HomeMy WebLinkAboutSUP 06-10X2A; AGUA HEDIONDA OUTER LAGOON MAINTENANCE; BEACH EQUILIBRIUM ANALYSIS OF NORTH BEACH DISPOSAL OPTIONS FOR DREDGED SANDS FROM AGUA HEDIONDA LAGOON, CARLSBAD, CA; 2017-06-15Beach Equilibrium Analysis of North Beach Disposal Options for Dredged
Sands from Agua Hedionda Lagoon, Carlsbad, CA
Dune erosion exposes
pre-disposal beach berm
Submitted by:
sand remaining @ t = + 90 days
= 41,941 cubic yards
Scott A. Jenkins, Ph.D.
Dr Scott A. Jenkins Consulting
14765 Kalapana St
Poway, CA 92064
Submitted to:
Sheila Henika, P.E. MBA-TM
Cabrillo I LLC
Encina Power Station
4600 Carlsbad Blvd.
Carlsbad, CA 92008
Draft: 19 May 2017; Revised 15 June 2017
Dune sands accrete as
break-point bar
Executive Summary: A detailed set of beach profile surveys at North Beach in Carlsbad CA
were provided by Cabrillo Power I LLC, delineating beach surfaces before and after the
2104/2015 dredging of Agua Hedionda Lagoon, (AHL), which placed 64,968 yds3 between
Maple A venue and the north inlet jetty to Agua Hedionda Lagoon. The surveys were accurately
performed by Noble Engineers using differential GPS and known historic benchmarks. Three-
dimensional CAD models were lofted from the measured points along the four (4)North Beach
survey range lines (Cab 1-07 -Cab 1-10) to delineate the beach surfaces immediately before
North Beach dredge disposal (based on the 22 December 2014 profile measurements) and
immediately after dredge disposal (based on the 17 April 2017 profile measurements). When
these two surfaces were lofted together in a common reference frame, it was determined that
13,780 cubic yards of beach fill have been retained after placing 64,968 cubic yards on North
Beach between 23 March 2015 and 15 April 2015. This calculates to an average sand loss rate of
1,969 yds3/day and projects a sand retention time for the entire fill volume of only 33 days.
To understand the reasons for the poor sand retention characteristics of North Beach, a
baseline beach evolution study was conducted using the Coastal Evolution Model (CEM) to
hindcast the fate of beach fill placed on North Beach. The CEM was developed at the Scripps
Institution of Oceanography with a $1,000,000 grant from the Kavli Foundation, (see
http://repositories.cdlib.org/sio/techreport/58/ ), and is based on latest thermodynamic beach
equilibrium equations published in the Journal of Geophysical Research. Inputs to the CEM
baseline study were based on measured shoaling wave data, grain size data for the dredged
sands, and daily beach fill volumes were derived from the dredge monitoring reports to the
Regional Water Quality Control Board (Cabrillo, 2015) and from Cabrillo dredging data bases.
Between 1998 and 2015 there have been eight (8) different events when Agua Hedionda
dredged sands have been disposed as beach fill on North Beach. Historic dredged sand volumes
placed on North Beach ranged from 62,030 yds3 to 161,525 yds3. The CEM beach evolution
simulations of these events determined that the minimum sand loss rate occurs when North
Beach fill volumes equal to the critical mass Ve,;, = 79,471 yds3, which is the theoretical
maximum carrying capacity of North Beach for supporting a beach profile in equilibrium. The
carrying capacity of a beach is limited by the width of the wave-cut platform in the bedrock on
which beach sands have accumulated over geologic time scales. The wave-cut platform at North
Beach is only 550 ft. to 600 ft. in width. Many of the beaches throughout north San Diego
County are perched on narrow wave-cut platforms. The platforms are narrow because they were
carved by wave action into erosion resistant bedrock formations during the present high-stand in
sea level, and these narrow wave-cut platforms physically cannot hold large quantities of beach
sand; and often become fully denuded during periods of high-energy winter waves.
Another contributing factor to the limited carrying capacity of North Beach is that it is
exposed to a prevailing negative divergence of drift caused by the way the bathymetry
surrounding the Carlsbad Submarine Canyon influences wave shoaling at the southern end of
North Beach .. The presence of the Carlsbad Submarine Canyon creates a bright spot in the
shoaling wave pattern immediately north of the inlet jetties, where wave heights are locally
higher than further to the North around Maple Avenue. The prevailing littoral drift transports
beach sand southward throughout the entire Oceanside Littoral Cell; but at North Beach, the
alongshore in1balance in wave height causes higher southerly longshore transport rates of sand
exiting North Beach at the inlet jetties than enters North Beach at Maple A venue. This inequality
in sand transport rates between the north and south ends of North Beach is divergence of drift,
and when the sand transport rates are higher at the down-drift end of the beach, it becomes a
constant loss system referred to as negative divergence of drift. So, when beach fill volumes
exceed the critical mass of North Beach, the excess sand cannot be supported in equilibrium on
its narrow wave-cut platform and is quickly lost to the negative divergence of drift.
Historically, the CEM baseline study finds that when a standard 1 :10 (rise over run)
beach fill template is filled to critical mass, the theoretical minimum sand loss rate to negative
divergence of drift is 1,495 yds3/day, and the sand retention time is 53 days. When beach fill
sand volume is increased by 103% over critical mass (as occurred during the 2002/2003 dredge
event when 161,525 yds3 were placed on North Beach), the retention time is only increased by
26 % from T0 = 53 days to T0 = 67 days. This is not a good return on doubling the investment in
beach fill for North Beach because the sand loss rate increases by 61 % to 2,411 yds3/day, or an
increase in sand loss of 916 yds3 /day over what would have otherwise occurred if the beach fill
volume were limited to critical mass. Unfortunately, such increases in sand loss at North Beach
correlate with proportional increases of sand influx rates into Agua Hedionda Lagoon.
The 2014/2015 survey data show that AHL sand influx rates also increase when the fill
volumes are less than the critical mass. Sand influx rates in 2014/2015 were 1,969 yds3/day when
only 64,968 cubic yards were placed on North Beach (14,503 yds3 below critical mass
requirements). Bear in mind that the critical mass is the minimum volume of sand required to
establish an equilibrium beach profile on a wave-cut platform; and a beach is in its most stable
state with an equilibrium profile. But with a prevailing negative divergence of drift along North
Beach, equilibrium cannot be achieved due to insufficient sand volume, and consequently sand
loss rates increase with a destabilized non-equilibrium profile. The worst example of this in the
CEM baseline was the 2010/2011 dredging event when only 62,030 yds3 were placed on North
Beach, and sand loss rates rose to 2,050 yds3 /day with retention times of only 30 days.
Following CEM beach evolution analysis of the North Beach historic baseline, attention
was given to finding a more effective beach fill template that could increase sand retention using
beach fill from Agua Hedionda Lagoon dredging. Beach fill has typically been placed on
Carlsbad beaches using a standard beach fill template with a flat backshore platform and a I: I 0
(rise over run) seaward facing beach slope extending down to Oft. MLL W. This convention
dates back to the Regional Beach Sand Project, (AMEC, 2002). However, stable beach profiles
in Nature have a much more gradual, curving profile with slopes that range between 1 :50 to
3: 100. Formulations of equilibrium beach profiles are found in the U.S. Army Corps of
Engineers Shore Protection Manual and later the Coastal Engineering Manual; and the latest
most advanced formulation is known as the elliptic cycloids. The elliptic cycloid formulation can
account for continuous variations in the equilibrium beach profile due to variability in wave
height, period and direction when occurring in combination with variations in beach sediment
grain size and beach sand volume. Therefore, a new beach fill template has been proposed here
for North Beach referred to as the cycloid-dune template (see Figures ES 1-4). The shape of the
template is based on the extremal elliptic cycloid which is the equilibrium profile for the highest
wave in the period of record. But the extremal elliptic cycloid extends below the MLL W tide line
and earth moving equipment which spread out the beach fill cannot work below MLL W . So, the
template truncates the extremal elliptic cycloid at MLL W and places the residual volume of
critical mass (totaling 43 ,200 yds3) in a back-beach dune that stretches 3,200 ft. from the Agua
Hedionda north inlet jetty to Maple A venue.
While an elliptic cycloid is an equilibrium beach surface, it does not produce a state of
zero sand loss in the presence of a negative divergence of drift, which is the persistent littoral
drift state along North Beach. When the divergence of drift is negative, the equilibrium cycloidal
beach profile will progressively shift landward as it loses sand to negative divergence of drift,
eventually intersecting the basement surface of the critical mass envelope. Once this happens,
then the cycloidal shape of the profile is disrupted, and the equilibrium state of the profile is lost.
The concept behind the cycloid-dune template is that, as the cycloid begins to approach an
intersection with the basement surface of the critical mass envelope, (under the erosional effects
of continued negative divergence of drift), it also intersects the base of the dune and receives
additional sediment cover as the dune erodes and spreads out downslope across the still intact
cycloidal surface. Thus, the dune acts as a restoring mechanism that re-supplies the cycloid with
sand lost to negative divergence of drift.
The construction method envisioned for the cycloid-dune template begins with building
the back-beach dune portion first, starting at the north inlet jetty and adding sections to the
dredge pipeline until the build-out of the dune reaches Maple Ave. Building the dune first creates
a "safe" reservoir of sand before the template can be fully constructed, and sand from this
reservoir is only released to the lower eroded basement surface during periods of the highest
tides and waves. After the buildout of the dune to Maple Ave, the cycloid portion of the template
is laid out beginning from the toe of the dune and spreading the material down slope to MLLW,
and working back towards the north inlet jetty, removing pipeline sections as the cycloids are
completed
CEM beach evolution simulations of the cycloid-dune template show significant
improvements in sand loss rate and retention time relative to the historic baseline. Again, the
most efficient use of Agua Hedionda dredged sands occurs when the cycloid-dune template is
filled to no more than critical mass (79,471 yds3), which reduces average sand loss rates on
North Beach to an absolute minimum of 417 yds3 /day, while extending retention time to 190.6
days. This is a 3.6 fold improvement in sand retention time over historical dredge disposal
practices at North Beach, which could result in a reduction of sand influx rates into Agua
Hedionda Lagoon by a similar factor during the first six (6) months following North Beach
disposal. If the cycloid-dune template is filled to more than critical mass by adding more sand to
the back-beach dune, then North Beach retention time will increase beyond 190.6 days. If the
reserve sand volume in the dune were more than doubled to 95,529 yds3 (achieving a total
placement volume of V0 = 175,000 yds3) then retention time could be extended to a maximum of
222 days. But, again, this is not a good return on doubling the investment in reserve beach fill for
North Beach because retention time is only increased by an extra month while the sand loss rate
increases by 89 % to 787 yds3/day. Furthermore, it is simply not possible to place more sand than
the critical mass in the back beach dune and not have much of the dune sand prematurely erode
during periods of high waves and high tides, because the enlarged dune encroaches further
seaward into the middle bar-berm portion of the profile that is subject to more frequent wave
attack.
On the other hand, under-filling the cycloid-dune template, (by building a reduced dune),
leads to accelerated sand loss rates and reduced retention times. The prevailing negative
divergence of drift causes the initial cycloid profile in the lower portion of the template to shift
landward, and once intersection with the basement surface of the critical mass envelope occurs,
there are insufficient sand reserves in the reduced dune to resupply the cycloid in the presence of
continued negative divergence of drift. Once the reserve sand supply in the dune is exhausted,
the cycloidal shape of the profile is disrupted, and the equilibrium state of the profile is lost.
Even so, if the cycloid-dune template is filled to a volume equivalent to the 2104/2015 North
Beach disposal event (V0 = 64,968 yds3) by using a dune containing only 28,697 yds3, then sand
retention times are still significantly better than what was achieved using the standard 1: 10 (rise
over run) template. With the cycloid-dune template, retention times with only 64,968 yds3 of
beach fill were T0 = 11 7 days and sand loss rates were still small , 554 yds3/day, or a factor of 2.2
better than what was achieved using standard North Beach disposal practices during the
2104/2015 dredge event. With even smaller beach fill volumes, the cycloid-dune retention times
and sand loss rates rapidly degrade, but retention times remain equivalent to those of the
2104/201 5 North Beach disposal event for beach fill volumes as low as 37,000 yds3, fo r which
the back beach dune was reduced to vanishingly small.
25
24
23
22
21
20
19
18
17
16
15
i14
....1 13
~ 12 . 11
510
C: 9
.Q 8 ~ 7 Q.) w 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
----------, --------------------
'"" ,,
j
I
I
~
North Beach Profiles, Cab 1-07
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
\
\
' \
' ' I
" \.
'\ \.
\ '\
' .,
'~ " ... , ~
'' ,,
~ , ..
r-... "''-r--.. .....
"' .....
' ...... ... -.. \ ....... ,....
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Distance offshore from benchmark (ft.)
Figure ES-1: Proposed beach fill template for North Beach range Cab-107, based on the
extremal equilibrium profil e truncated at 0 ft. MLL W with a back beach dune to hold-and-
release residual critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 1998772.8
Easting (ft): 6226391.4
25
24
23
22
21
20
19
18
17
16
15
i'14
...J 13 ~ 12
. 11
~10
C: 9
.Q 8 iii > 7 Q.) ill 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
---------------. -. ------------
A
I \
\ ,
' i/
I =
North Beach Profiles, Cab 1-08
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
\
\
\.
'\ ~:::s. '\
\
\•
\. \.
I'\; \. ,,,,,
I\ "-
,.,, '
' ' I\. ' I',._ ......
I'-.. ........
I"-" ""r,... ......
r--.. ......
I"----1, .... ......
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Distance offshore from benchmark (ft.)
Figure ES-2: Proposed beach fill template for North Beach range Cab-108, based on the
extremal equilibrium profile truncated at O ft. MLL W with a back beach dune to hold-and-
release residual critical mass as the profile adj usts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 1999973.2
Easting (ft): 6225671.9
25
24
23
22
21
20
19
18
17
16
15
~ 14
...J 13 ~ 12
. 11
$10
C: 9
.Q 8 iii > 7 Q) w 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
--------' -I/ -., --------------------
A
I \
'
\
\
' __..,.,::A ' \
" \
I\.,
' I\
'
North Beach Profiles, Cab 1-09
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
\.
' "' ' ' \. "' "' ' ........ ~ ....
K_ ........ , .... ......
r---..: .....
'"" ----........... .....
0 W ~ 00 M 100 1W 1~ 100 1M ~ ffl ~ ~ ~ ~ m ~ ~ ~ ~
Distance offshore from benchmark (ft.)
Figure ES-3: Proposed beach fill template for North Beach range Cab-I09, based on the
extremal equilibrium profile truncated at 0 ft. MLL W with a back beach dune to hold-and-
release residual critical mass as the profile adj usts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 2000268.7
Easting (ft): 6225483.3
25
24
23
22
21
20
19
18
17
16
15
i 14
...J 13 :E 12
. 11
$10
C: 9 ,g 8
~ 7 Q) ill 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-----j -I -I -I --V ------------------. .
/\I
I \
\
\
\
" ' ' .....-N
I
I
'\
North Beach Profiles, Cab 1-10
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
'I.
' ' ''-',
\. . ....
" ' " .......
'\ ' ......, ~ ....
1--... .....
"-......
I'..., ......
r-,,. ...... ,.., "" f'<c ...
........... ' r----1'-_..,...., t--..
I I I I I I
0 W ~ 00 M 100 1W 1~ 100 1M ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Distance offshore from benchmark (ft.)
Figure ES-4: Proposed beach fill template for North Beach range Cab-Il0, based on the
extremal equilibrium profile truncated at 0 ft. MLL W with a back beach dune to hold-and-
release residual critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 2000741.1
Easting (ft): 6225218.1
Beach Equilibrium Analysis of North Beach Disposal Options for Dredged
Sands from Agua Hedionda Lagoon, Carlsbad, CA
by: Scott A. Jenkins, Ph.D.
1) Beach Profile Surveys and Dredge Disposal:
Four beach profile survey range lines were monitored on North Beach (between Maple
A venue and the north inlet jetty to Agua Hedionda Lagoon) before and after the 2014/15 Agua
Hedionda Lagoon dredging event. These surveys are plotted in Figures 1-4, and labeled from
south to north as: Cab 1-07, Cab 1-08, Cab 1-09, and Cab 1-10. The captions in Figures 1-4 also
give the California planar coordinates of the bench mark for each range line. Each range line was
surveyed four times, three times prior to the most recent Agua Hedionda beach disposal event,
17
16
15
14
13
12
11
10
9
8
~ 7
...J 6
...J 5 ~ 4 ~ 3
C: 2 .Q ro 1
~ 0
W -1
-2
-3
-4
-5
-6
-7
-8
-9
-10
North Beach Profiles, Cab 1-07
17 April 2015
22 December 2014
6 November 2014
5 September 2013
-11 ~ ........... ,...... ........... ,...... ........... l"'l""l'""l""l"'l""P"'ll"'l""l'""l""l"'l""P"'ll"'l""l'""l""l""l"'l"'l"'l""l'"'T"'l""l"'l"'rT"l"'T"'l""l"'l"'rT"l"TT ........... ,...... ..... 'l"T'I
0 100
Coordinates of Bench Mark:
Northing (ft): 1998772.8
Easting (ft): 6226391.4
200 300 400 500 600 700
Distance offshore from benchmark (ft.)
Figure 1: Measured beach profiles at survey range Cab 1-07 on North Beach, before and after
the most recent Agua Hedionda Lagoon dredging, which was begun on 31 December 20 14 and
completed on 15 April 2015. See Figure 5 for bench mark locations.
17
16
15
14
13
12
11
10
9
8
s: 7 _, 6 _, 5 ~ 4 ~ 3
C: 2 .Q 1 ro > 0 Q)
jjj -1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
0 100
Coordinates of Bench Mark:
Northing (ft): 1999973.2
Easting (ft): 6225671.9
North Beach Profiles, Cab 1-08
----17 April 2015
----22 December2014
----6 November 2014
----5 September 2013
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 2: Measured beach profiles at survey range Cab I-08 on North Beach, before and after
the most recent Agua Hedionda Lagoon dredging, which was begun on 3 1 December 2014 and
completed on 15 April 2015. See Figure 5 for bench mark locations.
17
16 North Beach Profiles, Cab 1-09
15 17 April 2015
14 22 December 2014
13 6 November 2014
12
11
5 September 2013
10
9
8
~ 7
...J 6
...J 5 :E 4 ~ 3
C: 2 .Q ro 1
> 0 (1)
[i] -1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
0 100 200 300 400 500
Distance offshore from benchmark (ft.)
Coordinates of Bench Mark:
Northing (ft): 2000268.7
Easting (ft): 6225483.3
+
600 700
Figure 3: Measured beach profiles at survey range Cab 1-09 on North Beach, before and after
the most recent Agua Hedionda Lagoon dredging, which was begun on 31 December 20 14 and
completed on 15 April 2015. See Figure 5 for bench mark locations.
18
17
16
15
14
13
12
11
10
9
~ 8
...J 7 ...J ~ 6
~ 5
C 4
.Q 3 ro > 2
Q) 1 ijj
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
0 100
Coordinates of Bench Mark:
Northing (ft): 2000741.1
Easting (ft): 6225218.1
North Beach Profiles, Cab 1-1 O
----17 April 2015
----22 December 2014
----6 November 2014
----5 September 2013
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 4: Measured beach profiles at survey range Cab I-10 on North Beach, before and after
the most recent Agua Hedionda Lagoon dredging, which was begun on 31 December 201 4 and
completed on 15 April 2015. See Figure 5 for bench mark locations.
4
3 E
25
20
u Q.) 1/)
-o 15 0 ·;::
Q.) ~
Q.) 10 > ro ~
5
COi P Station #043 -Camp Pendelton Nearshore, 33.2198 N , -117.4394 W
2.3-year mean = 0.97 m ~ Hrna"= 3.8 m <H> = 0.95 m
2.3-year mean = 13.8 sec <T> = 13.8 sec
\
0 ........................ ___.___.___.__.__.__,--'--''--'--'--'--,...._,...._,...._..__..__..__..__..,__..,___.___.__...._...._..,__
360 l
~ 320 ~ ... ~ 0
c: 280 -.2 0 ~ i5 240
Q.) > ro ~ 200
2.3-year mean = 276°
1/1/13 1/1/14 1/1/15
Figure 6a: Shoaled significant wave heights, periods and directions at Carlsbad State
Beach based on back refraction of wave monitoring data from CDIP Station 043 at Camp
Pendleton during the beach survey period. Data shown in black occurred during the
2014/15 Agua Hedionda Lagoon dredging event.
2) North Beach Sand Retention Issues:
The poor sand retention characteristics of North Beach (the receiver beach of
back-passing sands) are due to several factors including: the timing of placement of back-
passing sands, non-equilibrium distribution of those sands, unfavorable geomorphology,
and placing more sand than the geomorphology can support in equilibrium. Beginning
with timing, the largest fraction of sand that is lost from the beach fill placed on North
Beach occurs in the first few months after placement. Because the least tern nesting
season restricts Agua Hedionda Lagoon dredging to the winter season, placement of the
beach fill typically occurs in the midst of the onslaught of the largest winter waves.
However, during the period when sands from the 2014/15 dredge event were being
placed on North Beach, (23 March 2015 -15 April 2015) the winter waves were not
unusually intense, with the highest waves reach Hmax = 1.94 m while average significant
wave heights were <H> = 1.1 m, with an average wave period of <T> = 13 .8 sec and a
typical northwesterly wave direction averaging < a >= 279°, ( cf Figure 6b ). But even
these rather ordinary winter waves can exert significant erosional effects due to the way
waves refract and shoal at North Beach. The presence of the Carlsbad Submarine Canyon
immediately south of Agua Hedionda Lagoon creates a bright spot in the shoaling wave
pattern immediately north of the inlet jetties, where wave heights are locally higher than
further to the North around Maple Ave. This alongshore imbalance in wave energy leads
to a negative divergence of drift in the longshore transport rates, which in turn causes
higher southerly longshore transport rates of sand exiting North Beach at the inlet jetties
than enters North Beach at Maple Ave, (see Section 5 for more detail).
So we turn our attention to how the North Beach fill has been placed and what
quantities. Engineered beach fill has typically been placed on Carlsbad beaches with a
1: 10 (rise over run) slope. This convention dates back to the Regional Beach Sand
Project, (AMEC, 2002). However, stable beach profiles in Nature have a much more
gradual, curving profile with slopes that range between 1 :50 or 3: 100, (Inman et al.,
1993). The theory on equilibrium beach profiles began with Dean (1977) and Bowen
( 1980) who developed formulations for an equilibrium profile having the form, h = Ax 111 ,
where h is the local water depth, x is the horizontal distance offshore, m = 2/3, and A
is an empirical factor. Later Dean (1991) developed analytic approximations for the
empirical factor, A, and that formulation was incorporated into the U.S. Army Corps of
Engineers Shore Protection Manual and later the Coastal Engineering Manual. However,
recently Jenkins and Inman, (2006), proved that the Dean (1977 and 1991) solutions are
not unique, and represent only one of a family of equilibrium beach profiles known as
elliptic cycloids. The elliptic cycloid formulation can account for continuous variations in
the equilibrium beach profile due to variability in wave height, period and direction when
occurring in combination with variations in beach sediment grain size and beach sand
volume. Equilibrium beach profiles obey the maximum entropy production formulation
of the second law of thermodynamics, and are the most efficient shape for a beach profile
because it adjusts itself to dissipate all of the available wave energy. When the waves
encounter an inefficient, non-equilibrium beach shape, such as a steeply sloping beach fill
templates, then the wave energy is not fully dissipated and the excess wave energy begins
eroding and moving that beach fill around until an equilibrium profile is finally achieved.
While this is occurring, the beach fill can be highly mobile, particularly in large winter
waves; and at Carlsbad, the net southward flowing longshore currents (particularly in
winter) will rapidly transport the eroded beach fill from North Beach toward the south
and the inlet to Agua Hedionda Lagoon.
There are also geomorphic factors that contribute to poor retention of Agua
Hedionda dredge sands at the North Beach disposal site. A sandy beach cannot be
supported in equilibrium against wave forces without a wave-cut platform in the bed rock
to provide a foundation. Wave cut platforms are notches that have been eroded in the bed
rock during protracted still-stands in sea level. Once formed, sediment collects in these
notches forming a beach which is subsequently molded into an equilibrium shape by
wave action. Figure 7a shows an annotated seismic reflection profile measured by USGS
across the continental shelf off Carlsbad CA on range 223X of the 1991 Kolpack surveys,
(Kolpack, 1991). It shows a series of wave-cut platforms that were formed at present and
earlier still-stands of sea level, and subsequently covered with sediment. The most
striking feature in Figure 7a is how much more pronounced the paleo wave-cut platforms
are than the modem platform; and how very thin the sediment cover is over the modem
wave-cut platform, as compared with the thickness of Holocene sediment over the paleo
platforms. Although the paleo platforms have been subjected to longer periods of
sedimentation, the geometric constraints imposed by small wave-cut platforms prevent
them from retaining thick layers of sediment cover.
Many of the beaches throughout north San Diego County are perched on narrow
wave-cut platforms. The platforms are narrow because they were carved by wave action
from erosion resistant Del Mar formation during the present high-stand in sea level, and
these narrow wave-cut platforms physically cannot hold large quantities of beach sand;
and often become fully denuded during periods of high-energy winter waves, as shown in
Figure 7b. Sub-bottom surveys by Elwany, et al., (1999) discovered narrow wave cut
platforms and exposed hard bottom substrate in the surfzone and nearshore at North
Beach and South Beach (Figure 8) while 1884 railroad surveys reveal beach cobble
ridges before the influence of Mankind at Agua Hedionda Slough, (e.g. HWY 101 and
the deep water lagoon). When beach cobble ridges and hard-bottom features are found
this close to shore, it indicates that these beaches (particularly, North Beach and South
Beach) are not geomorphically well suited to retain large volumes of sand. In th_e
_Qarticular case of NortKBeach, attempts to back-pass and place more sand there than its
carrying capacity will simply result in low retention time and increased sand influx into
Agua Hedionda Lagoon. The remainder of this report focuses on determination of the
carrying capacity at North Beach and the optimal distribution of that carrying capacity
within a beach fill template in order to maximize sand retention time of dredged sands.
3) Critical Mass and North Beach Equilibrium Profiles:
The critical mass is the minimum volume of sediment cover required to maintain
equilibrium beach profiles and represents the nominal carrying capacity of a particular
beach. When a long term collection of beach profiles are plotted together over a broad
range of wave heights, a well-defined envelope of variability becomes apparent, (Figure
9a). This envelope of profile variability is referred to as the critical mass envelope, and
the volume of sand within critical mass envelope, Ve, increases with increasing wave
height and period but decreases with increasing beach grain size, as shown in Figure 9b.
The critical mass envelope is always limited by the breadth of the wave cut platform,
2
1.8
1.6
E 1.4
~ 1.2
·a5 1
I
~ 0.8
ctl ~ 0.6
0.4
0.2
CDIP Station #043-Camp Pendelton Nearshore, 33.2198 N, -117.4394 W
0 ~----.__.__..__......___.__.___.___.___.___. ___ .__.__..____.__.__.___.___.___.___._.__...__....._....__.__
20
u 16
Q.)
Cl)
u 0
-~ 12
CL
Q.) > co ~ 8
3/23/15 3/28/15 4/2/15 417/15 4/12/15 4/17/15 J~~6-day mean= 13.8 sec
4 ___._..__...._.,____.___,.__.__.___.____,_____._.__..__.,____.____.__.__.___.____,__,_.___.._...._____.____.__
320
a, 300 ::, .... I;"
c:: 280 .Q u ~ o 260
Q.) > co ~ 240
3/23/15
l
3/23/15
3/28/15 4/2/15 417/15 4/12/15 4/17/15
26-day mean = 279°
I
3/28/15 4/2/15 417/15 4/12/15 4/17/15
Figure 6b: Shoaled significant wave heights, periods and directions at Carlsbad State
Beach based on back refraction of wave monitoring data from CDIP Station 043 at Camp
Pendleton during the North Beach disposal period, 23 March-15 April 2015.
(5 September 2013, 6 November 2014 and 22 December 2014); and once immediately upon
completion of beach disposal on 17 April 2015. The dredge logs indicate that no dredging or
beach disposal was begun until 31 December 2014. Since the 22 December 2014 beach surveys
were performed just 9 days prior to onset of lagoon dredging, these surveys captured the receiver
beaches close their most denuded condition. In fact there had been no placement of new sands on
these beaches since April 2011; and inspection of the profile measurements in Figures 1-4
indicates little profile change between the 6 November 2014 and 22 December 2014 surveys
because much of the beach surface was exposed hard-bottom substrate (bedrock, cobbles and
basal conglomerate, see Figure 7).
Middle Beach was the first to receive beach fill from the 2014/15 dredge cycle beginning
on 31 December 2014, and received a total of 156,056 cubic yards; followed by South Beach that
began receiving 73,637 cubic yards of beach fill beginning on 21 February 2015. Unlike
previous dredge events, North Beach was the last to receive beach fill, and 64,968 cubic yards
were placed there between 23 March 2015 and 15 April 2015, (cf. Appendix-A). Therefore, the
17 April 2015 beach profile surveys represent the receiver beaches in their most built-out state,
because these surveys were performed only two days after the beach disposal of dredged sands
from Agua Hedionda was completed.
Three-dimensional CAD models were lofted from the measured points along the four (4)
North Beach survey range lines (Cab 1-07 -Cab 1-10) to delineate the beach surfaces
immediately before dredge disposal (based on the 22 December 2014 profile measurements) and
immediately after dredge disposal (based on the 17 April 2017 profile measurements). When
these two surfaces were lofted together in a common reference frame ( as determined by the
bench marks of each survey range line), places where the 17 April 2015 surface intersected the
22 December 2014 surface identified areas along the receiver beach where sand was not retained.
Conversely, places where these two beach surfaces remained separated identified areas where
dredged sands were being retained to at least some degree. This is shown in Figure 5 where the
fully built-out beach surface (post-dredge disposal, 17 April 2015) is lofted in brown, and the
severely eroded beach surface (pre dredge disposal, 22 December 2014) is lofted in silver. It is
clear from the large areas of silver in this composite CAD model, that beach fill has been poorly
retained on North Beach (cf. Cab 1-07 -Cab 1-10) despite the fact that this was the last beach to
receive beach fill. The eroded silver areas on North Beach between Cab I-07 and Cab I-10 in
Figure 5 are especially prominent in the seaward half of the bar-berm section of the beach
profile, but also in the upper portions of the profile on the berm itself. The mass properties tool
of the Solid Works 3-D CAD software was invoked to calculate the difference in beach volume
between the surfaces defined by the 22 December 2014 and the 17 April 2015 surveys, and
determined that 13,780 cubic yards of beach fill have been retained after placing 64,968 cubic
yards on North Beach between 23 March 2015 and 15 April 2015. This means that only 21 % of
the beach fill had been retained over a 3 ½ week period that ended just two days after completion
of pumping beach fill to North Beach! Clearly sand was being lost at a high rate (1,969 yds3/day,
or about 1/3 to 1/2 daily pumping rates) during placement of sand in the beach fill template. A
further concern is that the beach fill placed on North Beach is up-drift of the lagoon inlet in the
prevailing southerly littoral drift, particularly during the winter season when the large waves that
erode the beach are from the northwest. Consequently, when beach fill is not retained it is
immediately ingested by Agua Hedionda Lagoon, where it provides no useful function in
protecting the shoreline against erosion and wave overtopping, and where it restricts the tidal
prism of the lagoon and degrades the lagoon water quality.
-----------------0 2000 1000
Northing, ft
0
Figure 5: Three-dimensional composite CAD model of two overlaid beach surfaces on North Beach, 1) immediately before dredge disposal (as
delineated in silver from the 22 December 2014 profile measurements) and 2) immediately after dredge disposal (as delineated in brown by the 17
April 2015 profile measurements). CAD model shown with 10 to 1 vertical exaggeration
a)
-----MSL-----~--------=,=;;,:;-~0
present
wave-cut
platform
20 E
-40 ..c: -a. sediment
country rock
60 ~
-----paleo
wave-cut platform vertical exaggeration 23x
80
Ul<.--'-------'----J'----L--------'-------''----'----'-----'-----'---____._______._ _ __,________.___, 1 0 0
7 6 5 4 3 2 1 0
Distance , km
Figure 7: Wave-cut platforms in North San Diego County: a) Annotation ofUSGS
Geopulse sub-bottom seismic profile along range line 223-X in the inner shelf off
Carlsbad showing present and ancient wave cut platforms (after Kolpack, 1991); b)
exposed wave cut platform in Solana Beach during the 1983 El-Nino winter.
362000
361000 IN
360000
359000 1
358000
357000
Pacific Ocean
356000
·----........_
355000 D C A I,
354000
D 30-60% hard substrate
D 60-100% hard substrate
353000--Scale(ft.)
0 1000 2000 3000
352000
Encz311.s,f
r1V 7128198
1660000 1661000 1662000 1663000 1664000 1665000 1666000 1667000
. . . --:-s.-,.· ·-·· ·-·· ..... --... ---. .,. ...... ______ , .... ___ _ ,--~f ~ -<,_7
Figure 8: Nearshore survey (left) showing exposed rocky reefs, outcrops and other hard bottom substrate; and (right) 1884 railroad
survey map showing beach cobble ridge, both indicating minimal sediment cover on the beaches around Agua Hedionda Lagoon.
which forms a hard-bottom boundary condition on the critical mass envelope. The best way to
calculate the critical mass is to find the volume between the wave cut platform ( or its layer of
basal conglomerate) and the elliptic cycloid equilibrium profile that corresponds to the native
beach grain size in combination with the wave height and period of the extreme event wave in
the period ofrecord. The volume integral between the surfaces of the wave cut platform and the
extremal event elliptic cycloid then give the critical mass volume. In the case of North Beach, the
sub-bottom reflection data is too spotty between Maple A venue and the north inlet jetty of Agua
Hedionda Lagoon to resolve the complete surface of the wave-cut platform along the 3,200 ft.
length of the North Beach disposal site (between north inlet jetty to Maple Avenue). Therefore
we will use the surface given by the 22 December 2014 beach surveys as a surrogate bottom of
the critical mass envelope. This is a reasonable approximation because there has been no
placement of new sands on North Beach since the 2010/11 dredge event, which only placed
62,030 cubic yards on North Beach in April 2011 (cf. Appendix-A). Inspection of the profile
measurements in Figures 1-4 indicates little profile change between the 6 November 2014 and 22
December 2014 surveys because much of the beach surface was exposed hard-bottom substrate
(bedrock, cobbles and basal conglomerate).
The extremal elliptic cycloid equilibrium profile is a curve that is traced by a point on the
circumference of a rolling ellipse, see Figure 1 Ob. It is calculated from Jenkins and Inman (2006)
using the following:
h = 1rE X ( 1-COS 0 J + Z
2f!1) 0-sin0 I
(1)
Here Z1 is the elevation of the berm crest (cf. Figure 10a) given by Hunt's Formula [Hunt, 1959;
Guza and Thornton, 1985; Raubenheimer and Guza, 1996]:
z 1 =-rHb (2)
In equation (2), r is the runup factor taken herein as r = 0. 76, and H b is the breaking wave
height. The cycloid in (1) is based on the elliptic integral of the second kind that has an analytic
approximation, J!2l = J (2 -e 2 ) I 2 , where e is the eccentricity of the ellipse given by
e = J 1-b2 I a2 , with, semi-major and semi-minor axes are a, b, ( cf. Figure 1 Ob). The wave
parameter,e , in equation (1) is given by:
( J
l/2 4/5 ( )2/5 Hb a-H,,, e =a--.::::----Y g -2"5 gy (3)
here a= 21r/period is radian frequency, H 00 is incident wave height, g is the acceleration of
gravity, and y is the wave breaking criteria taken as y= 0.8. The rolling angle of the ellipse is:
(4)
10
a)
___ ........
15
V.E 33x
1600 1200 800 400 0
Distance, m
2500 E b) --D1 = 120 Jlffl. 0, = 80 µm (Rockport, TX) -.. --D1 = 200 Jlffl. O, = 100 µm (Torrey Pines, CA) "' E 2000 --D1=200JJffl.0,=20011m (Sc,ws Beach, CA) ---01 = 400 Jlffl, 0, = 150 µm (Duck. NC)
),,0
en 1500 Cl) ro :::E
"iii ~ 1000 ·.::
(.) -0
Q) 500 E ::J ~ 0
0 1 2 3 4 5
rms Incident Wave Height, H ,m
3 c) E r ' --01 = 120 Jlffl, 0, = 80 µm (Rod<port, TX)
" --D, = 2001im, 0, = 100 µm (T~ Pines, CA) u.J' en --D, = 200 µm, 0, = 200 µm (Saws Beach, CA)
Cl) 2 '---D, = 400 µm, O, = 150 µm (Duck, NC) Q) ~ C: ..l<: -~ ..c: t-
Cl) Cl) ro 1 :::E
"iii 2 ·.:: (.)
0
1600 1200 800 400 0
Distance, m
Figure 9: Features of the critical mass of sand: a) critical mass envelope for waves ranging from
lm to Sm in height; b) volume of critical mass as a function of wave height and sediment grain
size; c) variation in the thickness of the critical mass as a function of distance offshore.
a.
.5
0 r E ~-5 I\
-------MSL ------+
.c he g-10
0
15
20
b. type-a cycloid
C.
X P(3)
\
\
0=7t t \ h=2a
' ' ' .... -.. -
a) profiles: eccentricity and shear stress linearity
----e= 0.845 ;n=3
e = 0.798 : n = 2
----e=0.707;n= 1
----e=0.447 ;n=O
----e = O ; n = -0.33 ; brachistochrone solution
700 600 500 400 300 200
Cross-Shore Distance x2 ,m
P(2)
100
\
h
0
2
4
6
8
10
12
14
0
Bench
Mark
fO=O
_J
(/)
~
E
N J::
.c a. Q) 0
Figure 10. Equilibrium beach profile theory: a) nomenclature, b) mathematical basis for an
elliptic cycloid, c) Typical range of elliptic cycloids on a 700 m wide wave-cut platform.
Cycloids with eccentricity e = 0 are the same basic formulation as the original Dean ( 1977 and
1991) solutions in the U.S. Army Corps of Engineers Coastal Engineering Manual
where A is the shoaling factor relating breaker height to incident wave height, A = Hrol Hb,
( ½ )1/5
which for shoaling Airy waves, becomes A = 2 215 H 1.:o5 a-gy . The closure depth, he in
equation (4) is grain size and wave period dependent and is given by:
(5)
where k =a-I J ghc is the shallow water form of the wave number, Ke and 1/f -2.0 are non-
dimensional empirical parameters, set at Ke= 2.0 and lfJ -0.33; D50 is the median grain size;
and Do is a reference grain size taken as D0 = 100 µ m. Equation (5) is transcendental and is
solved numerically within the CEM.
Calculation of the extremal elliptic cycloid equilibrium profile at North Beach requires
knowledge of the characteristic median grain size, D50, of the dredged sediments to be placed
there. Recent sediment grain size analyses by Merkel, (2008) based on three sampling locations
on the flood tide bar in the West Basin of Agua Hedionda Lagoon (Samples Ll -L3) were
compared against native sediments on the three receiver beaches (RB 1-RB3). These grain size
distributions are plotted in Figure 11. Note North Beach is represented by samples RB 1. Grain
sizes at the lagoon sample sites and beach sites were similar with median grain sizes of 0.32
millimeters (320 microns) on the flood tide bar in the West Basin of Agua Hedionda, while
residual sediments that still remained on North Beach prior to disposal of material from the
2008/09 dredging averaged 0.374 millimeters (374 microns).
To determine the highest waves to effect North Beach disposal, the waves measured at ½
hour sampling intervals at CDIP Station 043 were back refracted into deep water from the
monitoring location off Camp Pendleton, and then forward refracted into North Beach. An
example ofthis procedure is shown in Figure 12 for a wave occurring 8 January 2002. This effort
produced a continuous wave record throughout the historic period when North Beach disposal of
Agua Hedionda Lagoon dredged sands was practiced, (1998-2015). The highest energy wave
( extremal) event occurred in January 2007, when a Gulf of Alaska storm brought 4.8 m high
waves approaching Carlsbad at 276 ° with a 15 second periods. This extreme event wave was
used to calculate the extremal elliptic cycloids on North Beach.
To calculate the critical mass of North Beach, we combine the extremal waves with the
D50 grain size values from Figure 11 to solve equations (1)-(5) for the extremal elliptic cycloid
profile. These profiles are plotted on the North Beach Range survey range lines (Cab-1-07 -Cab
1-10) in Figures 14-17. These profiles represent the beach shape that can be sustained in an
equilibrium state during the most severe wave events of the 1998-2015 North Beach disposal
period. These profiles form the top of the critical mass envelope, while the most eroded profile
(from the 22 December 2014 surveys) to have occurred in that same period ofrecord defines the
bottom of critical mass envelope. When lofted in the 3-D CAD SolidWorks software, the
SolidWorks volume tool calculates the critical mass envelope to hold of 79,471 cubic yards
A Dredge Area L 1
• Dredge Area L2
• Dredge Area L3 • A :. . • Reciever Beach RB 1 • • Reciever Beach RB2
• Reciever Beach RB3 A •• A
•
• A •• A
• • •
• •• •
A •
• • • •
A •
10 1 Grain Size (mm) 0.1
100
90
80
Q)
C> cu
70 -C:
Q) c., ... Q)
60 ~ .r::
C>
Q)
3: 50 .;..; .r::
C>
Q)
40 3:
Q) > .:;
~ 30 :1 E
20
10
0
0.01
:,
(.)
Figure 11: Grain size distributions form Agua Hedionda Lagoon (Samples LI -L3) and from
the receiver beaches (RB1-RB3). Note North Beach is represented by samples RBI, (from
Merkel, 2008).
33.200
33.175
33.150
33.125
33.100
33.075
117.450 11 7.425 117.400
0
117.375
Longitude
2 3
El.Jena\1&a Lagoon
117.350 117.325
4 5
Incident Wave Height at CDIP-043 = 1.66 m, Period = 18 sec, Direction = 263 deg
117.300
Figure 12: Regional wave shoaling during 8 January 2002 from back-refraction of wave
monitoring data at CDIP Satation # 043 in 20 m local depth off Camp Pendleton.
Carlsbad Waves Derived from CDIP Station #043 -Camp Pendelton, 33.2198° N , -117.4394° W
5
4
E
j;: 3 0)
"iij
I
~ 2
C'0 ~
25
20
u Q)
(/)
-o 15 0 ·.:::
Q) a..
Q) 10 > C'0 ~
5
360
340
Q) 320
2 ~ 300 0
c: 280 0
U 260 ~ i:S 240
~ 220 C'0 ~ 200
180
1998
1998
Hmax = 4.8 m ----~--..
long term mean= 0.95 m
2000 2002 2004 2006
2000 2002 2004 2006
2008
2008
long-term mean = 272°
2010 2012 2014 2016
2010 2012 2014 2016
160 ----r----.--.---,.---,--..--.--.----.--..---.--..----.--.....---.---r----r--.---,
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
Figure 13: Shoaled significant wave heights, periods and directions at Carlsbad State Beach
based on back refraction of wave monitoring data from CDIP Station 043 at Camp Pendleton for
the period ofrecord ofNorth Beach disposal, 1998-2016.
18
16
14
12
10
-8
~ ...J 6 ...J ~
E. 4
C
.Q 2 co > Q.) 0 [jj
-2
-4
-6
-8
-10
0 100
North Beach Profiles, Cab 1-07
----22 December2014
----Extremal Cycloid (H'""" = 4.8 m)
Critical Mass, Ve
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 14: Critical mass envelope at range line Cab I-07 on North Beach based on the extremal
elliptic cycloid solution using a 4.8 m high design wave height with 15 second wave period.
18
16
14
12
10
8
~ ...J 6 ...J
~
$ 4
C: ,Q 2 ro > Q) 0 iD
-2
-4
-6
-8
-10
0 100
North Beach Profiles, Cab 1-08
----22 December 2014
----Extremal Cycloid (Hrna, = 4.8 m)
Critical Mass, Ve
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 15: Critical mass envelope at range line Cab I-08 on North Beach based on the extremal
elliptic cycloid solution using a 4.8 m high design wave height with 15 second wave period.
18
16
14
12
10
8
~ ....J 6 ....J ~
$ 4
C
0 2 .:; ro > Q.) 0 ill
-2
-4
-6
-8
-10
0 100
North Beach Profiles, Cab 1-09
----22 December 2014
----Extremal Cycloid (Hmox = 4.8 m)
Critical Mass, Ve
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 16: Critical mass envelope at range line Cab I-09 on North Beach based on the extremal
elliptic cycloid solution using a 4.8 m high design wave height with 15 second wave period.
18
16
14
12
10
~ 8
....J ....J ~ 6
~
C 4
.Q ro 2 > Q)
[jJ
0
-2
-4
-6
-8
0 100
North Beach Profiles, Cab 1-10
----22 December 2014
----Extremal Cycloid (Hn~• = 4.8 m)
Critical Mass, Ve
200 300 400 500
Distance offshore from benchmark (ft.)
600 700
Figure 17: Critical mass envelope at range line Cab 1-10 on North Beach based on the extremal
elliptic cycloid solution using a 4.8 m high design wave height with 15 second wave period.
along the entire 3,200 ft of the North Beach disposal site. This volume represents the optimal
carrying capacity of the North Beach disposal site. Lesser amounts of beach fill will not be able
to sustain an equilibrium profile during the highest energy wave events; and without an
equilibrium profile, the beach will not dissipate all the incident wave energy, and the excess
wave energy will erode the beach. If North Beach is over-nourished with more than the critical
mass of sand, then two processes will intervene: a) the excess sand will spill off the wave cut
platform (which is 500 ft. to 600 ft. wide) and be re-suspended over the rocky outcrops and hard
bottom substrate at North Beach ( cf. Figure 8); and/or b) the excess sand will be swept away by
the net longshore transport (littoral drift) which flows from north to south throughout the
Oceanside Littoral Cell.
IIS-00'
L......L..J
0 10
km
------------
11,•10'
Figure 18: Oceanside Littoral Cell showing net north-to-south littoral drift, (from Inman and
Brush, 1970)
4) Cycloid Beach-Fill Template Design:
Ideally the optimal beach fill templates for North Beach would duplicate the critical mass
envelope in Figures 14-17, as these would prescribe an adequate amount of sand to support an
equilibrium profile in the presence of extreme event waves without exceeding the carrying
capacity of the otherwise limited wave cut platform that exists there. However, Figures 14-17
indicate that the critical mass envelope extends well below mean lower low water (MLL W) to
depths ranging from -4 ft. MLLW to -8 ft. MLLW. With present beach fill construction methods,
it is not possible to build a template that extends below the waterline. Beach fill is pumped to
North Beach via a hydraulic dredge pipeline and initially deposited as slurry. After the slurry
dewaters, the sands are spread out across the beach using conventional earth-moving equipment,
(Figure 19) which cannot effectively operate in anything deeper than ankle deep water.
Therefore, we must pose a beach-fill template that adapts to this construction constraint.
We begin by examining the percentage of time that a dry beach is available for
construction operations at the lower end of the beach profile during in the months of September
to mid-April, (the months during which dredge disposal is permitted in order to avoid impacting
the least tern nesting season). Figure 19 plots the relationship between ocean water level and
percent time a given elevation remains dry, (referred to as the hydroperiodfunction), based on
ocean water levels measured at the nearby Scripps Pier tide gage (NOAA# 9410230). Figure 19
indicates that the beach fill construction operations can proceed down to elevations as low as 0
ft. MLL Wat least 7% of the time, or during about 50 hours in a given month. These times are
clustered during the spring tides that occur twice each month. If the beach fill template is filled
from the top down (ie, spreading sand at the highest elevations of the template first, and then
proceeding downslope towards the lowest end), then 50 hours should be adequate to allow filling
the lowest portion of a template that terminates at Oft. MLL W.
A significant fraction of the critical mass envelope in Figures 14-17 lies below the Oft.
MLL W water level, and if the extremal cycloid profile is terminated at that elevation in the
beach fill template design, then additional sand must be added elsewhere to the template in order
to achieve the critical mass volume along the entire 3,200 ft. reach of the North Beach disposal
site. The additional sand is provided by combining a back-beach dune with the elliptic cycloid
that has been truncated at Oft. MLL W. The back-beach dune placement strategy was first
implemented in Carpinteria by Bailard and Jenkins (1980 and 1983) and later during the
replacement of seawalls at Mission Beach Sea (Jenkins 2014) and Del Mar (cf Figure 19a.).
These previous implementations of the back-beach dune strategy involved very popular beach
sites, yet no adverse recreational incidences were encountered. The back beach dune is a
conservation/storage mechanism that prevent rapid sand loss from over-builds of the intertidal
portion ofthe beach profile, yet still allows the fill site to receive its full allocation of critical
mass, and provides gradual re-nourishment as the dune erodes during brief periods of spring
tides and/or · gh waves. The dune proposed for the North Beach disposal site is shown in Figure
19b, and is roughly 9 ft high and 55 ft. wide, with a reserve storage capacity of 13.5 cubic yards
per running ft. of beach. When built along the 3,200 ft. length of the North Beach disposal site,
this dune will provide 43,200 yds3 sand perched in the upper portion of the truncated equilibrium
cycloid profile. The beach fill templates that result from this strategy are shown in Figures 21-24
for North Beach survey range lines Cab I07 -Cab I-10. When lofted over the entire 3,200 ft of
the North Beach disposal site yields using the SolidWorks 3-D CAD software, calculates that
these templates will provide 79,455 cubic yards of disposal volume, which compares almost
exactly with the required critical mass of 79,471 cubic yards, (the optimal carrying capacity of
the North Beach disposal site.)
~ ...J
...J
~
~
C 0 ·.;::; ro > Q)
w
Q) > Q)
...J
I...
2 ro ~
C ro
Q)
(.)
0
8
7
6
5
4
3
2
1
0
-1
-2
-3
0
La Jolla, Scripps Pier Tide Gage
NOAA # 9410230
EHW = +7.47 ft.
MHHW= +S.13 ft. --~ ~ -~ --~ ----~ ~ ---------~ --
MTL= -+2.76 ft.
Beach Dry @ 1 MLW 17% of the time
---------r --------------
Beach Dry @ MLLW 7% of the time --r---------,--------------
1 1 % Lowest Water Level
~I
~I
I
I
= -1 .2 ft. MLLW
I I ~ EL:W = -3.06 ft MLL W
10 20 30 40
'it,. I
~I
I
50 60
Percent Time Dry
70 80 90 100
Figure 19: Hydroperiod function of ocean water levels during the months of September-April,
based on the Scripps Pier tide gage (NOAA# 9410230; based on the 1983-2001 tidal epoch,
(from Jenkins and Taylor 2015; and Jenkins and Wasyl, 2011)
a)
back-beach dune
b)
10
9
8
:S 7 -6 ..c Cl "ii> 5 I
Cl) 4
C ::J 3 0
2
-I W I -r ...........
-I " / 13 5, ds S/n nn ng ft.
-1"·
-I/' ' .......... s1 ~av ~ar He ce
-/ ." ., /
-,,
~"· ,,
~~ -
-v' ~...___..__
0 -~ ~1,,1"'.' -..................
I ' I I I I I I I I I ' I I I I I I I I I I ' I I I I
0 10 20 30 40 50
Dune Width (ft.)
Figure 20: The back-beach dune beach fill placement strategy, a) as implemented in Del Mar
during seawall replacement; and b) as proposed at North beach in combination with a truncated
elliptic cycloid beach profi le.
60
25
24
23
22
21
20
19
18
17
16
15 i14
.....1 13 ~ 12
. 11
S10
C 9 ,g 8
~ 7 ~ 6
w 5
4
3
2
1
0
-1
-2
-3
-4
-5
----------~ --------------------
, ... ,,
I ,
~
~ ....
North Beach Profiles, Cab 1-07
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
\
\ ,
\.
' ' I
" 'I '\
\. "' I\. \
'I ' ' '-
:-.. " rx ...,
r-.,_,
'" ... ' " ..... "' '-
' ' ' ...... ......
~ \
""'" r-.
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Distance offshore from benchmark (ft.)
Figure 21: Proposed beach fill template for North Beach range Cab-107, based on the extremal
equilibrium profile truncated at O ft. MLL W with a back beach dune to hold-and-release residual
critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 1998772.8
Easting (ft): 6226391.4
'
25
24
23
22
21
20
19
18
17
16
15
~ 14
.J 13 ~ 12
. 11
~10
C 9
.Q 8 co > 7 Q) w 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
--------' -I --I -------------------
North Beach Profiles, Cab 1-08
22 December 2014 (most eroded historic profile)
Cycloi<I Beach Fill Template with Dune
I\ I \
\ ,
\
\
" ~~::S. \ \
' \. \.
i\: \.
' "' \,
' ' ' I\. " N.· ' r--.._ .......
N ......
"'r..... .....
r--... .....
f'\. ;, .,....._ ...., .....
0 W ~WM 100 1W ,~ 100 1M ~mm~~~~~~~~
Distance offshore from benchmark (ft.)
Figure 22: Proposed beach fill template for North Beach range Cab-108, based on the extremal
equilibrium profile truncated at O ft. MLL W with a back beach dune to hold-and-release residual
critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 1999973.2
Easting (ft): 6225671.9
25
24
23
22
21
20
19
18
17
16
15
~ 14
J 13 ~ 12
. 11
::::...1 0
C 9
. Q 8 co > 7 (I) w 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
----------------. ---------.
---
' I
~ -"'
A
I \
\
1
\
\
'\
_...;L:::S, \
\
\
I\.,
'
North Beach Profiles, Cab 1-09
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Templale with Dune
\.
" " ' I'\ ' ' ' I'\ -.....
"' ' ~ ........
K ......
'-.,,_ .....
""" -r-----~r-.. '
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Distance offshore from benchmark (ft.)
Figure 23: Proposed beach fill template for North Beach range Cab-I09, based on the extremal
equilibrium profile truncated at 0 ft. MLL W with a back beach dune to hold-and-release residual
critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 2000268.7
Easting (ft): 6225483.3
25
24
23
22
21
20
19
18
17
16
15
i 14
...J 13 ~ 12
. 11
~10
C 9 ._g 8
~ 7 Q) w 6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-----j -I -I -I --;r , --------------------
/\I
\
\
\
\
1
\
\
'\..
-r"'\ ,. \
I \.
\.
\
'\
~
North Beach Profiles, Cab 1-10
22 December 2014 (most eroded historic profile)
Cycloid Beach Fill Template with Dune
'-......
.....
' .. .......
'\ ....... .......... ... .... ......_ .......
' .....
'-.....
' .....
""" .....
~ ....
' ....
' ... __
1"---.. ~ -I I
I I I I I I
0 ~ ~ 00 M 100 1~ 1~ 100 1M ~ m ~ ~ ~ D m ~ ~ ~ ~
Distance offshore from benchmark {ft.)
Figure 24: Proposed beach fill template for North Beach range Cab-110, based on the extremal
equilibrium profile truncated at 0 ft. MLL W with a back beach dune to hold-and-release residual
critical mass as the profile adjusts to changing wave climate.
Coordinates of Bench Mark:
Northing (ft): 2000741.1
Easting (ft): 6225218.1
.... ------~ .... ------11114,.c,
2000 1000
Northing, ft:
0
Figure 25: Three-dimensional CAD model of the proposed composite cycloid/dune beach fill template on North Beach, where the silver surfaces
indicate the beach surface on which the template is built (from the 22 December 2014 profile measurements) and brown represents the beach surface
resulting from the proposed beach fill template.
5) Beach and Shoreline Evolution Analysis of North Beach Disposal Options
The potential benefits of the cycloid beach fill templates for North Beach disposal of
dredged sands from Agua Hedionda Lagoon are evaluated with Coastal Evolution Model (CEM)
whose architecture is shown in Figure 26 with computer code detailed in Jen.kins and Wasyl,
2005, which is available on-line from the Digital Library of the University of California at
(http://repositories.cdlib.org/sio/techreport/580 .
In the work described herein, the CEM is driven by the CDIP wave measurements in
Figures 6a & 6b and calibrated with beach profile measurements and dredge disposal volumes
preceding and following the most recent Agua Hedionda Lagoon dredging, December 2014 -
April 2015. The Coastal Evolution Model (CEM) is a process-based numerical model. It consists
of a Littoral Cell Model (LCM) and a Bedrock Cutting Model (BCM), (Figure 26), both coupled
and operating in varying time and space domains determined by sea level and the coastal
boundaries of the littoral cell at that particular sea level and time. Over the time scales of this
study, the LCM is the relevant module. At any given sea level and time, it accounts for transport
of mobile sediment along the coast by waves and currents. The BCM accounts for the cutting of
bedrock once the sediment cover is denuded by wave erosion. However bedrock cutting, and
notching of the bedrock to form a wave cut platform is a process that occurs over decadal to
millennial time scales.
~ ~ -a; oi -0 "O 0 "' ~ ~ "O -a; u
~ u -;;, ~ c -a; C
-0 ~ 0 .E ~
OI C <II E "O
::J "' u ~
.:,e. s u e ] cc
,. Forcing .Functions ......................................................... .
-----------;~, Wet/Dry t-----,
Precipitation Climate
-----< Watershed
Erosion
& Transport
Cycles
Wave
Climate
r Boundary.Conditions ................. F~rll~~·G;id····--: ~
j Control Cells ,-----, j ;
· Accretion I Nesting Regional · t!: • ;~;;:=~= l ~~::;::~_! ---~
,·················································································································· .. ········:,
Sediment • j=Gfuergy Flu• '.._ __ __, Refraction/
Budget Budget Diffraction '--
Beach· LJ Shor;-i___,__ Sediment . ~ Cover ------'-'
............................................................................................................................. -
[Coastal Evolution ......................... ~~;·r~.~~;······················· .............. j
:~ :
~--························································· ............................................... J
Sea Level
Change
GIS Accumulation
of Profiles
Imagery of
Coastal Morphology
Figure 26: Architecture of the Coastal Evolution Model (CEM); from Jenkins and Wasyl,
(2005).
In the LCM, the coastline of the far-field computational cell is divided into a series of
coupled control cells, as illustrated schematically in Figure 27b. Each control cell is a small
coastal unit of uniform geometry where a balance is obtained between shoreline change and the
inputs and outputs of mass and momentum. The model sequentially integrates over the control
cells in a down-drift direction so that the shoreline response of each cell is dependent on the
exchanges of mass and momentum between cells, giving continuity of coastal form in the down-
drift direction. While the overall computational domain of the far-field cell remains constant
throughout time, the beach profile within the individual control cells can change shape or shift on
or offshore, as shown in Figure 27c, in response to changes in wave height or longshore transport
rates, or due to the introduction of new sediment from dredge disposal as shown in Figure 27a.
These changes are computed from time-stepped solutions to the sediment continuity
equation (otherwise known as the sediment budget) applied to the boundary conditions of the
coupled control cell mesh for the larger scale region (farfield) round Agua Hedionda Lagoon, as
in Figure 28. The sediment continuity equation is written (Jenkins, et al, 2007):
dv' a ( av] av -=-&--U,-+J(t)-R(t) dt ay ay ay (5)
Where v' is the beach volume per unit length of shoreline (m3 /m), £ is the mass diffusivity, U,
is the longshore current, J(t) is the flux of new sediment into the control cell from dredge
disposal and R(t) is the flux of sediment lost from the control cell due to the tidal influx of
sediment into Agua Hedionda Lagoon. The first term in (1) is the surf diffusion while the second
is divergence of drift. For any given control cell that does not enclose the lagoon inlet, equation
(5) may be discretized in terms of the rate of change of beach volume, V, in time, t , given by:
dV dt =q,,,-qou,+J(f) (6)
and V = J [q;n -qout +J(t)]dt
Over any given period of time, T = nM , comprised of n number of time steps of interval M , the
volume change of the beach can be computed by discretizing equations (6) according to:
n ,1.V = L [q;n -qout +J(n)]nAf
I
(7)
Referring to the control cell schematic in Figure 27c, sediment is supplied to the control cell by
dredged beach fiH, J (t), or by the influx littoral drift from up-coast sources, q;11 = q LI , (where q L
is the longshore transport rate on the updrift side of the control cell). Sediment is lost from the
control cell due to the action of wave erosion and expelled from the control cell by exiting
a) Accretion / Erosion Wave
J
accretion
(sand delta)
\
t 1
b) Coupled Control Cells
c) Profile Changes
/ closure
depth
qin-0-qout
I
, ..... -
T
h
1
accretion --•----
erosion >
Figure 27: Computational approach for modeling shoreline change after Jenkins, et. al., (2007).
N
0
San Luis Rey River SCALE
2000· 6000" 10000· ---o· •ooo· aooo·
ELEVATION REF"ERENCE TO "4LLW
Oceanside
Buena Vista Lagoon
Carlsbad
Agua Hedionda lagoon
Batiqu1tos lagoon
Leucadia
Figure 28: Coupled control cell mesh used to in the CEM to model the beach evolution during
Agua Hedionda dredge disposal operations .
littoral drift, q0u, =qL2 , or by becoming ingested by the lagoon's tidal inlet, R(t). Here fluxes
into the control cell (J(t) and q LI) are positive and fluxes out of the control cell ( q L2 and q,;dJ
are negative. The beach sand volume change, d V/dt, is related to the change in shoreline
position, dX/dt, according to:
where
dV dX -=-·Z ·l
dt dt
Here, h is the height of the shoreline flux surface equal to the sum of the closure
(8)
depth below mean sea level, he, and the height of the berm crest, Z1, above mean sea level (from
Hunt's Formula.); and l is the length of the shoreline flux surface (see Figure lb). Hence,
beaches and the local shoreline position remain stable if a mass balance is maintained such that
the flux terms on the right-hand side of equation (2) sum to zero; otherwise the shoreline within
each control cell will move during any time step increment as:
Llx=-1-J[qin -qout +J(t)]dt =-1-f [q in -qo111 +J(n)]nM D.yh D.yh I
(9)
When dredge disposal produces a large episodic increase in J, an accretionary bulge in
the shoreline (like a river delta) is initially formed (cf. t, in Figure 27a). Over time the
accretionary bulge will widen and reduce in amplitude under the influence of surf diffusion and
advect down-coast with the longshore current, forming an accretion-erosion wave (cf. t2 & t3 in
Figure 27a). The local sediment volume varies in response to the net change of the volume
fluxes, between any given control cell and its neighbors, referred to as divergence of drift=
q;,, -q0u, , see Figure 27c. The mass balance of the control cell responds to a non-zero
divergence of drift with a compensating shift, Llx , in the position of the equilibrium profile
whose shape is calculated from equations (1)-(4) after Jenkins and Inman, (2006). This is
equivalent to a net change in the beach entropy of the equilibrium state. The divergence of drift
is given by the continuity equation of volume flux, requiring that dq/dt on the left hand side of
equation (5), is the net resultant of advective and diffusive fluxes of sediment plus the influx of
new sediment, J, from dredge disposal, per the right hand side of equation (1 ). In response to the
rate of change of volume flux through the control cell, the equilibrium profile will shift in time
according to equation (9). If the divergence of drift is positive because more sand fluxes into the
control cell due to longshore transport than leaves the cell, ( q;n -q0u, = qu -q L2 > 0 ), then the
equilibrium beach profile in that cell will shift seaward. Conversely, if the divergence of drift is
negative because less sand fluxes into the control cell than is expelled from the cell by longshore
transport, ( q;,, -q0u1 = q LI -q L2 < 0 ), then the equilibrium beach profile in that cell will shift
landward, as diagramed schematically in Figure 27c. If a negative divergence of drift causes the
equilibrium profile to shift sufficiently landward that it intersects the basement surface of the
critical mass envelope, then the cycloidal shape of the profile is disrupted, and the equilibrium
state of the profile is lost.
The formulation for the longshore transport rate q L is taken from the work of Komar and
Inman (1970) according to:
(10)
where q L is the local potential longshore transport rate; Cn is the phase velocity
of the waves; S yx = E sin a b cos a b is the radiation stress component; a h is the breaker angle
relative to the shoreline normal; E=l l 8pgH; is the wave energy density; p is the density of
water; g is the acceleration of gravity; H b is the breaking wave height; and, K is the transport
efficiency equal to:
K = 2.2.Js: (11)
(12)
Here c,b is the reflection coefficient which is calculated from the mean bottom slope, f3 (which
is known either from the measured profiles or from the elliptic cycloids); and, a is the radian
frequency = 2n/T, where T is the wave period. These equations relate longshore transport rate to
the longshore flux of energy at the break point which is proponional to the square of the
breaking wave height and breaker angle. By this formulation, the CEM computer code
calculates a local longshore transport rate for at the up-drift and down-drift sides of each side of
each control cells of the mesh in Figure 28.
5.1 Calibration of the Coastal Evolution Model for North Beach:
The Coastal Evolution Model (CEM) for North Beach was calibrated using the measured
pre-and post-dredging beach profiles for North Beach during the 2014-2015 dredging event, in
conjunction with daily beach fill placement volumes as reported in the monitoring report to the
Regional Water Quality Control Board, San Diego Region, (Cabrillo, 2015). Wave forcing for
the CEM was based on shoaling wave data from Figure 6b, while beach fill grain size was based
on Figure 11. Daily beach fill volumes were assumed to be laid out over the 22 December 2014
profiles from Figures 1-4 in a standard beach fill template with a flat backshore platform and a
1: 10 (rise over run) seaward facing beach slope extending down to 0 ft. MLL W. Throughout the
North Beach disposal period, that began on 23 March 2015 and ended on 15 April 2005, daily
beach fill increments ranged from 1,050 yds3/day to 6,060 yds3/day and were successively added
to the North Beach control cells in Figure 28, while the wave forcing continued to rearrange
those fill volume increments according to flux balance relations in equations (5) -(9). Free
parameters in the CEM, including the mass diffusivity in equation (5) and the longshore
transport efficiency in equation ( 10) were adjusted through successive iterative simulations until
the change in beach sand volume between 23 March 2015 and 17 April 2015 (when the post
dredging beach surveys were done) matched the volumetric changes of the measured profiles in
Figures 1-4. These volumetric changes were computed by the SolidWorks 3-D CAD model in
Figure 29.
Cab 1-10
Sand remaining 17 April 2015
13,780 cubic yards
Erosion exposes
pre-disposal
beach surface
per 22 Dec. 2014
survey
Figure 29: SolidWorks 3-D CAD model of a composite surface overlay of the modeled post-
disposal North Beach surface (brown) and the pre-disposal North Beach surface (silver). The
SolidWorks mass properties tool calculates a volume of 13,780 yds3, representing the volume of
sand retained after placing 64,968 yds3 over a 24 day period of beach nourishment.
In Figure 29, the CEM modeled beach surface on 17 April 2015 (represented in brown) shows
numerous patches where erosion has occurred and the pre-disposal beach surface (represented in
silver) is exposed. The mass properties tool in SolidWorks calculates that the volume in the
region between the two surfaces (representing the volume of beach fill retained) is 13,780 yds3,
which matches the retention calculated directly from the pre-and post dredging beach profile
measurements in Figures 1-4.
The time stepped CEM wave-driven flux calculations which led to this perfect calibration
result are plotted in Figure 30. Initially, as sand was being placed on North Beach, waves were
small, short period and approaching from the southwest (cf Figure 6b). Consequently, the
calibration simulation begins with weak northward flowing longshore transport, Figure 30a,
causing some of the previously placed dredged sands on Middle Beach to be transported around
the inlet jetties during ebb tide and arrive at North Beach. During this early period, more sand
enters the North Beach control cells at the north inlet jetty, than leaves North Beach from the
control cells at Maple Ave, and the difference between the cumulative net transport at the north
jetty vs Maple Ave (Figure 30 b) initially creates a positive divergence drift (Figure 30c).
Consequently, North Beach gains sand volume during the first 5 days from wave driven
transport, irrespective of the additional gains from North Beach dredge disposal. But then, by
day 6, circa 28 March 2015, a large west/northwest storm swell arrives with waves reaching 2 m
in height prior to breaking ( cf. Figure 6b ). Coinciding with this large swell, the longshore
transport reverses direction toward the south and increases in rate, (Figure 30a) resulting in
cumulative net transport toward the south at the north jetty that exceeds cumulative net transport
into North Beach at Maple Ave (Figure 30 b). The divergence of drift turns negative and remains
that way throughout the remainder of the North Beach disposal activities, resulting in a loss of
51,188 cubic yards of sand by 17 April 2015 due to wave-driven transport (Figure 30 c ).
Negative divergence of drift is prevalent along North Beach because of the way the prevailing
west/northwest swell and wind waves are refracted around the Carlsbad submarine canyon,
creating higher shoaled wave heights at the southern end of North Beach than found further north
near Maple Ave, where refraction effects of the Carlsbad Submarine Canyon are weaker, (cf.
Figure 12).
When the net sand loss to divergence of drift is superimposed on the incremental
sequence of beach fill being placed on North Beach, we get a look at how the sand retention on
North Beach varies throughout the disposal period (Figure 31 ). It appears from the black line in
Figure 30 that sand retention with the standard 1: 10 (rise over run) beach fill template reaches a
fairly constant level of about 20,000 cubic yards throughout most of the North Beach disposal
period, before falling off to 13,780 yds3. The retained sand volume never reaches anything close
to the total sand volume placed on North Beach (which was V0 = 64,968 yds\ By the time the
post dredging beach surveys were performed on 1 7 April 2015 (26 days after beach fill
placement began), only 21 % of the total volume of sand placed on North Beach remained, and
the average rate ofloss of beach fill was < dV I dt >= 1,969 yds3/day. Based on this average
loss rate, the retention time, T0 , for fill placed on North Beach during the 2014/2015 dredging
event was
T, -Vo
0 -< dV /dt >
64,968 = 33 da s
1,969 y (13)
70.00
60.00
M "' "O 50.00 >, -0
"' 40.00
-0 C co 30.00 "' :J 0 £ 20.00
> 10.00 <I
(I) 0.00 E :J ~ ·10.00
"O ffi -20.00
(f)
.!: -30.00
(l)
0) ffi -40.00
.s:::. t) -50.00
-60.00
80.0
--North Beach Disposal, J(n)
--Cumulative Divergence of Drift, I:(qu -ql2) nllt
--Beach Volume Retained, V(n)
23 March 2015
~ Begin North Beach
Disposal= 64,968 yds3
90.0
Julian Day, 2015
100.0
15 April 2015, North Beach
Fill Placed = 64,968 yds3
/
17 April 2015, Retention
= 13,780 yds3
I
110.0
Figure 31: CEM simulation of temporal variation in beach sand retention on North Beach (black
line) as a result of the net between the incremental sequence of beach fill placement (green line)
and the wave-driven divergence of drift (red line).
Q) 0.04 ..... Maple Ave. Q.., = Q0 ro a:: 0.03 North Jetty. Q,u = ql,
t:: -t 0 (.) 0.02 a. Q) "O ~ en .... ro ~ ro -0.01 £ \...C") I-en :::,
0 tJ) Q) "C \... >-0.00 ----o-'E ..c ro en -0.01 ::: O> .c t:: C 0 0 -0.02 C _J i
80.0 90.0 100.0 110.0
t:: 8.-90.0
enC"> ffi ~ 70.0 \... >-
1--..... o 50.0
a> en z "C Q) c 30.0
---Maple Ave, I;ql, nAt
---North Jetty. I:Qu nt:J
r-t
net loss
to south
i
> ro ·-en ro g 10.0 £.. _____ ____,,_-_-_-_-___ ___._ --------
::, ..c
E ..... -10.0 J ::, ..__..
O -30.0 --+~--.--.--..--.---.---.-~~.---.-~--.---r--~~-.---.--..--.---.---.-~~.---.-~~
t
'E ro ::: .c ,::
0 C
80.0 90.0 100.0 110.0 i
it:: c§ 20.00 --QC")
Q) en u -c 0.00 C >-
Q) -O> 0 \... en ~ -c -20.00
0 ~
Q) CJ')
-E 5 -40.00
ro £
::, -
23 March 2015
: (-Begin North Beach
Disposal = 64.968 ydsJ Average Loss Rate
<dV/dt> = 1,969 yds3/day
t
North Beach Loss
= 51 , 188 yds3
§ -60.00 -4~-.---.--~---.---.-~~.---.-~--.---.--~~-.---.--~---.---.-~~.---.-~~
0
80.0 90.0 100.0 110.0
Julian Day, 2015
Figure 30: Time stepped wave-driven fluxes during the North Beach CEM calibration: a)
longshore transport rate, b) cumulative net transport; and, c) cumulative divergence of drift.
It should be remembered that the very low retention time from equation (13) was a consequence
of several factors: 1) placement of a fill on a highly eroded North Beach surface, that had
probably been eroded to the basement of the critical mass envelope, (since it had been 3 years
since previous nourishment was provided by lagoon dredging disposal); and 2) the fill placed in
2015 was less than the critical mass requirement and was laid down in anon-equilibrium profile
shape. In the following section, we evaluate potential improvements in beach fill retention time
using the composite cycloid-dune beach fill template and the appropriate amounts of beach fill
volume.
5.2 Performance Simulations of the Proposed Cycloid Beach Fill Template:
In this section, the calibrated Coastal Evolution Model (CEM) is run in long-term
simulations of the fate of beach fill placed on North Beach throughout the entire period of record
(1998-2015) that Agua Hedionda Lagoon dredged sands have been disposed as beach fill on
North Beach. Wave forcing for these simulations was based on shoaling wave data from Figure
11 for the period 1998-2016, while beach fill grain size was based on Figure 11. Daily beach fill
volumes were derived from the dredge monitoring reports to the Regional Water Quality Control
Board (Cabrillo, 2015) and from the Cabrillo Power dredging data base contained in an Excel
spreadsheet < Dredge History.xis>. The spreadsheet contains volumetric time histories for eight
(8) separate North Beach disposal events that are summarized in Appendix-A. The CEM was
first run for these eight (8) events assuming the beach fill volumes were distributed using the
standard 1: 10 (rise over run) template laid out over an eroded basement surface that was
specified by the 22 December 2014 profiles from Figures 1-4. These runs were used to establish
a North Beach baseline performance standard for average sand loss rate,< dV I dt >, and
retention time, T0 • This baseline was then compared against a sensitivity analysis of the
proposed composite cycloid-dune beach fill template to determine possible advantages of this
new template design and establish the optimal beach fill volume for North Beach, given the
limitations of: 1) its small wave-cut platform, and 2) intrinsically high longshore transport rates
with negative divergence of drift in the presence of the prevailing west/northwest swell and wind
waves.
5.2.1: Historic Sand Retention Baseline: The baseline CEM simulation results are
plotted in Figure 32, showing average rate of loss of beach fill < dV I dt > (red) and the retention
time, T0 , (blue) as a function of the total beach fill volume, V0 • Sand loss rates are scaled against
the left hand axis in Figure 32, while retention time is plotted relative to the right hand axis. The
solution points for the eight (8) historic North Beach dredge disposal events that occurred
between 1998 and 2015 are plotted with star symbols that were subsequently connected by cubic
spline fitting functions plotted as the red and blue colored lines. The cubic spline best fit curves
in Figure 32 show a minimum in the sand loss rate for North Beach fill volumes near the critical
mass Ve,;, = 79,471 yds3, which is the theoretical maximum carrying capacity of North Beach for
supporting a beach profile in equilibrium. The theoretical minimum sand loss rate using the
standard 1: 10 (rise over run) beach fill template is < dV I dt >= 1,495 yds3 /day. When beach fill
volumes are less than critical mass, V0 <Ve,;,, there is insufficient sand to establish an
equilibrium profile. A beachi s in its most stable state with an_equilibrium profile, but orth
Beach has a prevailing negative divergence of drift so that when equilibrium cannot be achieved
due to insufficient sand volume, sand loss rates increase. For example, the measured sand loss
ia'3.00
"C
'--(I) a.
("') en
"C >, ..... 0
en
"C C
~ 2 00 :::,
0
£ -....;-
"C 3;
"C
-0 C
('()
Cl) 1 00 -0
(I) _, ro a::
en en 0 .....J
(I)
0) ('() '--(I)
> 000 <{
0.0
Historic North Beach Fill Retention
----Historic Loss Rate. yds3/day
----Historic Retention nme. days * * * Disposal Events. 1988-2015
t "Z, ,-g,
I;:: L-------------',~
catib,ation point /
(2014/2105)
I ,-.. II
I !i
t >
minimum loss rate = 1,495 yds3/day
• 11
• tll ...
20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
Total Disposal Volume, VO ( thousands of yds3)
220
210
200
190
180
170
160
150 en >,
140 ('()
"C
130 l-
120 (I).
110 E ~ 100 C
90 0 ~
80 2
70 (I) a::
60
50
40
30
20
10
0
180.0
Figure 32: CEM simulation of average rate ofloss of beach fill, < dV I dt > (red, left hand axis),
and the retention time, T0 , (blue, right hand axis), as a function of the total beach fill volume,
V0 , for 8 historic North Beach dredge disposal events, 1998-2015. CEM solution points are
plotted with star symbols that were connected by cubic spline fitting functions plotted as the
colored lines. Simulations based on standard 1: 10 (rise over run) beach fill template assumption.
rates during the 2014/2015 dredging event (where V0 = 64,968 yds3) were 32% higher than
higher the theoretical minimum (theoretical minimum when V0 ~ Vertt ). Consequently the
retention time of T0 = 3 3 days during the 2014/2015 dredging event would have increased to T0 =
53 days if the beach fill volume placed on North Beach were increased from V0 = 64,968 yds3 to
V0 = Ve,u = 79,471 yds3.
Figure11 also shows that retention time continues to increase as the disposal volume
placed on North Beach exceeds the critical mass volume, but the sand loss rate also increases,
which has a negative irrpact on the sand influx rates into Agua Hedionda Lagoon. For beach fill
volumes above critical mass the improvement in retention time is minor, because the excess sand
cannot be supported in equilibrium on the limited wave-cut platform, which is only 550 ft. to 600
ft. wide. The excess sand is quickly lost to the negative divergence a drift, (cf. Figures 30 b&c),
after which an equilibrium profile can be established, once V0 ~ Vertt . The initially high loss rate
of the excess sand contributes to a higher average sand loss rates than what would have
otherwise occurred if the beach fill volume were limited to the critical mass volume. Historically,
whatwe find with the standard beach fill template, is that when beach.fill sand volume is
increased by 103% over critical mass (as occurred during the 2002/2003 dredge event when V0 =
161 ,525 yds3), the retention time retention time is only increased by 26 % from T0 = 5-3 days to
T0 = 67 days. This is not a good return on doubling the investment in beach fill for North Beach
because the sand loss1 ate increases by 61 % to < dV I dt >= 2,411 yds3/day, or an increase in
sand loss of 916 yds3 /day over what would have otherwise occurred if the beach fill volume
were limited to critical mass.
5.2.2: Sand Retention with the Cycloid-Dune Template. The cycloid dune templates
proposed in Figures 20-24 are tested in long-term CEM simulations using the same model
calibration parameters and the same wave forcing and grain size inputs used in the historic
baseline simulations. We also assume that the proposed cycloid-dune template is laid out over an
eroded basement surface specified by the 22 December 2014 profiles from Figures 1-4, the same
assumption was made for the baseline simulations. Because these cycloid-dune simulations are
hypothetical, we do not limit ourselves to a mere handful of options for beach fill volumes, as
was the constraint with the historic baseline simulations in Section 5.2.1. Instead, a sensitivity
analysis is performed on beach sand loss rates and retention times using beach fill volumes that
range from V0 = 36,000 yds3 to V0 = 175,000 yds3. The dune portion of the proposed templates in
Figures 20-24 holds VD= 43,200 yds3 which were designed for a fill volume equal to the critical
mass, Ve,;, = 79,471 yds3• For the modeling scenarios that involved less than critical mass, the
dune portion of the template was proportionally reduced in volume until reaching the absolute
minimum fill volume scenario of V0 = 36,000 yds3 , for which no dune component remains in the
template. For the modeling scenarios where V0 >Ve,;,, the dune portion of the template was
proportionally increased in width until reaching the scenario of V0 = 175,000 yds3•
Because we do not have historical guidance on the temporal beach fill placement for
these hypothetical scenarios, we have made several additional assumptions. First, we assume that
the beach-fill is laid down at a constant daily rate of 4,500 yds-3 per day on North Beach, which.
was the average daily placement rate in the dredge monitoring reports to the Regional Water
Quality Control Board (Cabrillo, 2015) and in the Cabrillo Power Excel spreadsheet (<Dredge
History.xis>). Secondly, we assume tbat the back-beach dun portion of the composite cycloid-
dune template is built first, starting at the north inlet jetty and adding sections to the dredge
pipeline until the build-out of the dune reaches Maple Ave. Building the dune first creates a
"safe" reservoir of sand before the template can be fully constructed, and sand from this reservoir
is only released to the lower eroded basement surface during periods of the highest tides and
waves. After the buildout of the dune to Maple Ave, the cycloid portion of the template is laid
out beginning from the toe of the dune and spreading the material to down slope to MLL W, and
working back towards the north inlet jetty, removing pipeline sections as the cycloids are
completed.
CEM beach evolution simulations were performed on eighteen (18) different disposal
scenarios involving cycloid-dune beach fill placement on North Beach ranging from V0 = 36,000
yds3 to V0 = 175,000 yds3. Each cycloid-dune scenario was repeated 8 times using start dates and
wave forcing corresponding to the eight (8) historic North Beach dredge disposal events listed in
Appendix A. Selecting these specific start dates in the wave record in Figure 13 eliminates the
randomness effects of the historic occurrence of extreme waves, and allows for direct
comparisons with the results of the historic baseline in Section 5 .2.1. Sand loss rates and
retention times for the 8 separate outcomes of each scenario were ensemble averaged to produce
the points plotted as crosses in Figure 33, and these solution points were then fitted to cubic
splines (plotted in red for sand loss rates relative to the left hand axis; and plotted in blue for
retention time relative to the right hand axis). Sand loss rates were calculated from lofting the
beach surfaces in SolidWorks 3-D CAD at a given time, t=t,, during the CEM beach evolution
simulations. The mass properties tool in SolidWorks was used to calculate the volume change
between the beach surface at t = t; and the pre-disposal basement surface (represented by the 22
December 2014 surveys). An example of this procedure is illustrated by Figures 34 and 35 for
the disposal scenario V0 = Vc,u = 79,471 yds3 at time t;= 90 days. At 90 days into the CEM
beach evolution simulation, the dune has been eroded and re-distributed by extreme wave runup
at high tides, leaving a residual volume V, = 41 ,941 yds3 of sand remaining between the
basement surface (silver) and the new beach surface (brown). The new beach surface at t; = 90
days conforms closely to an elliptic cycloid profile. Given this residual sand volume the sand
loss rate that has occurred between the start of the CEM simulation at t = t O and t = t; = 90 days is
given by:
< dV I dt > = V0 -V, = 79,471-41,941 417 yds3/day
/=I, ti -{0 90 (1 4)
This gives an estimate ofretention time (at t, = 90 days) of
T. _ Vc,it = 79,471 x 90 = 190.6 da s
0 -(dV I dt),=,, (79,471-41,941) y (15)
Four such SolidWorks loftings of the CEM beach surfaces were done at four different times,
t, =t; ,t2 ,t3 ,!4 , during each of the 18 scenario simulations, and the sand loss rates and retention
>-{g 300 ....
Q)
Q
M Cl)
-0 >--0
Cl)
tJ C co Cl) 6 2 00
£
1\.-.....
tJ > -0 V
-0 C co Cl) 1.00 ..... 0
Q) -co a:::
Cl)
Cl)
0
...J
Q)
Ol C0 .... ~ 0.00
<(
0.0
North Beach Fill Retention
Cycloid-Dune Template
----Loss Rate. yds'lday
----Retention Time, days
minimum loss rate = 417 yds3/day
20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
Total Disposal Volume, V0 ( thousands of yds3)
180.0
220
210
200
190
180
170
160
150 Cl) >-C0 140 "C
130 1--8
120 oi
110 .s
I-100 c
90 0 :g
80 2
70 Q) a:::
60
50
40
30
20
10
0
Figure 33: Sensitivity analysis of average rate of loss of beach fill < dV I dt > (red, left hand
axis) and the retention time, T0 , (blue, right hand axis) as a function of the total beach fill
volume, V0 , using the proposed cycloid-dune templates (cf. Figures 20-24 ). Each solution point
(crosses) is an ensemble average of 8 modeled outcomes coinciding with the timing of historic
North Beach dredge disposal events, relative to the wave forcing in Figure 11 .
------------------0 2000 1000
Northing, ft
0
Figure 34: Three-dimensional CAD model of two overlaid surfaces on North Beach, 1) the beach surfaces on North Beach after waves re-work
79,471 yds3 of cycloid-dune beach fill, (brown) at t = +90 days post-dredge disposal; and 2) the bottom of the critical mass envelope or basement
surface (as delineated in silver from the 22 December 2014 profile measurements). CAD model shown with 10 to 1 vertical exaggeration
*
times calculated at each of those times were ensemble averaged to give the points and cubic
spline curves plotted in Figure 33.
While an elliptic cycloid is an equilibrium beach surface, it does not produce a state of
zero sand loss in the presence of a negative divergence of drift, which is the persistent littoral
drift state along North Beach. Recall from Section 5.0 that when the divergence of drift is
negative (because less sand fluxes into North Beach at Maple Ave than is expelled from the
North Beach at the inlet jetties, cf. Figure 30c), then the equilibrium cycloidal beach profile will
shift landward, eventually intersecting the basement surface of the critical mass envelope, (i.e.,
the 22 December 2014 profile). Once this happens, then the cycloidal shape of the profile is
disrupted, and the equilibrium state of the profile is lost. The concept behind the cycloid-dune
template is that, as the cycloid approaches an intersection with the basement surface of the
critical mass envelope, (under the erosional effects of continued negative divergence of drift), it
also intersects the base of the dune and receives additional sediment cover as the dune erodes and
spreads out downslope across the still intact cycloidal surface. So, the dune acts as a restoring
mechanism that re-supplies the cycloid with sand lost to negative divergence of drift.
Comparing the results in Figure 33 against the historic baseline in Figure 32.,_ the general
trends are similar, but the sand loss rates are greatly diminished and retention times significantly
increased by using the _pro osed cycloid-dune template (in Figures 20-24). Again, the most
efficienruse of Agua Hedionda Lagoon dredged sands occurs when the cycloid-dune template is
filled to no more than critical mass ( V0 ~ Vcm = 79,471 yds3), which reduces average sand loss
rates on North Beach to an absolute minimum of< dV I dt >= 417 yds3 /day, while extending
ret~ntion time to T0 = 190.6 days. This is a 3.6 fold improvement in sand retention time over
historical dredge disposal practices at North Beach, which could result in a reduction of sand
influx rates into Agua Hedionda Lagoon by a similar factor during the months following North
Beach disposal.
If the cycloid-dune template is filled to more than critical mass ( V0 > Vcri,) by adding
more sand to the back-beach dune, then North Beach retention time will increase beyond 190.6
days and reach as much as T0 = 222 days if the reserve sand volume in the dune were more than
doubled to VD= 95,529 yds3 (achieving a total placement volume of V0 = 175,000 yds3). But,
again, this is not a good return on doubling the investment in reserve beach fill for North Beach
because retention time is only increased by an extra month while the sand loss rate increases by
89 % to < dV I dt >= 787 yds3/day, with proportionally higher sand influx rates into Agua
Hedionda Lagoon for about 7 months post-North Beach disposal. Furthermore, it is simply not
possible to place more sand than the critical mass in the back beach dune and not have much of
the dune sand prematurely erode during periods of high waves and high tides, because the
enlarged dune encroaches further seaward. Once eroded the excess dune sands that spill out
across the active cycloid portion of the beach profile cannot be supported in equilibrium on the
limited wave-cut platform, which is only 550 ft. to 600 ft. wide.
On the other hand, under-filling the cycloid-dune template ( V0 < Vcru) with a reduced
dune, leads to accelerated sand loss rates and reduced retention times. The prevailing negative
divergence of drift causes the initial cycloid profile in the lower portion of the template to shift
landward, and once intersection with the basement surface of the critical mass envelope occurs,
there is insufficient sand reserves in the reduced dune to resupply the cycloid in the presence of
continued negative divergence of drift. Once the reserve sand supply in the dune is exhausted,
Dune erosion exposes
pre-disposal beach berm
Cab 1-10
sand remaining @ t = + 90 days
= 41,941 cubic yards
Dune sands accrete as
break-point bar
Figure 35: Cross-section of 3-D CAD model of two overlaid surfaces on North Beach, 1) the beach surfaces on North Beach after waves re-work
cycloid-dune beach fill, (brown) at t = +90 days post-dredge disposal; and 2) the bottom of the critical mass envelope (as delineated in silver from the
22 December 2014 profile measurements). CAD model shown with 10 to 1 vertical exaggeration.
the cycloidal shape of the profile is disrupted, and the equilibrium state of the profile is lost.
Even so, Figure 33 shows that if the cycloid-dune template is filled to a volume equivalent to the
2104/2015 North Beach disposal event ( V0 = 64,968 yds3) by using a dune containing only VD=
28,697 yds3 , then sand retention times are still significantly better than what was achieved using
the standard 1: 10 (rise over run) template. With the cycloid-dune template, retention times for V0
= 64,968 yds3 of beach fill were T0 = 117 days and sand loss rates were reduced to < dV I dt >=
554 yds3/day, or a factor of 2.2 better than what was achieved using standard North Beach
disposal practices during the 2104/2015 dredge event. With even smaller beach fill volumes, the
cycloid-dune retention times and sand loss rates rapidly degrade, but retention times remain
equivalent to those of the 2104/2015 North Beach disposal event for beach fill volumes as low as
V0 = 37,000 yds3, for which the back beach dune was reduced to vanishingly small (VD~ 1,000
yds3).
6) Summary and Conclusions:
A detailed set of beach profile surveys at North Beach in Carlsbad CA were provided by
NRG Cabrillo Power Operations Inc delineating beach surfaces before and after the 2104/2015
dredging of Agua Hedionda Lagoon, which placed 64,968 yds3 between Maple A venue and the
north inlet jetty to Agua Hedionda Lagoon. The surveys were accurately performed by Nobel
Engineers using differential GPS and known historic benchmarks. Three-dimensional CAD
models were lofted from the measured points along the 4 North Beach survey range lines (Cab I-
07 -Cab I-10) to delineate the beach surfaces immediately before North Beach dredge disposal
(based on the 22 December 2014 profile measurements) and immediately after dredge disposal
(based on the 17 April 2017 profile measurements). When these two surfaces were lofted
together in a common refe.r.ence frame, it was dete.r.mined that 13_, 780 cubic yards of beach fill
have been retained after placing 64,968 cubic yards on North Beach between 23 March 201 5 and
15 April 2015. This calculates to an average sand loss rate of 1,969 yds3/day and projects a sand
retention time for the entire fill volume of only 33 days.
To understand the reasons for the poor sand retention characteristics of North Beach, a
baseline beach evolution study was conducted using the Coastal Evolution Model (CEM) to
hindcast the fate of beach fill placed on North Beach. The CEM was developed at the Scripps
Institution of Oceanography with a $1,000,000 grant from the Kavli Foundation, (see
http://repositories.cdlib.org/sio/techreport/58/ ), and is based on latest thermodynamic beach
equilibrium equations published in the Journal of Geophysical Research. Inputs to the CEM
baseline study were based on measured shoaling wave data, grain size data for the dredged
sands, and daily beach fill volumes were derived from the dredge monitoring reports to the
Regional Water Quality Control Board (Cabrillo, 2015) and from an Cabrillo Power dredging
data base.
Between 1998 and 2015 there have been eight (8) different events when Agua Hedionda
dredged sands have been disposed as beach fill on North Beach. Historic dredged sand volumes
placed on North Beach ranged from 62,030 yds3 to 161 ,525 yds3. The CEM beach evolution
simulations of these events determined that the minimum in the sand loss rate occurs when North
Beach fill volumes equal to the critical mass Vc,u = 79,471 yds3, which is the theoretical
maximum carrying capacity of North Beach for supporting a beach profile in equilibrium. The
carrying capacity of a beach is limited by the width of the wave-cut platform in the bedrock on
which beach sands have accumulated over geologic time scales. The wave-cut platform at North
Beach is only 550 ft. to 600 ft. in width. Many of the beaches throughout north San Diego
County are perched on narrow wave-cut platforms. The platforms are narrow because they were
carved by wave action into erosion resistant bedrock formations during the present high-stand in
sea level, and these narrow wave-cut platforms physically cannot hold large quantities of beach
sand; and often become fully denuded during periods of high-energy winter waves.
Another contributing factor. to the limited carrying capacity ofNorth'Beach is that it is
exposed to a prevailing negative divergence of drift caused by the way the bathymetry
surrounding the Carlsbad Submarine Canyon influences wave shoaling at the southern end of
North Beach .. The presence of the Carlsbad Submarine Canyon creates a bright spot in the
shoaling wave pattern immediately north of the inlet jetties, where wave heights are locally
higher than further to the North around Maple A venue. The prevailing littoral drift transports
beach sand southward throughout the entire Oceanside Littoral Cell; but at North Beach, the
alongshore imbalance in wave height causes higher southerly longshore transport rates of sand
exiting North Beach at the inlet jetties than enters North Beach at Maple A venue. This inequality
in sand transport rates between the north and south ends of North Beach is divergence of drift,
and when the sand transport rates are higher at the down-drift end of the beach, it becomes a
constant loss system referred to as negative divergence of drift. So, when beach fill volumes
exceed the critical mass of North Beach, the excess sand cannot be supported in equilibrium on
its narrow wave-cut platform and is quickly lost to the negative divergence of drift.
Historically, The CEM baseline study finds that when a standard 1: 10 (rise over run)
beach fill template is filled to critical mass, the theoretical minimum sand loss rate to negative
divergence of drift is 1,495 yds3/day, and the sand retention time is 53 days. When beach fill
sand volume is increased by 103% over critical mass (as occurred during the 2002/2003 dredge
event when 161 ,525 yds3 were placed on North Beach), the retention time is only increased by
26 % from T0 = 53 days to T0 = 67 days. This is not a good return on doubling the investment in
beach fill for North Beach because the sand loss rate increases by 61 % to 2,411 yds3/day, or an
increase in sand loss of 916 yds3 /day over what would have otherwise occurred if the beach fill
volume were limited to critical mass. Unfortunately, such increases in sand loss at North Beach
correlate with proportional increases of sand influx rates into Agua Hedionda Lagoon.
The 2014/2015 survey data show that AHL sand influx rates also increase when the fill
volumes are less than the critical mass. Sand influx rates in 2014/2015 were 1,969 yds3 /day when
only 64,968 cubic yards were placed on North Beach (14,503 yds3 below critical mass
requirements). Bear in mind that the critical mass is the minimum volume of sand required to
establish an equilibrium beach profile on a wave-cut platform; and a beach is in its most stable
state with an equilibrium profile. But with a prevailing negative divergence of drift along North
Beach equilibrium cannot be achieved due to insufficient sand volume, and consequently sand
loss rates increase with a destabilized non-equilibrium profile. The worst example of this in the
CEM baseline was the 2010/2011 dredging event when only 62,030 yds3 were placed on North
Beach, and sand loss rates rose to 2,050 yds3 /day with retention times of only 30 days.
Following CEM beach evolution analysis of the North Beach historic baseline, attention
was given to finding a more effective beach fill template that could increase sand retention using
beach fill from Agua Hedionda Lagoon dredging. Beach fill has typically been placed on
Carlsbad beaches using a standard beach fill template with a flat backshore platform and a 1: 10
(rise over run) seaward facing beach slope extending down to Oft. MLLW. This convention
dates back to the Regional Beach Sand Project, (AMEC, 2002). However, stable beach profiles
in Nature have a much more gradual, curving profile with slopes that range between 1 :50 to
3: 100. Formulations of equilibrium beach profiles are found in the U.S. Army Corps of
Engineers Shore Protection Manual and later the Coastal Engineering Manual; and the latest
most advanced formulation is known as the elliptic cycloids. The elliptic cycloid formulation can
account for continuous variations in the equilibrium beach profile due to variability in wave
height, period and direction when occurring in combination with variations in beach sediment
grain size and beach sand volume. Therefore, a new beach filLtemplate.has been proposed here
for North Beach referred to as the cycloid-dune template (see Figures 20-24). The shape of the
template is based on the extremal elliptic cycloid which is the equilibrium profile for the highest
wave in the period of record. But the extremal elliptic cycloid extends below the MLL W tide line
and earth moving equipment which spread out the beach fill cannot work below MLL W. So, the
template truncates the extremal elliptic cycloid at MLL W and places the residual volume of
critical mass (totaling 43,200 yds3) in a back-beach dune that stretches 3,200 ft. from the Agua
Hedionda Lagoon north inlet jetty to Maple A venue.
While an elliptic cycloid is an equilibrium beach surface, it does not roduce a state of
zero sand loss in the presence of a negative divergence of drift, which is the persistent littoral
drift state along North Beach. When the divergence of drift is negative, the equilibrium cycloidal
beach profile will progressively shift landward as it loses sand to negative divergence of drift,
eventually intersecting the basement surface of the critical mass envelope. Once this happens,
then the cycloidal shape of the profile is disrupted, and the equilibrium state of the profile is lost.
The concept behind the cycloid-dune template is that, as the cycloid begins to approach an
intersection with the basement surface of the critical mass envelope, (under the erosional effects
of continued negative divergence of drift), it also intersects the base of the dune and receives
additional sediment cover as the dune erodes and spreads out downslope across the still intact
cycloidal surface. Thus, the dune acts as a restoring mechanism that re-supplies the cycloid with
sand lost to negative divergence of drift.
The construction method envisioned for the cycloid-dune template begins with building
the back-beach dune portion first, starting at the north inlet jetty and adding sections to the
dredge pipeline until the build-out of the dune reaches Maple Ave. Building the dune first creates
a "safe" reservoir of sand before the template can be fully constructed, and sand from this
reservoir is only released to the lower eroded basement surface during periods of the highest
tides and waves. After the buildout of the dune to Maple Ave, the cycloid portion of the template
is laid out beginning from the toe of the dune and spreading the material down slope to MLLW,
and working back towards the north inlet jetty, removing pipeline sections as the cycloids are
completed
CEM beach evolution simulations of the cycloid-dune template show significant
improvements in sand loss rate and retention time relative to the historic baseline. Again, the
most efficient use of Agua Hedionda dredged sands occurs when the cycloid-dune template is
filled to no more than critical mass (79,471 yds3), which reduces average sand loss rates on
North Beach to an absolute minimum of 417 yds3/day, while extending retention time to 190.6
day~. This is a 3.6 fold improvement in sand retention time over historical dredge disposal
practices at North Beach, which could result in a reduction of sand influx rates into Agua
Hedionda Lagoon by a similar factor during the first six (6) months following North Beach
disposal. If the cycloid-dune template is filled to more than critical mass by adding more sand to
the back-beach dune, then North Beach retention time will increase beyond 190.6 days. If the
reserve sand volume in the dune were more than doubled to 95,529 yds3 (achieving a total
placement volume of V0 = 175,000 yds3) then retention time could be extended to a maximum of
222 days. But, again, this is not a good return on doubling the investment in reserve beach fill for
North Beach because retention time is only increased by an extra month while the sand loss rate
increases by 89 % to 787 yds3/day. Furthermore, it is simply not possible to place more sand than
the critical mass in the back beach dune and not have much of the dune sand prematurely erode
during periods of high waves and high tides, because the enlarged dune encroaches further
seaward into the middle bar-berm portion of the profile that is subject to more frequent wave
attack.
On the other hand, under-filling the cycloid-dune template, (by building a reduced dune),
leads to accelerated sand loss rates and reduced retention times. The prevailing negative
divergence of drift causes the initial cycloid profile in the lower portion of the template to shift
landward, and once intersection with the basement surface of the critical mass envelope occurs,
there are insufficient sand reserves in the reduced dune to resupply the cycloid in the presence of
continued negative divergence of drift. Once the reserve sand supply in the dune is exhausted,
the cycloidal shape of the profile is disrupted, and the equilibrium state of the profile is lost.
Even so, if the cycloid-dune template is filled to a volume equivalent to the 2104/2015 North
Beach disposal event ( V0 = 64,968 yds3) by using a dune containing only 28,697 yds3 , then sand
retention times are still significantly better than what was achieved using the standard 1: 1 O (rise
over run) template. With the cycloid-dune template, retention times with only 64,968 yds3 of
beach fill were T0 = 117 days and sand loss rates were still small, 554 yds3 /day, or a factor of 2.2
better than what was achieved using standard North Beach disposal practices during the
2104/2015 dredge event. With even smaller beach fill volumes, the cycloid-dune retention times
and sand loss rates rapidly degrade, but retention times remain equivalent to those of the
2104/2015 North Beach disposal event for beach fill volumes as low as 37,000 yds3, for which
the back beach dune was reduced to vanishingly small.
7) References:
AMEC, 2002, "Regional Beach Sand Project Post-construction Monitoring Report for Intertidal,
Shallow Subtidal and Kelp Forest Resources", submitted to SANDAG,
http:/ /www.sandag.org.
Cabrillo, 2015, '"'Order 96-32: First Quarter 2105, Second Quarter 2015 and Final Monitoring
Report for Agua Hedionda Lagoon Dredging", submitted to California Regional Water
Quality Control Board, 30 pp.
CDIP, 1984-1988, "Coastal data information program, monthly reports," U.S. Army Corps of
Engineers, California Department of Boating and Waterways, Monthly Summary Reports
#97-#150.
CDIP, 1976-1995, "Coastal Data Information Program, Monthly Reports," U.S. Army Corps of
Engineers, California Department of Boating and Waterways, SIO Reference Series, 76-
20 through 95-20.
CDIP, 1993-1994, "Monthly Summary Report," SIO Reference Series (93-27) through (94-19).
CDIP, 2016, "Coastal Data Information Program" http://cdip.ucsd.edu/
Elwany, M . H. S., A. L. Lindquist, R. E. Flick, W. C. O'Reilly, J. Reitzel and W. A.
Boyd, 1999, "Study of Sediment Transport Conditions in the Vicinity of Agua Hedionda
Lagoon," submitted to California Coastal Commission, San Diego Gas & Electric, City
of Carlsbad.
Elwany, M. H. S., R. E. Flick, M. White, and K. Goodell, 2005, "Agua Hedionda Lagoon
Hydrodynamic Studies," prepared for Tenera Environmental, 39 pp.+ appens.
Ellis, J.D., 1954, "Dredging Final Report, Agua Hedionda Slough Encina Power Station," San
Diego Gas and Electric Co., 44pp.
Inman, D. L. and B. Brush, 1970, "The coastal challenge" Science, vol38, no. 5 pp36-45.
Inman, D. L. & S. A. Jenkins, 1985, "Erosion and accretion waves from Oceanside
Harbor," p. 591-593, in Oceans '85: Ocean Engineering and the Environment,
IEEE and Marine Technology Society, v. 1,674 pp.
Inman, D. L. and Masters, P. M., 1991, "Coastal sediment transport concepts and
mechanisms," Chapter 5 (43 pp.) in State of the Coast Report, San Diego
Region, Coast of California Storm and Tidal waves Study, U.S. Army Corps
of Engineers, Los Angeles District Chapters 1-10, Appen. A-1, 2 v.
Inman, D. L., M. H. S. Elwany and S. A. Jenkins, 1993, "Shorerise and bar-berm profiles on
ocean beaches," Jour. Geophys. Res., v. 98, n. ClO, p. 18,181-199.
Inman, D. L., S. A. Jenkins, and M. H. S. Elwany, 1996, "Wave climate cycles and
coastal engineering practice," Coastal Eng., 1996, Proc. 25th Int.
Conf,(Orlando), Amer. Soc. Civil Eng., Vol. 1, Ch. 25, p. 314-327.
Inman, D. L. & S. A. Jenkins, 1997, "Changing wave climate and littoral drift along the
California coast," p. 538-549 in 0 . T. Magoon et al., eds., California and the
World Ocean '97, ASCE, Reston, VA, 1756 pp
Inman, D. L. & S. A. Jenkins, 1999, "Climate change and the episodicity of
sediment flux of small California rivers," Jour. Geology, v. 107, p. 251-270.
Inman, D. L. & S. A. Jenkins, 2004, "Scour and burial of objects in shallow
water," p. 1020-1026 in M. Schwartz, ed., Encyclopedia of Coastal Science,
Kluwer Academic Publishers, Dordrecht, Netherlands.
Jenkins, S. A. and D. W. Skelly, 1988, "An Evaluation of the Coastal Data Base Pertaining to
Seawater Diversion at Encina Power Plant Carlsbad, CA," submitted to San Diego Gas
and Electric, Co., 56 pp.
Jenkins, S. A., D. W. Skelly, and J. Wasyl, 1989, "Dispersion and Momentum Flux Study of the
Cooling Water Outfall at Agua Hedionda," submitted to San Diego Gas and Electric, Co.,
36 pp.+ appens.
Jenkins, S. A. and J. Wasyl, 1993, "Numerical Modeling of Tidal Hydraulics and Inlet Closures
at Agua Hedionda Lagoon," submitted to San Diego Gas and Electric, Co., 91 pp.
Jenkins, S. A. and J. Wasyl, 1994, "Numerical Modeling of Tidal Hydraulics and Inlet Closures
at Agua Hedionda Lagoon Part II: Risk Analysis," submitted to San Diego Gas and
Electric, Co., 46 pp. + appens.
Jenkins, S. A. and J. Wasyl, 1995, "Optimization of Choke Point Channels at Agua
Hedionda Lagoon using Stratford Turbulent Pressure Recovery," submitted to San
Diego Gas and Electric, Co., 59 pp.
Jenkins, S. A. and J. Wasyl, 1997, "Analysis of inlet closure risks at Agua
Hedionda Lagoon, CA and potential remedial measures, Part II," submitted to San
Diego Gas and Electric, Co., 152 pp.+ appens.
Jenkins, S. A. and J. Wasyl, 1998a, Analysis of Coastal Processes Effects Due to the San
Dieguito Lagoon Restoration Project: Final Report, submitted to Southern California
Edison Co., 333 pp.
Jenkins, S. A. and J. Wasyl, 1998b, Coastal Processes Analysis of Maintenance Dredging
Requirements for Agua Hedionda Lagoon, submitted to San Diego Gas and Electric Co.,
176 pp.+ appens.
Jenkins, S. A. and D. L. Inman, 1999, A Sand transport mechanics for equilibrium in tidal inlets,
Shore and Beach, vol. 67, no. 1, pp. 53-58.
Jenkins, S. A. and J. Wasyl, 2001, Agua Hedionda Lagoon North Jetty Resoration Project: Sand
Influx Study, submitted to Cabrillo Power LLC., 178 pp. + appens.
Jenkins, S. A. and J. Wasyl, 2003, Sand Influx at Agua Hedionda Lagoon in the Aftermath of the
San Diego Regional Beach Sand Project, submitted to Cabrillo Power LLC., 95 pp. +
appens
Jenkins, S. A. and J. Wasyl, 2005 , Hydrodynamic Modeling of Dispersion and Dilution of
Concentrated Sea Water Produced by the Ocean Desalination Project at the Encina Power
Plant, Carlsbad, CA. Part II: Saline Anomalies due to Theoretical Extreme Case
Hydraulic Scenarios, submitted to Poseidon Resources, 97 pp.
Jenkins, S. A. and J. Wasyl, 2005, "Oceanographic considerations for
desalination plants in Southern California coastal waters," Scripps Institution
of Oceanography Tech. Rpt. No. 54, 109 pp + appendices.
http ://repositories.cdlib.org/si o/techreport/ 54/
Jenkins, S. A. and J. Wasyl, 2005, "Coastal evolution model," Scripps Institution of
Oceanography Tech. Rpt. No. 58, 179 pp + appendices.
http:/ /repositories.cdlib.org/sio/techreport/5 8/
Jenkins, S. A. and D. L. Inman, 2006, "Thermodynamic solutions for equilibrium
beach profiles", Jour. Geophys. Res., v.3 , C02003, doi:10.1029, 21pp.
Jenkins, S. A., Inman, D.L., Michael D. Richardson, M.D., Thomas F. Wever, T.F. and J.
Wasyl, 2007, "Scour and burial mechanics of objects in the nearshore", IEEE
Jour.Oc.Eng, vol.32, no. 1, pp 78-90.
Jenkins, S. A. and J. Wasyl, 2011, "Hydrodynamic Approach to Wetland Restoration by
Optimization of Bridge Waterways", Department of Transportation, District 11
Environmental Division, MS-242, Technical Report # l lAl 766, 258 pp.
Jenkins, S. A. and S. Taylor, 2015, "Storm and Tidal Conditions Determination
for Coastal Drainage Design," submitted to Office of Highway Drainage Design
Division of Design, MS 28, California Department of Transportation
Merkel, 2008, " Agua Hedionda Outer Lagoon Flood Shoal Maintenance Dredging Sediment
Characterization Report, Tech Rpt # ACOE-2001100328-SKB, submitted to Cabrillo
Power, LLC., 45 pp.
NOAA, 1998, A Verified/Historical Water Level Data@
http://www.opsd.nos.noaa.gov/data res.html
NWS, 2009, "National Weather Service Daily Climate Reports,"
http://www. wrh.noaa. gov /sgx/ o bs/rtp/ earls bad.html
U.S. Army Corps of Engineers, 1985, "Littoral zone sediments, San Diego Region,
October 1983 -June 1984", Coast of California Storm and Tidal Wave Study,
CCSTWS 85-11.
U.S. Army, Corps of Engineers (USACE), 1991, "State of the Coast Report, San Diego
Region," Los Angeles District, CA: Coast of California Storm and Tidal Waves
Study, Final Report 1.
U. S. Army, Corps of Engineers (USACE), 2006, "Coastal Engineering Manual,"
Engineering Manual 1110-2-1100, U.S. Army, Corps of Engineers, Washington, DC, (in
6 volumes).
U.S. Department of Commerce National Ocean Service, 1986, "Tide tables 1986, high and low
water predictions for west coast of North and South America", 234 pp.
USGS, 1997, "USGS Digital Data Series DDS-37 at INTERNET URL,"
http://wwwrvares.er.usgs.gov/wgn96cd/wgn/wq/region18/hydrologic unit code.
Van der Meer, J.W., 2002. Wave Run-up and Overtopping at Dikes. Technical Report,
Technical Advisory Committee for Water Retaining Structures (TA W), Delft, the Netherlands.
Appendix-A: North Beach Disposal History for Agua Hedionda Outer Lagoon
Dredging Disposal
Year Date Volume Influx Basin Volume *Location Comments
Start Finish cubic yard Days Yds3/Day cubic yard
Dec-97 Feb-98 59,072 92 642 Middle 59,072 M Modification
1998 Feb-98 Jul-98 214,509 150 1,430 Inner 120,710 M Modification 93,799 s
1999 Feb-99 May-155,000 99 304 510 Outer 155,000 N Maintenance
2000-Nov-141,346 N
Apr-01 422,541 701 603 Outer 195,930 M Maintenance 01 00 85,265 s
2002-161,525 N
Dec-02 Apr-03 354,266 730 . 485 Outer 131,377 M Maintenance 03 61,364 s
2004-100,487 N
Jan-05 Mar-05 348,151 704 495 Outer 170,515 M Maintenance 05 77,149 s
2006-149,168 N
Jan-07 Apr-07 333,373 763 437 Outer 121,038 M Maintenance 07 63,167 s
2008-104,141 N
Dec-08 Apr-09 299,328 733 408 Outer 102,000 M Maintenance 09 93,185 s
2010-62,030 N
Dec-IO Apr-11 226,026 736 307 Outer 93,696 M Maintenance 11 70,300 s
2014-64,968 N
Dec-10 Apr-11 294,661 736 400 Outer 156,056 M Maintenance 15 73,637 s
TOTAL 8,528,842 8,528,840
MAINTENANCE
TOTAL 8,255,261
*Location: N= North Beach; M = Middle Beach; S = South Beach