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Wave spectra generated by an extratropical cyclone in
the South Atlantic Ocean
By Cláudia K. Parise1? and Leandro Farina2,3 †, 1 Instituto de Geociências, Universidade Federal do Rio Grande
do Sul, Porto Alegre, Brazil; 2 Instituto de Matemtica and CECO - Centro de Estudos de Geologia Costeira e
Oceânica, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil; 3 BCAM - Basque Center for Applied
Mathematics, Bilbao, Basque Country, Spain
14 September 2014
ABSTRACT
The contribution of wave energy from an extratropical cyclone in the South Atlantic for the near shore
wave field is investigated. A third generation wave model is used to simulate the waves and the wave
spectra in the open ocean and in three location off the coast of Rio Grande do Sul, Brazil are analysed
for an this extreme event in September, 2006. The results show that 74% of the wave energy generated
by the extratropical cyclone in the open ocean was propagated to nearshore. The dominant waves took
48h travelling from the cyclone center towards the nearshore region of Cassino Beach. The resonance
interaction between the swell and sea waves generated by the cyclone is evidenced on the left quadrant
once 67% of the spectra observed had higher wave energy on the left of the circulation system.
Keywords: ocean waves modeling, extratropical cyclones, South Atlantic, ocean wave climate.
1. Introduction
Ocean waves generated by tropical and extratropical cyclones
is an increasingly studied topic of research, given the importance of these weather systems to the socio-economical activities near to the coastal and offshore regions. Extratropical cyclones are synoptic meteorological phenomena responsible for
a large transfer of momentum due to the friction of the wind on
the surface layers of the ocean, which makes them important in
the study of the generation and behavior of ocean waves. The
amount of energy exchanged between the surface ocean and the
air increases with the intensity, duration, fetch of wind and also
with the velocity of the low atmospheric pressure center. Thus,
a drastic combination for generating an extreme sea state is the
presence of strong wind with direction roughly invariant, acting
for a reasonably long time in a large area under the control of a
cyclone that moves slowly to the open ocean. Thus, the slower
the storm moves, the more energy is transferred to the ocean,
and consequently, the higher the wave heights.
A considerably large number of published works on the
?
Present address: Instituto Nacional de Pesquisas Espaciais, José dos
Campos, SP, Brazil
† Corresponding author.
e-mail: [email protected]
c 0000 Tellus
wave spectra generated by tropical cyclones and hurricanes
in the Northern Hemisphere is found in the literature (e.g.,
(MGH+ 03; ZH11)).
Young (You06) studied the directional spectrum of waves
during the passage of hurricanes based on data buoy and found
that in almost all quadrants of the storm, the dominant waves
are swell.
Lui et. al. (LXPB07) conducted a study to quantify the influence of the wind and the storm speed and intensity on the waves
in the Northern Hemisphere. They concluded that the asymmetric structure of wind-induced wave field is sensitive not only to
the asymmetric structure of the hurricane wind field, but also to
the variations in the storm translation speed and intensity. According to the authors, the significant wave height in the frontright quadrant of the storm rises as storm translation speed increases until it reaches a critical value, then the significant wave
height drops. The opposite occurs in the rear-left quadrant. This
effect is significant when the storm speed increases up to the
value of the group velocity of the dominant waves, and it is
less significant when the storm speed is greater than this group
velocity. On the other hand, as the intensity of the hurricane increases, the influence of the cyclone translation speed on the
asymmetric structure of the wave field is smaller.
The cyclogenesis in the South Atlantic Ocean has been also
studied by several researchers (Tal67; GR91; MS91a; MS91b;
JS93; Sin94; Sin95; RdCF02; PCNK09) although the amount
C. K. PARISE AND L. FARINA
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and quality of observational data on this hemisphere is more
limited. Thus, most works rely mainly on modelling results.
Melo Filho et al. (2008) (MFRH08) simulated an intense
cyclone event in the Southwestern Atlantic Ocean nesting a
global model (Wave Watch III) with a regional model (RefDif)
in order to analyse the wave spectra off the south (Florianopolis) and southeast (Vitoria) brazilian coast. They showed that
the cyclone, formed on May 31st 2006 reached the coast of
Brazil with a lag of three days. The maximum spectrum peaks
and Hs were 29m2 s−1 degree and 4.3 m in Florianopolis and
65m2 s−1 degree and 5.3 m in Vitoria. The authors associated
the higher values at the southeast of Brazil with the cyclone’s
track and location in the ocean.
Parise et. al. (PCNK09) monitored 23 events of meteorological tide in the Cassino Beach, Brazil, between June 2006 and
July 2007 whose meteorological conditions, i.e., mean sea level
pressure, zonal and meridional wind at 10 m height as well as
the trajectory of the cyclone were described. The authors used
Reanalysis data, spatial resolution of 2.5◦ × 2.5◦ and temporal
resolution of 6h (0000, 0600, 1200, 1800 UTC) (KKK+ 96), to
represent the atmospheric patterns on the two days before and
on the day of maximum elevation of the meteorological tide.
Rocha et. al.(RSdS03) reconstructed the sea state for six extratropical cyclones in the South Atlantic Ocean between April
and September 1999 using a global model (Wave Watch III) and
compared with altimeter data from Topex. Closer to the south
and southeast Brazilian coast, the hindcast results showed significant wave heights of up to 5 m in some of the events. Five
from the six cyclones began their development between 30◦ S
and 35◦ S, which is a potential area for cyclogenesis. Three of
them presented a typical trajectory for the South Atlantic region,
that is, eastward or southeastward displacement moving farther
away from their original position whist two of them showed
a different trajectory, moving northward. The longest cyclone
lifetime (150 h) was reported in April while the shortest cyclone
lifetime (54 h) was observed in August.
The objective of this work is to reproduce the wave spectra
during the occurrence of an intense extratropical cyclone over
the South Atlantic Ocean and to analyse its influence on the
waves off the coast of Rio Grande do Sul. In section 2. we describe the model and methods used and give information on the
extratropical cyclone event studied. The cyclone wave spectra
analysis in the open ocean as well as the impact of its waves on
the coast are presented in section 3.. Finally, some conclusions
are highlighted in the section 4..
2. Methods
2.1. Wave model and implementation
The wave spectra were generated by the global wave model
WAM (KLCMD+ 94), cycle 4.5 with a spatial resolution of
0.937◦ × 0.935◦ in a global domain from 82.7◦ N to 82.7◦ S,
imposing the condition of null wave spectrum on all continental
areas. The spectral resolution has 30 frequencies and 12 directions, with the first frequency taken as 0.0417724 Hz. The time
step of 3h was used. This implementation has been previously
used in (PF12).
We simulated the waves in the period from June 2006 to
July 2007, forced by wind stress fields from the CPTEC/INPEAGCM model whose characteristics, performance and implementation are described in (MCS+ 03; PBB+ 07; CMS+ 02;
MB09).
The simulations were performed from a hot start run of the
WAM model with a spin-up of 30 days. The output files were
stored at every 6 h, resulting in four daily spectral data.
2.2. Case study
We seleted for our study, the extratropical cyclone of September 2006 which was the most intense event in one year of observation between june 2006 and july 2007. The more intense
extratropical cyclone from this period occurred in the Atlantic
Ocean in September 1st -3rd , 2006. This cyclone had its genesis in September 1st at the 30◦ S cyclogenetic region and then
moved towards the Atlantic Ocean Basin. The presence of an
intense extratropical cyclone over the Atlantic Ocean caused
big waves in addition to an extreme storm surge event on the
Cassino Beach (PCNK09). The long lifetime (48 h) favoured a
large wind fetch parallel to the coast what resulted in a high meteorological tide of 1.9 m. The mean sea level pressure and the
wind patterns for that period are shown in Fig. 1.
In order to investigate the influence of the asymmetry of the
extratropical cyclone on the ocean wave spectra, these last were
obtained in the center (C) of the cyclone as well as in its periphery, i.e., at its right (R) and left (L), following the trajectory
performed by the storm (Fig. 2).
3. Results and Discussion
3.1. Wave Spectra in the Open Ocean
The evolution of the wave energy spectra generated by the
extratropical cyclone was simulated since its formation, development and dissipation. In 67% of the spectra obtained along
the trajectory of the cyclone, the wave energy was higher at the
left of the cyclone than at the right (Fig. 3). The spectrum maxima value occurred on September 1st (21 UTC), with values of
155m2 s−1 degree at the center of cyclone, 80 m2 s−1 degree at
the left and 60 m2 s−1 degree at the right of it (Fig. 4). The significant wave height during the life of the cyclone has reached
9.18 m at its center, 6.90 m and 6.68 m on the left and right of
it.
Due to the clockwise rotation of the cyclones in the Southern
Hemisphere and also to because of the direction of propagation,
i.e., from the continent towards the open ocean, the region L is
exposed to a longer wind forcing.
WAVE SPECTRA GENERATED BY AN EXTRATROPICAL CYCLONE IN THE SOUTH ATLANTIC OCEAN
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As the storm low pressure center moves it meets the previously generated waves, the swell. These longer waves eventually interact to the younger locally generated waves, the sea
waves. This wave-wave interaction in the same direction increases the wave heights in this region as a results of the resonance phenomenon. On the other hand, there is no contribution
from swell waves in the right side of the cyclone track, since in
this region, the cyclone generated swells that travelled in the opposite direction to the cyclone track. Thus, the asymmetry of the
wave spectra on the periphery of the cyclone can be explained
by the wave resonance occurring on the left of the cyclone track
center, as systematized in Fig. 5.
In order to visualize the predominant frequency band in the
spectra under the extratropical cyclone domain we computed
the one-dimensional spectra, which are shown in Fig. 4. We notice peaks at frequencies below 0.1 Hz for the three points (L, C
and R), indicating the dominance of long period waves.
3.2. Coastal Region
In order to study the propagating of the swell near to the
coast, we selected an offshore point at Cassino Beach (32◦ S,
50◦ W), a point to the left (37◦ S, 55◦ W) and a point on the right
(27◦ S, 45◦ W), for where we computed the wave energy spectra.
These three points are denoted, respectively by PC, PL and PR
and represented in Fig. 7 and 8, by the three back dots near the
coast.
In Fig. 6, we show the evolution of the bi-directional spectra
at the three points during the cyclone occurrence time. The spectra on PL besides being more intense than on PR did show bimodality, with the presence of shorter waves (around 8s) propagating from North-East and longer waves (around 15s) from
South-East. This indicates the influence of other local atmospheric systems in the region generating local waves eventually interacting with the swell generated by the cyclone over
the South Atlantic. At the right of cyclone center, however, bimodality was not observed. Further, the peak period around 15s
suggests the dominance of swell.
It is important to determine the propagation time of swell towards the nearshore region. The Fig. 7 shows the swell intensification near the points PC, PL and PR in September, 3rd since 03
to 21 UTC. The maximum spectrum peak off shore of the coast
of Rio Grande do Sul occurred at September 3rd at 21 UTC,
which carries a delay of 48 hours with respect to the spectral
peak at the cyclone center.
Fig. 9 shows the significant wave heights (Hs ) at 21:00 for
September 2nd and 3rd . In a range of 24 h the Hs at Cassino
Beach increased from 3.4 m to 8 m, with maximum wave energy
spectrum on 115 m−2 s−1 degree at PC, 60m−2 s−1 degree at PL
and 10m−2 s−1 degree at PR (Fig. 9).
4. Conclusions
The extratropical September 2006 in the South Atlantic was
chosen for the case study. This was the most intense and caused
the greater waterline displacement with respect to the mainland
in a year of monitoring (June 2006 to July 2007) in Praia do
Cassino (RS).
Of the 155m2 s◦ degree maximum spectral wave energy (on
day 01 at 21:00) in the center of the cyclone, 115m2 s◦ degree
(on day 03 at 21:00) was transferred toward the coastal central
point PC. Thus, 74% of the cyclone generate wave energy was
propagated towards the coastal area off shore of Rio Grande do
Sul, with a lag of 48 h. Hence, assuming that event as extreme in
an annual scale, this gives an indication of the amount of wave
energy that reaches the coast in similar situations.
The wave spectra obtained by the WAM model support the
theory of wave resonance in the neighbourhood of tropical
and extratropical cyclones. Objectively, we noticed that 67%
of the spectra obtained in the three days of the cyclone lifetime (here, September 1st -3rd ) were more intense at the left of
cyclone. This reflects the wave-wave interaction occurring between waves of different ages, with the same direction and generated by the cyclone winds. The presence of a longer fetch on
the left side also contributes to increase the wave heights.
The impact of the resonance phenomenon on the wave energy
spectra generated by extratropical cyclones would supply more
detailed informations if applied on a larger number of events.
Grounded in statistical tools, the future works aim to answer
the questions arising from the present study: Is there any relationship between the amount of wave energy reaching the coast
and the different cyclone tracks? Is the ocean wave resonance
phenomenon also observed in the other two cyclone tracks patterns proposed by (PCNK09)?.
Ackowledgements
The first author acknowledges financial support from CNPq
and the second author has done part of the research on this article while a member of the EU project FP7-295217 - HPC-GA.
His research was supported by Grant MTM2011-24766 of the
MICINN, Spain and also by the Basque Government through the
BERC 2014-2017 program and by Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
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Fig. 1.
The mean sea level pressure and the wind direction of the extratropical cyclone occurred in September 2006 are represented, where
three situations are presented. The first column shows the weather conditions two days prior to the maximum storm surge level. The second
column contains the atmospheric state on the day before the maximum
storm surge level while the third column on the day of maximum uplift
of the ocean. Modified from
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Fig. 2.
Trajectory of extratropical calculated by tracking the maximum relative vorticity at the center of a cyclone from its formation to dissipation
into the ocean. Modified from
WAVE SPECTRA GENERATED BY AN EXTRATROPICAL CYCLONE IN THE SOUTH ATLANTIC OCEAN
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Fig. 3.
First column: wave spectra to the left of the cyclone; Second column: wave spectra in the center of the cyclone; Third column: wave
spectra to the right of the cyclone. Dates and times are represented in the titles.
C. K. PARISE AND L. FARINA
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Fig. 4. Uni-dimensional spectrum of wave energy along the trajectory of the extratropical cyclone in the South Atlantic Ocean on 01/09/06.
Fig. 5.
Schematic figure showing the presence and absence of swell respectively to the left and right of the path of the cyclone, when this moves
from the first position (P1) to position 2 (P2).
WAVE SPECTRA GENERATED BY AN EXTRATROPICAL CYCLONE IN THE SOUTH ATLANTIC OCEAN
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Fig. 6.
Wave energy spectra obtained off the coast of RS. First column: the left wave spectra (37 S and 55 W); Second column: offshore wave
spectra at Cassino Beach (32 S and 50 W); Third column: wave spectra on the right (27 S and 45 W). Dates and times are represented in the titles.
C. K. PARISE AND L. FARINA
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Fig. 7. Evolution swell of 03h (left panel) to 21h (right graph) of 03 September.
Fig. 8. Evolution of the significant wave height in the range from 24h to 21h and 02 to 21h day of 03 September.
WAVE SPECTRA GENERATED BY AN EXTRATROPICAL CYCLONE IN THE SOUTH ATLANTIC OCEAN
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Fig. 9.
Uni-dimensional spectrum of wave energy off the coast of RS (32 S and 50 W) and points to the left and right of that resulting from the
passage of an extratropical cyclone in the South Atlantic Ocean.