1. Introduction
The surfzone (from the shoreline to the seaward extent of depth-limited wave breaking), the inner shelf (from 5- to ≈15-m depths where the surface and bottom boundary layers overlap; e.g., Lentz and Fewings 2012), and midshelf (offshore of the inner shelf to ≈50-m depth, where the surface and the bottom boundary layers are distinct; e.g., Austin and Lentz 2002) together represent the transition region from land to the open ocean. This region exchanges a wide variety of tracers. Terrestrial pollutants such as fecal indicator bacteria, pathogens, and human viruses (e.g., Reeves et al. 2004; Grant et al. 2005) enter the surfzone region and are dispersed by cross-shelf exchange. Similarly, nearshore, harmful algal blooms (i.e., red tides) are controlled by cross-shelf nutrient exchange (e.g., Anderson 2009; Omand et al. 2012). Intertidal invertebrate gametes must typically make their way from near the shoreline to much deeper waters (such as Donax clams; e.g., Laudien et al. 2001; Martel and Chia 1991), while the larvae must be transported onshore for recruitment in the intertidal zone (e.g., Shanks et al. 2010). Surfzone (Sinnett and Feddersen 2014) and inner-shelf (e.g., Fewings and Lentz 2011) temperature fluctuations are influenced by cross-shelf advective heat fluxes. Yet, the exchange of tracers (pollutants, nutrients, larvae, heat, etc.) spanning the surfzone through the midshelf is poorly understood.
Surfzone, inner shelf, and midshelf regions span drastically different dynamical regimes, with varying cross-shelf exchange processes due to wave, wind, buoyancy, and tidal forcing. Within the surfzone, horizontal eddies generated due to short-crested wave breaking (Clark et al. 2012; Feddersen 2014) induce cross-shore dye and drifter dispersion (Spydell et al. 2009; Clark et al. 2010). Surfzone, onshore, wave-induced mass flux is balanced by the offshore-directed undertow, which because of their different vertical structure can lead to cross-surfzone exchange (e.g., Garcez Faria et al. 2000; Reniers et al. 2004; Uchiyama et al. 2010; Kumar et al. 2012). Bathymetrically controlled (e.g., Reniers et al. 2009) and transient rip currents (e.g., Johnson and Pattiaratchi 2006) can also result in surfzone inner-shelf exchange. On an alongshore uniform beach, transient rip currents were the dominant surfzone to inner-shelf dye exchange mechanism (Hally-Rosendahl et al. 2014).
In the inner-shelf region, internal waves affect cross-shelf exchange. Baroclinic semidiurnal waves in the inner shelf (20-m depth) flux heat and nitrate farther inshore (Lucas et al. 2011; Wong et al. 2012). Internal wave mixing is responsible for pumping nutrients up into the euphotic zone, initiating phytoplankton blooms (Omand et al. 2012). Nonlinear internal waves (e.g., Pineda 1994; Nam and Send 2011) can advect cold waters from 6-m depth into the surfzone (Sinnett and Feddersen 2014) and are hypothesized to transport larvae onshore for recruitment (e.g., Pineda 1999).
At subtidal (≥33 hr) time scales, alongshelf, wind-driven upwelling and downwelling controls cross-shelf transport in the midshelf, where surface and bottom boundary Ekman layers do not overlap (Austin and Lentz 2002). However, in the inner shelf, surface and bottom boundary layers overlap, significantly reducing cross-shelf transport (Austin and Lentz 2002; Kirincich and Barth 2009). Nonetheless, inner-shelf cross-shelf currents can be driven by cross-shelf wind forcing (Tilburg 2003; Fewings et al. 2008). Outer shelf surface waters can intrude into the inner shelf from submesoscale activity or interaction with an upwelling front resulting in cross-shelf transport (e.g., Nidzieko and Largier 2013). The inner-shelf undertow due to surface gravity wave–induced, onshore, Stokes drift drives subtidal cross-shelf exchange especially during periods of weak winds and strong wave forcing (Lentz et al. 2008; Kirincich et al. 2009). Also, intrinsic variability due to meso- and submesoscale activity can lead to cross-shore eddy fluxes (Capet et al. 2008; Dong et al. 2009; Romero et al. 2013; Uchiyama et al. 2014, hereinafter U14).
Recent circulation modeling studies have simulated cross-shelf exchange. For example, Romero et al. (2013) applied the Regional Ocean Modeling System (ROMS) to characterize horizontal relative dispersion as a function of coastal geometry, bathymetry, and eddy kinetic energy in the Southern California Bight (SCB). Dispersal and dilution of an outer-shelf (water depth of 60 m) urban wastewater discharge in the San Pedro Bay (SPB) were simulated with ROMS to identify the possibility of contamination in water depth <10 m (U14). Harmful algal bloom transport from the outer to midshelf due to wind-driven currents was studied in the Salish Sea using ROMS (Giddings et al. 2014). However, inner-shelf processes were coarsely resolved in these studies, and wave-driven processes were neglected. Surfzone modeling studies typically do not include the inner-shelf, rotational, tidal, and buoyancy effects (e.g., Ruessink et al. 2001; Reniers et al. 2009; Feddersen et al. 2011; Castelle et al. 2014). However, the tracer in this region responds to the net effect of all these surfzone to midshelf processes. A coupled wave and circulation model with wind, wave, tide, and buoyancy forcing and sufficient resolution is required to accurately simulate inner-shelf and surfzone processes. Therefore, prior to studying cross-shelf exchange, a model must be concurrently applied from the midshelf to the surfzone and tested against field measurements.
The Coupled Ocean–Atmosphere–Wave–Sediment Transport model (COAWST; Warner et al. 2010) that couples ROMS and Simulating Waves Nearshore (SWAN v40.91) models (using the Model Coupling Toolkit) includes the buoyancy-, wind-, tide-, and wave-driven processes (McWilliams et al. 2004) to simulate exchange across all components of the shelf region. The COAWST modeling system has not been extensively tested to simulate currents, waves, and temperature in the shelf region. Here, COAWST (coupled ROMS–SWAN) is applied concurrently from the surfzone to the midshelf region adjacent to Huntington Beach, California, in the San Pedro Bay. Model performance is evaluated by statistical comparison of dense measurement of waves, circulation, and temperature on a 4-km-long cross-shore transect spanning the surfzone to midshelf (section 2a) as part of the August–October 2006 Huntington Beach experiment (HB06).
The model physics, grid setup, and surface and boundary forcing required to simulate the hydrodynamics during the HB06 experiment are described in section 3. Modeled waves, currents, and temperature from the surfzone to inner and midshelf are compared to observations in sections 4 and 5, with focus on subtidal time scales. Model data comparison at tidal time scales will be considered elsewhere. Subsequently, a range of midshelf to surfzone processes is examined jointly in the model and observations to gain insight of the dynamics across this region. The results are summarized in section 7.
2. Observations and methods
a. HB06 experiment description
Currents, waves, temperature, and sea surface elevation were measured from the surfzone to the midshelf adjacent to Huntington Beach, California, as a part of the HB06 experiment (Clark et al. 2010, 2011; Omand et al. 2011, 2012; Nam and Send 2011; Feddersen et al. 2011; Feddersen 2012; Rippy et al. 2013). The shoreline and bathymetry are predominantly alongshore uniform and face ~214° southwest. The coordinate system is defined such that positive cross-shore x and alongshore y are directed onshore and toward the northwest, respectively, with x = 0 at the shoreline (see Fig. 1a). The vertical coordinate z is positive upward, with z = 0 as the mean sea surface level. The mean water depth is h, such that the seabed is at z = −h. The time coordinate t starts from t = 0 corresponding to 1 August 2006 (UTC). At all locations (midshelf to surfzone), the bathymetry h(x, y) (Fig. 1) is given by the NOAA tsunami digital elevation model (DEM) with 9-m spatial resolution (Caldwell et al. 2011). Near the surfzone (x > −120 m), the cross-shore bathymetry profiles evolved in time (Clark et al. 2010) and often had terraced features not seen in the DEM bathymetry. However, because of the lack of measured bathymetry in the substantial part of the model grids (section 3), the DEM bathymetry is also used in the surfzone for model simulation (Fig. 1c).
HB06 instrument schematic: (a) Plan view of bathymetry adjacent to Huntington Beach in the San Pedro Bay, California, with labeled instrument sites (red squares) as a function of cross-shore x and alongshore y coordinates. The green curve represents the zero depth contour (h = 0 m). (b) Cross-shore transect at y = 0 m of shelf bathymetry on the shelf (h < 35 m) and (c) nearshore (h < 5 m) with cross-shelf and vertical instrument locations of thermistors (black) and velocity (red) are indicated. The vertical coordinate z = 0 m is at mean sea level and positive upward. The bathymetry h(x, y) is from the NOAA tsunami DEM (Caldwell et al. 2011). As surfzone bathymetry was variable, in (c), M1.5 is moved 20 m onshore so that it is in the correct mean water depth.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
Moorings equipped with thermistors and ADCP current meters were deployed on a cross-shore transect in water depths of 26, 20, 10, and 8 m (hereinafter denoted as M26, M20, M10, and M8, respectively) from August to October 2006 (see Fig. 1b and Table 1). Farther inshore in the same cross-shore transect, surfzone frames (M4, M3, and M1.5; Fig. 1c) were deployed in 4-, 3.2-, and 1.4-m mean water depth. Each frame was equipped with a pressure sensor and an acoustic Doppler velocimeter (ADV), measuring pressure, three-dimensional velocities, and bed location, and one or two thermistors (Fig. 1c). At the M1.5 deployment location, the mean (time averaged) water depth was h = 1.4 m and varied ±0.2 m during the 33-day deployment. The actual bathymetry evolves and varies from the DEM. To compare observed and modeled surfzone waves and currents at the same mean water depth h, the cross-shore location of M1.5 is considered to be 20 m farther onshore from where it was deployed (Fig. 1c).
List of midshelf to surfzone HB06 experiment cross-shore transect instrument sites, depth, deployment duration, and cross-shore (x) location. The cross-shore location in parentheses for M1.5 is the actual instrument location during the experiment. Here, the surfzone bathymetry is approximate, and the cross-shore location of M1.5 is considered to be 20 m onshore at the same mean water depth h = 1.4 m, as observed.
An additional mooring N10 with an ADCP was deployed in 10-m depth approximately 4 km northwest of the primary cross-shore transect (Figs. 1a,b). A Coastal Data Information Program (CDIP) directional wave buoy (Fig. 1a) deployed in 22-m water depth provided spectral wave estimates, while a meteorological station (N20; Fig. 1a) provided wind velocity measurements throughout the experiment period.
b. Methods
1) General methods
All measurements were hourly averaged, and the velocities rotated into the HB06 coordinate system cross-shore u and alongshore υ velocities. Hourly estimates of significant wave height (Hs) and (energy weighted) mean period (Tm) were estimated by standard spectral analysis techniques (see Kuik et al. 1988; Herbers et al. 1999) at surfzone frames and the CDIP buoy. The off-diagonal radiation stress term Sxy/ρ was estimated from the spectra and directional moments (Kuik et al. 1988) derived from the pressure sensor and ADV data (e.g., Feddersen 2004, 2012). Observed N20 wind velocities (Fig. 1a) were used to estimate the wind stresses using the neutral drag law of Large and Pond (1981) after correcting for the elevation of the wind sensor above the sea surface and accounting for the influence of waves (Large et al. 1995). Observed and modeled subtidal velocities and temperatures (denoted by subscript ST) are estimated by low-pass filtering using a PL64 filter (Limeburner et al. 1985) with a 33−1 cph half-amplitude cutoff.
2) Empirical orthogonal functional analysis
3) Model data comparison statistics
3. Model description, grid setup, and forcing
a. Model description
The open-source COAWST modeling system (Warner et al. 2010) couples an atmospheric [Weather Research and Forecasting (WRF) model], wave (SWAN), three-dimensional (3D) circulation and stratification (ROMS) and sediment transport models. The coupled modeling system has been validated in a variety of applications including the study of wave–current interaction and depth-varying cross- (e.g., undertow) and alongshore currents in the surfzone (Kumar et al. 2011, 2012) and a tidal inlet (Olabarrieta et al. 2011), atmospheric–ocean–wave interactions under hurricane forcing (Olabarrieta et al. 2012), and sediment dispersal in shallow semienclosed basins (Sclavo et al. 2013). Here, COAWST is used in a coupled ROMS and SWAN mode.
The third generation, spectral SWAN wave model (Booij et al. 1999; Ris et al. 1999) includes shoaling, wave refraction due to both bathymetry and mean currents, energy input due to winds, energy loss due to white-capping, bottom friction, and depth-limited breaking. SWAN inputs include a bathymetric grid, incident wave spectra boundary conditions, wind to allow wind-wave generation, and mean velocity for current-induced wave refraction. The model outputs directional wave spectra from which significant wave height Hs, mean wave period Tm, and radiation stress (e.g., Sxy/ρ) can be calculated.
ROMS is a three-dimensional, free-surface, bathymetry following numerical model–solving finite-difference approximation of Reynolds-averaged Navier–Stokes (RANS) equations with the hydrostatic and Boussinesq approximations (Shchepetkin and McWilliams 2005; Haidvogel et al. 2008; Shchepetkin and McWilliams 2009). The COAWST wave–current interaction algorithm is based on the vortex force formalism (Craik and Leibovich 1976), separating conservative (McWilliams et al. 2004) and nonconservative (depth-limited breaking-induced acceleration) wave-induced effects (Uchiyama et al. 2010; Kumar et al. 2012). ROMS and SWAN are two-way coupled (Warner et al. 2008b,a), allowing vertically sheared currents (Kirby and Chen 1989) to modify the wave field.
b. U14 model grids and forcing
Here, COAWST is set up as a one-way child grid to the grid system used by U14, providing initial and boundary conditions. The U14 grid system consists of quadruply nested model domains with an offline, one-way nesting technique (see Mason et al. 2010; U14). The U14 grids downscale from a domain of the U.S. West Coast and eastern Pacific (L0, resolution Δ = 5 km, area 4000 × 3000 km2), to the Southern California Bight (L1, Δ = 1 km, area 800 × 700 km2), to the interior bight region (L2, Δ = 250 m, area 500 × 300 km2; Fig. 2a), to the San Pedro Bay (L3, Δ = 75 m, area 80 × 70 km2; Fig. 2b). The model bathymetries are from the 30-arc-s global bathymetry [Shuttle Radar Topography Mission 30 arc s dataset (SRTM30); Becker et al. 2009], with refinement using the 3 s (~90 m) NOAA–NGDC coastal relief dataset for the nearshore regions. These domains have 40 (L0, L1, and L2) or 32 (L3) bathymetry-following vertical levels.
Model grids showing (a) interior shallower area of the SCB, (b) the SPB, (c) outer shelf to inner shelf and (d) midshelf to surfzone region adjacent to Huntington and Newport Beach in the SPB. The color shading represents the bathymetry, while red squares show the location of offshore moorings, CDIP wave buoy, and an array of surfzone frames, respectively. These grids have a resolution of 250 (L2), 75 (L3), 50 (L4), and 10 m (L5), respectively. Note that the water depth h is shown as a positive number in these figures.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The outermost U14 domain (L0) is forced with a combination of lateral boundary conditions from an assimilated global oceanic dataset (Carton and Giese 2008), relaxing to monthly averaged sea surface temperature and salinity, and includes freshwater flux from river runoff. A doubly nested WRF model with Δ = 18 km and Δ = 6 km, embedded within the NCEP North American Regional Reanalysis, provides surface wind stress, heat, and radiative and freshwater (evaporation–precipitation) flux boundary conditions to the parent (L0, Δ = 18 km) and all the child grids (Δ = 6 km). The model grid is spun for 15 yr with climatological surface forcing, prior to the 1 August 2006 experiment commencement.
Daily L0 solutions are used as a lateral boundary condition for L1. In addition, barotropic tidal elevation and velocities of M2, S2, N2, K2, O1, P1, Q1, Mf, and Mm are projected onto the lateral boundaries of L1 with amplitude and phases obtained from the TOPEX/Poseidon (TPXO7.1) global tidal prediction model (Egbert et al. 1994). The L1 solutions are used as L2 lateral boundary conditions, and L2 solutions provide L3 boundary conditions, both every 2 h.
c. HB06 model grids, setup, boundary conditions, and forcing
The U14 L3 grid provides boundary conditions for the HB06 L4 grid (Δ = 50 m) that has a 15-km cross-shore and 30-km alongshore region in the San Pedro Bay offshore of Huntington and Newport Beach, California, that spans the shelf break to inner shelf and surfzone (Fig. 2c). The L4 grid provides information to the innermost L5 grid (Δ = 10 m) that spans approximately 6 km alongshore and cross shore (Fig. 2d), which encompasses the midshelf to the surfzone, where the HB06 instrumentation was located (Fig. 1). L4 and L5 have 20 bathymetry-following levels, with bathymetry h(x, y) from the NOAA tsunami DEM (Caldwell et al. 2011). Biweekly bathymetry surveys from 7 September to 10 October, spanning ±500 m from the instrument transect, demonstrated surfzone bathymetric evolution (e.g., Clark et al. 2011). However, lack of coverage in the substantial part of L5 and the requirement for alongshore consistency does not allow for the use of observed bathymetry in model simulations.
The model simulations for both the L4 and L5 grids were conducted for 92 days (from 1 August to 1 November 2006) with a ROMS baroclinic time step of 8 and 4 s, respectively; the wave action density in SWAN evolves with a time step of 120 s and 60 s, respectively; and the exchange of information between the circulation and wave models occurred every 360 s.
ROMS bottom stress is determined using a logarithmic layer drag with a roughness length of z0 = 0.001 m, and a k−ε turbulence closure model is used to close the momentum balance equation. More complex bottom stress algorithms that include wave effects do not result in substantial improvement in 10–20-m water depths (Ganju et al. 2011). However, neglecting wave effects in the shallow waters of the surfzone and inner shelf may result in underestimated bottom stress (e.g., Feddersen et al. 2000). A horizontal eddy viscosity of 0.1 m2 s−1 is used. The SWAN wave action balance equation is solved in frequency and directional space with 48 frequencies between 0.01 and 1 Hz and 60 directional bands with a directional width of 6° spanning 360°. The parameter γ = 0.5 (ratio of wave height to water depth at which wave breaking occurs) is used to simulate inception of depth-limited wave breaking.
The SWAN L4 grid lateral boundary wave forcing is a frequency–directional wave spectra time series derived from regional, deep-water, CDIP wave buoy spectra estimates farther offshore that were transformed to the boundary with ray-based spectral refraction methods (O’Reilly and Guza 1991, 1993). The wave fields determined for L4 are subsequently used to provide spectral estimates of wave forcing for L5. Wind-wave generation within L4 and L5 is negligible. The ROMS L4 and L5 lateral open boundary conditions are inherited from L3 and L4, respectively. A Chapman boundary condition (Chapman 1985) assuming the signal leaves at the shallow-water speed, together with a Flather boundary condition (Flather 1976), radiates out barotropic (depth averaged) normal flows and sea surface elevation. A Chapman boundary condition is used for tangential barotropic velocities. The standard Orlanski radiation boundary condition (Raymond and Kuo 1984) is used for baroclinic (three dimensional) normal and tangential velocities. Temperature and salinity fields and baroclinic velocities are strongly nudged (Marchesiello et al. 2001; Mason et al. 2010) to incoming flow (ΔT = 30 min) and weakly nudged to outgoing flows (ΔT = 365 days) of the outer parent grid.
d. Model and observed winds
Accurate wind forcing is critical for SCB inner-shelf circulation modeling (Lentz and Winant 1986). The SCB has complex coastline shape and local islands, leading to significant wind variability at length scales from the SCB to <10 km (e.g., Winant and Dorman 1997; Conil and Hall 2006). The wind field used by ROMS in domains L4 and L5 must be consistent with the winds used in the L0–L3 nested domains that provide ocean currents and temperature boundary conditions to L4. Thus, the WRF model wind stress, which forces L0–L3, also forces L4 and L5, and observed winds are not used.
The WRF model has been extensively used to simulate wind stress in the eastern Pacific region and, in general, favorably compares against observations on seasonal and monthly scales (e.g., Boé et al. 2011) and daily mean wind speeds (e.g., Huang et al. 2013; Capps et al. 2014). However, validation near the land–sea boundary such as the HB06 region is limited. WRF-simulated hourly wind stresses τ are evaluated against those estimated using wind velocities measured at N20 (see Fig. 1a). Modeled and observed wind stresses are bandpass filtered at subtidal (denoted with the subscript ST; <33−1 cph) and diurnal (denoted with the subscript DU; 16−1 to 33−1 cph) frequency bands. Wind stress contribution is negligible at higher frequencies (>16−1 cph). Superscripts m and o denote modeled and observed quantities, respectively.
Observed cross-shore and alongshore diurnal wind stresses 
Observed (black) and modeled (red) wind stress at N20 (Fig. 1) vs time in the (top) diurnal (16−1 to 33−1 cph) and (bottom) subtidal (<33−1 cph) frequency bands and for (left) cross-shore (τx) and (right) alongshore (τy) components. Time corresponds to days from 1 Aug 2006 (UTC).
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
Observed subtidal cross-shore (Figs. 3c) and alongshore (Fig. 3d) wind stresses 
Differences in observed and modeled wind stress may occur because of WRF’s coarse resolution (i.e., Δ = 6 km) and down-scaling effects (from a larger grid) at the land–sea transition. In addition, uncertainties in observed wind stress estimation due to instrument or methodology errors may account for some differences in best-fit slopes, although likely not the correlations. As WRF winds must be used in L4 and L5 to maintain consistency with the offshore nested domains, differences in observed and modeled wind stress will lead to different model and observed subtidal circulation, in part motivating the statistical model data comparison (section 5).
4. Results: Direct model data comparison
The SPB midshelf to surfzone circulation dynamics are complex because of the interaction of coastally trapped waves (e.g., Hickey 1992), meso- and submesoscale eddies (e.g., Dong et al. 2009), wind (e.g., Lentz and Winant 1986), tidal, and wave breaking–induced forcing (Feddersen 2012). Here, the coupled ROMS–SWAN model performance is quantified from the midshelf to the surfzone by directly comparing model (from L5 grid; Fig. 2d) and observed time series of tidal, wave, and circulation parameters at different mooring locations.
a. Model data comparison of tidal elevation at M8
Model tidal forcing (sea surface elevation and barotropic velocities) is provided at the open lateral boundaries of grid L1 (see U14), approximately 800 km offshore from the HB06 region. Model barotropic tides subsequently propagate through the one-way nested grid system (Fig. 2) modified by model bathymetry, generating internal tides and tidal residual flows (e.g., Geyer and Signell 1990). The SCB has complicated bathymetry with variable coastline, islands, and ledges. There are only a limited number of model evaluation studies focused on barotropic tidal propagation in the SCB (Buijsman et al. 2012). In the surfzone, tides modulate the water depth, changing the cross-shore location of wave breaking and thereby also the location and strength of surfzone currents (Thornton and Kim 1993). Thus, modeling exchange between the midshelf to the surfzone requires accurate simulation of barotropic tides.
Model data comparison of tides is performed by comparing amplitude of the dominant tidal constituents (O1, K1, N2, M2, and S2) at M8 through harmonic analysis (T_TIDE package; Pawlowicz et al. 2002). Model diurnal tidal constituents (O1 and K1) have relatively small-amplitude error of <10% (Fig. 4), while semidiurnal tidal constituent (N2, M2, and S2) amplitudes are underestimated by ≈
Observed (black) and modeled (red) amplitude for tidal constituents O1, K1, N2, M2, and S2 at M8.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
b. Model data comparison of wave statistics at M4
Accurate model wave forcing is required for realistic simulation of surfzone circulation, alongshore tracer transport, and exchange between the surfzone and the inner shelf. Modeled and observed significant wave height Hs, mean wave period Tm, and radiation stress Sxy/ρ (where ρ is the water density) are compared at M4 (see Fig. 1c) outside the surfzone (x = −160 m) in ≈4-m water depth (Fig. 5). All wave properties are estimated over the 0.05–0.25-Hz frequency band.
Observed (black) and modeled (red) (a) significant wave height Hs, (b) mean wave period Tm, and (c) radiation stress component Sxy/ρ vs time at M4 (Fig. 1). Time corresponds to days from 1 Aug 2006 (UTC).
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
Observed M4 
Here, the coupled ROMS–SWAN model wave forcing, which depends upon wave dissipation (e.g., Battjes and Janssen 1978; Thornton and Guza 1983), drives surfzone circulation with the vortex force formalism (e.g., McWilliams et al. 2004; Uchiyama et al. 2010; Kumar et al. 2012). Cross-surfzone integrated, this forcing is equivalent to the incident radiation stress term Sxy/ρ, shown to drive surfzone alongshore currents and dominate the surfzone alongshore momentum balance (e.g., Longuet-Higgins 1970; Feddersen et al. 1998; Ruessink et al. 2001). At M4, seaward of the surf zone, the model Sxy/ρ reproduces the observations with small negative bias and RMSE = 0.03 m3 s−2. The model captures the day 61 Sxy/ρ sign change, which is important for the correct surfzone alongshore currents’ sign. The model accurately simulates the waves seaward of the surfzone (Fig. 5) due to the accurate, CDIP, wave buoy–derived wave boundary conditions. Similarly, accurate wave model performance is also found (not shown) at the CDIP wave buoy in 22-m water depth (see Fig. 1a).
c. Model data comparison of waves and currents in the nearshore (M3 and M1.5)
Wave variability in the nearshore and associated generation of undertow and alongshore and cross-shore currents induce tracer alongshore transport and cross-shore exchange. Model data comparison of hourly averaged waves and currents is performed at nearshore sites M3 (just seaward of the surfzone, at mean h = 3.2 m) and M1.5 (within the surfzone at mean h = 1.4 m; see Fig. 1). This region’s currents are strongly affected by the breaking of surface gravity waves. At M1.5 and M3, modeled currents are taken at the mean ADV sample volume vertical location above the bed, 0.8 and 0.4 m for M3 and M1.5, respectively. Note that as surfzone bathymetry evolved and was different than the fixed DEM bathymetry (e.g., Fig. 1), the cross-shore x location of M1.5 is shifted 20 m onshore (Table 1) so that the model data comparison is performed in the same mean h.
Seaward of the surfzone at M3, 
Observed (black) and modeled (red) hourly averaged (a),(b) significant wave height Hs, (c),(d) alongshore current υ, and (e),(f) cross-shore current u vs time at (left) just seaward of the surfzone M3 and (right) surfzone M1.5. In (c)–(f), model currents are at the average height above the bed of the ADVs. Time corresponds to days from 1 Aug 2006 (UTC).
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
At M3, the observed alongshore current 
At M3, the ADV, observed, cross-shore current 
The model has substantial capability in simulating wave heights and alongshore currents in the nearshore and surfzone at a particular mean water depth (Fig. 6), even though the cross-shore bathymetry profile is inaccurate. The model capability in simulating cross-shore currents at a particular height above the bed is reduced as u depends more on dynamical terms that have cross-shore gradients (Kumar et al. 2012). Nevertheless, with accurate bathymetry, the vertical profile of surfzone currents is simulated well with a wave-driven ROMS model (Uchiyama et al. 2010; Kumar et al. 2012). Given the differences in the model and observed cross-shore bathymetry profiles (section 2a), the fact that the modeled υ and u are reasonably consistent with the observed indicates that the model (without tuning) accurately simulates the dynamics of surfzone currents.
d. Model data comparison of subtidal velocity and temperature in midshelf (M26) and inner shelf (M8)
In the inner and midshelf of the SCB, wind forcing contributes to the subtidal along-shelf current dynamics (e.g., Lentz and Winant 1986). The modeled subtidal wind stress is not correlated with the observed (see section 3d). In addition, subtidal hydrodynamics are also influenced by large-scale pressure gradients (e.g., Hickey et al. 2003) and intrinsic variability manifested in the form of meso- and submesoscale eddies (e.g., Hickey 1992; Dong et al. 2009). Therefore, in a nondata-assimilated model simulation (as conducted here), modeled currents and temperature are not expected to be coherent with the observations. Nevertheless, a model data comparison of temporal and vertical structure of along-shelf current and temperature at the midshelf M26 and inner-shelf M8 moorings (see Fig. 1) is performed in the subtidal band to diagnose differences in vertical structure and temporal evolution.
At M26, the observed along-shelf current 
(left) Observed and (right) modeled subtidal alongshore velocity υST as a function of z and time at (top) M26 and (bottom) M8. The solid black lines denote zero υ. Time corresponds to days from 1 Aug 2006 (UTC).
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The midshelf M26 subtidal temperature 
As in Fig. 7, but for subtidal temperature TST.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
Although observed and modeled currents and temperature have similar temporal variability at mid- and inner-shelf locations (Figs. 7, 8), the model has no predictive capability. Inaccurate modeled variability is due in part to inaccurate wind stresses (Figs. 3c,d). Modeled variability is also set by lateral boundary conditions from the parent grids (Fig. 2), whose errors can be substantial and are not a priori known (McWilliams 2007, 2009). Both forcing and lateral boundary condition errors limit model predictability, motivating the statistical model data comparison presented in section 5.
5. Results: Statistical model data comparison
Here, the model’s ability to simulate the temporal variation and vertical structure of velocity and temperature from the mid- to inner shelf is examined by three statistical model data comparisons performed over the duration of each mooring deployment period (Table 1).
a. Vertical structure of mean velocity and temperature
First, a model data comparison is performed on mean velocities and temperatures at the midshelf (M26 and M20) and inner-shelf (M10 and M8) locations (Fig. 9). The mean denoted by 
Vertical profile of mean (left) alongshore velocity 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
b. Rotary velocity and temperature spectra
Rotary velocity (u, υ) spectra, separating clockwise (CW) and counterclockwise (CCW) motions (Gonella 1972), and temperature spectra are calculated midwater column at midshelf M26, inner-shelf M10, and surfzone M1.5 locations (Fig. 10). The 256-h spectral window (with 50% overlap) provides good spectral stability, although frequency resolution is insufficient to resolve distinct spectral peaks between inertial and diurnal or M2 and S2 tidal frequencies. Thus, model and observed spectra are compared in four frequency bands (shaded regions in Fig. 10): subtidal (ST; <33−1 cph), diurnal (DU; 33−1 to 16−1 cph), semidiurnal (SD; 16−1 to 10−1 cph), and high frequency (HF; >10−1 cph).
Observed (black) and modeled (red) middepth (left) velocity rotary spectra and (right) temperature spectra for (from top to bottom) midshelf M26, inner-shelf M10, and surfzone M1.5. The vertical bars represent the 95% confidence interval. For rotary velocity spectra, positive and negative frequencies are clockwise and counterclockwise motions, respectively. The ST (<33−1 cph), DU (33−1 to 16−1 cph), SD (14−1 to 10−1 cph), and HF (>10−1 cph) bands are indicated.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
At the midshelf M26, the ST rotary spectra are red, rapidly decreasing with frequency and are CW and CCW symmetric (black in Fig. 10a1). The M26 temperature spectra are also red in the ST band (black in Fig. 10a2). The DU band rotary and temperature spectra peak (Figs. 10a1,a2) is due to a combination of barotropic tides (for currents), inertial motions, surface heat flux, diurnal barotropic tidal forcing (e.g., Beckenbach and Terrill 2008), and wind forcing (Fig. 4). The larger CW versus CCW diurnal rotary variance suggests sea breeze–forced resonant internal waves that are nonevanescent because of the subtidal vorticity modifying the effective local Coriolis parameter (Lerczak et al. 2001; Nam and Send 2013). In the SD band, the rotary and temperature spectra peak (Figs. 10a1,a2) is at the M2/S2 tidal frequency, reflecting barotropic tides (currents) and semidiurnal internal waves. The M26 HF (>10−1 cph) rotary and temperature spectra are much weaker than in the other bands and fall off rapidly (Figs. 10a1,a2).
M26 modeled and observed rotary spectra compare favorably in most frequency bands, including the asymmetry in the DU band (red in Fig. 10a1). The CW to CCW ratio of integrated DU band rotary spectral density is similar for the model (3.7) and observed (3.8). The M26 modeled temperature spectra (red in Fig. 10a2) agrees with the observed in the ST band. In DU and SD bands, modeled spectral peaks are at the same frequency as observed but have smaller magnitudes by a factor of 5 (Fig. 10a2), likely because of weaker modeled mean stratification (Fig. 9a3). In the HF band, modeled rotary and temperature spectra are weaker than observed because of the lack of high-frequency surface and boundary forcing but also because of the hydrostatic, approximation-limiting, high-frequency variability.
The inner-shelf M10 observed rotary and temperature (Figs. 10b1,b2) are qualitatively similar to the midshelf M26, with some differences. The M10 observed ST rotary spectra has similar magnitude to M26 but is overall less red with a broader distribution of variance. The M10 DU band rotary spectra are similar in magnitude to M26 but are CW and CCW symmetric probably because of a stronger frictional response in the inner shelf (e.g., Lentz et al. 2001). The SD band rotary spectra are CW and CCW symmetric but slightly smaller than the DU band. In the SD band, the M10 observed temperature spectra is much weaker than at M26. Modeled M10 rotary spectra (Fig. 10b1) are similar to that observed in all frequency bands except HF. As at M26, modeled M10 temperature spectra (Figs. 10b2) in the DU, SD, and HF bands are underestimated, with large modeled SD band underestimation.
The surfzone M1.5 observed rotary spectra is whiter, with variance more broadly distributed (Fig. 10c1) than at M26 and M10. The observed ST band variance is nearly flat, the DU band peaks are weak, barely distinguishable from the confidence limits, and the SD band peaks are reduced and broader. The M1.5 observed temperature spectra is qualitatively similar to M10 but with a reduced SD band peak (Fig. 10c1). At M1.5, modeled rotary spectra capture the whitening of the observed and slightly underestimate the observed in all frequency bands. The surfzone M1.5 modeled temperature spectra have a similar pattern to, but underestimates, the variance in the observed temperature spectrum (Fig. 10c2).
c. EOF analysis of subtidal velocity and temperature
Given the good ST band spectral model data comparison, observed and modeled dominant vertical modes of subtidal velocities and temperature variability are compared. The temporal variability and vertical structure of subtidal velocities and temperature at moorings M26, M20, M10, and M8 are decomposed into vertical 
Percentage of subtidal velocity and temperature variance explained by the first EOF vertical mode at the indicated mooring site.
At midshelf (M26 and M20) and inner-shelf (M10 and M8) mooring locations, the observed subtidal flow is strongly polarized with 
Vertical (z) profiles of first cEOF, reconstructed, subtidal velocity and temperature variability for observed (black) and modeled (red) at (top to bottom) midshelves M26 and M20 and inner-shelves M10 and M8 sites: (left) the major Umaj (solid) and minor Umin (dashed) and (middle) principal angle θp (relative to +y) of the subtidal velocity ellipse. (right) Standard deviation σT of reconstructed temperature.
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The model largely reproduces the salient features of the observed subtidal velocity and temperature variability derived from the first cEOF (red in Fig. 11). The modeled subtidal velocity ellipses are similarly polarized 
6. Discussion
Modeled waves and currents are similar to observation in the surfzone (section 4), and modeled subtidal circulation and temperature variability is statistically similar to the observations (section 5). This motivates further analysis of the observations and model results from the midshelf to the surfzone.
a. The relationship between stratification and velocity vertical shear
The model stratification and subtidal velocity vertical shear are weaker than observed (Figs. 8, 9, and 11a1–e1). In a constant stress layer, larger stratification results in an increase in vertical shear (Businger et al. 1971). This pattern is consistent with the larger observed stratification and shear relative to the model. Model compensation of stratification and shear is investigated by examining the ratio of mean stratification to mean squared subtidal vertical shear N2/S2. Note that this ratio should not be confused with a gradient Richardson number as the observed and modeled mixing processes that set the mean stratification and subtidal vertical shear occur at shorter time scales that this analysis filters out.
The midshelf observed 
Continental shelf vertical mixing due to internal waves and bottom boundary layer processes for the subcritical Richardson number has been parameterized where the vertical eddy viscosity 
b. Model subtidal vertically integrated heat budget
Root-mean-square of modeled heat budget terms vs cross-shore distance at (a) synoptic (336−1 < Freq, < 33−1 cph) and (b) fortnightly and longer time scales (Freq. < 336−1 cph). Heat content time derivative 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
At synoptic time scales, the modeled vertically integrated temperature time derivative 
At fortnightly and longer time scales, the vertically integrated temperature time derivative and advective heat flux divergences are of similar magnitude at midshelf locations (x < −2500 m; Fig. 12b), with the surface heat flux a factor of 2 smaller. However, in the shallow-water depths of the inner-shelf (h < 13 m at x > −1600 m; Fig. 12b), a transition occurs where the surface heat flux and vertically integrated advective heat flux principally balance. Farther onshore and into the surfzone, the fortnightly temperature time derivative is less important. This model heat budget on fortnightly and longer time scales from August to October is similar to the summertime Martha’s Vineyard inner-shelf heat balance, where surface heat flux and lateral advective terms are in balance on time scales of weeks and months Fewings and Lentz 2011).
In section 6a, the similar observed and modeled 
c. Disconnect between surfzone and inner-shelf alongshore currents
Surfzone alongshore currents (Fig. 6) are driven largely by oblique incident wave forcing, whereas inner-shelf alongshore currents are due to a mix of wind, tidal, and buoyancy forcing and intrinsic variability. This difference results in distinct surfzone and inner-shelf alongshore current variability. At the surfzone M1.5, both observed and modeled υ have magnitude up to 0.5 m s−1 (Fig. 6d). At the inner-shelf M8, just 280 m offshore in 8-m water depth, the observed and modeled subtidal υST have much weaker magnitude of ≈0.1 m s−1 (Figs. 7c,d). The squared correlation between subtidal alongshore currents υST at M1.5 and (depth averaged) M8 is r2 = 0.11 for the observations and r2 = 0.04 for the model, both not significantly different from zero at 95% confidence. For the unfiltered (i.e., subtidal to high frequency) alongshore current, the squared correlations are essentially zero (r2 = 0.01) for both.
This weak relationship between M1.5 and M8 (cross-shore separated by 280 m) alongshore currents is in contrast to that observed at Duck, North Carolina (Feddersen et al. 1998), but not unexpected. Unlike the U.S. East Coast, in the SPB the alongshore wind stress τy and 
d. Cross-shelf coherence of mid- and inner shelf subtidal velocities and temperatures
Subtidal momentum and temperature can substantially vary from the mid- to inner shelf because of the changing relative importance of momentum (e.g., wind stress, pressure gradient, waves, advection, and eddies) and temperature (e.g., advective and surface heat flux) dynamics. Observed and modeled first vertical EOF, reconstructed, near-surface velocities and temperature [(5a)–(5c)] from mooring location M26–M8 (Fig. 11), together with (just seaward of surfzone) M4 subtidal velocity and temperature, are used to investigate the cross-shelf coherence in the subtidal band. Henceforth, the subscript ST is removed. Also, the superscript 1 refers to the first EOF mode, and the superscripts o and m suggest observed and modeled quantities, respectively.
The observed reconstructed subtidal alongshore velocities 
First EOF, reconstructed, near-surface, observed subtidal (a) cross-shore velocity 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
Observed 
Cross-shore EOF modes for near-surface (a) alongshore velocity std 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The decrease in modeled and observed near-surface υ(1) from the deeper midshelf to shallower inner-shelf has been previously observed (e.g., Lentz and Winant 1986; Lentz et al. 1999; Kirincich and Barth 2009) and is consistent with a larger bottom boundary layer role in shallower water. The coherent mid- to inner-shelf υ(1) variability is therefore consistent with subtidal wind forcing, alongshelf pressure gradients, or meso- and submesoscale eddies with length scale 
Observed 
Observed (black) and modeled (red) (a) alongshore component of the first cross-shore mode 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
These bulk (mid- to inner shelf), near-surface rf values are similar to inner-shelf rf estimated with the M10 depth-averaged, subtidal alongshore current 
e. Local alongshelf wind forcing in the San Pedro Bay inner shelf
The observed and modeled local-predicted 
(a) Observed 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The relationship between 
f. Inner-shelf alongshelf nonuniformity
Nonuniform alongshelf subtidal currents can occur because of nonuniform bathymetry; varying offshore flows (from boundary conditions); differences in wind, wave, or pressure gradient forcing; and intrinsically generated variability. Alongshelf nonuniform currents have a dynamical effect not included in local wind-driven balances [(12)]. At the HB06 site, the bathymetry is largely alongshelf uniform (Figs. 1a, 2d) on a scale of 5–10 km, although the coastline bends at y = 3.5 km. On a larger spatial scale (Figs. 2b,c), the shelf break is wider farther to northwest (+y) leading into Palos Verdes that bounds the San Pedro Bay. To the southeast (−y), the shelf break narrows from 10 to 2 km (Fig. 2c). This larger-scale variation, which is outside the smallest L5 grid domain, suggests that alongshelf effects may be important.
Here, nonuniformity in the observed and modeled inner-shelf, subtidal, depth-averaged, alongshelf current 
(a) Observed 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The observed and modeled 
g. Wind- versus wave-induced cross-shelf transport
In the midshelf, cross-shelf Ekman transport driven by alongshelf wind stress, that is, 
In general, mean RwE (solid black, Fig. 18) increases from the midshelf to the surfzone mainly because of decrease in the phase speed c. In the midshelf (x = −4000 m; Fig. 18), mean RwE ≈ 0.2. At cross-shore locations farther inshore (e.g., x = −800 m, h = 10 m), RwE ≈ 0.3, and in even shallower waters, RwE substantially increases, suggesting that wave-induced transport is almost of the same order as wind-induced transport. Although the wind stress 
The ratio of wave-driven to Ekman-driven cross-shelf transport 
Citation: Journal of Physical Oceanography 45, 6; 10.1175/JPO-D-14-0151.1
The observed and modeled Eulerian mean cross-shore velocity on the mid- and inner shelf (Figs. 9a2–e2) does not have a surface-intensified Stokes–Coriolis-driven Eulerian return flow to balance the onshore-directed Stokes drift transport that has been observed in the shelf region of U.S. East Coast (e.g., Lentz et al. 2008) and idealized modeling studies (e.g., Kumar et al. 2012), suggesting that the cross-shelf dynamics are much more complex than the idealized dynamics in Lentz et al. (2008). Diagnosing the detailed relative importance of wind- and wave-driven cross-shelf exchange processes is complex requiring analysis of momentum balances.
7. Summary
Accurately simulating cross-shore exchange from the surfzone to the midshelf requires a coupled wave and circulation model that includes tide, wind, buoyancy, and wave processes. The COAWST modeling system with coupled ROMS and SWAN includes all these processes, yet has not been extensively validated jointly from the midshelf to surfzone. Here, COAWST is applied to the midshelf to surfzone region of San Pedro Bay, with wave, surface forcing, and temperature, and velocity lateral boundary conditions are provided by other models. To test the model for use in studying cross-shelf exchange, modeled tides, waves, velocities, and temperatures are compared, primarily statistically, to field measurements from the Huntington Beach 2006 experiment.
In 8-m water depth, diurnal tidal constituents are well modeled, although semidiurnal tidal constituents are underestimated by ≈
The modeled, time-averaged cross- and alongshore velocity and surface temperature compare favorably to the observations. However, the modeled alongshore current vertical shear and stratification is weaker than those observed. Modeled and observed midwater column rotary velocity in the midshelf, inner shelf, and surfzone compare favorably in all but the high-frequency band (>10−1 cph). Midwater column temperature spectra are well reproduced in the subtidal band at all locations but underpredicted in the diurnal and semidiurnal possibly because of weaker modeled stratification. Both modeled and observed subtidal variance ellipses from the first cEOF reconstructed velocities are strongly polarized with the major velocity axis about 4 times the minor axis. Observed and modeled first EOF reconstructed temperatures are similar with largely depth uniform variability.
The observed and modeled ratio of mean stratification to root-mean-square subtidal velocity vertical shear 
The depth-averaged alongshore currents in 10-m depth, predicted from simple dynamics of wind forcing, bottom stress with best-fit linear drag coefficient, and local acceleration, explains ≈50% of both observed and modeled subtidal, depth-averaged 
Acknowledgments
Support for N. Kumar and F. Feddersen was provided by the Office of Naval Research (ONR). W. O’Reilly was supported by the California State Parks. J. McWilliams was supported by ONR N000141410626 and National Science Foundation OCE-1355970. Y. Uchiyama acknowledges Grant-In-Aid for Scientific Research C24560622. Data for the HB06 experiment were obtained within the framework of the Southern California Coastal Ocean Observing System (SCCOOS), National Oceanic and Atmospheric Administration (NOAA), Orange County Sanitation District (OCSD), and United States Geological Survey (USGS) programs at Huntington Beach. Thank you to George Robertson and Marlene Noble for the moored instrument data and to CDIP for the wave data. B. Woodward, B. Boyd, K. Smith, D. Darnell, I. Nagy, D. Clark, M. Omand, M. Rippy, M. McKenna, M. Yates, R.T. Guza, and D. Michrowski provided field support. Corey Olfe, Daniel Dauhajre, and Florian Lemarie prepared the boundary condition information required for model simulations. Computational support was provided by the COMPAS/ATLAS cluster maintained by Caroline Papadopoulos and Bruce Cornuelle. M. Olabarrieta, M. Omand, M. S. Spydell, S. H. Suanda, and Bruce Cornuelle provided useful feedback.
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