OCS Study

BOEMRE 2010-031

Inner-Shelf Surface Currents and

Characteristic Flow Patterns in the

Santa Barbara Channel

Final Technical Summary

Final Study Report
OCS Study

BOEMRE 2010-031

Inner-Shelf Surface Currents and

Characteristic Flow Patterns in the

Santa Barbara Channel

Final Technical Summary

Final Study Report

Author

J. Carter Ohlmann

Principal Investigator

Associated Authors

Satoshi Mitarai

Melanie Fewings

Prepared under BOEMRE Cooperative Agreement

M05AC12301

by

J. Carter Ohlmann 

ERI/UCSB

University of California

Santa Barbara, CA 93106
Disclaimer

This report has been reviewed by the Pacific Outer Continental Shelf Region, Bureau of 

Ocean Energy Management, Regulation and Enforcement, U.S. Department of the 

Interior and approved for publication. The opinions, findings, conclusions, and 

recommendations in this report are those of the authors, and do not necessarily reflect the 

views and policies of the Bureau of Ocean Energy Management, Regulation and 

Enforcement. Mention of trade names or commercial products does not constitute an 

endorsement or recommendation for use. This report has not been edited for conformity 

with Bureau of Ocean Energy Management, Regulation and Enforcement editorial 

standards.

Availability of Report

Extra copies of the report may be obtained from:

U.S. Dept. of the Interior

Bureau of Ocean Energy Management, Regulation and Enforcement

Pacific OCS Region

770 Paseo Camarillo

Camarillo, CA 93010

Phone: 805-389-7621

Suggested Citation

The suggested citation for this report is:

Ohlmann, J.C., 2010. Inner-shelf surface currents and characteristic flow patterns in the 

Santa Barbara Channel. BOEMRE OCS Study 2010-031. Earth Research Institute, 

University of California, Santa Barbara, California. BOEMRE Cooperative Agreement

M05AC12301, 45 pages.
Table of Contents

Technical Summary i 

Study Products iv 

Executive Summary v

Task 1: 1

Lagrangian Assessment of Simulated Surface Current Dispersion in 

the Coastal Ocean

Task 2: 12

Wave-driven inner-shelf motions in Southern California

Task 3: 27

Circulation patterns over the inner-shelf of the Santa Barbara Channel
i

Technical Summary

Study Title: Relationships between Inner-Shelf Surface Currents and Large-Scale 

Characteristic Flow Patterns in the Santa Barbara Channel

Report Title: Inner-Shelf Surface Currents and Characteristic Flow Patterns in the Santa 

Barbara Channel

Contract Number: M05AC12301

Sponsoring OCS Region: Pacific

Applicable Planning Area: Central and Southern California

Fiscal Years of Project Funding: FY2005-FY2010

Completion Date of the Report: October 2010

Costs: $259,685

Cumulative Project cost: $259,685

Principal Investigator: Carter Ohlmann

Key Words: ocean circulation, surface currents, inner-shelf, model validation, wavedriven currents

Background and Objectives:

During the 1990’s and early 2000’s, the BOEMRE sponsored the Santa Barbara Channel 

– Santa Maria Basin Coastal Circulation Study (SBC-SMB CCS), a large observational 

program aimed at improving the understanding and predictability of large-scale

circulation patterns within the study region. A key result of the SBC-SMB CCS has been 

identification of the roles of local winds and a generally poleward pressure gradient in 

forcing surface currents (Auad and Hendershott 1997), and the definition of characteristic 

circulation patterns for the Channel. Patterns were initially defined as “Upwelling”, 

“Cyclonic”, “Relaxation”, “Propagating Cyclones”, “Flood East” and Flood West” 

(Harms and Winant 1998), and later reduced to “Upwelling”, “Surface Convergence” and 

“Relaxation” (Winant et al. 2003). The characteristic patterns are extremely important 

because they provide a simple model for the large-scale circulation in the SBC-SMB. 

Data used in the SBC-SMB CCS do not resolve currents inshore of the 100 m isobath. 

Thus, results of that study hold for basin scale currents, and are not necessarily indicative 

of flows over the inner-shelf.

This project seeks to expand results of the SBC-SMB CCS by focusing on ocean 

circulation over the inner shelf. Particular questions to be addressed are:

• What are the characteristic patterns of circulation over the inner-shelf? 

• How do the inner-shelf patterns relate to the basin-scale patterns reported by Winant et 

al. (2003)? 

• What are the dominant forcing mechanisms?

• How well to modeled trajectories agree with observations?
ii

Subsequent to the proposed work being funded, significant coastal ocean observing 

system infrastructure was deployed in the study region. The observational array attracted 

modeling efforts. The proposed work plan evolved to take advantage of the added 

measurements, and contribute to the modeling studies. Results of the funded work thus 

extend beyond what was proposed. In addition to the proposed statistical analysis of inner 

shelf flows, the work revisits the historical SBC-SMB CCS drifter data over the inner 

shelf in conjunction with model results, and investigates the role of wave driven flows at 

the surf zone interface. Manuscripts on each of these three topics (tasks) are in various 

stages of the publication process and comprise this final report.

Description:

The inner-shelf circulation was studied through three distinct tasks that naturally follow 

the successful SBC-SMB CCS. 

Task 1: Lagrangian Assessment of Simulated Surface Current Dispersion in the Coastal 

Ocean

Model surface current trajectories computed from ROMS, a state-of-the-art ocean 

circulation model, were validated with historical drifter trajectories. The analysis required 

defining and implementing a quantitative comparison metric specific to Lagrangian data. 

Results show that model trajectories launched over the continental shelf throughout the 

SBC generally agree with observations.

Task 2: Wave-driven inner-shelf motions in Southern California

Drifting buoys that moved onshore generally appeared to decelerate as they reached the 

surf zone. This task tests the hypothesis that observed decelerations are a result of wave 

forced undertow. An undertow model gives decelerations that agree with observations. 

Results indicate that Eulerian observations may not necessarily capture all components of 

Lagrangian flows that move passive tracers.

Task 3: Circulation patterns over the inner-shelf of the Santa Barbara 

Channel

Relationships among moored velocity observations located on the inner-shelf were 

investigated. Results indicate that circulation patterns over the inner-shelf cannot be 

mostly explained by a few coherent statistical modes or patterns, as is the case for 

currents further offshore.

Significant Results: 

Task 1: Lagrangian Assessment of Simulated Surface Current Dispersion in the Coastal 

Ocean

A metric for quantitative assessment of modeled trajectories based on the two 

dimensional Kolmogorov-Smirnov statistical test is presented. The metric is used to show 

that ROMS model trajectories launched over the continental shelf throughout the SBC 

generally agree with observations with a few exceptions in specific regions.

Task 2: Wave-driven inner-shelf motions in Southern California

Drifting buoys that move onshore generally decelerate as they reached the surf zone. It is 

shown with model results that changes in the profiles of Stokes drift and undertow flow 

with water depth can give rise to enhanced offshore directed undertow flow, relative to 
iii

shoreward directed Stokes drift, of 2 cm/s over the depth of the drifter drogue (0.5 to 1.5 

meters beneath the surface) that may explain the observed decelerations. Thus, during 

conditions of weak winds and strong wave forcing, the ability of a water parcel to cross 

the interface of the outer edge of the surf zone may have significant depth dependence.

Task 3: Circulation patterns over the inner-shelf of the Santa Barbara 

Channel

Circulation patterns over the inner-shelf of the Santa Barbara Channel cannot be mostly 

explained by a few coherent statistical modes or patterns, as is the case for currents 

further offshore. Thus, the circulation modes presented in Winant et al. (2003) are not 

necessarily applicable to the inner-shelf.
iv

Study Products

Papers:

Ohlmann, J. C. and S. Mitarai, 2010. Lagrangian assessment of simulated surface current 

dispersion in the coastal ocean, Geophys. Res. Lett., 37, L17602, 

doi:10.1029/2010GL044436.

Ohlmann, J. C., M. R. Fewings, and C. Melton, Wave-driven currents just outside the 

surf zone in Southern California, Journal of Physical Oceanography, submitted 

manuscript in review.

Presentations:

Fewings, M.R., L. Washburn and J.C. Ohlmann, 2010. Flow patterns and connectivity on 

the inner shelf near Point Conception and around the Northern Channel Islands, 

California. Presented at 2010 Ocean Sciences conference, Portland, Oregon.
v

Executive Summary

Information Needed

The Santa Barbara Channel – Santa Maria Basin Coastal Circulation Study (SBC-SMB 

CCS), a large observational program aimed at improving the understanding and 

predictability of large-scale circulation patterns, focused on observations along the 100 m 

isobath and in deeper waters. A key result of the SBC-SMB CCS has been identification 

of the roles of local winds and a generally poleward pressure gradient in forcing surface 

currents, and the definition of characteristic circulation patterns for the Channel. Patterns 

were initially defined as “Upwelling”, “Cyclonic”, “Relaxation”, “Propagating 

Cyclones”, “Flood East” and Flood West” (Harms and Winant 1998), and later reduced 

to “Upwelling”, “Surface Convergence” and “Relaxation” (Winant et al. 2003). The 

characteristic patterns are extremely important because they provide a simple model for 

the large-scale circulation in the SBC based on knowledge of currents at a few isolated 

(i.e. current meter) locations. 

SBC-SMB data are from both current meter records and drifter tracks. Current meters 

were located throughout the SBC, but at depths of 100 m or greater (Harms and Winant 

1998). Drifters were deployed at various locations and allowed to sample throughout the 

SBC. However, drifter data within ~2 km of the shore (i.e. over the inner continental 

shelf) were eliminated because they recorded relatively small velocities and might have 

even been beached (Dever et al. 1998). The ARGOS-CODE drifters used in the SBCSMB study give position data with 1 km spatial accuracy every few hours and are not 

appropriate for resolving inner-shelf flow patterns. Thus, circulation patterns defined for 

the SBC hold only for basin-scale currents, and may not be indicative of flows over the 

inner-shelf. Dever et al. (1998) ultimately report that drifters over the inner-shelf 

“exhibited behavior quite different from drifters found in the open channel”. 

Information about flows over the inner-shelf, well inshore of the 100 m isobath is needed. 

The necessary information relates to questions such as: 1) What are the characteristic 

patterns of circulation over the inner-shelf? 2) How do the inner-shelf patterns relate to 

the basin-scale patterns reported by Winant et al. (2003)? 3) What are the dominant 

forcing mechanisms?

Research Summary

Task 1: Lagrangian Assessment of Simulated Surface Current Dispersion in the Coastal 

Ocean

A purely Lagrangian assessment of dispersion from modeled surface current trajectories 

in the coastal ocean is presented. Modeled trajectories come from ROMS simulations for 

the Southern California Bight during the 1996 through 1999 period. Data are from 

surface current trajectories collected primarily in the Santa Barbara Channel with CODE 

style drifters. Distributions of particle positions from trajectories emanating from launch 

locations within 10 kilometers of the coast throughout the Santa Barbara Channel that 

advect for one through four days (Lagrangian PDFs) are evaluated descriptively and 

quantitatively. The two dimensional Kolmogorov-Smirnov (K-S) statistical test for 
vi

comparing discrete sampled data with a known probability distribution is the quantitative 

basis. In general, dispersion distributions from observations are similar to Lagrangian 

PDFs computed from modeled trajectories and the K-S statistic quantifies this 

accordingly. A few specific regions of poor model-data agreement are indicated and 

discussed. The purely Lagrangian assessment, elucidates an improved understanding of 

model performance and ocean circulation beyond that offered in a Eulerian sense, and is 

necessary when modeled trajectories are utilized for applied oceanographic and marine 

ecology problems.

Task 2: Wave-driven inner-shelf motions in Southern California

Recent observational studies show wave-driven Eulerian offshore flow just beyond the 

surf zone, referred to as undertow, can be a significant component of the net cross-shore 

transport during periods of weak winds. This study explores the wave-driven undertow at 

two locations off the Southern California coast where shoreline, shelf, wind, and wave 

characteristics differ from those in previous studies. Both Eulerian and Lagrangian data 

are considered. Drifter observations show a consistent decrease in onshore velocity of 4 -

5 cm s-1 within a few hundred meters of the surf zone. Undertow is examined as an 

explanation for the observed Lagrangian decelerations. Eulerian velocities from bottommounted current profilers in water depths near 10 m, collected during times of light 

winds, are small (< ~1 cm s-1), consistent with model predictions for weak wave forcing. 

However, model results suggest weakly forced undertow can decrease the velocity of 

shoreward-moving drifters by > 2 cm s-1 in shallower waters (< 8 m). During light wind 

conditions, undertow may even prevent onshore transport at specific depths just outside 

the surf zone. Adding predicted Stokes drift velocities to the Eulerian ADCP observations 

improves their agreement with coincident Lagrangian drifter observations.

Task 3: Circulation patterns over the inner-shelf of the Santa Barbara 

Channel

Time series of water velocity from Acoustic Doppler Current Profilers in ~15 m water 

depth and wind stress from NDBC buoys are used to describe the dominant inner-shelf 

flow patterns and their relation to local wind forcing. The velocity time series are 2-10 

years long and cover 20 sites along the mainland north and south of Point Conception and 

around the Islands. The along-shelf flow on the mainland displays subtidal fluctuations 

that are coherent across most of the sites, suggesting strong along-shelf connectivity 

during poleward flow events. The cross-shelf circulation profiles form a surprisingly 

robust pattern, with important implications for larval transport. The mean profiles at 16 of 

the 20 sites have the same curved form, with the velocity more offshore at the surface and 

bottom than in the middle of the water column. This structure is similar to cross-shelf 

flow profiles found in the Middle Atlantic Bight and explained by a simple model with 

wind stress and pressure gradient forcing (Lentz, 2008). The remaining 4 sites, near 

headlands, have stronger, surface-intensified cross-shelf flow with a linear profile. The 

spatial and temporal complexity of the inner-shelf circulation around the Islands is 

underscored by empirical orthogonal function (EOF) analysis of the depth-average flow. 

Only one EOF out of 28 available is statistically unique, and it captures only 16% of the 

variance. This indicates the inner-shelf flow at the mainland and island sites as a whole is 

not well-organized or composed of only a few simple patterns. In contrast, EOF analysis 
vii

of mid- to outer-shelf flow yielded three statistically separate EOFs representing different 

surface flow states and capturing 50% of the variance (Harms and Winant, 1998).

Conclusions

The research shows that inner-shelf flows in the study area can be highly variable 

between sites. Modeled trajectories over the shelf generally agree with observations, 

however, they differ at a few specific locations. During periods of weak winds, often the 

case along the Santa Barbara coastline, wave forcing can influence the transport of 

passive tracers through the surf-zone interface. The research has thus provided new 

information about modeled surface current trajectory skill, spatial current coherence, and 

wave-driven flows over the inner-shelf, a region not considered in the SBC-SMB CCS.
1

Task 1: 

Lagrangian Assessment of Simulated Surface Current 

Dispersion in the Coastal Ocean

Carter Ohlmann and Satoshi Mitarai

Abstract: A purely Lagrangian assessment of dispersion from modeled surface current 

trajectories in the coastal ocean is presented. Modeled trajectories come from ROMS 

simulations for the Southern California Bight during the 1996 through 1999 period. Data 

are from surface current trajectories collected primarily in the Santa Barbara Channel 

with CODE style drifters. Distributions of particle positions from trajectories emanating 

from launch locations within 10 kilometers of the coast throughout the Santa Barbara 

Channel that advect for one through four days (Lagrangian PDFs) are evaluated 

descriptively and quantitatively. The two dimensional Kolmogorov-Smirnov (K-S) 

statistical test for comparing discrete sampled data with a known probability distribution 

is the quantitative basis. In general, dispersion distributions from observations are similar 

to Lagrangian PDFs computed from modeled trajectories and the K-S statistic quantifies 

this accordingly. A few specific regions of poor model-data agreement are indicated and 

discussed. The purely Lagrangian assessment, elucidates an improved understanding of 

model performance and ocean circulation beyond that offered in a Eulerian sense, and is 

necessary when modeled trajectories are utilized for applied oceanographic and marine 

ecology problems.

1. Introduction

Regional coastal ocean observing systems exist in part to provide stakeholders with the 

best possible information for addressing a wide variety of applied coastal problems. 

Many applications are inherently Lagrangian, requiring trajectories to determine the “fate 

and transport” or “connectivity” of tracers. For example, coastal water quality 

management, ecosystem management, spill remediation, and search-and-rescue 

operations all require knowledge of dispersion from water parcel trajectories. 

Lagrangian applications in the turbulent ocean require statistical approaches, and thus a 

large number of observations. Probability distributions of water parcel location as a 

function of initial position and advection time (hereafter “Lagrangian PDFs”) are the 

required quantities. Direct observations with water following drifters are too sparse for 

computation of meaningful Lagrangian PDFs for more than a few combinations of initial 

position and advection time. Trajectories computed from numerical circulation models 

must therefore be relied on. In a recent study, Mitarai et al. [2009] determine Lagrangian 

PDFs with millions of trajectories computed from the Eulerian output of the Dong and 

McWilliams [2007] Southern California Regional Ocean Modeling System (ROMS) 

simulations. Results of Mitarai et al. [2009] are a part of the planning process for 

designation of Marine Protected Areas in Southern California. 
2

Southern California ROMS simulations, the basis of the Mitarai et al. [2009] Lagrangian 

PDFs, compare favorably with observations in a Eulerian sense [Dong et al., 2009]. 

Comparisons show agreement in the first two statistical moments and lead Dong et al.

[2009] to conclude, “The model results resemble the observations in terms of the spatial 

structure and magnitude of the mean, interannual, seasonal, and intraseasonal variations”. 

Eulerian agreement is not necessarily indicative of accuracy in trajectories, dispersion, or 

Lagrangian PDFs. Various Eulerian flow patterns can yield similar low order statistical 

moments, relatively small errors in Eulerian velocity statistics can become substantial 

when integrated and eddy structures can manifest themselves differently in Eulerian and 

Lagrangian frames [Ohlmann and Niiler, 2005]. 

This paper uses in situ drifting buoy data to assess dispersion distributions from modeled 

trajectories in a purely Lagrangian sense. Such an assessment is necessary prior to using 

modeled trajectories and their derived products in applied problems. The analysis gives a 

spatially continuous distribution of model skill that can elucidate an improved 

understanding of both model performance and ocean circulation beyond that offered in a 

Eulerian assessment. Limited densities of Lagrangian observations typically preclude 

such studies. 

2. Data and Methods

2.1 ROMS Derived Trajectories

Results from the Southern California Bight ROMS simulations (SCB-ROMS), described 

in detail by Dong and McWilliams [2007] and Dong et al. [2009], are the basis for 

modeled trajectories. SCB-ROMS is a primitive equation hydrodynamic model with a 

free sea-surface, a horizontal curvilinear coordinate system, and a vertical sigma 

coordinate system [Shchepetkin and McWilliams, 2005]. The innermost of three nested 

grids has 1.0 km horizontal grid resolution. Model solutions are available for the 1996 

through 2003 period.

Particle trajectories are computed from Eulerian velocity fields at 1 m depth using fourth 

order Adams-Bashford-Moulton predictor-corrector scheme with no sub-grid scale 

energy (hereafter “modeled trajectories”). The two-dimensional (2-D) velocity fields at 1 

m are used for consistency with drifter observations. The 2-D modeled trajectories differ 

from the fully three-dimensional (3-D) trajectories described in Mitarai et al. [2009]. 

Fixed-depth tracking can lead to “beaching” compared with 3-D flows (particles that 

reach the shore in the surface layer continue their motion vertically in 3-D to satisfy 

continuity). Pathways of modeled trajectories are thus terminated when reaching a 

shoreline boundary just as in situ drifter observations terminate when they run ashore, or 

“beach”. 

Launch locations (located within 10 km of the coast), the scheme for launching modeled 

trajectories, and computation of Lagrangian PDFs from positions along surface current 

trajectories after some integration time, are all described in detail by Mitarai et al.

[2009]. Lagrangian PDFs are computed for 1, 2, 3, and 4 day advection times allowing 
3

trajectories to terminate through beaching. Nearly 200,000 trajectories launched from 

1996 through 1999 and weighted by month and year to agree with the temporal 

distribution of observed trajectories (described below) are the basis of the Lagrangian 

PDF calculations.

2.2 Drifter Data

Two of the densest in-situ drifter studies performed to date are attributable to the United 

States Bureau of Ocean Energy Management, Regulation and Enforcement [BOEMRE; 

e.g. Winant et al., 1999; Winant et al., 2003; Ohlmann and Niiler, 2005]. Drifter data 

used here are a subset of those collected from May 1993 through November 1999 in the 

Santa Barbara Channel (SBC) and Santa Maria Basin (SMB) as part of the BOEMRE 

funded Santa Barbara Channel – Santa Maria Basin Coastal Circulation Study. Drifter 

design, deployment scheme, and resultant data, are all described in detail by Dever et al.

[1998] and Winant et al. [1999, 2003]. Only observations from 1996 through 1999, the 

time period for which ROMS solutions are available, are considered here.

CODE design drifters are drogued at nominal depth near 1 m and follow water to within 

~0.01% of the wind speed [Davis, 1985]. Up to six drifter positions per day are obtained 

via Doppler ranging with the satellite based Argos system. Position accuracy ranges from 

~100 to 1000 m. Initially, single drifters were released roughly every two months from 12 

stations located throughout the SBC [Winant et al., 1999]. A dozen deployment locations 

in the SMB were added in May 1996. Deployment frequency decreased to near quarterly 

during the 1997 through 1999 period. Drifters have a nominal sampling life near 40 

days. However, near half the drifters reportedly beached giving many short-lived tracks 

[Dever et al., 1998]. 

Since only starting and ending position data are required for this study, raw Argos 

position data are utilized. All drifter position records contained within each of the Mitarai 

et al. [2009] launch sites during the 1996 through 1999 period are first identified. For 

each individual drifter that passes through a launch site, the position record closest to the 

center time of all position records within the launch site is identified as the starting 

record. Ending positions after 1, 2, 3, and 4 days are identified by linearly interpolating 

between records. Drifter tracks without position records within +/- 8 hours of the ending 

time may have significant error in interpolated position and are thus eliminated. Drifter 

trajectories within 5 days of a previous launch are eliminated to insure independent 

observations.

2.3 Comparison Metric

The Kolmogorov-Smirnov (K-S) test is a non-parametric statistical method for 

determining if two distributions differ [Press et al., 2002]. The test is based on the 

maximum difference in cumulative distribution functions (CDFs) of the distributions. It 

uses information from individual data points, can be used with relatively small sample 

sizes (as it does not require binning), can accept analytical PDFs, and can be applied to 

empirical distributions. These features make it attractive for comparing empirical PDFs 

with a limited number of drifter observations.
4

The K-S test has long been used with oceanographic data primarily to examine the 

Gaussianity of velocity distributions [e.g. Swenson and Niiler, 1996; Bracco et al., 2000; 

LaCasce, 2005]. More recently, van Sebille et al. [2009] use the K-S test for binary 

determination of model skill with some confidence level. Lagrangian PDFs of modeled 

dispersion are not expected to be isotopic or spatially homogeneous as with Gaussian 

velocity distributions [Mitarai et al, 2009]. The focus here is on the K-S test statistic as a 

quantitative metric for assessing agreement in the spatial distribution of the ending 

positions of modeled and observed trajectories. Modeled dispersion is represented with 

analytical Lagrangian PDFs, and dispersion observations are represented as discrete 

positions. 

The K-S test is based on the idea that different distribution functions, or data sets, give 

different CDFs, and the largest absolute difference in CDF values (D) is indicative of the 

probability of disagreement. The K-S test statistic (P)

 

€

P = 2 (−1)

j−1

j=1

∞

∑ exp -2 j

2 D N

1 + 1-r

2

(0.25- 0.75 N )





















 2



















 (1)

described by Press et al. [2002] quantifies the confidence level associated with D. For 

application here, D is the maximum absolute difference between CDFs obtained from 

SCB-ROMS Lagrangian PDFs and drifter observations, N is the number of statistically 

independent drifter observations, and r is the correlation coefficient for zonal and 

meridional drifter positions determined in a least squares sense. D is determined as a 

function of launch location and advection time by considering probabilities in each of the 

four quadrants about all given drifter positions as described by Fasano and Franceschini 

[1987] and Press et al. [2002]. 

The K-S statistic is applied to cases with more than 10 independent drifter observations, a 

sufficiently large threshold for reliable use of the test statistic while allowing 

comparisons for the majority of the SBC. Histograms of 1000 random draws of various 

sample sizes between 10 and 20 agree with the analytical solution (Equation 1) when P < 

~0.2. Equation 1 degrades slightly with increasing sample size for P > ~0.2, however, the 

implication, that compared distributions are not significantly different, still holds [i.e. 

Press et al., 2002]. Dependence of the P statistic on values of N and r is discussed in 

detail by Fasano and Franceschini [1987] for N = 5 to 5000.

3. Results 

A comparison of model Lagrangian PDFs and drifter observations is first indicated for a 

single arbitrarily selected launch site and four advection times to demonstrate the P value 

computation. Thirty in situ drifters emanate from the launch site during the model 

integration time. Positions of 17 independent drifters after 1, 2, 3, and 4 days of sampling 

are shown with corresponding Lagrangian PDFs (computed from positions of modeled 

trajectories weighted for temporal agreement with observations) in Figure 1 Lagrangian 

PDFs suggest primarily northwest movement towards the center of the SB Channel, and 

equator-ward movement around the east side of Santa Cruz Island. The PDFs show 
5

spread throughout almost the entire SBC after 3 days, with the largest densities nearest 

the deployment location (Figure 1c). 

The distribution of drifter positions after each of the four integration times is 

quantitatively compared with the corresponding model derived Lagrangian PDF through 

the P value (Equation 1). For each in situ drifter position (considering a specific 

integration time) the sample space is divided into four quadrants about that position as 

illustrated by dashed lines in Figure 1d. CDFs are then computed for each quadrant from 

the model Lagrangian PDF and drifter data as the integral of the modeled PDF and the 

relative number of drifter positions, respectively. D is computed as the maximum 

difference in model and observed CDFs considering the four sets (quadrants), and 

quantitative agreement between distributions is determined with P (Equation 1). 

In situ drifter positions always exist where the model derived Lagrangian PDFs are nonzero for the advection times considered. Drifter positions after 1, 2, and 4 days show 

good qualitative agreement with Lagrangian PDFs, and P ≥ 0.08 for these times (Figure 

1a,b,d). After 3 days, the Lagrangian PDF has a pronounced southward extension that is 

matched by only a single drifter (Figure 1c). This discrepancy gives rise to a larger 

maximum difference in CDFs, and thus a much smaller P value (P = 0.02). These 

qualitative relationships for various values of P aid interpretation of the quantitative

statistic.

Comparisons of modeled and observed dispersion distributions for six release sites and a 

2 day advection time show qualitative relationships for a larger range of P values. For the 

launch site near Point Conception, both modeled and in situ distributions indicate similar 

movement mostly to the south with relatively large energy and this agreement is 

quantified with P = 0.14 (Figure 2a). Both modeled and observed trajectories that 

emanate from the north shore of San Miguel island are most likely to be transported 

either along the coast of Santa Rosa Island, toward the center of the SBC or equatorward 

around the east side of the island, and again the good agreement is quantified with a large 

P (0.77; Figure 2d).

Release sites with poor qualitative agreement have P values much less than the statistical 

threshold at the 95% confidence level. The majority of drifters released from the 

northwest tip of Santa Cruz Island end up to the northeast of the launch location after 2 

days (Figure 2e). The PDF from modeled trajectories that emanate from this site has its 

greatest weighting directly south of the launch location where less than 20% of the 

drifters go (P = 0.03). Southward movement in model trajectories also differs from 

northeastward in situ drifter movement for the launch site on the north coast of Santa 

Cruz Island (P = 0.02; Figure 2f). 

The cases shown in Figure 2 demonstrate major directional differences in observed and 

modeled trajectories when P ≤ 0.05. Qualitatively good agreement exists in Figures 1 and 

2 when P > 0.05. The spatial distribution of low P values, where modeled trajectories 

terminate in very different locations than observed, is relevant to the quest for improved 

model skill.
6

P values are computed for all defined launch sites and 1–4 day advection where > 10 

independent drifter observations emanate, and all trajectories have ending positions 

within the ROMS domain. These constraints limit the advection times considered and 

explain why the set of launch sites resolved varies with advection time (Figure 3). The 

majority of launch site and advection time combinations considered give P > 0.05 

indicating good agreement between ending distributions of modeled and observed 

trajectories. However, regions of poor agreement (P ≤ 0.05) exist for launch sites in the 

northwest SBC for the 1-day advection time, and along the north coast of Santa Cruz and 

Santa Rosa Islands for all advection times (Figure 3).

Inconsistencies between simulated dispersal patterns and historical drifter data are not 

necessarily due to inaccuracies of the circulation simulations themselves. Some 

differences are expected given the 1 km resolution of ROMS, unresolved eddy energy 

known to exist [e.g. Ohlmann et al., 2007], and the small size of Channel Island gaps. 

The ROMS trajectories do not include forcing from tides. Despite the fact that tidal flows 

in the SBC are mostly rectilinear with velocities < 5 cm/s, tidal energy in flows between 

Channel Islands can be significantly larger [Munchow, 1998] and this may explain low P

values for launch locations near island gaps. The region of disagreement in the northwest 

SBC (Figure 3a) is characterized by large wind stress gradients that may not be 

adequately resolved in the ROMS simulations [e.g. Dong et al., 2009]. The K-S test 

presented here allows the skill of future ROMS configurations (i.e. with tides and/or finer 

spatial resolution) to be quantitatively evaluated for most of the coastal domain in the 

SBC. 

4. Conclusions and Summary

A purely Lagrangian validation of ROMS coastal dispersal simulations in the SBC region 

is presented. The Lagrangian assessment, believed to be the first of its kind, is a 

necessary step in understanding model skill and offers insight into model performance 

beyond traditional Eulerian comparisons. The assessment provides both quantitative and 

qualitative information regarding interpretation of model trajectory PDFs. “Fate and 

transport” type models that utilize simulated trajectories for applied problems should 

undergo this sort of Lagrangian assessment on their way to operational use.

The K-S test statistic P derives from the maximum difference in CDFs computed from 

model-based analytical PDFs and individual observations. The K-S test is appropriate for 

this application as it can be used with relatively small sample sizes, can accept analytical 

PDFs, and can be applied to empirical distributions. In addition to interpreting P in the 

usual binary statistical sense (accepting or rejecting a null hypothesis that the 

distributions differ), a more quantitative interpretation is used. Significant directional 

differences between modeled Lagrangian PDFs and observed drifter distributions exist 

when P ≤ 0.05. Distributions show qualitatively good agreement when P > 0.05 as the 

binary statistic suggests. 

The study focuses on ROMS derived trajectories that emanate from launch sites within 

10 km of the coastline in the SBC from 1996 through 1999 and advect for up to 4 days. 
7

The spatial domain over which comparisons are performed extends far beyond the more 

traditional Eulerian approach, typically confined to locations of a few scattered moorings. 

For the cases considered, ROMS-derived PDFs and in situ drifter observations do not, in 

general, differ substantially. The assessment indicates that observed and modeled 

Lagrangian distributions show consistently (among advection times) poor agreement in 

regions along the north coasts of Santa Cruz and Santa Rosa Islands, likely due to strong 

tidal flows through island gaps not resolved in simulations. Poor agreement in the 

northwest SBC for 1-day advection suggests a local, short-time mechanism. The K-S 

metric presented here enables a quantifiable Lagrangian skill assessment of future model 

configurations that attempt improved simulations.
8

References:

Bracco, A., J.H. LaCasce, and A. Provenzale (2000), Velocity PDFs for oceanic floats, J. 

Phys. Oceanogr., 30, 461–474. 

Davis, R.E. (1985), Drifter observations of coastal surface currents during CODE: The 

method and descriptive view, J. Geophys. Res., 90, 4741-4755.

Dever, E.P., M.C. Hendershott, and C.D. Winant (1998), Statistical aspects of surface 

drifter observations of circulation in the Santa Barbara Channel, J. Geophys. Res., 103, 

24,781–24,797.

Dong, C.M., and J.C. McWilliams (2007), A numerical study of island wakes in the 

Southern California Bight, Cont. Shelf Res., 27(9), 1233–1248, doi: 

10.1016/j.csr.2007.01.016.

Dong, C.M., E.Y. Idica, and J.C. McWilliams (2009), Circulation and Multiple-scale 

Variability in the Southern California Bight, Prog. Oceanogr., 82(3), 168-190, doi: 

10.1016/j.pocean.2009.07.005.

Fasano, G., and A. Franceschini (1987), A multidimensional of the Kolmogorov-Smirnov 

test, Monthly Notices Royal Astronomy Society, 225, 155-170.

LaCasce, J.H. (2005). On the Eulerian and Lagrangian velocity distributions in the North 

Atlantic. J. Phys. Oceanogr., 35(12), 2327–2336, doi: 10.1175/JPO2833.1.

Mitarai, S., D.A. Siegel, J.R. Watson, C. Dong and J.C. McWilliams (2009), Quantifying 

Connectivity in the Coastal Ocean, J. Geophys. Res., 114, C10026, doi:

10.1029/2008JC005166.

Munchow, A. (1998), Tidal currents in a topographically complex channel, Cont. Shelf 

Res., 18, 561-584.

Ohlmann, J.C., and P.P. Niiler (2005), Circulation over the continental shelf in the 

northern Gulf of Mexico, Prog. Oceanogr., 64, 45-81, doi: 

10.1016/j.pocean.2005.02.001.

Ohlmann, J.C., P.F. White, L. Washburn, E. Terrill, B. Emery, and M. Otero (2007), 

Interpretation of coastal HF radar derived surface currents with high resolution drifter 

data, J. Atmos. Oceanic Technol., 24, 666–680, doi: 10.1175/JTECH1998.1.

Peacock, J.A., (1983), Two-dimensional goodness-of-fit testing in astronomy, Monthly 

Notices Royal Astronomy Society, 202, 615-627.

Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, (2002), Numerical 

Recipes in C: The Art of Scientific Computing, Cambridge University Press.

Shchepetkin, A.F., and J.C. McWilliams (2005), The regional oceanic modeling system 

(ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic 

model, Ocean Modelling, 9(4), 347–404, doi: 10.1016/j.ocemod.2004.08.002.

Swenson, M.S., and P.P. Niiler (1996), Statistical analysis of the surface circulation of 

the California Current, J. Geophys. Res., 101, 22,631–22,645.

van Sebille, E., P.J. van Leeuwen, A. Biastoch, C.N. Barron, and W.P.M. de Ruijter 

(2009), Lagrangian validation of numerical drifter trajectories using drifting buoys: 

Application to the Agulhas system, Ocean Modelling, 29, 269-276, doi: 

10.1016/j.ocemod.2009.05.005.

Winant, C.D., D.J. Alden, E.P. Dever, K.A. Edwards, and M.C. Hendershott (1999), 

Near-surface trajectories off central and southern California, J. Geophys. Res., 104, 

15,713–15,726.

Winant, C.D., E.P. Dever, and M.C. Hendershott (2003), Characteristic patterns of shelf 

circulation at the boundary between central and southern California, J. Geophys. Res., 

108(2), 3021, doi:10.1029/2001JC001302.
9

Figure 1. Lagrangian PDFs (color contours) from model output and locations of 17 

surface drifters (blue dots) considering trajectories that emanate from a single launch site 

(white circle) for advection times of a) 1 day, b) 2 days, c) 3 days and d) 4 days. P values 

for the various advection times are a) 0.11, b) 0.12, c) 0.02 and d) 0.08. Dashed black 

lines in panel d, used to explain calculation of P, are discussed in the text. PDF units are 

km-2.
10

Figure 2. As in Figure 1 for selected launch sites (white circles) and an advection time 

of 2 days. P values for the various launch sites are a) 0.14, b) 0.05, c) 0.55, d) 0.77, e) 

0.03 and f) 0.02. Sample size (n) for each comparison ranges from 13 to 16 and is 

indicated in the upper right of each panel.
11

Figure 3. P values (colors) quantifying agreement between modeled and observed 

distributions of positions along trajectories for various coastal launch sites (locations of 

colored circles) and advection times of a) 1 day, b) 2 days, c) 3 days, and d) 4 days. Only 

cases with > 10 statistically independent drifter observations, and trajectories (observed 

and modeled) that remain within the model domain, are considered. Red sites (P > 0.05) 

indicate locations where observations are not distinctly unrepresentative of samples from 

corresponding model PDFs, at the 95% confidence level.
12

Task 2:

Wave-driven inner-shelf motions in Southern California 

Carter Ohlmann and Melanie Fewings

1. Introduction

When surface gravity wave propagation is viewed in a reference frame rotating with the 

Earth, the Coriolis force destroys the exact quadrature between horizontal and vertical 

wave orbital velocities. This leads, in the wave-averaged momentum equation, to a 

Reynolds stress with vertical shear (Hasselmann, 1970). For a linear, steady state model 

with negligible turbulent mixing, the wave-driven shear stress generates (for an alongshore uniform domain) a mean Eulerian current that is exactly equal and opposite to the 

Stokes (1847) drift flow. 

Observational studies of wave driven flow just seaward of the surf zone, referred to as 

undertow, are only recently appearing. Lentz et al. (2008) analyze moored profile data 

collected off the Massachusetts and North Carolina coasts, and find wave driven 

undertow to be the dominant component of the depth averaged cross-shelf flow (see also 

Fewings et al. 2008 for the combined effects of waves and wind). Both observed and 

modeled profiles have maximum velocities near the surface that decrease with depth. The 

shape differs from parabolic undertow profiles found in the surf zone where turbulent 

mixing is not negligible (e.g. Reniers et al. 2004). Kirincich et al. (2009) similarly 

investigate the wave driven undertow off the Oregon coast, characterized by a steep 

narrow shelf and a jagged coastline that contrast the Lentz et al. (2008) study site. 

Although the wave-driven flows observed off Oregon are similar to the Lentz et al. 

(2008) observations and model results, Kirincich et al. (2009) conclude that wave driven 

cross-shore processes off the Oregon coast are not significant when compared with local 

Ekman dynamics. 

This study explores the wave driven undertow off the Southern California coast where 

shoreline, shelf, wind, and wave characteristics differ from those in the aforementioned 

studies. Santa Barbara lies almost directly east of Point Conception along a south-facing 

coastline such that direct effects of prevailing northwest winds and large swells from the 

North Pacific are limited (e.g. Brink and Muench, 1986, Winant et al. 2003). The 

northern Channel Islands are located ~40 km offshore and block nearly all swell from the 

southern hemisphere. The coastline is mostly jagged with largely sandy beaches, the shelf 

is steep and narrow, and waves are mostly short period with small amplitude. Huntington 

Beach, located between Los Angeles and San Diego, is characterized by a straight 

southwest-facing coastline and steep narrow shelf. During summer (Austral winter), HB 

receives direct impact from long-period, small-amplitude southern hemisphere swell (that 

can manifest in large breakers) and small amplitude, short-period wind waves.

Results are based on the analysis of coincidently sampled Eulerian and Lagrangian 

observations, an expansion of past studies. The Lagrangian drifter data show a consistent 

decrease in onshore velocity just outside of the surf zone. Cross-shore variations in 

undertow profiles are examined as an explanation for the observed Lagrangian 
13

decelerations. Eulerian observations from a few bottom-mounted current profilers 

provide an inconclusive picture, as the measured wave driven undertow is mostly 

extremely small (< ~1 cm s-1). However, the Lentz et al. (2008) model suggests undertow 

can significantly decrease the velocity of onshore moving drifters in the region shoreward 

of moored observations. Model results are consistent with observations at the mooring 

locations. Stokes drift, a Lagrangian phenomenon, is shown to rectify differences 

between the Eulerian and Lagrangian current observations.

2. Observations

Data are collected within ~1 km of the offshore edge of the surf zone in water depths 

ranging from ~2 to ~20 m, off the coasts of Santa Barbara and Huntington Beach, 

California (Figure 1; the study sites are subsequently refered to as “SB” and “HB”, 

respectively). Eulerian velocity profiles and surface wave information are from bottom 

mounted upward looking acoustic Doppler current profilers (ADCPs) manufactured by 

RD Instruments (San Diego, CA). Santa Barbara data are from a single 600 kHz ADCP 

located ~0.5 km from the shoreline in a water depth of ~10 m that sampled from 18 

November 2007 through 17 November 2008 (recovered quarterly to obtain data, and 

redeployed, resulting in a few missing days of data). Current vectors from the ADCP are 

averaged within 0.35 m bins every 4 minutes. 

Huntington Beach velocity profiles are sampled as part of the HB06 experiment (e.g. 

Spydell et al. 2010) at four cross-shore locations in water depths of ~8 (2000 kHz), ~10 

(1200 kHz), ~14 (600 kHz), and ~18 m (600 kHz) located ~0.6, ~1, ~2, and ~3 km from 

the shoreline, respectively. The mooring locations are subsequently referred to as “MG”, 

“MF”, “ME”, and “MD”, respectively. ADCP data at MG fail to adequately resolve the 

upper ~3 m of the water column, and are thus neglected. Average profiles are created in 1 

m bins every 6 minutes with 600 kHz data, and for 0.5 m bins every 3 minutes with the 

1200 kHz data. Data at MF and MD exist from July through October 2006, and data at 

ME extend from late September through October 2006. Significant wave height (Hsig), 

dominant wave period, and associated direction are determined with ADCP observations 

every 2 hours, through bursts of 2400 samples at a rate of 2 Hz (so surface wave 

frequencies are not aliased) and RD Instruments WavesMon v3.05 software. Huntington 

Beach wave data collected after 28 September 2006 appear suspect and are thus 

disregarded. 

ADCP data are processed with bin locations defined relative to the time-varying ocean 

surface for determination of accurate near surface velocities. Tidal components are 

removed from ADCP data using T_TIDE (Pawlowicz et al. 2002), and the de-tided data 

are low pass filtered (1/36 hr-1). Coordinate systems are defined such that the major and 

minor principal axes components of sub-tidal flow (u and v, respectively; major axis is in 

direction of greatest sub-tidal flow variance) align with the along- and cross-shore 

directions, respectively, and v is positive in the onshore direction.

Lagrangian observations are collected with Microstar drifters, drogued between ~0.5 and 

~1.5 m beneath the surface, that sample their GPS position every 10 minutes. Microstar 

drifters follow horizontal motion of water to within ~0.1% of the wind speed (~1 cm s-1
14

for 10 m s-1 winds). Details of drifter design, operation and water-following 

characteristics are given in Ohlmann et al. (2005). At Santa Barbara, 12 drifters are 

deployed roughly once each week (50 occurrences) during the ADCP sampling time. 

Considering occasional redeployments of drifters that quickly reached the surf zone, this 

gives a total of ~750 trajectories. At Huntington Beach, ~15 drifters are deployed on 15 

days from 14 September trough 11 October 2006, resulting in a total of ~275 tracks 

considering redeployments. Drifter velocities are computed as a centered difference in 

position.

Spectral wave data from National Data Buoy Center (NDBC) buoys 46216 (located ~17 

km southwest of SB) and 46230 (located ~2 km south-southwest of HB) are used to 

compute the Lagrangian Stokes velocity following

 

€

vst(z) = Hsig

2 ωk

16

cosh[2k(z + h)]

sinh2

(kh) cos(θw) (1)

where ω is wave frequency (rad s-1), k is wavenumber (rad m-1), θw is incident wave 

direction (relative to shore normal), h is water depth, and z is the vertical coordinate. 

Discussion of this formulation appears in Lentz et al. (2008) and Kirincich et al. (2009). 

The NDBC buoys measure wave energy and direction in nine continuous frequency 

bands. In Santa Barbara, vst(z) is computed with Hsig from ADCP observations, colored 

by normalized spectral energy coincidently observed at NDBC buoy 46216. Limited Hsig

data from ADCPs in Huntington Beach requires that spectral wave data observed at 

NDBC buoy 46230 be propagated from the 22 meter isobath using conservation of wave 

energy. Directional relationships are determined spectrally at both locations to properly 

isolate the cross shore component. Given the interest in drifter decelerations, vst(z) is 

computed over the 0.5 to 1.5 m depth range, and subsequently indicated as vst(1m).

Wind data are collected at the Santa Barbara airport, located ~18 km west of the Santa 

Barbara mooring, and at a moored buoy located ~2 km directly offshore of MD at 

Huntington Beach. To isolate wave driven flow, only data collected during periods of low 

winds (wind stress τ < 0.05 N m-2) are presented. This “low wind” threshold gives similar 

results, but with more data, compared with τ < 0.03 N m-2 used by Lentz et al. (2008) and 

Kirincich et al. (2009).

To further isolate surface wave forcing (the focus of this study), Eulerian observations

during low wind, large wave conditions are examined relative to the mean flow during 

low wind, small wave conditions. Small and large wave regimes are defined using Hsig

and vst(1m) criteria at SB and HB, respectively. Poorly resolved spectral wave data (due 

to the relatively distant location of buoy 46216) and little long-period swell at the Santa 

Barbara site make Hsig criteria preferable. The close proximity of spectral wave data and 

the contribution of long period swell (with little influence on vst(z)) to Hsig at Huntington 

Beach make the vst(1m) criteria preferable. Mean values of Hsig and vst(1m) for the low 
15

wind period, defined as 

€

Hsig and 

€

vst(1m), and their associated standard deviations, 

defined as σHsig and σvst, are computed at each of the sites. Mean small wave quantities 

are computed from observations at Santa Barbara (Huntington Beach) during times when 

Hsig < ( 

€

Hsig - 0.5σHsig) (vst(1m) < ( 

€

vst(1m) - 0.5σvst)), and mean large wave quantities are 

computed from observations when Hsig > ( 

€

Hsig + 0.5σHsig) (vst(1m) > ( 

€

vst(1m) + 0.5σvst)). 

The aforementioned statistics are given in Table 1. The small change in 

€

Hsig between the 

small and large wave cases at Huntington Beach (0.23 m), relative the near tripling in 

 

€

vst(1m) (0.37 to 1.02 cm s-1

), demonstrates motivation for the site specific data filters.

 

3. Results

3.1 Drifter Decelerations 

Consistent deceleration in the onshore velocity of drifters approaching the surf zone 

during low wind conditions is the most interesting observational result. For drifters 

deployed in Santa Barbara that move into waters shallower than 5 m, the onshore velocity 

component is mostly constant, between ~2 and 12 cm s-1, between the ~12 and 5 m 

isobaths (Figure 2a). Once drifters reach water shallower than ~4 or 5 m, their onshore 

velocities consistently decrease. Onshore velocities inshore of the 3 m isobath are always 

< ~5 cm s-1. The average velocity decreases from ~6 cm s-1 offshore of the 5 meter 

isobaths to ~2 cm s-1 at the 3 meter isobath, a cross shore distance of ~100 meters.

The observed deceleration at Huntington Beach occurs in deeper water, and the depth at 

which deceleration begins is more variable than in Santa Barbara. These results likely 

reflect the elevated and more variable wave energy in Huntington Beach that manifest in 

a surf zone with a deeper outer edge, and an outer edge with greater depth variability. 

For drifters deployed in Huntington Beach that move onshore of the 10 m isobath during 

low winds, the onshore velocity component varies between ~15 and 5 cm s-1 (Figure 2b). 

The average velocity gradually decreases from ~6 cm s-1 at the 12 m isobath, to < ~3 cm 

s

-1

 inshore of the 10 m isobath. Average values inshore of the 8 meter isobath are 

similarly < ~3 cm s-1, but come from a reduced number of observations collected during 

periods of a narrower surf zone. Velocities less than zero (i.e. they reverse direction and 

move offshore) routinely occur.

3.2 Wave Driven Flow

Observed mean wave driven undertow flow profiles are computed by subtracting the 

mean low wind, small wave profiles from the mean low wind, large wave profiles. The 

mean undertow in Santa Barbara is 0.7 ± 1 cm s-1 in the topmost ADCP bin considered 

(~2 m depth), and decreases somewhat linearly with depth to ~0 ± 1 cm s-1 just above the 

bottom (Figure 3a). In Huntington Beach, the mean observed undertow profile also shows 

a velocity near 0.7 ± 1cm s-1 in the topmost ADCP bin considered (~2 m), that decreases 

with depth to ~0 ± 1 cm s-1 at ~ 6 m depth and beyond (Figure 3b). 

Mean theoretical undertow profiles computed using the Lentz et al. (2008) model, forced 

with the same spectral wave data used to compute vst(z) during the low wind and large 

wave regime, are in good qualitative agreement with observations (Figure 3). In Santa 

Barbara, the mean modeled undertow velocity at 2 m is ~0.7 cm s-1, nearly the same as 
16

observed. In Huntington Beach, the modeled value is slightly larger than observed. The 

correlation coefficient (computed from linear least squares) between the depth averaged 

cross shore undertow flow from observations and the Lentz et al (2008) model is 0.67 in 

Santa Barbara. A statistically significant relationship does not exist in Huntington Beach 

where observations span a narrow range, compared with Santa Barbara. 

3.3 Eulerian and Lagrangian Velocity Comparisons

Drifter velocities and coincidently sampled 20 minute average ADCP velocities are 

compared to determine if measurement differences can be rectified by subtracting vst(1m)

from Lagrangian drifter observations. Comparisons are made with average velocity over 

the top three bins of ADCP data collected at Santa Barbara (DEPTH RANGE) and MF 

(Huntington Beach; DEPTH RANGE) when drifters are within 200 and 400 m of the 

moorings, respectively. SAY WHY DEPTH AVERAGING Beyond these distances, 

correlation coefficients decrease dramatically. Comparisons are made with 250 drifter 

velocites from 42 different days at Santa Barbara, and with 95 drifter velocites from 13 

different days at Huntington Beach. 

Root mean square (rms) velocity differences for along- and cross-shore components at 

both Santa Barbara and Huntington Beach are between 3.2 and 3.3 cm s-1 (Figure 4). 

Mean differences, however, are near 0.75 cm s-1 in the alongshore direction, but > 2.0 cm 

s

-1

 in the cross-shore direction, with drifters recording greater onshore and downcoast 

(equatorward) flow as expected. Spatial inhomogeneity, difference in sampling depth, 

and non-normal wave incidence likely explain the ~0.75 cm s-1 difference that exists in 

both velocity components. Polarity at both locations suggests drifter observations give 

vst(1m) = ~1.25 cm s-1 that is not resolved in ADCP measurements. When ADCP 

velocities are extrapolated to the drifter sampling depth, mean differences at Huntington 

Beach decrease by ~0.3 and 0.6 cm s-1 in the along- and cross-shore directions, 

respectively (mean differences at Santa Barbara are nearly unchanged). Cross-shore 

velocity differences, beyond those in the along-shore direction, are consistent with the 

magnitude of both vst(1m) and undertow velocities determined from observations, as 

described below.

The difference between the Eulerian (ADCP) and Lagrangian (drifter) velocities is a 

strong function of direction (Figure 5). Maximum differences generally align with the 

direction of vst(1m), and directions of maximum difference are almost exactly orthogonal 

to directions of 0 mean difference. At Santa Barbara, vst(1m) is primarily from southwest 

(~25 to 45°) of shore normal. Directions of maximum rms (3.61 cm s-1) and mean (2.53 

cm s-1) velocity differences are 45 and 20°, respectively. At Huntington Beach, vst(1m) is 

from a larger range of angles (~5 to 50° southwest of shore normal) that similarly aligns 

with directions of maximum rms (3.43 cm s-1 from 45°) and mean (2.13 cm s-1 from 45°) 

velocitiy differences. Mean differences at Santa Barbara and Huntington Beach decrease 

by up to ~0.50 and 0.65 cm s-1, respectively, in the expected directions, when vst(1m) is 

added to the ADCP velocities (black and grey dots in Figure 5).

4. Discussion

Observed wave forcing just outside the surf zone at Santa Barbara and Huntington Beach 

is weaker than reported by Lentz et al. (2008) and Kirincich et al. (2009) for the Oregon, 
17

Massachusetts, and North Carolina coasts (for the chosen sampling periods). Background 

(low wind and small wave) velocity profiles removed to isolate wave driven flow are 

computed by Lentz et al. (2008) and Kirincich et al. (2009) as averages during times 

when Hsig < 0.75 m and 0.70 m, respectively. The Santa Barbara observations are 

characterized by 

€

Hsig = 0.81 m during the large wave regime, and the background flow 

profile removed is computed for times of Hsig < 0.38 m (Table 1). The smaller undertow 

velocities observed at Santa Barbara are commensurate with weaker wave forcing. 

The average undertow during the low wind and small wave regime at Huntington Beach 

is greater than that during the low wind and large wave regime, when wave regime is 

defined with Hsig criteria (as for Santa Barbara). Long period southern hemisphere swell 

of varying amplitude often contributes to Hsig at Huntington Beach. Such waves are 

characterized by large phase speed, c, and undertow is proportional to c

-1

 (for constant 

Hsig/h). Thus, use of vst(1m) for defining wave regimes at Huntington Beach. Despite 

 

€

Hsig = 0.72 during the low wind and small regime (defined with vst(1m)), background 

flow removed is much smaller than in previous studies. The Lentz et al. (2008) model 

accurately represents the observed undertow for smaller Hsig than previously examined. It 

is, however, important that the correct amplitude is given for steep, short period waves 

that have the greatest contribution to vst(z), and thus undertow. While the observed 

undertow (< ~1 cm s-1) is undoubtedly small, that is the case at two discrete locations. 

Understanding the influence of wave forcing on observed drifter decelerations requires 

vst(1m) and associated undertow between 0.5 and 1.5 m depth to be considered for a 

range of h. Mean values of observed wave spectra during the large wave regime are used 

to compute vst(1m) and force the Lentz et al. (2008) model for h < ~15 m at both Santa 

Barbara and Huntington Beach using a constant sloping bottom and realistic bathymetry. 

For h > ~5 and ~6 m at Santa Barbara and Huntington Beach (considering realistic 

bathymetry), respectively, vst(1m) and its resultant undertow combine for no net crossshore wave driven flow within the 0.5 to 1.5 m depth range (Figure 6). When h shoals to 

~5 m at Santa Barbara, the undertow magnitude overcomes vst(1m), resulting in a net 

offshore velocity that increases to ~2 cm s-1 as h decreases to ~3 m. The mean observed 

onshore drifter velocity at Santa Barbara decreases by ~3 cm s-1 between h = 5 and 3 m 

(Figure 2). The velocity change is sensitive to cross-shore variations in bathymetry and to 

the location where the eddy viscosity specified in the model increases to represent the 

surf zone. The Lentz et al. (2008) model results thus suggest the transition of the wave 

driven undertow profile from a Hasselmann profile offshore to a parabolic profile near 

the surfzone can play a primary role in forcing observed drifter decelerations at Santa 

Barbara. 

At Huntington Beach, the Lentz et al. (2008) model indicates undertow magnitude 

overcomes us when h shoals to ~6 m, and the modeled deceleration is much more abrupt 

(for realistic bathymetry) than at Santa Barbara. Modeled offshore velocity at Huntington 

Beach increases from near -1 to ~2 cm s-1 as h decreases from ~6 to ~3 m (Figure 6). 

However, the mean observed onshore drifter velocity decelerates as h shoals from ~13 to 

~8 m, much deeper than the model indicates (Figure 2). Long period southern hemisphere 

swell, with relatively small amplitude, resulted in large breakers making for a surf zone 

that is much wider than the model predicts. Mean observed velocities decrease from ~10 

to ~2 cm s-1, much larger than the model shows. Transient rip currents, routinely 
18

observed at Huntington Beach, likely explain occasional flow reversals observed just 

beyond the surf zone, and perhaps contribute to decelerations (Figure 2). 

5. Conclusions and Summary

Recent studies suggest the Hasselmann (1970) wave driven undertow flow can be a 

significant part of the cross-shore momentum budget just beyond the surf zone, when 

examined in a Eulerian sense (Lentz et al. 2008, Kirincich et al. 2009). This study 

explores the undertow flow in Southern California (a region with wave, shelf, and 

shoreline characteristics that differ from those of past studies) with both Eulerian and 

Lagrangian observations. Mean observed Eulerian undertow flows for the time period 

characterized by little wind and the strongest wave forcing are < 1 cm s-1. Velocities 

reach ~2 cm s-1 near the surface during the largest wave event observed. Small undertow 

velocities reflect small wave forcing compared with past studies, and agree with 

predicted undertow magnitudes. 

Lagrangian observations give the more interesting results. The mean velocity of 

shoreward moving drifters during times of weak wind and strong wave forcing decreases 

by between 4 and 8 cm s-1 just beyond the outer edge of the surf zone at two Southern 

California locations. The Lentz et al. (2008) model suggests the depth dependent wave 

driven undertow explains ~3 cm s-1 of the observed decelerations. The increased 

undertow in the model comes from changes in the depth dependent flow that arise from 

changes in h through Hsig/h, and increased eddy viscosity approaching the surf zone. 

During periods of relatively weak net (depth integrated) onshore transport, as is often the 

case in Southern California, the wave driven undertow flow may retard, or even prevent, 

onshore flow at specific depths. The new Lagrangian observations add strength to the 

final conclusion in Lentz et al. (2008), that cross-shore transport to/from the surf zone, 

important for a variety of applied problems, is not fully understood. 
19

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260.

Spydell, M., F. Feddersen, and R.T. Guza, 2009: Observations of drifter dispersion in the 

surfzone: The effect of sheared alongshore currents. J. Geophys. Res. Oceans, 114, 

C07028, doi:10.1029/2009JC005328.

Stokes, G. G., 1847: On the theory of oscillatory waves. Trans. Cambridge Philos. Soc., 

8:441–455.

Winant, C. D., E. P. Dever, and M. C. Hendershott (2003), Characteristic patterns of shelf 

circulation at the boundary between central and southern California, J. Geophys. Res., 

108(C2), 3021, doi:10.1029/2001JC001302.
20

site low wind low wind, small waves low wind, large waves

SB 

€

Hsig = 0.54 ± 0.33 m

 

€

vst(1m)=0.45±0.28 cm s-1

n = 357 days

 

€

Hsig -sw = 0.41 ± 0.06 m

 

€

vst-sw(1m)=0.27±0.11 cm s-1

n = 105 days

 

€

Hsig -lw = 0.81 ± 0.27 m

 

€

vst-lw(1m)=0.79±0.45 cm s-1

n = 46 days

HB 

€

Hsig = 0.82 ± 0.17 m

 

€

vst(1m)=0.63±0.28 cm s-1

n = 99 days

 

€

Hsig -sw = 0.72 ± 0.17 m

 

€

vst-sw(1m)=0.37±0.09 cm s-1

n = 36 days

 

€

Hsig -lw = 0.95 ± 0.14 m

 

€

vst-lw(1m)=1.02±0.20 cm s-1

n = 26 days

Table 1. Significant wave height and undertow statistics by site (rows) during periods of 

low winds (column1), low winds and small waves (column 2), and low winds and large 

waves (column 3). Means, standard deviations and sample size (n) are indicated. 

Quantitative definitions for the 3 regimes are given in the text. Undertow values at an 

indicated depth of “1 m” are depth averaged between 0.5 and 1.5 m beneath the sea 

surface.
21

Figure 1. Mooring locations at the Santa Barbara (SB) and Huntington Beach (HB) sites, 

located along the Southern California coast. Bathymetry contours are shown at 10 and 20 

meters. Location of NDBC moorings are shown with triangles. Principle axis coordinate 

system rotations are shown.
22

Figure 2. Onshore component of drifter velocity versus water depth, during low wind 

conditions, for all drifters that move shoreward of the a) 5 meter isobath at Santa Barbara, 

and b) 10 meter isobath at Huntington Beach. Last positions recorded by drifters prior to 

recovery are indicated with grey dots. Means of onshore velocities interpolated to the 

locations of integer bathymetry values are shown with black dots and connected with 

black lines.
23

Figure 3. Mean Hasselmann (1970) flow profiles computed from ADCP data (black 

dots) collected at a) Santa Barbara and b) Huntington Beach. Grey dots indicate ± 1 

standard deviation. Thin solid line: corresponding mean profile from Lentz et al. (2008) 

model forced with observed wave characteristics during times of observations.
24

Figure 4. Coincidently sampled Eulerian and Lagrangian along-shore (a,c) and crossshore (b,d) average velocities for each drifter that sampled within 200 meters of the SB 

ADCP (a,b), and 400 meters of the HB ADCP (c,d). Solid and dotted lines give best 

(least squares) fit and 1:1 lines, respectively. Drifter drogues extend from 0.5 to 1.5 

meters depth. ADCP velocities are averages over the top 3 available bins, which extend 

from 1.9 to 2.6 and 1.8 to 2.8 m depth at the SB and HB moorings, respectively. 
25

Figure 5. Differences between coincidently sampled Eulerian and Lagrangian velocities 

(shown in Figure 4) as a function of direction with (gray dots) and without (black dots) 

adding predicted Stokes drift to the ADCP velocities. Left and right panels give data from 

SB and HB, respectively. Top and middle rows give rms and mean difference values, 

respectively. Distributions of Stokes drift directions are given in the bottom panels, with 

0° being shore-normal and negative angles indicating waves from a more up-coast 

(poleward) direction.
26

Figure 6. Sum of us and predicted undertow flow averaged over the 0.5 to 1.5 meter 

depth range for Santa Barbara (top left) and Huntington Beach (top right). Undertow 

velocity is computed with the Lentz et al. (2008) model forced with observed mean large 

wave conditions, using realistic bathymetry (black curves) and a constant sloping bottom 

(grey curves). Water depth as a function of offshore distance for Santa Barbara (left) and 

Huntington Beach (right) is shown in the bottom panels. Vertical dashed lines represent 

an estimated range for the outer edge of the surf zone.
27

Task 3:

Circulation patterns over the inner-shelf of the Santa 

Barbara Channel

Carter Ohlmann and Melanie Fewings

1. Introduction

The regional circulation in the Santa Barbara Channel (SBC), beyond the inner shelf, is 

relatively well studied. The southward-flowing California Current separates from the 

mainland near Point Conception (Checkley and Barth, 2009). Three circulation patterns, 

accounting for ~50% of the observed velocity variance in the SBC, are described by 

Winant et al. (2003). However, the circulation patterns in the central SBC are not 

necessarily indicative of the inner shelf circulation. For example, wind stress in the area 

southeast of Point Conception, in the "upwelling shadow" or lee of the bend in the 

coastline, is much weaker than further offshore, and is expected to drive different 

circulation patterns near the shore. 

Over the past 10 years, current profiles have been recorded at 21 sites in 10-18 m water 

depth along the mainland coast and at the Islands (Figure 1). These data are used to 

describe a variety of flow states that exist over the inner shelf region, that are not 

necessarily correlated to the Winant et al. (2003) SBC scale flow patterns. The moored 

observations provide a much longer time record than can be obtained with the release of 

drifting buoys as originally proposed.

2. Data 

The water velocity data were collected by the Partnership for Interdisciplinary Studies of 

Coastal Oceans (PISCO), the Santa Barbara Coastal Long-Term Ecological Research 

project (SBC- LTER) and the Channel Islands National Marine Sanctuary (CINMS) 

during 1999-2009. Water velocity was measured at 21 sites in 15-18 m water depth every 

1 m from 2.5 meters above bottom (mab) to about 3 m below the mean water surface 

using bottom-mounted acoustic Doppler current profilers (ADCPs), except at two SBCLTER sites on the mainland, CAR and MKO, where the water depths are 8 and 10 m and 

the velocity was measured every 0.5 m from 1.5 mab to 1.5 m below the surface. Water 

velocity was recorded as 2-min averages, low-pass filtered with a 1-hr moving window, 

and interpolated onto a common 20-min time base to form the ``high-frequency" data set. 

ADCP bin depths were determined based on transducer height (mab) and position of the 

signal beam intensity maximum denoting the water surface. Data from ADCP bins within 

~15% of the water depth below the surface are contaminated by side-lobe reflections and 

were discarded, based on abrupt changes in the ADCP signal percent good and the tidal 

velocity and phase profiles computed with the T\_TIDE Matlab package (Pawlowicz et 

al., 2002). Each 20-min average velocity profile in which at least 75% of the bins 

contained good data was linearly interpolated in the vertical direction to fill holes in the 

profile that are assumed to be from fish or drift kelp blocking the beams. Wind velocity 

and air pressure data are from 6 National Data Buoy Center (NDBC) buoys 
28

(http://www.ndbc.noaa.gov), 9 mainland coastal meteorological stations (mainly 

airports), and 4 island-based meteorological stations. Sea level data are from coastal tide 

gauges maintained by the National Oceanic and Atmospheric Administration 

(http://tidesandcurrents.noaa.gov) at Port San Luis, Santa Barbara, and Santa Monica.

To calculate wind stress τs, the drag law of Smith [1988] was used. To calculate depthaverage velocities, data from the top and bottom good ADCP bins were extrapolated to 

the surface and bottom of the water column assuming a constant velocity near-surface

and near-bottom, and then a trapezoidal estimate of the vertical integral was computed. In 

order to focus on time scales of days and longer, tides and other high-frequency motions 

were removed by detiding the velocities with T_TIDE [Pawlowicz et al., 2002], filling 

gaps < 24 hr in all time series by linear interpolation, and low-pass filtering with a (33 

hr)-1 half-amplitude cutoff. The low-pass-filtered velocity observations are subsequently 

referred to as subtidal flow. Velocity and wind stress at each location are transformed 

into local along-shelf/cross-shelf coordinate systems based on the principal axes of the 

low-pass filtered wind stress or depth-average flow, with the major principal axis 

defining the along-shelf direction (Figures 2 and 3). The along-shelf flow is v, positive 

west- or northward, and the cross-shelf flow is u, positive north- or eastward. The 

symbols uda, and vda are used to indicate depth-average velocity components. Alongshelf pressure differences were estimated from the coastal tide gauge data with synthetic 

subsurface pressure (SSP) constructed similarly to Harms and Winant [1998]. This 

method takes into account the effects of both sea level and atmospheric pressure in 

determining the dynamically relevant subsurface pressure in the water column. 

3. Results 

3.1. Velocity patterns at the mainland and Islands are distinct 

The mainland and the Islands have distinctly different water velocity patterns (Figure 3). 

On average, the circulation tends to be poleward along the mainland and eastward or very 

weak at the islands, though there is also strong variability in the flow on time scales of 

days. In summer, the flow is more strongly poleward (or weaker equatorward) at nearly 

all sites. North of Point Arguello at PTS and PUR, the mean flow is 0-5 cm/s, and 

weakens in summer. South of Point Arguello, except at JAL in the lee of a headland, the 

flow is stronger (0-10 cm/s) and strengthens in summer. At the Islands, the mean flow is 

generally eastward up to 12 cm/s or very weak (< 2 cm/s), with the strongest flows near 

headlands and inter-island channels. The one site with substantial westward flow is on the 

south side of Santa Cruz Island at VAL, adjacent to a deep basin (> 2000 m). There is a 

region of very weak mean flow variability on the north side of Santa Cruz Island, at PRO 

and PEL, as compared to other sites. Although the average directions of flow at the 

mainland and Islands are opposite, the entire region south of Point Conception makes an 

adjustment toward more poleward flow in summer. The summer-intensified poleward 

flow along the mainland south of Point Conception is a signature of buoyancy-driven 

coastal flows associated with relaxation of the prevailing upwelling-favorable winds 

[Cudaback et al. 2005, Melton et al. 2009]. At the Island sites, the mean flow also 

becomes more westward (or weaker eastward) in summer. 
29

Everywhere except north of Point Conception, there is a pattern of more westward flow 

in summer months. The circulation at all sites varies strongly on time scales of days. The 

variability in the along-shelf flow is generally stronger than the average flow. North of 

Point Conception, that is true in every month (only the variability over the entire year is 

shown). On the mainland south of Point Conception, the variability is stronger than the 

mean during winter but not summer. The subtidal variability along the mainland weakens 

by about half in summer (not shown) when the mean flow strengthens. At the Islands, the 

mean flow is also weaker than the variability except at sites near headlands (BAY, BEA, 

SRS). The strong variability in the flow indicates the nearshore water circulation in the 

SCB is characterized by frequent flow relaxations and reversals on time scales of days, 

rather than by a consistent direction of along-shelf flow. 

If the mean flow is in the same direction as the major principal axis, the depth-average 

cross-shelf velocity uda will be zero. The observed uda is very weak (< 1.5 cm/s in all 

months) at all sites except BEA and MKO, which are near headlands. Correspondingly, at 

sites with substantial mean flow (speed > 2 cm/s), the direction of the long-term mean 

flow vector uda is within 4 deg of the major principal axis direction except at those two 

sites near headlands (BEA, MKO; Table 1). Since the major principal axis direction will 

be along-isobath if the flow is geostrophic, this suggests the mean flow is nearly alongisobath except near headlands. 

To determine whether the circulation over the entire region can be characterized by a few 

simple patterns, we calculated the empirical orthogonal functions (EOFs) of the depthaverage along- shelf flow vda and the near-surface cross-shelf flow us (from the top good 

ADCP bin at each site). That EOF analysis yielded only one statistically separate 

circulation mode out of 32 modes (Figure 4a). That first EOF explains 24% of the overall 

subtidal velocity variance in us and vda at all sites combined, and up to 75% (64%) of the 

variance in vda (us) at particular sites (Figure 4b). Generally, the sites at which the EOF 

captures a substantial amount of variance are western sites exposed to the large-scale 

wind field and not sites in the lee of Point Conception. Because not all mainland and 

island sites had ADCP deployments that overlapped in time, all the ADCP sites cannot be 

included in a single EOF analysis. Nevertheless, the mode in Figure 4a is not sensitive to 

the choice of sites to include. A similar first EOF emerges if CAR, or BAY and BEA, 

are not included. Without BAY and BEA, it is possible to include MKO on the mainland; 

the results are similar to Figure 4, and the EOF amplitude at MKO is < 1 cm/s and 

explains none of the variance at MKO, similar to nearby sites. The only statistically 

unique EOF captures little of the flow variance in the eastern Channel. 

3.2. Vertical profiles of velocity are consistent over the region

The long-term mean along-shelf velocity profile is surface-intensified at most sites, and 

constant vertically at the others. The along-shelf velocity is generally unidirectional: the 

velocity at each depth in the water column is in the same direction as the depth-average 

flow (Figure 5). Along the mainland (at the Islands) the velocities become more poleward 

(equatorward) with height above bottom. Flow speeds are 0-6 cm/s near the bottom and 

0-10 cm/s near the surface. At mainland sites, the vertical shear in the along-shelf flow is 

strongest near the bottom and approaches zero near the surface (Figure 5, top). On the 
30

north sides of the Islands, the shear is nearly constant throughout the water column so the 

profiles are more linear (Figure 5, bottom, open symbols). In general, the shear is less 

than 0.5 (cm/s)/m. 

The variability in the subtidal along-shelf flow, as measured by its standard deviation at 

each ADCP bin depth, ranges from 1-10 cm/s and tends to be larger at sites and ADCP 

bin depths with larger mean flow speeds (r2 = 0.3 for correlation between flow speed and 

standard deviation). Seasonal variations in the along-shelf flow involve strengthening and 

weakening of the profiles in Figure 5 by a factor of about 2 or less, in accordance with 

the monthly arrows in Figure 2, without substantial changes in the profile shapes. 

Surprisingly, nearly all the time-average profiles of cross-shelf flow are very similar

(Figure 6). The profiles are C-shaped, with offshore or weak flow near the surface and 

bottom and onshore flow in the middle of the water column. The long-term mean vertical 

profiles of cross-shelf velocity are strikingly similar at 18 of the 21 sites. The cross-shelf 

velocities are weaker on the north sides of the Islands than at mainland or south Island 

sites. Generally, the cross-shelf flow is O(1 cm/s) or less at all depths except near 

headlands (BEA, which is off scale in Figure 6 left column; and MKO). The subtidal 

variability (standard deviation) in cross-shelf flow ranges from <0.5 cm/s at PEL north of 

Santa Cruz Island to 3 cm/s along the mainland. The main effect of seasonal variations is 

to strengthen and weaken the curvature of the cross-shelf flow profiles so the velocities 

vary by a factor of ~2 (not shown). 

The cross-shelf flow profiles depend somewhat on the choice of coordinate system. The 

profile shapes in Figure 6 are not artifacts of uncertainty in the ADCP compass 

directions: the C-shapes are not sensitive to rotating the coordinate system +/-5 deg. The 

cross-shelf direction can be defined as the direction that has zero depth-average flow in 

the long-term time-average sense (Figure 6, right panels) or as the minor principal axis 

direction (Figure 6 left panels, and elsewhere in this manuscript). The cross-isobath 

direction is a third option, but sufficiently detailed bathymetry is not available. The crossshelf flow profiles collapse better in the first coordinate system, as do similar profiles in 

the Middle Atlantic Bight [Lentz, 2008]. Three of the 21 sites (PUR, NAP, BEA) do not 

fit the C-shaped pattern in either coordinate system, and two (MKO, SCP) fit the pattern 

in one coordinate system but not the other. Those five sites are colored grey in Figure 6. 

Nevertheless, the C-shaped pattern is very robust. 

3.3 Response to Wind 

At western sites exposed to the prevailing equatorward winds, most of the variance in the 

flow is explained by local wind. The along-shelf flow vda and the near-surface and nearbottom cross- shelf velocities us and ub are significantly correlated with the wind stress at 

the 95% confidence level at most sites (Figures 7 and 8). At "exposed" sites in the 

western half of the study area, up to 60% of the velocity variance can be explained by 

local wind forcing alone, particularly at BAY and BEA for vda, and SRS and sites north 

of Point Conception for us and ub. 
31

The sites where the flow is strongly correlated with the buoy winds in Figures 7 and 8 are 

generally the same sites that have substantial spatial amplitudes in the EOF mode shown 

in Figure 4. The time series amplitude of that EOF mode is strongly positively correlated 

with equatorward wind stress at buoys 46053 (r2 = 0.7) and 46054 (r2 = 0.6), suggesting 

the spatial pattern of that EOF is a good representation of the spatial pattern of response 

to wind forcing. 

At sites in the lee of Point Conception in the eastern SBC, local wind explains little of the 

velocity variance (Figures 7 and 8). The water velocity at sheltered sites is generally not 

better predicted by the land-based wind stations (Figure 1) than by buoy 46053 or 46054, 

and even for sites where a land station does give a somewhat higher r2, the correlation of 

wind and flow is not strong (r2 <0.35). The circulation at sites in the lee of Point 

Conception is not well explained by local wind forcing. 

The response of the cross-shelf flow to wind has a two-layered structure. The sign of the 

correlation of us and ub with wind stress is consistent with a two-layer coastal upwelling 

and downwelling circulation at all sites: equatorward wind stress fluctuations are 

associated with south/westward near-surface flow and north/eastward near-bottom flow 

(Figure 8). For example, when the wind at buoy 46054 is upwelling-favorable, at SMS 

the near-surface flow is directed offshore, the near-bottom flow is onshore, and the two 

velocities are highly correlated in time both with the wind stress (r2 = 0.5, Figure 8) and 

with each other (r2 = 0.5, Figure 9). The time average of each two-layered response 

contributes to the corresponding C-shaped profile (Figure 6) by turning the near-surface 

flow offshore. 

3.4. Response to coastal sea-level gradient 

The lack of correlation between flow and local wind at many sheltered sites (Figures 7 

and 8) suggests nearshore flow in this region is strongly influenced by pressure gradients. 

The pressure gradients may be set up by the local topography or associated with the 

energetic mesoscale eddy field or with remotely-generated coastal-trapped waves, both of 

which influence the mid- and outer-shelf flow in the SBC [Auad and Hendershott, 1997]. 

With the exception of JAL in the lee of Point Conception, the mean flow along the 

mainland (Figure 3) opposes the large-scale wind stress (Figure 2) at all times of year, 

also indicating that local wind is not the only forcing influencing the along-shelf flow. 

Though the mean along-shelf pressure gradient is too small to observe, the poleward 

mean flow is consistent with the existence of a mean poleward pressure gradient force 

suggested in previous studies along the U.S. West Coast. 

During weak winds ((|τ|<0.05 Pa) the average cross-shelf velocity profiles are J-shaped, 

rather than the C-shaped profiles during all wind conditions (Figure 6), consistent with 

flow driven by an alongshelf pressure gradient. Sea level gradients measured along the 

mainland coast (and transformed into synthetic subsurface pressure gradients) have a 

significant effect on velocity at the mainland but not Island sites. The effect of pressure 

gradient forcing is weaker poleward flow during equatorward sea-level anomalies, and 

stronger poleward flow during poleward sea level anomalies (Figure 10). Associated 
32

with that poleward flow is enhanced offshore flow near the bottom of the water column, 

consistent with bottom Ekman layer dynamics. 

To determine the effect of the fluctuating coastal ssp gradient (∆ssp) between Port San 

Luis and Santa Monica on local flow, it is important to note that ∆ssp is itself negatively 

correlated with local wind forcing. The correlation squared of ∆ssp with poleward wind 

stress at buoy 46054 on subtidal time scales is a maximum of 0.36, for ∆ssp lagging wind 

stress by 15 hours. This indicates the observed ∆ssp fluctuations are ~35% a response to 

local wind, and not due only to mesoscale eddies or remotely-generated coastal-trapped 

waves. The effect of ∆ssp itself on the flow can be determined during weak wind forcing. 

During weak winds (|τ|<0.05 Pa), the flow along the mainland is substantially different 

depending on the sign of the ∆ssp anomaly. 

Conditionally-averaged patterns of depth-average flow for various wind and ∆ssp forcing 

states reveal several effects of wind and pressure gradient forcing. They are: 

Strong equatorward (upwelling-favorable) wind stress at buoy 46053 in the eastern 

SBC is associated with equatorward flow everywhere in the domain, even within the 

wind shadow of Point Conception. During very strong poleward ∆ssp forcing, the 

mainland flow in the wind shadow is weak but not poleward. 

Poleward (downwelling-favorable) wind stress, which occur mainly in winter, are 

associated with strongly poleward flow at mainland sites but not at the Islands. As the 

wind stress goes from equatorward to poleward the flow on the mainland changes from 

equatorward or zero flow to increasingly strong poleward flow at all sites. At the Islands, 

however, the strong equatorward flows at BAY, BEA, SRS, MOR, and SCP weaken but 

do not reverse (except weakly at SCP, and the southward component of flow at BEA does 

reverse to northward). The flow at the Islands is not strongly poleward for any 

combination of wind and ∆ssp forcing. 

Poleward pressure gradient anomalies are associated with poleward flow along the 

mainland, except during strong equatorward wind stresses, which overcome the poleward 

pgf and result in equatorward flow along the mainland. During moderate equatorward 

winds a poleward pressure gradient force is still associated with poleward flow along the 

mainland.

Equatorward pressure gradient anomalies are not associated with equatorward flow 

along the mainland. Equatorward ∆ssp anomalies are associated with poleward flow 

along the mainland during weak wind stresses, and weak flow on the mainland during

weak equatorward wind stresses. This is again consistent with previous studies 

suggesting a mean poleward pressure gradient force (pgf) exists on the U.S. West Coast. 

That mean pgf would be added to the ∆ssp anomaly observed here and is apparently 

strong enough to make the net pgf poleward at all times. 

Near-zero ∆ssp anomalies are also associated with poleward flow along the mainland 

during weak wind stresses, and even weak equatorward wind stresses. This suggests the 
33

mean pressure gradient force along the mainland is poleward, in accordance with 

previous studies of the Southern California Bight and West Coast of North America (as

mentioned above). 

The measured coastal pressure gradient anomaly has little effect on flow at the islands. 

The flow at some Island stations CUY, SMS, PRO, PEL, and VAL is weak even during 

wind forcing. This suggests the substantial flow that does at times exist at VAL (Figure 

3) is not produced by either local wind (as represented by buoy 46053) or the coastal 

∆ssp. The tendency of wind stress to drive flow in the direction of the wind stress is 

consistent for any value of ∆ssp, but the strength of the flow response is stronger at 

mainland sites than at Island site connection between flow at the mainland and flow at the 

Islands. 

4. Conclusions

The presence of only one separate EOF out of 32 modes is in contrast to the Winant et al. 

(2003) study that focuses on the deeper SBC. The result indicates that the nearshore flow 

at the mainland and islands cannot be described as the combination of a few simple, 

distinct velocity patterns. The ~75% of the subtidal velocity variance not accounted for 

by EOF 1 is apparently not strongly coherent over the study area, suggesting different 

wind and pressure gradient forcing is important at different sites and/or local topography 

plays a dominant role in driving the nearshore flow. Furthermore, flow variability in the 

nearshore region exists with higher frequency than the synoptic to seasonal scales 

described by Winant et al. (2003).
34

References

Auad, G., and M. Hendershott, 1997: The low frequency transport in the Santa Barbara 

Channel: description and forcing, Continental Shelf Research, 17,779-802.

Checkley, D.M., and J.A. Barth, 2009: Patterns and processes in the California Current 

System, Progress in Oceanography, 83, 49-64.

Cudaback, C.N., L. Washburn, and E. Dever, 2005: Subtidal inner-shelf circulation near

Point Conception, California, J. Geophys. Res., 110, C10007, 

doi:10.1029/2004JC002608.

Harms, S., and C.D. Winant, 1998: Characteristic patterns of the circulation in the Santa 

Barbara Channel, J. Geophys. Res., 103, 3041 – 3065.

Lentz, S.J., 2008: Seasonal Variations in the circulation over the Middle Atlantic Bight 

continental shelf, J. Phys. Oceanogr., 38, 1486–1500.

Melton, C., L. Washburn, and C. Gotschalk, 2009: Wind relaxations and poleward flow 

events in a coastal upwelling system on the central California coast, J. Geophys. Res.,

114, C11016, doi:10.1029/2009JC005397.

Pawlowicz, R., R. C. Beardsley, and S. J. Lentz, 2002: Harmonic analysis including error 

estimates in MATLAB using T TIDE. Computers and Geosciences.

Smith, S.D., 1988: Coefficients for sea surface wind stress, heat flux and wind profiles as 

a function of wind speed and temperature. J. Geophys. Res., 93, 15,467–15,472.

Winant, C.D., E.P. Dever, and M.C. Hendershott, 2003: Characteristic patterns of shelf 

circulation at the boundary between central and southern California, J. Geophys. Res., 

108(C2), 3021, doi:10.1029/2001JC001302.
35
36

Figure 1. Map of study region near Point Conception, California. Isobaths are drawn 

every 100 m. The four Northern Channel Islands are, from west to east: San Miguel, 

Santa Rosa, Santa Cruz, and Anacapa. Large dashed box indicates area covered by maps 

in Figures 3 and after. Upper right: map of western United States; black rectangle 

indicates location of study region.
37

Figure 2. Time-mean wind stress (arrows) by month, and principal axis ellipses for 33-hr 

low- pass filtered wind stress, displayed as in Harms and Winant (1998). Dots with white 

centers indicate wind measurement locations. The baseline of the arrows is aligned with 

the minor principal axis (x) at each site. January is indicated by ``J". Large dashed box 

indicates area covered by maps in Figures 3 and after.
38

Figure 3. Time-mean, depth-average along-shelf flow (arrows) by month, displayed as in 

Harms and Winant (1998). Dots with white centers indicate mooring locations. The 

baselines of the arrows are aligned with the minor principal axis (x) at each site. January 

is indicated by ``J". At each site, only months with at least three weeks of data are 

included. The semi-minor and -major axes of the principal axis ellipses (grey) indicate 

the standard deviations of the cross- and along- shelf flow.
39

Figure 4. (a) Spatial pattern of first EOF of depth-average along-shore flow and nearsurface cross-shore flow. (b) Percent of variance this EOF explains in each flow 

component at each site (bold if >20%).
40

Figure 5. Vertical profiles of time-mean along-shore velocity at (top) mainland and 

(bottom) island sites.
41

Figure 6. Vertical profiles of time-mean cross-shelf flow at all sites, in two coordinate 

systems. Left column: principal axes coordinates. Right column: The coordinate system 

that has uda = 0. Light grey profiles are sites that do not fit the C-shape pattern in both 

coordinate systems. Open symbols are sites with less than 2 years of data.
42

Figure 7. Correlation of depth-average along-shelf flow vda with local wind stress at 

buoy 46054 (black arrows) or 46053 (grey arrows), at zero lag. The tail of each arrow is 

at the location of an ADCP. Length of arrow indicates correlation coefficient squared 

(r2). Arrows are oriented parallel to the local major principal axis direction (y). Direction 

of arrow indicates the flow direction when the wind stress fluctuation is poleward 

(downwelling-favorable, as shown by thick arrows labeled "wind stress"). Wind buoys 

4western and eastern thick arrows, respectively.
43

Figure 8. Correlation of near-surface cross-shelf flow us (filled arrows) and near-bottom 

cross- shelf flow ub (white arrows) with local wind stress at buoy 46054 (black) or 46053

(grey), at zero lag. The tail of each arrow is at the location of an ADCP. Length of arrow 

indicates correlation coefficient squared (r2). Arrows are oriented parallel to the local 

minor principal axis direction (x). Direction of arrow indicates the flow direction when 

the wind stress fluctuation is equatorward (upwelling-favorable, as shown by thick 

arrows labeled "wind stress"). Wind buoys 46054 and 46053 are located at the tails of the 

thick arrows.
44

Figure 9. Example of relation of cross-shelf velocities near-surface and near-bottom to 

each other and to wind forcing. (a) y-component of wind stress (positive poleward) at 

buoy 46054, hourly (thin grey line) and low-pass filtered with a 33-hr cutoff (black line). 

(b) Cross-shelf velocities at SMS (positive onshore), low-pass filtered with a 33-hr cutoff. 

Grey: near-bottomADCP bin 2. Black line: near-surface velocity from top good ADCP 

bin.
45

Figure 10. Velocity profiles along the mainland coast during weak winds (|τ|<.05 Pa) and 

(top) equatorward or (bottom) poleward pressure gradient force anomaly (|ΔSSPa| > 300 

Pa). Left panels: along-shelf flow, positive poleward. Right panels: cross-shelf flow, 

positive onshore. For sites at the Islands, the profiles are not significantly different for the 

two pressure gradient cases.