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REVISED

Southern California Deep-Water Wave Climate: Characterization and Application to Coastal Processes

Revised for

Journal of Coastal Research

April 18, 2007

Peter N. Adams1 Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093-0209, [email protected]

Douglas L. Inman Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093-0209, [email protected]

Nicholas E. Graham Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093 Hydrologic Research Center, San Diego, CA 92130, [email protected]

1 Now at Department of Geological Sciences, 241 Williamson Hall, University of Florida, Gainesville, FL 32611, [email protected]

LRH: Adams, et al. RRH: Southern California Wave Climate and Coastal Response ABSTRACT

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 (1948-1998) for waves generated in the North Pacific winter. Deep-water wave height, period, and direction are examined with respect to the Southern Oscillation Index (SOI) and the Pacific Decadal

Oscillation (PDO). Storms occurring during strong La Niña intervals, when the SOI is greater than 1.0, concurrent with either cool- or warm-phase of the PDO are indistinguishable in wave character. In marked contrast, wave conditions arising from storms during strong El Niño intervals, when the SOI is less than -1.0, concurrent with the PDO cool-phase (1948-1977) differ greatly from wave conditions of storms during strong El Niño intervals concurrent with the PDO warm-phase (1978-1998). Our statistical analyses characterize the deep-water winter wave

climate as consistent during La Niña intervals (mean values Hs = 3.3 m, Ts = 13.0 s, a= 293˚, for the highest 5% of waves), but variable during El Niño intervals depending on PDO phase (Hs =

3.64 m, Ts = 13.8 s, a= 292˚ during the PDO cool-phase, and Hs = 4.82 m, Ts = 15.1 s, a= 284˚ during the PDO warm-phase, for the highest 5% of waves). The dominant characteristics for the different operational modes of wave climate determined in this study provide realistic inputs for numerical models aimed at understanding paleo and future coastal change within the SCB.

SWAN-modeled wave transformations for the southern portion of the Oceanside Littoral Cell show nearshore wave heights during westerly wave conditions are roughly twice those of northwesterly wave conditions for the same deep-water wave heights and periods, thereby increasing wave energy flux at the beach, during the westerly storm-source conditions, by an average of 320% (74 kW/m vs. 23 kW/m).

- 2 - INTRODUCTION

The deep-water ocean wave field (wave height, period, and direction) dictates the wave energy delivered to the coastal zone, hence, studies of coastal evolution require an understanding

(or characterization) of deep-water wave climate. Deep-water waves are transformed through shoaling, refraction, and diffraction into nearshore waves, whose conditions dictate the spatial distribution of wave energy along a coastline (e.g. MUNK and TRAYLOR, 1947; INMAN and

MASTERS, 1994). As such, variations in the deep-water ocean wave field directly modulate the power that forces the evolution of coastal morphology (GILBERT, 1890; JOHNSON, 1919; INMAN et al., 2005).

Most measurements of wave conditions cannot be directly used to detect long-term trends in deep-water wave conditions because either the records are of short duration, or the instruments are positioned over bathymetry shallower than storm wave base. The oldest buoy measurements in the NE Pacific are from the early 1970's (NDBC buoy #46001, in the Gulf of Alaska is the longest continuously operational buoy with its first measurements in 1972). However, most instruments have only been operational for less than 20 years, making their records of insufficient length to detect decadal, climatically driven, trends in deep-water wave conditions.

Shallow water buoy and wave array measurements record transformed wave conditions, after shoaling, refraction, and diffraction, and therefore do not directly characterize open ocean wave climate. In addition, most deep-water buoys began as and remain non-directional measurement devices.

- 3 - To resolve this paucity in data, numerical models of ocean-atmosphere interaction have been developed to simulate wave conditions over the open ocean, given a known wind field

(TOLMAN, 1999). Hindcasts from these models, have been verified through comparison to measured conditions (GRAHAM and DIAZ, 2001; WANG and SWAIL, 2001; CAIRES et al., 2004;

GRAHAM, 2005). These studies show that although various wave hindcasts have a range of biases and uncertainties arising from both wave model limitiations and the wind data used to drive them, they are very useful for examining both long-term trends and particular events.

The causes and character of inter-decadal to interannual climate variability over the

Pacific sector has been studied closely over the past few decades (BJERKNES, 1969; LAU, 1985;

MANTUA et al., 1997). El Niño-Southern Oscillation (ENSO) tends to vary on a timescale of 2 –

7 years, and has particularly strong effects on the intensity of the winter circulation over the

North Pacific. These changes tend to result in stronger storms taking more southerly tracks over the Northeast Pacific during strong El Niño years making the Southern California coast particularly sensitive to ENSO state (SEYMOUR et al., 1984; INMAN et al., 1996; SEYMOUR, 1998;

GRAHAM, 2005). Wave climate, precipitation, and riverine sediment flux are strongly influenced by El Niño events (SEYMOUR et al., 1984; CAYAN et al., 1999; INMAN and JENKINS, 1999;

STORLAZZI and GRIGGS, 2000; ANDREWS et al., 2004; GRAHAM, 2005; PINTER and VESTAL, 2005), and determine the supply of sediment to beaches – a variable of fundamental importance in coastal evolution. The decadal to interdecadal variability in North Pacific winter circulation also influences the Southern California climate (GRAHAM and DIAZ, 2001; GRAHAM, 2005; ALLAN and

KOMAR, 2006; KNOWLES et al., 2006), which is quantified by the Pacific Decadal Oscillation

(PDO) index (MANTUA et al., 1997; MANTUA and HARE, 2002).

- 4 - Several teams of researchers have drawn attention to a decadal trend of increased storm intensity, wave height, and wave period affecting the U.S. Pacific coast, extending from

Washington to south-central California, during the past ~25 years (early 1980's to present), that may be linked to climate change and ENSO variability (GRAHAM and DIAZ, 2001; WANG and

SWAIL, 2001; ALLAN and KOMAR, 2006). They report a latitudinal dependence of the magnitudes of (i) wave height and (ii) wave runup level that increase from Pt. Arguello, California to the coast of Washington. Similar results were found by STORLAZZI and WINGFIELD (2005) in their analysis of data from eight deep-water buoys during 1980-2002. BROMIRSKI et al. (2003) showed that for the central California coast, extreme winter non-tidal residual levels have been increasing since 1950, and correlate temporally to sea level pressure anomalies that are thought to be related to changes in winter storm strength and track in the northeast Pacific. In contrast, XU and NOBLE

(2007) compared wind and wave data from deep-water and nearshore buoys within the Southern

California Bight (SCB), and found negligible temporal trend in the data.

The SCB was selected for this study because it has a long historical record of waves and includes highly populated areas where knowledge of wave forcing is essential to the present and future of coasts and beaches. Wave hindcast and forecast procedures were first developed here by SVERDRUP and MUNK (1947) for World War II amphibious landings (e. g. INMAN, 2003). The application of wave energy flux to the nearshore areas of the SCB soon followed, including the first wave climate in the form of tables of hindcast waves for stations along the California coast

(ARTHUR et al., 1947). As a consequence, an unusually long historical record of waves and associated beach response is available for the SCB as discussed below.

- 5 - HISTORIC SOUTHERN CALIFORNIA WAVE CLIMATE

Wave climate can be defined as the set of prevailing wave conditions within a particular oceanic or coastal region over a defined time interval (INMAN and MASTERS, 1994). Most of the wave energy for the SCB is generated by mid-latitude winter cyclones (storms) in the North

Pacific. Other important sources of wave energy include (a) waves generated by the prevailing northwesterly winds along the California coast during spring and summer, and (b) swells from winter storms in the Southern Hemisphere mid-latitudes which are common, though generally delivering small waves. Eastern Pacific tropical storms occasionally produce large waves in the offshore Southern California region as do local wind episodes (generally from the northwest or southeast) usually associated with passing or approaching low pressure centers (MUNK and

TRAYLOR, 1947; HORRER, 1950; SEYMOUR et al., 1984; STRANGE et al., 1989; O'REILLY, 1993;

INMAN et al., 1996; SEYMOUR, 1996; FLICK, 1998; SEYMOUR, 1998; STORLAZZI et al., 2000).

As a convenient, though not rigorous, way to think about the SCB wave climate, we describe six characteristic "wave types" assembled from various data sources (1 and Table 1).

The concept of characteristic "wave types" associated with wave generation source and intensity was introduced by MUNK and TRAYLOR (1947) and ARTHUR et al. (1947). The six characteristic

"wave types" shown in 1 are based on their original concept of generation area with central values and likely ranges of open ocean wave height, period, and direction (Table 1). Here we have updated this schematic to include the more recent understanding of wave climate,

- 6 - particularly the occurrence of decadal ENSO cycles (e.g. MCPHADEN et al., 2006), and the extensive historic record of hindcast computations and measurements of various kinds.

The historic record for the SCB includes five hindcast studies of the North Pacific Ocean ranging from three years (1936 – 38) to the recent 50-year (1948 – 98) data set, analyzed herein

(e.g. ARTHUR et al., 1947; NATIONAL_MARINE_CONSULTANTS, 1960; MARINE_ADVISERS, 1961;

METEOROLOGY_INTERNATIONAL_INC., 1977; GRAHAM and DIAZ, 2001). In addition, NOAA buoys in the eastern North Pacific have provided continuous wave measurements during the past 30 years (e.g. INMAN and JENKINS, 2005a; ALLAN and KOMAR, 2006). Also, nearshore wave measurements range from systematic visual estimates along beaches (e.g. SHEPARD and INMAN,

1951) to energy-frequency spectra from nearshore wave arrays (e.g. PAWKA et al., 1976) and a multi-station long-term series of measurements in the SCB known as the Coastal Data

Information Program (CDIP) (SEYMOUR et al., 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 dominant wave type affecting the

SCB. These Aleutian low–source waves can be subdivided into those occurring more frequently in La Niña years, and those occurring more frequently in El Niño years – the main difference being wave approach direction. During La Niña years, the Aleutian low occupies it's typical location in the North Pacific (centered approximately at 50˚ N, 155˚W), and generates waves that approach the SCB from the northwest; a scenario we will refer to as "Aleutian Low"-type conditions (Type 1 on 1 and Table 1). During El Niño years, the Aleutian low occupies a more southern location due to the anomalous distribution of sea surface temperatures (SSTs), and

- 7 - waves in the SCB exhibit more westerly approach directions. Hence, we refer to these as

"Pineapple Express"-type conditions, to indicate that the wave source is close to the Hawaiian

Islands (Type 2 on 1 and Table 1).

Northwest swell from regional fair weather winds generated along the California coast is typically intermediate in wave height and period (Type 3 on 1 and Table 1). Tropical storms that form off the coast of Mexico can generate waves of intermediate height and period, but are short- lived events (Type 4 on 1 and Table 1), (INMAN et al., 1996; INMAN and JENKINS, 1997). Periods of Southern Hemisphere swell appear along the SCB coast during summer months and are characterized by small wave heights of longer period than Aleutian low waves, and can therefore result in very large breakers in areas of pronounced wave convergence (Type 5 on 1 and Table

1). Sea breeze waves are generated by winds blowing over local waters within the SCB, and are most commonly associated with onshore winds replacing the rising air from land heating, particularly during clear summer weather (Type 6 on 1 and Table 1). However, high pressure over the four corners area (junction of Utah, Colorado, New Mexico, and Arizona), causes strong offshore winds known as Santa Annas which result in high waves along the eastern side of the

Channel Islands.

The effect of sheltering on frequency-directional spectra has been studied in detail from wave-directional arrays off Torrey Pines Beach in the SCB, and in comparison with synthetic aperture radar (SAR) mounted on aircraft (PAWKA et al., 1976; PAWKA et al., 1980; PAWKA,

1983; PAWKA et al., 1983, 1984). Two examples of sheltering effects include Point Conception, at the northern end of the SCB, which blocks waves that approach from directions north of 315˚,

- 8 - and San Clemente Island, which causes a deep trough in the directional spectrum at Torrey Pines

Beach, with a northern peak associated with the window between San Clemente and San Miguel-

Santa Rosa Islands, and a southern peak due to wave refraction over Cortez and Tanner Banks.

In general, the SCB coastal/island geometry can be described by three fundamental factors: (i) the regional trend of the coastline within the SCB is NW-SE, (ii) Point Conception blocks northwesterly waves, and (iii) the Channel Islands and complex bathymetry of the California

Borderlands complicate swell patterns through refraction, diffraction, and sheltering. These factors favor waves with westerly approaches to deliver the bulk of coastal wave energy. We note, however, that because of the aforementioned complexities of SCB bathymetry, the precise spatial distribution of wave energy along the SCB coast is highly dependant on deep-water wave direction.

ENSO AND PDO

The coupled ocean-atmosphere instability known as the El Niño Southern Oscillation

(ENSO) produces El Niño episodes when SSTs in the eastern and central equatorial Pacific

Ocean warm above the climatological mean by 1-3 ˚C (with respect to seasonal averages). Such episodes tend to reoccur on time scales of 2 – 7 years. The changes in sea surface temperatures

(SSTs) alter patterns of convective precipitation in the tropical Pacific, which in turn causes changes in the winter circulation patterns over the North Pacific, resulting in a tendency for stronger storms to track farther south and east than usual (BJERKNES, 1969; LAU, 1985).

Not surprisingly, there is a general tendency for larger waves from westerly approaches to affect Southern California waters in El Niño years – a tendency that is particularly apparent

- 9 - during strong El Niño episodes, when eastern tropical Pacific SSTs are much warmer than normal, as occurred during the winters of 1982-83 and 1997-98 (GRAHAM, 2003). During El

Niño years, it is common to see a negative sea level pressure anomaly in the North Pacific centered at approximately 40˚N, 160˚W, which has the effect of shifting storm tracks to the south and east, strengthening wave activity within the SCB. Additionally, there is a tendency for increased precipitation in Southern California during strong El Niño years (particularly noticeable during individual strong El Niño events), a factor which alters typical patterns of riverine sediment delivery to the littoral system (CAYAN et al., 1999; INMAN and JENKINS, 1999).

In contrast to El Niño episodes, La Niña episodes are periods when SSTs in the eastern tropical Pacific are well below average. Such episodes tend to occur during some years between

El Niño episodes, and drive an atmospheric response that is roughly opposite, yet somewhat less systematic, to that observed during El Niño episodes (HOERLING and TING, 1994). During La

Niña years, the storm track tends to shift northward, and does not extend to the east over the sub- tropical latitudes of the Northeast Pacific. Although storm intensity may be high during La Niña years, the northwesterly wave approach is blocked by the coastal salient at Point Conception, which provides protection to the SCB coast from large wave attack.

El Niño activity can be quantified by several different indicies, based on temperature or atmospheric pressure anomalies in the equatorial Pacific. One widely used index is the NINO3

SST index which is the area-averaged SST anomaly over the region from 150˚W – 90˚W longitude and 5˚N – 5˚S latitude (see KAPLAN et al. (1998) for a reconstruction of equatorial

SSTs). In this paper we use the Southern Oscillation index (SOI), the historically longest index

- 10 - (WALKER, 1928), computed as the normalized sea level pressure difference between Tahiti and

Darwin, Australia (2a).

Climatic variability observed in the North Pacific has been referred to as the Pacific

Decadal Oscillation (PDO, 2b) or Pacific Decadal Variability (MANTUA et al., 1997). The PDO refers to the observed low-frequency variability (on the order of 20-50 years) in the strength of winter circulation over the North Pacific. The characteristic pattern of changes (or tendencies) with winter North Pacific circulation associated with PDO are essentially the same as those associated with El Niño / La Niña variability. Over the past century, it is clear that PDO variability mimics a smoothed expression of changes in the frequency and intensity of El Niño /

La Niña episodes.

PDO is a useful index of changes in the intensity of the winter circulation over the North

Pacific, and thus the tendencies for changes in winter cyclone tracks and strength. The original

(and most frequently used) measure of PDO is the time series of SSTs averaged over the central

North Pacific (as expressed by their first principal component). This PDO index provides a natural proxy for integrated storm activity over the North Pacific, as there is a strong correlation between PDO and winter wave climate indices in the North Pacific (MANTUA et al., 1997).

Positive values of the PDO index (PDO warm phase) reflect periods when North Pacific sea surface temperature anomalies are positive. When winter cyclones are strong, frequent, and relatively south of their normal track during the PDO warm-phase in the Eastern Pacific, they produce cool SSTs over the central Pacific Ocean and produce large waves with approach directions favorable to deliver more wave energy to the SCB than usual. When winter cyclones

- 11 - are weaker, less frequent, and tracking further north, SSTs are warmer and swells delivered to the SCB tend to be smaller with more northwesterly approach directions. In this paper, we use the SST-based PDO index as originally defined by MANTUA et al. (1997), (2b).

The wind fields responsible for wave generation in the North Pacific have a characteristic variability that correlates with PDO phase. During periods of PDO warm-phase (when PDO index is positive), mid-latitude wind fields generally witness a westerly intensification, in accordance with observed mean sea level pressure changes (Graham and Diaz, 2001). El Niño intervals exhibit similar wind fields to those of the PDO warm phase, though the individual storm events are generally short-lived (several days or less).

WAVE CLIMATE HINDCAST RECORD

In what follows, we investigate the correlations between ENSO/PDO and regional wave climate in the SCB (3), by applying simple statistical procedures to the results from a numerical hindcast of deep-water winter wave conditions. In doing so, we reprise elements of previous work (GRAHAM, 2005), adding some new analyses and providing results from a high-resolution regional wave model. We attempt to address two principal questions: (1) What are the characteristic wave conditions in deep water off Southern California produced during various

ENSO and PDO climatic states? (2) How do changes 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 numerical hindcast for the 50-year period 1948-1998 described in GRAHAM and DIAZ (2001) and GRAHAM (2003). The wind forcing

- 12 - for the wave data comes from the NCEP-NCAR reanalysis project (KALNAY et al., 1996; KISTLER et al., 2001). This data set represents the last full cycle of decadal climate change (full PDO cycle, 2b). The hindcast domain is the North Pacific Ocean (20N - 60N, 150W - 110W) with a spatial resolution of 1˚ latitude x 1.5˚ longitude. Data were produced for winter months

(DJFM), with 3 hourly spectra recorded in 20 frequency bins (covering the wave period range of

~ 4.5 s – 26 s), and 5 degree directional resolution grouped in 72 bins. The summary outputs used in this paper, calculated from wave energy in the spectral bins, are (1) significant wave height (Hs) in deep water, (2) peak (spectrally-dominant) wave period of the significant wave

height (Ts), and (3) peak (spectrally-dominant) wave direction (a, for the reference deep-water location 33N, 121.5W (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 advantage of representing an open ocean wave climate signal, not subject to island sheltering, shoaling, and the complex refraction and diffraction patterns within the SCB, discussed by PAWKA (1983),

PAWKA et al. (1984), and O'REILLY and GUZA (1993).

GRAHAM (2005) made a comparison of the 50-year hindcast record with measurements, where available, from NOAA buoys. Generally, good agreement was found although there was a slight low bias off Southern California for hindcast wave heights from the northwest associated with (i) underestimates of northwesterly coastal winds in the NCEP-NCAR reanalysis, and (ii) coarse resolution of coastal geometry. Treating the 50-year hindcast record as a time series,

GRAHAM (2005) used empirical orthogonal functions to show that wave height and wave energy incident to the coast increase over the 50-year period.

- 13 - STATISTICAL ANALYSIS

Trend Analysis

Temporal trends in the wave height, period, and direction time series are difficult to detect by simple inspection (e.g. 4a). Following the work of HURST (1951), we use a cumulative residual analysis to find intervals in the time series that depart significantly from mean values.

In a cumulative residual analysis, the mean of the time series is subtracted from each observation to obtain a time series of residuals (departures from the mean). The residuals are then cumulatively summed and plotted as a separate time series. Positive slopes on a cumulative residual time series indicate intervals where the variable of interest is consistently above the mean value and negative slopes correspond to intervals below the mean (e.g. 4b).

Significant wave heights are plotted as mean monthly values and mean annual values in

4a. The residuals, computed by subtracting the mean (1.67 m) from the data set, are cumulatively summed to obtain the cumulative residual plot shown in 4b for mean monthly and mean annual significant wave height. Negative slopes, which dominate the record prior to 1977, indicate a below-mean trend in wave heights, whereas positive slopes, which dominate the record after 1977, indicate an above-mean trend in wave heights. Likewise, peak wave period

(5) is analyzed by subtracting the mean (12.4 s) and cumulatively summing the residuals. 5b shows a below-mean trend (negative slopes) in peak wave period prior to 1977, and an above- mean trend (positive slopes) in peak wave period after 1977. Peak wave directions, analyzed in

6, do not show the strongly consistent monotonic slopes exhibited by the cumulative residual analysis of wave heights and periods. There are, however, several intervals displaying north-of-

- 14 - mean trends in peak wave directions prior to 1977, and two strongly west-of-mean trend intervals after 1977, suggesting a shift from northwesterly to westerly peak wave directions over the span of the data set. The brief reversals in slope in 6b may be consistent with minor warm spells during the cool decades and minor cool spells during the warm decades of the PDO record

(2b).

Population Distributions

The ENSO periodicity (2 – 7 years) and decadal shift from cool-phase to warm-phase

PDO conditions during the mid-1970's prompt us to examine several subsets of the 50-year hindcast record. By "filtering" on the basis of SOI and PDO states, we identify systematic differences in wave climate as summarized in Table 2.

Histograms of the significant wave height, peak wave period, and wave direction for all hindcast data over the 50-year record are shown in 7. Bin sizes of 0.1 m, 2 s, and 5˚ are used for the 3 histograms of 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 small or average events, but rather by infrequent, often catastrophic, extreme events. Because wave energy flux governs most coastal processes and energy flux is proportional to the square of the wave height, we chose to analyze the characteristics of the highest 5% (95th percentile and above) of waves in the numerical hindcast data set. We find that the highest 5% of waves account for 23% of the total wave energy in the hindcast record, thereby

- 15 - making it a useful statistic in determining the characteristics of waves of geomorphic consequence. Histograms of significant wave height, peak wave period, and peak wave direction of the highest 5% of waves in the 50-year hindcast data set are shown in 8, with mean values and standard deviations of the populations reported in Table 2, as subset B.

As expected, the population of highest 5% of waves (Table 2, subset B and 8) is markedly different in its mean characteristics as compared to the entire population of hindcast data. Mean significant wave height is more than double that of the entire population (Hs,5% =

3.98 m vs. Hs,all = 1.68 m), mean peak wave period is greater by 14% (Ts,5% = 14.1 s vs. Ts,all =

12.4 s), and wave direction is more westerly by 7˚ (a5% = 289˚ vs. aall = 296˚), reflecting the importance of El Niño storm waves in the highest 5% record.

As stated earlier, sources responsible for generating waves associated with El Niño storm events differ from those that generate La Niña storm waves. We apply simple statistical procedures to filter the hindcast data based upon SOI values and report the results in Table 2

(subsets C, D). The population distributions of wave characteristics for all SOI negative (El

Niño) data (subset D) show only slightly larger wave heights as compared to all SOI positive (La

Niña) data (subset C), whereas wave characteristics of the highest 5% (95th percentile) of SOI negative (El Niño) data (subset F) show substantially higher, longer-period, and more westerly waves, as compared to the highest 5% (95th percentile) of waves during SOI positive (La Niña) climatic conditions (subset E). The same analysis is performed for SOI strongly positive or negative (defined herein to be >+1.0 or <-1.0, respectively) conditions, to gain an understanding of the distribution of wave characteristics during periods of intense La Niña or El Niño

- 16 - conditions. The analyses suggest that intense El Niño conditions yield storm waves that are higher and of longer period than storm waves generated by La Niña conditions (Table 2, subsets

G, H, I, and J). In general, population distributions for the three wave variables analyzed tend to separate into two characteristic wave types based on ENSO state, as shown in the histograms of the highest 5% of waves occurring during strong La Niña and El Niño periods, in 9.

Examination of the cumulative residual analyses in 4b, 5b, and 6b, suggests that trend changes in the three major variables coincide with the climatic regime change from PDO cool- phase to PDO warm-phase in 1977 (2b). We analyze population distributions of all observations of significant wave height, peak wave period, and peak wave direction, as separated by PDO state (Table 2, subsets K and L). In general, waves occurring during the PDO warm-phase

(1978-1998) are higher, of longer period, and come from a more westerly direction than waves occurring during the PDO cool-phase (1948-1977).

Convolving the SOI and PDO associations, we present the population distributions for the highest 5% of waves occurring during strongly La Niña conditions (SOI > +1.0) during the

PDO cool-phase (1948-1977) and PDO warm-phase (1978-1998) in 10. The population distributions in 10 show that there is little difference in the wave conditions when comparing La

Niñas occurring during PDO cool-phase (1948-1977) and La Niñas occurring during the subsequent PDO warm-phase (1978-1998) (Table 2, subsets O and P). In other words, La Niña wave events (highest 5%) appear to be consistent in character and uncorrelated to the state of the

Pacific Decadal Oscillation. However, the same is not true for El Niño storm conditions. We perform a similar analysis on the highest 5% of waves occurring during strongly El Niño

- 17 - conditions (SOI < -1.0) for the PDO cool-phase (1948-1977) and PDO warm-phase (1978-1998) and present the results in 11. PDO warm-phase El Niño waves, are higher, of longer period, and approach from a more westerly orientation than those of the PDO cool-phase (Table 2, subsets Q and R). These conditions favor greater energy flux to the coast because (1) wave energy density increases as the square of wave height, and (2) a more direct angle of wave approach increases the energy flux to the coast.

The observed difference in El Niño wave character with respect to PDO state, brings up an intriguing question – Does PDO serve as an index for El Niño severity? Given that there is not, as yet, a clearly defined mechanism other than ENSO related SST distribution to explain

PDO behavior, we suspect that the answer to this question is no. However, we are prompted to analyze our data in light of this question. 12 shows the 99th, 95th, and 50th percentile monthly averaged wave heights plotted as a function of SOI for two separate populations – PDO cool- phase (1948-1977, left columns), and PDO warm-phase (1978-1998, right columns).

Comparison of the trends of the best-fit linear regressions on the SOI data shows stronger dependence (more-negative trend) of wave height during PDO warm-phase as compared to PDO cool-phase. An alternate explanation of this observation, however, is that more individual El

Niño storm events occurred per month during PDO warm-phase, increasing monthly percentile values of significant wave height.

Regardless of the reason, the above statistical analysis suggests that the deep-water wave climate within the SCB during the latter 20 years of the hindcast (1978-1998, PDO warm-phase) was characterized by larger, longer-period waves from more westerly directions. This may be

- 18 - due to the related increased frequency of El Niño events, or an increased intensity of El Niño wave conditions, or a combination of both.

COASTAL WAVE ENERGY FLUX

The question of actual wave energy delivered to the Southern California coast is addressed by SWAN simulations of wave transformation from deep to shallow water using typical storm wave conditions for "Aleutian Low" (La Niña) and "Pineapple Express" (El Niño) events, respectively, as deep-water input conditions. SWAN is a third generation spectral wave transformation model that has been developed (BOOIJ et al., 1999; RIS et al., 1999) and validated in numerous recent studies (BENTLEY et al., 2002; ROGERS et al., 2003; KEEN et al., 2004;

SIGNELL et al., 2005; ZIJLEMA and VAN DER WESTHUYSEN, 2005).

13 shows calculated wave heights within the SCB from two SWAN simulations. 13a uses typical deep-water wave conditions that characterize an "Aleutian Low" (northwesterly) source

as model input (Hs = 5 m, Ts = 15 s, a = 305˚), whereas 13b uses typical deep-water wave conditions that characterize a "Pineapple Express" (westerly) source as model input (Hs = 5 m, Ts

= 15 s, a = 270˚). Both sets of input conditions assume a JONSWAP frequency spectrum

(HASSELMANN et al., 1976), and 15˚ spread in the directional spectrum. The wave height maps, in 13, show the profound sheltering effect of Point Conception and the Channel Islands, examined by PAWKA et al. (1984), O'REILLY (1993) and O'REILLY and GUZA (1993), and identify specific regions within the SCB that are well protected during both simulations. The spatial distributions of sheltering effects differ markedly for the two simulations, illustrating the strong

- 19 - dependence of coastal wave conditions on wave direction. The magnitudes of coastal wave heights show that more energy reaches coastal regions under conditions of "Pineapple Express" than under "Aleutian Lows".

To better understand differences in coastal wave energy at a finer scale, we conducted nested SWAN simulations for the two sets of input conditions described above, at higher spatial resolution, on the Torrey Pines subcell region of the Oceanside Littoral Cell. 14a,b show the bathymetry (from the NGDC 3 arc-second coastal relief model data set) to a depth of 300 m for the Torrey Pines subcell, and color maps of nearshore significant wave heights calculated by

SWAN for "Aleutian Low" and "Pineapple Express" conditions, respectively. It is noteworthy that a consistent spatial pattern of nearshore wave height persists in both "Aleutian Low" and

"Pineapple Express" simulations. Within the region of alongshore positions 63 km to 72 km, wave heights are relatively large as compared to the adjacent regions 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, depending on deep-water wave direction. 15a shows the alongshore variability in wave height at the 5-meter bathymetric contour for the "Aleutian Low" and "Pineapple Express" conditions, respectively. On average, "Pineapple Express" nearshore wave heights are 2.9 m, whereas "Aleutian Low" nearshore wave heights are 1.5 m. Examining the longshore pattern of nearshore wave heights, it is evident that over the northern portion of the region shown (positions 33 – 60 km), "Pineapple Express" nearshore wave heights are more than twice those of the "Aleutian Low", whereas in the southern portion of the Torrey Pines subcell region (longshore positions 65 – 90 km), "Pineapple Express" nearshore wave heights are roughly 1.5 times those of the "Aleutian Low". 15b shows the alongshore variability in

- 20 - nearshore wave direction. For both "Aleutian Low" and "Pineapple Express" conditions, wave directions vary in tandem alongshore, suggesting that the bulk of wave refraction occurs outside the nearshore zone in both simulations. 15c shows the alongshore variability in wave energy flux (wave power), computed from the wave height output at the 5-meter bathymetric contour.

On average, "Aleutian Low" nearshore wave energy fluxes are 23 kW/m, whereas "Pineapple

Express" nearshore wave energy fluxes are 74 kW/m. The mean difference in wave energy flux between "Aleutian Low" and "Pineapple Express" conditions is approximately 51 kW/meter shoreline (i.e. "Pineapple Express" energy flux is ~320% of "Aleutian Low" energy flux).

Coastal processes are driven by the magnitudes and directions of wave energy flux, whose value is proportional to the square of the wave height. El Niño storm waves during PDO warm-phase intervals deliver the most energy to the coast. If the angle of wave approach is sufficiently high, these conditions may result in rapid rates of sediment transport within the littoral cells. Where there is a prolonged negative divergence of littoral drift (INMAN and DOLAN,

1989), we expect to see a systematic decrease in beach sediment with time, resulting in exposure of the coastal bedrock (platforms and sea cliffs) to wave attack. When this occurs, the natural protection of the beach is gone, and the only defense available to sea cliffs is their inherent lithologic strength, which depends on rock type. Much of the developed, heavily-populated, cliffed coast of California is composed of weakly-consolidated sedimentary rock, underscoring the potentially catastrophic consequences of prolonged exposure to westerly storm waves.

- 21 - CONCLUSIONS

Recent modeling studies investigating large-scale coastal response to nearshore wave conditions show promise of improving our understanding of coastal geomorphic evolution

(ASHTON et al., 2001; VALVO et al., 2006). The quantitative understanding of the characteristic wave conditions developed here, may be particularly useful in investigating Holocene evolution of the SCB. Paleoclimate records, such as the one inferred to document flood-dominated sedimentation in Laguna Pallcacocha in Equador, may contain signals of El Niño dominated periods, during which similar wave conditions may have been likely (RODBELL et al., 1999; MOY et al., 2002). An assemblage of radiocarbon dates of Pismo clam shells, compiled by MASTERS

(2006), indicates that sandy beaches of southern California were sensitive to ENSO climate during the Holocene. Combining wave transformation modeling (13-15) with recent sea level history and climate proxy records may provide insight on the locations of past coastal erosion rates within the SCB. Likewise, the combination of wave modeling, our current understanding of ENSO/PDO climatic cyclicity, and projections of future sea level rise are expected to provide valuable estimates on the location and magnitude of future coastal erosion.

In this paper, we perform a series of simple statistical analyses on a 50-year numerical hindcast record of deep-water wave heights in the Southern California coastal ocean. Our results suggest that characteristics of El Niño storm waves, the most geomorphically significant wave type to the southern California coast, have increased, with El Niño storm waves during the PDO warm-phase being higher, of longer period, and approaching from a more westerly direction than

El Niño storm waves occurring during the PDO cool-phase. Characteristics of the highest 5% of

La Niña storm waves appear to maintain consistent conditions irrespective of PDO climatic state.

- 22 - The characteristic wave conditions derived from the statistical analysis presented in this paper should provide valuable input conditions needed by numerical models investigating paleo and future geomorphic evolution of the southern California coast.

ACKNOWLEDGEMENTS

We gratefully acknowledge the Office of Naval Research, the California Energy

Commission, and the Kavli Institute for research support. Pat Masters provided valuable editorial comments. We thank Kraig Winters for his assistance with numerical modeling procedures, and the WHOI/USGS Joint Research groups for SWAN instruction. This manuscript benefited from the comments of two anonymous reviewers.

- 23 - TABLES

Table 1. Characteristic waves of the Southern California Bight with values of significant wave heights, period, and wave directions at deep-water location 33˚N, 121.5˚W (hindcast node).

a a a Hs Ts a (meters) (seconds) (degrees) 1. "Aleutian Low" 2 < 4 < 9 12 < 14 < 18 275 < 295 < 320 (La Niña – type winter N. Pacific swell) b

2. "Pineapple Express" 2 < 5 < 11 12 < 15 < 17 240 < 270 < 280 (El Niño – type winter N. Pacific swell) c

3. Northwest Swell d ½ < 1 < 2 6 < 8 < 10 270 < 290 < 320 (from regional fair weather winds)

4. Tropical storm e 1 < 3 < 9 10 < 12 < 14 150 < 200 < 260 (June thru October) 5. Southern Hemisphere Swell f ½ < 1 < 2 16 < 18 < 20 180 < 190 < 230 (summer)

6. Local Sea breeze ½ < ¾ < 1 ½ 2 < 5 < 7 Variable (summer)

a Range of data with modal values in bold.

b Based on the data sets of ARTHUR et al. (1947), NATIONAL MARINE CONSULTANTS (1960), METEOROLOGY INTERNATIONAL INC. (1977), GRAHAM and DIAZ (2001), and ALLAN and KOMAR (2006).

c 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).

d Based on the data sets of ARTHUR et al. (1947), MUNK and TRAYLOR (1947), SHEPARD and INMAN (1951), and CDIP (1983-1998).

e From HORRER (1950), MUNK and TRAYLOR (1947), CDIP (1983-1998), and (SAUNDERS and LEA (2005).

f Based on the data sets of ARTHUR et al. (1947), MUNK and TRAYLOR (1947), HORRER (1950), ARTHUR (1951), MARINE ADVISERS (1961) for the years 1948-1950, MUNK et al. (1963), SNODGRASS et al. (1966), INMAN and JENKINS (2005b), and STORLAZZI and WINGFIELD (2005).

- 24 - Table 2. Summary of histogram analyses of 50-year wave hindcast record for Southern California Bight. Means (m) and standard deviations () reported for each wave variable.

Subset Identifier (Letter) and Description No. Obs. Hs (m) Ts (s) ap (˚) in subset m +/- s m +/- s m +/- s (% total) A. All Waves (1947-1998) 48,446 1.68 +/- 0.89 12.4 +/- 2.6 296 +/- 13 (shown in Figure 7) (100%) B. Highest 5% of Waves (1947-1998) 2,422 3.98+/- 0.76 14.1 +/- 2.4 289 +/- 12 (shown in Figure 8) (5%) C. La Niñas, All SOI + 20,256 1.54 +/- 0.77 12.3 +/- 2.5 297 +/- 13 (42%) D. El Niños, All SOI - 28,190 1.77 +/- 0.96 12.6 +/- 2.6 296 +/- 13 (58%) E. La Niñas, Highest 5% 1,013 3.45 +/- 0.51 13.5 +/- 2.5 291 +/- 11 (shown in Figure 9) (~2%) F. El Niños, Highest 5% 1,410 4.26 +/- 0.83 14.4 +/- 2.3 288 +/- 12 (shown in Figure 9) (~3%) G. Strong La Niñas, All SOI > +1.0 11,340 1.47 +/- 0.72 12.1 +/- 2.5 297 +/- 14 (~23%) H. Strong El Niños, All SOI < -1.0 16,385 1.86 +/- 0.99 12.6 +/- 2.5 296 +/- 14 (~34%) I. Strong La Niñas, Highest 5% of SOI > +1.0 567 3.26 +/- 0.47 13.0 +/- 2.6 294 +/- 12 (shown in Figure 10) (1%) J. Strong El Niños, Highest 5% of SOI < -1.0 819 4.41 +/- 0.82 14.7 +/- 2.2 286 +/- 12 (shown in Figure 11) (2%) K. PDO cool-phase (1947-1977) 28,099 1.56 +/- 0.78 12.2 +/- 2.5 298 +/- 13 (58%) L. PDO warm-phase (1978-1998) 20,347 1.83 +/- 1.00 12.7 +/- 2.6 295 +/- 14 (42%) M. PDO cool-phase (1947-1977), Highest 5% 1,405 3.48 +/- 0.48 13.5 +/- 2.6 293 +/- 12 (3%) N. PDO warm-phase (1978-1998), Highest 5% 1,017 4.47 +/- 0.87 14.5 +/- 2.3 286 +/- 11 (2%) O. Strong La Niñas, PDO cool-phase (1947- 443 3.26 +/- 0.50 13.0 +/- 2.6 295 +/- 12 1977), Highest 5% of SOI > +1.0 (0.9%) (shown in Figure 10) P. Strong La Niñas, PDO warm-phase (1978- 124 3.25 +/- 0.36 12.9 +/- 2.5 290 +/- 11 1998), Highest 5% of SOI > +1.0 (0.3%) (shown in Figure 10) Q. Strong El Niños, PDO cool-phase (1947- 365 3.64 +/- 0.43 13.8 +/- 2.5 292 +/- 14 1977), Highest 5% of SOI < -1.0 (0.8%) (shown in Figure 11) R. Strong El Niños, PDO warm-phase (1978- 455 4.82 +/- 0.87 15.1 +/- 2.1 284 +/- 10 1998), Highest 5% of SOI < -1.0 (0.9%) (shown in Figure 11)

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FIGURE CAPTIONS

Figure 1. Orientations for six major wave types characterizing coastal wave energy delivered to the Southern California Bight (SCB). (1) "Aleutian Low" (2) "Pineapple Express" (3) Northwest Swell (4) Tropical Storm (5) Southern Hemisphere Swell (6) Local Sea Breeze. See Table 1 for characteristic height, period, and direction.

Figure 2. Time series record of Southern Oscillation Index (a) and Pacific Decadal Oscillation Index (b). Data from NOAA-NWS Climate Prediction Center website

- 31 - (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 reference location (33˚N, 121.5˚W). Inset map of Eastern Pacific Ocean shows location of Hawaii, SCB, and outline of California.

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

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

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

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

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

Figure 9. Histograms of (a) significant wave height, (b) peak wave period, and (c) peak wave direction for highest 5% of wave heights during strong La Niñas (SOI > +1.0) and strong El Niños (SOI < -1.0), respectively (subsets E and F, Table 2).

Figure 10. Fractional histograms of (a) significant wave height, (b) peak wave period, and (c) peak wave direction for highest 5% of waves for strong La Niñas during the PDO cool-phase (1948-1977), and for strong La Niñas during the PDO warm-phase conditions (1978-1998) (subsets I, O, and P, Table 2).

Figure 11. Fractional histograms of (a) significant wave height, (b) peak wave period, and (c) peak wave direction for highest 5% of waves for strong El Niños during the PDO cool-phase (1948-1977), and for strong El Niños during the PDO warm-phase conditions (1978-1998) (subsets J, Q, and R, Table 2).

Figure 12. Analysis of monthly average significant wave height percentiles (99th, 95th, and 50th) as a function of Southern Oscillation index (SOI) for separate populations of PDO cool- phase (1948-1977), and PDO warm-phase (1978-1998) intervals.

Figure 13. SWAN model-derived maps of wave heights within the SCB during (a) "Aleutian Low" wave source conditions and (b) "Pineapple Express" wave conditions. Models are

- 32 - initialized with deep-water wave conditions for typical "Aleutian Low" storm source (Hs = 5

m, Ts = 15 s, a = 305˚) and for typical "Pineapple Express" storm (Hs = 5 m, Ts = 15 s, a = 270˚), respectively.

Figure 14. Nested SWAN model results for nearshore waves within Torrey 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 (contour interval = 25 m). White circles mark alongshore distance (km) from northern limit of Oceanside littoral cell at Dana Point.

Figure 15. (a) Longshore variation in wave height along 5-meter bathymetric contour. (b) Longshore variation in wave direction along 5-meter bathymetric contour. (c) Longshore variation in wave energy flux along 5-meter bathymetric contour. Gray asterisks represent output from "Aleutian Low" conditions. Black circles represent output from "Pineapple Express" conditions.

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