A hydrologic and geomorphic model of estuary breaching and closure

Geomorphology 191 (2013) 64–74

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A hydrologic and geomorphic model of estuary breaching and closure Andrew Rich ⁎, Edward A. Keller Department of Earth Science, University of California, 1006 Webb Hall, Santa Barbara, CA 93106, USA

a r t i c l e

i n f o

Article history: Received 27 September 2012 Received in revised form 25 January 2013 Accepted 10 March 2013 Available online 16 March 2013 Keywords: Estuary hydrology Inlet breaching and closure Model Coastal processes

a b s t r a c t To better understand how the hydrology of bar-built estuaries affects breaching and closing patterns, a model is developed that incorporates an estuary hydrologic budget with a geomorphic model of the inlet system. Erosion of the inlet is caused by inlet flow, whereas the only morphologic effect of waves is the deposition of sand into the inlet. When calibrated, the model is able to reproduce the initial seasonal breaching, seasonal closure, intermittent closures and breaches, and the low-streamflow (closed state) estuary hydrology of the Carmel Lagoon, located in Central California. Model performance was tested against three separate years of water-level observations. When open during these years, the inlet was visually observed to drain directly across the beach berm, in accordance with model assumptions. The calibrated model predicts the observed 48-h estuary stage amplitude with root mean square errors of 0.45 m, 0.39 m and 0.42 m for the three separate years. For the calibrated model, the probability that the estuary inlet is closed decreases exponentially with increasing inflow (streamflow plus wave overtopping), decreasing 10-fold in probability as mean daily inflow increases from 0.2 to 1.0 m 3/s. Seasonal patterns of inlet state reflect the seasonal pattern of streamflow, though wave overtopping may become the main hydrologic flux during low streamflow conditions, infrequently causing short-lived breaches. In a series of sensitivity analyses it is seen that the status of the inlet and storage of water are sensitive to factors that control the storage, transmission, and inflow of water. By varying individual components of the berm system and estuary storage, the amount of the time the estuary is open may increase by 57%, or decrease by 44%, compared to the amount of time the estuary is open during calibrated model conditions for the 18.2-year model period. The individual components tested are: berm height, width, length, and hydraulic conductivity; estuary hypsometry (storage to stage relationship); two factors that control wave-swash sedimentation of the inlet; and sea level rise. The elevation of the berm determines the volume of water that must enter the estuary in order to breach, and it modulates the wave-overtopping flux and frequency. By increasing estuary storage capacity, the estuary will breach less frequently (−27% change in time open for modeled excavation scenario) and store water up to 3 months later into the summer. Altering beach aquifer hydraulic conductivity affects inlet state, and patterns of breaching and water storage. As a result of sea-level rise of 1.67 m by 2100, and a beach berm that remains in its current location and accretes vertically, the amount of time the estuary remains open may decrease by 44%. Such a change is an end-member of likely scenarios given that the berm will translate landwards. Model results indicate that the amount of time the estuary is open is more sensitive to changes in wave run-up than the amount of sand deposited in the inlet per each overtopping wave. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Bar-built, coastal lagoons in the 21st century will experience a number of stressors that will affect their function. These include 0.42–1.67 m of sea-level rise (Dalrymple et al., 2012), changing precipitation and temperature patterns (Seager and Vecchi, 2010), and a growing human population that is largely concentrated near the coast. As population growth continues, so too will the anthropogenic impact on streamflow (Beighley et al., 2003), which is a strong driver of the function of bar-built estuaries. Similarly, the growth and decay of beach barriers is linked to sediment availability (Carter et al., 1989) ⁎ Corresponding author. Tel.: +1 805 893 4207. E-mail address: [email protected] (A. Rich). 0169-555X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.geomorph.2013.03.003

and therefore engineering practices such as the impoundment of sediment by dams (Willis and Griggs, 2003), beach groins and jetties. As shown here, the existence and characteristics of beach barriers fundamentally controls estuary dynamics. Predicting how these stresses may impact estuaries is important because estuaries are considered to be the most valuable biome on earth per-area (Costanza et al., 1997). This paper seeks to determine: 1) if the breaching and closing processes can be modeled with a hydrologic and geomorphic model, 2) how estuarine variability, such as differences in beach-berm heights or estuary storage, affect estuary function, and 3) how sea-level rise will affect estuary function. Bar-built coastal lagoons exist in microtidal (Cooper, 2001) and mesotidal environments, are wave-exposed, and often occur where streamflow is highly seasonal, such as in California (Elwany et al.,

A. Rich, E.A. Keller / Geomorphology 191 (2013) 64–74

1998), Australia (Ranasinghe and Pattiaratchi, 2003), and South Africa (Cooper, 2001). Estuaries are fronted by high supratidal beach-berms when there is ample coarse littoral sediment (Kjerfve and Magill, 1989; Cooper, 2001). For estuaries fronted by a supratidal beach berm, wave energy is the major control on berm-height (Takeda and Sunamura, 1982), though aeolian processes may contribute via dune formation in the backbeach. Lower beach-berms occur when nearshore conditions are dissipative (Cooper, 2001). There is a considerable amount of research concerning the processes that maintain an open inlet for larger, more tidally dominated systems (Escoffier, 1940; Jarrett, 1976; van de Kreeke, 1985; Ranasinghe and Pattiaratchi, 2003). Relatively little work has investigated the controls on estuary breaching and closing, especially of smaller, bar-built estuarine systems, and such research has been predominantly empirical. For a Southern California lagoon, Elwany et al. (1998) showed that streamflow is the major control on inlet state, and that tidal prism and wave processes play a smaller role during closure. By analyzing a record of estuary closures of unprecedented detail and length, Behrens (2012) showed that the length of time the estuary remains closed before breaching is a function of streamflow, estuary storage at breaching levels and barrier seepage, whereas inlet closure probability is best predicted using a ratio of inlet discharge to sediment transport by waves. The understanding of inlet morphodynamics was improved by Baldock et al. (2008) who was able to accurately predict channel inlet elevation change by sand deposition using predictions of shore-normal, wave-swash run-up heights. Other authors emphasize the role of wave overtopping to induce breaching (Hart, 2007) – or as a counterbalance to evaporative losses (Rustomji, 2007) – while Kirk (1991) emphasizes the importance of barrier material in transmitting floods. Together these and other studies demonstrate that estuary function is a result of many interacting processes, and that isolating the effect of a single property on function is difficult. Therefore, the approach taken in this work is to develop a model of lagoon breaching and closing, and then to investigate how individual properties of the estuary influence its function. The model addresses one of the processes that breach bar-built coastal lagoons, namely fluvial erosion of the beach barrier by channelized flow through the estuary inlet. The two processes not addressed are wave erosion and seepage-induced transport by exfiltrating groundwater on the beachface. Seepage forces increase directly with groundwater hydraulic gradient (Howard and McLane, 1988), and therefore inversely with beach width (Kraus et al., 2008). Wave erosion can cause breaching in two ways: incision of the beach berm by overtopping waves or by landward erosion of the beachface as a result of backswash. The erosive ability of overtopping waves is a function of the height of overwash (Donnelly et al., 2006), and the geometry and slope of the back-berm (Pierce, 1970); minor overwash builds the berm, whereas steep, narrow berms promote erosion. This paper is organized as follows: a description of the study site; development of the hydrologic and geomorphic model; and a results section highlighting the calibrated model results, followed by a sensitivity analysis of the model, and a discussion of drivers of estuary change. 2. Study site The Carmel Lagoon is fronted by a steep, reflective beach composed of coarse sand derived from the Carmel Watershed (Storlazzi and Field, 2000). The beach sits in a coastal embayment, with a southern longshore sediment transport direction (Howell, 1972) and 100 m water depths within half of a kilometer. Nearby beaches have been observed to accrete and erode up to 60 m in a season (Bascom, 1951), and there is potentially a long-term net erosion of the beach (Storlazzi and Field, 2000). From September to May, deepwater Hs generally range from 1.3 to 3.7 m, sometimes exceeding 9 m, with directions of 270°–310° and wavelengths ranging 10–17 s. During

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the summer, waves approach from similar directions, but with smaller Hs and shorter wavelengths. Waves coming from the Northwest arrive to the Carmel Beach unrefracted and unimpeded (Storlazzi and Field, 2000). For three scenarios, ranging 27° in deepwater wave direction and each of different wavelength, refraction and shoaling modeling of waves traveling from deepwater to 15 m depth reveals that waves undergo less than a 10% change in wave height and wavelength offshore of the Carmel Lagoon (Laudier et al., 2011). The Carmel River drains 660 km 2 of mountainous topography, and the flow is highly variable (Fig. 1). As measured 5 km upstream of the Carmel Lagoon, more than 90% of yearly streamflow occurs between January and May, and yearly mean streamflow varies from zero flow to 14.5 m 3/s. Such variability is often related to anomalies in tropical sea-surface temperatures (Cayan et al., 1999), though the prevalence of low flows in the Carmel River are also the result of groundwater pumping of the alluvial aquifer (Kondolf et al., 1987), and until 2003 by abstractions of water at two upstream, nearly sediment-filled reservoirs (MPWMD, 2008). To protect nearby properties from flooding, the Carmel Lagoon is sometimes artificially breached preceding the first major streamflow of the year, at which time it would imminently breach otherwise (James, 2005). Once breached, the Carmel Lagoon inlet may migrate up to 500 m north, 200 m to the south, or, about 50% of the time, it will remain in its initial breach location, directly across the beach berm (James, 2005). The estuary was excavated and widened in 1997 and 2004 in order to increase habitat area (James, 2005), resulting in a 24% increase in estuary storage at typical breaching levels (James, 2005; Hope, 2007). The Monterey Peninsula Water Management District (MPWMD) has operated a water-level recorder since 1993 in the Carmel Lagoon; the USGS operates a streamflow gage 5 km upstream of the estuary; two wave buoys measure waves within 50 km; and tides are measured 9 km north of the estuary. 3. Methods The breaching and closing model is based upon a hydrologic mass-balance approach for estuary storage, with hydrologic fluxes from streamflow, wave-overtopping, inlet discharge, evaporation, and groundwater flow through the barrier. The model consists of the following components: 1) a water balance for the estuary basin and 2) a channel inlet component, for which channel geometry, fluvial erosion and wave deposition are calculated. 3.1. Estuary mass balance The volume of water in the estuary through time is a function of the difference in the fluxes of water flowing into or out of the estuary. The mass balance is written as:
 ΔS ¼ qriver þ qovertop þ qinlet þ qgroundwater þ qevaporation Δt

ð1Þ

where ΔS is the change in storage, Δt is the timestep, qriver is streamflow, qovertop is the flux from wave overtopping of the beach berm, qinlet is flow through the berm inlet, qgroundwater is groundwater flow between the estuary and ocean through the beach barrier, and qevaporation is evaporation of water from the estuary surface. River flow and evaporation (DWR, 1974) are model boundary conditions, whereas the other fluxes are dependent upon estuary, tidal or wave conditions. 3.2. Channel inlet discharge Channel inlet flow only occurs when the estuary or tidal level is higher than the inlet, and its velocity is determined by Manning's equation. The depth, direction, and slope of inlet flow depend upon

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Fig. 1. Site Map. a. LiDAR DEM (csc.noaa.gov) of Carmel Lagoon showing Carmel River, beach-berm elevation, and location of waterlevel gage within the estuary. Wave rose shows incident wave directional distribution. b. location map of Carmel Lagoon.

the tide level, estuary stage, and the height of the inlet (Fig. 2). The width of the channel is calculated using hydraulic geometry relationships, relating flow magnitude to channel width (O'Brien, 1931; Hughes, 2002; Behrens et al., 2009), and is calculated as: W¼

ϕ −0:002 −0:153 S θQ d50

A B

La

go

on

ð2Þ

3.3. Inlet erosion and sedimentation

l ne

an

et Inl

where θ and ϕ are coefficients, Q is flow discharge, d50 is median grain size, and S is the slope of the channel (Lee and Julien, 2006). The model assumes that the inlet channel flows directly across the beach berm (i.e. no migration of channel), and that the beach width remains constant. The channel inlet elevation cannot exceed the elevation of the beach berm.

Be r

m

le

ng th

Ch

Beach Berm (B L) beachface slope, ß

ηlagoon

B

Changes to the channel inlet elevation are calculated by treating the inlet as an alluvial channel that is subject to deposition of sand by wave-swash deposition and erosion by fluvial transport: Δz ¼ ðqswash −qfluvial ÞΔt

h idt hw c ea

Fixed (MSL)

depth

slope (s)

R (wave run-up)

Rc

ηinlet Rinlet

ð3Þ

stillwater level where qswash is wave-swash deposition, and qfluvial is fluvial erosion. The change in channel inlet height occurs at the estuary side of the inlet, whereas the beachside of the inlet remains fixed at mean tide (Fig. 2). The vertical erosion of sand by inlet discharge is calculated by adapting the bedload transport equation of Meyer-Peter and Müller (1948) as: 3=2

qfluvial ¼ ψðτ−τ crit Þ

ð4Þ

Fig. 2. Beach berm and definitions of variables. A. Beach width, berm height and length are constant for each simulation. B. Cross section through the inlet channel showing wave run-up (R), freeboard height of inlet channel (Rinlet), freeboard height of the beach-berm (RC; for wave overtopping calculation), stillwater level, elevation of the inlet (ηinlet), and elevation of the lagoon waterlevel (ηlagoon). Changes in inlet elevation are a result of ΔZ (see text). Inlet water depth and slope are dependent upon ηlagoon, ηinlet, beach width, and the elevation of the tide when it is above mean sea level (MSL). The left edge of the berm remains fixed through all simulations at MSL. ηinlet cannot erode lower than MSL.

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where ψ is a coefficient, τcrit is the shear stress below which transport does not occur for the bedload material, and τ is shear stress caused by the water flowing through the inlet. τcrit is predicted using the formulation of Miller et al. (1977). Deposition of sand onto the channel inlet by overtopping waveswash is calculated using the methods of Baldock et al. (2008). While longshore transport processes are clearly important in the sedimentation of inlets, cross-shore, swash-driven sedimentation is likely more important for the closure of supratidal inlet systems, especially on embayed coasts where longshore currents are weak (Ranasinghe and Pattiaratchi, 1999). The probability of a wave overtopping the channel inlet is a function of the wave run-up (R) of breaking wave bores, and the height difference between the stillwater level and the channel inlet (Hunt, 1959) (Rinlet; Fig. 2), where: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ¼ C tanβ Hs  L0 :

ð4Þ

C is a calibration coefficient, Hs is significant offshore wave height, tanß is beachface slope, and L0 is offshore wavelength. Assuming a Rayleigh distribution of wave run-up, the probability of a wave overtopping the beach-berm is: h i 2 PðR > Rinlet Þ ¼ exp −ðRinlet =RÞ :

ð5Þ

The probability of waves overtopping the freeboard height of the inlet channel (Rinlet) is calculated at each time step because the inlet elevation is dynamic. To calculate the flux of deposited sand from wave overwash for a model timestep, the following method is applied: qswash ¼ htsand  N  P

ð6Þ

where htsand is the height of sand deposited per wave (m) that overtops the berm inlet and N is the number of waves that arrive at the beachface per timestep as determined from the wave period (Baldock et al., 2008).

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In this work the effect of refraction and shoaling in the near shore are not incorporated. Rather, wave data observed at NOAA buoy 46042 located 57 km NW of the lagoon was transformed linearly to Scripps buoy 46239 located 27 km to the SE of the lagoon (Fig. 1). This was achieved through a linear regression of 2.5 years of contemporaneous Hs and Tp data between both buoys. 3.5. Estuary storage Converting estuary storage to water-level, and vice-versa, is performed using a hypsometric relationship of water storage to water-level. Two hypsometric curves (James, 2005; Hope, 2007) were used for the model simulations to account for changes to the estuary bathymetry due to a restoration project that excavated a portion of the estuary. Both hypsometric curves are extended beyond their original coverage using LiDAR observations from 2010 (csc.noaa.gov). 3.6. Goundwater flow Groundwater flow between the estuary and the ocean is calculated analytically by assuming Dupuit conditions for groundwater flow, Input Variables Hypsometric curve Max berm height Beach width Berm length Hydraulic conductivity Beachface slope Inlet roughness

Initial Conditions Estuary storage (S0) Inlet elevation (ηinlet, 0)

Convert estuary storage (S) to elevation (ηlagoon); then subtract Hevap

OUTPUT ηlagoon > ηinlet or ηtide >ηinlet

yes

Calculate channel depth, channel width and channel velocity

no

Calculate channel inlet discharge (Qinlet)

Calculate groundwater discharge (Qgw)

Calculate groundwater discharge (Qgw)

Calculate change in estuary storage (ΔS)

Calculate change in estuary storage (ΔS)

ΔS = (Qstr + Qgw + Qover)Δt

ΔS =(Qstr + Qinlet + Qgw + Qover)Δ

qfluvial=0

Calculate fluvial erosion from inlet discharge (qfluvial)

3.4. Wave overtopping and wave transformations The hydrologic flux from wave overtopping is calculated using the wave overtopping model of Van der Meer and Janssen (1995), which was calibrated specifically for the Carmel Lagoon (Laudier et al., 2011). The form of the wave overtopping equation is dependent upon the Irribaren number (ζ):
pffiffiffiffiffiffiffiffiffiffiffiffi−1 qffiffiffiffiffiffiffiffiffi tan β gH3S BL Q ¼ Aζ exp½−BRc =γ r ζHs  qffiffiffiffiffiffiffiffiffi Q ¼ Cζ exp½−DRC =γr HS  gH3S BL

ζ>2

ζ≤2

ð7aÞ ð7bÞ

pffiffiffiffiffiffiffiffiffiffiffiffiffi where ζ ¼ tanβ= HS =L0 , RC is the freeboard height of the beachberm (Fig. 2B), Lo is the offshore wavelength, A, B, C and D are calibration coefficients, γr is a beach condition reduction factor, HS is the significant wave height, and BL is the length of the berm over which overtopping occurs (Fig. 2A; Van der Meer and Janssen, 1995; Laudier et al., 2011). In the original formulation, significant waveheight and peak wavelength at the toe of the beachface were used (Van der Meer and Janssen, 1995), whereas Laudier et al. (2011) used refracted wave conditions at 15 m depth. Laudier et al. (2011) implemented the overtopping equation in a quasi-2D manner by calculating the flux for 5 m intervals along dGPS beach surveys. For this work, the flux is calculated in a 1D manner where the beachface slope and berm height are constant along the length of the berm and for the duration of each model run. An ad-hoc adjustment was applied to the wave overtopping whereby it is limited to a total peak flux of 5 m 3/s.

Si+1 = Si + ΔS Calculate swash deposition into channel inlet (qswash) Calculate elevation change of channel inlet Δηinlet=(qswash-qfluvial)Δt ηinlet, i+1= ηinlet, i

+ Δηinlet

OUTPUT Fig. 3. Flow diagram of a model timestep.

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Table 1 Data sources for model boundary conditions. Model Input Source Tides Streamflow Waves

Evaporation

Station

Frequency and units

NOAA/NOS/CO-OPS USGS

Monterey, Ca. 9413450 60-min, m NAVD88 Carmel River near 15-min, m3/s Carmel, 11143250 National Data Buoy Monterey 46042 and 60-min, Hs and Tp Center and California Point Sur 46239 Data Information Project DWR, 1974 Central Coast Coastal Inches per month Valleys and Plains

a vertical beachface, and vertical backside of the beach berm. A vertical beachface eliminates the filtering effect of a sloping beachface (Turner, 1993), and a vertical back-beach produces constant groundwater flow lengths in contrast to varied flow lengths that arise with a sloped back-beach. Tidal and lagoon elevations are the boundary conditions for groundwater flow. When streamflow is below a threshold, a groundwater inflow component from the catchment is modeled to contribute to estuary storage. 3.7. Model setup The routine for each model timestep is portrayed in Fig. 3, along with the input variables necessary to run the model. Table 1 lists the model boundary conditions, or the data necessary to derive the boundary conditions and their sources. All model scenarios were performed at 15-min timesteps and all model inputs were interpolated to this interval. 3.8. Model calibration

Hs (m)

Input (m3/s)

The model is calibrated during water year 2003 when multiple observations of the inlet indicate that it was immobile and drained directly across the beach berm (James, 2005). During the opening

and closing period, the following parameters were calibrated: htsand, ψ, C, ϕ and θ. The model was calibrated by minimizing the root mean square error between the observed and modeled 48-h stage amplitude on the basis that it most closely reflects the dynamics of the lagoon, which is the fundamental purpose of this study (Janssen and Heuberger, 1995). The hydraulic conductivity of the beach aquifer and the magnitude of the groundwater inflow are adjusted to maximize model fit during the low-flow, closed period. 4. Results 4.1. Model confirmation Breaching events are identified in the observed records when the water-level falls precipitously, and seasonal closure events are identified when the water-levels cease to oscillate. As seen in Figs. 4 (WY1996) and 5 (WY2002), the breaching model is capable of predicting the initial breaching, seasonal closure, intermittent closures and breaches, and the low-streamflow estuary hydrology. Fig. 6 shows only the portion of water year 2004 when the estuary was continuously opening and closing in order to more clearly highlight model performance during such conditions. For water years 2002 and 2004, the inlet channel was observed to remain in roughly the same location (Fig. 7), draining directly across the ~ 60 m berm and down the beachface (James, 2005), in agreement with model assumptions. In these years, during the open period, the 48-h root mean square error is 0.50 and 0.64 m, respectively (Table 2). In other years, the inlet meanders to the north or south, increasing the inlet length up to 10 × the direct configuration, causing significant differences between the observed and modeled water level. This is illustrated in Fig. 8 where the inlet configuration was observed in its direct configuration from February 1st to April 6th, and, following a 10 m 3/s streamflow storm, the inlet terminus was observed to meander 500 m from its initial position (James, 2005), as has been observed in the Russian River Lagoon (Behrens et al., 2009). Prior to the increase in inlet length (Fig. 8), the model predicts rapid fluctuations in estuary stage, similar to observed data, with an RMSE of 0.45 m. When the inlet length increases following the storm

20 streamflow 10 0 10/95 10

wave overtopping

11/95

12/95

01/96

02/96

03/96

04/96

05/96

06/96

07/96

08/96

09/96

10/96

11/95

12/95

01/96

02/96

03/96

04/96

05/96

06/96

07/96

08/96

09/96

10/96

5 0 10/95 4.5

stage (m, NAVD88)

4

berm inlet model

3.5

observed

3 2.5 2 1.5 10/95

11/95

12/95

01/96

02/96

03/96

04/96

05/96

06/96

07/96

08/96

09/96

10/96

Fig. 4. Model validation for water year 1996. Top box is observed streamflow (USGS gage 11143250) and predicted wave overtopping flux, and middle box is transformed significant wave height (see text for explanation). Bottom box shows model results and observed water level at Carmel Lagoon. Water level data is from Monterey Peninsula Water Management District (James, 2005). Berm inlet height is a model output.

A. Rich, E.A. Keller / Geomorphology 191 (2013) 64–74

69

Hs (m) Input (m3/s)

20 missing data

streamflow

10

wave overtopping

0 10/01 10

11/01

12/01

01/02

02/02

03/02

04/02

05/02

06/02

07/02

08/02

09/02

10/02

11/01

12/01

01/02

02/02

03/02

04/02

05/02

06/02

07/02

08/02

09/02

10/02

5 0 10/01 4.5

stage (m, NAVD88)

4

berm inlet

3.5

model observed

3 2.5 2 1.5 10/01

11/01

12/01

01/02

02/02

03/02

04/02

05/02

06/02

07/02

08/02

09/02

10/02

Fig. 5. Model validation for water year 2002. See Fig. 4 for description.

event, the model continues to predict >1 m fluctuations in estuary stage, whereas the observed data indicates a muted amplitude oscillation due to the reduced hydraulic efficiency of the channel. With the increased channel length, the model error nearly doubles to 0.87 m. A similar event occurs in April 1996 (Fig. 4), which explains the large deviation between the model and observed data for that period. Despite the poor model performance for the elongated inlet conditions, the model is capable of predicting the seasonal closure date within 10.5 days. 4.2. The effect of inflow on inlet state

Hs (m)

Input (m3/s)

Using the calibrated conditions, the model was run for an 18.2-year period, from 1993 to 2011. Under calibrated conditions, the amount

of time that the estuary is open is controlled principally by the magnitude of inflow, which consists of streamflow and overtopping. The inlet is considered open when the estuary waterlevel is higher than the inlet. As mean daily inflow increases from 0 to 2 m 3/s, the probability that the lagoon is closed decreases exponentially (Fig. 9); 98.5% of open days occur when estuary inflow is greater than 0.5 m 3/s and only 12.5% of closed days occur above 0.5 m 3/s. The segregation of inlet state by inflow highlights the importance of inflow on inlet state, though the small overlap between estuary state and inflow indicates that factors other than inflow influence estuary state, albeit to a small degree. Demonstrating the relative importance of wave overtopping versus streamflow is achieved by running the model with zero wave-overtopping and normal streamflow, and subsequently with normal wave overtopping and zero streamflow. With

15

streamflow wave overtopping

10 5 0 01/04

02/04

03/04

01/04

02/04

03/04

04/04

05/04

10 5 0 04/04

4.5 berm height

4

stage (m, NAVD88)

model 3.5

observed

3 2.5 2 1.5 01/04

02/04

03/04

04/04

Fig. 6. Model validation during open period of water year 2004. See Fig. 4 for description.

05/04

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Hs (m) Input (m3/s)

70

20

streamflow wave overtopping

10 0 10

05/00

06/00

07/00

04/00

05/00

06/00

07/00

5 0

stage (m, NAVD88)

04/00

3.5

~60m channel

~500m channel

RMSE =0.45m

RMSE =0.87m

3 2.5 2 model observed

1.5 04/00

05/00

06/00

07/00

Fig. 8. Effect of inlet length on model performance. Model inlet length is 60 m for entire simulation. Channel inlet observations denoted as stars (James, 2005).

open 40–100% of the time — though for March the estuary is open 100% for 14 of the 18 years. By fall to early winter, streamflow input volumes often decrease to zero (15 of 18 years), causing the estuary to convert to a coastal lake with water levels often > 1 m below the berm. During this period, wave overtopping becomes important in regards to the hydrology of the estuary, providing, along with groundwater seepage through the berm and estuary periphery, the main influx of water into the estuary. In some years (5 of 18), streamflow input remains zero in January while wave overtopping reaches its peak, allowing breaches to occur from overtopping alone. Such breaches are short-lived because there is not sustained inlet flow to erode the inlet and the concurrent high wave energy quickly rebuilds the inlet. 500

zero wave-overtopping the inlet remains open for 38.9% of the time, and with zero streamflow it remains open for 0.1%. Under current streamflow and predicted wave overtopping, it is modeled to remain open for 39.5% of the time. A similar relationship is observed on a monthly basis; in January through April, volumetrically the greatest wave overtopping and streamflow months, the estuary is generally

400

# of days open

Fig. 7. Observations of inlet locations for water years 1996, 2002 and 2004. Figures modified by permission from James (2005).

300 200 100 0

0

1

2

3

500

Water year Calibration 2003 Validation 1996 2002 2004

Period of statistic

13/Dec/2002–17/Jul/2003

15/Dec/1995–05/Jun/1996 01/Dec/2001–28/May/2002 29/Dec/2003–30/Apr/2004

RMSE (m)

Period of statistic

0.44

Entire water year

0.65 0.50 0.64

Entire water year Entire water year Entire water year

RMSE (m) 0.37

0.45 0.39 0.42

400

# of days closed

Table 2 Model performance statistics. Root mean square error (RMSE) of the observed and predicted 48-h estuary stage amplitude. The first statistic corresponds to when the estuary is actively opening and closing, and the second statistic is for the entire water year (October to September).

300

n = 2119 3 n = 258 (when input = 0m /s)

200 100 0

0

1

2

3

mean daily inflow (streamflow + wave overtopping,m3/s) Fig. 9. Hydrologic inflow and days open. Histograms of model results of the number of days open and closed for streamflow plus wave overtopping.

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4.3. Model sensitivity 6

5

elevation (m, NAVD88)

To determine the effect of individual model components on estuary function, the calibrated model is re-run while only changing one variable at a time. The model period is 18.2 years long and encapsulates long-term fluctuations in the El Niño Southern Oscillations thereby by eliminating the bias such fluctuations may introduce. The wave buoy ceased to function during portions of the intense 1998 El Niño winter, and this non-consecutive 360 day period was removed from the analysis. The variation in the model components was chosen to reflect physically realistic variability in such components. The calibrated values, model sensitivity values, and model results are shown in Table 3, and the full hypsometry and excavated hypsometry curves are shown in Fig. 10. The hypsometry sensitivity results demonstrate that the accommodation space within the estuary plays a fundamental role in its functioning. For the ‘full hypsometry’ conditions, the frequency of estuary waterlevel fluctuations and breaching events increases (Fig. 11). In the excavated hypsometry conditions, the estuary retains stored water three months later than the ‘full hypsometry’ conditions, and for a 3-week period, it breaches nine-fold less than the ‘full hypsometry’. Excavating the current estuary would reduce the time open by 27% and filling it with sediment would increase time open by 18%. From three observations Carmel lagoon berm heights appear to vary from 4 to 5 m NAVD88, though a dune formed in 2010 in the back-beach with elevations of 5.5 m NAVD88. Berm-height for the calibrated model simulations was 4.2 m NAVD88. The effects of a decreased (increased) berm-height on estuary breaching are two-fold: 1) an increase (decrease) in wave overtopping frequency and magnitudes, and 2) a decrease (increase) in volume of water necessary to breach the berm. For 4 of the 18 years, the calibrated model permitted large wave-overtopping events to initialize short-lived breaches up to a month earlier than the higher berm. Once the estuary is breached, the high-berm scenario behaves similar to the calibrated conditions (4.2 m NAVD88). When the berm height is decreased from 4.2 m NAVD 88 to 3.2 m NAVD 88, wave overtopping becomes a strong determinant of estuary functioning, causing short, frequent breaches, even when streamflow is still zero. At a 95% daily stream flow exceedance (14.7 m 3/s), it takes 0.2, 0.5 and 1.3 days to fill the estuary (with no outflow and zero initial storage) when the berm height is 3.2, 4.2 and 5.5 m NAVD88, respectively. This daily streamflow magnitude is exceeded 15 out of the 18 years, whereas the 99% daily exceedance flow is reached in 12 of the 18 years. At the 99% flow exceedance, it takes 12 h to fill the high-berm estuary

4

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MHHW Carmel Hypsometry

1

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excavated hypsometry full hypsometry

MLLW

0 0

500,000

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volume (m3) Fig. 10. Observed and Modeled Carmel Lagoon Hypsometry. ‘Carmel hypsometry’ is from James (2005), and ‘excavated hypsometry’ and ‘full hypsometry’ were used in the sensitivity analyses. The tidal data MHHW, MSL, and MLLW represent the mean higher-high water, mean sea level, and mean lower-low water, respectively (tidesandcurrents.noaa.gov).

to breaching levels; at such timescales, the role of water transmission through the beach berm in estuary functioning is unimportant. Therefore, fairly common daily streamflow volumes are capable of breaching even the high-berm scenarios. The impact of monotonically increasing beach-berm heights from near tidal levels to ~6 m above mean higher-high water is an exponential-like decrease in percent time open of the estuary inlet (Fig. 12). As shown in Table 3, during the 18.2-year model scenario the inlet of the high-berm scenario is open only 3% less than the calibrated conditions, whereas a low-berm height causes a 25% increase in the time the estuary is open. Other results from the long-term modeling are non-linear, as well. A ten-fold increase in hydraulic conductivity causes a − 44% change in time open, but a ten-fold decreased hydraulic conductivity causes only a 10% increase in time open (Table 3). An increased hydraulic conductivity causes breaches to occur only during high streamflow events, whereas during the low-flow summer conditions, estuary

Table 3 Calibrated values of the breaching model, their range of values tested in the sensitivity analysis and their effect on the amount of days the estuary is open during the 18.5-year modeling scenario. Model values used in the sensitivity analysis are either shown directly or are a factor of the Calibrated Value (e.g. 10×). Four of the model parameters were not tested in the sensitivity analysis. Calibrated value

Sensitivity analysis Number of days open

% change from best fit

High value

Low value

High

Low

High

Low

2× – 2× – – 5.5 240 10× 400 – Excavated hypsometry – 1.67

0.5× – 0.5× – – 3.2 10 0.1× 10 – Full hypsometry – 0.42

2400 – 1754 – – 2408 3907 1388 2268 – 1809

2654 – 3059 – – 3100 2102 2742 2700 – 2928

−3% – −29% – – −3% 57% −44% −9% – −27%

7% – 23% – – 25% −15% 10% 9% – 18%

– 1388

– 2136

– −44%

– −14%

Model value

htsand, m/wave Ψ, erosion C, run-up adjustment ϕ, hydraulic geometry θ, hydraulic geometry ηb, berm ht, m NAVD88 Beach width, m Hydraulic conductivity, k (m/s) Berm length, m Beach face slope, m/m Hypsometry

0.0017 2.15E−07 0.47 0.43 0.67 4.2 60 0.0062 160 0.09 See Fig. 10

Groundwater inflow, m3/s Sea level rise (m)

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Fig. 11. Estuary Hypsometry Sensitivity. Model results showing the effect of estuary hypsometry on breaching and closing dynamics. Bottom two boxes show model output from the calibrated model (current hypsometry) and the altered estuary hypsometry scenarios. Note the increase in breaching frequency in the ‘full hypsometry’ conditions, and the increased water retention in the ‘excavated hypsometry’ conditions.

storage is negligible and strongly influenced by tidally modulated groundwater flow (Fig. 13). Breaching occurs throughout the year, and water storage, and consequently residence times, are great during the reduced hydraulic conductivity conditions. During high streamflow, the calibrated model and the reduced hydraulic conductivity scenario behave similarly. Sea level is predicted to rise by between 0.42 and 1.67 m by 2100 (Dalrymple et al., 2012), and will likely cause the beach-berm to translate landward. The effects of sea level rise on estuary function were evaluated by increasing tidal elevations and berm elevations by the sea level rise predictions, but keeping the beach berm in its current location. By not translating the berm landwards, the predictions should be interpreted as the maximal effect that sea-level rise may have on the time open. The 0.42 m sea-level rise scenario causes a 14% decrease in time open and the 1.67 m sea-level rise causes a 44% decrease. 5. Discussion The model results indicate that the functioning of bar-built, coastal lagoons are strongly dependent upon a variety of factors that control

100

% time open

80

60

40

20

0

2

3

4

5

6

7

8

berm height (m, NAVD88) Fig. 12. Sensitivity analysis of beach berm height on the percent of time that the inlet is open. Each point represents the results of an 18.2-year model run for given beach berm height.

the storage, inflow, and transmission of water. For the estuary system itself, realistic variations in each of the factors investigated here produces more than a 7% change in the amount of time the estuary is open. Understanding how these factors affect estuary function allows for improved restoration and management of these systems for their ecological value. For example, with the use of the model developed here, resource managers were provided quantitative predictions of the effects of a proposed estuary excavation project on the breaching and closing regime of a coastal estuary in Santa Barbara, Ca. (Rich, 2012). Existing at the nexus of the coastal environment and watershed outlet, the function of these systems is affected by a number of drivers. These drivers can be grouped as: 1) water and sediment discharge, 2) land use, 3) climate and sea level, 4) estuary geomorphology, and 5) coastal and barrier beach change. For the calibrated Carmel Lagoon model, when beach berm heights adequately reduce the wave overtopping flux, streamflow is the primary determinant on inlet state and on estuary storage. Elwany et al. (1998) demonstrated that the long-term pattern of inlet state correlates well with streamflow and Behrens (2012) showed that both closure and breaching timing are persistently influenced by streamflow. It is therefore expected that processes affecting runoff flow-durations – such as groundwater pumping (Winter et al., 1998) and urbanization (Ferguson and Suckling, 1990) – will strongly impact estuary function. It is not clear if global warming will lead to a more El Niño-like climate (Collins, 2005), with its attendant increased yearly streamflow (Cayan et al., 1999) and increased wave heights along western North America (Allan and Komar, 2006). If El Niños do become more frequent, they will cause lagoons to remain open longer because estuary closure is more sensitive to increases in streamflow than increases in wave height (Behrens, 2012). If the beach berm remains in its current location, sea-level rise will cause the estuary to function more like a coastal lake. Other watershed processes will also impact estuary function, primarily by controlling estuary geomorphology and hypsometry. The size (volume, area, etc.) of coastal estuaries in active tectonic environments scale with watershed precipitation and stream gradient (Rich and Keller, 2012). The nature of this scaling is a function of a variety of factors, with lithology, tectonics, and sediment flux likely as key drivers. Sediment flux is influenced by land use

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Fig. 13. Sensitivity analysis of beach hydraulic conductivity. Bottom two boxes show model output from the calibrated model (calibrated hydr. cond.) and the altered beach hydraulic conductivity scenarios.

changes and reservoir construction (Syvitski et al., 2005), and significant sediment aggradation has been observed in a Central California lagoon, likely as a result of land use change (Revell et al., 2010). Operative estuarine and coastal processes are those that control the form, composition, size and existence of the beach berm, and the functioning of the channel inlet. The construction of dams and beach groins reduces littoral sediment supply, causing beach narrowing (Willis and Griggs, 2003) and potentially reduction of beach-berm heights. Dams also alter the caliber of sediment a river transports (Kondolf, 1997), potentially impacting the composition (e.g. hydraulic conductivity) of the beach barrier. Changes in grain size also impacts surfzone sediment transport direction (Dean, 1973) and therefore processes affecting estuary closure (Ranasinghe and Pattiaratchi, 2003). 5.1. Model uncertainty The results indicate that the model works best when the channel inlet flows directly from the estuary to the beachface, in accordance with model assumptions. There does not exist a functional predictive model of channel migration, and pursuing such a model is beyond the scope of this work. Nonetheless, the model is still able to accurately predict the seasonal closure timing within 10.5 days when this assumption is invalid. The inlet configuration impacts the hydraulic efficiency of the inlet and erosive ability of the flow itself (van de Kreeke, 1985), and is therefore important in the closure process (Behrens, 2012). The absence of a nearshore wave transformation model introduces uncertainty into the model and results. This uncertainty is small for Carmel Lagoon (Laudier et al., 2011), though if not, the heuristic value of this work is still valid. For longer model runs, the uncertainty in other model parameters likely produces a greater amount of uncertainty than the lack of a wave model. The beachface slope, which at Carmel has been observed to vary from 0.08 to 0.22 (Laudier et al., 2011), introduces a large uncertainty into the wave run-up height, which varies linearly with the beachface slope. For a given offshore wave conditions, wave overtopping is a nonlinear function of berm height, the reduction factor (ϒr), and the beachface slope (Laudier et al., 2011), all of which are not likely constant for > 1-month periods.

6. Conclusions The model results show that the breaching and closing of the bar-built, Mediterranean climate, Carmel Lagoon can be predicted using a hydrologic and geomorphic model. When calibrated, the model is able to reproduce the initial seasonal breaching, seasonal closure, intermittent closures and breaches, and the low-streamflow estuary hydrology. For three years when the estuary inlet drains directly across the beach berm, and during the portion of the year when the inlet is actively opening and closing, the root mean square errors of calibrated versus observed 48-h estuary stage amplitude are 0.65 m, 0.50 m and 0.64 m. For the entirety of the three years, model performance improves to 0.45 m, 0.39 m and 0.42 m. Model performance deteriorates when the channel inlet migrates from the direct configuration to one ~ 10 × longer. Under calibrated conditions, the probability that the Carmel Lagoon inlet is closed is strongly linked to inflow and seasonal patterns of inlet state are a reflection of streamflow seasonality. The probability of the inlet being closed decreases 10-fold as mean daily inflow increases from 0.2 to 1.0 m 3/s, whereas 98.5% of open days occur when estuary inflow is greater than 0.5 m 3/s. The estuary may breach from overtopping alone, but such breaches are short-lived. Wave overtopping does not play a large role in determining inlet state under calibrated conditions. In conjunction with beach processes, the hydrologic water balance controls the functioning of these systems. Therefore, factors that alter the storage, transmission, and inflow control estuary function. Changes to estuary hypsometry or beach-berm height increase storage volumes; increasing berm heights diminishes the overtopping flux, rendering streamflow the important control on breaching, whereas a reduced berm height allows wave overtopping to influence breaching. By excavating an estuary it will breach less frequently and store water for longer periods. The transmission of inflow through the berm is controlled by the hydrologic properties of the berm itself, including the beach width and length, and its hydrologic transmissivity. The effect of altered beach conditions is not always linear, however. The tendency for the inlet to be closed increases with wave energy and wave run-up, and the availability of beach sand is relatively less important in the closure process. Lastly, if beach berms remain in their current locations, but aggrade vertically under predicted sea level rise conditions, sea level rise will cause coastal lagoons to reduce

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the amount of time they are open by up to 44%. This prediction is an end-member and does not account for beach-berm migration. Finally, watershed and coastal processes that affect estuary function can be grouped as follows: 1) water and sediment discharge, 2) land use, 3) climate and sea level, 4) estuary geomorphology, and 5) coastal and barrier beach change. Restoration and management of these systems should account for the above factors, especially for changes in streamflow. References Allan, J.C., Komar, P.D., 2006. Climate controls on US west coast erosion processes. Journal of Coastal Research 511–529. Baldock, T.E., Weir, F., Hughes, M.G., 2008. Morphodynamic evolution of a coastal lagoon entrance during swash overwash. Geomorphology 95 (3–4), 398–411. Bascom, W.N., 1951. The relationship between sand size and beach face slope. Transactions of the American Geophysical Union 32, 866–874. Behrens, D.K., 2012. The Russian River Estuary: Inlet Morphology, Management, and Estuarine Scalar Field Response. Dissertation, Univ. of California, Davis, 340 pp. Behrens, D.K., Bombardelli, F.A., Largier, J.L., Twohy, E., 2009. Characterization of time and spatial scales of a migrating rivermouth. Geophysical Research Letters 36 (9), L09402. Beighley, R.E., Melack, J.M., Dunne, T., 2003. Impacts of California's climatic regimes and coastal land use change on streamflow characteristics. Journal of the American Water Resources Association 39 (6), 1419–1433. Carter, R.W.G., Forbes, D.L., Jennings, S.C., Orford, J.D., Shaw, J., Taylor, R.B., 1989. Barrier and lagoon coast evolution under differing relative sea-level regimes: examples from Ireland and Nova Scotia. Marine Geology 88, 221–242. Cayan, D.R., Redmond, K.T., Riddle, L.G., 1999. ENSO and hydrologic extremes in the Western United States. Journal of Climate 12 (9), 2881–2893. Collins, M., 2005. El Niño- or La Niña-like climate change? Climate Dynamics 24 (1), 89–104. Cooper, J.A.G., 2001. Geomorphological variability among microtidal estuaries from the wave-dominated South African coast. Geomorphology 40 (1–2), 99–122. Costanza, R., d'Arge, R., de Groot, R., Farber, S., Grasso, M., Hannon, B., Limburg, K., Naeem, S., O'Neill, R.V., Paruelo, J., Raskin, R.G., Sutton, P., van den Belt, M., 1997. The value of the world's ecosystem services and natural capital. Nature 387 (6630), 253–260. Dalrymple, R.A., Breaker, L.C., Brooks, B.A., Cayan, D.R., Griggs, G.B., Han, W., Horton, B.P., Hulbe, C.L., Mcwilliams, J.C., Mote, P.W., Pfeffer, W.T., Reed, D.J., Shum, C.K., Holman, R.A., Linn, A.M., Mcconnell, M., Gibbs, C.R., Ortego, J.R., 2012. Sea-level rise for the coasts of California, Oregon, and Washington: past, present, and future. National Research, Council.The National Academies Press, Washington DC. Dean, R.G., 1973. Heuristic Models of Sand Transport in the Surf Zone, Australian Conference on Coastal Engineering (1st: 1973: Sydney, N.S.W.). Institution of Engineers, Australia, Sydney, N.S.W. Donnelly, C., Kraus, N., Larson, M., 2006. State of knowledge on measurement and modeling of coastal overwash. Journal of Coastal Research 22 (4), 965–991. DWR, 1974. Vegetative Water Use in California. State of California, The Resources Agency, Department of Water Resources, Sacramento. Elwany, M.H.S., Flick, R.E., Aijaz, S., 1998. Opening and closure of a marginal Southern California lagoon inlet. Estuaries 21 (2), 246–254. Escoffier, F.F., 1940. The stability of tidal inlets. Shore & Beach 8, 114–115. Ferguson, B.K., Suckling, P.W., 1990. Changing rainfall–runoff relationships in the urbanizing Peachtree Creek Watershed, Atlanta, Georgia. Journal of the American Water Research Association 26 (2), 313–322. Hart, D.E., 2007. River-mouth lagoon dynamics on mixed sand and gravel barrier coasts, 9th International Coastal Symposium. Journal of Coastal Research, Gold Coast, Australia, pp. 927–931. Hope, A., 2007. Carmel river lagoon: hydrographic survey and stage–volume relationship. Prepared for: Monterey Peninsula Water Management District. Howard, A.D., McLane III, C.F., 1988. Erosion of cohesionless sediment by groundwater seepage. Water Resources Research 24 (10), 1659–1674. Howell, B.F., 1972. Sand movement along Carmel River State Beach, Carmel, California (71 pp.). Hughes, S.A., 2002. Equilibrium cross sectional area at tidal inlets. Journal of Coastal Research 18 (1), 160–174. Hunt, I.A., 1959. Design of seawalls and breakwaters. Proceedings of the American Society of Civil Engineers 85, 123–152.

James, G., 2005. Surface Water Dynamics at the Carmel Lagoon Water Years 1991 Through 2005. Monterey Peninsula Water Management Agency, Monterey, Ca. Janssen, P.H.M., Heuberger, P.S.C., 1995. Calibration of process-oriented models. Ecological Modelling 83, 55–66. Jarrett, J.T., 1976. Tidal prism–inlet area relationships. US Army Coastal Engr. Res. Cent, p. 55. G.I.T.I. Report 3. Kirk, R.M., 1991. River-beach interaction on mixed sand and gravel coasts: a geomorphic model for water resource planning. Applied Geography 11 (4), 267–287. Kjerfve, B., Magill, K.E., 1989. Geographic and hydrodynamic characteristics of shallow coastal lagoons. Marine Geology 88 (3–4), 187–199. Kondolf, G.M., 1997. PROFILE: hungry water: effects of dams and gravel mining on river channels. Environmental Management 21 (4), 533–551. Kondolf, G.M., Maloney, L.M., Williams, J.G., 1987. Effects of bank storage and well pumping on base flow, Carmel River, Monterey County, California. Journal of Hydrology 91, 351–369. Kraus, N., Munger, S., Patsch, K., 2008. Barrier beach breaching from the lagoon side, with reference to Northern California. Shore & Beach 76 (2), 33–43. Laudier, N.A., Thornton, E.B., MacMahan, J., 2011. Measured and modeled wave overtopping on a natural beach. Coastal Engineering 58 (9), 815–825. Lee, J.-S., Julien, P.Y., 2006. Downstream hydraulic geometry of alluvial channels. Journal of Hydraulic Engineering 132 (12), 1347–1352. Meyer-Peter, E., Müller, R., 1948. Formulas for bed-load transport. Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research, Delft, Netherlands. Miller, M.C., McCave, I.N., Komar, P.D., 1977. Threshold of sediment motion under unidirectional currents. Sedimentology 24 (4), 507–527. MPWMD, 2008. California American Water Production by Source for Customers in its Mains System; Water Years 1996–Present. Monterey Peninsula Water Management District, Monterey. O'Brien, M.P., 1931. Estuary tidal prisms related to entrance areas. Journal of Civil Engineering 738–739. Pierce, J.W., 1970. Tidal inlets and washover fans. Journal of Geology 78 (2), 230–234. Ranasinghe, R., Pattiaratchi, C., 1999. The seasonal closure of tidal inlets: Wilson inlet — a case study. Coastal Engineering 37 (1), 37–56. Ranasinghe, R., Pattiaratchi, C., 2003. The seasonal closure of tidal inlets: causes and effects. Coastal Engineering Journal 45 (4), 601–627. Revell, D., Williams, P., Rich, A., Bozkurt, S., Collison, A., Ginney, E., Kunz, D., Vandever, J., Gamble, J., 2010. An Assessment of Potential Restoration Actions To Enhance The Ecological Functions Of The Lower Santa Ynez River Estuary. ESA-PWA, San Francisco. Rich, A., 2012. Restoration of Devereux Slough: Effects on Estuary Breaching and Closing, Cheadle Center for Biodiversity and Ecological Restoration. Univ. of California Santa Barbara, Santa Barbara, Ca. Rich, A., Keller, E., 2012. Watershed controls on the geomorphology of small coastal lagoons in an active tectonic environment. Estuaries and Coasts 35 (1), 183–189. Rustomji, P., 2007. Flood and drought impacts on the opening regime of a wavedominated estuary. Marine and Freshwater Research 58 (12), 1108–1119. Seager, R., Vecchi, G.A., 2010. Greenhouse warming and the 21st century hydroclimate of southwestern North America. Proceedings of the National Academy of Sciences 107 (50), 21277–21282. Storlazzi, C.D., Field, M.E., 2000. Sediment distribution and transport along a rocky, embayed coast: Monterey Peninsula and Carmel Bay, California. Marine Geology 170 (3–4), 289–316. Syvitski, J.P.M., Vörösmarty, C.J., Kettner, A.J., Green, P., 2005. Impact of humans on the flux of terrestrial sediment to the Global Coastal Ocean. Science 308 (5720), 376–380. Takeda, I., Sunamura, T., 1982. Formation and height of berms. Transactions, Japanese Geomorphological Union 3 (2), 145–157. Turner, I., 1993. Water table outcropping on macro-tidal beaches: a simulation model. Marine Geology 115, 227–238. van de Kreeke, J., 1985. Stability of tidal inlets, Pass Cavallo, Texas. Estuarine, Coastal and Shelf Science 21 (1), 33–43. Van der Meer, J.W., Janssen, W., 1995. Wave run-up and wave overtopping at dikes. In: Kabayashi, D. (Ed.), Wave Forces on Inclined and Vertical Wall Structures. American Society of Civil Engineers, New York, pp. 1–27. Willis, C.M., Griggs, G.B., 2003. Reductions in fluvial sediment discharge by Coastal Dams in California and implications for beach sustainability. Journal of Geology 111 (2), 167–182. Winter, T.C., Harvey, J.W., Franke, O.L., Alley, W.M., 1998. Ground water and surface water a single resource. United States Geological Survey Circular 1139.