- Pacific Disaster Net

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Marine Geology 187 (2002) 279^297
www.elsevier.com/locate/margeo
Sea-cli¡ erosion as a function of beach changes and
extreme wave runup during the 1997^1998 El Nin‹o
Asbury H. Sallenger Jr. a; , William Krabill b , John Brock a , Robert Swift c ,
Serdar Manizade c , Hilary Stockdon a
a
US Geological Survey, Center for Coastal Geology, 600 Fourth Street South, St. Petersburg, FL 33701, USA
b
NASA, Wallops Flight Facility, GSFC, Wallops Island, VA, USA
c
EG and G, Wallops Flight Facility, GSFC, Wallops Island, VA, USA
Received in revised form 28 February 2002
Abstract
Over time scales of hundreds to thousands of years, the net longshore sand transport direction along the central
California coast has been driven to the south by North Pacific winter swell. In contrast, during the El Nin‹o winter of
1997^1998, comparisons of before and after airborne lidar surveys showed sand was transported from south to north
and accumulated on the south sides of resistant headlands bordering pocket beaches. This resulted in significant beach
erosion at the south ends of pocket beaches and deposition in the north ends. Coincident with the south-to-north
redistribution of sand, shoreline morphology became prominently cuspate with longshore wavelengths of 400^700 m.
The width and elevation of beaches were least where maximum shoreline erosion occurred, preferentially exposing
cliffs to wave attack. The resulting erosional hotspots typically were located in the embayments of giant cusps in the
southern end of the pocket beaches. The observed magnitude of sea cliff retreat, which reached 14 m, varied with the
number of hours that extreme wave runup exceeded certain thresholds representing the protective capacity of the
beach during the El Nin‹o winter. A threshold representing the width of the beach performed better than a threshold
representing the elevation of the beach. The magnitude of cliff erosion can be scaled using a simple model based on
the cross-shore distance that extreme wave runup exceeded the pre-winter cliff position. Cliff erosion appears to be a
balance between terrestrial mass wasting processes, which tend to decrease the cliff slope, and wave attack, which
removes debris and erodes the cliff base increasing the cliff slope. 7 2002 Elsevier Science B.V. All rights reserved.
Keywords: erosion; beaches; El Nin‹o; sea cli¡s
1. Introduction
Sea-cli¡ erosion is highly episodic, commonly
occurring during severe storms that have elevated
wave energy and rainfall. Rates of erosion are
* Corresponding author.
E-mail address: [email protected] (A.H. Sallenger Jr.).
controlled by a number of factors including the
sea cli¡’s composition, and its susceptibilities to
wave impact and mass wasting due to saturation
of sediments by rain water and other processes.
For example, in southern California, rates of seacli¡ erosion appear to be controlled by the
strength of the rock rather than by spatial variations in wave energy (Benumof et al., 2000).
Along reaches of coast where sea-cli¡ composi-
0025-3227 / 02 / $ ^ see front matter 7 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 5 - 3 2 2 7 ( 0 2 ) 0 0 3 1 6 - X
MARGO 3136 16-7-02 Cyaan Magenta Geel Zwart
280
A.H. Sallenger Jr. et al. / Marine Geology 187 (2002) 279^297
tion is relatively uniform, erosion has been observed to decrease as fronting beaches become
more substantial (e.g. Giese and Aubrey, 1987;
Everts, 1991; Carter and Guy, 1988). The implication is that beaches protect the sea cli¡s from
wave attack. Shih et al. (1994) and Ruggiero et al.
(1996) attempted to quantify the role of waves in
sea-cli¡ erosion. They concluded that increased
duration or probability of runup exceeding the
elevation of the base of a cli¡, leads to enhanced
sea-cli¡ retreat. In contrast, for some cases, waves
may not be the dominant forcing. Hampton and
Dingler (1998) documented sea-cli¡ erosion in
central California primarily caused by freshwater
processes such as groundwater seepage and surface-water runo¡. Hapke and Richmond (in
press) compared and contrasted cli¡ failures resulting from earthquake shaking to failures resulting from wave attack.
During a major El Nin‹o in 1982^1983, intense
winter storms caused extensive changes to
beaches, dunes, and sea cli¡s along the US west
coast (e.g. Komar, 1986; Griggs and Brown,
1998). During an El Nin‹o winter, Paci¢c storm
tracks move farther to the south than usual, generating unusually powerful waves in California,
along the southern part of the west coast (Seymour, 1998; Allen and Komar, 2000a; Allen
and Komar, 2000b; Storlazzi and Griggs, 2000).
In a series of papers focused on the Oregon coast
in the Paci¢c Northwest, Komar and co-workers
observed net northward sand transport in pocket
beaches during severe El Nin‹o winters, presumably a result of this southerly shift in storm tracks
generating a more southerly wave approach (Komar, 1986; Komar et al., 1988; Komar and
Good, 1989; Komar, 1998; Revelle et al., in
press). They hypothesized that the net sand transport led to exposure of sea cli¡s in the southern
ends of pocket beaches to wave attack, resulting
in erosional hotspots.
With forecasts of extreme winter storms on the
US west coast during the the 1997^1998 El Nin‹o,
an opportunity arose to examine sea-cli¡ erosion
with unprecedented spatial coverage using airborne scanning lidar1 , a technology only recently
applied to coastal change (Brock et al., 1999;
Brock et al., in press ; Carter and Shrestha,
1997; Gutierrez et al., 1998; Sallenger et al.,
1999a, 1999b; Krabill et al., 2000; Sallenger et
al., 2001a, 2001b; Revelle et al., in press; Sallenger et al., in press). USGS, with our partners
in NASA and NOAA, conducted extensive coastal surveys on the US west coast, at the beginning
of and following the 1997^1998 El Nin‹o winter
(October^March) utilizing NASA’s Airborne
Topographic Mapper (ATM) (Sallenger et al.,
1999b).
In this paper, we use the ATM data to develop
relationships between sea-cli¡ erosion and beach
changes within pocket beaches in central California. Speci¢cally, we test the following hypotheses:
(1) During the 1997^1998 El Nin‹o winter, net
sand transport was in the opposite direction to
the long-term net direction along the central California coast.
(2) This net sand transport, preferentially denuded beaches in the southern ends of pocket
beaches, exposing cli¡s to the attack of waves,
creating erosional hotspots.
(3) The magnitude of observed sea-cli¡ erosion
was a function of beach characteristics, where
wide, high beaches served to protect cli¡s and
limit erosion relative to narrow, low beaches.
(4) A simple model, based on the horizontal
position of extreme wave runup relative to the
horizontal position of the sea cli¡, can be used
to scale sea-cli¡ erosion.
2. Methods
2.1. NASA’s Airborne Topographic Mapper
Most previous investigations of sea-cli¡ erosion
used sequential aerial photography, historic maps,
and/or ground surveys to develop cli¡-position
time series and magnitudes of cli¡ retreat (e.g.
Jones and Williams, 1991; Kirk, 1975; Lajoie
and Mathieson, 1985; Carter and Guy, 1988;
Sunamura and Horikawa, 1972 ; and Hampton
1
Lidar stands for ‘light detecting and ranging’, similar to
radar that stands for ‘radio detecting and ranging’. Both are
now accepted words.
and Dingler, 1998). Airborne scanning lidar provides estimates of elevation every few m2 over
regional scales of tens to hundreds of kilometers
of coast, allowing unprecedented assessment of
the spatial variability of beach and sea-cli¡
changes.
The ATM was mounted in a NOAA two-engine Twin Otter aircraft from NOAA’s Aircraft
Operations Center at MacDill Air Force Base,
Tampa, FL. The transmitted pulse of the ATM’s
blue^green laser is re£ected to the earth’s surface
using a rotating scan mirror. The rotating mirror
produces an elliptical scan pattern with a swath
width of 350 m, about 50% of the aircraft altitude. The aircraft pitch, roll, and heading are obtained with an inertial navigation system and the
positioning of the aircraft is found with Ashtech
Global Positioning System (GPS) receivers using
kinematic di¡erential techniques (Krabill and
Martin, 1987). The local meteorological conditions such as air pressure, temperature and relative humidity are also recorded and used to help
resolve ambiguities.
The precise ephemeris of the GPS constellation
is used to solve for the aircraft trajectory because
the distance between base station and rover exceeds 30^40 km. With the aircraft parked close
to the base station, GPS data sets from both the
aircraft and base station are obtained for about
45 min prior to and after each survey. These stationary data sets are used to resolve carrier phase
ambiguities.
Extensive intercomparisons were made between
ATM and ground-based systems on beaches. In
general, the vertical accuracy of the ATM for
beach mapping applications was approximately
15 cm RMS (Sallenger et al., in press).
2.2. Calculating wave runup
The parameters used in this paper to scale the
magnitude of sea-cli¡ erosion incorporate, in several di¡erent ways, wave runup, similar to the
approach of Sallenger (2000) to scale the impact
of storms on barrier islands. Runup was calculated as described below.
Using data from Duck, NC, Holman (1986)
found the 2% exceedence of runup, which includes
281
both swash height and wave setup as
R2% ¼ Ho ð0:83 ho þ 0:2Þ
ð1Þ
The Iribarren number is
ho ¼ L=ðHo =Lo Þ1=2
ð2Þ
where L is the local beach slope, Ho is the deep
water signi¢cant wave height, and Lo is the deepwater wavelength. Hence, a representative runup
elevation, that is, the 2% exceedence runup elevation relative to a ¢xed vertical datum is
R ¼ R2% þ Rmean
ð3Þ
where Rmean is mean sea level obtained from a tide
gauge and includes astonomical tides and sea level
anomalies such as highs observed along the US
west coast during El Nin‹o conditions (e.g. Flick,
1998). Using Holman’s data (Holman, 1986) and
additional runup data they gathered on the Oregon coast, Ruggiero et al. (1996) found the 2%
exceedence of runup to be
R2% ¼ 0:27ðLHo Lo Þ0:5
ð4Þ
3. Observations
Over time scales of hundreds to thousands of
years, the net longshore sand transport direction
for central California has been to the south. This
is clearly indicated by the region’s coastal morphology, which displays several examples of classic log-spiral shape embayments (Fig. 1). The logspiral has been shown to develop on rugged
coasts, with persistent net longshore transport direction, the spiral opening away from a relatively
resistant headland in the down-drift direction (e.g.
Yasso, 1965). The spiral develops until net longshore transport is minimized, i.e. when dominant
waves refract so that they are parallel to the shape
of the bay’s shoreline. The net southerly transport
is driven by swell waves generated in the North
Paci¢c by winter storms.
In central California during the 1997^1998 El
282
Fig. 1. Location of the pocket beaches studied (Montara and Paci¢ca) and characteristic coastal morphology on the central west
coast of the US consisting of log-spiral bays. The spiral opens to the south indicating the southerly net long-term sand transport
in the region over time scales of hundreds to thousands of years.
283
Fig. 2. Ground photographs showing (A) Montara State Beach, a pocket beach. The view is to the north from the southern enclosing headland. (B) The seawall protecting a restaurant located in the southern end of the beach. The seawall location is shown
in Fig. 3B.
284
Fig. 3. (A) Shaded relief map of Montara derived from ATM data. Note that these high-resolution topographic data clearly show the form and location of the
coastal highway. Beach changes that occurred during the El Nin‹o winter are superimposed. Scale ranges from +5 m of accretion (dark blue) to 35 m of erosion
(bright red). (B) Plot of shoreline (MHHW) change and beach volume change for Montara versus latitude. (A) and (B) are scaled the same in latitude.
285
Fig. 4. Schematic de¢ning critical terms used in scaling cli¡ erosion. Symbols: S, shoreline position; D, base of cli¡ position;
B, beach width.
Nin‹o winter, there was clear evidence of net
northward sand transport, opposite to the longterm net indicated by coastal morphology. We
focus on two pocket beaches, Montara (1.5-km
long) and Paci¢ca (5-km long), each characterized
by prominent headlands at both ends (Figs. 1, 2A
and 7). Using the ATM, both beaches were surveyed at the beginning and end of the El Nin‹o
winter, i.e during September 1997 and again in
April 1998.
At Montara, sand was eroded from the southern end of the pocket beach, transported to the
north, and deposited against the northern headland, which acted like a groin trapping sand on its
updrift side (Fig. 3A). The shaded relief depiction
of the pocket beach clearly shows some of the
capabilities of the spatially dense and high-resolution ATM data; note the coastal highway, the
town of Montara, and the sea cli¡s with eroded
‘arroyos’ that channelize rain-water runo¡. Superimposed on the shaded relief is vertical change of
the beach during the El Nin‹o winter illustrating
the distinctive northward redistribution of sand.
We only have two surveys, pre- and post-El
Nin‹o, hence we cannot generalize as to what occurs during normal non-El Nin‹o winters. However, the net transport direction during the observed El Nin‹o was opposite that indicated by
long-term trends (Fig. 1).
At intervals of 20 m along the beach, shoreline
positions were calculated at the Mean Higher
High Water (MHHW) line using procedures de-
286
veloped by Stockdon et al. (in press). This is an
objective measure of shoreline position based on a
contour of elevation relative to a ¢xed datum.
The shoreline accreted in the north nearly 40 m,
while it eroded in the south as much as 60 m (Fig.
3B). Note that the spatial variation of beach volume change closely tracks the shoreline change,
indicating that the beaches maintained their general form during the redistribution of sand. The
beach volume changes were evaluated within a
1-m-wide strip oriented shore-normal between
the cli¡ and shoreline. Also note that the seawall
is located near the location of maximum shoreline
erosion (Figs. 2B and 3B). This seawall was built
during the last major El Nin‹o in 1982^1983 to
protect the eroding sea cli¡ which threatened a
cli¡-top restaurant.
As noted above, the vulnerability of sea cli¡s to
erosion by waves may be a function, in part, of
the degree of protection a¡orded by the beach.
The wider the beach and the higher the sand elevation at the base of the cli¡, the more protection
a¡orded. Beach width, B, as de¢ned here is the
cross-shore distance between the MHHW shoreline position, S(x), and the position of the cli¡
base, D(x), e.g. the pre-El Nin‹o beach width, indicated by the su⁄x pre , is given by
Bpre ¼ Dpre ðxÞ3 Spre ðxÞ
ð5Þ
(Fig. 4A). Bpre ranged from a maximum of approximately 100 m near the south end of the
beach and decreased to near zero at the north
end (Fig. 5A). The redistribution of sand during
the El Nin‹o winter caused a signi¢cant narrowing
of the beach in the south and an increase in width
in the north (Fig. 5B,C).
The elevation of sand at the base of the cli¡,
D(z)(Fig. 4), changed similarly. Dpre (z) was as
much as 2.5 m higher at the south end of the
pocket beach than in the central section (Fig.
6A). This general trend reversed during the El
Nin‹o winter (Fig. 6B). The vertical changes in
D(z) between the pre and post surveys ranged
from 3 m of erosion in the south to over W2 m
of accretion in the central and north (Fig. 6C). In
terms of change during the El Nin‹o winter, both
beach width and sand elevation at the base of the
cli¡ had minima in the vicinity of the seawall
where there was extensive sea cli¡ erosion during
the 1982^1983 El Nin‹o, prompting the original
seawall construction. During the 1997^1998 El
Nin‹o, there was no signi¢cant sea-cli¡ erosion at
Montara where at least one potential erosional
hotspot exposed by beach changes was protected
by the seawall.
In contrast to Montara, some sea cli¡s in the
vicinity of Paci¢ca eroded extensively. The beach
of interest here, de¢ned by Mussel Rock to the
north and Mori Point to the south (Fig. 7), has a
history of episodic sea-cli¡ retreat (Lajoie and
Mathieson, 1985), and is heavily protected with
a variety of engineering works along its southern
half. We focus on beach and cli¡ changes in the
northern half, i.e. North Esplanade Beach, where
a number of houses were condemned as sea-cli¡
erosion threatened (Fig. 8 ; Sallenger et al.,
1999b). Vertical changes during the El Nin‹o winter are draped onto the 3-D lidar-based map
showing where the sea cli¡ eroded and houses
were lost. Note the subtle protruding part of the
sea cli¡ in the central area of the photograph and
in the 3-D plot where there was little change. This
is an area of resistant bedrock. The remainder of
the sea cli¡ is composed of weakly lithi¢ed/indurated eolian and alluvial deposits, mostly sand
and gravel.
As at Montara, the sand was redistributed from
south to north (Fig. 9A). At North Esplanade,
however, the shoreline change trend had largescale oscillations superimposed, representing large
cuspate features that had a wavelength of about
700 m, much larger than normal beach cusps
whose wavelengths are typically 6 100 m (e.g.
Sallenger, 1979). The development of cusp embayments was associated with W20 m of erosion and
cusp horns with W20 m of shoreline accretion.
Similar features were present at Montara
although with a somewhat smaller wavelength,
550 m (Fig. 3). Inman (1987) and Hicks and Inman (1987) have shown how such features could
migrate alongshore. These large-scale cusps may
be associated with rhythmic o¡shore bar features
of the same wavelength (e.g. Sallenger et al.,
1985), although we cannot demonstrate the association here. Komar and Good (1989) related the
287
Fig. 5. Beach width, B, for Montara determined as the cross-shore distance between shoreline, S(x), and the base of the cli¡,
D(x). (A) Pre-El Nin‹o. (B) Post-El Nin‹o. (C) Change in beach width between the two times.
position of troughs of similar scale features with
enhanced dune erosion and destruction of property on the Oregon coast.
Sea-cli¡ erosion, E, in the Paci¢ca pocket beach
reached 14 m and was localized at one of the
maxima of shoreline erosion (compare Fig.
9A,B). There were several shoreline-erosion maxima, each associated with a trough in the rhythmic shoreline change pattern. The greatest maxima occurred adjacent to the seawall, hence there
was no cli¡ retreat there. The next greatest was
adjacent the 14-m sea-cli¡ retreat hotspot, located
immediately north of the sea cli¡ composed of
bedrock. The close proximity of the bedrock
may have contributed to the shoreline erosion,
perhaps as a subtle groin-like feature, although
there was no obvious updrift sand accumulation,
or as a seawall-like feature with end e¡ects.
An e¡ective beach width, Beffective , is de¢ned as
the distance from the post-El Nin‹o shoreline,
Sstorm (x), to the pre-El Nin‹o sea-cli¡ position,
Dpre (x), i.e.
Beffective ¼ Dpre ðxÞ3Sstorm ðxÞ
ð6Þ
(see Fig. 4). Beffective represents the exposure of the
cli¡ to wave attack during the El Nin‹o winter,
where the beach changes are assumed to occur ¢rst
exposing the pre-El Nin‹o cli¡ position to wave attack. Similarly, we de¢ne an e¡ective sand elevation at the base of the cli¡, Deffective (z), which is
the elevation of the post-El Nin‹o beach surface at
288
Fig. 6. Sand elevation, D(z), at the base of the cli¡. (A) Pre-El Nin‹o. (B) Post-El Nin‹o. (C) Change between pre- and postEl Nin‹o.
the pre-El Nin‹o sea-cli¡ position, Dpre (x) (Fig.
4B). Both Beffective and Deffective (z) have minima,
which are not adjacent to the bedrock or seawall,
at the 14-m sea-cli¡ retreat hotspot. (Compare
Figs. 9 and 10.)
4. Scaling cli¡ erosion
In this section, we compare observed magnitudes of sea-cli¡ retreat to di¡erent scaling parameters. The scaling parameters are based on
calculations of wave runup elevations, by methods
discussed earlier, that occurred during the El
Nin‹o winter. We present, in Table 1, results using
Rz calculated using both Eqs. 1 and 4, based on
the work of Holman (1986) and Ruggiero et al.
(1996), respectively. For ease of presentation in
the text and illustrations, we present the results
of the calculations based only on Holman’s equation. Correlations between runup-based parameters and observed cli¡ erosion were, for the most
part, similar using either equation.
R was calculated hourly over the El Nin‹o winter (although some data were missing during
March 1998) using wave data from NOAA San
Francisco buoy, o¡shore San Francisco Bay, and
sea level data from a tide gauge in San Francisco
289
Fig. 7. Map of the Paci¢ca cell. The southern half of the cell has extensive man-made modi¢cations such as near-continuous seawalls of various designs. This paper focuses on the more natural beach areas in the northern half of the cell.
(Fig. 1). Runup was calculated using two di¡erent
types of beach slopes, a variable L consisting of
local estimates of L at the post-El Nin‹o MHHW
every 20 m along the beach and a mean L found
from all the variable L adjacent to the sea cli¡
(excluding only the estimates adjacent to the seawall and bedrock cli¡). Calculations using both
slopes are included in Table 1.
As discussed above, we assume that the redistribution of beach sand exposes the sea cli¡ to
wave attack. Hence, a critical parameter (as in-
troduced above) is Deffective (z) representing the exposure of the cli¡ due to this redistribution.
We ¢rst calculate the amount of time in hours
that the runup during the El Nin‹o winter exceeds
Deffective (z) and investigate the relationship of this
quantity to cli¡ change (Fig. 11A). We have included all data for the northern part of the Pacifica study area excluding only the resistant seawall
and bedrock reaches. The cluster of points near
zero represent stable sea-cli¡ areas that occur
north of 37.65‡ latitude (Fig. 9B). Exclusion of
290
291
Fig. 9. (A) Shoreline changes at Paci¢ca during the El Nin‹o winter showing the developing giant cusps and net redistribution of
sand to the north. (B) Measured cli¡ erosion from pre- and post-El Nin‹o winter lidar data. Sea-cli¡ erosion is estimated from
volume of material removed from the cli¡ (m3 /m) divided by the height of the cli¡; hence, it is a measure representing change
over the entire height of the cli¡ rather than at one speci¢c elevation. The occurrences of cli¡ advance (positive values) are noise,
complicated somewhat by occurrences of debris at the base of the cli¡ caused by mass wasting higher on the cli¡ face.
data adjacent to the seawall and bedrock assures
that we are considering sea cli¡s that have similar
strength (i.e. erosion potential).
There appears to be a rough relationship between increasing sea cli¡ erosion and increased
time when runup exceeds Deffective (z), where
r2 = 0.49 using the mean slope for all locations
and 0.56 using measured slope at each location.
(Mean slope example shown in Fig. 11A.) On the
coast of Oregon, Ruggiero et al. (1996) compared
the hours that runup exceeded the sand elevation
at the base of the cli¡ and sea cli¡ retreat with
encouraging results. However, this kind of analysis utilizing D(z) does not include the role of
Fig. 8. (A) Photograph of the Paci¢ca region where extensive sea-cli¡ erosion occurred during the El Nin‹o winter showing threatened houses at the top of the cli¡. Location of the photograph is shown in Fig. 7. (B) 3-D view using lidar data acquired prior
to the El Nin‹o winter of the area shown in (A). Note that the buildings are clearly shown. Superimposed on the topography is
vertical change with hot (red) colors indicating loss over the El Nin‹o winter.
292
Fig. 10. Beffective and Deffective (z) at Paci¢ca showing the increased vulnerability of the southern beach to cli¡ erosion over the
course of the El Nin‹o winter.
beach width in protecting sea cli¡s. If there was a
wide beach, say hundreds of meters wide with a
prominent berm, the sea cli¡ will not necessarily
be attacked by runup when D(z) is exceeded.
With the spatially dense lidar data de¢ning the
geometry of the beach, we can examine horizontal
thresholds that incorporate the protective role of
beach width. We estimate the horizontal position
of the runup relative to MHHW shoreline position by
RðxÞ ¼ ðRðzÞ3 corÞ=Lstorm
ð7Þ
where cor is elevation of MHHW above
NAVD88. Recall that e¡ective beach width,
Beffective , is relative to MHHW as well. Hence,
we ¢nd the hours during the El Nin‹o winter
that R(x) s Beffective (i.e. when the runup collides
with the sea cli¡) and correlate hours of exceedence versus cli¡ change (Fig. 11B). The correlation with cli¡ change is improved for hours exceeding Beffective , r2 = 0.71(mean slope), compared
to hours exceeding Deffective (z), r2 = 0.49 (Table 1;
Fig. 11A,B). The improvement is presumably because beach width is a signi¢cant factor for protection of the beach by wave attack.
Komar et al. (1999) proposed a simple model
for dune erosion where the amount of erosion is
determined by the cross-shore distance that extreme wave runup exceeds the position of the initial dune scarp. The assumption is that the erosion process is independent of time, that the dune
scarp retreats until no longer impacted by runup.
We have applied this type of model here to scale
sea-cli¡ erosion (Fig. 4B). The beach slope is assumed to be constant as the sea cli¡ retreats. The
cli¡ erodes landward until runup elevation, R(z),
no longer exceeds D(z) or, as depicted in Fig. 4B,
until runup position, R(x), no longer exceeds
D(x). Hence, where R(x) s Dpre (x), the magnitude
of sea-cli¡ retreat is
Epredicted ¼ Dpre ðxÞ3RðxÞ
ð8Þ
(Fig. 4B). However, R(x) is a distribution of runup realizations over the El Nin‹o winter, not a
single value. There is no clear choice of the proper
statistic to use in a prediction of E. Rather, we
examine the general approach of Eq. 8 by de¢ning
a scaling for sea-cli¡ retreat where we hypothesize
Eobserved should vary with Escaled , i.e.
Eobserved ¼ fðEscaled Þ ¼ fðDpre ðxÞ3Rmean ðxÞÞ
ð9Þ
where Rmean (x) is the mean of R(x) for all
R(x) s Dpre (x). Escaled appears to vary reasonably
well with Eobserved accounting for nearly 70% of
the variance (r2 = 0.69 for mean slope ; Fig. 12,
Table 1).
5. Discussion
Since the observed location and magnitude of
sea-cli¡ erosion could be positively correlated
293
with parameters representing the spatial variability and magnitude of wave runup, wave attack
appears important to the observed erosion. The
waves could serve to (1) remove debris that accumulates at the base of the cli¡ due to other processes forcing erosion, such as mass wasting of
rain-saturated sediments, and (2) attack the cli¡
base directly undermining the overburden directly
inducing erosion.
If mass wasting processes are important, as described for example by Hampton and Dingler
(1998), a sensible balance, similar to that described by Emery and Kuhn (1982), is as follows.
Mass wasting processes tend to decrease the cli¡
slope by moving sediment from higher on the cli¡
face to lower. Wave attack removes sediment that
accumulates at the cli¡ base by mass wasting, increasing the cli¡ slope. If wave attack is absent,
mass wasting would proceed until the cli¡ slope is
decreased su⁄ciently to limit further mass wasting. Hence, sustained cli¡ retreat cannot, in principle, proceed with mass wasting alone. Wave attack is required to maintain a relatively steep
slope and sustained cli¡ retreat.
On the other hand, waves could force both the
erosion, by undermining the cli¡, and removal of
the sediment at the cli¡’s base. Hence, waves
alone could induce a sustained cli¡ retreat.
Our lidar survey data, consisting of two snapshots in time, cannot distinguish the relative importance of these potential processes. Potentially,
each of the described processes has a role, yet
their individual dominance is elusive.
Table 1
Correlation coe⁄cients for di¡erent comparisons
Comparison
Runup equations
L
r2
Eobserved (measured) versus Escaled (Eq. 9)
Holman (Eq. 3)
Holman (Eq. 3)
Ruggiero et al. (Eq.
Holman (Eq. 3)
Holman (Eq. 3)
Holman (Eq. 3)
Holman (Eq. 3)
mean
variable
mean
variable
mean
variable
mean
variable
mean
variable
mean
variable
0.69
0.63
0.65
0.43
0.71
0.71
0.77
0.72
0.49
0.56
0.53
0.61
Hours Rx exceeds Beffective (Eq. 2) versus Eobserved (measured)
Hours Rz exceeds Dzeffective (measured) versus Eobserved (measured)
6)
6)
6)
6)
6)
6)
294
Fig. 11. Hours that R(z) s Deffective (z) (A) and hours that R(x) s Beffective (B) for Paci¢ca during the El Nin‹o winter.
295
Fig. 12. Plot of scaled sea-cli¡ erosion versus measured sea-cli¡ erosion.
6. Conclusions
(1) Along the central California coast the long
term (hundreds to thousands of years) net transport direction is from north to south. However,
on pocket beaches during the El Nin‹o winter of
1997^1998, sand was transported from south to
north and accumulated on the south sides of resistant headlands. This resulted in beach erosion
in the south ends of pocket beaches and deposition in the north ends. The beach morphology
evolved into prominent giant cusps with longshore spacing of 400^700 m.
(2) The beach evolution during the El Nin‹o
winter preferentially exposed sea cli¡s to wave
attack, creating hotspots of cli¡ retreat. Speci¢cally, beach width and the elevation of the beach
at the base of the cli¡ were minima where maximum shoreline erosion occurred due to both the
net northward transport and the development of
cusp troughs.
(3) The observed magnitude of sea-cli¡ retreat,
which reached 14 m, was correlated with the number of hours extreme wave runup exceeded certain
thresholds representing the protective capacity of
the beach during the El Nin‹o winter. A threshold
296
representing the width of the beach performed
better than a threshold representing the elevation
of the beach.
(4) A simple model was tested as a means to
scale sea-cli¡ retreat. The model predicts that the
cli¡ would erode the cross-shore distance that extreme wave runup exceeded the pre-El Nin‹o cli¡
position. The observed sea-cli¡ retreat was found
to vary with a scaled estimate of this predicted
erosion.
(5) We assume a balance between terrestrial
mass wasting which tends to decrease cli¡ slope
and marine wave attack which tends to increase
slope by removal of debris and eroding the cli¡
base.
Acknowledgements
This paper is part of a NASA (Sold Earth and
Natural Hazards Program) and USGS (Coastal
and Marine Program) collaboration. We thank
J. Sonntag, E.B. Fredericks, and J.K. Yungel of
EG and G, Wallops Island, VA, and Gaithersburg, MD; D. Eslinger, A. Meredith, and M.
Hearne of NOAA’s Coastal Services Center,
Charleston, SC; M. Hansen, K. Morgan, D.
Krohn, R. Peterson, B.J.Reynolds, and E. Nelson
of the USGS Center for Coastal Geology, St. Petersburg, FL; and B. Richmond, M. Hampton, A.
Gibbs, T. Reiss, J. Horsman, and G. Luepke of
the USGS, Menlo Park, CA. Furthermore, we
thank NOAA’s Aircraft Operations Center, Tampa, FL, for outstanding aircraft support and the
NOAA pilots Michele Finn, Steve Nokutis, and
Tom Strong who operated the aircraft within mission constraints with a high level of skill and professionalism.
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- Pacific Disaster Net

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