the effect of barotropic and baroclinic tides on coastal...

GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

The effect of barotropic and baroclinic tides on coastal1

dispersion2

Sutara Suanda, Falk Feddersen, Matthew Spydell

Scripps Institution of Oceanography, La Jolla, California, USA3

Nirnimesh Kumar

University of Washington, Seattle, Washington, USA4

Sutara Suanda, Scripps Institution of Oceanography, UCSD, 9500 Gilman Dr., La Jolla CA 92093-

0209 ([email protected])

D R A F T April 12, 2018, 11:02am D R A F T

X - 2 SUANDA, ET AL.: DISPERSION IN COASTAL MODELS

The effects of barotropic and baroclinic tides on coastal drifter dispersion are5

examined with realistic high-resolution Central Californian shelf simulations.6

For virtual drifters tracked in three-dimensions over 48 h, the horizontal rela-7

tive dispersion and vertical dispersion are similar between simulations with no8

tides and with barotropic tides. In contrast, including baroclinic tides induces9

a factor 2–3 times larger horizontal dispersion and a factor 2 times larger ver-10

tical dispersion. Vertical dispersion is enhanced by baroclinic tides through in-11

creased vertical velocities and sub-surface model vertical diffusivity. The increase12

in horizontal dispersion with vertical mixing is qualitatively consistent with weak-13

mixing shear dispersion and demonstrates the need to include baroclinic tides14

and three-dimensional tracking for coastal passive tracer dispersion. For surface15

following drifters, horizontal dispersion is similar in all simulations. However,16

after 48 h ensemble drifter trajectory differences between simulations with no17

tides and baroclinic tides are 10 km, suggesting their importance for search-and-18

rescue or oil-spill response operations.19


SUANDA, ET AL.: DISPERSION IN COASTAL MODELS X - 3

1. Introduction

Tracer dispersion in the coastal ocean is relevant to pollutant dispersal [e.g., Boehm et al.,20

2002; Macfadyen et al., 2011; Poje et al., 2014], search-and-rescue operations [e.g., Spaulding21

et al., 2006], and the connectivity of marine organisms [e.g., Pineda et al., 2007; Cowen and22

Sponaugle, 2009]. Lagrangian analysis of surface-following drifters [e.g., Davis, 1985; Spydell23

et al., 2009; Ohlmann et al., 2012], dye releases [e.g., Sundermeyer and Ledwell, 2001; Dale24

et al., 2006; Clark et al., 2010; Moniz et al., 2014; Hally-Rosendahl et al., 2014], and virtual25

drifter tracking with high-frequency radar velocities [e.g., Rypina et al., 2016], provide estimates26

of dispersal patterns and dispersion rates at different space- and time-scales that inform coastal27

resource management. Due to limited Lagrangian observations, marine connectivity [Mitarai28

et al., 2009; Petersen et al., 2010; Drake et al., 2011] and pollutant dispersion [e.g., Thyng and29

Hetland, 2017] are also estimated by virtual drifters advected with realistic numerical models.30

The broad range of space- and time-scales from the nearshore (O(10) m and O(1) min) to31

the outer continental shelf (O(10) km, O(1) day), also present a challenge to coastal numer-32

ical modeling. Regional operational models such as those from Integrated Ocean Observing33

Systems (https://ioos.noaa.gov/) can well-represent wind-driven and mesoscale dynamics [e.g.,34

Veneziani et al., 2009], but typically have relatively coarse horizontal resolution (O(1− 3) km)35

and poorly resolve continental shelf circulation from the shoreline to 100-m water depth [e.g.,36

Mitarai et al., 2009; Drake et al., 2011]. Both a U. S. West-Coast wide dispersal study with a37

3-km resolution model [Drake et al., 2011] and regional study with a 1-km resolution model38

[Mitarai et al., 2009], describe the effects of large space-scale (> 10 km) and long time-scale39

(> 10 day) dispersion processes. Because < 1-km spatial scales within a model can impact40



coastal dispersion estimates [e.g., Rasmussen et al., 2009; Bracco et al., 2018], these processes41

are resolved by further model nesting [e.g., Romero et al., 2013], or parameterized within the42

Lagrangian submodel [e.g., Lacorata et al., 2014; Rypina et al., 2016]. For oil-spill response ap-43

plications, or to compare with surface-following drifter observations, some model-based disper-44

sion studies focus on near-surface horizontal (two-dimensional, 2D) dispersion [e.g., Ohlmann45

and Mitarai, 2010; Romero et al., 2013; Thyng and Hetland, 2017]. However, non-buoyant46

tracers such as pollutants, nutrients, and larvae are advected by the full three-dimensional (3D)47

flow field, with a potentially important relationship between horizontal and vertical dispersion.48

Many previous U. S. West-Coast model-based dispersion studies have not included tides [e.g.,49

Mitarai et al., 2009; Drake et al., 2011; Kim and Barth, 2011]. Although hindcast [Kurapov50

et al., 2017] and operational models [Chao et al., 2017] of the region have recently incorporated51

tides, dispersion studies with realistic models that incorporate tides remain limited [e.g., Romero52

et al., 2013]. Barotropic (surface) and baroclinic (internal) tides potentially impact dispersion53

through processes including barotropic tidal rectification [e.g., Ganju et al., 2011], internal wave54

shear dispersion [Young et al., 1982; Steinbuck et al., 2011; Kunze and Sundermeyer, 2015],55

and internal wave Stokes’ Drift [Wunsch, 1971]. In realistic coastal models, the importance56

of including barotropic (BT) and baroclinic (BC) tides relative to coastal processes driven by57

winds, stratification, and bathymetric variability on tracer dispersion is not well understood.58

In a study using a high resolution (250-m grid spacing) coastal model that included BT and59

BC tides, horizontal dispersion was due to a combination of submesoscale processes and tides60

[Romero et al., 2013]. However, no distinction between BT and BC tidal effects were made and61



no direct comparison of dispersal rates or drifter trajectories between models that include and62

neglect tides were provided.63

The effect of BT and BC tides on mid- to inner-shelf stratification and vertical mixing were64

examined using three Central California (U.S. West-Coast) simulations with identical realistic65

wind and large-scale boundary conditions but with either no-tides, BT-only tides, or both BT66

and BC tides [Suanda et al., 2017]. Tidal effects were isolated by analysis of a time period67

with similar volume-averaged heat content and upwelling mean flows in the three simulations.68

Relative to simulations without BC tides, the onshore-propagating dissipating baroclinic tide69

increased mid-water column vertical mixing and reduced subtidal stratification with comparable70

magnitude to the observed natural seasonal cycle [Suanda et al., 2017]. Here, the effects of71

BT and BC tides on 3D and surface-following (2D) coastal dispersion are examined with a72

Lagrangian drifter study using the three simulations of Suanda et al. [2017].73

The model setup, drifter tracking methods, and Lagrangian statistics are described in Sec-74

tion 2. Horizontal and vertical dispersion statistics in the no-tides, BT-tides, and BC-tides simu-75

lations are compared in Section 3. The mechanisms inducing additional vertical and horizontal76

dispersion with BC tides, the differences between 3D and 2D dispersion, and the trajectory dif-77

ference between simulations are discussed in Section 4. Results are summarized in Section 5.78

2. Model and Methods

2.1. ROMS simulations

Realistic continental shelf hydrodynamics within the Central Californian coastal up-79

welling system are simulated with ROMS (Regional Ocean Modeling System), a three-80

dimensional, terrain-following, open source numerical model that solves the Reynolds-averaged81



Navier-Stokes equations with hydrostatic and Boussinesq approximations [Shchepetkin and82

McWilliams, 2005; Haidvogel et al., 2008; Warner et al., 2010]. The ROMS setup is briefly83

described here with further details in Suanda et al. [2016, 2017]. Three levels of offline nesting84

(downscaling) transmit large scale variability through open boundary conditions from a U. S.85

West-Coast-wide ocean simulation to a continental shelf domain [e.g., Marchesiello et al., 2001;86

Mason et al., 2010; Suanda et al., 2017]. The shelf domain is about 80-km by 25-km wide, with87

a horizontal grid spacing of 200 m, and 42 vertical levels (Fig. 1). The k− ε turbulence closure88

model, representing subgrid vertical mixing, gives the time- and space-varying vertical eddy89

diffusivity KV [e.g., Umlauf and Burchard, 2005; Warner et al., 2005]. All levels of nesting90

use the same realistic COAMPS daily-averaged atmospheric forcing with ≈ 9-km resolution91

[Hodur et al., 2002]. The model is run for 60 days from 1 June to 31 July 2000.92

Three continental shelf simulations are conducted. The first has no barotropic or baroclinic93

tides (referred to as no-tides, NT). A second simulation includes barotropic tides (local tides,94

LT) by adding harmonic sea level and barotropic velocity of eight astronomical semidiurnal95

and diurnal tidal constituents and two overtides from the ADCIRC Tidal Constituent Database96

for the Eastern North Pacific Ocean [e.g., Mark et al., 2004] to the domain open boundaries97

(Fig. 1a). The third simulation has both barotropic and baroclinic tides (with-tides, WT), inher-98

iting boundary conditions with the addition of the ADCIRC barotropic tidal forcing applied on99

the prior level of nesting. Barotropic-to-baroclinic tidal conversion within the larger domain re-100

sult in a net onshore, remotely-generated, semidiurnal internal tide energy flux of≈ 100 Wm−1101

on the boundary of the continental shelf domain [Suanda et al., 2017].102

2.2. Lagrangian drifter tracking (LTRANS)



In the three simulations (WT, LT, NT), virtual Lagrangian drifters are released and tracked103

with the offline software package LTRANS [North et al., 2006], utilizing the ROMS model104

three-dimensional (3D) and time-dependent velocities and diffusivity. In the East-West (x)105

direction drifters are advected by,106

xn+1 = xn + uδt+ [2KHδt]1/2Rn, (1)

where xn is the drifter x-position at time-step n, u is the ROMS x-velocity interpolated to drifter107

position, KH = 1 m2 s−1 is a constant horizontal diffusivity, the LTRANS time-step δt = 120 s,108

andRn is a normally-distributed random number. North-South (y) drifter advection is analogous109

to (2). Vertical (z) drifter advection is given by110

zn+1 = zn +

(w +

∂KV

∂z

)δt+ [2KV δt]

1/2Rn (2)

where the space- and time-dependent vertical diffusivityKV from k−ε closure is interpolated to111

the drifter position. Because KV varies in z, an additional term ∂KV /∂z is included to account112

for Lagrangian advection to regions of high diffusivity [e.g., Davis, 1991; North et al., 2006;113

Schlag and North, 2012].114

2.3. Drifter releases

The specific five-day time period of upwelling-favorable conditions and similar heat content115

across NT, LT, WT [Suanda et al., 2017], was chosen for drifter release experiments. Time-116

dependent model winds were from the northwest, increasing in intensity from ≈ 5 m s−1 to117

≈ 10 m s−1 over the five days (Fig. 1c). Barotropic tides had a 2 m maximum tide range118

(Fig. 1d), and were very similar in LT and WT [Suanda et al., 2017].119



In each simulation, drifters are repeatedly released in two near-surface patches centered on120

the 30- and 50-m isobaths in regions of relative along-shore uniformity (black dots, Fig. 1 a).121

Each patch extends 500 m by≈ 4 km by 2 m in the cross-, along-isobath, and vertical directions122

with release spacing of 125 m, 200 m and 1 m respectively (Fig. 1b). A total of twenty one123

releases separated by ∆t = 6 h were conducted over the 5-day period resulting in 6300 drifters124

in each patch. After release, drifters are tracked for 48 h. Drifters crossing land, sea-surface, or125

bottom boundaries are specularly reflected. In 48 h, ≈ 2% of released drifters leave the model126

domain and are only included in the analysis when within the domain.127

2.4. Drifter statistics

Bulk drifter relative dispersion rates are quantified by temporal growth in drifter position128

variance from the 30- and 50-m isobath releases, respectively. The time-staggered releases129

are recast into hours after release t [e.g., Davis, 1983]. In the x-direction, the patch relative130

dispersion D2xx [e.g., LaCasce, 2008; Rypina et al., 2016] is131

D2xx(t) =

⟨(∆x(t)−∆xi(t))

2⟩, (3)

where ∆x(t) is a drifter’s East-West displacement from release location, ∆xi is the mean East-132

West displacement of all drifters in a release i (center of mass), and the ensemble average 〈·〉133

is over all drifters in a release and all 21 releases. An analogous expression to (3) is defined134

in the North-South (y) direction (D2yy(t)) and also for the cross-dispersion D2

xy(t). These D2135

components are used to define principal axes directions (x′, y′) such that D2y′y′ and D2

x′x′ are the136

relative dispersion in the major and minor axis direction, respectively [e.g., Sundermeyer and137

Ledwell, 2001; Romero et al., 2013; Rypina et al., 2016]. The principal axes dispersion defines138



a bulk horizontal relative dispersion ellipse with area (ensemble patch size),139

D2E(t) = π(D2

x′x′D2y′y′)

1/2. (4)

The horizontal diffusivity KE is based on the time-derivative of ellipse area,140

KE(t) =1

2

dD2E

dt, (5)

where derivatives are estimated as forward Euler differences. To minimize error in noisy esti-141

mates of KE , a time-smoothing box car filter with linearly increasing span up to 24 h is used142

before calculating the time derivative.143

In the vertical (z), the relevant statistic is absolute dispersion as the sea-surface is adjacent144

to the release location [e.g., Clark et al., 2010; Spydell and Feddersen, 2012]. The absolute145

vertical dispersion D2zz is defined as,146

D2zz(t) = 〈∆z(t)2〉, (6)

where ∆z is the drifter displacement from its release location. A corresponding vertical diffu-147

sivity Kz is defined analogous to the horizontal diffusivity (5).148

3. Results

A snapshot of drifter positions at t = 30 h for all 30-m isobath releases shows the initial149

center of mass and dispersal pattern in the NT, LT, and WT simulations (Fig. 2a–c). In all150

three simulations, the release center of mass (white circles, Fig. 2a–c) has migrated south151

and offshore of their initial location (white strip, Fig. 2a), consistent with coastal upwelling.152

Drifters remain onshore of the shelf-break (≈ 100-m isobath) and form alongshore-elongated153

patches, as in previous studies [e.g., Davis, 1985; Dever et al., 1998; Romero et al., 2013]. In154



geographic coordinates, the alongshore drifter dispersion in WT (Fig. 2c) is larger than in NT155

or LT (Fig. 2a,b).156

3.1. Horizontal relative dispersion

In all three simulations with 30-m isobath releases, the relative dispersion major axis is 3–4×157

larger than the minor-axis (Fig. 2d–f) at t = 30 h. At this time, the horizontal relative dispersion158

ellipse area D2E (4) is very similar between NT and LT (Fig. 2d, e). In contrast, the WT D2

E is159

about twice as large as NT and LT (Fig. 2f). The drifter probability distribution in both x′ and y′160

directions are similar in NT and LT (shaded curves, Fig. 2d, e). The WT simulation probability161

distributions are significantly wider (Fig. 2f) consistent with the larger D2E . Results are similar162

for the 50-m isobath release.163

Time series of bulk ellipse area D2E(t) (4) and bulk diffusivity KE(t) (5) further quantify the164

dispersion differences between WT, NT and LT for 30-m and 50-m isobath releases (Fig. 3).165

For t < 10 h, drifters occupy less than 3 km2 (Fig. 3a–b), with rapidly increasing KE (Fig. 3c–166

d) for both 30-m and 50-m isobath releases in all simulations. For longer times (t > 10 h),167

D2E and KE continue increasing but without a clear indication of reaching a diffusive limit of168

constant KE . Over the 48 h, NT and LT D2E and KE are similar while WT D2

E and KE are a169

factor 2–3× larger than NT and LT for both 30-m and 50-m releases (Fig. 3). The similarity170

between LT and NT horizontal dispersion statistics indicates that at this location barotropic tides171

only induce a weak increase in horizontal dispersion relative to the horizontal stirring in NT. In172

contrast, baroclinic tides induce a 2–3× increase in horizontal dispersion statistics.173

3.2. Vertical drifter dispersion



Increased horizontal dispersion in WT relative to NT and LT is also mirrored in the vertical174

drifter dispersion. At t = 24 h the NT and LT vertical drifter distributions are similar (green175

and red lines, Fig. 4a) having dispersed from their near-surface release (−3 ≤ z ≤ −1 m) down176

to about z = −12 m, with no drifters below z = −15 m. In contrast, the WT simulation has a177

smaller near-surface drifter fraction relative to NT and LT with substantial drifter fraction below178

z = −15 m (black line, Fig. 4a). After 48 h, drifter dispersionD2zz is about 50 m2 in NT and LT,179

whereas WTD2zz is 4 times larger than NT and LT (Fig. 4b). For WT, the vertical diffusivity Kz180

is fairly constant over the 48 h (Fig. 4c), implying diffusive vertical drifter dispersal. The NT181

and LT Kz are similar, initially increasing and becoming approximately constant for t > 30 h182

(Fig. 4c), suggesting that barotropic tides do not have a large effect on the vertical dispersion of183

near-surface released drifters. For t < 24 h, the WT Kz is factor 5–10× larger than the LT and184

NT Kz. For longer times (t > 40 h), the WT Kz is a factor of 2–2.5× larger than LT and NT.185

Thus, baroclinic tides in this region also significantly increase drifter vertical dispersion.186

3.3. Eulerian profiles

Root-mean-square (rms) Eulerian profiles of horizontal speed (V = (u2 + v2)1/2), shear187

(S = ((∂zu)2 + (∂zv)2)1/2), vertical velocity w, and model vertical eddy diffusivity KV (Fig. 5)188

are examined to understand differences between WT, NT and LT horizontal and vertical drifter189

dispersion. Here, the rms is taken through both time (5 day period, 01–06 July) and space (20 km190

following the 30-m isobath) and includes both tidal and subtidal time-scales. The vertical pro-191

files of rms(V ) (Fig. 5a) and rms (S) (Fig. 5b) are not significantly affected by the presence192

of BT or BC tides. This suggests that the increased WT horizontal dispersion is not due to193

horizontal stirring processes. In all three simulations, model rms(KV ) are generally similar in194



the upper 10-m (Fig. 5c) as wind-driven processes dominate near-surface mixing [e.g., Allen195

et al., 1995; Austin and Lentz, 2002; Wijesekera et al., 2003], and are not significantly modified196

by BT or BC tides [Suanda et al., 2017]. This 10-m thick surface layer roughly corresponds to197

the depth reached by NT and LT drifters after 24 hours (Fig. 4a). Note, that in this upper layer198

the rms(KV ) are dominated by the time mean. Below z = −10 m, WT rms(KV ) is larger than199

NT or LT due to dissipating BC tides [Suanda et al., 2017]. Throughout the water column, WT200

rms(w) is significantly (4–5×) larger than in the NT and LT simulations (Fig. 5d). The WT201

rms(w) vertical profile has mid-water column maximum, similar to the expected structure of a202

mode-1 baroclinic tide. The additional vertical stirring provided by WT rms(w) together with203

the sub-surface enhanced WT rms(KV ) induces increased vertical drifter dispersion relative to204

NT and LT (Fig. 4).205

4. Discussion

4.1. Shear dispersion due to coastal baroclinic tides

Horizontal dispersion in the NT and LT simulations is presumably due to horizontal stirring206

by coastal eddies on length-scales spanning 1–10 km (Fig. 2). As the WT, LT, and NT simula-207

tions all have similar rms horizontal velocities (Fig. 5a), the horizontal stirring is likely similar208

and cannot explain the enhanced D2E and KE in WT. In WT, increased vertical mixing by baro-209

clinic tides potentially induces additional horizontal dispersion through shear dispersion [e.g.,210

Young et al., 1982; Steinbuck et al., 2011]. Classic vertical shear dispersion [e.g., Taylor, 1953],211

an asymptotic state with vertically-uniform drifter distribution (i .e., strong mixing), has hori-212

zontal diffusivity inversely proportional to the vertical diffusivity, contrary to the results here.213



However, shear dispersion in an unbounded fluid [Saffman, 1962] or with weak mixing [Young214

et al., 1982], KE increases with Kz.215

For the 30-m isobath release, the near-surface released WT drifters are concentrated in the216

upper-half of the water column (Fig. 4a) and D2zz < h2 over 48 h (Fig. 4b), indicating no217

influence of the lower boundary. Furthermore, Young et al. [1982] introduce a non-dimensional218

parameter k∗ = Kzm2/ω to distinguish strong (k∗ � 1) and weak (k∗ � 1) mixing regimes,219

where m and ω are the vertical wavenumber and frequency of oscillatory shear, respectively.220

Applied to the WT simulation at the 30-m isobath, the t = 48 h WT vertical diffusivity is221

Kz = 4.7× 10−4 m2 s−1 (Section 3.2) and a mode-1 semi-diurnal (12.42 h period) internal tide222

hasm = π/h = 0.1 rad/m and ω = 1.4×10−4 rad/s. This yields k∗ = 0.03, indicating a weak223

mixing regime where horizontal dispersion increases with vertical dispersion. This is consistent224

with the larger horizontal and vertical dispersion in the WT simulation relative to NT and LT.225

4.2. Horizontal dispersion with 2D surface tracking

Three-dimensional (3D) drifter evolution is not necessarily important for all coastal tracers.226

For example, planning for search-and-rescue or oil-spill response applications require knowl-227

edge of surface-following (2D) horizontal relative dispersion statistics over time. This raises the228

question of whether including BT and BC tides is similarly important to accurately represent the229

horizontal dispersion of surface-following material. Here, the z = −1 m near-surface released230

drifters are advected only in the horizontal, thus maintaining a constant z-level as a surface231

drifter. Lagrangian statistics from 2D-advection are denoted WT2D, and are not affected by232

shear dispersion. The full 3D tracking with mixing (Section 3) for z = −1 m eleased drifters is233

denoted WT3D, with a similar distinction for NT and LT simulations.234



The horizontalD2E andKE in WT2D is about eight times smaller than the WT3D tracking after235

48 h (Fig. 6a). Both NT and LT 2D KE values are smaller than their 3D counterparts (dashed236

curves in Fig. 6a compared to solid curves Fig. 3a), reinforcing the connection between vertical237

motion and increased horizontal drifter dispersion. Furthermore, the KE for WT2D, NT2D,238

and LT2D are similar, indicating that including BT or BC tides does not significantly alter 2D239

horizontal relative dispersion statistics within realistic coastal simulations. Thus in this region,240

BC and BT tides can be neglected in operational models used for planning oil-spill plume241

sizes [e.g., Thyng and Hetland, 2017; Macfadyen et al., 2011] or other applications that require242

surface-following horizontal relative dispersion statistics.243

In practice, specific search-and-rescue or oil-spill response missions require actual drifter244

trajectories, not relative dispersion statistics. To quantify the difference in individual drifter245

trajectories between WT2D and NT2D, an ensemble separation statistic s̄(WN) is defined as246

s̄(WN)(t) =⟨[(∆x(WN)(t))2 + (∆y(WN)(t))2]1/2

⟩, (7)

where ∆x(WN)(t) and ∆y(WN)(t) are the time-dependent East-West and North-South separations247

from individual release locations between the WT2D and NT2D simulations, respectively, and248

the ensemble average 〈·〉 is over all drifter trajectories and releases. The ensemble LT2D and249

NT2D separation s̄(LN) is similarly defined as in (7).250

The WT2D and NT2D ensemble separation s̄(WN) grows with time, with values of s̄(WN) =251

4 km at t = 24 h and s̄(WN) = 10 km at t = 48 h (Fig. 6b). The magnitude of s̄(WN) is252

significantly greater than the WT2D relative horizontal dispersion DE (Fig. 6a). Although253

the bulk relative dispersion is similar betwen WT2D and NT2D, individual particle trajectories254

are substantially different and reflect the importance of BC tides. In contrast, the ensemble255



separation s̄(LN) is much smaller than s̄(WN), reaching only s̄(LN) = 2 km at t = 48 h, and is256

comparable in magnitude to the LT2D relative horizontal dispersion DE (Fig. 6a). As BT tidal257

currents are relatively small and predictable on the Central Californian coast [Rosenfeld et al.,258

2009; Buijsman et al., 2011; Suanda et al., 2017], adding BT tides to models will result in a259

small decrease in drifter trajectory uncertainty. For a model with BC tides, trajectory uncertainty260

can increase if the BC tide amplitude and phase is incorrect. This region has strong BC tides261

from multiple sources [Kumar et al., 2017; Buijsman et al., 2011] with BC tidal phasing that262

is difficult to predict [Nash et al., 2012] due to background stratification changes and coastal263

eddies. Thus, BC tides in an model must be well validated to be used for operational missions.264

5. Summary

The effects of BT and BC tides on coastal drifter dispersion are examined with realistic high-265

resolution Central Californian shelf simulations. For 3D tracked drifters over 48 h, the hori-266

zontal relative dispersion and vertical dispersion are similar between simulations with no tides267

and with BT tides. In contrast, BC tides induce a factor 2–3 times larger horizontal dispersion268

and a factor 2 times larger vertical dispersion through increased vertical velocities and sub-269

surface model vertical diffusivity. The increase in horizontal dispersion with vertical mixing is270

qualitatively consistent with weak-mixing shear dispersion. For surface-following (2D) drifters,271

horizontal relative dispersion is similar in the WT, LT, and NT simulations, and much weaker272

than the horizontal dispersion in WT with 3D-tracking. In contrast, after 48 h drifter trajectory273

differences between simulations with no tides and BC tides are 10 km, much larger than hori-274

zontal relative dispersion estimates from an individual model. This suggests the importance of275

BC tides for search-and-rescue or oil-spill response operations. However, these results results276



apply to the Central Californian continental shelf region and requires accurate BC tide predic-277

tions. Other regions have different relative strengths of BC and BT tides, which will affect their278

relative importance on coastal dispersion with both 3D-tracking and 2D-tracking.279

Acknowledgments. We gratefully acknowledge support from the Office of Naval Research280

award N00014-15-1-260. S.H.S. acknowledges National Science Foundation support through281

OCE-1521653. We thank Arthur Miller, Emanuele DiLorenzo, Kevin Haas, Donghua Cai,282

and Chris Edwards for their support in the modeling effort. Many helpful conversations with283

colleagues from the ONR Inner-Shelf Departmental Research Initiative are also appreciated.284

In accordance with AGU policy, model results are available through ftp site at the Integra-285

tive Oceanography Division of Scripps Institution of Oceanography, ftp://ftp.iod.ucsd.edu/falk/.286

Please email [email protected] for further details.287

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Figure 1. (a) Continental shelf model domain. Bathymetry is contoured in white curves in 10 m

increments with the 100 m isobath highlighted by the black and white curve. Black dots denote release

locations of near-surface drifters along the 30- and 50-m isobaths. (b) Schematic of a portion of the

drifter release pattern expanded from black square in panel a. The dashed line is the release isobath and

each black dot is the release location at three vertical levels (z = −1,−2,−3 m). (c) Regional model

winds and (d) modeled sea surface elevation versus time. In (c) and (d), vertical line colors indicate

drifter release times (separated by 6 hours) between 07/01 (dark blue) to 07/06 (dark red).



Figure 2. Top (a - c): Snapshot of all (n = 21) 30-m isobath drifter releases versus latitude and

longitude at t = 30 hours after release in the (a) NT, (b) LT, and (c) WT simulations. Colors indicate

release times (see Figure 1c, d). Each release center of mass is denoted by white circles. Black curve

is the 100 m isobath and drifter release locations are marked by the white strip in panel (a). Bottom

(d - f): Snapshot of all 30-m isobath drifter releases in the principal axes coordinate system (x′, y′) at

t = 30 hours after release. The white ellipses indicate the horizontal dispersion ellipse with area D2E

(4). Dark shaded curves are the normalized probability distribution functions along each axes.



Figure 3. Top (a, b): Horizontal relative dispersion ellipse area D2E (Eq. 4) and bottom (c, d):

horizontal diffusivity KE (Eq. 5) versus time after release t for the (a, c) 50-m and (b, d) 30-m isobath

releases. The WT, LT, NT simulations are indicated in legend (panel a).



Figure 4. (a) Vertical drifter location probability distribution function at t = 24 hours after release

from the 30-m isobath. The initial release locations at z = −1,−2,−3 m are indicated by dashed cyan

lines and reach fractional value of 0.33. (b) Vertical drifter dispersion D2z and (c) one-half its time

derivative analogous to Eq. 5, versus time after drifter release. The WT, LT, NT simulation line colors

are indicated in legend (panel a).



Figure 5. Vertical profiles of 30-m isobath root-mean-square (rms) Eulerian quantities: (a) rms

horizontal velocity (V =√u2 + v2), (b) rms shear (S =

√u2z + v2z ), (c) rms model vertical eddy

diffusivity (KV ), and (d) rms vertical velocity (w). The root-mean-square is calculated in both time

between 07/01 - 07/06 and 20 km following the 30-m isobath latitude 34.9o and 35.1oN. The bottom 2

m of the water column is masked due to tidal sea level fluctuations.



Figure 6. (a) Horizontal relative dispersion ellipse area D2E versus time after drifter release from

the z = −1 m, 50-m isobath. Two methods of drifter tracking are from the full 3D velocity field

and vertical mixing (WT3D, solid black), and the 2D surface horizontal velocity only (WT2D, NT2D

and LT2D, dashed). The WT, LT, NT simulation line colors are indicated in legend. (b) Ensemble

separations s̄(WN) (7) and s̄(LN) versus time after drifter release from the 50-m isobath for 2D tracking.


the effect of barotropic and baroclinic tides on coastal...

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