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DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.

Modeling Surfzone/Inner-shelf Exchange

Prof. Falk Feddersen Scripps Institutions of Oceanography IOD/SIO/UCSD 0209

9500 Gilman Drive La Jolla, CA 92093-0209

858.534.4345, 858.534.0300 (FAX), falk@coast.ucsd.edu http://iod.ucsd.edu/∼ falk

Award Number: N00014-13-1-0179 Award Number: N00014-15-1-2607 Award Number: N00014-15-1-2631

LONG-TERM GOALS The exchange of tracer (contaminants, pathogens, sediment, or larvae) between the surfzone, the inner-shelf, and onto the mid-shelf is important to Navy operations yet is poorly understood. Breaking-wave driven surfzone processes are radically different from the wind, stratification, (non- breaking) wave, and rotation driven processes in the inner-shelf. The time-scales of the processes is also quite different in these two regions. The interaction of these processes governs this exchange, and depends on the waves, wind, tide, and stratification. The long-term goal is to understand the processes that drive cross-shore exchange across both the surfzone and inner-shelf and develop an integrated modeling capability that includes all the relevant surfzone and shelf physics to make accurate predictions. OBJECTIVES The time-scales of exchange processes in the surfzone (< 10 min) and inner-shelf (hours+) are quite different. The interaction of these processes governs this exchange, and depends on the waves, wind, tide, and stratification. To study exchange between the surfzone and inner-shelf, the specific objectives are to: 1. Complete analysis of the IB09 experiment, in particular examining the mechanisms of sur- fzone

to inner-shelf dye tracer exchange over 6 hours by performing coupled surfzone and inner-shelf dye mass balances (graduate student Kai Hally-Rosendahl).

2. Test and calibrate the model with coupled surfzone, inner-shelf, and mid-shelf observations from the ONR funded HB06 experiments led by the PI.

3. Develop offline coupling of the wave-resolving surfzone model funwaveC and the wave- averaged model COAWST (coupled ROMS/SWAN) to study the interaction of transient rip currents on a stratified inner-shelf.

4. Develop parameterizations for the breaking-wave eddy generation mechanisms into wave resolving models.

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5. Use the model to diagnose mechanisms of tracer exchange and determine their importance given different incident wave, wind, stratification, tide, and Coriolis conditions that would be appropriate for various regions in the world of interest to the Navy. This work will quantitatively improve out ability to make predictions of the fate of pollutants and contaminants, in addition to other tracers, in the nearshore region.

APPROACH Tasks 1–3 have had substantial progress. Note that this is work was performed as a collabora- tioen between the PI and postdoctoral researcher Nirnimesh Kumar. Task 4 is underway and will lead to Task 5

Task 1. IB09 experiment analysis: Dye tracer mass budgets

Graduate student Kai Hally-Rosendahl has been analyzing the IB09 experiment data as part of his PhD thesis. He has two publications [Hally-Rosendahl et al., 2014, 2015] and is scheduled to defend in Fall 2015. The goal is to close a coupled surfzone and inner-shelf dye mass balance Task 2. Testing the Model with Coupled Inner-shelf and Surfzone Observations from HB06 The PI led the ONR-funded Fall 2006 HB06 field experiment focusing on surfzone and inner- shelf transport and fate near Huntington Beach CA. The experiment had had significant surfzone and inner-shelf dye, temperature, wave, and current observations with which to compare to the coupled surfzone-inner shelf model and examine the processes of surfzone/inner-shelf exchange. A cross-shore tripod and mooring array, spanning 4 km, was deployed to measure waves currents and temperature over 2 months over the late summer to fall transitional break-down of stratification. These long time-series [Wong et al., 2012; Nam and Send, 2011; Omand et al., 2012], spanning near-shoreline to 27 m depth, are ideal observations with which to test the combined IS/SZ model and its ability to reproduce waves, currents, and observations. The COAWST model (coupled ROMS/SWAN) is run for 3 months during the HB06 experi- ment at Huntington Beach held in Aug-Oct 2006. This work was done in collaboration with Jim McWilliams at UCLA. A series of nested model grids from the Eastern Pacific to the inner-shelf provides boundary information across grids down to the finest-scale inner-shelf grid with resolution of ∆ = 10 m. Wind forcing and net surface heat flux during the simulation period are obtained from a 6 km resolution Weather Research Forecasting (WRF) simulation, while boundary con- dition for sea surface temperature and salinity are obtained from AVHRR based climatology for the study area. The model prognostic variables (sea surface elevation, alongshore and cross-shore velocity, and sea surface temperature) are compared to measurement of hydrodynamic parameters for a period of ≈ 3 months. Task 3. Coupling the wave-resolving surfzone model funwaveC and the wave-averaged model COAWST (coupled ROMS/SWAN). Transient rip current ejection of surfzone water onto the inner-shelf has many potential implications for the dilution of polluted near-shoreline waters and cross-shore exchange of larvae, nutrients, sediment, and other tracers. The ejection of vorticity filaments of surfzone origin will lead to intrinsic

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shelf variability. More recently, it has been recognized that the surfzone often has a lateral temperature difference from the inner-shelf and that the inner-shelf very close to the well-mixed surfzone can be strongly stratified [Hally-Rosendahl et al., 2014; Marmorino et al., 2013; Sinnett and Feddersen, 2014]. Thus, inner-shelf stratification may affect the cross-shore ex- tent of transient rip currents which, through transport of surfzone water, will also have an affect on inner-shelf stratification. Only wave-resolving (e.g., Boussinesq) models (such as funwaveC) include the finite-crest length wave breaking physics to generate surfzone eddies and the resulting rip currents [Feddersen, 2014]. Wave-averaged models such as Delft3D, NearCom or COAWST (coupled ROMS/SWAN) cannot. Without these processes, cross-shelf eddy fluxes or cross-shelf material exchange on the inner-shelf will not be resolved. However, wave-resolving models (funwaveC) do not include im- portant shelf physics such as vertically sheared currents or stratification, and are computationally expensive. Thus, wave-resolving and wave-averaged models must be coupled in order to prop- erly represent all aspects of cross-shelf exchange. The approach here is the use a wave-resolving Boussinesq model to parameterize the vorticity generation due to short-crested breaking of indi- vidual waves. The Boussinesq model funwaveC used here, developed by the PI and distributed as open-source software, has been validated in ONR funded studies for surfzone waves, mean cur- rents, and surfzone eddies [Feddersen et al., 2011; Feddersen, 2014], surfzone drifter dispersion [Spydell and Feddersen, 2009], surfzone dye dispersion [Clark et al., 2011], and shoreline runup [Guza and Feddersen, 2012] We have developed off-line coupling methods to allow the breaking wave surfzone eddy gener- ation mechanism (funwaveC) to be inserted into the wave-resolving COAWST (coupled ROMS/SWAN) model so that surfzone eddies and transient rip currents are accurately generated. Task 4. Parameterizing Wave-Resolving Surfzone Eddy Generation In order to capture the appropriate surfzone eddy physics and the inner-shelf stratified physics, we seek to parameterize the surfzone eddy generation within wave-resolving models for use in wave-averaged models. This is computationally much more efficient that the funwaveC and COAWST model coupling explored in Task 3. Within a wave-resolving Boussinesq model, the eddy (vertical vorticity) generation is due to short-crested breaking of individual waves. The Boussinesq model funwaveC used here, developed by the PI and distributed as open-source software, has been vali- dated in ONR funded studies for surfzone waves, mean currents, and surfzone eddies [Feddersen et al., 2011; Feddersen, 2014], surfzone drifter dispersion [Spydell and Feddersen, 2009], surfzone dye dispersion [Clark et al., 2011], and shoreline runup [Guza and Feddersen, 2012] The overall approach is to develop and test parameterizations for incorporating the vorticity generation due to finite-crest length wave breaking in manners analogous to methodologies used to force 2D turbulence [e.g., Maltrud and Vallis, 1991; Srinivasan and Young, 2014] or those used for open ocean wave breaking effects on mixed layers [Sullivan et al., 2004, 2007]. We will then develop a subroutine for COAWST-ROMS that provides the finite-crest breaking wave eddy forcing as a body force to ROMS given the wave information provided by SWAN.

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WORK COMPLETED This overall effort began in March 2013. Here, tasks completed over the past year are reported: • SIO graduate student Kai Hally-Rosendahl has published two related papers on observations of

surfzone/inner-shelf tracer exchange [Hally-Rosendahl et al., 2014, 2015].

• One-way offline coupling methods for the wave-resolving funwaveC and wave-averaged COAWST (ROMS/SWAN) models has been completed.

• An analysis of the subtidal (time-scales longer than an inertial period, > 33 hr) variability in the observations and model, and a model-data comparison has been published in J. Physical Oceanography [Kumar et al., 2015a].

• Analysis of the diurnal and semi-diurnal internal variability in the observations and model, and a model-data comparison have been completed and are revised to J. Physical Oceanography [Kumar et al., 2015b].

• Idealized simulations (based on HB06 conditions) of transient rip currents on a stratified inner-shelf have been performed with the coupled funwaveC/COAWST model and presented at the Fall AGU meeting. This work is being written up now [Kumar and Feddersen, 2015].

• Development of parameterizations of surfzone breaking-wave eddy generation for wave- resolving models is underway. Over 250 simulations have been completed and processed

RESULTS Task 1. IB09 experiment analysis: Dye tracer mass budgets These are a subset of results presented in Hally-Rosendahl et al. [2015]. Aerial images (e.g., Fig- ures 1a-1f) spanning 0:42-4:53 h after the t0 = 10:39 h start of the dye release are partitioned into three time periods based on temporal gaps in images and the dye plume evolution: period I (early-release, 11:21-11:53 h), period II (mid-release, 12:08-13:01 h), and period III (late-release, 14:56-15:32 h). Approximately 40 min after the release begins (Figure 1a, period I), surfzone dye has advected about 600 m alongshore at ≈ 0.25 m s−1, consistent with in situ VSZ = 0.22 m s−1. Surfzone dye is

ejected onto the inner-shelf in narrow (≈ 50 m) alongshore bands (Figure 1a), presumably due to transient rip currents [e.g., HR14]. As the dye release continues (Figures 1b-1d, period II), the leading portion of inner-shelf dye is alongshore-patchy with length scales ≈ 50 m (as in Figure 1a). Behind the

leading edge, slower alongshore advection of inner-shelf dye (e.g., the feature at y ≈ 1250 m and

1500 m in Figures 1e and 1f, respectively, period III) is apparent at a speed of ≈ 0.15 m s−1,

consistent with in situ VIS = 0.14 m s−1(not shown). At these longer times and downstream distances (Figures 1e and 1f, period III), inner-shelf dye advects alongshore, disperses cross-shore, and moves to larger alongshore length scales. In particular, Figures 1e and 1f reveal a coherent nearshore eddy feature (at y ≈ 1250 m and 1500 m, respectively) with an alongshore length scale ≈ 300 m, roughly

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six times larger than the length scales of inner-shelf dye patches when recently ejected from the surfzone (Figure 1.)

Figure 1: Aerial multispectral images of surface dye concentration D (ppb, see colorbar) versus cross-shore coordinate x and alongshore coordinate y for six times (indicated in each panel). The

mean shoreline is at x = 0 m. Green star indicates location of continuous dye release (starting at t0

= 10:39 h). Yellow diamonds indicate cross-shore array f1-f6 locations, and yellow circles indicate SA1-SA4 locations. Light gray indicates regions outside the imaged area, and black indicates

unresolved regions due to foam from wave breaking. Vertical dashed cyan line at xb divides the surfzone (SZ) and inner-shelf (IS), and horizontal cyan line divides the near- and far-field regions A

and B (see panel (a)). Plume leading edge yp(t) is shown with green triangles at x ≈ − 100 m (for

panel (f), yp ≈ 3250 m). Panels (a), (b)-(d), and (e)-(f) are in time periods I, II, and III, respectively.

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( b) t = 12: 35 h

0 5 10 15

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Figure 2: Aerial multispectral images of inner-shelf surface dye concentration D (ppb, see col- orbar) versus cross-shore coordinate x and alongshore coordinate y for (a) a transient rip current ejection event at t = 12:22 h and (b) the subsequent dye evolution at t =12:35 h approximately 150 m downstream. Gray denotes the surfzone, largely unresolved in the aerial imagery due to

foam from wave breaking. The near-shoreline dye release is at (x, y) = (− 10, 0) m.

The observed surfzone to inner-shelf dye ejections are episodic and short-lived (O(1) min) and have small alongshore length scales (O(10-100) m; Figures 1 (y ≤ 1500 m), and 2). An example rip current event is highlighted using two of the aerial images (Figure 2). Just offshore of the dye

( a) t = 12: 22 h

y (

m)

y (

m)

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0 r ∫t0 r

Figure 3: inner-shelf Mis(t), total Mtot(t), and released dye mass versus time as indicated in the legend. Red line shows the dye mass released at the pump since t =10:39 hr (M (t) = t Q dτ , where Qr is the dye release rate).

release at t = 12:22 h (Figure 2a), a rip current ejects concentrated (≥ 15 ppb) dye out of the surfzone through a 20 m wide neck, terminating in a roughly 50 m wide rip current head 100 m offshore of the surfzone boundary. Gradients between dye-rich and dye-free water are very strong (Figure 2a). On a subsequent aerial pass (t = 12:35 h, Figure 2b), the ejected dye has advected

≈ 150 m alongshore, dispersed to larger spatial scales, and lost its clear rip current signature. Other dye ejections with similar spatial scales and evolution are seen throughout the 23 aerial images (e.g., Figure 1). The observed ejection events are episodic and brief (O(1) min) and occur at random alongshore locations, indicating that these rips are transient and are not bathymetrically controlled, consistent with the approximately alongshore-uniform bathymetry at Imperial Beach. In order to address the objectives, the released dye must be accounted for. Historically, this has been a significant challenge with subsurface dye releases. Through the closure of dye mass balances (e.g., Figure 3), we have quantified the surfzone to inner-shelf tracer flux and shown that a parameterization based on rip current exchange velocity works well [Hally-Rosendahl et al., 2015]. Task 2. Model-data comparison and diagnosis of internal motions on the mid to inner-shelf In 20 m depth, modeled semi-diurnal horizontal kinetic energy (HKE) varies between 0 − 6.5 Jm−2 on multi-day and longer timescales (Fig. 4a), unrelated to the local spring-neap cycle (not shown). Two 24-h time-periods are described in detail. The first, denoted period I, occured during elevated HKE and large HKE temporal variation (day 11.5–12.5, gray shading in Fig. 4a). The second, denoted period II, corresponds to weak HKE and negligible temporal variation (day 31.5–32.5, yellow shading in Fig. 4b).

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Period I modeled F is strong (> 1 Wm−1) and obliquely incident (with respect to the 100 m contour) at the shelf break and in the southern canyon adjacent to Newport beach (Fig. 4b). At the northwestern canyon (x = − 8 km and y = 6 km, Fig. 4b) F is < 0.25 Wm−1 and is directed offshore. Period I semi-diurnal baroclinic flux divergence is positive (indicating generation) at the northwestern canyon and also at the shelf break offshore of Huntington Beach (Fig. 4b). At the southern canyon and onshore of the 50 m contour is negative, associated with energy dissipation. During period II, F varies significantly in magnitude and direction relative to period I. Period II F

≈ 0.5 Wm−1 and is directed onshore adjacent to the northwestern canyon, is negligible at the

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Period I

Time (days) Period II 10−4 (Wm −2)

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x (km) Figure 4: (a) Modeled 24-h averaged semi-diurnal depth-integrated horizontal kinetic energy HKE versus time at M20 with periods of strong HKE (denoted I, gray, 11.5-12.5 day) and weak HKE (denoted II, yellow, 31.5-32.5 days) highlighted. (b,c) Modeled baroclinic energy flux F (arrows) and energy flux divergence (shading) versus cross-shore x and alongshore y coordinate in h <100 m for (b) period I and (c) period II highlighted in (a). Gray patch represents land, solid

black lines are depth-contours, and black squares are moorings M26, M20, M10 and M8.

HK

E (J

m−

2 )

y (k

m)

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shelf break offshore of Huntington beach, and is directed offshore at the southern canyon offshore of the Newport beach (Fig. 4c). The baroclinic flux divergence is weak and mostly negative along the shelf break and at the northwestern canyon (Fig. 4b), while strong and positive (3×10−4 Wm−2) is modeled at the southern canyon offshore of Newport beach. In certain regions the sign of is switched between periods I and II, potentially indicating a transition from generation to dissipation regions. These period I and II examples of semi-diurnal internal energy flux variability illustrate the complex, multi-directional, variable remote and locally generated semi-diurnal internal tide in the SPB. These two examples, suggest that in order to accurately model the semi-diurnal internal tide would require accurate spatially-temporally variable F as boundary conditions, accurate representation of variable generation and dissipation, and accurate mean stratification. Task 3. Coupling wave-resolving (funwaveC) and wave-averaged (COAWST) models: Transient rip currents on a stratified inner-shelf

As discussed earlier, wave-resolving models (funwaveC) do not include stratification or vertical flow variation, and wave-averaged models (COAWST or Delft3D), do not include the surfzone eddy generation by ∇ × Fbr. Thus, these two models must be coupled or ∇ × Fbr must be parameterized in order to accurately represent transient rip current effects on inner-shelf variability. The wave-resolving funwaveC and wave-averaged COAWST-ROMS has been coupled being coupled in order to diagnose the effect of breaking-wave eddy generation on rip currents on a stratified inner-shelf [Kumar and Feddersen, 2015]. This successful coupling means that surfzone eddy generation mechanism (funwaveC) and 3D processes including stratification (COAWST) to be resolved, and allows for study of transient rip currents on a stratified inner-shelf An example idealized surfzone and stratified inner-shelf simulation that highlights the interaction of rip currents with inner-shelf stratification over 24 hrs is shown in Fig. 5. In this simulation, directionally spread waves generate vertical vorticity (surfzone eddies) and the breaking wave generated turbulence makes the surfzone vertically uniform in temperature. The surfzone eddies lead to transient rip currents that eject onto the inner-shelf. These resulting inner-shelf eddies (of surfzone origin) have a strong influence on inner-shelf temperature structure. These eddies are in cyclostrophic balance and have associated vertical velocity drawing up colder water from below. The temperature structure seen here is reminiscent of features seen in surfzone aerial IR images [Marmorino et al., 2013]. The time-evolution of these features also reveals interesting features that have not yet been considered (Fig. 5. The rip currents ejected onto the inner-shelf lead to the development of a temperature front 2–3 surfzone widths from shore, with sloping isopycnals. This frontal structure, under the influence of waves and Coriolis may undergo additional larger scale instability providing a new mechanism for exchange from the near inner-shelf to much farther offshore. These effects are being explored in [Kumar and Feddersen, 2015].

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17.5 18.2 18.9 19.6

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−600 −400 −200 0 −600 −400 −200 0 −600 −400 −200 0 x (m) x (m) x (m)

Figure 5: Temperature (a1-a5) and vertical vorticity (b1-b5) at z = − 1 m versus cross-shore x and

alongshore coordinates y; and temperature (c1-c5) versus cross-shore x and vertical z coordinates at y = − 600 m at times 1 (a1-c1), 6 (a2-c2), 12 (a3-c3), 18 (a4-c4) and 24 (a5-c5) hours.

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Task 4. Parameterizing the Breaking wave..

As a preliminary result to how to parameterize breaking wave surfzone eddy generation, we focus on quantifying an individual wave breaking event. We take inspiration from [Sullivan et al., 2007], who parameterized the effects of individual wave breaking in a LES model of the ocean mixed layer. Here, the idea is to use funwaveC to parameterize the vorticity variability forcing terms and then stochastically insert them into the a ROMS model that includes the surfzone. As ROMS is a primitive equation model, vertically integrated it is simply the shallow water equations. Thus, the generated eddies would be able to evolve according to 2D turbulence. The wave forcing vector due to an individual breaking wave is represented as F, which can be divided into an irrotational scalar (φF ) and a rotational vector quantity (ψF ) such that

F = − ∇ φF + ∇ × ψF

where the rotational part of the wave forcing is the part that has a non-zero curl, ie,

∇ × F = − ∇ ψF (1)

If we can parameterize the breaking wave forcing events via ψF , then, similar to [Sullivan et al., 2007], these events can be inserted as forcings into ROMS.

Fig. 6 is an example of the application of this decomposition to a single wave breaking event. Simulations were conducted for an alongshore uniform beach, with the cross-shore profile representative of the HB06 beach profile. At the offshore boundary two wave trains with same amplitude and frequency, but different angle of incidence are allowed to propagate towards the shoreline, thus creating regions of constructive and destructive interference. The consistent group pattern begins to generate rip currents. The wave breaking (see normalized eddy viscosities), forces non-zero ∇ × F. This can be isolated by solving (1) to get ψF (right panel). This can then be used to force surfzone eddies in COAWST. Currently about 250 model simulations over a range of breach slopes and wave conditions have been completed and are being used to extract the breaking wave forcing which will be parameterized.

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Figure 6: Maps of (left to right) vorticity, sea-surface elevation η, breaking-eddy viscosity, forcing of vorticity ∇ × F, and forcing streamfunction ψF as a function of cross-shore coordinate x and

alongshore coordinate y. IMPACT/APPLICATIONS This work will have significant impact as it will allow for a single model to be used to study exchange processes from the surfzone to the shelf-break. RELATED PROJECTS These projects are directly related to the upcoming ONR Inner-shelf and also part of the ONR funded “Shelf Modeling” NOPP project. REFERENCES Clark, D. B., F. Feddersen, and R. T. Guza, Modeling surfzone tracer plumes: 2. transport and

dispersion, J. Geophys. Res., 116(C11028), doi:10.1029/2011JC007211, 2011.

Feddersen, F., The generation of surfzone eddies in a strong alongshore current, J. Phys. Ocean., 44, 600–617, doi:10.1175/JPO-D-13-051.1, 2014.

Feddersen, F., D. B. Clark, and R. T. Guza, Modeling of surfzone tracer plumes: 1. Waves, mean currents, and low-frequency eddies, J. Geophys. Res., 116(C11027), doi: 10.1029/2011JC007210, 2011.

Guza, R. T., and F. Feddersen, Effect of wave frequency and directional spread on shoreline runup,

Geophys. Res. Lett., 39, doi:10.1029/2012GL051959, 2012.

Hally-Rosendahl, K., F. Feddersen, and R. T. Guza, Cross-shore tracer exchange between the surfzone and inner-shelf, J. Geophys. Res., pp. n/a–n/a, doi:10.1002/2013JC009722, 2014.

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Hally-Rosendahl, K., F. Feddersen, D. B. Clark, and R. T. Guza, Surfzone to inner-shelf exchange estimated from dye tracer balances, Journal of Geophysical Research: Oceans, pp. n/a–n/a, doi:10.1002/2015JC010844, 2015.

Kumar, N., and F. Feddersen, The interaction of transient rip currents and stratification on a strati- fied inner-shelf, in prep, 2015.

Kumar, N., F. Feddersen, J. C. McWilliams, Y. Uchiyama, and W. O’Reilly, Mid-shelf to surf zone coupled ROMS-SWAN model-data comparison of waves, currents, and temperature: Diagno- sis of subtidal forcings and response, J. Phys. Ocean., 45, 1464–1490, doi:10.1175/JPO-D-14- 0151.1, 2015a.

Kumar, N., F. Feddersen, S. Suanda, J. C. McWilliams, Y. Uchiyama, and W. O’Reilly, Mid- shelf to surf zone coupled ROMS-SWAN model-data comparison ofcurrents, and temperature: Diagnosis of diurnal and semi-diurnal forcings and response, J. Phys. Ocean., revised, 2015b.

Maltrud, M. E., and G. K. Vallis, Energy spectra and coherent structures in forced two- dimensional and beta-plane turbulence, Journal of Fluid Mechanics, 228, 321–342, doi: 10.1017/S0022112091002720, 1991.

Marmorino, G. O., G. B. Smith, and W. D. Miller, Infrared Remote Sensing of Surf-Zone Eddies, IEEE J. Selected Topics in Applied Earth Observations and Remote Sensing, 6(3, SI), 1710– 1718, doi:10.1109/JSTARS.2013.2257695, 2013.

Nam, S., and U. Send, Direct evidence of deep water intrusions onto the continental shelf via surging internal tides, J. Geophys. Res., 116, doi:10.1029/2010JC006692, 2011.

Omand, M. M., F. Feddersen, P. J. S. Franks, and R. T. Guza, Episodic vertical nutrient fluxes and nearshore phytoplankton blooms in southern california, Limnol. Oceanogr., 57, 1673–1688, doi:10.4319/lo.2012.57.6.1673, 2012.

Sinnett, G., and F. Feddersen, The surf zone heat budget: The effect of wave breaking, Geophys. Res. Lett., doi:10.1002/2014GL061398, 2014.

Spydell, M. S., and F. Feddersen, Lagrangian drifter dispersion in the surf zone: Directionally spread, normally incident waves, J. Phys. Ocean., 39, 809–830, 2009.

Srinivasan, K., and W. R. Young, Reynolds stress and eddy diffusivity of beta-plane shear flows, Journal of the Atmospheric Sciences, 71(6), 2169–2185, doi:10.1175/jas-d-13-0246.1, n/a, 2014.

Sullivan, P., J. McWilliams, and W. Melville, The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations, J. Fluid Mech., 507, 143–174, doi:10.1017/S0022112004008882, 2004.

Sullivan, P. P., J. C. McWilliams, and W. K. Melville, Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers, J. Fluid Mech., 593, 405–452, doi:10.1017/S002211200700897X, 2007.

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Wong, S. H. C., A. E. Santoro, N. J. Nidzieko, J. L. Hench, and A. B. Boehm, Coupled physical, chemical, and microbiological measurements suggest a connection between internal waves and surf zone water quality in the Southern California Bight, Continental Shelf Research, 34, 64–78, doi:10.1016/j.csr.2011.12.005, 2012.

PUBLICATIONS Publications supported by this project appearing this year, submitted, or in preparation include: 1. Hally-Rosendahl, K., F. Feddersen, D. B. Clark, and R. T. Guza, Surfzone to inner-shelf

exchange estimated from dye tracer balances, J. Geophys. Res., 10.1002/2015JC010844, 2015.

2. Spydell, M. S. F. Feddersen, M. Olabarrieta, J. Chen, R. T. Guza, B. Raubenheimer, and S. Elgar, Observed and Modeled Drifters at a Tidal Inlet, J. Geophys. Res., 120, doi:10.1002/2014JC010541, 2015.

3. Kumar, N., F. Feddersen, J. C. McWilliams, Y. Uchiyama, and W. O’Reilly, Mid-shelf to surf zone coupled ROMS-SWAN model-data comparison of waves, currents, and temperature: Diagnosis of subtidal forcings and response, J. Phys. Ocean., 45, 1464-1490,doi:10.1175/JPO- D-14-0151.1, 2015a.

4. Kumar, N., F. Feddersen, S. Suanda, J. C. McWilliams, Y. Uchiyama, Mid-shelf to surf zone coupled ROMS-SWAN model-data comparison ofcurrents, and temperature: Diagnosis of diurnal and semi-diurnal forcings and response, revised to J. Phys. Ocean., 2015b.

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