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

Abstract

Changes in deep-water wave climate drive coastal morphologic change according to unique shoaling transformation patterns of
waves over local shelf bathymetry. The Southern California Bight has a particularly complex shelf configuration, of tectonic
origin, 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 to global climate change, will significantly alter the heights, periods,
and directions of waves approaching the California coasts. In this paper, we present the results of a series of numerical
experiments that explore the sensitivity of longshore sediment transport patterns to changes in deep water wave direction,
for several wave height and period scenarios. We outline 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 proscribed deep water wave conditions. The sediment transport model employs
two significant assumptions: (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 evaluate transport are calculated at the 5-meter isobath, as
opposed to the wave break point. To illustrate 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 exposures and 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. Where sheltered, an
increase in wave height enhances accretion, and where exposed, increases in wave height and period enhance erosion. In contrast,
all simulations run for the Torrey Pines site, oriented with a north-to-south trending coastline, resulted in erosion, the
magnitude of which was strongly influenced by wave height and less so by wave period. At both sites, the absolute value of
coastal accretion or erosion strongly increases with a shift from northwesterly to westerly waves. These results provide some
examples of the potential outcomes, which may result from increases in cyclonic activity, El Niño frequency, or other changes
in ocean storminess that may accompany global climate change.

Full text

Effects of climate change and wave direction on longshore
sediment 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 change
according to unique shoaling transformation patterns of waves over local shelf bathymetry.
The Southern California Bight has a particularly complex shelf configuration, of tectonic
origin, 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 to
global climate change, will significantly alter the heights, periods, and directions of waves
approaching the California coasts. In this paper, we present the results of a series of
numerical experiments that explore the sensitivity of longshore sediment transport patterns
to changes in deep water wave direction, for several wave height and period scenarios. We
outline 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 proscribed
deep water wave conditions. The sediment transport model employs two significant
assumptions: (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 evaluate
transport are calculated at the 5-meter isobath, as opposed to the wave break point. To
illustrate 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 exposures
and 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. Where
sheltered, an increase in wave height enhances accretion, and where exposed, increases in
wave height and period enhance erosion. In contrast, all simulations run for the Torrey
Climatic Change (2011) 109 (Suppl 1):S211–S228
DOI 10.1007/s10584-011-0317-0
P. N. Adams (*)
Department of Geological Sciences, University of Florida, Gainesville, FL 32611, USA
e-mail: adamsp@ufl.edu
D. L. Inman
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
J. L. Lovering
Department of Geological Sciences, University of Florida, Gainesville, FL 32611, USA

Pines site, oriented with a north-to-south trending coastline, resulted in erosion, the
magnitude of which was strongly influenced by wave height and less so by wave period. At
both sites, the absolute value of coastal accretion or erosion strongly increases with a shift
from northwesterly to westerly waves. These results provide some examples of the potential
outcomes, which may result from increases in cyclonic activity, El Niño frequency, or other
changes 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 to
assess 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 models
that predict the forcing scenarios and coastal change models that predict the coast’s
response.
Coastal landforms exhibit dynamic equilibrium by adjusting their morphology in
response to changes in sea level, sediment supply, and ocean wave climate. Global climate
change exerts varying degrees of influence on each of these factors. Proxy records indicate
that wave climate has influenced coastal sedimentary accretion throughout the Holocene
(Masters 2006) and, although the causative links between climate change and severe storms
are 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 open
ocean storms) will bring about changes in the locations and magnitudes of coastal erosion
and accretion in the future (Slott et al. 2006). Numerous studies indicate that changes in
ocean wave climate are detectable (Gulev and Hasse 1999; Aumann et al. 2008; Komar and
Allan 2008; Wang et al. 2009), but translating these open ocean changes to nearshore
erosional driving forces is complex, and requires an understanding of the interactions
between wave fields and the bathymetry of the continental shelf. Along the southern
California coast, from Pt. Conception to the U.S./Mexico border, the situation is further
complicated 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 (wave
height, period, and direction) on the magnitudes of coastal erosion and accretion at two,
physiographically different sites within the Southern California Bight (SCB). We consider
the physical setting of this location, describe our mathematical modeling approach, and
present the results of a series of numerical experiments that explore a range of wave
climates. Lastly, we discuss the implications of the modeled coastal behavior in light of
some 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 northwestern
boundary 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 active
margin, between the Pacific and North American plates, are responsible for shaping the
shallow ocean basins, continental shelf, and large-scale terrestrial landmasses (Christiansen
and Yeats 1992). The edges of the plates on either side of the boundary have been folded
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and fractured by transpressional plate motions, creating the high relief terrestrial landscape,
pocket beaches backed by resistant bedrock sea cliffs, narrow continental shelf, deeply incised
submarine canyons, and irregularly shaped submarine basins that are characteristic of a
collisional coasts, as classified by (Inman and Nordstrom 1971). In particular, the coastal
mountain ranges and local shelf basins have been constructed by crustal displacement along a
network 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 bathymetry
that makes up the California Borderlands (Legg 1991), that feature the Channel Islands, as
well as numerous submerged seamounts and troughs (Fig. 1).
The wave climate of Southern California has been extensively studied since the
pioneering investigations that applied the theoretical relationships of wave transformation to
predict 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 Atmospheric
Administration (NOAA) have greatly assisted understanding of deep-water wave conditions
within the SCB (O’Reilly et al. 1996). Monitoring efforts continued to be improved through
the development of the Coastal Data Information Page (CDIP) program, Scripps Institution
of Oceanography, which provides modeled forecasts at a number of locations. Within the
SCB, the presence of the Channel Islands (Fig. 1) significantly alters the deep-water (open
ocean) wave climate to a more complicated nearshore wave field along the Southern California
coast. The islands intercept waves approaching from almost any direction and the shallow water
bathymetry adjacent to the islands refracts and reorients wave rays to produce a complicated
wave energy distribution along the coast of the Southern California mainland. Several studies
have targeted the sheltering effect of the Channel Islands within the SCB and the complexity of
modeling wave transformation through such a complicated bathymetry (Pawka et al. 1984;
O’Reilly and Guza 1993;Rogersetal.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 modern
shoreline shown as a white line. Note complex appearance of high relief terrestrial landscape and irregular
submarine basin bathymetry. Digital elevation data obtained from the NOAA National Geophysical Data
Center Coastal Relief Model (http://www.ngdc.noaa.gov/mgg/coastal/startcrm.htm). The mean sea level
shoreline and 5-m isobath were interpolated from this data set as well
Climatic Change (2011) 109 (Suppl 1):S211–S228 S213

reflection off sheer cliff faces in the Channel Islands can be a very important process in the
alteration of wave energy along the mainland coast (O’Reilly et al. 1999). The resulting
distribution of wave energy at the coast consists of dramatic longshore variability in wave
energy flux and radiation stress. These factors are considered to be fundamental in generating
the nearshore currents responsible for longshore sediment transport and the maintenance of
sandy beaches. Some studies highlight evidence for changing storminess and wave climate in
the 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, to
understand the correlation of decadal-to-interannual climate variability with offshore wave
fields. Their study found that El Niño winters during Pacific Decadal Oscillation (PDO) warm
phase 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 two
components: (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 a
defined bathymetric grid, and reports coastal wave conditions, and (2) an empirically-
derived longshore sediment transport formulation, referred to herein as CGEM (Coastal
Geomorphic Erosion Model), that utilizes the coastal wave conditions derived by the wave
transformation model to compute divergence of volumetric transport rates of nearshore
sediment, also known as divergence of drift (Inman 1987; Inman and Jenkins 2003). This
divergence of drift is the difference between downdrift and updrift volumetric transport
rates (sediment outflow minus sediment inflow), and represents the volume of sedimentary
erosion or accretion at a coastal compartment over the model time step. The interaction
between the two components of the model is shown schematically in Fig. 2.
Two significant assumptions, and one model limitation, are invoked to simplify
calculations. First, wave transformation is calculated to the fixed 5-meter isobath, which
is usually seaward of the wave break point. Although the sediment transport model calls for
wave conditions at the break point, wave breaking proceeds over a breaker zone, that can
be several tens of meters wide, depending on the slope of the beach. Through several tests
of 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 relationship
between SWAN and CGEM components
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conditions (i.e. H
s
=4–5 m and T=14 s), wave breaking initiates over a depth of 9–10 m
with the percentage of wave breaking increasing shoreward. We consider the mean water
depth within this breaker zone (4.5–5 m) to be a reasonable representative value to use for
breakpoint conditions in our modeling procedure. Second, the longshore sediment transport
formulation assumes a transport-limited case, as opposed to a supply-limited case. The
transport-limited assumption results in the calculation of potential divergence of drift,
which would reflect the case of an inexhaustible supply of nearshore sediment. If terrestrial
sediment supply to the coast is limited, from decreased riverine inputs for example, this
assumption may be challenged. Lastly, the two components of the model are not yet
backward coupled, meaning that nearshore bathymetry is not updated after a calculation of
divergence of drift is conducted. Hence, the model should not be run over a time series of
changing wave conditions to simulate the evolutionary behavior of a coast. In this paper, we
present the results of instantaneous scenarios of divergence of drift for individual sets of
deep-water wave conditions.
3.1 Wave transformation model
SWAN, short for Simulating WAves Nearshore, is a 3rd generation, finite-difference, wave
model that operates on the principle of a wave action balance (energy density divided by
relative frequency) (Holthuijsen et al. 1993; Booij et al. 1999). In the absence of wind
forcing, this model requires only two general inputs to perform a computation of the wave
field throughout a region—bathymetry and deep-water wave conditions.
Ocean bathymetry exhibits a strong control on the direction and rate of wave energy
translation. When the water depth is shallower than half the wavelength, interaction of wave
orbitals with the sea floor causes shoaling transformation and refraction of waves, so the spatial
pattern of nearshore wave energy depends strongly on the distribution of seafloor elevation. A
review of some studies that investigated how bathymetric changes influence shoreline change
by altering shoaling and refraction patterns is provided by (Bender and Dean 2003). In this
study, we used two bathymetric grids for the wave transformation modeling, both obtained
from 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 approximately
124,000 km
2
, in which each value represents the conditions for a 0.72 km
2
area of sea
surface. Two smaller, high resolution grids (3 arc-sec), referred to herein as “nests”,wereused
to evaluate local wave conditions on a finer spatial scale. The nests named SntBrb and
TorPns, for portions of the Santa Barbara and Torrey Pines coasts respectively, each occupy
approximately 700 km
2
within the domain of the main (coarse) grid (Fig. 3), resulting in each
cell of output representing wave conditions over a 0.0072 km
2
area of sea surface.
At the western and southern margins of the coarse grid, deep-water wave conditions are
proscribed as boundary conditions, consisting of significant wave height, peak period with
a JONSWAP frequency distribution (Hasselmann et al. 1973), and peak direction with a
cosine square spread of 15°. The wave field is computed from the grid boundaries over the
input bathymetry to the coast. Example results from a SWAN run for the coarse grid are
provided in Fig. 3. From the SWAN output of the coarse grid, the boundary conditions for
the individual nests were obtained (examples provided in Figs. 4and 5). Because the goal
of the investigation was to examine “snapshots”of longshore distribution of erosion/
accretion patterns resulting from various deep-water wave scenarios, all SWAN runs
conducted in this study were performed in stationary mode. Temporally evolving wave
Climatic Change (2011) 109 (Suppl 1):S211–S228 S215

fields, such as those produced during a storm were not examined, thereby avoiding the
problem 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 transport
model includes the complete oceanic grids of significant wave height and peak directions at
each “wet node”within the particular nest being examined. CGEM queries and interpolates
the SWAN output at a known set of locations within the nest that constitute the 5-meter
isobath, using an alongshore spacing of 100 m. These longshore sets of wave height and
direction form the basis of the sediment transport computation, which originates from a
semi-empirical formulation originally proposed by Komar and Inman (1970). This
relationship was later modified and named the CERC formula (Rosati et al. 2002), which
has 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 results
in close agreement with processed based models (Haas and Hanes 2004). In its most
general form, the volumetric longshore sediment transport rate, Q
l
, can be expressed as
Ql¼Il
ðrsrwÞgNo
ð1Þ
Fig. 3 Example wave height and direction output from SWAN wave transformation model over the entire
coarse grid of the Southern California Bight. Locations of the two study sites explored in this study are
shown in boxes
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where I
l
is the immersed-weight transport rate (Inman and Bagnold 1963), ρ
s
and ρ
w
are
densities of quartz sediment (2,650 kg/m
3
) and seawater (1,024 kg/m
3
), respectively, gis the
gravitational acceleration constant (9.81 m/s
2
), and N
o
is the volume concentration of solid
grains (1—porosity), set to 0.6, for all numerical experiments in this study. The subscript lis
used 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 longshore
sediment transport. If wave rays approach the beach at an angle perfectly orthogonal to
the trend of the coast, the longshore component of wave energy flux is zero, and there
is no net longshore current to drive longshore sediment transport. If wave rays
approach 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 input
conditions of H
sig
=2 m, T=12 s, and α=270°. a. Wave height map showing results over entire Southern
California Bight and location of SntBrb nest (box). b. Wave height map showing results over the nested Santa
Barbara 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 contour
interval shown in thin white lines), location of sites SB-1 (red star) and SB-2 (blue star). Location of 5-meter
isobath shown in thick white line. Wave heights on A., B., and C. are plotted with respect to the same
colorbar whose units are meters
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there is a component of wave energy flux parallel to the shoreline, which drives
longshore sediment transport.
Along the 5-meter isobath, the coastal orientation is computed by a downcoast-moving
sliding window computation, which fits a trendline to 5 adjacent points and reports an
azimuth value for the midpoint of the segment. The coastal orientation is subtracted from
the queried wave direction along the isobath to provide an angle of incidence.
3.2.2 Wave energy flux
The longshore componentof wave energy flux is considered to provide the fluid thrust required
to move sediment under the influence of the breaking wave bore. The governing equation is
Pl¼ECn ¼1
8rwgH2Cn sin acos að2Þ
where Eis wave energy density, Cis nearshore wave celerity, which is depth controlled, nis
ratio of group to individual wave speed (~1 in shallow water and 1/2 in deep water), His
Fig. 5 Example wave height and direction output from SWAN wave transformation model for input
conditions of H
sig
=2 m, T=12 s, and α=270°. a. Wave height map showing results over entire Southern
California Bight and location of TorPns nest (box). b. Wave height map showing results over the nested
Torrey Pines grid (TorPns), approximately 40 km of north–south trending coast, and location of region of
interest (box). c. Detailed wave height map showing wave direction vectors, bathymetric contours (10 m
contour interval shown in thin white lines), location of sites TP-1 (red star) and TP-2 (blue star). Location of
5-meter isobath shown in thick white line. Wave heights on a., b., and c. are plotted with respect to the same
colorbar whose units are meters
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nearshore (breaking) wave height, αis the angle of incidence, the trigonometric components
of which result from the tensor transformation of the onshore flux of longshore directed
momentum (Longuet-Higgins and Stewart 1964). As noted above, we estimate breaking wave
height by evaluating this quantity at the 5-meter isobath. The immersed weight transport rate
is simply a scaled version of the longshore component of wave energy flux
Il¼KPlð3Þ
where 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, but
found 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 can
show that a simple relationship for the divergence of drift is obtained by applying the vector
differential operator to the volumetric longshore sediment transport rate using a dot product,
rQl¼@Ql
@xð4Þ
where xis 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 the
sign convention that divergence is defined as the net difference between sediment inflow and
sediment outflow, making positive divergence of drift (where inflow exceeds outflow) result
in 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 with
longshore sediment transport, as expected. At longshore positions where transport is
increasing at the greatest rate (positively sloping inflection points), divergence of drift is at
a local minimum; where transport is decreasing at the greatest rate (negatively sloping
inflection points), divergence of drift is at a local maximum; where transport is at a local
minimum 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 conditions
might affect the magnitude of erosion and accretion along the Southern California coast, we
conducted a series of controlled numerical experiments at two physiographically-distinct,
reaches of the Southern California coast, which we refer to as the Santa Barbara (SntBrb
nest) and Torrey Pines (TorPns nest) sites. The goal of these experiments is to test the
hypothesis that deep water wave direction exhibits critical control on the longshore sediment
transportpatterns at coastal sites within the bathymetrically complex SCB. Each of the locations
chosen witness unique swell patterns resulting largely from their relative orientations with
respect to the deep water wave field of the North Pacific Ocean, each site’s local shelf
bathymetry, and the blocking patterns that the Channel Islands provide to each site (Fig. 3). The
two sites represent end member coastal orientations within the Bight; the SntBrb nest exhibits
a west-to-east general shoreline orientation, whereas the TorPns nest exhibits a north-to-south
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general shoreline orientation. For each experiment, we conducted 104 SWAN-CGEM
simulations that vary deep water wave direction from 260° to 320° in 5° intervals for four
pairs of wave height period scenarios: (1) H=2 m, T=12s,(2)H=2m,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 wave
conditions 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 Barbara
county, California, has been the site of regular nourishment due to chronic sand loss and the
community 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 two
sets of deep water wave conditions, which differ only in wave direction. Blue lines show results of deep
water conditions H
sig
=4 m, T=16 s, and α=320°. Red lines show results of deep water conditions H
sig
=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
S220 Climatic Change (2011) 109 (Suppl 1):S211–S228

beach width, morphology, and sediment volume over the past 30 years with anecdotal photo
histories documenting wide, well-vegetated, sandy beaches in the 1970’s, which were fully
inundated during the El Niño winters of 1982–83 and 1997–98 (Sylvester 2010). Waves
entering the Santa Barbara channel, as swell, have been modeled by (Guza et al. 2001), and
are 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 in
Fig. 4. The wave height distribution pattern for the entire SCB (Fig. 4a) illustrates the
blocking effect of the Channel Islands. Figure 4b shows the decrease (by more than half) in
wave height as waves enter shallow water. Figure 4c shows the significant amount of
refraction that occurs as waves approach the nearshore and the significant sheltering
experienced by the Goleta Beach site, herein referred to as SB-2 (blue star), as compared to
the 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 the
vicinity of SB-1 and SB-2. Figure 6shows the strong influence exerted by wave direction at
the Santa Barbara site. Output from two SWAN simulations are passed to CGEM to
examine longshore patterns of potential sediment transport rate and divergence of drift. For
each SWAN simulation, deep water wave height and period are set to 4.0 m and 16 s, but
the deep water wave direction is 320° (northwesterly) in case A, representative typical La
Niña storm wave conditions, as opposed to 270° (westerly) in case B, representative of El
Niño storm wave conditions, during which time the jet stream occupies a more southern
position than usual due to the anomalous atmospheric pressure distribution (Storlazzi and
Griggs 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 (H
sig
=4 m), everywhere along the
5 km reach. For Case B, the wave heights are substantially higher, approximately 2°m
everywhere along the reach. The angle of incidence varies for both Case A and Case B, but
in the same pattern, developing a sizable longshore component of wave energy flux. The
longshore sediment transport rates vary in much the same manner as wave heights for the
two cases, with appreciable transport in Case B, and negligible transport in Case A. The
potential 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 drift
is 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 produced
divergence of drift patterns which are reported for SB-1 and SB-2 in Fig. 7. This compendium
of experiment results illustrates that the exposed SB-1 site experiences increasing erosion as
wave conditions become more westerly. This is in contrast to the sheltered SB-2 site, which
becomes more accretionary as wave direction becomes more westerly. Increasing deep-water
wave 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 causes
enhanced erosion at SB-1, but causes decreased accretion at SB-2.
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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 any
longshore 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 Scripps
and 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 Pines
site to a SWAN simulation for a moderate, westerly swell (H=2 m, T=12 s, α=270°) in
Fig. 5. The demonstrable change in wave height visible around 33.05° north latitude in
Fig. 5b is a result of waves penetrating through a window between Santa Catalina and San
Clemente Islands during periods of westerly swell. The general shore-normal orientation of
the wave field (for input conditions shown) promotes nearshore wave height increase as a
result 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, the
significant 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 for
the SntBrb nest at sites SB-1 and SB-2. Positive values of divergence of drift represent accretion and negative
values represent erosion
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sites TP-1 and TP-2 is very small (<1.0 m). However, in the TorPns nest, this may be due to
blockage of waves by the Channel Islands rather than to severe refraction as in the SntBrb
nest. Angles of incidence for both case A and B at TorPns are small, approximately less
than +/−5°. For case B, between kilometer markers 23 and 25.7, angle of incidence is
negative which results in northward-directed longshore sediment transport pattern in this
region, 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-1
and 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 two
sets of deep water wave conditions, which differ only in wave direction. Blue lines show results of deep
water conditions H
sig
=4 m, T=16 s, and α=320°. Red lines show results of deep water conditions H
sig
=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
Climatic Change (2011) 109 (Suppl 1):S211–S228 S223

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 are
reported for TP-1 and TP-2 in Fig. 9. All simulations run for the Torrey Pines site resulted
in erosion. At TP-1, the peak in magnitude of potential divergence of drift occurs when
waves are just north of westerly (275°–290°). Increases in wave period slightly increased
erosion 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 wave
height causes potential divergence of drift to approximately triple across the directional
range. 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 in
Southern California has been presented. The procedure combines a spectral wave
transformation model with a calculation of gradients (divergence) in longshore sediment
transport rates, assuming transport-limited conditions. To illustrate some specific coastal
impacts 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 wave
height/wave period combinations.
Fig. 9 Compendium of potential divergence of drift results from 104 SWAN-CGEM model simulations for
the TorPns nest at sites TP-1 and TP-2
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This study demonstrates that the longshore sediment transport patterns in the littoral
zone, and therefore the locations of erosional hotspots, along the Southern California coast
are extremely sensitive to deep water wave direction. We speculate that this sensitivity is
due to two principle reasons: (1) the severe refraction required by northwesterly waves in
order to be incident upon south facing coasts (e.g. SntBrb nest), which could also be
considered a sheltering effect of Pt. Arguello, and (2) the sheltering effects of the Channel
Islands (blocking of incoming swells and additional refraction of grazing waves) on west
facing coasts (TorPns nest). Observations of wave interruption by islands were made
decades ago by Arthur (1951).
Although the cross-shore transport of sediment in the littoral zone is not specifically
addressed in these numerical experiments, we acknowledge its potential importance during
large wave events. Long-period swells, often associated with large wave events, will increase
refraction, which increases the cross-shore component of wave energy flux. Associated high
wave set-up can promotes off-shore transport and the temporary storage of littoral sediment in
offshore bars. Despite the fact that cross-shore transport can be strong during events, the
associated “erosion”is often temporary, as recovery proceeds relatively rapidly after a large
wave event via onshore transport of bar sediment.
It is noteworthy that the Santa Barbara wave direction experiment illustrated how the
divergence of drift at a site exposed to the open ocean (SB-1) experiences enhancement of
erosion as the wave field intensifies (increased wave heights and periods), whereas the
divergence of drift at a site locally sheltered by a headland (SB-2) experiences enhancement
of accretion as the deep water wave heights are increased. The fact that the sheltered site
experienced slight decreases in accretion for increased wave periods may be due to the
higher degree of refraction that the longer period swells undergo before reaching the coast.
The Torrey Pines experiment reveals interesting behavior regarding the direction of
longshore transport and erosion. As shown in Fig. 8, for a westerly wave field of strong
intensity (H
s
=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. The
result of this change in angle of incidence is a change in direction of longshore transport
from northward to southward. However, divergence of drift is negative for this set of deep
water 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 a
unique control on nearshore wave fields at this site.
It is observed that at both SB-1 (SntBrb nest) and TP-2 (TorPns nest), negative
divergence 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 to
the 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 the
shoreline at TP-2 is consistently retreating more rapidly than the shoreline at TP-1? Several
explanations are offered to address these discrepancies and we suspect the answer is a
combination of these. First, as mentioned above, the erosion/accretion portion of the CGEM
model assumes transport-limited conditions, meaning that deficiencies in sediment supply
are not considered to play a role in coastal landform evolution. If sediment supply is limited
at 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 coastal
sites and does not address the rocky cliffs that back the beaches along much of the Southern
California coast. During high wave conditions when sediment supply is limited, it is quite
likely that beach sand is temporarily stored offshore in bars and waves directly impact the
Climatic Change (2011) 109 (Suppl 1):S211–S228 S225

bedrock cliffs, whose retreat is not governed by Eq. (4) above. To simulate shoreline retreat
of 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 longshore
sediment transport patterns are highly sensitive to deep water wave conditions, and
particularly, to wave direction.
These results have implications regarding climate change, longshore sediment transport
patterns, and the distribution of hotspots of coastal erosion within the SCB. Our numerical
simulations illustrate a dramatic increase in absolute value of divergence of drift as wave
climate approaches westerly deep water wave directions. It has been documented that during El
Niño winters, waves entering the Southern California Bight tend to be more westerly than
during non El Niño winters (Adams et al. 2008). Therefore, model results presented herein are
consistent with the observations of severe coastal change in California during the El Niño
winters of 1982–83, and 1997–98 (Storlazzi et al. 2000). Recent research investigating
tropical cyclonic behavior during the early Pliocene (5–3 ma) reveals a feedback that may
serve to increase hurricane frequency and intensity in the central Pacific during warmer
intervals (Federov et al. 2010). This is relevant to Earth’s current climate trend because the
early Pliocene is considered a possible analogue to modern greenhouse conditions. Federov et
al. (2010) provide results of numerical simulations of tropical cyclone tracks in early Pliocene
climate, which illustrate a dramatic poleward shift in sustained hurricane strength within the
eastern Pacific Ocean. This pattern results in increased westerly storminess, implying that
warmer 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 reviewers
as 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 the
other guest editors of this special issue.
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