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Effects of Climate Change and Wave Direction on Longshore Sediment
Transport Patterns in Southern California
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Peter N. Adams
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Department of Geological Sciences, University of Florida, Gainesville, FL 32611, Tel.: 352846-0825, Fax: 352-392-9294, email: adamsp@ufl.edu
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Douglas L. Inman
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Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093
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Jessica L. Lovering
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Department of Geological Sciences, University of Florida, Gainesville, FL 32611
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Submitted to Climatic Change: 02-27-2010
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Reviews received: 01-10-2011
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Revised and returned: 03-04-2011
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Adams et al., revision for Climatic Change – Mar. 2011
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Abstract
Changes in deep-water wave climate drive coastal morphologic change according to
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unique shoaling transformation patterns of waves over local shelf bathymetry. The
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Southern California Bight has a particularly complex shelf configuration, of tectonic origin,
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which poses a challenge to predictions of wave driven, morphologic coastal change.
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Northward shifts in cyclonic activity in the central Pacific Ocean, which may arise due to
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global climate change, will significantly alter the heights, periods, and directions of waves
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approaching the California coasts. In this paper, we present the results of a series of
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numerical experiments that explore the sensitivity of longshore sediment transport
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patterns to changes in deep water wave direction, for several wave height and period
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scenarios. We outline a numerical modeling procedure, which links a spectral wave
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transformation model (SWAN) with a calculation of gradients in potential longshore
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sediment transport rate (CGEM), to project magnitudes of potential coastal erosion and
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accretion, under proscribed deep water wave conditions. The sediment transport model
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employs two significant assumptions: (1) quantity of sediment movement is calculated for
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the transport-limited case, as opposed to supply-limited case, and (2) nearshore wave
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conditions used to evaluate transport are calculated at the 5-meter isobath, as opposed to
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the wave break point. To illustrate the sensitivity of the sedimentary system to changes in
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deep-water wave direction, we apply this modeling procedure to two sites that represent
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two different coastal exposures and bathymetric configurations. The Santa Barbara site,
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oriented with a roughly west-to-east trending coastline, provides an example where the
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behavior of the coastal erosional/accretional character is exacerbated by deep-water wave
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climate intensification. Where sheltered, an increase in wave height enhances accretion,
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and where exposed, increases in wave height and period enhance erosion. In contrast, all
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simulations run for the Torrey Pines site, oriented with a north-to-south trending coastline,
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resulted in erosion, the magnitude of which was strongly influenced by wave height and
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less so by wave period. At both sites, the absolute value of coastal accretion or erosion
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strongly increases with a shift from northwesterly to westerly waves. These results
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provide some examples of the potential outcomes, which may result from increases in
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cyclonic activity, El Niño frequency, or other changes in ocean storminess that may
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accompany global climate change.
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Keywords: Climate Change, Coastal Erosion, Longshore Sediment Transport, Southern
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California
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1 Introduction
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In California, 80% of the state's residents live within 30 miles of the coast (Griggs et
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al., 2005). To mitigate the effects of climate change on coastal communities, it is necessary
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to assess the oceanographic and geomorphic changes expected within the coastal zone.
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Effective planning for the future of the California coast will need to draw on climate models
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that predict the forcing scenarios and coastal change models that predict the coast's
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response.
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Coastal landforms exhibit dynamic equilibrium by adjusting their morphology in
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response to changes in sea level, sediment supply, and ocean wave climate. Global climate
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change exerts varying degrees of influence on each of these factors. Proxy records indicate
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that wave climate has influenced coastal sedimentary accretion throughout the Holocene
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(Masters, 2006) and, although the causative links between climate change and severe
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storms are not reconciled in the scientific literature (Emanuel, 2005; Emanuel et al., 2008),
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it is well-accepted that changes in ocean wave climate (i.e. locations, frequency, and
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severity of open ocean storms) will bring about changes in the locations and magnitudes of
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coastal erosion and accretion in the future (Slott et al., 2006). Numerous studies indicate
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that changes in ocean wave climate are detectable (Gulev and Hasse, 1999; Aumann et al.,
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2008; Komar and Allan, 2008; Wang et al., 2009), but translating these open ocean changes
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to nearshore erosional driving forces is complex, and requires an understanding of the
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interactions between wave fields and the bathymetry of the continental shelf. Along the
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southern California coast, from Pt. Conception to the U.S./Mexico border, the situation is
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further complicated by the intricate shelf bathymetry and the presence of the Channel
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Islands, which prominently interfere with incoming wave field (Shepard and Emery, 1941).
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In this paper we investigate potential effects of changes in ocean wave climate
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(wave height, period, and direction) on the magnitudes of coastal erosion and accretion at
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two, physiographically different sites within the Southern California Bight (SCB). We
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consider the physical setting of this location, describe our mathematical modeling
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approach, and present the results of a series of numerical experiments that explore a range
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of wave climates. Lastly, we discuss the implications of the modeled coastal behavior in
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light of some possible scenarios of global climate change.
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2 Geomorphic and Oceanographic Setting
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For the purposes of this study, we consider the SCB to extend from a northwestern
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boundary at Point Arguello (34.58˚ N, 120.65˚ W, Fig. 1) to the U.S.-Mexico border (32.54˚
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N, 117.12˚ W, Fig. 1) south of San Diego. Tectonic processes along this active margin,
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between the Pacific and North American plates, are responsible for shaping the shallow
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ocean basins, continental shelf, and large-scale terrestrial landmasses (Christiansen and
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Yeats, 1992). The edges of the plates on either side of the boundary have been folded and
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fractured by transpressional plate motions, creating the high relief terrestrial landscape,
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pocket beaches backed by resistant bedrock sea cliffs, narrow continental shelf, deeply
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incised submarine canyons, and irregularly shaped submarine basins that are
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characteristic of a collisional coasts, as classified by (Inman and Nordstrom, 1971). In
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particular, the coastal mountain ranges and local shelf basins have been constructed by
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crustal displacement along a network of subparallel strike-slip faults, which characterize
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the plate interface (Hogarth et al., 2007). In general, these motions have resulted in the
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highly irregular, complex bathymetry that makes up the California Borderlands (Legg,
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1991), that feature the Channel Islands, as well as numerous submerged seamounts and
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troughs (Fig. 1).
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The wave climate of Southern California has been extensively studied since the
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pioneering investigations that applied the theoretical relationships of wave transformation
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to predict breakers and surf along the beaches of La Jolla, California (Munk and Traylor,
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1947; Sverdrup and Munk, 1947). Buoys maintained by the National Oceanic and
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Atmospheric Administration (NOAA) have greatly assisted understanding of deep-water
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wave conditions within the SCB (O’Reilly et al., 1996). Monitoring efforts continued to be
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improved through the development of the Coastal Data Information Page (CDIP) program,
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Scripps Institution of Oceanography, which provides modeled forecasts at a number of
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locations. Within the SCB, the presence of the Channel Islands (Fig. 1) significantly alters
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the deep-water (open ocean) wave climate to a more complicated nearshore wave field
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along the Southern California coast. The islands intercept waves approaching from almost
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any direction and the shallow water bathymetry adjacent to the islands refracts and
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reorients wave rays to produce a complicated wave energy distribution along the coast of
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the Southern California mainland. Several studies have targeted the sheltering effect of the
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Channel Islands within the SCB and the complexity of modeling wave transformation
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through such a complicated bathymetry (Pawka et al., 1984; O’Reilly and Guza, 1993;
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Rogers et al., 2007). It has also been documented that wave reflection off sheer cliff faces in
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the Channel Islands can be a very important process in the alteration of wave energy along
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the mainland coast (O’Reilly et al., 1999). The resulting distribution of wave energy at the
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coast consists of dramatic longshore variability in wave energy flux and radiation stress.
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These factors are considered to be fundamental in generating the nearshore currents
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responsible for longshore sediment transport and the maintenance of sandy beaches.
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Some studies highlight evidence for changing storminess and wave climate in the northeast
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Pacific Ocean (Bromirski et al., 2003; 2005). Recently, (Adams et al., 2008) examined a 50-
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year numerical hindcast of deep-water, winter wave climate in the bight, to understand the
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correlation of decadal-to-interannual climate variability with offshore wave fields. Their
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study found that El Niño winters during Pacific Decadal Oscillation (PDO) warm phase have
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significantly more energetic wave fields than those during PDO-cool phase, suggesting an
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interesting connection between global climate change and coastal evolution, based on
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patterns of storminess.
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3 Model Description
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The numerical model employed to evaluate potential coastal change consists of two
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components: (1) a spectral wave transformation model, known as SWAN (Booij et al.,
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1999), that calculates shoaling and refraction of a proscribed deep water wave field over a
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defined bathymetric grid, and reports coastal wave conditions, and (2) an empirically-
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derived longshore sediment transport formulation, referred to herein as CGEM (Coastal
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Geomorphic Erosion Model), that utilizes the coastal wave conditions derived by the wave
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transformation model to compute divergence of volumetric transport rates of nearshore
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sediment, also known as divergence of drift (Inman, 1987; Inman and Jenkins, 2003). This
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divergence of drift is the difference between downdrift and updrift volumetric transport
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rates (sediment outflow minus sediment inflow), and represents the volume of
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sedimentary erosion or accretion at a coastal compartment over the model time step. The
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interaction between the two components of the model is shown schematically in Figure 2.
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Two significant assumptions, and one model limitation, are invoked to simplify
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calculations. First, wave transformation is calculated to the fixed 5-meter isobath, which is
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usually seaward of the wave break point. Although the sediment transport model calls for
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wave conditions at the break point, wave breaking proceeds over a breaker zone, that can
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be several tens of meters wide, depending on the slope of the beach. Through several tests
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of the SWAN wave model, we have determined that, under vigorous deep water wave
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conditions (i.e. Hs=4-5 meters and T=14 s), wave breaking initiates over a depth of 9-10
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meters with the percentage of wave breaking increasing shoreward. We consider the mean
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water depth within this breaker zone (4.5-5 m) to be a reasonable representative value to
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use for breakpoint conditions in our modeling procedure. Second, the longshore sediment
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transport formulation assumes a transport-limited case, as opposed to a supply-limited
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case. The transport-limited assumption results in the calculation of potential divergence of
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drift, which would reflect the case of an inexhaustible supply of nearshore sediment. If
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terrestrial sediment supply to the coast is limited, from decreased riverine inputs for
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example, this assumption may be challenged. Lastly, the two components of the model are
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not yet backward coupled, meaning that nearshore bathymetry is not updated after a
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calculation of divergence of drift is conducted. Hence, the model should not be run over a
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time series of changing wave conditions to simulate the evolutionary behavior of a coast.
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In this paper, we present the results of instantaneous scenarios of divergence of drift for
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individual sets of deep-water wave conditions.
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3.1 Wave Transformation Model
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SWAN, short for Simulating WAves Nearshore, is a 3rd generation, finite-difference,
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wave model that operates on the principle of a wave action balance (energy density divided
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by relative frequency) (Holthuijsen et al., 1993; Booij et al., 1999). In the absence of wind
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forcing, this model requires only two general inputs to perform a computation of the wave
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field throughout a region - bathymetry and deep-water wave conditions.
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Ocean bathymetry exhibits a strong control on the direction and rate of wave energy
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translation. When the water depth is shallower than half the wavelength, interaction of
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wave orbitals with the sea floor causes shoaling transformation and refraction of waves, so
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the spatial pattern of nearshore wave energy depends strongly on the distribution of
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seafloor elevation. A review of some studies that investigated how bathymetric changes
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influence shoreline change by altering shoaling and refraction patterns is provided by
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(Bender and Dean, 2003). In this study, we used two bathymetric grids for the wave
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transformation modeling, both obtained from the National Geophysical Data Center
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(NOAA) U.S. coastal relief model grid database
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(http://www.ngdc.noaa.gov/mgg/coastal/coastal.html). A spatially-coarse grid (30 arc-
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sec) was used to evaluate wave conditions over the entire bight (32˚-35˚N, 121˚-117˚W),
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providing 480 x 360 cell matrices of wave heights and directions covering approximately
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124,000 km2, in which each value represents the conditions for a 0.72 km2 area of sea
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surface. Two smaller, high resolution grids (3 arc-sec), referred to herein as “nests”, were
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used to evaluate local wave conditions on a finer spatial scale. The nests named SntBrb and
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TorPns, for portions of the Santa Barbara and Torrey Pines coasts respectively, each occupy
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approximately 700 km2 within the domain of the main (coarse) grid (Fig. 3), resulting in
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each cell of output representing wave conditions over a 0.0072 km2 area of sea surface.
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At the western and southern margins of the coarse grid, deep-water wave
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conditions are proscribed as boundary conditions, consisting of significant wave height,
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peak period with a JONSWAP frequency distribution (Hasselmann et al., 1973), and peak
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direction with a cosine square spread of 15 degrees. The wave field is computed from the
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grid boundaries over the input bathymetry to the coast. Example results from a SWAN run
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for the coarse grid are provided in Figure 3. From the SWAN output of the coarse grid, the
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boundary conditions for the individual nests were obtained (examples provided in Figures
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4 and 5). Because the goal of the investigation was to examine "snapshots" of longshore
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distribution of erosion/accretion patterns resulting from various deep-water wave
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scenarios, all SWAN runs conducted in this study were performed in stationary mode.
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Temporally evolving wave fields, such as those produced during a storm were not
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examined, thereby avoiding the problem of swell arrival timing often associated with
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stationary runs (Rogers et al., 2007).
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3.2 Longshore Sediment Transport Model
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The output passed from the wave transformation model to the longshore sediment
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transport model includes the complete oceanic grids of significant wave height and peak
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directions at each “wet node” within the particular nest being examined. CGEM queries and
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interpolates the SWAN output at a known set of locations within the nest that constitute
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the 5-meter isobath, using an alongshore spacing of 100 meters. These longshore sets of
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wave height and direction form the basis of the sediment transport computation, which
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originates from a semi-empirical formulation originally proposed by Komar and Inman
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(1970). This relationship was later modified and named the CERC formula (Rosati et al.,
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2002), which has been used in several coastal evolution modeling studies recently (Ashton
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et al., 2001; Ashton and Murray, 2006). The CERC formula has been tested and found to
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provide results in close agreement with processed based models (Haas and Hanes, 2004).
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In its most general form, the volumetric longshore sediment transport rate, Ql, can be
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expressed as
Ql 
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Il
( s   w )gN o
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(1)
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where Il is the immersed-weight transport rate (Inman and Bagnold, 1963), s and w are
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densities of quartz sediment (2650 kg/m3) and seawater (1024 kg/m3), respectively, g is
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the gravitational acceleration constant (9.81 m/s2), and No is the volume concentration of
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solid grains (1 - porosity), set to 0.6, for all numerical experiments in this study. The
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subscript l is used to represent the longshore component of any variable with which it is
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associated.
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3.2.1 Angle of Incidence
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The angle of incidence is of primary importance in the calculation of longshore
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sediment transport. If wave rays approach the beach at an angle perfectly orthogonal to the
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trend of the coast, the longshore component of wave energy flux is zero, and there is no net
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longshore current to drive longshore sediment transport. If wave rays approach the beach
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at an oblique angle (somewhere between orthogonal and parallel), there is a component of
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wave energy flux parallel to the shoreline, which drives longshore sediment transport.
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Along the 5-meter isobath, the coastal orientation is computed by a downcoast-
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moving sliding window computation, which fits a trendline to 5 adjacent points and reports
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an azimuth value for the midpoint of the segment. The coastal orientation is subtracted
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from the queried wave direction along the isobath to provide an angle of incidence.
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3.2.2 Wave Energy Flux
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The longshore component of wave energy flux is considered to provide the fluid
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thrust required to move sediment under the influence of the breaking wave bore. The
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governing equation is
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1
Pl  ECn   w gH 2Cnsin  cos 
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where E is wave energy density, C is nearshore wave celerity, which is depth controlled, n is
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ratio of group to individual wave speed (~1 in shallow water and 1/2 in deep water), H is
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nearshore (breaking) wave height,  is the angle of incidence, the trigonometric
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components of which result from the tensor transformation of the onshore flux of
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longshore directed momentum (LonguetHiggins and Stewart,1964). As noted above, we
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estimate breaking wave height by evaluating this quantity at the 5-meter isobath. The
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immersed weight transport rate is simply a scaled version of the longshore component of
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wave energy flux
(2)
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Il  KPl
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where the scaling parameter, K, is set to 0.8 in this study. It is noted that Komar and Inman
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(1970) tested this relationship at different locations, where beach sediment sizes differed,
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but found that the relationship held, irrespective of sedimentary texture.
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3.2.3 Divergence of Drift
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After presenting the relationships for the longshore component of wave energy flux,
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immersed weight transport rate, and volumetric longshore sediment transport rate, we can
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show that a simple relationship for the divergence of drift is obtained by applying the
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vector differential operator to the volumetric longshore sediment transport rate using a
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dot product,
 Ql 
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
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Ql
x
(3)
(4)
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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
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longshore reach dx, during the time interval that these wave conditions are applied.
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Herein, we adopt the sign convention that divergence is defined as the net difference
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between sediment inflow and sediment outflow, making positive divergence of drift (where
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inflow exceeds outflow) result in accretion at a site, whereas negative divergence of drift
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(where outflow exceeds inflow) results in erosion. The longshore pattern of divergence of
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drift is therefore out of phase with longshore sediment transport, as expected. At
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longshore positions where transport is increasing at the greatest rate (positively sloping
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inflection points), divergence of drift is at a local minimum; where transport is decreasing
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at the greatest rate (negatively sloping inflection points), divergence of drift is at a local
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maximum; where transport is at a local minimum or maximum, divergence of drift should
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be zero.
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4 Numerical Experiments and Results
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To provide insight on how climate change-driven alteration of deep water wave
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conditions might affect the magnitude of erosion and accretion along the Southern
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California coast, we conducted a series of controlled numerical experiments at two
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physiographically-distinct, reaches of the Southern California coast, which we refer to as
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the Santa Barbara (SntBrb nest) and Torrey Pines (TorPns nest) sites. The goal of these
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experiments is to test the hypothesis that deep water wave direction exhibits critical
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control on the longshore sediment transport patterns at coastal sites within the
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bathymetrically complex SCB. Each of the locations chosen witness unique swell patterns
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resulting largely from their relative orientations with respect to the deep water wave field
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of the North Pacific Ocean, each site's local shelf bathymetry, and the blocking patterns that
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the Channel Islands provide to each site (Fig. 3). The two sites represent end member
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coastal orientations within the Bight; the SntBrb nest exhibits a west-to-east general
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shoreline orientation, whereas the TorPns nest exhibits a north-to-south general shoreline
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orientation. For each experiment, we conducted 104 SWAN-CGEM simulations that vary
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deep water wave direction from 260˚ to 320˚ in 5˚ intervals for four pairs of wave height
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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
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s. These ranges span the distributions of deep water wave conditions documented for the
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SCB by Adams et al. (2008).
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4.1 Site 1 - Santa Barbara
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The western end of Goleta Beach, adjacent the UCSB campus in southeastern Santa
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Barbara county, California, has been the site of regular nourishment due to chronic sand
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loss and the community desire to maintain a recreational beach. The site has witnessed
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profound changes in beach width, morphology, and sediment volume over the past 30
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years with anecdotal photo histories documenting wide, well-vegetated, sandy beaches in
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the 1970's, which were fully inundated during the El Niño winters of 1982-83 and 1997-98
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(Sylvester, 2010). Waves entering the Santa Barbara channel, as swell, have been modeled
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by (Guza et al., 2001), and are regularly forecasted by the Coastal Data Information
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Program, CDIP.
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4.1.1 SWAN Transformed Wave Field
SWAN output from a moderate, westerly swell (H=2 m, T=12 s,  = 270˚) is shown in
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Figure 4. The wave height distribution pattern for the entire SCB (Fig. 4A) illustrates the
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blocking effect of the Channel Islands. Fig. 4B shows the decrease (by more than half) in
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wave height as waves enter shallow water. Fig. 4C shows the significant amount of
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refraction that occurs as waves approach the nearshore and the significant sheltering
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experienced by the Goleta Beach site, herein referred to as SB-2 (blue star), as compared to
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the exposed site SB-1 (red star) located immediately west of Goleta Point, 1 km from SB-2.
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4.1.2 CGEM Results
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It is instructional to observe the results of two CGEM simulations plotted along
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shore in the vicinity of SB-1 and SB-2. Figure 6 shows the strong influence exerted by wave
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direction at the Santa Barbara site. Output from two SWAN simulations are passed to
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CGEM to examine longshore patterns of potential sediment transport rate and divergence
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of drift. For each SWAN simulation, deep water wave height and period are set to 4.0 m
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and 16 s, but the deep water wave direction is 320˚ (northwesterly) in case A,
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representative typical La Niña storm wave conditions, as opposed to 270˚ (westerly) in
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case B, representative of El Niño storm wave conditions, during which time the jet stream
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occupies a more southern position than usual due to the anomalous atmospheric pressure
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distribution (Storlazzi and Griggs, 2000). Comparison of the two deep water input cases is
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as follows. Along the 5-meter isobath, the significant wave height for Case A
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(northwesterly) is very small (<0.5 m), in comparison to deep water inputs conditions
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(Hsig=4 m), everywhere along the 5 km reach. For Case B, the wave heights are
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substantially higher, approximately 2 meters everywhere along the reach. The angle of
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incidence varies for both Case A and Case B, but in the same pattern, developing a sizable
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longshore component of wave energy flux. The longshore sediment transport rates vary in
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much the same manner as wave heights for the two cases, with appreciable transport in
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Case B, and negligible transport in Case A. The potential divergence of drift pattern for
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Case B shows loss of sediment (erosion) at SB-1 (red star) and gain of sediment (accretion)
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at SB-2 (blue star). Potential divergence of drift is negligible along the length of the 5 km
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reach for Case A.
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4.1.3 SntBrb Experiment
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The 104 SWAN-CGEM simulations which were run for the SntBrb experiment
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produced divergence of drift patterns which are reported for SB-1 and SB-2 in Figure 7.
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This compendium of experiment results illustrates that the exposed SB-1 site experiences
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increasing erosion as wave conditions become more westerly. This is in contrast to the
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sheltered SB-2 site, which becomes more accretionary as wave direction becomes more
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westerly. Increasing deep-water wave height causes enhancement of erosional or
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accretional behavior at both SB-1 and SB-2, depending on the site tendency under milder
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conditions. Increasing wave period causes enhanced erosion at SB-1, but causes decreased
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accretion at SB-2.
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4.2 Site 2 - Torrey Pines
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Torrey Pines beach, located approximately 7 km north of Scripps Pier in La Jolla,
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California, has been the site of many scientific inquiries in the field of coastal processes
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(Thornton and Guza, 1983; Seymour et al., 2005; Yates et al., 2009). The relatively straight,
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north-south trending reach resides within the Oceanside littoral cell and owes any
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longshore variation in wave energy flux to the blocking effects of the Channel Islands,
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rather than to complexities of nearshore bathymetry, save for the areas around the Scripps
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and La Jolla submarine canyons in the southern portion of the TorPns nest.
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4.2.1 SWAN Transformed Wave Field
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As for the Santa Barbara site discussed above, we show the behavior of the Torrey
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Pines site to a SWAN simulation for a moderate, westerly swell (H=2 m, T=12 s,  = 270˚) in
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Figure 5. The demonstrable change in wave height visible around 33.05˚ north latitude in
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Figure 5B is a result of waves penetrating through a window between Santa Catalina and
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San Clemente Islands during periods of westerly swell. The general shore-normal
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orientation of the wave field (for input conditions shown) promotes nearshore wave height
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increase as a result of shoaling in the absence of refraction.
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4.2.2 CGEM Results
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Comparative examples of CGEM simulations from the TorPns nest for Cases A and B
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(described above in Section 4.1.2) are given in Figure 8. Just as for the SntBrb nest, the
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significant wave height for Case A along the 5-meter isobath in the vicinity of Torrey Pines
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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
358
blockage of waves by the Channel Islands rather than to severe refraction as in the SntBrb
359
nest. Angles of incidence for both case A and B at TorPns are small, approximately less than
360
+/- 5˚. For case B, between kilometer markers 23 and 25.7, angle of incidence is negative
361
which results in northward-directed longshore sediment transport pattern in this region,
362
as opposed to the southward directed transport elsewhere in the nest. For case A,
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363
divergence of drift pattern is negligible everywhere within the 5 km span surrounding TP-1
364
and TP-2, whereas for case B, a strongly negative potential divergence of drift (erosion)
365
emerges at Torrey Pines Beach, near TP-1 and TP2.
366
4.2.3 TorPns Experiment
367
As for the SntBrb nest discussed in Section 4.1.3, the 104 SWAN-CGEM simulations,
368
which were run for the TorPns experiment produced divergence of drift patterns which are
369
reported for TP-1 and TP-2 in Figure 9. All simulations run for the Torrey Pines site
370
resulted in erosion. At TP-1, the peak in magnitude of potential divergence of drift occurs
371
when waves are just north of westerly (275˚ - 290˚). Increases in wave period slightly
372
increased erosion for 2 meter waves, and shifted the peak direction for maximum erosion
373
for 4 meter waves, at TP-1. At TP-2, wave height has a profound influence; doubling of the
374
deep water wave height causes potential divergence of drift to approximately triple across
375
the directional range. Increasing wave period, however, had negligible effect at site TP-2.
376
5 Summary and Implications
377
A numerical modeling procedure for assessing the patterns of littoral sediment
378
transport in Southern California has been presented. The procedure combines a spectral
379
wave transformation model with a calculation of gradients (divergence) in longshore
380
sediment transport rates, assuming transport-limited conditions. To illustrate some
381
specific coastal impacts resulting from climate change, we have applied this procedure to
382
two physically-distinct sites within the SCB. We conducted a sensitivity analysis at the two
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study sites, whereby effects of variability in deep water wave direction were explored for
384
four wave height / wave period combinations.
385
This study demonstrates that the longshore sediment transport patterns in the
386
littoral zone, and therefore the locations of erosional hotspots, along the Southern
387
California coast are extremely sensitive to deep water wave direction. We speculate that
388
this sensitivity is due to two principle reasons: (1) the severe refraction required by
389
northwesterly waves in order to be incident upon south facing coasts (e.g. SntBrb nest),
390
which could also be considered a sheltering effect of Pt. Arguello, and (2) the sheltering
391
effects of the Channel Islands (blocking of incoming swells and additional refraction of
392
grazing waves) on west facing coasts (TorPns nest). Observations of wave interruption by
393
islands were made decades ago by Arthur (1951).
394
Although the cross-shore transport of sediment in the littoral zone is not specifically
395
addressed in these numerical experiments, we acknowledge its potential importance
396
during large wave events. Long-period swells, often associated with large wave events, will
397
increase refraction, which increases the cross-shore component of wave energy flux.
398
Associated high wave set-up can promotes off-shore transport and the temporary storage
399
of littoral sediment in offshore bars. Despite the fact that cross-shore transport can be
400
strong during events, the associated “erosion” is often temporary, as recovery proceeds
401
relatively rapidly after a large wave event via onshore transport of bar sediment.
402
It is noteworthy that the Santa Barbara wave direction experiment illustrated how
403
the divergence of drift at a site exposed to the open ocean (SB-1) experiences enhancement
404
of erosion as the wave field intensifies (increased wave heights and periods), whereas the
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405
divergence of drift at a site locally sheltered by a headland (SB-2) experiences
406
enhancement of accretion as the deep water wave heights are increased. The fact that the
407
sheltered site experienced slight decreases in accretion for increased wave periods may be
408
due to the higher degree of refraction that the longer period swells undergo before
409
reaching the coast.
410
The Torrey Pines experiment reveals interesting behavior regarding the direction of
411
longshore transport and erosion. As shown in Figure 8, for a westerly wave field of strong
412
intensity (Hs = 4 m, T = 16 s, a = 270˚), the angle of incidence between position markers 23-
413
25.75 km is negative, but changes to positive between position markers 25.75-28 km. The
414
result of this change in angle of incidence is a change in direction of longshore transport
415
from northward to southward. However, divergence of drift is negative for this set of deep
416
water wave conditions at both TP-1, where transport direction is northward, and TP-2,
417
where transport direction is southward. This persistence of erosional character at this site,
418
irrespective of transport direction, suggests that continental shelf bathymetry may exert a
419
unique control on nearshore wave fields at this site.
420
It is observed that at both SB-1 (SntBrb nest) and TP-2 (TorPns nest), negative
421
divergence of drift (erosion) appears to operate under all deep water conditions simulated.
422
This brings up two questions: (1) Why does the coast at SB-1 protrude seaward relative to
423
the coast at SB-2, if the SB-1 shoreline is retreating under all simulated conditions? (2) Why
424
does the Torrey Pines coastline maintain a relatively straight appearance if the shoreline at
425
TP-2 is consistently retreating more rapidly than the shoreline at TP-1? Several
426
explanations are offered to address these discrepancies and we suspect the answer is a
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combination of these. First, as mentioned above, the erosion/accretion portion of the
428
CGEM model assumes transport-limited conditions, meaning that deficiencies in sediment
429
supply are not considered to play a role in coastal landform evolution. If sediment supply
430
is limited at these sites, then the model may overestimate the magnitude of divergence of
431
drift. Second, the model only considers the movement of sediment alongshore at these
432
coastal sites and does not address the rocky cliffs that back the beaches along much of the
433
Southern California coast. During high wave conditions when sediment supply is limited, it
434
is quite likely that beach sand is temporarily stored offshore in bars and waves directly
435
impact the bedrock cliffs, whose retreat is not governed by Equation (4) above. To
436
simulate shoreline retreat of an exposed cliffed coast, bare bedrock cutting processes must
437
be adequately modeled. Neither of these caveats, however, changes the fact that the
438
gradients in potential longshore sediment transport patterns are highly sensitive to deep
439
water wave conditions, and particularly, to wave direction.
440
These results have implications regarding climate change, longshore sediment
441
transport patterns, and the distribution of hotspots of coastal erosion within the SCB. Our
442
numerical simulations illustrate a dramatic increase in absolute value of divergence of drift
443
as wave climate approaches westerly deep water wave directions. It has been documented
444
that during El Niño winters, waves entering the Southern California Bight tend to be more
445
westerly than during non El Niño winters (Adams et al., 2008). Therefore, model results
446
presented herein are consistent with the observations of severe coastal change in
447
California during the El Niño winters of 1982-83, and 1997-98 (Storlazzi et al., 2000).
448
Recent research investigating tropical cyclonic behavior during the early Pliocene (5-3 ma)
449
reveals a feedback that may serve to increase hurricane frequency and intensity in the
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450
central Pacific during warmer intervals (Fedorov et al., 2010). This is relevant to Earth’s
451
current climate trend because the early Pliocene is considered a possible analogue to
452
modern greenhouse conditions. Federov et al. (2010) provide results of numerical
453
simulations of tropical cyclone tracks in early Pliocene climate, which illustrate a dramatic
454
poleward shift in sustained hurricane strength within the eastern Pacific Ocean. This
455
pattern results in increased westerly storminess, implying that warmer climates will cause
456
the SCB to witness greater absolute values of divergence of drift. In other words, a more
457
volatile coastline, exhibiting higher magnitude erosion and accretion, might be expected as
458
a result of increased frequency of strong westerly waves.
459
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Figures
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Figure 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.
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Figure 2. Schematic diagram of numerical modeling procedure used in this study, showing
relationship between SWAN and CGEM components.
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Figure 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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Figure 4. Example wave height and direction output from SWAN wave transformation
model for input conditions of Hsig =2 m, T =12 s, and  =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 meter 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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657
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659
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Figure 5. Example wave height and direction output from SWAN wave transformation
model for input conditions of Hsig =2 m, T =12 s, and  =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 meter 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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Figure 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 Hsig=4 m, T=16 s, and =320˚.
Red lines show results of deep water conditions Hsig =4 m, T =16 s, and  =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.
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Figure 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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Figure 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 Hsig=4 m, T=16 s, and =320˚.
Red lines show results of deep water conditions Hsig =4 m, T =16 s, and  =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.
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Figure 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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