Journal of Geophysical Research: Oceans
RESEARCH ARTICLE
10.1029/2018JC014505
Key Points:• A numerical wave model is
integrated for 10 years to study thewind-generated waves in the SCB• The analysis of the model results andthe observational data shows thatthe wind-generated waves in the SCB
vary in multiple temporal scales• Effects of currents and topography
on waves in the SCB are investigatedCorrespondence to:
C. Dong,
cmdong@nuist.edu.cn

Citation:
Cao, Y., Dong, C., Uchiyama, Y., Wang, J.,& Yin, X. (2018). Multiple-scale variationsof wind-generated waves in theSouthern California Bight. Journal ofGeophysical Research: Oceans, 123,
9340–9356. https://doi.org/10.1029/
2018JC014505
Received 22 AUG 2018
Accepted 6 DEC 2018
Accepted article online 9 DEC 2018
Published online 26 DEC 2018
Corrected 29 JAN 2019
This article was corrected on 29 JAN
2019. See the end of the full text for
details.

Multiple-Scale Variations of Wind-Generated Waves
in the Southern California Bight
Yuhan Cao1

, Changming Dong1,2, Yusuke Uchiyama3, Jin Wang1, and Xunqiang Yin4

1

Oceanic Modeling and Observation Laboratory, School of Marine Sciences, Nanjing University of Information Science andTechnology, Nanjing, China, 2Department of Atmosphere and Oceanic Sciences, University of California, Los Angeles,
CA, USA, 3Department of Civil Engineering, Kobe University, Kobe, Japan, 4The First Institute of Oceanography, State
Oceanic Administration, Qingdao, China

Abstract A numerical wave model is applied to study the wind-generated wave in the Southern California
Bight (SCB). Observational data available in this area are used to validate the numerical model results. The
model is integrated for 10 years (2004–2013). The comparison of the model results with observations showsthat the model well reproduces the wave variations in the SCB. The multiple-scale variations in the waveﬁeld
are examined: interannual, seasonal, intraseasonal, and diurnal. The signiﬁcant wave height and swell wave
height distributions display distinct patterns during different seasons. On the interannual scale, the wave
variation in the SCB is inﬂuenced by El Niño–Southern Oscillation activities. Intraseasonal scale events occur
frequently. Land/sea breezes cause the diurnal variation. The effects of topography (especially islands) andcurrents on waves are analyzed. The islands in the SCB provide signiﬁcant sheltering effects to the coast fromdeep-ocean waves. The effect of background currents on waves is discussed.

Plain Language Summary A numerical model is used to simulate the wind waves in the Southern
California Bight (SCB). The analysis of the model results together with the observational data show that thewind waves in the SCB vary from season to season, from year to year, events with periods from a few days totens of days happen frequently, and waves near the coast change directions in 24 hr. The effects of currents
and topography on the waves are discussed.
1. Introduction
The wind-generated wave plays an important role in the air-sea interaction. Investigation of multiple-scalevariations can help us to better understand physical processes in the Southern California Bight (SCB). The
wind-generated wave plays an important role in the air-sea interaction. Investigation of multiple-scale variations can help us to better understand physical processes in the SCB.
The SCB lies on the west coast of the United States, which features a particularly complex shelf conﬁgurationof tectonic origin. Numerous offshore islands and shallow banks in the bight provide signiﬁcant shelter to thecoast from deep ocean waves. The bight extends from approximately 32°N to Point Conception at 34.5°N
shown in Figure 1, in which eight islands are presented: Santa Rosa, San Miguel, Anacapa, and Santa Cruzislands fringing the Santa Barbara Channel, Santa Catalina Island near the Palos Verdes Peninsula, and San
Clemente, Santa Barbara, and San Nicolas islands far offshore. The water depth is the deepest in the southwest and decreases steeply around the islands and near the coast. Wave climate in the region is affectedby the prevailing northwest winds along the California coast, tropical storms, and swell propagating fromthe west and northwest, with associated wave refraction and diffraction (Adams et al., 2008; Arthur & Siple,
1951; Dong et al., 2009; O’Reilly et al., 1999; O’Reilly & Guza, 1993; Pawka et al., 1984). The sea surface wave
plays an important role in the air-sea exchange, such as the momentum and carbon dioxide exchanges.
The wave includes two parts: the local wind-driven wave and the swell propagating from the remote wind
wave. Due to the variation of the wind and effects of wave propagation, both the two types of waves carry
multiple-scale variations. Investigation of multiple-scale variations can help us to better understand wave
dynamics in the SCB, which is not well documented in literature. The knowledge of multiple-scale variationin the wind-generated wave is necessary in variety of applications including sediment transports, coastal erosion, design of coastal constructions, and pollution transports.

©2018. American Geophysical Union.
All Rights Reserved.

CAO ET AL.

The study of the variability and dynamic processes of waves in the California coasts including the SCB has
been reported in literature. Seymour (1996) reports that wave height increases during westerly storm

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Figure 1. Simulation domain. Shaded is the bathymetry (unit: m) from ETOPO1. The red ﬁve-pointed stars and yellow circle
represent buoy stations and the red triangles represent the location of the selected model experiment points. The yellow
dot in the Santa Barbara Channel is the site for the test of diurnal variation. Inset map of northeastern Paciﬁc Ocean shows
location of the Southern California Bight (SCB).

events associated with El Niño phases. Eshleman et al. (2005) uses the Simulating WAves Nearshore (SWAN)
model (Booij et al., 1999) to simulate the wave process off San Francisco, California, and analyzes theeffect of beach shape variations on wave energy. Rogers et al. (2007) numerically simulate the SCB wind
waves using the SWAN model and propose that the sheltering effects are important. Adams et al. (2008)
examine the historic wave climate events in the deep water of the Southern California and its relationshipwith the El Niño–Southern Oscillation (ENSO) events. Xu and Noble (2009) analyze wave data from 18
buoys in the SCB to characterize the spatial and temporal variability of the regional wave climate and pointout that Point Conception shelters most of the Bight from being directly impacted by the North Paciﬁcweather. Inside the Santa Barbara Channel, wave heights are commonly only a quarter to half of those in
the open ocean. Adams et al. (2011) combine the SWAN model with the Coastal Geomorphic Erosion
Model to explore the sensitivity of longshore sediment transport patterns to changes in deep-water wave
direction. The numerical models are based on practical boundary conditions to estimate monitoring andprediction of waves in the SCB (Crosby et al., 2016; O’Reilly et al., 2016). Driven by the variations ofatmospheric forcing with the complex bathymetry in the SCB, the oceanic circulation in the area possesses
multiple-scale variation suggested by Dong et al. (2009), which implies the possibility of existence of thesame multiple-scale variability in the wind-generate waveﬁeld. However, the latter topic has not beenreported in literature.
The present study applies a high-resolution wave model to analyze the multiple-scale variability of surface
wave in the SCB. This paper is organized as follows: the data used in the study is described in section 2. In
section 3, the model conﬁguration is introduced. Section 4 is the model results including the analysis of theinterannual, seasonal, intraseasonal, and diurnal variations of the SCB waveﬁelds during the 10 years (2004–
2013). Sheltering effects of islands and current inﬂuences on waves are discussed in section 5, and the summary is presented in section 6.

2. Model Conﬁguration
The SWAN model version 41.10 (Booij et al., 1999, 2001) is used to simulate the wave dynamics in the SCB. Its
governing equation in a spherical coordinate is based on the spectral action balance equation given as
follows:

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Table 1Conﬁgurations of the Simulating WAves Nearshore Model
Parameter
Time step (min)Number of meshes in θ
space
Lowest discrete frequency(Hz)
Highest discrete frequency(Hz)Physics process
Shape of the spectra
Propagation scheme
Spatial resolution (km)Temporal resolution (hr)Coordinate
Mode

Value/scheme
5240.0418
1
GEN3 JANSSEN (Cavaleri and Malanotte-Rizzoli
1981)
JONSWAP
Backward Space Backward Time (BSBT)
2×2
1
Spherical
Nonstationary 2-D mode

10.1029/2018JC014505∂N ∂cλ N ∂cφ N ∂cσ N ∂cθ N Stot
þ
þ
þ
þ
¼
∂t
∂λ
∂φ
∂σ
∂θ
σ

(1)

where N is the action density with respect to longitude λ and latitude
φ, σ is the relative radian frequency, θ is the wave propagation direction, cλ, cφ are the propagation velocities of the wave energy in geographic space, and cσ , cθ are the propagation velocities in the
spectral σ and θ spaces. It is noted that the advection by the ambient
current is not included on the right side of the equation, but its effecton the wave is discussed in section 5. The source term Stot is represented as
Stot ¼ Sin þ Snl3 þ Snl4 þ Sds;w þ Sds;b þ Sds;br(2)

where Sin is the wind-generated energy input, Snl3 and Snl4 are triplet
and quadruplet wave-wave interactions, respectively, Sds,w is the dissipation by the white capping, Sds,b is the dissipation by the depthinduced wave breaking, and Sds,br is the dissipation by the bottom
friction. In the model, the transfer of wind energy to the waves is described by a resonance mechanism(Phillips, 1957) and a feedback mechanism (Miles, 1960). Both linear and exponential wind input growths
are included in the model. The whitecapping formulations are based on a pulse-based model(Hasselmann, 1974), as adapted by the WAMDI group (Hasselmann et al., 1988). The bottom friction models
selected for the SWAN are the empirical model of JONSWAP (Hasselmann, 1973) form with a friction coefﬁcient of Cbottom = 0.067 m2/s3, the drag law model of Collins (1972), and the eddy-viscosity model ofMadsen et al. (1988). For the energy dissipation in random waves due to depth-induced breaking, the borebased model of Battjes and Janssen (1978) is used. Quadruplet (deep water) and triad-wave (shallow water)interactions are activated using the default settings for the Discrete Interaction Approximation (DIA)(Hasselmann et al., 1985) and the Lumped Triad Approximation (LTA). In the SWAN, a partially modeled diffraction is added to the model using a phase-decoupled refraction diffraction approach (Holthuijsen et al., 2003).

The parameters and conﬁgurations used in the SWAN are listed in Table 1. An unsteady two-dimensional calculation mode is adopted with the grid deﬁned on a spherical coordinate system between latitudes 32°–35°N
and longitudes 117°–121°W. The model is started from a rest state and assumes constant values at times after
the end of each input parameter. The extra 3-day model simulation prior to the designed period is conducted
for the initial condition. The model is run for 10 years from 1 January 2004 to 31 December 2013.
2.1. Bathymetry Data
Bathymetric data used for the present wave model is from ETOPO1 (Amante & Eakins, 2009), provided fromthe National Oceanic and Atmospheric Administration (NOAA), which is a 1-arc min global relief model of the
Earth’s surface that integrates land topography and ocean bathymetry. In other words, it represents a spatial
resolution of 0.0167° × 0.0167°.
2.2. Atmospheric Forcing
An hourly sampled Weather Research and Forecasting Model (WRF) 10-m wind ﬁeld data with 6 km in horizontal resolution for 10 years from 2004 to 2013 are used to drive the SWAN. The domain of the input windis larger than the computational one, which is between latitudes 25°–40°N and longitudes 110°–130°W. The
WRF product has been validated against observational data, and the details can be found in Renault
et al. (2016).
2.3. Lateral Boundary Conditions
For the boundary conditions, six-hourly signiﬁcant wave height of combined wind waves and swell, mean
wave direction, and mean wave period of the ERA-Interim reanalysis data, which are provided by theEuropean Centre Medium-Range Weather Forecasts, are used for the SWAN model. In the model, the
JONSWAP spectrum is used as the shape of the spectra (both in frequency and direction) at the boundaryof the computational grid in the case of parametric spectral input. The peak enhancement parameter ofthe spectrum is set as default value. The parametric spectra at the boundary are deﬁned, which consist of

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Table 2
Information of Buoy Data in the Simulation Area

No.

Long.
(°W)

Lat.
(°N)

Missingdata(Hsign)Observation
numbers(Hsign)Missing
data(MWD)

Observation
numbers
(MWD)

46025
46047
46053
46054
46069
46086
46216
46217
46218
46224
46225

119.1
119.5
119.9
120.5
120.2
118.0
119.8
119.4
120.8
117.5
117.4

33.7
32.4
34.2
34.3
33.6
32.5
34.3
34.2
34.4
33.2
32.9

7%
19%
6%
32%
21%
9%
9%
11%
18%
10%
10%

80,76670,92582,15558,96268,51579,226
79,253
77,262
71,28478,28378,590

46%
51%
38%
99%
38%
19%
42%
43%
44%
43%
42%

47,23942,84354,094529
53,90470,48250,68849,23548904
49,80050,586Note. MWD = mean wave direction.

10.1029/2018JC014505

two parts, the ﬁrst part deﬁnes the boundary segments where thespectra are given and the second part deﬁnes the spectral parametersof these spectra. The ERA-Interim reanalysis data (Dee et al., 2011)
assimilates ocean wave height data derived from spaceborne radar
altimeters into the wave model. Parametric wave quantities of ERAInterim are based on the Wave Modeling approach (Komen et al.,1994). A four-dimensional variational data assimilation scheme is usedin ERA-Interim. The ERA-Interim provides a variety of products withdifferent spatial resolutions from 0.125° to 3°. For the current study,
the highest one with the resolution of 0.125 ° is selected.

3. Observational Data and Model Validation

Validation of the model result for signiﬁcant wave height (Hsign) andmean wave direction (MWD) is conducted by using hourly observational Hsign and MWD data from 11 National Data Buoy Center buoys
in the SCB (Figure 1) over the 2004–2013 period. The average numberof null values of the measured wave height data from 11 buoys is
about 13%. The detailed information on the wave measurements at these stations is listed in Table 2.
The observed Hsign is calculated by taking the average of the highest one third of all wave heights during a
20-min sampling period. The directions of waves at the dominant period are coming which measured indegrees, increasing clockwise with the northward one as 0° and the eastward one as 90°. The correlation coefﬁcients between the hourly SWAN data and buoy observations are between 0.50 and 0.67. The mean Hsignand the MWD of the simulated and observed data at 11 stations are 1.46 (276.62°) and 1.50 m (262.32°),
respectively. The relative errors of mean simulated Hsign and MWD are 2.4% and 5.4%, respectively. The mean

12
1 n
1
2
∑ ðx i  x Þ ,x ¼ ∑ni¼1 x i , where n is the number of elements in the samstandard deviation (STD ¼
n i¼1nple and x is a data vector) of the simulated and observed Hsign at 11 stations are 0.63 and 0.58 m, respectively.
The relative error of mean STD of simulated Hsign is 7.9%.
Figure 2 displays the means and STDs of observed and modeled Hsign and MWD at the individual 11 stations.
At Station 46054, the mean observed Hsign is 1.95 m and the mean modeled one is 1.96 m. The STDs ofobserved and modeled are 0.77 and 0.71, respectively. At Station 46053, both the mean observed and modeled Hsign are 1.24 m. The STDs of observed and modeled are 0.51 and 0.58, respectively. At Station 46047, themean observed Hsign is 2.10 m and the mean modeled one is 2.00 m. The STDs of observed and modeled are
0.83 and 0.74, respectively. At Stations 46054, 46053, and 46047, the mean observed (modeled) MWDs are
290.0° (296.6°), 269.8° (272.7°), and 292.3° (300.9°), respectively. The STDs of observed (modeled) MWD at
the three stations are 29.1 (26.1), 22.6 (36.4), and 39.0 (30.2), respectively. The above numbers suggest that
the SWAN model well reproduces Hsign and MWD in the SCB.

4. Results
In this section, the multiple-scale variations of the waves in the SCB are examined using the SWAN data: interannual, seasonal intraseasonal, and diurnal. Before discussing the temporal variation, we present 10-year
mean states of sea surface wind, signiﬁcant wave height, swell wave height, and peak wave period, shown in
Figure 3. Mean wind speed |U| (Figure 3a) is calculated using the zonal (Ui) and meridional (Vi) components ofwind aspﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1
jUj ¼ ∑ni¼1 Ui 2 þ V i 2n(3)

where i represents the hourly time step and n is the total number of hours during periods from 2004 to 2013.
The mean wind speed for the SCB is between 3 m/s and 9 m/s, with the highest in the open sea and the area
near Point Conception in the SCB, the wind speed decrease dramatically from offshore to nearshore. The
wind direction over the SCB is predominantly from the northwest. Figure 3b shows relatively large Hsign in
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Figure 2. Signiﬁcant wave height comparisons between National Data Buoy Center and Simulating WAves Nearshore(SWAN) for 2004–2013. The blue circles and red triangles represent, respectively, the SWAN data and measured signiﬁcant wave height at each buoy location. The blue and red error bars represent, respectively, the standard deviation of
SWAN and measured signiﬁcant wave height. The mean bias is smaller than 0.3 m. There is a good agreement between
SWAN and observation data. MWD = mean wave direction.

the southwest part of the SCB ranging from 2 to 2.5 m. The distribution of the waveﬁeld is basically consistent
with that of the local wind ﬁeld. In the nearshore areas, Hsign is relatively small ranging from 0.5 m to 1 m. Hsignis also observed to gradually decrease from 2 m in the deep ocean to 0.5 m near the shore. Additionally,

Figure 3. Ten-year average (2004–2013) distribution of 10-m wind, signiﬁcant wave height, swell wave height, and peak
period in the Southern California Bight. (a) Ten-meter winds (vectors; unit: m/s) and wind speed (color shadings, unit: /s);(b) signiﬁcant wave height (shade; unit: m) and mean wave direction (vector); (c) swell wave height (color shadings, unit: );(d) peak period (color shadings, unit: s).

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Figure 4. Monthly averages of mean wind speed in the lager domain (blue solid line, unit: m/s), peak wave period (bluedotted line, unit: s), signiﬁcant wave height (black solid line, unit: m), and swell wave height (black dotted line, unit: m)
for 2004 to 2013.

waves in the southeastern side of the islands exhibit a further decrease in the wave height. Wave height on
the upwind side relative to the islands is approximately twice as large as that on the lee side of the islands.
The direction of wave propagation (see in Figure 3b) is generally southeastward in deep water andeastward in shallow water. The change of wave direction in the nearshore is mainly due to thebathymetric refraction of waves.
Figure 3c shows the time-averaged spatial distribution of swell wave height ( Hswell ¼ 4
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ω
2π∫0 swell ∫0 E ðω; θÞdωdθ, whereωswell = 2πfswell, E is the variance density spectrum, and fswell = 0.1 Hz bydefault). The general pattern of the spatial distribution of the Hswell is similar to that of the Hsign inthe whole SCB, but in the lee sides of islands, the spatial distribution of the Hswell is more signiﬁcantly
affected by the islands than that of Hsign. It is easy to see from the ﬁgure, the sheltered area of the swellis larger than the mixed wave (Figure 3b) in the SCB, especially, the waveﬁeld in the lee side of Santa
Catalina Island. The remotely generated wave energy propagating into the bight is dissipated by thewave breaking and diffraction near the offshore islands (O’Reilly & Guza, 1993). The upwave from theisland is blocked from propagating to the sheltered region. The wave at the sheltered region can bereconstructed by adding the wave information that does arrive at the point (amplitudes and phases),radiating from the upwave crest. Repeating this reconstruction in the area downwave from the incident
crest gives the entire waveﬁeld in this area, including the sheltered area. The local wind-generated wave
is the direct response to the wind, which is affected by an island in a limited lee area. These different
processes lead to the signiﬁcant difference between the swell and mixed wave in the lee sides of islands.
In the deep area, Hswell is 0.8 to 1 m, while Hswell in the shallow water is 0.2 to 0.4 m. In the sheltering
area of the islands, Hswell is only about 0.2 m. Figure 3d shows the time-averaged peak period (PER). It isfound that the period is signiﬁcantly affected by the wind. The period around Point Conception is relatively large, ranging from 9.5 to 10 s. At the southwestern corner of the model domain, the maximum
value of the peak period is 10 s. The wind speed near the shore is small, and the peak period is also
reduced. In the island sheltering areas, as the wave energy is dissipated, the peak period decreases
signiﬁcantly.
4.1. Seasonal Variation
This section discusses the perennial average and the seasonal distribution of the wave ﬁeld in the SCB.
Figure 4 shows the time series of the perennial averages for wind speed, Hsign, Hswell, and PER. The perennial average of the wind ﬁeld and waveﬁeld is obtained by calculating an area average of the 10 years’monthly mean. The area of the wind ﬁeld covers the larger area, and that of the wave ﬁeld is the SCB.
From the time series, the seasonal characteristics of wave height and peak period are large in winter andCAO ET AL.

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Figure 5. Mean seasonal variations in the Southern California Bight. (a) The 10-m wind speed (unit: m/s), (b) signiﬁcant wave height, (unit: m), (c) swell wave height,(unit: m), and (d) peak period (unit: s).

small in summer, with the maxima in January and the minima in August. These results are consistent
with the seasonality of the wind ﬁeld (Figure 4). The wind speed is generally the largest in winter andthe smallest in summer. The correlation coefﬁcient between the wind speed and Hsign, Hswell, and the
PER are 0.97, 0.98, and 0.97, respectively, with a 95% conﬁdence level. The correlation coefﬁcientshows that the variability of the waveﬁeld in this area is signiﬁcantly affected by the local wind.
Figure 5 shows the seasonal spatial distribution of the wind and wave ﬁelds in the SCB. The four seasons areclassiﬁed as December–February (winter), March–May (spring), June–August (summer), and September–
November (fall). The wind speeds in spring and summer are larger than fall and winter. Wave heights, peak
periods are larger in spring and winter than those in fall and summer. In summer, wind speed reaches 9 m/s
near Point Conception, but in other offshore areas, the wind speed is much lower, only 3 to 4 m/s, and thewind speed variations on the lee side of the island occur more signiﬁcantly than those in other areas. The
minimum Hsign is 0.25 m. The nearshore Hswell is 0.25 m. The minimum peak period of 7 s is noted in the sheltered areas of the islands in the SCB. In winter, the maximum wind speed is 7 m/s and the minimum windspeed is 4.5 m/s. The maximum Hsign is 2.5 m, which is mainly distributed in the southwest corner of the study
area. The Hsign is mostly 2 m, which is mainly distributed in coastal areas and island shelters. The maximum
Hswell is 1.5 m. In the leeward region of the island, the gradient of wave height is large. The PER is 10.5 s, which
is mainly distributed in the deep water and the area near Point Conception.
4.2. Interannual Variation
Figure 6 shows the annually averaged time series of sea surface wind speed and wave ﬁeld in the SCB. It isfound that the variation of Hsign resembles that of the wind speed. The correlation coefﬁcient between thewind speed and Hsign is 0.73. In 2005, the wave height and period are large. Afterward, the wave heightCAO ET AL.

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Figure 6. Time series of annual mean of the wind speed (unit: m/s; blue dotted line), signiﬁcant wave height (unit: m; blackline), mean period (unit: s; blue line), and swell wave height (unit: m; black dotted line) in the Southern California Bight
between 2004 and 2013.

and period decrease to smaller values in 2007. The wave height and period begin to increase again, reaching
the largest in 2010. The wind speed has a similar oscillation during this period.
Waves modulate energy ﬂuxes across the air-sea interface and into the upper ocean, thereby playing important roles in air-sea interaction processes (Young et al., 2011). ENSO is an irregular periodic variation in sea
surface temperatures and winds over the tropical eastern Paciﬁc Ocean, affecting the Paciﬁc basin-scale climate change. In order to explore the relationship between ENSO and the wave height, the characteristics of
the interannual variation of the wave ﬁeld in the SCB are analyzed to be related to the ENSO index (Niño3.4
index) during 2004–2013. The Niño3.4 index (Saha et al., 2017) is deﬁned as sea surface temperature anomalies in the Niño 3.4 region (5°S–5°N, 170°–120°W), which has been obtained from the website: http://www.cpc.
ncep.noaa.gov/data/indices. In 2009–2010 (Yuan et al., 2012), a relatively strong El Niño event occurs when
the Niño3.4 index is largest during the 10 years.
To further investigate the relationship of the waves in the SCB with the ENSO, we apply a low-pass ﬁlter toremove the seasonal signals from the monthly Hsign and Niño 3.4 index (Figure 7). In 2010 when the El
Niño event happens, the trade winds become weaker, which implies the weakening of the whole subtropicalatmospheric circulation near the sea surface, including the SCB area. Usually weak wind drives low wave

Figure 7. (a) The interannual variability of signiﬁcant wave height and Niño 3.4 index. The left ordinate represents theannual average of the Hsign (without the seasonal signal), and the right represents Niño 3.4 index (without the seasonal
signal). The red solid lines represent model data and the blue solid lines represent Niño3.4 index. (b) The number of themonth exceptional Hsign at station 46225 compared with the Niño3.4 index.

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Figure 8. Time series of daily averaged signiﬁcant wave height (red line) and wind speed (blue line) during April 2010. The
correlation between wind speed and Hsign reaches 0.83.

height, however, as we see from Figure 7a that the wave heights are the largest in the 10 years. The cause of
the strong wave in the ENSO year is considered as high frequency of storm occurrence (Adams et al., 2008;
Seymour et al., 1985; Storlazzi & Griggs, 2000). From the observations at the buoy stations are relatively complete. Figure 7b shows that there are more large wave events in 2010 than other years at Station 46225.

4.3. Intraseasonal Variation
This subsection mainly analyzes the intraseasonal variability of Hsign. As an example, Figure 8 shows the daily
time series of Hsign and average wind speed in April 2010. A strong correlation of 0.83 exists between windspeed and Hsign, which shows that the wind ﬁeld within 1 month has a great impact on the waveﬁeld. The
wind ﬁeld and wave ﬁeld share an oscillation period of about 7 days. Figure 9 shows that both the wind
and wave spatial distributions have clear similar patterns between 23 and 29 April 2010 with a repeating pattern of decrease and increase. From the ﬁgure, it can be seen that along most of the coastal areas, both wave
heights and wind speeds are small. On 23 April, both wave heights and wind speeds exhibit large values inmost of the SCB, the wave height and wind speed decrease to small values on 25 April 25, and afterward, thewave height and wind speed begin to increase again.

Figure 9. Temporal variations of daily-averaged wind speed (m/s) and signiﬁcant wave height (m) in April 2010. (a–h) For 23–29 April 2010, (a and e) for 23 April,(b and f) for 25 April, (c and g) for 27 April, and (d and h) for 29 April.

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Figure 10. Wind rose on 25–27 July 2010 (a) and 27–29 August 27-29, 2010 (b) at Santa Barbara buoy station. The range ofwind speed (unit: m/s) is represented by the different colors shown in the legend.

4.4. Diurnal Variation
While the California Current is a persistent cold southward current ﬂowing through the SCB accompanied by
the northward countercurrent close to the shore, diurnally ﬂuctuating ﬂows are also quite substantial.
Because of existence of the deserts in Southern California, the coastal land-sea breeze is pronounced during
boreal summer that is speculated to inﬂuence on ﬂows and waves at the diurnal frequency. Hughes et al.
(2007) use observational data to analyze the diurnal variations of the wind ﬁeld near the coast of Southern
California during summer and notice a signiﬁcant diurnal cycle in the direction of the offshore wind. The
land-sea breeze systems have a signiﬁcant impact on the costal wave characteristics (Remya & Kumar, 2013).
To investigate the diurnal variation of waves in the SCB, a wave buoy located in the Santa Barbara Channel,
approximately 3 m away from the shore (Figure 1), is used as a case study. Wind roses on 25–27 July 2010 and
25–27 August 2010 are shown in Figure 10. Winds are distributed in multiple directions near the shore, andthe wind directions are generally onshore during the day and offshore at night. Furthermore, the windspeeds change greatly between 1 and 7 m/s. Figure 11 shows diurnal variation of the air temperature, windﬁeld, and waveﬁeld during same period in the local time. The air temperature changes between 12 and 17 °C
in the two period. The wind speeds vary between 1 and 7 m/s with a diurnal oscillation. It can be seen from
Figure 11 that in the high frequency of the variation (diurnal variation), the wave variation is not in the samepace as the wind variation and slightly lags behind the wind variation, which is different from that in thelonger time scale, such as intraseasonal, seasonal, and interannual variations (in the longer time scale, wind,
and wave variations are in the same pace, see Figures 4, 6, and 8.
In summary, waves in the SCB have a signiﬁcant seasonal variation: in winter, the Hsign, Hswell, and PRE arelarge, and small in summer. In the interannual scale, waves are affected by the ENSO activities. In the intraseasonal scale, winds have a great impact on the waves in the SCB. Sea breeze and land breeze has impacts
on the waves in the diurnal scale.

5. Discussion
A capability of wave diffraction in SWAN version 41.10 provides us a great opportunity to realistically describe
the propagation process of waves in the nearshore, including areas sheltered by islands and semienclosed
basins. In addition, the governing equation of the SWAN model is based on the spectral action balance equation, which represents conservation of spectral wave action density with background currents that interact
with waves. Therefore, the SWAN model is suitable to study the inﬂuence of current on wave propagation.
In this section, sheltering effects of islands and oceanic currents on waves are discussed.
5.1. Sheltering Effects of Islands
Pawka et al. (1984) show that low-frequency waves have a strong refraction effect near the island in the SCB
using a numerical model. O’Reilly et al. (1999) use a spectral analysis of buoy data to study the dissipation ofwave energy by the reﬂection from cliffs on the coast of California. Their results show that swells are affected

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Figure 11. Diurnal variation of winds, waves and air temperature observed by Santa Barbara buoy. The diurnal variation (a)on 24–27 July 2010 and (b) on 26–29 August 2010 in local time.

by the sheltered of Point Conception and the Channel Islands. León and Soares (2005) employ a wave modelwith a very ﬁne grid to simulate the sheltering effect of the Azores Islands (Portugal) in the North Atlantic
Ocean. They ﬁnd that in strong wind conditions, the sheltering effect of islands is signiﬁcant. The presenceof the Azores Islands induces a spread of energy and changes in the directional wave spectrum while reducing the wave height. León and Soares (2010) ﬁnd that the islands block the propagation and generation ofwaves in the lee side that modify the resulting sea states to reduce the signiﬁcant wave height and to change
the peak period. Previous researches have recognized that islands have a signiﬁcant sheltering effect oncoastal areas due to attenuation of surface gravity waves.
In this section, we investigate the inﬂuence of the islands in the SCB on wave propagation under high windconditions. Figure 12 shows an example of the island sheltering effects on wave variables in January for 10
years. When the waves propagate from the northwest, the sheltering effect of the six islands retard the arrivalof the signiﬁcant wave height front to the coast of the continental SCB (Figure 12a). Generally, swells propagate from the northwest to the bight (Figure 12b) and the wave height decreases behind the islands. The spatial distribution of wave direction (Figure 12c) demonstrates that the mean propagation directions are
signiﬁcantly different on both the up and downwind sides of the islands. The peak period (Figure 12d) on
the leeward side shows signiﬁcant reduction.
To discuss the island effects on wave propagation, we choose six points around Santa Catalina Island deﬁned
clockwise from the northern tip, as denoted by the red triangles in Figure 1. The rose diagram (Figure 13) ofwave directions and heights at the six selected points in January 2011 shows that wave heights greater than
1 m are mostly observed at the Point A, followed by Points E and F on the upstream of the island in terms ofwind. At the Points B, C, and D on the leeward side, the wave heights are mostly less than 1 m, especially at

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Figure 12. Island sheltering in the Southern California Bight. (a) Signiﬁcant wave height, (shaded; unit: m); (b) swell wave
height, (unit: m); (c) is mean wave direction (unit: °); (d) peak wave period (unit: s). Panels are for indicated variables inJanuary from 2004 to 2013.

the Point B. The wave directions are southward for all the points except Points B and C. These results
demonstrate that Santa Catalina Island acts as a barrier and blocks wave propagation on the lee side of
the island, resulting in decrease in wave height in that area.
The presence of Santa Catalina Island also induces the spread of energy, thus changing the wave spectrum.
The energy balance equation of the present SWAN model solves directional wave spectrum with discrete 24
directions and 25 frequency bands. Figures 14 and 15 show the inﬂuence of the Santa Catalina Island sheltering effect on the wave energy distribution.
Figure 14 displays the directional wave spectrum at the six points (red triangles in the Figure 1) surrounding Santa Catalina Island derived from the SWAN model for 14 January 2011 at 15:00 UTC. The directional
wave spectrum at Point A (Figure 14a), which is located on the upwind side of the island, shows a bimodal spectrum, and the energy density is stronger than the other points. Two wind wave systems are present at Point A, while Points B (Figure 14b) and C (Figure 14c) exhibit only single component wind waves.
In the frequency wave spectra plot shown in Figure 15, the spectra at Points A, B, and C are characterized by asingle peak, which exhibits dominance of the prevailing wind wave component. The swell energy is basicallydissipated at Points B and C. On the other hand, Points D, E, and F are characterized by two peaks and theswell wave is the dominant component. These ﬁgures indicate that the wave energy at Points A, E, and F
on the windward side is larger than those on the lee side. The energy of the wave spectrum at the threepoints (B, C, and D) in the sheltered areas is small. More importantly, the spectral directions at Points B and
C are largely altered to the southeastward, consistent with Figure 14. These results demonstrate that theislands in the SCB play an important role in the dissipation of wave spectrum energy and diffractive
directional modiﬁcations.

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Figure 13. Mean wave direction roses around Santa Catalina Island derived from Simulating WAves Nearshore simulation for January 2011 at the six points marked
by red triangles shown in Figure 1. The range of Hsign (units: m) is represented by the different colors shown in the legend.

Figure 14. Directional wave spectra derived from Simulating WAves Nearshore model for 14 January 2011 at 1500 UTC at the locations marked by yellow triangles in
Figure 1. The circles indicate the wave frequency from the center out with 0.2-Hz intervals.

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Figure 15. Frequency spectra derived from the Simulating WAves Nearshore model for 14 January 2011 at 15:00 UTC at the
six locations marked by red triangles in Figure 1.

5.2. Current Effects on Waves
To investigate the effect of oceanic currents on waves, the hourly background currents with the 1-km horizontal resolution are employed in the SWAN model obtained from the Regional Ocean Modeling Systemsimulation (Dong et al., 2009, 2012).
Oceanic current effects play roles in ocean waves generation, propagation and dissipation, which are summarized as follows: (a) when the current and wave are in the same (opposite) direction, the relative wave
height will decrease (increase; Rusu & Soares, 2011; Tolman, 1991, 2010); (b) imposed additional currents(waves) affect bottom friction coefﬁcient of the waves (currents; Mao & Xia, 2018). For instance, waves collocating with the background currents have more bottom friction and thus have a more signiﬁcant impact near
the shore (Signell et al., 1990); (c) and wave frequency shifts by the background current due to Doppler Effect.
Uchiyama et al. (2009) discuss the important feedback effects of surf zone littoral current on the waves withemphases on Doppler shift by currents, changes in wave-averaged surface elevation in the wave dispersion
relation, and the variation of Reynolds stress associated with turbulent littoral currents, due to the wavecurrent interaction. (Rusu & Soares, 2011). In the SWAN model, the evolution of the action density N is governed by the action balance equation (Chiang, 1983; Booij et al., 1999; Komen et al., 1994):  ∂cσ N ∂cθ N Stot∂Nþ ∇! cg þ uc N þ
þ
¼
x
∂t
∂σ
∂θ
σ

(4)

where uc is the ambient current and cg = ∂σ/∂k is the group velocity. For linear waves, dispersion relation
isσ 2 = g|k| tanh (|k|d). The second term in the left hand side of equation (4) combines the group velocity
and background current velocity to represent the effect of shifting the radian frequency due to variations
in depth and mean currents. Hence, this term represents depth- and current-induced wave refraction.
Figure 16a shows a typical example of wave energy variation under the inﬂuence of background current
where wave energyE ¼ 1 =16 ρgH2sign . From Figure 16a, one can see that the values of the energy difference
ratio on the northern side of Santa Rosa Island and the southwest side of Santa Catalina Island, where cycloniceddies are presented, are larger than offshore. Near the Santa Rosa Island, the values of energy difference
ratio are positive where the angle between waves and currents is greater than 90°. However, on the upwindside and the northside of Santa Rosa Island, the angle between waves and currents is less than 45°, whichleads to negative values of energy difference ratio. Therefore, the southeastward California Current, thenorthwestward Counter Current, topographically inﬂuenced currents behind islands and headlands, andother ambient currents have a signiﬁcant impact on changing wave energy in the SCB.
In order to diagnose gross effects of currents on alteration of wave energy, the Doppler shift and currentinduced advection are considered. The absolute radian frequency ω is given by the sum of the relative
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Figure 16. Normalized differences of the wave energy (shaded; units: J) between the two cases with current effects
included and wave-only for July 2011 (a). Sum of (uE)x and (vE)y terms in the equation (5) (shaded; units: w) is calculated
2
for July 2011 (b). Normalized differences of the source terms (c: energy generation; d: energy dissipation; unit: W/m )derived from model data between the wave-current interaction for the two cases with current effects included and onlywave-only for July 2011. The blue and red arrows represent the direction of the wave and current, respectively.

radian frequency σ, and the multiplication of the wavenumber k and ambient current velocity vector uc = (u,v), given by the formula for Doppler shift:ω = σ + k1u + k2v. According to equation (2), the variations of wave
growth by wind and total wave dissipation due to the current effects are calculated in Figures 16c and 16d.
Overall, the spatial patterns of wave generation and dissipation are closely correlated with Figure 16a.
For narrow-banded random and breaking waves, Jie and Slinn (2003) employed the following expression:
Et þ



 

 
u þ C g1 E x þ v þ C g2 E y
1 þ S11 ux þ S12 uy þ v x þ S22 v y ¼ εb2(5)where εb is the ensemble-averaged dissipation function, u and v are the current velocity components in the x
and y directions, and Sij (i,j = 1, 2) is the wave radiation stress tensor. The spectrally integrated form of the
wave energy balance equation (5) is useful to diagnose gross effects of currents on alteration of wave energy,
because the interaction terms (i.e., the three last terms on the left-hand side) collectively representing work
done by radiation stress Sij are exposed (e.g., Jie & Slinn, 2003). (uE)x and (vE)y are current-induced advectionof wave energy in the current effects. In other words, they collectively represent divergence and convergenceof wave energy associated with the background currents. It is worth noting that the sum of these two terms(we call the convergence term) is found to have the largest magnitude among the other terms and is 4–5
times as large as the sum of the three radiation stress terms. Figure 16b shows the convergence term forJuly 2011. The pattern of the convergence terms is approximately identical to that of wave energy variation(Figure 16a).

6. Summary
The wind-generated wave plays an important role in the air-sea interaction. The multiple-scale variation is an
essential part for the wave dynamics. Exploration of multiple-scale wave variations is important for us to better understand the wave dynamics and the physical processes in the upper ocean. Using numerical wave

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model and observation data, the spatial and temporal variability of the wave ﬁeld in the SCB is investigated.
The temporal multiple scales are presented in the wave ﬁeld: interannual, seasonal, intraseasonal, and diurnal. Seasonal variation is the most prominent in the SCB wave variability. The maximum values of Hsign, Hswell,and the wave peak period occur during winter and the minimum in summer. ENSO events have footprints on
the wave interannual variation. The intraseasonal events can be detected. The diurnal cycle is due to the landsea breeze.
The effects of island sheltering and currents on waves are discussed. The eight islands located in the SCB
cause refraction and diffraction, resulting in the wave height to decrease and the wave direction to change
in lee sides of islands. Due to the sheltering effect of the islands, the impact of waves on the southern
California coast is greatly reduced. The detailed diagnosis reveals that the wave energy convergence associated with background currents is responsible for altering the waves in the SCB, with coincident modiﬁcation of the wind input and wave dissipation.
Acknowledgments
This study is supported by the National
Key Research and Development
Program of China (2016YFC1401407)
and the Natural Science Foundation of
Jiangsu Higher Education Institution ofChina (16KJB170011). C. D. appreciates
the support from the National Key
Research and Development Program ofChina (2017YFA0604100), the National
Program on Global Change and Air-Sea
Interaction (GASI-03-IPOVAI-05),
the National Key Research andDevelopment Program of China(2016YFA0601803), the National Natural
Science Foundation of China (41476022
and 41490643), the Startup Foundation
for Introducing Talent of Nanjing
University of Information Science andTechnology (2014r072), Programfor Innovation Research andEntrepreneurship team in Jiangsu
Province, the Bureau of Ocean Energy
Management Environmental Studies
Program (M14AC00021), the Japan
Society for the Promotion of Science(JSPS) Grant-in-aid for ScientiﬁcResearch (15H04049, 15KK0207, and
18H03798), the Public science andtechnology research funds projects ofocean (201505013), and the
Postgraduate Research & Practice
Innovation Program of Jiangsu Province(KYCX18_1020). The buoy data aredownloaded from https://www.ndbc.
noaa.gov maintained by the National
Data Buoy Center.

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Erratum
In the originally published version of this article, Figure 12 was incorrectly published with same image as
Figure 11. This error has been corrected, and this may be considered the ofﬁcial version of record.

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