter (austral summer) represents the average from January to March (JFM), boreal spring (austral autumn) represents the average from April to June (AMJ), boreal summer (austral winter) represents the average from July to September (JAS), and boreal autumn (austral spring) represents the average from October to December (OND).

b. Methodology for the time-slice simulations

To generate more stable statistics and eliminate possible complications in the response that might depend on the phase of El Niño–Southern Oscillation (ENSO), for example, we have chosen to follow the same strategy used in Zhao et al. (2009) and Fan et al. (2013). Namely, we use seasonally varying SSTs with no interannual variability as the lower boundary condition for the atmospheric model in all time-slice simulations.

The projection experiments as well as the control are listed in Table 1. For the control climatological SST simulation (present climate time slice), a time averaged SST over the time period of 1982–2000 was calculated using the NOAA optimum interpolation SST analysis dataset (Reynolds et al. 2002). We then perturb the control simulation with SST anomalies taken from various climate models with projections near the end of the twenty-first century for the future time slice. We consider four anomaly patterns. Three are obtained from the three models [GFDL CM2.1; Met Office (UKMO) Hadley Centre Coupled Model, version 3 (HadCM3); and Max Planck Institute (MPI) ECHAM5] that have the ability to simulate several different El Niño metrics in the current climate (van Oldenborgh et al. 2005). The fourth SST pattern is obtained by taking the ensemble mean for the 18 CMIP3 models (ENS18). All results are taken from the A1B simulation in the CMIP3 archive (https://esg.llnl.gov:8443/index.jsp) (Meehl et al. 2007) utilized extensively by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). We compute the multimodel ensemble mean SST anomaly by differencing the period 2081–2100 and the period 2001–20 from the historical simulations (labeled 20C3M in the CMIP3 archive). For each of the three individual models, we first use one realization (run 1 in the CMIP3 archive) to compute the linear trend from 2000 to 2100 and then use this linear trend to calculate the SST anomaly for an 80-yr period (comparable time period with the multimodel ensemble mean). The SST anomalies are computed separately for each month at each grid point.

Table 1.

Model experiments: All SST anomalies are taken from the A1B simulation in the CMIP3 archive (https://esg.llnl.gov:8443/index.jsp) (Meehl et al. 2007) utilized extensively by the IPCC AR4 assessments.

Model experiments: All SST anomalies are taken from the A1B simulation in the CMIP3 archive (https://esg.llnl.gov:8443/index.jsp) (Meehl et al. 2007) utilized extensively by the IPCC AR4 assessments.
Model experiments: All SST anomalies are taken from the A1B simulation in the CMIP3 archive (https://esg.llnl.gov:8443/index.jsp) (Meehl et al. 2007) utilized extensively by the IPCC AR4 assessments.

The seasonal SST anomalies for all four models are presented in Fig. 1. The warming patterns are similar among the four seasons for each model with stronger warming during the boreal summer. The HadCM3 anomaly is relatively large in the Pacific and relatively small in the Atlantic, while ECHAM5 has the largest average anomalies over the ocean domain. The CMIP3 SST-ensemble anomaly is much smoother compared to individual realizations since many features are smoothed out through the ensemble averaging. In general, the warming is stronger in the Northern Hemisphere and the SST anomaly in the Southern Ocean is much smaller compared to the rest of the global ocean. Notice that all four patterns show an anomaly from near-zero to −3 K (GFDL CM2.1) in the northernmost North Atlantic. This phenomenon is caused by the gradual weakening of the North Atlantic meridional overturning circulation during the twenty-first century because of increasing levels of greenhouse gas concentrations in the atmosphere (e.g., Dixon et al. 1999).

Fig. 1.

Seasonal mean SST anomaly (left)–(right) from GFDL CM2.1, Met Office HadCM3, MPI ECHAM5, and CMIP3 SST ensemble.

Fig. 1.

Seasonal mean SST anomaly (left)–(right) from GFDL CM2.1, Met Office HadCM3, MPI ECHAM5, and CMIP3 SST ensemble.

To generate the initial condition for the wave-coupled system, a 1-yr integration of the coupled system is conducted for all experiments. For this 1-yr run, the wave model starts from a calm sea; the atmospheric and land initial conditions at 1 January 1980 are taken from the end of a 10-yr run of the HiRAM that uses climatological SSTs. The spinup time needed for the wave model by itself is less than 1 month and is dominated by transit times of swell through the Pacific Ocean.

The control run and each of the perturbed runs are of 10-yr length, which is treated as 10 ensemble members for each experiment. The control run is shown to have good agreement with ECMWF Interim Re-Analysis (ERA-Interim) data (Hemer et al. 2013a). Compared to the climatology described in section 3, the control run produces slightly higher annual mean U10 and significant wave height in the Southern Ocean and lower U10 and significant wave height in the western North Pacific region (Fan et al. 2013).

3. Wind-sea and swell seasonal climatology

The seasonal variations of U10, wind sea, and swell are analyzed in this section.

a. 10-m winds

The seasonal mean U10 values are presented in Fig. 2. The magnitude of the wind speed (color) were calculated by averaging the 6-hourly wind magnitude, and the wind directions (arrows) were calculated by averaging the x and y components of the wind vectors separately. The highest wind speeds (12–13 m s−1) are found in the region of the westerlies during the respective hemisphere winter season.

Fig. 2.

Seasonal averaged 10-m wind magnitude (color) and direction (arrow) for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The lengths of the arrows are scaled with the 10-m wind magnitudes. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

Fig. 2.

Seasonal averaged 10-m wind magnitude (color) and direction (arrow) for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The lengths of the arrows are scaled with the 10-m wind magnitudes. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

The seasonal variability of westerly winds in the Northern Hemisphere (NH) is much greater than in the Southern Hemisphere (SH). In the NH, the westerlies are mainly dominated by North Atlantic Oscillation (NAO) in the North Atlantic and are cyclonic around the Icelandic low (Hurrell and van Loon 1997) and dominated by ENSO in the North Pacific and are cyclonic around the Aleutian low (Rasmusson and Wallace 1983). Their strength vary from 7–8 m s−1 with a small meridional extent between 45° and 60°N in JAS to 11–12 m s−1 with much larger meridional extent between 30° and 60°N in JFM. While for the SH, the strength of the westerlies only vary from 10–11 m s−1 in JFM to 12–13 m s−1 in JAS, and its northern extent only varies about 5° maximum through the four seasons. In general, the Southern Ocean winds are strong all year.

The strength of the trade winds is much stronger during the boreal winter and spring compared to summer and autumn in the NH but do not vary as much with seasons in the SH. These results are consistent with the satellite measurements (Halpern et al. 1994). The Indian Ocean monsoon is strongest during the boreal summer, with 10–11 m s−1 winds blowing northwest in the SH and northeast in the NH. The Somalia low level coastal jet also peaks during the boreal summer and makes the winds stronger between the northeast coast of Africa and the west coast of India.

b. Energy content and propagation pattern of wind sea and swells

The fraction of total swell energy in the entire wave spectrum S is averaged for the four seasons and shown in Fig. 3. Swell energy dominates more than 90% of the World Ocean basins for all four seasons in most regions, with the following exceptions: 1) the North Atlantic midlatitude storm region, where S is lowest along the eastern coast of North America and increases eastward along the storm track; 2) the trade wind regions in the western Pacific (during boreal winter) and Indian Ocean monsoon region (mainly during austral winter), where the wave spectrum is dominated by wind sea along the east coasts of continents and gradually becomes swell dominant toward the east; and 3) the Southern Ocean, where on average the energy contribution from the wind seas and the swells are comparable during the austral winter and spring. Also notice that the semienclosed seas (e.g., the Gulf of Mexico and Caribbean Sea, the Mediterranean Sea, and the South China Sea) are mostly dominated by wind seas because of the difficulty of swell propagating into these regions.

Fig. 3.

Seasonal mean distribution of S for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The white regions represent ice-covered areas.

Fig. 3.

Seasonal mean distribution of S for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The white regions represent ice-covered areas.

The equatorial area has the highest swell fraction (S > 0.9) throughout the year, especially the tropical Indian Ocean, where more than 95% (S > 0.95) of the wave energy is from swells all year. The subtropical areas in the Southern Hemisphere (between 20° and 40°S) also have very high swell fraction (S ≈ 0.85) throughout the year, because of the year-round weak wind and very strong swells propagating from the Southern Ocean.

The overall global pattern of swell fraction agrees with Semedo et al. (2011), who calculated the swell fractions using the ERA-40 wave spectra. However, the swell fractions in our study are generally lower than in Semedo et al. (2011), especially in the Southern Ocean, where they found swells dominate throughout the year. WAVEWATCH III uses a different spectral partitioning scheme (as described in section 2) from that used by Semedo et al. (2011) with WAM could be a possible reason for these differences, since different partitioning schemes may cause differences in wind-sea and swell energy estimates. Another reason could be that WAM used to create ERA-40 data was configured with a relatively low angular and frequency resolution, with 12 directions and 25 intrinsic frequencies, whereas the wave spectrum in WAVEWATCH III used in this study is discretized into 24 directions and 40 frequencies. Therefore, the ERA-40 spectra have a broad directional distribution and the low-frequency swells in the Pacific are not always well represented (Janssen 2004). Tolman (1992) also pointed out that the influence of numerical errors on wave growth rates, response to turning winds, propagation of swells, and dynamical interaction between swells and wind sea is closely related to both the spatial and spectrum resolution of the wave model. A significant part of the numerical errors can be eliminated by using a finer spatial resolution and extended frequency range. Furthermore, the different seasonal partition (World Meteorological Organization definition) used in Semedo et al. (2011) may also contribute to the difference in the swell fraction between these two studies.

The seasonal mean wind-sea and swell energy density and peak directions are presented as arrows in Fig. 4. The arrow colors and length represent the total energy density of the swell and wind-sea part of the wave spectrum. The corresponding wind-sea and swell significant wave heights are presented in Fig. 5 and 6 as well. The maximum wind-sea and swell energy densities (significant wave heights) are generally found at the midlatitude storm region and decrease toward the equator for each season. The average wind-sea directions (arrows in Fig. 5 and warm colors in Fig. 4) follow the average wind directions closely for all four seasons, while the swell directions (arrows in Fig. 6 and cold colors in Fig. 4) can be very different, even opposite to the wind directions (see Fig. 2).

Fig. 4.

Seasonal mean peak swell and wind-sea propagation direction for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The color and length of the arrows represent the total energy density in the swell part (cold colors) and wind-sea part (warm colors) of the wave spectrum. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

Fig. 4.

Seasonal mean peak swell and wind-sea propagation direction for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The color and length of the arrows represent the total energy density in the swell part (cold colors) and wind-sea part (warm colors) of the wave spectrum. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

Fig. 5.

Seasonal averaged wind-sea significant wave height (color) and peak propagation direction (arrow) for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

Fig. 5.

Seasonal averaged wind-sea significant wave height (color) and peak propagation direction (arrow) for (a) JFM, (b) AMJ, (c) JAS, and (d) OND. The arrows are plotted at every 20th grid point (~10°) for easy viewing.

Fig. 6.

As in Fig. 5, but for swell significant wave height.

Fig. 6.

As in Fig. 5, but for swell significant wave height.

1) The midlatitude and high-latitude region

In the Southern Ocean, the swell directions are close to the wind-sea directions for all four seasons, except along the Antarctic ice boundaries, where the swell directions start to turn southward. The maximum wind-sea energy density (significant wave height) is found in the Indian Ocean sector of the Southern Ocean for all four seasons, while the maximum swell energy density (significant wave height) is found to the south of southwest Australia. During the austral winter, the wind-sea energy density reaches its maximum (>12 kJ m−2) with a peak direction toward the east. The maximum swell energy density also reaches its maximum with a slightly lower magnitude (~11 kJ m−2) and slightly steered to the south of the wind-sea direction. At 30°–35°S, the Southern Ocean swells start to gradually turn northward and propagate toward the NH with much lower energy density (<4 kJ m−2), consistent with the idealized simulations of Alves (2006) where Southern Ocean generated swell was observed in all the world’s ocean basins. The wind-sea and swell energy density in the Southern Ocean decreases through the austral spring and reaches their minimum of 7–8 kJ m−2 during the austral summer, while their propagation directions do not vary much with seasons.

In the North Atlantic, the maximum wind-sea energy density is also larger than the maximum swell energy density during the boreal winter and autumn, and the centers of both maximum energy densities are found at the northeast sector of the North Atlantic. During the boreal winter, the wind-sea energy density reaches its maximum (~8.5 kJ m−2) and the peak propagation directions are mainly directed toward the east (northeast at the northern end). The peak swell propagation directions are steered 45°–90° to the right of the wind-sea directions with a lower energy density of 7–7.5 kJ m−2. As in the Southern Ocean, the wind-sea and swell directions do not vary much seasonally, but the magnitude of their energy density changes significantly between seasons.

Contrary to the North Atlantic, the maximum wind-sea and swell energy density in the North Pacific have comparable magnitude during boreal winter and autumn. The center of the maximum wind-sea energy is found to the southwest of the Aleutian Islands, while the center of the maximum swell energy is to the southeast. During the boreal winter, both the wind-sea and swell energy densities reach their maximum (~8 kJ m−2). The wind-sea peak directions are cyclonic around the Aleutian low, while the peak swell directions are directed toward the southeast. These swells can propagate all the way across the equator and toward the Southern Ocean with much lower energy density (<3 kJ m−2). Unlike the Southern Ocean and the North Atlantic, both the wind-sea and swell propagation directions vary with seasons corresponding to the wind pattern changes. The wind-sea peak directions are mainly directed eastward to the south of the Aleutian Islands during the boreal spring and autumn with relatively lower energy density (~6 kJ m−2), and the angle between the swell and wind-sea directions are smaller compared to the boreal winter. During the boreal summer, the wind-sea energy density reaches the minimum of less than 3 kJ m−2, and its peak propagation direction is eastward along the Aleutian Islands and northward south of the Aleutian Islands. The corresponding swells are propagating eastward toward the North American coast with a minimum energy density of the year.

In this study, both the wind-sea and swell significant wave height in the midlatitude region (Fig. 5, 6) are considerable higher than in Semedo et al. (2011) because of the low bias in ERA-40, as we discussed in section 1.

2) Equatorial region

The wind-sea energy densities in the equatorial Pacific Ocean vary from 3 to 4 kJ m−2 during the winter and are approximately 1 kJ m−2 during the summer for both hemispheres, following the variations of the trade winds. Their directions do not vary much through the year and mainly propagate westward. Although the swell energy densities do not vary much in the tropics, their peak directions change dramatically with seasons. During the boreal winter, the swell fields in the tropical North Pacific are dominated by the North Pacific midlatitude storms and mainly propagate southward. When these swells get to the tropical South Pacific, they encounter the northeastward-propagating swells from the Southern Ocean. The nonlinear interaction among these swells result in eastward-propagating swells, which is opposite to the trade wind and thus the wind-sea peak propagating directions. During the boreal summer, the swells in the entire tropical Pacific Ocean are dominated by the Southern Ocean swells and mainly propagate northward. For the boreal spring and autumn, the swell strength from the North Pacific storm track and the Southern Ocean are comparable. Thus, the swells are propagating southeast (northeast) in the tropical North (South) Pacific and eastward at the equator.

While the swells in the Indian Ocean are dominated by the Southern Ocean storms and mainly propagate northward with similar energy density all year, the wind-sea energy density and directions vary significantly with season following the changes of the Indian Ocean monsoon. The angle between the wind seas and the swells can vary from a few degrees to 180°.

In the presence of swells outrunning relatively weak winds, which is typical in the tropics, the velocity spectra no longer have universal shapes, so the classical Monin–Obukhov similarity theory is no longer valid (Drennan et al. 1999; Semedo et al. 2009; Smedman et al. 2009). The presence of counter and cross swells can result in drag coefficients that are much larger than the value for a pure wind sea, while upward momentum transfer is associated with fast-traveling swell running in the same direction as the wind (wind sea). Hence the swells can significantly affect the momentum fluxes, SST, and mixed layer depth, particularly in the tropical Pacific and Indian Ocean, and may play an important role in ENSO as well (Cavaleri et al. 2012). Similarly, misalignment of wind and waves (Stokes drift mainly generated by wind seas) modulates wave-driven Langmuir mixing rates in the surface ocean (Van Roekel et al. 2012). Although our study does not address these effects, we highlight here the potential importance of swells in climate studies.

We document in Table 2 the global averaged mean wave energy density and the fraction of it that is contained in the swells. The global wave energy reaches its highest value in the austral winter when the Southern Ocean waves are the strongest. Even though the Northern Hemisphere waves in the midlatitude storm region are the strongest during the boreal winter, the global wave energy is the lowest during that season. This result emphasizes the importance of Southern Ocean waves on global surface ocean wave energy.

Table 2.

Global averaged mean wave energy density (kJ m−2) and the percentage of wave energy that is contained in swells . Here, E is the total wave energy in Eq. (2), W is the wind-sea fractions in Eq. (1), and Aocean is the total ocean area.

Global averaged mean wave energy density  (kJ m−2) and the percentage of wave energy that is contained in swells . Here, E is the total wave energy in Eq. (2), W is the wind-sea fractions in Eq. (1), and Aocean is the total ocean area.
Global averaged mean wave energy density  (kJ m−2) and the percentage of wave energy that is contained in swells . Here, E is the total wave energy in Eq. (2), W is the wind-sea fractions in Eq. (1), and Aocean is the total ocean area.

3) The North American coasts

We now highlight the behavior of the wind sea and swells near the North American coasts. As shown in Fig. 4, both swell and wind sea are highest around the North American coasts during the boreal winter and lowest during the boreal summer.

Along the west coast of North America, the wind seas are propagating toward the coast for all four seasons with stronger eastward- and northeastward-propagating waves toward the North American coast to the north of 40°N and weaker southward-propagating waves along the North American coast south of 40°N. The swells to the north of 40°N are dominated by the North Pacific midlatitude storms and mainly propagate eastward toward the North American west coast. To the south of 40°N, the swells are dominated by the North Pacific midlatitude storms during the boreal winter and autumn and propagate southeastward along the North American coast. This region is also dominated by the Southern Ocean swells during the boreal summer that propagate northeastward toward the North American coast. During the boreal spring, however, the energy of the swell from the Southern Ocean is comparable to that from the North Pacific midlatitude storm region in the subtropics. The interaction of these swells results in eastward-propagating swells toward the North American coast. In summary, to the north of 40°N, the North American west coast is affected by strong wind seas and swells all year, especially during the boreal winter. To the south of 40°N, the North American west coast is mainly affected by swells, since wind seas propagate away from the coast.

Along the east coast of North America, the wind sea and swell are strong at the midlatitude region and propagate away from the coast, except during the boreal summer, when they are weak and propagate northward along the coast. In the tropics, the wind seas are weaker and mainly propagate westward toward the North American coast all year. The swells mainly propagate either southward or southwestward along the North American coast in the tropics, except during the boreal summer, when swells propagate westward toward the North American coast. Thus, the Gulf of Mexico and Caribbean regions are affected by wind seas and swells all year round, while the rest of the North American east coast is not affected much.

4. Wind-sea and swell projection for the twenty-first century

In this section, we explore the potential changes in wind-sea and swell climate attributable to climate change through time-slice simulations. The seasonal ensemble mean wind-sea and swell projections from the four experiments are given in Figs. 7 and 8, and the ensemble annual mean projections are given in Fig. 9. The stippled areas on the figures indicate where the magnitude of the multimodel ensemble mean exceeds the intermodel standard deviation, which serves as a measure of the agreements among the four projections.

Fig. 7.

Ensemble wind-sea (left) energy and (right) propagation direction response to SST warming at the end of the twenty-first century during the seasons of (a),(b) JFM, (c),(d) AMJ, (e).(f) JAS, and (g).(h) OND. The colors are the energy density difference between the projections and the control run. The stippled areas show where the magnitude of the multimodel ensemble mean exceeds the intermodel standard deviation. The black and red arrows represent the wind-sea direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

Fig. 7.

Ensemble wind-sea (left) energy and (right) propagation direction response to SST warming at the end of the twenty-first century during the seasons of (a),(b) JFM, (c),(d) AMJ, (e).(f) JAS, and (g).(h) OND. The colors are the energy density difference between the projections and the control run. The stippled areas show where the magnitude of the multimodel ensemble mean exceeds the intermodel standard deviation. The black and red arrows represent the wind-sea direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

Fig. 8.

As in Fig. 7, but for ensemble swell energy and propagation direction.

Fig. 8.

As in Fig. 7, but for ensemble swell energy and propagation direction.

Fig. 9.

Ensemble annual mean wind-sea and swell (a),(c) energy and (b),(d) direction response to SST warming at the end of the twenty-first century. The colors are the energy density difference between the projections and the control run. The stippled areas show where the magnitude of the multimodel ensemble mean exceeds the intermodel standard deviation. The black and red arrows represent the wind-sea/swell direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

Fig. 9.

Ensemble annual mean wind-sea and swell (a),(c) energy and (b),(d) direction response to SST warming at the end of the twenty-first century. The colors are the energy density difference between the projections and the control run. The stippled areas show where the magnitude of the multimodel ensemble mean exceeds the intermodel standard deviation. The black and red arrows represent the wind-sea/swell direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

a. Wind sea

During the boreal winter (JFM), a dipole pattern is observed (Fig. 7a) with energy increases in the northeast Atlantic and decreases in the midlatitudes. The increases are much stronger (>2 kJ m−2) than the decreases (up to 1.2 kJ m−2). Large angle differences are found in the North Atlantic (Fig. 7b), with the wind-sea propagation directions being more zonal–steered clockwise toward Europe at high latitudes and anticlockwise toward North America in the subtropics. Such ocean wave changes are caused by changes in the surface winds (Fan et al. 2013), which are associated with more frequent occurrence of the positive phases of NAO under global warming (Meehl et al. 2007).

Robust strong wind-sea energy increases are observed in the Southern Ocean for all seasons (Figs. 7a,c,e,g), which are consistent with the surface wind responses presented in Fan et al. (2013). As Kushner et al. (2001) and Sobel and Camargo (2011) pointed out, the extratropical circulation response to global warming consists of a Southern Hemisphere summer half-year poleward shift of the westerly jet and a year-round positive wind anomaly in the stratosphere and the tropical upper troposphere. The tropospheric wind response projects strongly onto the model’s southern annular mode (SAM), which is the leading pattern of variability of the extratropical zonal winds. Based on satellite measurements, both Hemer et al. (2010) and Izaguirre et al. (2011) found that the positive phase of SAM is associated with wave height increases in the Southern Ocean and decreases in the southern part of the South Atlantic and Indian Ocean. This is the phenomenon we observe in our projections.

As Fan et al. (2013) has pointed out, the 2100 ozone concentrations are very similar to the 1980 values. Hence, maintaining the ozone concentration unchanged in our projections does not qualitatively affect the results. In the  appendix, we found that doubling CO2 does not affect the projection in this section much either. This lack of sensitivity is because the shift of the jet stream is determined not directly by the changes in the CO2 concentration but mainly by the overall warming or cooling of the ocean surface caused by the CO2 changes (Lee 1999).

The wind-sea directions hardly change in the Southern Ocean for all seasons (Figs. 7b,d,f,h) given the strong energy increase. In contrast, large direction changes are observed around 30°–35°S in South Pacific, with wind-sea propagations being steered anticlockwise to have a more northward component during the austral winter (Fig. 7f). This directional change is consistent with regional Australian studies (Hemer et al. 2013b), which reported anticlockwise rotation of wave directions as one of the larger projected wave climate change signals along the southeastern Australian coast. They attributed this change within the Tasman Sea to the sensitivity of wave direction to the position of the subtropical ridge (STR) in the region and the projected southward shift in the position of the STR under climate change.

In the South Pacific, accompanying the strong increase of wind-sea energy in the Southern Ocean are patches of decreasing wind-sea energy to its north. Notice that the area of decrease to the west of the South American coast extends southward during the austral autumn (AMJ) and reaches all the way to Antarctica during the austral winter (JAS), and retreats back during the austral spring (OND). Izaguirre et al. (2011) found that the positive phase of Niño-3 is correlated with wave height decrease in the southeastern Pacific, especially to the west of the South American coast and the Drake Passage. Even though our experiments are designed to eliminate the possible complications in the response that might depend on the phase of ENSO, the SST anomalies in the eastern and central Pacific exhibit a more pronounced warming with patterns that resemble El Niño SST anomalies (Fan et al. 2013). Thus, the projected changes in the wave field may be described as El Niño like.

Changes in the ensemble annual mean wind-sea energy (Fig. 9a) show a consistent projected increase in the Southern Ocean with an area of decrease to the west of the southern tip of South America and agree well with the projected change in annual mean significant wave height by Hemer et al. (2013a). In the North Atlantic, we observe a weak dipole pattern of wind-sea energy increase in the northeast sector and decrease in the southwest sector. These changes are dominated by wind-sea changes in the boreal autumn (OND) and winter (JFM) in this region. The mean wave direction change is in general very small (a few degrees) with an exception at midlatitude (~30°N) west Pacific and west Atlantic, where waves are steered more toward the coasts of China and United States, respectively.

b. Swells

The most dominant feature of projected swell energy change is the strong increase in the southwestern Pacific and Indian Ocean sector of the Southern Ocean during the austral autumn (Fig. 8c) and winter (Fig. 8e) and a weak energy increase in the western Pacific sector of the Southern Ocean during the austral summer (Fig. 8a) and spring (Fig. 8g). Since the swell responses in the Southern Ocean dominate the swell response in the entire Pacific Ocean during the austral autumn and winter, the different magnitude of energy increase among the four projections result in very different swell energy responses in the Pacific Ocean (not shown). However, despite the large discrepancies that exist on the swell energy responses among different projections, the swell direction responses are quite small and consistent among the four models (not shown).

The global averaged mean wave energy density and the fraction contained in swells are documented in Table 2. All four SST perturbations show an increase in global mean wave energy during the austral winter, while there is not much change in the other seasons. This increase is mainly induced by the strong wind-sea and swell increase in the Southern Ocean. The increase of swell energy from the Southern Ocean is the main contributor for the global wave energy increase since the percentage of swells also increases in all four projections. Hemer et al. (2013a) also reported wave period increase over 33.6% of the global ocean during the austral winter through a multimodel ensemble study and attributed this increase to the increased Southern Ocean wave activity.

The projected swell energy increase in the Southern Ocean during the austral autumn and winter dominates the annual mean swell energy change in the Southern Ocean (Fig. 9c). The most pronounced increase in annual mean swell energy is found in the Indian Ocean and west Pacific Ocean sector of the Southern Ocean. No significant swell energy change is found in the North Pacific, and very weak decreases are found in the North Atlantic.

5. Summary and conclusions

In this study, we analyzed the seasonal structure of the surface wind, wind sea, and swell from the 29-yr global wind and surface gravity wave climatology produced by Fan et al. (2013) using a coupled atmosphere–wave model. We also considered future scenarios based on climate projections for the latter portion of the twenty-first century.

a. Characterizing the 29-yr climatology from Fan et al. (2013)

Our swell energy fraction analysis based on the 29-yr climatology of Fan et al. (2013) shows that swell energy dominates most of the World Ocean basins for all four seasons. The equatorial area has the highest swell fraction (>90%) throughout the year, especially the tropical Indian Ocean, where more than 95% of the wave energy is from swells all year round. Wind-sea dominance is mainly found in the semienclosed seas (e.g., the Gulf of Mexico and Caribbean Sea, the Mediterranean Sea, and the South China Sea) for all seasons because of the sheltering effects and limited fetch. The Southern Ocean, trade wind region, Indian monsoon region, and the western part of North Atlantic also show wind-sea dominance during some seasons.

The overall global pattern of swell fraction in our study agrees with Semedo et al. (2011), who calculated the swell fractions using the ERA-40 wave spectra. However, the swell fractions in our study are generally lower, especially in the Southern Ocean, where Semedo et al. (2011) found swell dominates all seasons. Different partition schemes used in the two studies [Hanson and Phillips (2001) in this study and Bidlot (2001) in Semedo et al. (2011)] may be one of the reasons for such differences. The other reason lies in the higher spatial and spectra resolution used in our model compared with the WAM configuration in ERA-40.

Wind seas are well correlated with the surface winds in both energy content and propagation direction for all seasons. The Southern Ocean swells contribute significantly to the swell field in the global ocean basins. The swell propagation direction is very close to the wind sea in the Southern Ocean for all seasons, while large angles are found between swells and wind seas in the Northern Hemisphere midlatitude storm region. The wind sea always follows the trade wind direction and propagates to the west in the tropics. In contrast, the swell propagation direction varies significantly with season. We speculate that this variation is regulated by the nonlinear interactions between swells from the Southern Ocean and the Northern Hemisphere midlatitude storm region. Thus, swells opposing or outrunning relatively weak winds is a common phenomenon in the tropics (Fig. 4). The presence of these swells can significantly affect the momentum fluxes, SST, and mixed layer depth, particularly in the tropical Pacific and Indian Ocean (Cavaleri et al. 2012).

The northern part (north of 40°N) of the North American west coast is affected by strong wind seas and swells all year, while the rest of the west coast is only affected by weaker swells. The majority of the North American east coast is not affected much by either wind seas or swells, while the Gulf of Mexico and Caribbean region are affected by wind seas and weak swells during all seasons.

b. Projections for the twenty-first century

We used the same coupled system as Fan et al. (2012) to investigate the wind-sea and swell climate changes to the SST and sea ice anomalies in the late twenty-first century by perturbing the SSTs with anomalies generated by global model projections. The ensemble mean of the four projections were analyzed. Features of projected change in wind-sea climate observed in our study are consistent with a broader understanding of wave and climate variability as a response to projected changes in atmospheric circulations. Atmospheric circulations are driven by ocean surface temperature. The poleward shift of the jet streams, which resulted in more frequent occurrence of positive phase of NAO and SAM, is determined mainly by the overall warming or cooling of the ocean surface attributable to the changes in the CO2 (Lee 1999). Since ocean waves are driven by the surface wind, their response to climate change is closely associated with the surface wind responses. To illustrate the major robust responses, a schematic drawing is given in Fig. 10.

Fig. 10.

Schematic plot of projected wind-sea and swell changes for (a) boreal winter and (b) austral winter–autumn. The red shading indicates increase in swell energy. The red (blue) box and oval indicates increase (decrease) in wind-sea energy. The black/gray rotation arrows indicate wind-sea/swell direction changes.

Fig. 10.

Schematic plot of projected wind-sea and swell changes for (a) boreal winter and (b) austral winter–autumn. The red shading indicates increase in swell energy. The red (blue) box and oval indicates increase (decrease) in wind-sea energy. The black/gray rotation arrows indicate wind-sea/swell direction changes.

The wind-sea responses show close association with the responses of climate indices. The dipole pattern in the North Atlantic during the boreal winter (JFM) and corresponding propagation directions change (steered clockwise toward Europe at high latitudes and anticlockwise toward North America in the subtropics) is associated with more frequent occurrence of the positive phases of NAO under global warming (Meehl et al. 2007). The wind-sea energy increase in the Southern Ocean is associated with the continuous shift of SAM toward its positive phase (Arblaster et al. 2011). We see an El Niño–like response in the strong seasonal variation of wind-sea energy decrease to the west of the South American coast, which is attributable to the pronounced SST warming in the eastern and central Pacific that resemble El Niño SST anomaly patterns. Anticlockwise rotation of wind-sea direction is also found in the southwestern Pacific that is associated with the southward shift of subtropical ridge. No robust wind-sea response is found in the North Pacific storm track region.

The most significant response in the swells is the strong energy increase in the western Pacific and Indian Ocean sector of the Southern Ocean during the austral winter (JAS) and autumn (AMJ), which is associated with the wind-sea increase there. In general, the swell responses to global warming are less robust among the different projections compared to the wind-sea responses (not shown). This behavior is because the wind sea is mainly driven by the surface wind. Thus, changes in the wind-sea field are highly correlated with changes in the local wind speed (Gulev and Grigorieva 2006). In contrast, swells are nonlocal in that they carry information from the wind sea and propagate thousands of kilometers across the ocean without local momentum input from the wind.

Our projections considered only the influence of SST changes on global wind-sea and swell responses and maintained the radiative forcing unchanged. Questions may arise regarding how different the projected changes will be if we consider the effect of both ozone recovery and doubling CO2. An additional sensitivity experiment was conducted in the  appendix to address this question. Small differences are observed in the experiment with specified ozone concentrations for 2100 and doubled CO2 concentrations. These results suggest that the response of the wind-sea and swell field to climate change can be well estimated from experiments using only SST anomalies, with radiative forcing unchanged from their 1980 values.

c. Comments on future research avenues

Many wave-dependent processes are currently parameterized within coupled ocean–atmosphere general circulation models using wind-dependent parameterizations (Axell 2002; Cavaleri et al. 2012; Dufresne et al. 2013). This is a valid simplification if winds and waves are in equilibrium. However, our results show that local wind-wave equilibrium is not the case over the majority of the ocean, with swell dominating the global wave field. These results suggest the importance of incorporating sea-state-dependent parameterizations of these processes into coupled climate models. A straightforward means for doing so is to incorporate a dynamical ocean surface wave model, such as used here, into coupled climate models.

Even though this study is conducted under limited climate change scopes, it is a useful first step toward more comprehensive wave climate change studies. The projected changes in significant wave height (incorporating both wind-sea and swell energy) are qualitatively typical of other studies within the current generation of wave climate projections (Hemer et al. 2013a). The results have pointed out the importance of Southern Ocean swells on global wave climate changes.

This study has also emphasized the importance of global dynamical wave projection studies. The regional dynamical wave projections and statistical wave projections are unable to correctly represent the swells, which constitute the dominant fraction of wave energy for most of the World Ocean basins (Table 2). This shortcoming thus emphasizes the limitations of wave climate projection studies using regional dynamical wave models and statistical approaches.

Acknowledgments

The authors thank Drs. I. M. Held and M. Winton for valuable discussions on the interpretation of these results and Z. Liang for helping to develop the coupled atmosphere–wave model system used in this study. Yalin Fan was partially supported by the Hurricane Forecast Improvement Program by NOAA. We thank the anonymous reviewers for their critical comments, all of whom greatly helped to improve this manuscript.

APPENDIX

Ozone Recovery and Doubling CO2 Effects

The projection study in section 4 focused on the influence of SST change on global wind-sea and swell responses and maintained the radiative forcing unchanged. Since the southern annual mode (SAM) controls the wind response and hence the wind-sea response in the Southern Ocean and thus plays an important role on swell responses globally, questions may arise on how different the projected shift in the SAM will be if we consider the effect of both ozone recovery and doubling CO2. To address this question, one more experiment, SST-Ozone-CO2, was conducted (Table 1) by doubling CO2 and using ozone concentration values at the end of the twenty-first century in addition to the SST anomaly. For this experiment, we use the SST anomaly from the ensemble of 18 CMIP3 models (same as the ENS18 experiment). The wind-sea and swell changes for all four seasons in the ENS18 experiment are given in Fig. A1, and the changes for the SST-Ozone-CO2 are given in Fig. A2.

Fig. A1.

(left) Wind-sea energy and propagation direction response to SST warming at the end of the twenty-first century from the ENS18 experiment during the seasons of (a) JFM, (b) AMJ, (c) JAS, and (d) OND. (right) As in (left), but for the swell response. The colors are the energy density difference between the projections and the control run. The black and red arrows represent the wind-sea direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

Fig. A1.

(left) Wind-sea energy and propagation direction response to SST warming at the end of the twenty-first century from the ENS18 experiment during the seasons of (a) JFM, (b) AMJ, (c) JAS, and (d) OND. (right) As in (left), but for the swell response. The colors are the energy density difference between the projections and the control run. The black and red arrows represent the wind-sea direction from the control run and projection run, respectively. The arrows are plotted at every 20th grid point (~10°) in latitude/longitude directions for easy viewing.

Fig. A2.

As in Fig. A1, but for the SST-Ozone-CO2 experiment.

Fig. A2.

As in Fig. A1, but for the SST-Ozone-CO2 experiment.

For the SST-Ozone-CO2 experiment, the global structure of seasonal mean wind-sea and swell responses are in general similar to the ENS18 experiment. Relatively small differences are found in the Southern Ocean for all four seasons, with more obvious changes during the boreal winter (JFM) and summer (JAS). Compared with the ENS18 experiment, the SST-Ozone-CO2 experiment shows a weaker increase of wind-sea energy in the sector south of Australia during the boreal winter (austral summer), which is corresponding to very weak decrease in the swell fields. During the boreal summer (austral winter), the SST-Ozone-CO2 experiment shows a stronger increase of wind sea in the Southern Ocean to the south of Australia, but the band of increase is narrower and more to the north. At the same time, the swell shows a weaker increase in this region because of the limited fetch. Hence, few changes are observed in this region for the significant wave height responses, since they reflect the combination of the swell and wind-sea energy, as reported in Fan et al. (2013).

As Fan et al. (2013) pointed out, the 2100 ozone concentration is very similar to the 1980 value, and the differences we observe in the Southern Ocean should be mainly caused by the effect of doubling CO2. The fact that we do not observe much difference in the Southern Ocean between these two experiments suggests that the shift of the jet stream is determined not directly by the changes in the CO2 concentrations but mainly by the overall warming or cooling of the ocean surface caused by the CO2 changes (Lee 1999). Through similar analysis, Fan et al. (2013) also found that the qualitative response of the surface wind and significant wave height field to global warming still holds even if they are obtained from experiments using the SST anomalies only and kept the radiative forcing agents unchanged as the 1980 values.

We also notice that the western Pacific shows a stronger decrease of both wind sea and swell during the boreal autumn (OND). This decrease is caused by the hurricane frequency change in the western Pacific attributable to the doubling of CO2. Fan et al. (2013) found that, after the doubling of CO2 concentration, the hurricane frequency decrease was enhanced for the west Pacific. As a result, the seasonal averaged surface wind and hence wind-sea energy and corresponding swell energy decrease in the SST-Ozone-CO2 experiment.

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Footnotes

*

Current affiliation: Naval Research Laboratory, Stennis Space Center, Mississippi.