A global climatology of wind–wave
interaction
Article
Published Version
Hanley, K. E., Belcher, S. E. and Sullivan, P. P. (2010) A global
climatology of wind–wave interaction. Journal of Physical
Oceanography, 40 (6). pp. 1263-1282. ISSN 0022-3670 doi:
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A Global Climatology of Wind–Wave Interaction
KIRSTY E. HANLEY AND STEPHEN E. BELCHER
Department of Meteorology, University of Reading, Reading, United Kingdom
PETER P. SULLIVAN
National Center for Atmospheric Research, Boulder, Colorado
(Manuscript received 1 October 2009, in final form 6 January 2010)
ABSTRACT
Generally, ocean waves are thought to act as a drag on the surface wind so that momentum is transferred
downward, from the atmosphere into the waves. Recent observations have suggested that when long wave-
length waves—which are characteristic of remotely generated swell—propagate faster than the surface wind,
momentum can also be transferred upward. This upward momentum transfer acts to accelerate the near-
surface wind, resulting in a low-level wave-driven wind jet. Previous studies have suggested that the sign
reversal of the momentum flux is well predicted by the inverse wave age, the ratio of the surface wind speed to
the speed of the waves at the peak of the spectrum. Data from the 40-yr ECMWF Re-Analysis (ERA-40) have
been used here to calculate the global distribution of the inverse wave age to determine whether there are
regions of the ocean that are usually in the wind-driven wave regime and others that are generally in the wave-
driven wind regime. The wind-driven wave regime is found to occur most often in the midlatitude storm tracks
where wind speeds are generally high. The wave-driven wind regime is found to be prevalent in the tropics
where wind speeds are generally light and swell can propagate from storms at higher latitudes. The inverse
wave age is also a useful indicator of the degree of coupling between the local wind and wave fields. The
climatologies presented emphasize the nonequilibrium that exists between the local wind and wave fields and
highlight the importance of swell in the global oceans.
1. Introduction
Ocean surface waves are the medium that transfer
momentum across the air–sea interface. Currently, all
operational ocean–atmosphere models only allow the
momentum flux t
tot
to be positive, from atmosphere to
ocean. Recent observations during conditions when waves
propagate faster than the wind have reported upward
momentum flux from the waves to the atmosphere (e.g.,
Drennan et al. 1999; Grachev and Fairall 2001) and the
occurrence of low-level wave-driven jets (e.g., Smedman
et al. 1999). The wave-driven wind regime was first re-
ported by Harris (1966), who showed in a laboratory
wave tank that a progressive water wave leads to airflow
in the direction of wave propagation.
Wind–wave equilibrium, or a fully developed sea, is
a state of wind and wave alignment where the shape of
the wave spectrum and the peak frequency are both sta-
tionary in time. Such a sea state is usually described by
asymptotic values of integrated spectral parameters: for
example, significant wave height H
s
and the spectral peak
frequency f
p
. Pierson and Moskowitz (1964) used a care-
fully chosen dataset representative of fully developed
seas to propose universal relations for fully developed
asymptotic limits that are based on similarity analysis.
Alves et al. (2003) have shown that the Pierson and
Moskowitz (1964) fully developed asymptotic limit for
the peak frequency can be expressed in terms of the
wave age, c
p
/(U
10
cosu), as
c
p
(U
10
cosu)
5 1.2, (1)
where c
p
is the peak phase speed of the waves, U
10
is the
10-m wind speed, and u is the relative angle between the
wind and the waves. When c
p
/(U
10
cosu) , 1.2, waves
grow by absorbing momentum from the wind.
In reality, the ocean is often fetch and duration limited
so that fully developed seas are uncommon. Ocean waves
Corresponding author address: Kirsty E. Hanley, Department of
Meteorology, University of Reading, Earley Gate, P.O. Box 243,
Reading RG6 6BB, United Kingdom.
E-mail: k.e.hanley@rdg.ac.uk
J
UNE 2010 H A N L E Y E T A L . 1263
DOI: 10.1175/2010JPO4377.1
Ó 2010 American Meteorological Society
occur over a broad range of wavelengths, ranging from a
few centimeters to a few hundred meters, with contri-
butions from both wind waves and swell. Wind waves are
locally generated, short-wavelength waves that travel
slower than the surface wind. They require momentum
from the wind to grow and as a result are strongly coupled
to the local wind field (Janssen 1989). In contrast, long-
wavelength swell waves are usually generated remotely
by storms and can propagate thousands of kilometers
across the ocean, without momentum input from the
wind. Drennan et al. (2003) used data from five field
campaigns to study the influence of wave age on the air–
sea momentum flux during pure wind sea conditions.
They found that pure wind seas are frequent in coastal
regions, in enclosed seas, and during extreme wind events;
however, in the open ocean swell is usually present. The
results of the Coupled Boundary Layers and Air–Sea
Transfer (CBLAST) field campaign, which took place in
the North Atlantic (Edson et al. 2007), demonstrated that
in light wind conditions (,4ms
21
) winds and waves are
usually in a state of nonequilibrium where c
p
exceeds U
10
,
indicating that remotely generated swell is present.
Until recently, it was thought that swell, which is weakly
coupled to the local wind, does not interact with the air-
flow. Experiments have shown that swell does interact
with the airflow by giving momentum to the wind and
inducing a wave-driven wind. Measurements of t
tot
by
Drennan et al. (1999) in Lake Ontario show that, for
swell aligned with the wind, t
tot
may sometimes be neg-
ative. Observations by Smedman et al. (1999, 2003) in the
Baltic Sea have shown that, during swell-dominated con-
ditions, the wind profile is no longer logarithmic. They
observed a wind speed maximum near or below the lowest
wind speed measurement of 10 m. From results obtained
during several sea expeditions, Grachev and Fairall (2001)
found that, in the equatorial west Pacific Ocean, upward
momentum transfer occurs about 10% of the time. Cal-
culations by Hanley and Belcher (2008), which were in
agreement with the ocean observations of Grachev and
Fairall (2001), demonstrated that the sign reversal of
the air–sea momentum flux from positive (i.e., into the
waves) to negative (i.e., out of the waves) occurs when
the inverse wave age drops below about 0.15. Therefore,
the inverse wave age is chosen here as a simple but ef-
fective parameter to characterize the wind–wave regime:
the wind-driven wave regime occurs when (U
10
cosu)/c
p
.
1/1.2 5 0.83, and the wave-driven wind regime occurs
when 0 , (U
10
cosu)/c
p
, 0.15.
In the intermediate range of inverse wave age, 0.15 ,
(U
10
cosu)/c
p
, 0.83, the sea state is mixed; that is, it is
composed of both wind sea and swell. In this range, there
are both growing waves extracting momentum from the
wind and fast waves imparting momentum to the wind.
It is likely a smooth transition from one regime to another.
When (U
10
cosu)/c
p
. 0.83, there are waves in the spec-
trum moving faster than the wind, which put small
amounts of momentum back into the atmosphere. Simi-
larly, when (U
10
cosu)/c
p
, 0.15, there are still growing
waves extracting momentum. Therefore the limits that
have been chosen here to characterize each regime are
not hard limits.
The global importance of swell has been identified by
Chen et al. (2002), who collocated a global dataset of
simultaneous measurements of H
s
and U
10
from the
Ocean Topography Experiment/National Aeronautics and
Space Administration (NASA) Scatterometer (TOPEX/
NSCAT) and TOPEX/Quick Scatterometer (TOPEX/
QuikSCAT) missions to observe the spatial pattern of
both wind sea and swell. They determined the global
distribution of wind waves and swell using the wind–wave
relation for fully developed seas given by Hasselmann
et al. (1988), assuming that measurements of H
s
less than
the fully developed limit are from a growing sea and
measurements of H
s
that are greater are swell. Chen et al.
(2002) find that swell occurs more than 80% of the time
in most of the world’s oceans. They identify three ‘‘swell
pools’’ in the tropics where the probability of swell is
more than 95%. In contrast, Chen et al. (2002) find that
wind waves occur most frequently in the midlatitudes,
decreasing to a minimum at the equator.
The goal of this paper is to use the 40-yr European
Centre for Medium-Range Weather Forecasts (ECMWF)
Re-Analysis (ERA-40) wave dataset to develop a new
climatology of wind–wave interaction, as diagnosed by
the inverse wave age. The availability of wave data makes
it possible to construct a global climatology of wave
processes and wind–wave interaction that accounts for
both wind waves and swell. McWilliams and Restrepo
(1999) construct a global wave climatology using wind
data to parameterize the waves. This method assumes
wind–wave equilibrium and therefore ignores remotely
generated swell. When wave data are used, the complete
spectrum can be considered. The first question addressed
here is, to what extent is the local wave field coupled to
the local wind field? In section 3, ERA-40 data are used to
study the effects of a storm passing through the Southern
Ocean and to compute climatologies of the 10-m wind
speed and the peak wave phase speed. These climatol-
ogies illustrate that, in many regions, the local wave state
is not tied to the local wind conditions and highlight the
importance of swell in the global oceans.
A second question is, can the sea state be broadly cat-
egorized into two regimes, wind-driven waves or wave-
driven winds? This question is addressed in section 4,
where the ERA-40 data are used to produce a global
climatology of inverse wave age. This will determine the
1264 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 40
regions of the ocean that are usually in the wind-driven
wave regime and the regions that are predominantly in the
wave-driven wind regime. The climatology of (U
10
cosu)/c
p
provides the spatial distribution of each regime but does
not provide information about how frequently each re-
gime occurs. Therefore, in section 4b a different technique
is used to determine the global frequency of occurrence of
the two regimes.
2. The ERA-40 wave data
The ECMWF has produced a 45-yr global reanalysis of
atmospheric and wave data called ERA-40 (Uppala et al.
2005), which covers the period September 1957–August
2002. The reanalysis is produced using the ECMWF In-
tegrated Forecasting System, an atmosphere model cou-
pled to a wave model. Global observations of the 10-m
wind speed obtained from shipborne and buoy mea-
surements and, since August 1993, the European Remote
Sensing Satellite (ERS) scatterometer are assimilated
into ERA-40 using a variational assimilation scheme (de
las Heras et al. 1994). Also, since August 1993 significant
wave heights obtained from the ERS altimeter have been
assimilated. Although the quality and coverage of the
observations improves over the ERA-40 period, the re-
analysis ensures that the data are continuous.
TheERA-40wavereanalysisisproducedusingthe
wave model WAM (Hasselmann et al. 1988). WAM is
coupled to the atmosphere model by a sea-state-
dependent Charnock parameter devised by Janssen
(1991). To produce the reanalysis, WAM is forced by the
10-m winds from the latest 6-h forecast on a 1.5831.58
global resolution grid with data stored every 6 h. WAM
computes the full two-dimensional wave spectrum from
which a number of integrated parameters can be obtained:
for example, the significant wave height, the mean wave
period, and the mean wave direction. The ERA-40 re-
analysis gives these diagnostics for the entire spectrum
and also for both the wind-wave and swell components.
The wind sea is defined as the part of the spectrum for
which the friction velocity in the direction of wave prop-
agation is greater than 0.05 3 c,wherec is the frequency-
dependent phase speed. The rest of the spectrum is defined
as swell (Hasselmann et al. 1988). Janssen et al. (1997)
compared the analyzed wave data with independent buoy
measurements and found a good agreement.
Caires et al. (2004) recommend the use of ERA-40 data
for global wave studies because they compare better with
observations than other available reanalyses [e.g., Na-
tional Centers for Environmental Prediction–National
Center for Atmospheric Research (NCEP–NCAR)].
Because of their superior agreement with observations,
theERA-40wavedataareconsideredtobethebest
data currently available to produce a global climatology
of ocean wave processes and wind–wave interaction.
However, Caires et al. (2004) find the ERA-40 dataset
tends to underestimate wind speeds above 14 m s
21
.
Partly as a result of this, the high peaks in significant
wave height are underestimated in the ERA-40 dataset.
3. Surface wave characteristics
To understand how the local wave field is coupled to
the local wind field, the ERA-40 data are first used to
study the global patterns of U
10
, H
s
, and c
p
. The ERA-40
data provide the components of the 10-m wind speed,
u
10
and y
10
, which define the magnitude and direction of
U
10
. The significant wave height is one of the diagnostics
given in the ERA-40 wave data. The ERA-40 wave data
also provide the peak period T
p
of the one-dimensional
frequency spectrum. Each spectral component travels
with its own phase velocity determined by the linear
dispersion relation c 5 g/v, where the angular frequency
v 5 2pf. The group of waves travels at the group ve-
locity c
g
defined as the ratio of the group length to the
group period (i.e., c
g
5 dv/dk). Using the linear dis-
persion relation, c
p
can be calculated from T
p
as
c
p
5
gT
p
2p
. (2)
Themeanwavedirectionhu
w
i is also one of the di-
agnostics given in the ERA-40 wave data; therefore, c
p
has components (c
p
sinhu
w
i, c
p
coshu
w
i). The spectral peak
generally represents the longer-wavelength waves; there-
fore, c
p
is a good measure of the speed of swell.
a. A Southern Ocean storm
To gain an understanding of the relationship between
wind waves and swell, the ERA-40 wave data are first
used to study U
10
and c
p
in the Indian Ocean after the
passage of a storm in the adjacent part of the Southern
Ocean between 14 and 16 July 1989.
Figure 1 shows the mean sea level pressure, U
10
and c
p
from the ERA-40 data at 0000 UTC 14 July. An intense
low pressure system is building in the Southern Ocean at
458E with a minimum mean sea level pressure of 940 mb.
The highest wind speeds of 25 m s
21
, which are located
to the northwest of the low pressure center, have the
potential to generate waves of c
p
5 1.2U
10
5 30 m s
21
.
At the center of the storm, wind speeds fall below
4ms
21
. The strong winds associated with the low pres-
sure system generate waves with peak phase speeds equal
to the maximum wind speeds of 24 m s
21
. Both the wind
and the waves move cyclonically around the low, showing
that the waves here are strongly forced by the wind. At
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