Journal of Coastal Research
00
0
000–000
Coconut Creek, Florida
Month 0000
Remote Sensing of Small-Scale Storm Variations in Coastal
Seas
Ferdinando Reale†, Fabio Dentale†, Eugenio Pugliese Carratelli†§, and Lucio Torrisi‡
†
Maritime Engineering Division
University of Salerno (MEDUS)
Department of Civil Engineering
Via Ponte don Melillo, 84084,
Fisciano (Salerno), Italy
fdentale@unisa.it
§
University Centre for Research
on Major Hazards (C.U.G.RI.)
Piazza Vittorio Emanuele, 84084,
Penta di Fisciano (Salerno), Italy
‡
Centro Nazionale di Meteorologia
e Climatologia Aeronautica (CNMCA)
Via Pratica di Mare 45, 00040,
Pratica di Mare (Roma), Italy
ABSTRACT
Reale, F.; Dentale, F.; Pugliese Carratelli, E., and Torrisi, L., 0000. Remote sensing of small-scale storm variations in
coastal seas. Journal of Coastal Research, 00(0), 000–000. Coconut Creek (Florida), ISSN 0749-0208.
Estimating extreme values of significant wave heights (SWH) is a necessity in many branches of coastal science and
engineering. Storm intensity, however, is not a smooth varying quantity, but it oscillates with random variations around
a generally regular trend; the estimated value of extreme sea states is, therefore, necessarily affected by the sampling
time of the available data. This is especially important when making use of synthetic data deriving from weather and
wave simulation systems, which artificially smoothen the SWH record history. Active remote sensing provides valuable
help to overcome this problem: the work described here very briefly recalls the available satellite SWH and wind
measurements and shows how such data may help clarify and reduce a possible cause of error in wave climate
evaluation, and especially so along coastal areas.
ADDITIONAL INDEX WORDS: Altimeter SWH, extreme events, Tyrrhenian Sea, Arabian/Persian Sea, wave model,
gustiness, small-scale storm variations.
INTRODUCTION
Extreme wave storm statistics are an essential tool of ocean
engineering, especially so in relation to coastal engineering.
The traditional—and until recently the prevalent—source of
data is the historical wave buoy record: by analysing long time
series of significant wave height (SWH), average and peak
wave period (Tm and Tp), or other spectral parameters
deriving from sampled wave records, and by fitting appropriate extreme value distributions such as Gumbel, FisherTippet, etc., a SWH versus return time (RT) curve can often be
fitted to provide a satisfactory design tool for a given site.
Some recent developments are reported by Komar and Allan
(2008); Li et al. (2011); and Pugliese Carratelli et al. (2007),
among others.
An appropriate choice of the sampling frequency of the wave
records is an important aspect of this kind of investigation: it is
a well-known fact that intensity of a storm—as measured by its
SWH, for instance—is not a smooth varying quantity, but it
randomly oscillates around a generally slowly varying trend.
As a consequence, the use of data with a lower resolution (such
as a 3 h sampling, for instance) would cause a considerable
DOI: 10.2112/JCOASTRES-D-12-00239.1 received 21 November 2012;
accepted in revision 24 February 2013; corrected proofs received
23 April 2013.
Published Pre-print online 9 May 2013.
Ó Coastal Education & Research Foundation 2013
reduction of the extreme value of the computed SWH as a
function of the RT. Figure 1 provides an example of the effect of
different sampling intervals: by making use of 18 years of
recorded buoy data, the maximum SWH/RT curve was
calculated first with the smallest available sampling interval
(300 ) and then by degrading the data to a sampling interval of 3
hours.
This clearly shows that the use of low time resolution data
can cause a very serious bias in the definition of the design
climate in a given site; this, however, does not pose any problem
in current coastal engineering practise—as long as a wave buoy
has been present in the intended site for an adequate number of
years—since most of the available time series are nowadays
produced and supplied with a high enough sampling frequency
(usually 20 or 30 min).
The situation is quite different for locations where there is no
instrumentation, as is the case not only in developing
countries, but also in many coastal areas where the land
morphology makes the transposition of nearby buoy data
subjective and unreliable. Even more critical is the reconstruction of wave climate for the design of platforms and for
coastal sea route planning. The use of different technologies to
produce ‘‘synthetic’’ data is therefore a necessity; in addition,
the design requirements have become more stringent so that
the methods to estimate wave climate must be constantly
updated.
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Reale et al.
Figure 1. Extreme SWH as a function of the RT computed with half-hourly (solid line) and 3 hourly (dashed line) for Ponza (left) and Cetraro (right) wave buoys.
Peak over threshold (POT) method with threshold ¼ 4 m. Wave buoy data from Italian Environmental Agency (ISPRA).
PRESENT TRENDS FOR EXTREME SEA STATE
EVALUATION
It has now become common practise in coastal and ocean
engineering to analyse the wave climate by using archived data
from spectral wave models, driven in turn by global and
regional weather models. The quality of the extreme SWH
estimate depends of course on the quality of the whole weather
models and wave models chain (WMþWM); global WMþWM
are run mostly by national and international weather services,
such as the United Kingdom Meteorological Office (UKMO),
the European Centre for Medium-Range Weather Forecasts
(ECMWF), and the National Oceanic and Atmospheric Administration; local area models are also run by private companies,
and the results are widely accessible at a price.
WMþWM have been, and still are, the object of intense
research work aimed at improving their accuracy. Calibration
and assessment studies have been carried out for years, and the
results are regularly published; no extensive review of the
literature is here possible, or indeed useful, but the interested
reader may find the relevant information in ECMWF (2012)
library, which is constantly updated, while Accadia et al.
(2007), Inghilesi et al. (2012), and Violante-Carvalho et al.
(2012), among others, provide remarkable examples. However,
most of the calibration and validation studies are aimed at
improving the forecasting or hindcasting performance of the
systems, rather than at estimating SWH for very high return
periods. Where this has been attempted, it has been done either
by using high sampling intervals wave meter data, as for
instance in Mittendorf, Sweetman, and Zielke (2008), or by
smoothing out altimeter data (about 5 km resolution) to better
match the resolution of the model (Hanafin et al., 2012). At
present, WMþWM data cannot provide a reliable estimate of
extreme SWH sea states over short timescales.
It is quite obvious that size of the spatial computational grid
Du and Dk and the strictly related computational steps Dt are of
paramount importance: if the size or the duration of a
meteorological phenomenon are smaller than the sampling
interval, the estimated probability of a given extreme event will
certainly be biased. This is particularly true for enclosed or
semienclosed seas such as the Mediterranean, and in general
coastal areas where the local effects of topography and
temperature gradients are more relevant.
In coastal engineering practise, an important practical
aspect must be taken into account, i.e., that the constraint in
accuracy is often given by the archiving procedure of the data
rather than by the computational algorithms, as schematically
shown in Figure 2, the storage interval Dts is by far larger than
the computational steps in time Dt, and it is a much more
important limiting factor than space resolution.
Dts for ECMWF available data (be it analysis or reanalysis
such as ERA-40) is presently 6 hours, quite unsuitable for these
kinds of applications; other agencies (e.g., UKMO) provide data
with a higher sampling rate (down to 1 h). ECMWF is now (J.
Figure 2. Storage and computational intervals in weather models and wave
models chain (WMþWM).
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Figure 3. Jason-1 (left) and Envisat (right) tracks on Arabian/Persian Gulf (top) and South Tyrrhenian Sea (bottom).
Bidlot, personal communication) considering improving this
aspect by storing and supplying not only wave data at the fixed
time steps but also their maximum values within the storage
interval Dts.
This is of paramount importance in the context of ocean and
coastal engineering, since extreme sea states are influenced by
the irregular wind structure at sea level (gustiness), which
produces in turn small-scale storm variations (SSSV), i.e., local
and temporal reinforcement of the sea state. The term ‘‘small
scale’’ refers here to the smallest resolvable scales of an
atmospheric dynamic model, although still much larger than
the typical wave period. The problem discussed here is not
linked to the so called ‘‘freak’’ or ‘‘anomalous’’ wave.
Numerical operators systematically oversmooth wind values
(Chèruy et al., 2004), so that weather models will always filter
out scale phenomena smaller than a certain scale—and such a
scale is often much larger than the grid size. Frehlich and
Sharman (2004) show the effects of spatial filtering in
mesoscale models. No matter how fine the computational
mesh, certain phenomena are inherently random and will
never be the object of deterministic forecast or hindcast.
The present trend toward finer grids and shorter computational time steps as well as the general improvement in the
technology are certainly leading to increasing overall accuracy:
Tisler et al. (2007) describe the necessity of downscaled
atmospheric fields, and it has indeed been proven that
higher-resolution models lead to higher wind speeds, especially
in coastal areas (Cavaleri and Bertotti, 2006; Chen et al., 2010;
Gaslikova and Weisse, 2006).
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Figure 4. Spurious SWH value induced by presence of a small island. (Color for this figure is available in the online version of this paper.)
THE ROLE OF REMOTE SENSING
Remote sensing data have been of paramount importance in
wave hindcasting and forecasting for many years. Active
sensors, in particular, such as synthetic aperture radar
(SAR), radio altimeters, and scatterometers, provide wave
and wind measurements that are routinely assimilated and/or
used to assess the reliability of wave model forecast.
Klemas (2009) examined the use of satellite and airborne
remote sensors to evaluate costal effects of storms; SAR
applications are described in a vast literature, such as in
Pugliese Carratelli, Dentale, and Reale (2006, 2007).
Altimeter data in particular are an important element of
wave climate studies: TOPEX/Poseidon, ERS-2, Jason-1,
Envisat, Jason-2, and now CryoSat have been providing radio
altimeter wind and SWH data for many years and for all the
seas of the word. A classical description of radar altimeter
characteristics, parameters, and limitations is reported by
Chelton et al. (2001); more recent developments are given by
Bouffard et al. (2008), Clarizia et al. (2012), and Pugliese
Carratelli et al. (2008). Note that radar impulses are normally
averaged over about 1 second to provide 1 Hz measurements,
i.e., about 7 km apart from each other, with a footprint about 12
km long and 6 km wide. Such data are routinely used by
weather centres to improve prediction or to verify the analysis
of sea state. They have also been often used to produce wave
climate studies, which are far too numerous to be reviewed
here: some notable examples are given by Feng et al. (2006);
Sarkar, Mohan, and Kumar (1997); and Woolf, Cotton, and
Challenor (2003).
A satellite altimeter pass provides practically instantaneous
information of spatial changes (SSSV in space), while a wave
buoy supplies a local description of SSSV in time—as has been
shown above. Even though the two are obviously related, it is
too early at this stage to determine a relation between the two
aspects. The present work is aimed at showing that satellite
altimeter data can provide useful indication about the entity
and extent of spatial SSSV.
DATA, APPLICATIONS, AND EXAMPLES
Two distinct coastal seas have been taken as test sites: the
first in the Southern Tyrrhenian Sea (STS), where an excellent
record of wave buoy measurements and WMþWM results is
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Figure 5. South Tyrrhenian Sea altimeter data (left, SWH; right, wind speed; curve, best fit parabola).
available, and the second in the Arabian/Persian Sea (PG),
which provides an interesting test area because of the low
occurrence of rain—a well-known factor of disturbance for
altimeter data.
A number of Jason-1, Jason-2 (five in the PG and five in the
STS), and ESA Envisat (22 in PG and 13 in STS) altimeter
satellite tracks were considered (Figure 3). All the available
passes for such tracks were examined, and those where SWH
was consistently above 1 m (PG) and 2 m (STS) were taken into
account.
Not all the altimeter signals are necessarily related to real
variations of the wave height, since its response is affected by
many errors, especially in the vicinity of a coast: Figure 4 shows
how the presence of a small island can give a spurious SWH
value. Some care was therefore taken to eliminate this kind of
disturbance by comparing subsequent passages over the same
track. A further effect is linked to the loss of accuracy in the
transition from land to sea: a discussion of such effects is reported
by Goı̀mez-Enri et al. (2010); all the passages employed here have
been depurated form the part affected by this transition.
Rain effects and/or slicks (Tournadre et al., 2006) may also
confuse the results, so all the passages where available second
band values (C band for Jason-1 and Jason-2 and S band for
Envisat) were inconsistent with the Ku band were excluded
from the present analysis. Most of the remaining oscillation
around the trend is thus certainly a measure of the oscillations
of storm intensity, over a spatial scale between 10 and 25 km,
related to wind reinforcements (gustiness).
After this preliminary phase, SWH and wind velocity data for
each passage were plotted in space, and an interpolating curve
(trend) was calculated. Examples for STS and PG are shown in
Figures 5 and 6, respectively. This allows one to visualise the
presence of random oscillations, in both wind (gustiness) and
SWH (SSSV), on both seas.
The oscillations are thus measured with reference to the
interpolating curve, which necessarily involves some degree of
arbitrariness; it is thus also necessary to get a better
understanding of which space and time scale SWH values
can confidently be considered as deterministic, i.e., reliably
estimated by the model, and which must be considered to be
purely random in nature.
Some indication of the scale, i.e., of the typical dimension of a
SSSV, can indeed be obtained by considering the spatial
autocorrelation C(i) of the normalized SWH and wind data,
that for a generic discrete real waveform Y (be it SWH or wind
velocity) is given by Eq. 1.
Journal of Coastal Research, Vol. 00, No. 0, 0000
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Figure 6. Persian Gulf altimeter data (left, SWH; right, wind speed; curve, best fit parabola).
CðiÞ ¼
þ‘
X
YðmÞ Yði þ mÞ
m¼‘
N
X
j¼1
Figure 7. Spatial correlations of SSSV.
ð1Þ
Yj2
where N is the length of the discrete waveform.
The distance LC of the first zero-crossing of C(x) (see Figure 7)
can be taken to be an indicator of the space scale. Figures 8 and
9 show some examples.
It is interesting to note that while the Tyrrhenian data yield
LC values that may range up to about 50 to 60 km, the Gulf data
considered generally show a much smaller correlation distance.
Some insight can also be gained by analysing the along track
spectra of altimeter 1 Hz SWH values (Figure 10). It appears
that, at least for the cases examined, which are all taken in
enclosed seas, there is a consistent amount of irregular
fluctuations for 1/L . 0.025 , i.e., for L , 40 km, and it is to
be expected that this could be the threshold below which the
fluctuations should be considered random. This could be very
different for open oceans.
Quantitative information on SSSV indication can be obtained
by considering the standard deviation r of both wind and wave
(Eq. 2):
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u N
uX
u ðYi Ti Þ2
u
t
ð2Þ
r ¼ 1¼1
ðN 1Þ
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Figure 8. Spatial correlations of SSSV for Mediterranean storms.
where Yi is the measured value of sample (wind speed or SWH),
Ti is the value of the average trend line at the same position,
and N is the number of (1 Hz) measurements. A scatter index
CV ¼ r/l for each pass was also considered, by taking l as the
mean of all the N values of the passage (N in the cases
examined varies between 20 and 90). The scatter indexes CV
can be treated in turn as random variables, and Figure 11
shows their empirical frequency distributions as well as their
cumulate functions.
The average SWH CV values are found to be around 0.1: if a
normal distribution is assumed, a SWH value 30% higher than
the trend is to be expected with a 2.5% probability, while the
empirical cumulate functions suggest only a 20% increase with
the same probability level: in any case this is by no means a
negligible effect for all practical purposes related to coastal
engineering.
In order to provide a specific guidance to engineering
practise, more extensive site-specific data should be gathered; it is, however, reasonable to assume that if the objective
of the analysis is the design of a rigid structure (i.e., sensitive
to wave actions of a short duration), the extreme SWH values
resulting from model data should be increased by assuming
an extra random effect according to the distributions
suggested above.
The statistical parameters CV and LC for the wind values
seem to be quite similar to those of the SWH, against physical
intuition, which suggests that oscillation of wave height should
be similar but reduced compared with those of the wind, and
possibly with a larger coherence. This is an aspect that might
be related to the implicit spatial averaging process of 1 Hz
altimeter data, and it obviously requires further research.
There seems to be no doubt that the main cause of SSSV is
gustiness: a number of theoretical results prove such a
connection. Hsu and Blanchard (2007) used the gust factor
concept to improve the friction velocity estimates. Abdalla and
Cavaleri (2002) actually simulated SSSV by feeding synthetic
gusty wind series to a wave model and provide some evidence of
SSSV with CV values not unlike those found in the present
work. On a large scale similar effects have been found by using
SAR on the North Sea (Pleskachevsky, Lehner, and Rosenthal,
2012).
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Figure 9. Spatial correlations of SSSV for Persian Gulf storms.
Figure 10. Along track spectra of altimeter 1 Hz SWH for different cycles of Jason-1 track 44 in the South Tyrrhenian Sea. (Color for this figure is available in the
online version of this paper.)
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Figure 11. Empirical frequency distribution and cumulate function for SWH CV values in the South Tyrrhenian Sea (left) and Persian Gulf (right).
Since the physical effects and the reconstruction algorithms
for SSSV are radically different and independent from each
other, a confirmation of the connection between gustiness and
SSSV can be found by considering the scatter index CV for
altimeter wind speed (Figure 12), which shows a similar
behaviour to the CV of SWH.
In any case the existence and the importance of subgrid
oscillation is obvious; it is worth asking if improvements of
model resolution might lead to simulation of such oscillations.
A number of tests were therefore carried out on a storm that
took place in the Southern Tyrrhenian Sea in November 2010
by making use of the results of NETTUNO model.
NETTUNO is a high-resolution (0.058) WAM application
developed by the Italian Meteorological Centre (CNMCA) in
cooperation with the Italian National Research Council
(ISMAR-CNR). (Bertotti et al., 2010) and driven by the
COSMO-ME (Consortium for Small-Scale Modelling-Mediterranean) atmospheric model. COSMO-ME, presently at 7-km
resolution, is based on the COSMO model, the standard
regional weather forecasting tool of Italian, German, and many
other national meteorological offices. Information about it is
available at http://www.cosmo-model.org.
The storm was monitored by four wave meters run by the
Italian Wavemeter Network (Ponza and Cetraro buoys) and
by the Campania Region Civil Protection Department (Capri
and Cilento), and three altimeter satellite passes are
available (Jason-1, Envisat, and ERS-2). Figure 13 shows
the time behaviour of SWH as recorded by one of the buoys
Figure 12. Empirical frequency distribution for wind speed CV values in the South Tyrrhenian Sea (left) and Persian Gulf (right).
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Figure 13. (a) CNMCA NETTUNO SWH simulation on 09 November at 12:00. (b) Comparison between Capri buoy and NETTUNO model grid points. (c)
Location of buoy and grid points.
(Capri) and by the four NETTUNO model grid points around
it.
In Figure 14 satellite-measured SWH data for ERS-2 track
629 and corresponding simulated NETTUNO values in the
same area are shown.
By comparing altimeter data in space, as well as wave buoy
data in time, with the NETTUNO forecast, it appears that
while—apart from the bias—the general trends seem to match
quite well, there are virtually no small-scale oscillations in the
model results, which obviously dampens all oscillation with a
wavelength of 20 km or more. These results seem to show
that—as stated above—certain local phenomena cannot be
simulated in a model, and highlight the opportunity of making
use of satellite altimeter data in order to take SSSV into
account.
CONCLUSIONS AND PERSPECTIVES
Small-scale storm variations can affect extreme significant
wave height; the importance of taking this aspect into account
when analysing extreme wave climate must not be overlooked.
By analysing satellite altimeter tracks it appears that the
present numerical modelling techniques are unable to evaluate
such variations of both wind (gustiness) and sea sate. The
problem can only be partially solved by increasing the
resolution of the computational schemes. As a consequence,
in order to correctly evaluate extreme sea states, the use of
synthetic data must necessarily be supplemented by stochastic
information on the effect of gustiness. Satellite altimeter data
can supply useful information about the intensity of SSSV
phenomena both in wind and in wave intensity.
Remote sensing data are therefore a vital tool to improve the
understanding of extreme wave heights, and especially so in
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Figure 14. (a) CNMCA NETTUNO SWH simulation on 09 November 2010 at 21:00, with ERS-2 track 629. (b) Comparison between SWH ERS-2 track 629
altimeter data and corresponding CNMCA NETTUNO simulation. Simulated data are collocated along the altimeter track.
enclosed seas and in the vicinity of the coast. From the limited
investigation carried out so far, it is already possible to derive
some cautionary suggestion about SWH extreme values.
Further developments should be aimed at correlating space
dependent SSSVs as revealed by satellite altimeter measurement to time variation as measured by wave buoys.
ACKNOWLEDGMENTS
Work funded and supported by University Centre for
Research on Major Hazards (CUGRI).
The authors are grateful to R. Inghilesi (ISPRA), G.
Nardone (ISPRA), and M. Biafore (Campania Civil Protection
Department) for help and useful advice over many years.
Data provided by: Weather and wave modelling, Italian Air
Force Weather Service (CNMCA) and ECMWF Meteorological Archival and Retrieval System (MARS); Altimeter, RADS
(Radar Altimeter Database System Satellite) and ESA/EO
Project 1172 ‘‘Remote Sensing of Wave Transformation’’; and
Wavemeter, RON (Italian National Wavemeter Network) and
Campania Regional Civil Protection Department.
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