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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] )
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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).
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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.
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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).
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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).
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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.
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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.
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