effects of climate change and wave direction on...

Effects of climate change and wave direction on longshoresediment transport patterns in Southern California

Peter N. Adams & Douglas L. Inman &

Jessica L. Lovering

Received: 21 September 2011 /Accepted: 26 September 2011 /Published online: 24 November 2011# Springer Science+Business Media B.V. 2011

Abstract Changes in deep-water wave climate drive coastal morphologic changeaccording to unique shoaling transformation patterns of waves over local shelf bathymetry.The Southern California Bight has a particularly complex shelf configuration, of tectonicorigin, which poses a challenge to predictions of wave driven, morphologic coastal change.Northward shifts in cyclonic activity in the central Pacific Ocean, which may arise due toglobal climate change, will significantly alter the heights, periods, and directions of wavesapproaching the California coasts. In this paper, we present the results of a series ofnumerical experiments that explore the sensitivity of longshore sediment transport patternsto changes in deep water wave direction, for several wave height and period scenarios. Weoutline a numerical modeling procedure, which links a spectral wave transformation model(SWAN) with a calculation of gradients in potential longshore sediment transport rate(CGEM), to project magnitudes of potential coastal erosion and accretion, under proscribeddeep water wave conditions. The sediment transport model employs two significantassumptions: (1) quantity of sediment movement is calculated for the transport-limited case,as opposed to supply-limited case, and (2) nearshore wave conditions used to evaluatetransport are calculated at the 5-meter isobath, as opposed to the wave break point. Toillustrate the sensitivity of the sedimentary system to changes in deep-water wave direction,we apply this modeling procedure to two sites that represent two different coastal exposuresand bathymetric configurations. The Santa Barbara site, oriented with a roughly west-to-east trending coastline, provides an example where the behavior of the coastal erosional/accretional character is exacerbated by deep-water wave climate intensification. Wheresheltered, an increase in wave height enhances accretion, and where exposed, increases inwave height and period enhance erosion. In contrast, all simulations run for the Torrey

Climatic Change (2011) 109 (Suppl 1):S211–S228DOI 10.1007/s10584-011-0317-0

P. N. Adams (*)Department of Geological Sciences, University of Florida, Gainesville, FL 32611, USAe-mail: [email protected]

D. L. InmanScripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA

J. L. LoveringDepartment of Geological Sciences, University of Florida, Gainesville, FL 32611, USA

Pines site, oriented with a north-to-south trending coastline, resulted in erosion, themagnitude of which was strongly influenced by wave height and less so by wave period. Atboth sites, the absolute value of coastal accretion or erosion strongly increases with a shiftfrom northwesterly to westerly waves. These results provide some examples of the potentialoutcomes, which may result from increases in cyclonic activity, El Niño frequency, or otherchanges in ocean storminess that may accompany global climate change.

1 Introduction

In California, 80% of the state’s residents live within 30 miles of the coast (Griggs et al.2005). To mitigate the effects of climate change on coastal communities, it is necessary toassess the oceanographic and geomorphic changes expected within the coastal zone.Effective planning for the future of the California coast will need to draw on climate modelsthat predict the forcing scenarios and coastal change models that predict the coast’sresponse.

Coastal landforms exhibit dynamic equilibrium by adjusting their morphology inresponse to changes in sea level, sediment supply, and ocean wave climate. Global climatechange exerts varying degrees of influence on each of these factors. Proxy records indicatethat wave climate has influenced coastal sedimentary accretion throughout the Holocene(Masters 2006) and, although the causative links between climate change and severe stormsare not reconciled in the scientific literature (Emanuel 2005; Emanuel et al. 2008), it is well-accepted that changes in ocean wave climate (i.e. locations, frequency, and severity of openocean storms) will bring about changes in the locations and magnitudes of coastal erosionand accretion in the future (Slott et al. 2006). Numerous studies indicate that changes inocean wave climate are detectable (Gulev and Hasse 1999; Aumann et al. 2008; Komar andAllan 2008; Wang et al. 2009), but translating these open ocean changes to nearshoreerosional driving forces is complex, and requires an understanding of the interactionsbetween wave fields and the bathymetry of the continental shelf. Along the southernCalifornia coast, from Pt. Conception to the U.S./Mexico border, the situation is furthercomplicated by the intricate shelf bathymetry and the presence of the Channel Islands,which prominently interfere with incoming wave field (Shepard and Emery 1941).

In this paper we investigate potential effects of changes in ocean wave climate (waveheight, period, and direction) on the magnitudes of coastal erosion and accretion at two,physiographically different sites within the Southern California Bight (SCB). We considerthe physical setting of this location, describe our mathematical modeling approach, andpresent the results of a series of numerical experiments that explore a range of waveclimates. Lastly, we discuss the implications of the modeled coastal behavior in light ofsome possible scenarios of global climate change.

2 Geomorphic and oceanographic setting

For the purposes of this study, we consider the SCB to extend from a northwesternboundary at Point Arguello (34.58° N, 120.65° W, Fig. 1) to the U.S.-Mexico border(32.54° N, 117.12° W, Fig. 1) south of San Diego. Tectonic processes along this activemargin, between the Pacific and North American plates, are responsible for shaping theshallow ocean basins, continental shelf, and large-scale terrestrial landmasses (Christiansenand Yeats 1992). The edges of the plates on either side of the boundary have been folded

S212 Climatic Change (2011) 109 (Suppl 1):S211–S228

and fractured by transpressional plate motions, creating the high relief terrestrial landscape,pocket beaches backed by resistant bedrock sea cliffs, narrow continental shelf, deeply incisedsubmarine canyons, and irregularly shaped submarine basins that are characteristic of acollisional coasts, as classified by (Inman and Nordstrom 1971). In particular, the coastalmountain ranges and local shelf basins have been constructed by crustal displacement along anetwork of subparallel strike-slip faults, which characterize the plate interface (Hogarth et al.2007). In general, these motions have resulted in the highly irregular, complex bathymetrythat makes up the California Borderlands (Legg 1991), that feature the Channel Islands, aswell as numerous submerged seamounts and troughs (Fig. 1).

The wave climate of Southern California has been extensively studied since thepioneering investigations that applied the theoretical relationships of wave transformation topredict breakers and surf along the beaches of La Jolla, California (Munk and Traylor 1947;Sverdrup and Munk 1947). Buoys maintained by the National Oceanic and AtmosphericAdministration (NOAA) have greatly assisted understanding of deep-water wave conditionswithin the SCB (O’Reilly et al. 1996). Monitoring efforts continued to be improved throughthe development of the Coastal Data Information Page (CDIP) program, Scripps Institutionof Oceanography, which provides modeled forecasts at a number of locations. Within theSCB, the presence of the Channel Islands (Fig. 1) significantly alters the deep-water (openocean) wave climate to a more complicated nearshore wave field along the Southern Californiacoast. The islands intercept waves approaching from almost any direction and the shallowwaterbathymetry adjacent to the islands refracts and reorients wave rays to produce a complicatedwave energy distribution along the coast of the Southern California mainland. Several studieshave targeted the sheltering effect of the Channel Islands within the SCB and the complexity ofmodeling wave transformation through such a complicated bathymetry (Pawka et al. 1984;O’Reilly and Guza 1993; Rogers et al. 2007). It has also been documented that wave

Fig. 1 Hillshade view of a 30-arc second digital elevation model of Southern California Bight with modernshoreline shown as a white line. Note complex appearance of high relief terrestrial landscape and irregularsubmarine basin bathymetry. Digital elevation data obtained from the NOAA National Geophysical DataCenter Coastal Relief Model (http://www.ngdc.noaa.gov/mgg/coastal/startcrm.htm). The mean sea levelshoreline and 5-m isobath were interpolated from this data set as well

Climatic Change (2011) 109 (Suppl 1):S211–S228 S213

http://www.ngdc.noaa.gov/mgg/coastal/startcrm.htm

reflection off sheer cliff faces in the Channel Islands can be a very important process in thealteration of wave energy along the mainland coast (O’Reilly et al. 1999). The resultingdistribution of wave energy at the coast consists of dramatic longshore variability in waveenergy flux and radiation stress. These factors are considered to be fundamental in generatingthe nearshore currents responsible for longshore sediment transport and the maintenance ofsandy beaches. Some studies highlight evidence for changing storminess and wave climate inthe northeast Pacific Ocean (Bromirski et al. 2003, 2005). Recently, (Adams et al. 2008)examined a 50-year numerical hindcast of deep-water, winter wave climate in the bight, tounderstand the correlation of decadal-to-interannual climate variability with offshore wavefields. Their study found that El Niño winters during Pacific Decadal Oscillation (PDO) warmphase have significantly more energetic wave fields than those during PDO-cool phase,suggesting an interesting connection between global climate change and coastal evolution,based on patterns of storminess.

3 Model description

The numerical model employed to evaluate potential coastal change consists of twocomponents: (1) a spectral wave transformation model, known as SWAN (Booij et al.1999), that calculates shoaling and refraction of a proscribed deep water wave field over adefined bathymetric grid, and reports coastal wave conditions, and (2) an empirically-derived longshore sediment transport formulation, referred to herein as CGEM (CoastalGeomorphic Erosion Model), that utilizes the coastal wave conditions derived by the wavetransformation model to compute divergence of volumetric transport rates of nearshoresediment, also known as divergence of drift (Inman 1987; Inman and Jenkins 2003). Thisdivergence of drift is the difference between downdrift and updrift volumetric transportrates (sediment outflow minus sediment inflow), and represents the volume of sedimentaryerosion or accretion at a coastal compartment over the model time step. The interactionbetween the two components of the model is shown schematically in Fig. 2.

Two significant assumptions, and one model limitation, are invoked to simplifycalculations. First, wave transformation is calculated to the fixed 5-meter isobath, whichis usually seaward of the wave break point. Although the sediment transport model calls forwave conditions at the break point, wave breaking proceeds over a breaker zone, that canbe several tens of meters wide, depending on the slope of the beach. Through several testsof the SWAN wave model, we have determined that, under vigorous deep water wave

Fig. 2 Schematic diagram of numerical modeling procedure used in this study, showing relationshipbetween SWAN and CGEM components


conditions (i.e. Hs=4–5 m and T=14 s), wave breaking initiates over a depth of 9–10 mwith the percentage of wave breaking increasing shoreward. We consider the mean waterdepth within this breaker zone (4.5–5 m) to be a reasonable representative value to use forbreakpoint conditions in our modeling procedure. Second, the longshore sediment transportformulation assumes a transport-limited case, as opposed to a supply-limited case. Thetransport-limited assumption results in the calculation of potential divergence of drift,which would reflect the case of an inexhaustible supply of nearshore sediment. If terrestrialsediment supply to the coast is limited, from decreased riverine inputs for example, thisassumption may be challenged. Lastly, the two components of the model are not yetbackward coupled, meaning that nearshore bathymetry is not updated after a calculation ofdivergence of drift is conducted. Hence, the model should not be run over a time series ofchanging wave conditions to simulate the evolutionary behavior of a coast. In this paper, wepresent the results of instantaneous scenarios of divergence of drift for individual sets ofdeep-water wave conditions.

3.1 Wave transformation model

SWAN, short for Simulating WAves Nearshore, is a 3rd generation, finite-difference, wavemodel that operates on the principle of a wave action balance (energy density divided byrelative frequency) (Holthuijsen et al. 1993; Booij et al. 1999). In the absence of windforcing, this model requires only two general inputs to perform a computation of the wavefield throughout a region—bathymetry and deep-water wave conditions.

Ocean bathymetry exhibits a strong control on the direction and rate of wave energytranslation. When the water depth is shallower than half the wavelength, interaction of waveorbitals with the sea floor causes shoaling transformation and refraction of waves, so the spatialpattern of nearshore wave energy depends strongly on the distribution of seafloor elevation. Areview of some studies that investigated how bathymetric changes influence shoreline changeby altering shoaling and refraction patterns is provided by (Bender and Dean 2003). In thisstudy, we used two bathymetric grids for the wave transformation modeling, both obtainedfrom the National Geophysical Data Center (NOAA) U.S. coastal relief model grid database(http://www.ngdc.noaa.gov/mgg/coastal/coastal.html). A spatially-coarse grid (30 arc-sec)was used to evaluate wave conditions over the entire bight (32°–35°N, 121°–117°W),providing 480×360 cell matrices of wave heights and directions covering approximately124,000 km2, in which each value represents the conditions for a 0.72 km2 area of seasurface. Two smaller, high resolution grids (3 arc-sec), referred to herein as “nests”, were usedto evaluate local wave conditions on a finer spatial scale. The nests named SntBrb andTorPns, for portions of the Santa Barbara and Torrey Pines coasts respectively, each occupyapproximately 700 km2 within the domain of the main (coarse) grid (Fig. 3), resulting in eachcell of output representing wave conditions over a 0.0072 km2 area of sea surface.

At the western and southern margins of the coarse grid, deep-water wave conditions areproscribed as boundary conditions, consisting of significant wave height, peak period witha JONSWAP frequency distribution (Hasselmann et al. 1973), and peak direction with acosine square spread of 15°. The wave field is computed from the grid boundaries over theinput bathymetry to the coast. Example results from a SWAN run for the coarse grid areprovided in Fig. 3. From the SWAN output of the coarse grid, the boundary conditions forthe individual nests were obtained (examples provided in Figs. 4 and 5). Because the goalof the investigation was to examine “snapshots” of longshore distribution of erosion/accretion patterns resulting from various deep-water wave scenarios, all SWAN runsconducted in this study were performed in stationary mode. Temporally evolving wave


http://www.ngdc.noaa.gov/mgg/coastal/coastal.html

fields, such as those produced during a storm were not examined, thereby avoiding theproblem of swell arrival timing often associated with stationary runs (Rogers et al. 2007).

3.2 Longshore sediment transport model

The output passed from the wave transformation model to the longshore sediment transportmodel includes the complete oceanic grids of significant wave height and peak directions ateach “wet node” within the particular nest being examined. CGEM queries and interpolatesthe SWAN output at a known set of locations within the nest that constitute the 5-meterisobath, using an alongshore spacing of 100 m. These longshore sets of wave height anddirection form the basis of the sediment transport computation, which originates from asemi-empirical formulation originally proposed by Komar and Inman (1970). Thisrelationship was later modified and named the CERC formula (Rosati et al. 2002), whichhas been used in several coastal evolution modeling studies recently (Ashton et al. 2001;Ashton and Murray 2006). The CERC formula has been tested and found to provide resultsin close agreement with processed based models (Haas and Hanes 2004). In its mostgeneral form, the volumetric longshore sediment transport rate, Ql, can be expressed as

Ql ¼ Ilðrs � rwÞgNo

ð1Þ

Fig. 3 Example wave height and direction output from SWAN wave transformation model over the entirecoarse grid of the Southern California Bight. Locations of the two study sites explored in this study areshown in boxes


where Il is the immersed-weight transport rate (Inman and Bagnold 1963), ρs and ρw aredensities of quartz sediment (2,650 kg/m3) and seawater (1,024 kg/m3), respectively, g is thegravitational acceleration constant (9.81 m/s2), and No is the volume concentration of solidgrains (1—porosity), set to 0.6, for all numerical experiments in this study. The subscript l isused to represent the longshore component of any variable with which it is associated.

3.2.1 Angle of incidence

The angle of incidence is of primary importance in the calculation of longshoresediment transport. If wave rays approach the beach at an angle perfectly orthogonal tothe trend of the coast, the longshore component of wave energy flux is zero, and thereis no net longshore current to drive longshore sediment transport. If wave raysapproach the beach at an oblique angle (somewhere between orthogonal and parallel),

Fig. 4 Example wave height and direction output from SWAN wave transformation model for inputconditions of Hsig=2 m, T=12 s, and α=270°. a. Wave height map showing results over entire SouthernCalifornia Bight and location of SntBrb nest (box). b. Wave height map showing results over the nested SantaBarbara grid (SntBrb), approximately 50 km of west-east trending coast, and location of region of interest(box). c. Detailed wave height map showing wave direction vectors, bathymetric contours (10 m contourinterval shown in thin white lines), location of sites SB-1 (red star) and SB-2 (blue star). Location of 5-meterisobath shown in thick white line. Wave heights on A., B., and C. are plotted with respect to the samecolorbar whose units are meters


there is a component of wave energy flux parallel to the shoreline, which driveslongshore sediment transport.

Along the 5-meter isobath, the coastal orientation is computed by a downcoast-movingsliding window computation, which fits a trendline to 5 adjacent points and reports anazimuth value for the midpoint of the segment. The coastal orientation is subtracted fromthe queried wave direction along the isobath to provide an angle of incidence.

3.2.2 Wave energy flux

The longshore component of wave energy flux is considered to provide the fluid thrust requiredto move sediment under the influence of the breaking wave bore. The governing equation is

Pl ¼ ECn ¼ 1

8rwgH

2Cn sina cosa ð2Þ

where E is wave energy density, C is nearshore wave celerity, which is depth controlled, n isratio of group to individual wave speed (~1 in shallow water and 1/2 in deep water), H is

Fig. 5 Example wave height and direction output from SWAN wave transformation model for inputconditions of Hsig=2 m, T=12 s, and α=270°. a. Wave height map showing results over entire SouthernCalifornia Bight and location of TorPns nest (box). b. Wave height map showing results over the nestedTorrey Pines grid (TorPns), approximately 40 km of north–south trending coast, and location of region ofinterest (box). c. Detailed wave height map showing wave direction vectors, bathymetric contours (10 mcontour interval shown in thin white lines), location of sites TP-1 (red star) and TP-2 (blue star). Location of5-meter isobath shown in thick white line. Wave heights on a., b., and c. are plotted with respect to the samecolorbar whose units are meters


nearshore (breaking) wave height, α is the angle of incidence, the trigonometric componentsof which result from the tensor transformation of the onshore flux of longshore directedmomentum (Longuet-Higgins and Stewart 1964). As noted above, we estimate breaking waveheight by evaluating this quantity at the 5-meter isobath. The immersed weight transport rateis simply a scaled version of the longshore component of wave energy flux

Il ¼ KPl ð3Þwhere the scaling parameter, K, is set to 0.8 in this study. It is noted that Komar and Inman(1970) tested this relationship at different locations, where beach sediment sizes differed, butfound that the relationship held, irrespective of sedimentary texture.

3.2.3 Divergence of drift

After presenting the relationships for the longshore component of wave energy flux,immersed weight transport rate, and volumetric longshore sediment transport rate, we canshow that a simple relationship for the divergence of drift is obtained by applying the vectordifferential operator to the volumetric longshore sediment transport rate using a dot product,

r � Ql ¼ @Ql

@xð4Þ

where x is the position along the coast or, in CGEM, position along the 5-meter isobath.This quantity is, effectively, the calculated change in sediment volume over the longshore

reach dx, during the time interval that these wave conditions are applied. Herein, we adopt thesign convention that divergence is defined as the net difference between sediment inflow andsediment outflow, making positive divergence of drift (where inflow exceeds outflow) resultin accretion at a site, whereas negative divergence of drift (where outflow exceeds inflow)results in erosion. The longshore pattern of divergence of drift is therefore out of phase withlongshore sediment transport, as expected. At longshore positions where transport isincreasing at the greatest rate (positively sloping inflection points), divergence of drift is ata local minimum; where transport is decreasing at the greatest rate (negatively slopinginflection points), divergence of drift is at a local maximum; where transport is at a localminimum or maximum, divergence of drift should be zero.

4 Numerical experiments and results

To provide insight on how climate change-driven alteration of deep water wave conditionsmight affect the magnitude of erosion and accretion along the Southern California coast, weconducted a series of controlled numerical experiments at two physiographically-distinct,reaches of the Southern California coast, which we refer to as the Santa Barbara (SntBrbnest) and Torrey Pines (TorPns nest) sites. The goal of these experiments is to test thehypothesis that deep water wave direction exhibits critical control on the longshore sedimenttransport patterns at coastal sites within the bathymetrically complex SCB. Each of the locationschosen witness unique swell patterns resulting largely from their relative orientations withrespect to the deep water wave field of the North Pacific Ocean, each site’s local shelfbathymetry, and the blocking patterns that the Channel Islands provide to each site (Fig. 3). Thetwo sites represent end member coastal orientations within the Bight; the SntBrb nest exhibitsa west-to-east general shoreline orientation, whereas the TorPns nest exhibits a north-to-south


general shoreline orientation. For each experiment, we conducted 104 SWAN-CGEMsimulations that vary deep water wave direction from 260° to 320° in 5° intervals for fourpairs of wave height period scenarios: (1) H=2 m, T=12 s, (2) H=2 m, T=16 s, (3) H=4 m,T=12 s, (4) H=4 m, T=16 s. These ranges span the distributions of deep water waveconditions documented for the SCB by Adams et al. (2008).

4.1 Site 1—Santa Barbara

The western end of Goleta Beach, adjacent the UCSB campus in southeastern Santa Barbaracounty, California, has been the site of regular nourishment due to chronic sand loss and thecommunity desire to maintain a recreational beach. The site has witnessed profound changes in

Fig. 6 Example CGEM output along 5-meter isobath within the nested Santa Barbara Grid (SntBrb) for twosets of deep water wave conditions, which differ only in wave direction. Blue lines show results of deepwater conditions Hsig=4 m, T=16 s, and α=320°. Red lines show results of deep water conditions Hsig=4 m,T=16 s, and α=270°. Red and blue stars show locations of SB-1 and SB-2, used for numerical experiments.LST is an abbreviation of longshore sediment transport


beach width, morphology, and sediment volume over the past 30 years with anecdotal photohistories documenting wide, well-vegetated, sandy beaches in the 1970’s, which were fullyinundated during the El Niño winters of 1982–83 and 1997–98 (Sylvester 2010). Wavesentering the Santa Barbara channel, as swell, have been modeled by (Guza et al. 2001), andare regularly forecasted by the Coastal Data Information Program, CDIP.

4.1.1 SWAN transformed wave field

SWAN output from a moderate, westerly swell (H=2 m, T=12 s, α=270˚) is shown inFig. 4. The wave height distribution pattern for the entire SCB (Fig. 4a) illustrates theblocking effect of the Channel Islands. Figure 4b shows the decrease (by more than half) inwave height as waves enter shallow water. Figure 4c shows the significant amount ofrefraction that occurs as waves approach the nearshore and the significant shelteringexperienced by the Goleta Beach site, herein referred to as SB-2 (blue star), as compared tothe exposed site SB-1 (red star) located immediately west of Goleta Point, 1 km from SB-2.

4.1.2 CGEM results

It is instructional to observe the results of two CGEM simulations plotted along shore in thevicinity of SB-1 and SB-2. Figure 6 shows the strong influence exerted by wave direction atthe Santa Barbara site. Output from two SWAN simulations are passed to CGEM toexamine longshore patterns of potential sediment transport rate and divergence of drift. Foreach SWAN simulation, deep water wave height and period are set to 4.0 m and 16 s, butthe deep water wave direction is 320° (northwesterly) in case A, representative typical LaNiña storm wave conditions, as opposed to 270° (westerly) in case B, representative of ElNiño storm wave conditions, during which time the jet stream occupies a more southernposition than usual due to the anomalous atmospheric pressure distribution (Storlazzi andGriggs 2000). Comparison of the two deep water input cases is as follows. Along the 5-meter isobath, the significant wave height for Case A (northwesterly) is very small(<0.5 m), in comparison to deep water inputs conditions (Hsig=4 m), everywhere along the5 km reach. For Case B, the wave heights are substantially higher, approximately 2°meverywhere along the reach. The angle of incidence varies for both Case A and Case B, butin the same pattern, developing a sizable longshore component of wave energy flux. Thelongshore sediment transport rates vary in much the same manner as wave heights for thetwo cases, with appreciable transport in Case B, and negligible transport in Case A. Thepotential divergence of drift pattern for Case B shows loss of sediment (erosion) at SB-1(red star) and gain of sediment (accretion) at SB-2 (blue star). Potential divergence of driftis negligible along the length of the 5 km reach for Case A.

4.1.3 SntBrb experiment

The 104 SWAN-CGEM simulations which were run for the SntBrb experiment produceddivergence of drift patterns which are reported for SB-1 and SB-2 in Fig. 7. This compendiumof experiment results illustrates that the exposed SB-1 site experiences increasing erosion aswave conditions become more westerly. This is in contrast to the sheltered SB-2 site, whichbecomes more accretionary as wave direction becomes more westerly. Increasing deep-waterwave height causes enhancement of erosional or accretional behavior at both SB-1 and SB-2,depending on the site tendency under milder conditions. Increasing wave period causesenhanced erosion at SB-1, but causes decreased accretion at SB-2.


4.2 Site 2—Torrey pines

Torrey Pines beach, located approximately 7 km north of Scripps Pier in La Jolla,California, has been the site of many scientific inquiries in the field of coastal processes(Thornton and Guza 1983; Seymour et al. 2005; Yates et al. 2009). The relatively straight,north–south trending reach resides within the Oceanside littoral cell and owes anylongshore variation in wave energy flux to the blocking effects of the Channel Islands,rather than to complexities of nearshore bathymetry, save for the areas around the Scrippsand La Jolla submarine canyons in the southern portion of the TorPns nest.

4.2.1 SWAN transformed wave field

As for the Santa Barbara site discussed above, we show the behavior of the Torrey Pinessite to a SWAN simulation for a moderate, westerly swell (H=2 m, T=12 s, α=270°) inFig. 5. The demonstrable change in wave height visible around 33.05° north latitude inFig. 5b is a result of waves penetrating through a window between Santa Catalina and SanClemente Islands during periods of westerly swell. The general shore-normal orientation ofthe wave field (for input conditions shown) promotes nearshore wave height increase as aresult of shoaling in the absence of refraction.

4.2.2 CGEM results

Comparative examples of CGEM simulations from the TorPns nest for Cases A and B(described above in Section 4.1.2) are given in Fig. 8. Just as for the SntBrb nest, thesignificant wave height for Case A along the 5-meter isobath in the vicinity of Torrey Pines

Fig. 7 Compendium of potential divergence of drift results from 104 SWAN-CGEM model simulations forthe SntBrb nest at sites SB-1 and SB-2. Positive values of divergence of drift represent accretion and negativevalues represent erosion


sites TP-1 and TP-2 is very small (<1.0 m). However, in the TorPns nest, this may be due toblockage of waves by the Channel Islands rather than to severe refraction as in the SntBrbnest. Angles of incidence for both case A and B at TorPns are small, approximately lessthan +/−5°. For case B, between kilometer markers 23 and 25.7, angle of incidence isnegative which results in northward-directed longshore sediment transport pattern in thisregion, as opposed to the southward directed transport elsewhere in the nest. For case A,divergence of drift pattern is negligible everywhere within the 5 km span surrounding TP-1and TP-2, whereas for case B, a strongly negative potential divergence of drift (erosion)emerges at Torrey Pines Beach, near TP-1 and TP2.

Fig. 8 Example CGEM output along 5-meter isobath within the nested Torrey Pines Grid (TorPns) for twosets of deep water wave conditions, which differ only in wave direction. Blue lines show results of deepwater conditions Hsig=4 m, T=16 s, and α=320°. Red lines show results of deep water conditions Hsig=4 m,T=16 s, and α=270°. Red and blue stars show locations of TP-1 and TP-2, used for numerical experiments.LST is an abbreviation of longshore sediment transport


4.2.3 TorPns experiment

As for the SntBrb nest discussed in Section 4.1.3, the 104 SWAN-CGEM simulations,which were run for the TorPns experiment produced divergence of drift patterns which arereported for TP-1 and TP-2 in Fig. 9. All simulations run for the Torrey Pines site resultedin erosion. At TP-1, the peak in magnitude of potential divergence of drift occurs whenwaves are just north of westerly (275°–290°). Increases in wave period slightly increasederosion for 2°m waves, and shifted the peak direction for maximum erosion for 4°m waves,at TP-1. At TP-2, wave height has a profound influence; doubling of the deep water waveheight causes potential divergence of drift to approximately triple across the directionalrange. Increasing wave period, however, had negligible effect at site TP-2.

5 Summary and implications

A numerical modeling procedure for assessing the patterns of littoral sediment transport inSouthern California has been presented. The procedure combines a spectral wavetransformation model with a calculation of gradients (divergence) in longshore sedimenttransport rates, assuming transport-limited conditions. To illustrate some specific coastalimpacts resulting from climate change, we have applied this procedure to two physically-distinct sites within the SCB. We conducted a sensitivity analysis at the two study sites,whereby effects of variability in deep water wave direction were explored for four waveheight/wave period combinations.

Fig. 9 Compendium of potential divergence of drift results from 104 SWAN-CGEM model simulations forthe TorPns nest at sites TP-1 and TP-2


This study demonstrates that the longshore sediment transport patterns in the littoralzone, and therefore the locations of erosional hotspots, along the Southern California coastare extremely sensitive to deep water wave direction. We speculate that this sensitivity isdue to two principle reasons: (1) the severe refraction required by northwesterly waves inorder to be incident upon south facing coasts (e.g. SntBrb nest), which could also beconsidered a sheltering effect of Pt. Arguello, and (2) the sheltering effects of the ChannelIslands (blocking of incoming swells and additional refraction of grazing waves) on westfacing coasts (TorPns nest). Observations of wave interruption by islands were madedecades ago by Arthur (1951).

Although the cross-shore transport of sediment in the littoral zone is not specificallyaddressed in these numerical experiments, we acknowledge its potential importance duringlarge wave events. Long-period swells, often associated with large wave events, will increaserefraction, which increases the cross-shore component of wave energy flux. Associated highwave set-up can promotes off-shore transport and the temporary storage of littoral sediment inoffshore bars. Despite the fact that cross-shore transport can be strong during events, theassociated “erosion” is often temporary, as recovery proceeds relatively rapidly after a largewave event via onshore transport of bar sediment.

It is noteworthy that the Santa Barbara wave direction experiment illustrated how thedivergence of drift at a site exposed to the open ocean (SB-1) experiences enhancement oferosion as the wave field intensifies (increased wave heights and periods), whereas thedivergence of drift at a site locally sheltered by a headland (SB-2) experiences enhancementof accretion as the deep water wave heights are increased. The fact that the sheltered siteexperienced slight decreases in accretion for increased wave periods may be due to thehigher degree of refraction that the longer period swells undergo before reaching the coast.

The Torrey Pines experiment reveals interesting behavior regarding the direction oflongshore transport and erosion. As shown in Fig. 8, for a westerly wave field of strongintensity (Hs=4 m, T=16 s, a=270°), the angle of incidence between position markers 23–25.75 km is negative, but changes to positive between position markers 25.75–28 km. Theresult of this change in angle of incidence is a change in direction of longshore transportfrom northward to southward. However, divergence of drift is negative for this set of deepwater wave conditions at both TP-1, where transport direction is northward, and TP-2,where transport direction is southward. This persistence of erosional character at this site,irrespective of transport direction, suggests that continental shelf bathymetry may exert aunique control on nearshore wave fields at this site.

It is observed that at both SB-1 (SntBrb nest) and TP-2 (TorPns nest), negativedivergence of drift (erosion) appears to operate under all deep water conditions simulated.This brings up two questions: (1) Why does the coast at SB-1 protrude seaward relative tothe coast at SB-2, if the SB-1 shoreline is retreating under all simulated conditions? (2)Why does the Torrey Pines coastline maintain a relatively straight appearance if theshoreline at TP-2 is consistently retreating more rapidly than the shoreline at TP-1? Severalexplanations are offered to address these discrepancies and we suspect the answer is acombination of these. First, as mentioned above, the erosion/accretion portion of the CGEMmodel assumes transport-limited conditions, meaning that deficiencies in sediment supplyare not considered to play a role in coastal landform evolution. If sediment supply is limitedat these sites, then the model may overestimate the magnitude of divergence of drift.Second, the model only considers the movement of sediment alongshore at these coastalsites and does not address the rocky cliffs that back the beaches along much of the SouthernCalifornia coast. During high wave conditions when sediment supply is limited, it is quitelikely that beach sand is temporarily stored offshore in bars and waves directly impact the


bedrock cliffs, whose retreat is not governed by Eq. (4) above. To simulate shoreline retreatof an exposed cliffed coast, bare bedrock cutting processes must be adequately modeled.Neither of these caveats, however, changes the fact that the gradients in potential longshoresediment transport patterns are highly sensitive to deep water wave conditions, andparticularly, to wave direction.

These results have implications regarding climate change, longshore sediment transportpatterns, and the distribution of hotspots of coastal erosion within the SCB. Our numericalsimulations illustrate a dramatic increase in absolute value of divergence of drift as waveclimate approaches westerly deep water wave directions. It has been documented that during ElNiño winters, waves entering the Southern California Bight tend to be more westerly thanduring non El Niño winters (Adams et al. 2008). Therefore, model results presented herein areconsistent with the observations of severe coastal change in California during the El Niñowinters of 1982–83, and 1997–98 (Storlazzi et al. 2000). Recent research investigatingtropical cyclonic behavior during the early Pliocene (5–3 ma) reveals a feedback that mayserve to increase hurricane frequency and intensity in the central Pacific during warmerintervals (Federov et al. 2010). This is relevant to Earth’s current climate trend because theearly Pliocene is considered a possible analogue to modern greenhouse conditions. Federov etal. (2010) provide results of numerical simulations of tropical cyclone tracks in early Plioceneclimate, which illustrate a dramatic poleward shift in sustained hurricane strength within theeastern Pacific Ocean. This pattern results in increased westerly storminess, implying thatwarmer climates will cause the SCB to witness greater absolute values of divergence of drift.In other words, a more volatile coastline, exhibiting higher magnitude erosion and accretion,might be expected as a result of increased frequency of strong westerly waves.

Acknowledgements This manuscript benefitted from thoughtful comments of three anonymous reviewersas well as conversations with Shaun Kline. This research was funded by the California Energy Commission’s(CEC) Public Interest Energy Research Program. Special thanks are due to Guido Franco at the CEC, and theother guest editors of this special issue.

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