adamsetal2008socalwaveclimate

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Journal of Coastal Research 24 4 1022–1035 West Palm Beach, Florida July 2008

Southern California Deep-Water Wave Climate:Characterization and Application to Coastal ProcessesPeter N. Adams †, Douglas L. Inman ‡, and Nicholas E. Graham §

†Department of Geological SciencesUniversity of Florida241 Williamson HallP.O. Box 112120Gainesville, FL 32611, [email protected]

‡Scripps Institution of OceanographyUniversity of California at San DiegoLa Jolla, CA 92093-0209, U.S.A.

§Scripps Institution of OceanographyUniversity of California at San DiegoLa Jolla, CA 92093, U.S.A.Hydrologic Research CenterSan Diego, CA 92130, U.S.A.

ABSTRACT

ADAMS, P.N.; INMAN, D.L., and GRAHAM, N.E., 2008. Southern California deep-water wave climate: Characteriza-tion and application to coastal processes. Journal of Coastal Research, 24(4), 1022–1035. West Palm Beach (Florida),ISSN 0749-0208.

We consider the effect of decadal climate change on the historic wave climate of the Southern California Bight (SCB)using a 50 year hindcast record (1948–98) for waves generated in the North Pacic winter. Deep-water wave height,period, and direction are examined with respect to the Southern Oscillation Index (SOI) and the Pacic Decadal

Oscillation (PDO). Storms occurring during strong La Nina intervals, when the SOI is greater than 1.0, concurrentwith either a cool or warm phase of the PDO, are indistinguishable in wave character. In marked contrast, waveconditions arising from storms during strong El Nino intervals, when the SOI is less than 1.0, concurrent with thePDO cool phase (1948–77), differ greatly from wave conditions of storms during strong El Nino intervals concurrentwith the PDO warm phase (1978–98). Our statistical analyses characterize the deep-water winter wave climate asconsistent during La Nina intervals (mean values H s 3.3 m, T s 13.0 s, 293 , for the highest 5% of waves),but variable during El Nino intervals depending on PDO phase ( H s 3.64 m, T s 13.8 s, 292 during the PDOcool phase, and H s 4.82 m, T s 15.1 s, 284 during the PDO warm phase, for the highest 5% of waves). Thedominant characteristics for the different operational modes of wave climate determined in this study provide realisticinputs for numerical models aimed at understanding past and future coastal change within the SCB. SimulatingWAves Nearshore (SWAN)-modeled wave transformations for the southern portion of the Oceanside littoral cell showthat nearshore wave heights during westerly wave conditions are roughly twice those of northwesterly wave conditionsfor the same deep-water wave heights and periods, indicating increasing wave energy ux at the beach during thewesterly storm-source conditions by an average of 320% (74 kW/m vs. 23 kW/m).

ADDITIONAL INDEX WORDS: Wave climate, coastal, Southern California Bight, wave energy.

INTRODUCTION

The deep-water ocean wave eld (wave height, period, anddirection) dictates the wave energy delivered to the coastalzone; hence, studies of coastal evolution require an under-standing (or characterization) of deep-water wave climate.Deep-water waves are transformed through shoaling, refrac-tion, and diffraction into nearshore waves, the conditions of which dictate the spatial distribution of wave energy along acoastline ( e.g., INMAN and M ASTERS , 1994; M UNK and T RAY -LOR , 1947). As such, variations in the deep-water ocean waveeld directly modulate the power that forces the evolution of coastal morphology (G ILBERT , 1890; I NMAN , J ENKINS , andM ASTERS , 2005; J OHNSON , 1919).

Most measurements of wave conditions cannot be directlyused to detect long-term trends in deep-water wave condi-tions because either the records are of short duration, or theinstruments are positioned over bathymetry shallower thanstorm wave base. The oldest buoy measurements in the NEPacic are from the early 1970s (National Data Buoy Center

DOI: 10.2112/07-0831.1 received 24 January 2007; accepted in revi- sion 8 May 2007.

buoy 46001, in the Gulf of Alaska, is the longest continuouslyoperational buoy—its rst measurements were recorded in1972). However, most instruments have only been operation-al for less than 20 years, making their records of insufcientlength to detect decadal, climatically driven, trends in deep-water wave conditions. Shallow-water buoy and wave-arraymeasurements record transformed wave conditions, aftershoaling, refraction, and diffraction, and therefore they donot directly characterize open-ocean wave climate. In addi-tion, most deep-water buoys began as and remain nondirec-tional measurement devices.

To resolve this paucity in data, numerical models of ocean-

atmosphere interaction have been developed to simulatewave conditions over the open ocean, given a known windeld (T OLMAN , 1999). Hindcasts from these models have beenveried through comparison to measured conditions (C AIRES

et al., 2004; G RAHAM , 2005; G RAHAM and D IAZ , 2001; W ANG

and S WAIL , 2001). These studies show that although variouswave hindcasts have a range of biases and uncertainties aris-ing from both wave-model limitations and the wind data usedto drive them, they are very useful for examining both long-term trends and particular events.



1023Southern California Wave Climate and Coastal Response

Journal of Coastal Research, Vol. 24, No. 4, 2008

The causes and character of interdecadal to interannualclimate variability over the Pacic sector have been studiedclosely over the past few decades (B JERKNES , 1969; L AU ,1985; M ANTUA et al., 1997). El Nino–Southern Oscillation(ENSO) tends to vary on a timescale of 2–7 years, and it hasparticularly strong effects on the intensity of the winter cir-culation over the North Pacic. These changes tend to result

in stronger storms taking more southerly tracks over thenortheast Pacic during strong El Nino years, which makesthe Southern California coast particularly sensitive to ENSOstate (G RAHAM , 2005; I NMAN , J ENKINS , and E LWANY , 1996;SEYMOUR , 1998; S EYMOUR et al., 1984). Wave climate, pre-cipitation, and riverine sediment ux are strongly inuencedby El Nino events (A NDREWS et al., 2004; C AYAN , R EDMOND ,and R IDDLE , 1999; G RAHAM , 2005; I NMAN and J ENKINS ,1999; P INTER and V ESTAL , 2005; S EYMOUR et al., 1984;STORLAZZI and G RIGGS , 2000), and they determine the sup-ply of sediment to beaches—a variable of fundamental im-portance in coastal evolution. The decadal to interdecadalvariability in North Pacic winter circulation also inuencesthe Southern California climate (A LLAN and K OMAR , 2006;

GRAHAM , 2005; G RAHAM and D IAZ , 2001; K NOWLES , DETTIN -GER , and C AYAN , 2006), which is quantied by the PacicDecadal Oscillation (PDO) index (M ANTUA and H ARE , 2002;M ANTUA et al., 1997).

Several teams of researchers have drawn attention to adecadal trend of increased storm intensity, wave height, andwave period affecting the U.S. Pacic coast, extending fromWashington to south-central California, during the past 25years (early 1980s to present) that may be linked to climatechange and ENSO variability (A LLAN and K OMAR , 2006;GRAHAM and D IAZ , 2001; W ANG and S WAIL , 2001). They re-port a latitudinal dependence of the magnitudes of (i) waveheight and (ii) wave runup level, which increase from Point Arguello, California, to the coast of Washington. Similar re-

sults were found by S TORLAZZI and W INGFIELD (2005) intheir analysis of data from eight deep-water buoys over theperiod 1980–2002. B ROMIRSKI , F LICK , and C AYAN (2003)showed that for the central California coast, extreme winternontidal residual levels have been increasing since 1950 andcorrelate temporally with sea-level pressure anomalies thatare thought to be related to changes in winter storm strengthand track in the northeast Pacic. In contrast, X U and N O -BLE (2007) compared wind and wave data from deep-waterand nearshore buoys within the Southern California Bight(SCB) and found a negligible temporal trend in the data.

The SCB was selected for this study because it has a longhistorical record of waves and includes highly populated ar-eas, where knowledge of wave forcing is essential to the pre-

sent and future of coasts and beaches. Wave hindcast andforecast procedures were rst developed here by S VERDRUP

and M UNK (1947) for World War II amphibious landings ( e.g.,INMAN , 2003). The application of wave energy ux to thenearshore areas of the SCB soon followed, including the rstwave climate in the form of tables of hindcast waves for sta-tions along the California coast (A RTHUR et al., 1947). As aconsequence, an unusually long historical record of wavesand associated beach response is available for the SCB asdiscussed herein.

HISTORIC SOUTHERN CALIFORNIA WAVECLIMATE

Wave climate can be dened as the set of prevailing waveconditions within a particular oceanic or coastal region overa dened time interval (I NMAN and M ASTERS , 1994). Most of the wave energy for the SCB is generated by mid-latitudewinter cyclones (storms) in the North Pacic. Other impor-tant sources of wave energy include (i) waves generated bythe prevailing northwesterly winds along the California coastduring spring and summer, and (ii) swells from winter stormsin the Southern Hemisphere midlatitudes, which are com-mon, although they generally deliver small waves. EasternPacic tropical storms occasionally produce large waves inthe offshore Southern California region, as do local wind ep-isodes (generally from the northwest or southeast), which areusually associated with passing or approaching low-pressurecenters (F LICK , 1998; H ORRER , 1950; I NMAN , J ENKINS , andE LWANY , 1996; M UNK and T RAYLOR , 1947; O’R EILLY , 1993;SEYMOUR , 1996; S EYMOUR , 1998; S EYMOUR et al., 1984;STORLAZZI , WILLIS , and G RIGGS , 2000; S TRANGE , GRAHAM ,and C AYAN , 1989).

As a convenient, though not rigorous, way to think aboutthe SCB wave climate, we describe six characteristic ‘‘wavetypes’’ assembled from various data sources (Figure 1, Table1). The concept of characteristic ‘‘wave types’’ associated withwave-generation source and intensity was introduced byMUNK and T RAYLOR (1947) and A RTHUR et al. (1947). Thesix characteristic ‘‘wave types’’ shown in Figure 1 are basedon their original concept of generation area with central val-ues and likely ranges of open-ocean wave height, period, anddirection (Table 1). Here, we have updated this schematic toinclude the more recent understanding of wave climate, par-ticularly the occurrence of decadal ENSO cycles ( e.g., MC -P HADEN , ZEBIAK , and G LANTZ , 2006), and the extensive his-

toric record of hindcast computations and measurements of various kinds.The historic record for the SCB includes ve hindcast stud-

ies of the North Pacic Ocean ranging from three years(1936–38) to the recent 50 years (1948–98) data set analyzedherein ( e.g., ARTHUR et al., 1947; G RAHAM and D IAZ , 2001;M ARINE ADVISERS , 1961; M ETEOROLOGY INTERNATIONAL

INC ., 1977; N ATIONAL M ARINE CONSULTANTS , 1960). In ad-dition, National Oceanic and Atmospheric Administration(NOAA) buoys in the eastern North Pacic have providedcontinuous wave measurements over the past 30 years ( e.g., ALLAN and K OMAR , 2006; I NMAN and J ENKINS , 2005a). Also,nearshore wave measurements range from systematic visualestimates along beaches ( e.g., SHEPARD and I NMAN , 1951) to

energy-frequency spectra from nearshore wave arrays ( e.g.,P AWKA et al., 1976) and a multistation long-term series of measurements in the SCB known as the Coastal Data Infor-mation Program (CDIP) (S EYMOUR , SESSIONS , and C ASTEL ,1985). References most applicable to the six characteristic‘‘wave types’’ are listed in the footnotes in Table 1.

Waves from the Aleutian low-pressure system are the dom-inant wave type affecting the SCB. These Aleutian low–source waves can be subdivided into those that occur morefrequently in La Nina years and those that occur more fre-



1024 Adams, Inman, and Graham


Figure 1. Orientations for six major wave types characterizing coastalwave energy delivered to the Southern California Bight (SCB): (1) Aleu-tian low, (2) Pineapple Express, (3) northwest swell, (4) tropical storm,(5) Southern Hemisphere swell, and (6) local sea breeze. See Table 1 forcharacteristic height, period, and direction.

Table 1. Characteristic waves of the Southern California Bight with val-ues of signicant wave heights, period, and wave directions at deep-waterlocation 33 N, 121.5 W (hindcast node).

H S * (m) T S * (s) * ( )

1. Aleutian low(La Nina–typewinter N. Pacic

swell)† 2 4 9 12 14 18 275 295 3202. Pineapple Express(El Nino–typewinter N. Pacicswell)‡ 2 5 11 12 15 17 240 270 280

3. Northwest swell§(from regional fairweather winds) ½ 1 2 6 8 10 270 290 320

4. Tropical storm**(June thru Octo-ber) 1 3 9 10 12 14 180 190 230

5. Southern Hemi-sphere swell†(summer) ½ 1 2 16 18 20 150 200 260

6. Local sea breeze(summer) ½ ¾ 1½ 2 5 7 Variable

* Range of data with modal values in bold .† Based on the data sets of Arthur et al. (1947), National Marine Con-sultants (1960), Meteorology International Inc. (1977), Graham and Diaz(2001), and Allan and Komar (2006).‡ Based on the data sets of Seymour (1998), Inman and Masters (1991),CDIP (1983–1998), Inman and Jenkins (1997), Graham and Diaz (2001),and Allan and Komar (2006).§ Based on the data sets of Arthur et al. (1947), Munk and Traylor (1947),Shepard and Inman (1951), and CDIP (1983–1998).** From Horrer (1950), Munk and Traylor (1947), CDIP (1983–1998),andSaunders and Lea (2005).†† Based on the data sets of Arthur et al. (1947), Munk and Traylor(1947), Horrer (1950), Arthur (1951), Marine Advisers (1961) for the years1948–50, Munk et al. (1963), Snodgrass et al. (1966), Inman and Jenkins(2005b), and Storlazzi and Wingeld (2005).

quently in El Nino years—the main difference is wave ap-proach direction. During La Nina years, the Aleutian low oc-cupies its typical location in the North Pacic (centered atapproximately at 50 N, 155 W) and generates waves thatapproach the SCB from the northwest; a scenario we willrefer to as Aleutian low–type conditions (Type 1 on Figure 1and Table 1). During El Nino years, the Aleutian low occupiesa more southern location due to the anomalous distributionof sea-surface temperatures (SSTs), and waves in the SCBexhibit more westerly approach directions. Hence, we referto these as Pineapple Express–type conditions, to indicatethat the wave source is close to the Hawaiian Islands (Type2 on Figure 1 and Table 1).

Northwest swell from regional fair weather winds gener-ated along the California coast is typically intermediate inwave height and period (Type 3 on Figure 1 and Table 1).Tropical storms that form off the coast of Mexico can generatewaves of intermediate height and period, but these are short-lived events (Type 4 on Figure 1 and Table 1) (I NMAN andJ ENKINS , 1997; I NMAN , J ENKINS , and E LWANY , 1996). Peri-ods of Southern Hemisphere swell appear along the SCBcoast during summer months and are characterized by smallwave heights of longer period than Aleutian low waves, which

can therefore result in very large breakers in areas of pro-nounced wave convergence (Type 5 on Figure 1 and Table 1).Sea-breeze waves are generated by winds blowing over localwaters within the SCB, and they are most commonly asso-ciated with onshore winds replacing the rising air from landheating, particularly during clear summer weather (Type 6on Figure 1 and Table 1). However, high pressure over thefour corners area (junction of Utah, Colorado, New Mexico,and Arizona) causes strong offshore winds known as Santa Anas, which result in high waves along the eastern side of the Channel Islands.

The effect of sheltering on frequency-directional spectrahas been studied in detail from wave-directional arrays off Torrey Pines Beach in the SCB and by comparisons with syn-

thetic aperture radar (SAR) mounted on aircraft (P AWKA ,1983; P AWKA et al., 1976, 1980; P AWKA , INMAN , and G UZA ,1983, 1984). Two examples of sheltering effects include PointConception, at the northern end of the SCB, which blockswaves that approach from directions north of 315 , and SanClemente Island, which causes a deep trough in the direc-tional spectrum at Torrey Pines Beach, with a northern peakassociated with the window between San Clemente and SanMiguel–Santa Rosa Islands, and a southern peak due to waverefraction over Cortez and Tanner Banks. In general, the





Figure 2. Time series record of Southern Oscillation Index (a) and Pa-cic Decadal Oscillation Index (b). Data are from NOAA National Weath-er Service Climate Prediction Center website (http://www.cpc.noaa.gov/ data/indices/soi) and Nathan Mantua’s University of Washington website(http://jisao.washington.edu/pdo/PDO.latest), respectively.

Figure 3. Map of Southern California Bight (SCB) showing hindcast ref-erence location (33 N, 121.5 W). Inset map of eastern Pacic Oceanshows location of Hawaii, SCB, and outline of California.

SCB coastal/island geometry can be described by three fun-damental factors: (i) the regional trend of the coastline withinthe SCB is NW-SE, (ii) Point Conception blocks northwest-erly waves, and (iii) the Channel Islands and complex ba-thymetry of the California Borderlands complicate swell pat-terns through refraction, diffraction, and sheltering. Thesefactors favor waves with westerly approaches for delivery of the bulk of coastal wave energy. We note, however, that be-cause of the aforementioned complexities of SCB bathymetry,the precise spatial distribution of wave energy along the SCBcoast is highly dependent on deep-water wave direction.

EL NIN O–SOUTHERN OSCILLATION ANDPACIFIC DECADAL OSCILLATION

The coupled ocean-atmosphere instability known as the ElNino–Southern Oscillation (ENSO) produces El Nino epi-sodes when sea-surface temperatures (SSTs) in the easternand central equatorial Pacic Ocean warm above the clima-tological mean by 1–3 C (with respect to seasonal averages).Such episodes tend to reoccur on timescales of 2–7 years. Thechanges in SSTs alter patterns of convective precipitation inthe tropical Pacic, which in turn cause changes in the wintercirculation patterns over the North Pacic, resulting in a ten-

dency for stronger storms to track further south and eastthan usual (B JERKNES , 1969; L AU , 1985).

Not surprisingly, there is a general tendency for larger

waves from westerly approaches to affect Southern Californiawaters in El Nino years—a tendency that is particularly ap-parent during strong El Nino episodes, when eastern tropicalPacic SSTs are much warmer than normal, as occurred dur-ing the winters of 1982–83 and 1997–98 (G RAHAM , 2003).During El Nino years, it is common to see a negative sea-level pressure anomaly in the North Pacic centered at ap-proximately 40 N, 160 W, which has the effect of shiftingstorm tracks to the south and east and strengthening waveactivity within the SCB. Additionally, there is a tendency forincreased precipitation in Southern California during strongEl Nino years (particularly noticeable during individualstrong El Nino events), which alters typical patterns of riv-erine sediment delivery to the littoral system (C AYAN , RED -MOND , and R IDDLE , 1999; I NMAN and J ENKINS , 1999).

In contrast to El Nino episodes, La Nina episodes are pe-riods when SSTs in the eastern tropical Pacic are well belowaverage. Such episodes tend to occur during some years be-tween El Nino episodes, and they drive an atmospheric re-sponse that is roughly opposite, yet somewhat less system-atic, to that observed during El Nino episodes (H OERLING

and T ING , 1994). During La Nina years, the storm tracktends to shift northward, and it does not extend to the eastover the subtropical latitudes of the northeast Pacic. Al-though storm intensity may be high during La Nina years,the northwesterly wave approach is blocked by the coastalsalient at Point Conception, which provides protection to theSCB coast from large wave attack.

El Nino activity can be quantied by several different in-dices, based on temperature or atmospheric pressure anom-alies in the equatorial Pacic. One widely used index is theNINO3 SST index, which is the area-averaged SST anomalyover the region from 150 W to 90 W longitude and 5 N to5 S latitude (see K APLAN et al. [1998] for a reconstruction of equatorial SSTs). In this paper, we use the Southern Oscil-lation Index (SOI), the historically longest index (W ALKER ,1928), computed as the normalized sea-level pressure differ-ence between Tahiti and Darwin, Australia (Figure 2a).





Figure 4. (a) Mean monthly (winter months, Dec–Mar) and mean an-nual signicant wave heights for the 50 y wave hindcast record. Mean of entire record is 1.67 m. (b) Monthly and annual cumulative residuals of signicant wave height.

Figure 5. (a) Mean monthly (winter months, Dec–Mar) and mean an-nual peak wave period for the 50 y wave hindcast record. Mean of entirerecord is 12.4 s. (b) Monthly and annual cumulative residuals of peakwave period.

Climatic variability observed in the North Pacic has beenreferred to as the Pacic Decadal Oscillation (PDO; Figure

2b) or Pacic Decadal Variability (M ANTUA et al., 1997). ThePDO refers to the observed low-frequency variability (on theorder of 20–50 y) in the strength of winter circulation overthe North Pacic. The characteristic patterns of changes (ortendencies) in winter North Pacic circulation associatedwith PDO are essentially the same as those associated withEl Nino–La Nina variability. Over the past century, it hasbeen clear that PDO variability mimics a smoothed expres-sion of changes in the frequency and intensity of El Nino–LaNina episodes.

PDO is a useful index of changes in the intensity of wintercirculation over the North Pacic and, thus, the tendenciesfor changes in winter cyclone tracks and strength. The orig-inal (and most frequently used) measure of PDO is the time

series of SSTs averaged over the central North Pacic (asexpressed by their rst principal component). This PDO in-dex provides a natural proxy for integrated storm activityover the North Pacic because there is a strong correlationbetween PDO and winter wave climate indices in the NorthPacic (M ANTUA et al., 1997). Positive values of the PDO in-dex (PDO warm phase) reect periods when North PacicSST anomalies are positive. When winter cyclones are strong,frequent, and relatively south of their normal track duringthe PDO warm phase in the eastern Pacic, they produce cool

SSTs over the central Pacic Ocean and produce large waveswith approach directions favorable to deliver more wave en-ergy to the SCB than usual. When winter cyclones are weak-er, less frequent, and tracking further north, SSTs are warm-er and swells delivered to the SCB tend to be smaller withmore northwesterly approach directions. In this paper, weuse the SST-based PDO index as originally dened by M AN -TUA et al. (1997) (Figure 2b).

The wind elds responsible for wave generation in theNorth Pacic have a characteristic variability that correlateswith PDO phase. During periods of PDO warm phase (whenPDO index is positive), midlatitude wind elds generally wit-ness a westerly intensication, in accordance with observedmean sea-level pressure changes (G RAHAM and D IAZ , 2001).El Nino intervals exhibit similar wind elds to those of thePDO warm phase, although the individual storm events aregenerally short-lived (several days or less).

WAVE CLIMATE HINDCAST RECORD

In what follows, we investigate the correlations betweenENSO/PDO and regional wave climate in the SCB (Figure 3),by applying simple statistical procedures to the results froma numerical hindcast of deep-water winter wave conditions.In doing so, we reprise elements of previous work (G RAHAM ,2005), add some new analyses, and provide results from a





Figure 6. (a) Mean monthly (winter months, Dec–Mar) and mean an-nual peak wave direction for the 50 y wave hindcast record. Mean of entire record is 296 . (b) Monthly and annual cumulative residuals of peak wave direction.

high-resolution regional wave model. We attempt to addresstwo principal questions: (1) What are the characteristic wave

conditions in deep water off Southern California producedduring various ENSO and PDO climatic states? (2) How dochanges in ENSO and PDO climatic states correlate to deep-water and nearshore wave climate of the SCB?

The wave data set used in this study comes from the nu-merical hindcast for the 50 year period 1948–98 described inGRAHAM and D IAZ (2001) and G RAHAM (2003). The wind forc-ing for the wave data comes from the National Centers forEnvironmental Protection–National Center for AtmosphericResearch (NCEP-NCAR) reanalysis project (K ALNAY et al.,1996; K ISTLER et al., 2001). This data set represents the lastfull cycle of decadal climate change (full PDO cycle, Figure2b). The hindcast domain is the North Pacic Ocean (20 –60N, 150–110 W) with a spatial resolution of 1 latitude 1.5

longitude. Data were produced for winter months (DJFM),with three hourly spectra recorded in 20 frequency bins (cov-ering the wave period range of 4.5 s to 26 s), and ve-degreedirectional resolution grouped in 72 bins. The summary out-puts used in this paper, calculated from wave energy in thespectral bins, are (1) signicant wave height ( H s) in deep wa-ter, (2) peak (spectrally dominant) wave period of the signif-icant wave height ( T s), and (3) peak (spectrally dominant)wave direction ( ), for the reference deep-water location 33N, 121.5 W (Figure 3), a hindcast node in the model domain.

This location was chosen for its position west (oceanward) of the Channel Islands in the SCB. This location has the ad-vantage of representing an open-ocean wave climate signalnot subject to island sheltering, shoaling, and the complexrefraction and diffraction patterns within the SCB, discussedby P AWKA (1983), P AWKA , INMAN , and G UZA (1984), andO’REILLY and G UZA (1993).

GRAHAM

(2005) made a comparison of the 50 year hindcastrecord with measurements, where available, from NOAAbuoys. Generally, good agreement was found, although therewas a slight low bias off Southern California for hindcastwave heights from the northwest associated with (i) under-estimates of northwesterly coastal winds in the NCEP-NCARreanalysis, and (ii) coarse resolution of coastal geometry.Treating the 50 year hindcast record as a time series, G RA -HAM (2005) used empirical orthogonal functions to show thatwave height and wave energy incident to the coast increasesover the 50 year period.

STATISTICAL ANALYSIS

Trend AnalysisTemporal trends in the wave height, period, and direction

time series are difcult to detect by simple inspection ( e.g.,Figure 4a). Following the work of H URST (1951), we used acumulative residual analysis to nd intervals in the time se-ries that departed signicantly from mean values. In a cu-mulative residual analysis, the mean of the time series issubtracted from each observation to obtain a time series of residuals (departures from the mean). The residuals are thencumulatively summed and plotted as a separate time series.Positive slopes on a cumulative residual time series indicateintervals where the variable of interest is consistently abovethe mean value, and negative slopes correspond to intervals

below the mean ( e.g., Figure 4b).Signicant wave heights are plotted as mean monthly val-ues and mean annual values in Figure 4a. The residuals,computed by subtracting the mean (1.67 m) from the dataset, are cumulatively summed to obtain the cumulative re-sidual plot shown in Figure 4b for mean monthly and meanannual signicant wave height. Negative slopes, which dom-inate the record prior to 1977, indicate a below-mean trendin wave heights, whereas positive slopes, which dominate therecord after 1977, indicate an above-mean trend in waveheights. Likewise, peak wave period (Figure 5) was analyzedby subtracting the mean (12.4 s) and cumulatively summingthe residuals. Figure 5b shows a below-mean trend (negativeslopes) in peak wave period prior to 1977 and an above-mean

trend (positive slopes) in peak wave period after 1977. Peakwave directions, analyzed in Figure 6, do not show the strong-ly consistent monotonic slopes exhibited by the cumulativeresidual analysis of wave heights and periods. There are,however, several intervals displaying north-of-mean trendsin peak wave directions prior to 1977, and there are twostrongly west-of-mean trend intervals after 1977, suggestinga shift from northwesterly to westerly peak wave directionsover the span of the data set. The brief reversals in slope inFigure 6b may be consistent with minor warm spells during





Table 2. Summary of histogram analyses of 50 y wave hindcast record for Southern California Bight. Means ( ) and standard deviations ( ) are reported for each wave variable.

Subset Identier (letter) and Description No. Obs. in Subset (%) Total H S (m)( )

T S (s)( )

p ( )( )

A. All waves (1947–98)(shown in Figure 7) 48,446 (100%) 1.68 0.89 12.4 2.6 296 13

B. Highest 5% of waves (1947–98)

(shown in Figure 8) 2422 (5%) 3.98 0.76 14.1 2.4 289 12C. La Ninas, all SOI 20,256 (42%) 1.54 0.77 12.3 2.5 297 13D. El Ninos, all SOI 28,190 (58%) 1.77 0.96 12.6 2.6 296 13E. La Ninas, highest 5%

(shown in Figure 9) 1013 ( 2%) 3.45 0.51 13.5 2.5 291 11F. El Ninos, highest 5%

(shown in Figure 9) 1410 ( 3%) 4.26 0.83 14.4 2.3 288 12G. Strong La Ninas, all SOI 1.0 11,340 ( 23%) 1.47 0.72 12.1 2.5 297 14H. Strong El Ninos, All SOI 1.0 16,385 ( 34%) 1.86 0.99 12.6 2.5 296 14I. Strong La Ninas, highest 5% of SOI 1.0

(shown in Figure 10) 567 (1%) 3.26 0.47 13.0 2.6 294 12J. Strong E. Ninos, highest 5% of SOI 1.0

(shown in Figure 11) 819 (2%) 4.41 0.82 14.7 2.2 286 12K. PDO cool phase (1947–77) 28,099 (58%) 1.56 0.78 12.2 2.5 298 13L. PDO warm phase (1978–98) 20,347 (42%) 1.83 1.00 12.7 2.6 295 14M. PDO cool phase (1947–77), highest 5% 1405 (3%) 3.48 0.48 13.5 2.6 293 12N. PDO warm phase (1978–98), highest 5% 1017 (2%) 4.47 0.87 14.5 2.3 286 11

O. Strong La Ninas, PDO cool phase (1947–77),highest 5% of SOI 1.0(shown in Figure 10) 443 (0.9%) 3.26 0.50 13.0 2.6 295 12

P. Strong La Ninas, PDO warm phase (1978–98),highest 5% of SOI 1.0(shown in Figure 10) 124 (0.3%) 3.25 0.36 12.9 2.5 290 11

Q. Strong El Ninos, PDO cool phase (1947–77),highest 5% of SOI 1.0(shown in Figure 11) 365 (0.8%) 3.64 0.43 13.8 2.5 292 14

R. Strong El Ninos, PDO warm phase (1978–98),highest 5% of SOI 1.0(shown in Figure 11) 455 (0.9%) 4.82 0.87 15.1 2.1 284 10

the cool decades and minor cool spells during the warm de-cades of the PDO record (Figure 2b).

Population Distributions

The ENSO periodicity (2–7 y) and decadal shift from cool-phase to warm-phase PDO conditions during the mid-1970sprompted us to examine several subsets of the 50 year hind-cast record. By ‘‘ltering’’ on the basis of SOI and PDO states,we identied systematic differences in wave climate as sum-marized in Table 2.

Histograms of the signicant wave height, peak wave pe-riod, and wave direction for all hindcast data over the 50 yearrecord are shown in Figure 7. Bin sizes of 0.1 m, 2 s, and 5are used for the three histograms of Figure 7, respectively.Mean values and standard deviations of the populations are

reported in Table 2, as subset A.Most coastal change (beach-sand redistribution and sea-

cliff retreat) is accomplished not by the accumulation of smallor average events, but rather by infrequent, often catastroph-ic, extreme events. Because wave energy ux governs mostcoastal processes and energy ux is proportional to thesquare of the wave height, we chose to analyze the charac-teristics of the highest 5% (95th percentile and above) of waves in the numerical hindcast data set. We nd that thehighest 5% of waves account for 23% of the total wave energy

in the hindcast record, thereby making it a useful statistic indetermining the characteristics of waves of geomorphic con-sequence. Histograms of signicant wave height, peak waveperiod, and peak wave direction of the highest 5% of wavesin the 50 year hindcast data set are shown in Figure 8; meanvalues and standard deviations of the populations are re-ported in Table 2, as subset B.

As expected, the population of highest 5% of waves (Table2, subset B, and Figure 8) is markedly different in its meancharacteristics as compared to the entire population of hind-cast data. Mean signicant wave height is more than doublethat of the entire population ( H s, 5% 3.98 m vs. H s ,all 1.68m), mean peak wave period is greater by 14% ( T s, 5% 14.1 svs. T s, all 12.4 s), and wave direction is more westerly by 7( 5% 289 vs. all 296 ), reecting the importance of El

Nino storm waves in the highest 5% record. As stated earlier, sources responsible for generating wavesassociated with El Nino storm events differ from those thatgenerate La Nina storm waves. We applied simple statisticalprocedures to lter the hindcast data based upon SOI values,and we report the results in Table 2 (subsets C, D). The pop-ulation distributions of wave characteristics for all negativeSOI (El Nino) data (subset D) show only slightly larger waveheights as compared to all positive SOI (La Nina) data (sub-set C), whereas wave characteristics of the highest 5% (95th





Figure 7. Histograms of (a) signicant wave height, (b) peak wave pe-riod, and (c) peak wave direction for all hindcast data over the 50 y record(subset A, Table 2).

Figure 8. Histograms of (a) signicant wave height, (b) peak wave pe-riod, and (c) peak wave direction for highest 5% of waves during the 50y hindcast record (subset B, Table 2).

percentile) of negative SOI (El Nino) data (subset F) showsubstantially higher, longer-period, and more westerly wavesas compared to the highest 5% (95th percentile) of waves dur-ing positive SOI (La Nina) climatic conditions (subset E). Thesame analysis was performed for strongly positive or negativeSOI (dened herein to be 1.0 or 1.0, respectively) con-ditions, to gain an understanding of the distribution of wavecharacteristics during periods of intense La Nina or El Ninoconditions. The analyses suggest that intense El Nino con-ditions yield storm waves that are higher and of longer periodthan storm waves generated by La Nina conditions (Table 2,subsets G, H, I, and J). In general, population distributionsfor the three wave variables analyzed tend to separate intotwo characteristic wave types based on ENSO state, as shownin the histograms in Figure 9 of the highest 5% of waves

occurring during strong La Nina and El Nino periods. An examination of the cumulative residual analyses in Fig-ures 4b, 5b, and 6b, suggests that trend changes in the threemajor variables coincide with the climatic regime changefrom cool-phase PDO to warm-phase PDO in 1977 (Figure2b). We analyzed population distributions of all observationsof signicant wave height, peak wave period, and peak wavedirection, as separated by PDO state (Table 2, subsets K andL). In general, waves that occur during the PDO warm phase(1978–98) are higher, of longer period, and come from a more

westerly direction than waves that occur during the PDO coolphase (1948–77).

After convolving the SOI and PDO associations, we presentthe population distributions for the highest 5% of waves thatoccurred during strongly La Nina conditions (SOI 1.0)during the PDO cool phase (1948–77) and PDO warm phase(1978–98) in Figure 10. The population distributions in Fig-ure 10 show that there is little difference in the wave condi-tions when comparing La Ninas occurring during PDO coolphase (1948–77) and La Ninas occurring during the subse-quent PDO warm phase (1978–98) (Table 2, subsets O andP). In other words, La Nina wave events (highest 5%) appearto be consistent in character and uncorrelated to the state of the Pacic Decadal Oscillation. However, the same is not truefor El Nino storm conditions. We perform a similar analysison the highest 5% of waves occurring during strongly El Nino

conditions (SOI 1.0) for the PDO cool phase (1948–77)and PDO warm phase (1978–98) and present the results inFigure 11. PDO warm-phase El Nino waves, are higher, havea longer period, and approach from a more westerly orien-tation than those of the PDO cool phase (Table 2, subsets Qand R). These conditions favor greater energy ux to thecoast because (i) wave energy density increases as the squareof wave height, and (ii) a more direct angle of wave approachincreases the energy ux to the coast.

The observed difference in El Nino wave character with





Figure 9. Histograms of (a) signicant wave height, (b) peak wave pe-riod, and (c) peak wave direction for highest 5% of wave heights duringstrong La Ninas (SOI 1.0) and strong El Ninos (SOI 1.0), re-spectively (subsets E and F, Table 2).

Figure 10. Fractional histograms of (a) signicant wave height, (b) peakwave period, and (c) peak wave direction for highest 5% of waves forstrong La Ninas during PDO cool-phase conditions (1948–77) and forstrong La Ninas during the PDO warm-phase conditions (1978–98) (sub-sets I, O, and P, Table 2).

respect to PDO state, brings up an intriguing question: DoesPDO serve as an index for El Nino severity? Given that thereis not, as yet, a clearly dened mechanism other than ENSO-related SST distribution to explain PDO behavior, we suspectthat the answer to this question is no. However, we wereprompted to analyze our data in light of this question. Figure12 shows the 99th, 95th, and 50th percentile monthly aver-aged wave heights plotted as a function of SOI for two sep-arate populations—PDO cool phase (1948–77, left columns)and PDO warm phase (1978–98, right columns). A compari-son of the trends of the best-t linear regressions of the SOIdata shows stronger dependence (more negative trend) of wave height during the PDO warm phase as compared to thePDO cool phase. An alternate explanation of this observation,

however, is that more individual El Nino storm events oc-curred per month during the PDO warm phase, increasingmonthly percentile values of signicant wave height.

Regardless of the reason, this statistical analysis suggeststhat the deep-water wave climate within the SCB during thelatter 20 years of the hindcast (1978–98, PDO warm phase)was characterized by larger, longer-period waves from morewesterly directions. This may be due to the related increasedfrequency of El Nino events, or an increased intensity of ElNino wave conditions, or a combination of both.

COASTAL WAVE-ENERGY FLUX

The question of actual wave energy delivered to the South-ern California coast is addressed by SWAN simulations of wave transformation from deep to shallow water using typi-cal storm wave conditions for ‘‘Aleutian low’’ (La Nina) and‘‘Pineapple Express’’ (El Nino) events, respectively, as deep-water input conditions. SWAN is a third generation spectralwave transformation model that has been developed (B OOIJ ,R IS , and H OLTHUIJSEN , 1999; R IS , H OLTHUIJSEN , andBOOIJ , 1999) and validated in numerous recent studies(BENTLEY et al., 2002; K EEN et al., 2004; R OGERS , H WANG ,and W ANG , 2003; S IGNELL et al., 2005; Z IJLEMA and VAN DER

WESTHUYSEN , 2005).Figure 13 shows calculated wave heights within the SCB

from two SWAN simulations. Figure 13a uses typical deep-water wave conditions that characterize an Aleutian low(northwesterly) source as model input ( H s 5 m, T s 15 s,

305 ), whereas Figure 13b uses typical deep-water waveconditions that characterize a Pineapple Express (westerly)source as model input ( H s 5 m, T s 15 s, 270 ). Bothsets of input conditions assume a Joint North Sea Wave At-mospheric Program frequency spectrum (H ASSELMANN et al.,1976) and 15 spread in the directional spectrum. The wave-height maps, in Figure 13, show the profound sheltering ef-





Figure 11. Fractional histograms of (a) signicant wave height, (b) peakwave period, and (c) peak wave direction for highest 5% of waves forstrong El Ninos during PDO cool-phase conditions (1948–77) and forstrong El Ninos during the PDO warm-phase conditions (1978–98) (sub-sets J, Q, and R, Table 2).

Figure 12. Analysis of monthly average signicant wave height percen-tiles (99th, 95th, and 50th) as a function of Southern Oscillation Index(SOI) for separate populations of PDO cool-phase (1948–77) and PDOwarm-phase (1978–98) intervals.

fect of Point Conception and the Channel Islands, examinedby P AWKA , INMAN , and G UZA (1984), O’R EILLY (1993), andO’REILLY and G UZA (1993), and they identify specic regionswithin the SCB that are well protected during both simula-tions. The spatial distributions of sheltering effects differmarkedly for the two simulations, illustrating the strong de-pendence of coastal wave conditions on wave direction. Themagnitudes of coastal wave heights show that more energyreaches coastal regions under conditions of Pineapple Ex-press than under Aleutian lows.

To better understand differences in coastal wave energy ata ner scale, we conducted nested SWAN simulations for thetwo sets of input conditions described previously, at higherspatial resolution, on the Torrey Pines subcell region of the

Oceanside littoral cell. Figures 14a–b show the bathymetry(from the NGDC three arc-second coastal-relief-model dataset) to a depth of 300 m for the Torrey Pines subcell and colormaps of nearshore signicant wave heights calculated bySWAN for Aleutian low and Pineapple Express conditions,respectively. It is noteworthy that a consistent spatial pat-tern of nearshore wave height persists in both simulations.Within the region of alongshore positions 63 km to 72 km,wave heights are relatively large as compared to the adjacentregions both to the north and to the south. This appears to

be a result of narrow windows that open to allow waves to

pass between different pairs of the Channel Island, depend-ing on deep-water wave direction. Figure 15a shows thealongshore variability in wave height at the 5 m bathymetriccontour for the Aleutian low and Pineapple Express condi-tions, respectively. On average, Pineapple Express nearshorewave heights are 2.9 m, whereas Aleutian low nearshorewave heights are 1.5 m. By examining the longshore patternof nearshore wave heights, it is evident that over the north-ern portion of the region shown (positions 33–60 km), Pine-apple Express nearshore wave heights are more than twicethose of Aleutian low, whereas in the southern portion of theTorrey Pines subcell region (longshore positions 65–90 km),Pineapple Express nearshore wave heights are roughly 1.5times those of Aleutian low. Figure 15b shows the alongshore

variability in nearshore wave direction. For both Aleutianlow and Pineapple Express conditions, wave directions varyin tandem alongshore, suggesting that the bulk of wave re-fraction occurs outside the nearshore zone in both simula-tions. Figure 15c shows the alongshore variability in wave-energy ux (wave power), computed from the wave heightoutput at the 5 m bathymetric contour. On average, Aleutianlow nearshore wave-energy uxes are 23 kW/m, whereasPineapple Express nearshore wave-energy uxes are 74kW/m. The mean difference in wave-energy ux between





Figure 13. SWAN model–derived maps of wave heights within the SCBduring (a) Aleutian low wave-source conditions and (b) Pineapple Expresswave conditions. Models are initialized with deep-water wave conditionsfor typical Aleutian low storm source ( H s 5 m, T s 15 s, 305 )and for typical Pineapple Express storm ( H s 5 m, T s 15 s, 270 ),respectively.

Figure 14. Nested SWAN model results for nearshore waves within Tor-rey Pines subcell region of Oceanside Littoral Cell, Southern California.(a) Color map of nearshore wave heights for Aleutian low conditions. (b)Color map of nearshore wave heights for Pineapple Express conditions.Both panels (a) and (b) show bathymetric contours to 300 m depth (con-tour interval 25 m). White circles mark alongshore distance (km) fromnorthern limit of Oceanside Littoral Cell at Dana Point.

Aleutian low and Pineapple Express conditions is 51 kW/mshoreline ( i.e., Pineapple Express energy ux is 320% of Aleutian low energy ux).

Coastal processes are driven by the magnitudes and direc-tions of wave-energy ux, the values of which are proportion-al to the square of the wave height. El Nino storm wavesduring PDO warm-phase intervals deliver the most energy tothe coast. If the angle of wave approach is sufciently high,these conditions may result in rapid rates of sediment trans-port within the littoral cells. Where there is a prolonged neg-ative divergence of littoral drift (I NMAN and D OLAN , 1989),

we expect to see a systematic decrease in beach sedimentwith time, resulting in exposure of the coastal bedrock (plat-forms and sea cliffs) to wave attack. When this occurs, thenatural protection of the beach is gone, and the only defenseavailable to sea cliffs is their inherent lithologic strength,which depends on rock type. Much of the developed, heavilypopulated, cliffed coast of California is composed of weaklyconsolidated sedimentary rock, underscoring the potentiallycatastrophic consequences of prolonged exposure to westerlystorm waves.

CONCLUSIONS

Recent modeling studies investigating large-scale coastalresponse to nearshore wave conditions show promise of im-proving our understanding of coastal geomorphic evolution(ASHTON , MURRAY , and A RNAULT , 2001; V ALVO , MURRAY ,and A SHTON , 2006). The quantitative understanding of thecharacteristic wave conditions developed here may be partic-ularly useful in investigating Holocene evolution of the SCB.Paleoclimate records, such as the one inferred to documentood-dominated sedimentation in Laguna Pallcacocha in Ec-uador, may contain signals of El Nino–dominated periods,during which similar wave conditions may have been likely(MOY et al., 2002; R ODBELL et al., 1999). An assemblage of radiocarbon dates of Pismo clam shells, compiled by M AS -TERS (2006), indicates that sandy beaches of Southern Cali-fornia were sensitive to ENSO climate during the Holocene.Combining wave transformation modeling (Figures 13–15)with recent sea-level history and climate proxy records mayprovide insight into the locations of past coastal erosion rateswithin the SCB. Likewise, the combination of wave modeling,our current understanding of ENSO/PDO climatic cyclicity,and projections of future sea-level rise is expected to providevaluable estimates on the location and magnitude of futurecoastal erosion.





Figure 15. (a) Longshore variation in wave height along 5 m bathymet-ric contour. (b) Longshore variation in wave direction along 5 m bathy-metric contour. (c) Longshore variation in wave-energy ux along 5 mbathymetric contour. Gray asterisks represent output from Aleutian lowconditions. Black circles represent output from Pineapple Express con-ditions.

In this paper, we performed a series of simple statisticalanalyses on a 50 year numerical hindcast record of deep-wa-ter wave heights in the Southern California coastal ocean.Our results suggest that characteristics of El Nino stormwaves, the most geomorphically signicant wave type to theSouthern California coast, have increased, and El Nino stormwaves during the PDO warm phase are higher, have a longerperiod, and approach from a more westerly direction than ElNino storm waves that occur during the PDO cool phase.Characteristics of the highest 5% of La Nina storm wavesappear to maintain consistent conditions irrespective of PDOclimatic state. The characteristic wave conditions derivedfrom the statistical analysis presented in this paper shouldprovide valuable input conditions needed by numerical mod-els investigating past and future geomorphic evolution of theSouthern California coast.

ACKNOWLEDGMENTS

We gratefully acknowledge the Ofce of Naval Research,the California Energy Commission, and the Kavli Institutefor research support. Pat Masters provided valuable editorial

comments. We thank Kraig Winters for his assistance withnumerical modeling procedures, and the Woods Hole Ocean-ographic Institution/United States Geologic Survey Joint Re-search groups for SWAN instruction. This manuscript bene-ted from the comments of two anonymous reviewers.

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