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1 INTRODUCTION

Observations of the sheltering effect of islands of ar-bitrary shape were reported previously in Pawka (1983) and Pawka et al. (1984). Using the SeaSat al-timetry data, Young (1989) detected a significant broadening of the spectrum during propagation across Australian coral reefs, and a substantial wave height reduction for significant distances due to the sheltering effect.

This study was conducted in North Pacific, around the Northern Channel Islands, that run from east to west between 20-98 km offshore, in California, USA. In this area, the sheltered effects of the Chan-nel Islands on the wave field, depends critically on the swell direction as shown in O’Reilly et al. (1999).

The Santa Barbara Channel (SBC), bounded to the south by the four northern most Channel Islands (San Miguel, Santa Rosa, Santa Cruz and Anacapa Figure 2), is approximately 100 km long by 40 km wide with a narrow (3-10 km wide) shelf on both the mainland and island sides of the channel and a cen-tral basin that extends to a depth of 500 m (Harms and Winant, 1998).

The choice of this location follows from earlier stud-ies that have shown important local disturbances in the wave fields produced by islands, which require very fine modeling and analysis to be identified, as global area models miss the peculiarities of the

fields, as shown for example by Ponce de León and Guedes Soares (2005, 2010).

The study region is partially sheltered from the often intense (specially in summer) north and north-westerly wind by the mountain range along the channel’s northern coast, so there can be large differ-ences in wind strengths from west (stronger) to east along the Santa Barbara channel (Dorman and Wi-nant, 2000).

This study aims to investigate the influence of the is-lands on the local wave climatology using swell spectra retrieved in the sheltered and non-sheltered zones from SAR and wave buoys moored nearby. Additionally, the performance of the WAM model around the islands will be assessed by comparing with the measured spectra.

2 MATERIAL AND METHODS

2.1 SAR

SAR is the premier sensor to detect small surface roughness changes of the order of the radar wave-length, independently of solar illumination and tak-ing advantage of the long-range propagation charac-teristics of radar signals (McCandless and Jackson, 2004). The directional spectra reconstruction using SAR images have been tackled by different authors and methods (Mastenbroek and de Valk, 2000; Schulz-Stellenfleth et al., 2005). In the present work, the improved algorithm version developed by Has-

“ Sheltering effect of islands on the Pacific swell”.

J.F. Humeniuk1, S. Ponce de León2, N. Violante-Carvalho1, L.M. de Carvalho3,C. Guedes Soares2

1COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil 2Instituto Superior Técnico, Lisboa, Portugal 3 Rio de Janeiro State University (UERJ), Rio de Janeiro, Brazil

ABSTRACT : The sheltering effect of coastal islands on the Pacific Ocean swell is studied in the present work. Wave spectra were retrieved from ERS-2 SAR (European Remote Sensing Satellite 2, Synthetic Aper-ture Radar) measurements in the shadow zone of the islands to investigate the swell evolution. Comparisons were made between the swell spectra retrieved in the sheltered and non-sheltered zones from SAR and wave buoys from the National Data Buoy Center moored nearby. Several SAR images were selected from the Euro-pean Space Agency (ESA) data base that satisfied a threshold minimum wind speed and particular wave prop-agation directions for the area. Information from a third generation wave model was used to compare the di-rectional wave spectra with the remote sensing data employed.

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selmann and Hasselmann (1991) at the Max Panck Institute (MPI) will be used, as described below.

The SAR image dated 2007 December 2nd at 18:39 UTC was selected from the on-line database of the Catalog of ESA (EOLI) which satisfied the criteria of minimum wind speed and certain wave propaga-tion direction (from NW). From this image, two sub-images of 512 x 512 pixels (5 x 5 km) were delim-ited according the WAM hindcast peak period (Tp) and significant wave height (Hs) maps evolution per-formed from 2007 November 27th to December 11th, one in the non-sheltered zone (buoy 46053) and one in the sheltered zone (buoy 46069). In this way, the SAR spectra were retrieved as near as pos-sible to the position of the wave buoys of Figure 1. For the SAR spectra, the retrieval MPI scheme was used, which inverts the nonlinear SAR ocean wave imaging process and minimize the cost function to adjust the first-guess information and improve the spectra consistency following the method described in Violante et al. (2012).

Figure 1. SAR image dated 2nd December 2007 at 18:39 UTC.

2.2 NDBC Buoys

Hourly meteorological data (Hs and Tp) were re-trieved from directional and non-directional buoys from the National Data Buoy Center of NOAA (NDBC) according to Table 1 (more details see NOAA/NDBC 2013). Additionally, the directional spectra at the location of the buoys were obtained.

Table 1. NOAA NDBC wave buoys information.

Buoys Latitude Longitude Depth (m)

46053 N 34º14’52” W 119º50’28” 449.9 46054 N 34º16’28” W 120º27’42” 460 46025 N 33º44’58” W 119º03’10” 905.3 46069 N 33º40’13” W 12012’00” 1020

2.3 The winds fields

The wind fields were produced by CFSR, which is a third generation reanalysis product (Saha et al., 2010). It is a global, high resolution, coupled atmos-phere-ocean-land surface-sea ice system designed to provide the best estimate of the state of these cou-pled domains over this period. The CFSR global at-mosphere resolution is about 38 km with 64 levels. The global ocean is 0.25° at the equator, extending to a global 0.5° beyond the tropics, with 40 levels. The subset of ds093.1 - NCEP Climate Forecast Sys-tem Reanalysis (CFSR) Selected Hourly Time-Series Products was used, with a temporal resolution of 1 hour, coverage from January 1979 to December 2010 at spatial resolution of 0.31º. The high resolution wind data set NCAR Mesoscale Model MM5 was used only at the third nested grid with matched in spatial resolution with the wind input data. MM5 da-ta have 15 vertical levels, a horizontal resolution of 5 km and with a 3 hourly time step (Chen and Dudhia, 2001).

3 THE WAM MODEL The wave model WAM (Komen et al., 1994) com-putes the 2D-wave variance spectrum through inte-gration of the wave energy transport equation:

(1) (2)

where F represents the spectral density with respect to frequency, direction, latitude, longitude, respec-tively, and the rates of change of the position and propagation of the wave energy spectrum in physical and spectral space. The source function Stot is repre-sented as a superposition of the wind input Sin, white capping dissipation Sdis, nonlinear interactions Snl and bottom friction Sbf.

In this work, the version of the wave model used is the WAM 4.54 (Günther and Behrens, 2011), which has a new semi implicit scheme based on the devel-opments at ECMWF for the source function integra-tion (Hersbach and Janssen 1999) and an update dis-sipation model (Bidlot et al., 2005).

The present WAM model configuration is composed of four grids covering the North Pacific Ocean from 75ºN to 20ºS and 125ºW to 61ºE. The bathymetry grid data (Figure 2) comes from the GEODAS NO-AA’s National Geophysical Data Centre (NGDC), with a resolution of 1 min of degree in latitude and longitude, which is linearly interpolated spatially to the different wave model grids (Table 2).

( ) ( ) ( )tStotFCt

tFg ,,,,

,,,, λφθσλφθσ =⋅∇+∂

∂

bfdsnlwindtot SSSSS +++=

3

Figure 2. The region of study, the bathymetry nested grid 3 and the location of the wave buoys.

Table 2. WAM model numerical parameters. dt integration time step.

Parameters Coarse Grid 1

Nested Grid 1

Nested Grid 2

Nested Grid 3

dt (s) 120 90 10 2 dx=dy (º) 0.5 0.25 0.025 0.0125 Wind In-put (h)

3 3 3 3

Limits (N , S)

75 , 20 64 , 20 35 , 32.5 34 , 33.5

Limits (W , E)

125 , 61 170 , 100 239 , 243 239 , 241

Model Type

deep deep shallow water

shallow water

For the four grids (Table 2), the solution of the en-ergy balance equation was provided for 36 direc-tional bands measured clockwise with respect to true north, and 30 frequencies logarithmically spaced from the minimum frequency of 0.0325 Hz up to 0.5156 Hz. The physical processes activated in the hindcast WAM simulations are wave generation by wind; nonlinear interactions between four spectral wave components; white capping wave energy dissi-pation; bottom friction dissipation based on the em-pirical JONSWAP model with a constant friction co-efficient equal to 0.067m2s-3 and depth induced-breaking dissipation.

4 RESULTS AND DUSCUSSION

The analysis will be done first by comparing the 1D spectra estimated from the wave buoys and WAM data. Secondly, the 2D spectra will be inter-compared from the different sources data: SAR, buoys and WAM at sheltered and non-sheltered zones.

4.1 Spectra 1D

The comparison of one dimensional spectra from wave buoys and WAM is shown in Figure 3 at loca-tions 46069 (non-sheltered zone) and 46053 (shel-tered zone). As can be seen, at 46053 WAM underes-timates the wave energy peak if compared against the buoy 1D spectrum. At locations 46069 and 46063 (non-sheltered zones) the spectral wave en-ergy is higher than at locations 46053, 46054 and 46025 (not all shown) in sheltered zones. The spec-tra from the locations 46053 and 46025 are affected by the possible sheltering effect of the Punta Con-ception (Figure 2) and Channel islands showing a lower level of the spectral wave energy (Figure 3). A spectral wave energy decrease in the island’s shel-tered zones was previously reported in the North At-lantic and Mediterranean by Ponce de León and Guedes Soares (2005, 2010). At location 46069, a perfect agreement of the absolute spectral peaks was obtained between WAM and buoy as can be seen (Figure 3). However, for the secondary peak, WAM gives unrealistic peak.

Figure 3. 1D wave spectra from wave buoy and WAM nested grid 3 at location 46069 (top) and 46053 (bottom). The scatter plot for the Hs obtained from the nested grid 3 against the wave buoy data at location 46025 is shown in Figure 4. As seen a high resolution correlation was obtained with a cc of 0.98, low data dispersion (s.i.=0.12) and slope of 0.9.

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Figure 4. Scatter plots for the Hs at location 46025 (cc-correlation coefficient, s.i.-scatter index, n-number of records). 4.2 2D Spectra

In order to assess in more detail the sheltering effect of the islands, the swell spectra retrieved in the non-sheltered and sheltered zones from SAR and wave buoys are compared in Figures 5 and 6, respectively. Top panels show the SAR spectra which were re-trieved as near as possible to the position of the wave buoys following the method described in sec-tion 2, and bottom panels show the wave buoy spec-tra.

While Figure 5 shows 46069 (non-sheltered), Figure 6 shows location 46053 (sheltered). For the location 46069, which is more offshore and South of the Channel islands, the comparison of the bidimen-sional wave spectra from the three sources (SAR, buoy and WAM) shows that all these spectra are similar in shape and magnitude (Figure 5 and Figure 7).

At location 46053 (sheltered zone), all three spectra are similar with the exception of the wave buoy spectrum which is showing a sea system in the NW sector (Figure 6 bottom). The WAM model repro-duced a similar directional spectral distribution as can be seen (Figure 7 bottom), however the WAM spectrum is narrower than the SAR and buoy spec-tra.

Figure 5. Spectra from SAR subimage (top) and wave buoy (bottom) 46069 in offshore non-sheltered zone. Date: 2nd December 2007 at 19 UTC.

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Figure 6. Spectra from SAR subimage (top) and wave buoy (bottom) 46053 in the sheltered zone. Date: 2nd December 2007 at 19 UTC.

Figure 7. Computed WAM directional wave spectra at locations 46069 (top) and 46053 (bottom). Date: 2nd December 2007 at 19 UTC According to the NOAA CFSR reanalysis and from the MM5 wind field evolution, the four days’ wind history before the SAR image (dated: 2nd December 2007 at 19 UTC) chosen for the study was character-ized by wind speeds of about 5-8 m/s blowing from the NW and NE in the morning and from the midday up to the moment of the SAR image the wind turned to blow from the SE with values not higher than 10 m/s (Figure 8). The WAM model Hs map under the-se conditions shows that the maxima values of Hs (1.9 m) were mainly observed in the Western side of

the nested grid. Values lower than 1 m were mostly observed in the sheltered zones and between the is-lands and the continent (Figure 8).

The waves are propagating at around 130º and a sec-ondary wave energy peak can be observed in the NW sector. The Hs values from SAR, wave buoy and WAM are similar (Table 3) with values ranging 1.05 m (SAR) up to 1.59 m (WAM). It is necessary to point out that the WAM peak period is overestimated (17.7 seconds) if compared with the measured values that are about 10-12 seconds (Table 3).

Figure 8. WAM Hs map (top) and the TP map (bottom). Date: 2nd December 2007 at 19 UTC.

Table 3 shows the measured and WAM computed wave parameters Hs and Tp. From Table 3 it can be observed that the Hs from SAR shows a higher value (1.6 m) than the values from the buoy and WAM (0.77 and 0.78 m, respectively). In addition, the peak periods are also similar in the measurements with values of 9.8 seconds and 12.9 seconds, where as the WAM peak period is an overestimated value (16.1 seconds).

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Table 3. The significant wave height (Hs) and the peak pe-riod (Tp) measured by SAR and wave buoys and computed by

WAM model around the islands.

Hs (m) Tp (s) Zones SAR Buoy WA

M SAR Buoy WA

M

Shel-

tered

Buoy

46053 1.64 0.77 0.78 9.80 12.9

16.1

3

Non-

shel-

tered

Buoy

46069 1.06 1.3 1.59 10.04 12.12

17.7

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The results from the hindcast show some inacuraci-ties in the WAM performance which probably are as-sociated with the missing of physical processes in WAM model that in the region of the Channel Is-lands are important such as diffraction and reflec-tions of the waves.

5 CONCLUSIONS

The first results produced in this study have allowed the interesting conclusion that SAR data can be successfully used to determine the wave spectra around islands, identifying the shadowing effect of the islands. Comparisons with spectra from buoy measurements and numerical models are fair but encouraging. Several additional situations need to be analysed before more general conclusions can be derived. A third generation wave model accounting for the diffraction and reflections phenomena (two important physical processes in the Channel Islands region) will be applied.

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