OCS Study 

•

MMS 2006-009 

Transport over the Inner-Shelf of the 

Santa Barbara Channel 

Final Technical Summary 

Final Study Report 

U.S. Department of the Interior 

Minerals Management Service

Pacific OCS Region 

OCS Study 

MMS 2006-009 

Transport over the Inner-Shelf of the 

Santa Barbara Channel 

Final Technical Summary 

Final Study Report 

Author 

J. Carter Ohlmann 

Principal Investigator 

Prepared under MMS Cooperative 

Agreement No. 1435-01-00-CA-31063 

by 

Coastal Marine Institute 

Marine Science Institute 

University of California 

Santa Barbara, CA 93106-6150 

U.S. Department of the Interior 

Minerals Management Service Camarillo

Pacific OCS Region February 2006
Disclaimer 

This report has been reviewed by the Pacific Outer Continental Shelf Region, Minerals Management 

Service, U.S. Department of the Interior and approved for publication. The opinions, findings, 

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

the views and policies of the Minerals Management Service. 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 Minerals Management Service editorial standards. 

Availability of Report

Extra copies of the report may be obtained from: 

U.S. Dept. of the Interior 

Minerals Management Service 

Pacific OCS Region 

770 Paseo Camarillo 

Camarillo, CA 93010 

Phone: 805-389-7621 

A PDF file of this report is available at: 

http://www.coastalresearchcenter.ucsb.edu/CMI/ 

Suggested Citation 

The suggested citation for this report is: 

J. Carter Ohlmann. Transport over the Inner-Shelf of the Santa Barbara Channel. MMS OCS Study 

2006-009. Coastal Research Center, Marine Science Institute, University of California, Santa 

Barbara, California. MMS Cooperative Agreement Number 1435-01-00-CA-31063. 29 pages. 
Table of Contents 

FINAL TECHNICAL SUMMARY........................................................................ 1 

FINAL STUDY REPORT....................................................................................... 3 

 

 1. Introduction.................................................................................................... 3 

 

 2. Coastal drifter (instrumentation).................................................................... 4 

 2.1. Design .................................................................................................. 4 

 2.2. Performance ......................................................................................... 6 

 

 3. Experimental design....................................................................................... 8 

 3.1. Study region......................................................................................... 8 

 3.2. Sampling scheme ................................................................................. 9 

 

 4. Results............................................................................................................ 10 

 4.1. Drifter tracks ........................................................................................ 10 

 4.2. Velocity statistics................................................................................. 12 

 4.3. Lagrangian statistics............................................................................. 14 

 4.4. Dispersion statistics ............................................................................. 15 

 4.5. Comparison with HF radar derived velocities ..................................... 16 

 4.6. Comparison with HF radar derived trajectories................................... 19 

 

 5. References...................................................................................................... 21 

 
List of Tables

Table 1. Summary of Aquadopp-drifter deployments ........................................... 7 

Table 2. Data summary for the radar grid drifter deployments ............................. 9 

List of Figures 

Figure 1. Schematic of the coastal drifter .............................................................. 5 

Figure 2. Coastal drifter tracking software screen ................................................. 6 

Figure 3. Map showing the location of the study area........................................... 8 

Figure 4. The complete set of drifter tracks collected............................................ 11 

Figure 5. Drifter tracks collected on various dates, 2003 ...................................... 12 

Figure 6. Velocity statistics computed .................................................................. 13 

Figure 7. Mean autocovariance carves for the velocity components ..................... 15 

Figure 8. Mean squared dispersion......................................................................... 16 

Figure 9. Root mean squared error......................................................................... 18 

Figure 10. Average separation distance as a function of time.................................. 20 

 

 

 

 
Transport over the Inner-Shelf 

1

FINAL TECHNICAL SUMMARY 

STUDY TITLE: Transport over the Inner-Shelf of the Santa Barbara Channel 

REPORT TITLE: Transport over the Inner-Shelf of the Santa Barbara Channel 

CONTRACT NUMBER: 1435-01-00-CA-31063 

SPONSORING OCS REGION: Pacific 

APPLICABLE PLANNING AREA(S): Southern California 

FISCAL YEAR(S) OF PROJECT FUNDING: FY 01, FY 02 

COMPLETION DATE OF REPORT: April 2005 

COSTS: FY 01 - $97,480; FY 02 - $87,032 

CUMULATIVE PROJECT COST: $184,512 

PROJECT MANAGERS: Russell J. Schmitt

AFFILIATION: Coastal Research Center, Marine Science Institute, University of 

California, Santa Barbara, CA 93106 

ADDRESS: University of California, Santa Barbara, CA 93106-6150 

PRINCIPAL INVESTIGATOR: J. Carter Ohlmann 

ADDRESS: Institute for Computational Earth System Science, University of California, 

Santa Barbara, CA 93106 

KEY WORDS: Ocean circulation, drifting buoys, radar data, Lagrangian circulation

BACKGROUND: Existing studies in the Santa Barbara Channel have focused on the basin 

scale circulation, but little is known about ocean currents over the inner-shelf.

OBJECTIVES: Descriptive and statistical views of regional circulation, examination of smallscale flow patterns unresolved in H.F. radar data, and investigation of the accuracy of particle 

paths determined from Eulerian H.F. radar fields. 

DESCRIPTION: A total of 17 deployments over the inner-shelf off the Santa Barbara coast 

during 2003 with a fleet of 15 drifters yielded 171 drifter tracks. Additionally, drifters were 

repetitively deployed within a 2 km square HF radar grid located further offshore giving 128 

much shorter tracks. 
Final Technical Summary – Ohlmann 

2

SIGNIFICANT CONCLUSIONS/ STUDY RESULTS: The inner-shelf drifters generally 

move up-coast and on-shore, in opposition to the prevailing direction of wind forcing, with 

mean velocities between 3.5 and 34.5 cm s-1. This suggests that pressure and/or Coriolis 

forces may play significant roles in the local dynamics. Velocity variance is near the same 

order as mean values indicating the importance of high frequency fluctuations in the region. 

Comparisons between drifter and HF radar velocities indicate that rms differences decrease 

from ~10 to ~6 cm s-1 when the number of drifter observations in an HF radar bin increases to 

more than 30. This result is supported by EKE computations which demonstrate increased 

energy with more drifter observations. Thus, motions on scales not resolved with HF radar 

observations are a significant component of the local circulation. Comparison between 

observed drifter tracks and tracks computed with Eulerian HF radar fields shows the two 

diverge at rates of roughly 5 and 9 cm sec-1 in the along- and across-shore directions, 

respectively. Knowledge of such directional biases is necessary for developing sub-grid-scale 

parameterizations to be used with HF radar fields for accurately determining pathways in the 

coastal ocean. 

STUDY PRODUCTS: 

Publications: 

Ohlmann, J. C., P.F. White, A. L. Sybrandy, and P. P. Niiler, GPS-Cellular drifter technology for 

coastal ocean observing systems, Journal of Atmospheric and Oceanic Technology, in 

press. 

Ohlmann, J. C., and P. F. White, Lagrangian circulation characteristics over the inner shelf of the 

Santa Barbara channel. In preparation for Continental Shelf Research 

Research Presentations: 

Presentations were made at the TOS and LAPCOD meetings held during the summer of 2005. 
Transport over the Inner-Shelf 

3

FINAL STUDY REPORT 

1. Introduction

The Santa Barbara Channel (SBC) exhibits two primary characteristics that continually prompt 

regional oceanographic studies. First, the Channel contains significant natural oil and gas 

resources, including one of the world’s largest natural hydrocarbon seeps, and commercial 

operations. The fate of naturally seeping hydrocarbons and potentially leaked or spilled oil is of 

interest. Second, the location of the SBC at the northern edge of the Southern California Bight 

leads to ecological diversity, as both northern and southern species exist. Understanding larvae 

transport pathways is necessary for sound ecological management. The Channel Islands 

National Marine Sanctuary (a marine protected area; http://channelislands.noaa.gov/), and the 

United States Minerals Management Service (MMS) Rigs-to-Reefs conversions are specific 

examples of local ecological programs. 

The SBC is roughly 100 km long by 50 km wide, is oriented in the east-west direction, and is 

located at the northern edge of the Southern California Bight. Four Channel Islands comprise the 

southern boarder. Narrow continental shelves extend ~5 km offshore along both the northern 

and southern boundaries. Water depth in the center of the channel reaches 600 m. Complicated 

bathymetry, a highly variable wind field, and strong spatial gradients also characterize the 

channel (e.g. Dorman and Winant 2000). Three year mean SST and current velocity values just 

beyond the northwestern edge of the channel are 13 C and 20 cm s-1, respectively. 

Corresponding SST and surface velocity values at the eastern end are 16 C and 5 cm s-1 (Harms 

and Winant 1998). 

Ocean circulation studies in the Channel have been ongoing since at least the significant 1969 oil 

spill. Using drift cards and hydrographic surveys, Kolpack (1971) observed a cyclonic gyre in 

the western half of the Channel and northwesterly flow in the east Channel. Current meter data, 

collected from April – June 1983, at 13 locations around the periphery of the Channel, confirmed 

part of the Kolpack gyre (Brink and Muench 1986). Time varying currents were found to not 

necessarily be related to local wind forcing as in other California coastal regions (e.g. Davis 

1985, Lenz and Winant 1986, Lenz 1994). 

A more comprehensive observational program that extended northward into the Santa Maria 

basin (SMB) was carried out in the 1990s. Eight moorings were deployed around the perimeter 

of the SBC for near 3 years (generally 1993 to 1996). In addition, 347 surface drifters were 

deployed in the SBC-SMB region between mid-1993 and the end of 1999. The mooring data 

were used to present the large scale SBC circulation in terms of 6 characteristic patterns that 

develop in response to wind and sea level forcing (Harms and Winant 1998). Statistical analysis 

of the Argos tracked drifter data provide a more complete spatial description of the 6 patterns 

and indicate Lagrangian time and space scales of 1 day and less than 10 km (Dever et al. 1998). 

Small scale flow features tracked by the drifters have been described by Winant et al. (1999). 

The 6 large scale patterns have been reduced to 3 over an increased spatial domain (Winant et al. 

2003). The modeling study of Oey et al. (2001) indicates the dominant modes arise from an 

imbalance between a mostly westward sea level gradient, a mostly eastward wind stress, and 
Final Study Report – Ohlmann 

4

Coriolis. Oey et al. (2001) give 2 circulation regimes; 1 during winds of nearly equal strength 

throughout the SBC, and 1 for a strong along-channel wind gradient. 

The existing SBC circulation studies have focused on the basin scale. Current meter moorings 

and drifter releases have typically been along the 100 m isobath, or deeper, throughout the 

Channel. Service Argos tracked drifters sample roughly 4 or 5 times daily with spatial accuracy 

of order 100 meters or more. Surface drifters eventually sample the inner-shelf region (depths < 

~100 m) but with coarse resolution. The discrepancy in scale has led Dever et al. (1998) to 

completely disregard drifter observations collected near the coast. High frequency Doppler radar 

(HF radar) data exists for the SBC (Beckenbach and Washburn 2004) but necessary averaging 

gives hourly data on a 2 km grid, which is also too coarse to resolve inner-shelf dynamics 

(Ohlmann et al. in press). Additionally, CODAR data is suspect in the near-shore region where 

beam direction becomes mostly aligned with wave crests and the deep-water wave 

approximation is violated (Graber et al. 1997). 

The objective of this research is to describe and quantify the surface velocity field over a portion 

of the SBC inner-shelf with high-resolution Lagrangian drifters. Inner-shelf dynamics are 

important for determining the fate of larvae, often spawned very near the coast. The economic 

detriment of oil and other pollutants primarily occurs when the contaminants reach the surf-zone, 

which requires passing over the inner shelf region. Drifters give direct information about 

pathways of passive tracers and provide Lagrangian data which allows achievement of the 

following: 

 • Descriptive and statistical views of regional circulation. 

• Examination of small-scale flow patterns unresolved in HF radar data. 

• Investigation of the accuracy of particle paths determined from Eulerian fields.

This is the first inner-shelf drifter study known to utilize data with such high resolution in time 

and space collected over the course of a year. Results should pave the way for more 

comprehensive programs, involving expanded observations and a modeling component, with the 

goal of identifying the roles of the various forcing mechanisms and dynamical quantities and 

accurately forecasting the flow field. 

2. Coastal drifter (instrumentation) 

2.1 Design 

Development of a drifter suitable for use in the coastal ocean is the first component of this 

research. Coastal drifters must be small and space efficient for transport and deployment from 

small boats, and must be economical so they can be deployed in large numbers. In addition, they 

must have spatial resolution of a few meters, and sample their position every few minutes to 

properly resolve characteristic scales of inner-shelf motions. Near-real-time data telemetry is 

required so the drifters can be used to aid in the tracking and recovery of missing objects, and for 

recovery of the drifters themselves without visual monitoring. Recoverability and redeployment 
Transport over the Inner-Shelf 

5

greatly enhances drifter economy. Drifter electronics must be suitably energy efficient so they 

can sample and transmit every few minutes for a number of days at a time. 

A corner-radar-reflector type drogue was selected for the coastal drifter for two primary reasons 

(Figure 1). First, this is a known calibrated drag element in existing use (Niiler et al. 1995). 

Second, the design allows the drogue to be collapsed so that a large number can be stowed on, 

and deployed from, a small (20 ft) skiff. A surface float houses all the drifter electronics, and 

provides buoyancy so that the droque remains centered at a depth of 1 m. The spherical shape 

minimizes drifter slip due to surface wave forcing. 

Figure 1. Schematic of the coastal drifter. 

Drifter position is obtained with GPS technology. GPS gives position data with the highest 

spatial and temporal resolution at the lowest possible cost. Data transmission in near-real-time 

can be carried out through either satellite or cellular systems. Satellite allows for large area 

coverage but comes at significant cost. Cellular systems require that drifters sample within a 

limited line-of-sight radius of cellular base stations. However, cellular communications costs are 

near $0.50 per drifter-day for 10 minute position records, and there are few restrictions on the 

quantity of data that can be transmitted. The Mobitex (www.mobitex.org) cellular 

communications system was selected for data transmission. Mobitex is a packet-switched, 

narrowband, data-only technology ideally suited for applications such as interactive messaging, 
Final Study Report – Ohlmann 

6

e-mail, telemetry, telematics/positioning, alarms, and forms-based transmissions. It allows for 

two-way communications so drifters can be commanded remotely. Cellular coverage is 

excellent in coastal southern California, from Point Conception to the Mexican border within 

~40 km of the shore. Data records transmitted across the Mobitex network are received by a host 

computer continuously connected to the Web, allowing near-real-time data to be accessed from 

any computer connected to the Internet. 

A map-based drifter monitoring software system developed in Matlab facilitates drifter 

management (Figure 2). The Matlab Coastal Drifter Tracking Software (CDTS) was developed 

to monitor movement so drifters could be retrieved prior to leaving a study region (including 

beaching). Viewing the relative positions of all drifters on a map also facilitates an efficient 

order of recovery. The CDTS obtains drifter data from the host computer every minute, or upon 

user request, and displays the drifter positions on a map, and detailed information in a 7-column 

table. Tracks can be toggled on and off both the tabular and map displays. 

Figure 2. Coastal drifter tracking software screen. The interactive software displays tracks for selected drifters, 

along with status data for the entire fleet. Drifter tracks to be displayed are selected by toggling the drifter 

identification number. “out [hidden]” on the status table indicates the drifter is sampling but its track is not being 

displayed on the map. “NOT REPORTING!” indicates the drifter is not activated. The screen shows data collected 

on 6 December 2002, played back on 18 June 2004. 

2.2 Performance 

To test the variance in GPS position data, a set of 14 drifters were activated in fixed positions. 

Each drifter obtained position data every 10 minutes for nearly 2 days (269 position records per 

unit). Standard deviation in position for each of the 14 drifters ranges from 2.9 to 6.8 m. The 

overall standard deviation for all drifters is 4.06 m. 
Transport over the Inner-Shelf 

7

To quantify water-following characteristics, a drifter was configured with a pair of Nortek 

Aquadopp acoustic current meters, located at the top and bottom of the drogue. Drifter slip, 

which gives the rate and direction that water parcels slip by the drifter, was computed as the 

mean of the upper and lower Aquadopp velocities. Results of 6 Aquadopp-drifter deployments 

are summarized in Table 1. Slip ranges from 0.22 to 2.04 cm s-1 in relatively calm wind and 

wave conditions. The smallest slip values occur during times when the average wind speed over 

the deployment period is < 1 m s-1, and significant wave height is < 1 m. The largest slip values 

occur in the roughest conditions encountered, and nearest the shore where the steepest waves are 

expected. 

Table 1. Summary of Aquadopp-drifter deployments. Values are means over each deployment lasting ~30 minutes. 

Aquadopp current quantities (Upper, Lower, Slip, and Shear) are given as a velocity followed by the direction of 

motion. Wind and Wave values are given as the direction they are coming from. Slip is computed as the average of 

the upper and lower mean Aquadopp velocity vectors. Shear is the difference between the mean velocity vectors 

(lower-upper). Wind values are from the NOAA East Santa Barbara Channel buoy. Wave height and direction are 

from local estimates. 

Deployment 

Date 

Water 

Depth 

(m) 

Upper 

Velocity 

(cm s-1) 

(degrees) 

Lower 

Velocity 

(cm s-1) 

(degrees) 

Slip 

(cm s-1) 

(degrees) 

Shear 

(cm s-1) 

(degrees) 

Wind 

(m s-1) 

(degrees) 

Waves 

(m) 

(degrees) 

Drifter 

Movement 

(cm s-1) 

(degrees) 

 6 Aug 2004 15 0.15 183 1.03 240 0.56 234 0.96 247 < 1 315 < 1 210 7 330 

18 Aug 2004 90 1.00 61 2.73 203 1.02 185 3.57 213 2.0 299 < 1 210 30 185 

31 Aug 2004 5 0.68 146 0.79 68 0.57 103 0.94 22 < 1 228 < 1 230 6 352 

31 Aug 2004 125 0.23 179 0.21 184 0.22 181 0.03 318 < 1 228 < 1 280 14 39 

13 Sept 2004 5 1.72 233 2.56 198 2.04 211 1.54 157 2.5 270 1.0 225 13 324 

13 Sept 2004 25 0.32 131 2.96 229 1.47 222 3.01 234 2.5 270 1.0 245 77 315 

The drifter slip analysis indicates the presence of vertical shear extending over the vertical 

distance of the drogue (0.45 to 1.55 m beneath the surface). The shear profile is not necessarily 

uniform. Velocity measurements at the top and bottom of the drogue may not accurately 

integrate the velocity over the entire drogue, resulting in a perceived, rather than actual, slip. 

This integration effect, combined with the small slip values, suggests the drifters follow the mean 

flow over the drogue area to within ~1-2 cm s-1. During deployments demonstrating a slip larger 

than 1 cm s-1, the slip is aligned (180° out of phase) with the wave stress to within 25°, 

suggesting surface waves are “pushing” the drifter through water. 

Results of the limited Aquadopp-drifter tests show that slip values are less than ~2 cm s-1 during 

relatively calm conditions, consistent with results given in Davis (1985) for a similar drogue 

design. The data are insufficient for demonstrating clear relationships with wind speed and 

significant wave height. A further understanding of slip requires sampling in a wider range of 

conditions and a better understanding of vertical shear over the drogue depth. In the meantime, 

slip quantification allows the data to be properly interpreted. 
Final Study Report – Ohlmann 

8

3. Experimental design 

3.1 Study region 

Inner-shelf surface currents in the region near Coal Oil Point (Figure 3) are being studied. This 

is a location of active natural oil and gas seepage, and has been the site of numerous MMS 

funded field studies. The region is located within the SBC high frequency (HF) radar sampling 

domain, and is near the routinely sampled Naples reef LTER study site. The location is also 

within a few miles of the Goleta pier boat launch and the UCSB campus. 

Figure 3. Map showing the location of the study area along with the deployment grids. 

Two deployment grids are defined. The first (hereafter inner-shelf grid) is comprised of two 

irregularly spaced (1.5 by 1.5 km) 3 by 3 grids with 0.5 and 1 km spacing between adjacent 

stations (Figure 3). The two grids are spaced 0.5 km apart in the offshore direction. The second 

(hereafter HF radar grid) is a regularly spaced 5 by 5 grid located further offshore within a 2 by 2 

km HF radar bin (0.5 km spacing). This is the location where HF radar radials that are 

orthogonal, and HF radar performance is expected to be optimal. Spacing for the first grid 

allows examination of spatial coherence for a variety of along-shore and across-shore distances. 

Spacing for the second grid allows for the uniform distribution of drifters within the HF radar 

grid cell. 
Transport over the Inner-Shelf 

9

3.2 Sampling scheme 

After a series of test deployments during the instrument development period, 17 inner-shelf 

deployments were performed between14 November, 2002 and 2 December, 2003 (Table 2). 

Releases were originally planned for every three weeks but turned out to be irregularly spaced in 

time. Boat scheduling proved more difficult than expected, releases were cancelled due to rough 

conditions and a nonfunctional boat hoist, and the drifters were temporarily removed from 

service for a firmware upgrade and a subsequent rebuilding (17 July to 23 September). A total of 

4 HF radar grid deployments occurred between 10 July 2003 and 24 August 2004. These 

deployments occurred during the summer months when conditions in the SBC were relatively 

calm. 

Table 2. Data summary for each of the 17 inner-shelf and 4 HF radar grid drifter deployments. 

deployment 

date 

# drifters 

deployed 

avg start 

time 

(UTC) 

avg stop 

time 

(UTC) 

avg u 

velocity 

(cm/s) 

avg v 

velocity 

(cm/s) 

avg 

along 

shore 

velocity 

(cm/s) 

avg 

across 

shore 

velocity 

(cm/s) 

11/14/2002 5 18:10 20:00 -4.47 12.25 -8.28 10.09 

3/3/2003 13 18:00 23:34 -11.37 5.01 -12.17 1.03 

4/11/2003 10 16:00 21:20 -18.33 16.70 -20.98 8.19 

4/17/2003 12 17:00 21:10 -10.81 15.09 -13.42 11.68 

4/24/2003 8 16:40 20:50 3.62 12.48 -1.48 12.75 

5/22/2003 15 16:40 22:50 -9.48 12.77 -10.94 8.72 

6/4/2003 1 18:20 20:50 -30.71 11.99 -32.59 -3.34 

6/9/2003 16 16:10 19:50 4.34 4.35 2.25 5.71 

6/19/2003 13 16:00 21:30 -3.88 5.51 -5.60 3.84 

6/26/2003 9 15:40 21:00 1.36 4.77 -0.47 4.96 

7/17/2003 7 15:43 20:30 -6.45 5.21 -7.26 3.01 

9/23/2003 8 16:50 21:50 0.72 5.77 -1.62 5.48 

9/30/2003 9 16:10 21:30 -30.36 10.36 -30.33 -0.54 

10/14/2003 9 16:20 21:30 -19.47 15.71 -21.86 8.48 

10/28/2003 10 17:40 23:40 -20.60 7.162 -20.74 1.06 

11/25/2003 14 17:30 23:20 -11.69 10.15 -13.87 5.50 

12/2/2003 12 17:10 21:40 -3.41 5.34 -5.05 3.66 

---------------- 

7/10/2003 18 16:20 21:49 -25.61 29.61 -30.13 24.00 

7/19/2004 31 15:20 22:50 -11.07 19.88 -13.63 17.95 

8/12/2004 30 16:20 22:20 -19.09 14.76 -20.46 11.86 

8/24/2004 23 15:50 21:32 -2.81 16.79 -5.75 16.11 
Final Study Report – Ohlmann 

10

For the inner-shelf grid deployments, drifters were generally released between 0800 and 0930 

local time and recovered between 1200 and 1500 local time. The short sampling durations were 

required to recover drifters before they entered the surf zone and washed ashore. For the HF 

radar grid deployments, drifters were also deployed in the morning. As they exited the 2 by 2 

km HF radar grid, they were picked up and redeployed at the stations furthest from the other 

drifters, so as to keep a mostly uniform spatial distribution in the box. Typically 2 or 3 drifters 

were picked up at a time and redeployed at the upstream edge of the box. Each drifter was 

redeployed roughly twice during each 5 to 7 hour experiment. The inner-shelf and HF radar grid 

experiments resulted in a total of 171 and 128 drifter tracks, respectively. 

4. Results 

4.1 Drifter tracks 

The purely descriptive view of the local circulation as inferred from the complete set of innershelf drifter trajectories shows that currents are almost always moving in the up-coast direction, 

and mostly in the on-shore direction (Figure 4). Interestingly, this occurs despite the prevailing 

winds being from the northwest, opposite the general direction of drifter movement. 149 of the 

171 inner-shelf drifter tracks moved into shallower water during their deployment periods. The 

propensity for cross-shore movement, relative to along-shore motion, is greatest in the HF radar 

deployment grid and then again very near the shore. The former is consistent with the presence 

of a mid-basin cyclonic gyre, or the “cyclonic” regime reported by Oey et al (2001). The latter is 

likely due to wave-stress forcing which becomes more pronounced with decreased depth. For 

the inner-shelf deployments, track lengths tend to increase with distance from the shore 

indicating the weakest velocities nearest the coast. The overall picture suggests that the local 

circulation is not a simple balance between surface and bottom stress, but that pressure and/or 

Coriolis forces may play a significant role. 
Transport over the Inner-Shelf 

11

Figure 4. The complete set of drifter tracks collected. 

Sets of tracks collected contemporaneously indicate the sorts of high frequency variations in 

currents that exist in the region. On 2 December, 2003, drifters move somewhat coherently, but 

the closer to shore a drifter, the more its track is oriented in the cross-shore direction (Figure 5a). 

Tracks collected on 11 April, 2003, show significantly greater velocities away from the coast 

(Figure 5b). Pronounced differences in the circulation can exist across distances of a km or less 

(Figure 5c; 17 July 2003), and velocities can change abruptly in time (Figure 5d; 26 June 2003). 

Maps showing trajectories for each of the individual deployment days are on the web at 

http://www.icess.ucsb.edu/~kirk/drifter/SBCIS/index_deployments.htm. In general, daily tracks 

demonstrate a variety of high-frequency small-scale motions that exist in the region. 
Final Study Report – Ohlmann 

12

Figure 5. Drifter tracks collected on a) 2 December, 2003, b) 11 April, 2003, c) 17 July, 2003, and d) 26 June, 

2003. 

4.2 Velocity Statistics 

Mean velocities and their corresponding deviations have been computed on a 0.75 km grid as 

follows. Velocities were determined from a first difference in drifter positions at the midpoint 

between successive position records. Velocity values were then grouped in square bins and 

statistics computed for bins with observations on at least 5 sampling days. This arbitrary 

threshold was selected to eliminate statistics computed from observations collected during a 

limited time, and to give results over the course of several synoptic events. Mean vectors are 

included with variance ellipses to identify variations with distance from shore and quantify the 

high frequency variations indicated above. They do not depict accurate annual averages. 

Mean velocity vectors range from 3.5 to 34.5 cm s-1 and are mostly oriented parallel to the 

straight section of coast between the Coal Oil and Naples headlands (Figure 6a). There are two 

notable exceptions. Within 1 km of the coastline, mean velocities are mostly directed onshore, 

presumably following wave stress forcing. Between roughly 1.5 and 2.5 km offshore, velocities 

are also directed in the onshore direction. This is a function of the deployment scheme. No 

drifters are deployed in this region. Drifters enter from either offshore or onshore only during 
Transport over the Inner-Shelf 

13

times of cross-shore flow, and therefore possess a sampling bias. The mean field also shows a 

general increase in velocity with distance offshore. In general, mean velocities are in direct 

opposition to the local wind stress suggesting the importance of pressure forces in driving the 

local circulation. 

Figure 6. Velocity statistics computed for 0.75 km x 0.75 km bins in which data was collected during at least 5 

different days. a) Mean velocity vectors, and b) associated variance ellipses. 
Final Study Report – Ohlmann 

14

Variance ellipses associated with the mean values are illustrated in Figure 6b. The ellipses vary 

in size, eccentricity, and orientation indicating the inhomogeneous nature of the flow field in the 

study region. Major axis length ranges from 18 to 323 cm2

 s

-2 with the largest values generally 

existing in the offshore region. Ellipses near the coast are smaller, but with similar eccentricity 

and along bathymetry orientation. The large eccentricity ellipses near the 50 m isobath arise 

from flow associated with a strong localized along-shore jet that occasionally occurs. In general, 

the ellipses indicate the magnitude of the along-shore velocity component to be the largest source 

of temporal variability. Pronounced spatial variations in the time-varying flow also exist. 

4.3 Lagrangian Statistics 

Lagrangain time and length scales quantify how drifter movement is correlated with previous 

samples. Such information is useful for defining appropriate decorrelation scales for coastal 

ocean models, and for validating modeled trajectory statistics. The Lagrangian scales are based 

on the velocity covariance defined as 

u x t u x t dt

T

R T t x j

t T

t

ij i ( , ) ( , ) 1 ( , , , ) 0 0 0 0

0

0

τ = ′ ′ +τ ∫

+

 (1) 

where ) ( , 0 u x t i

′ is the velocity residual, at time t, for the i

th drifter track that passes through the 

point x0 at time t0, ( , ) 0 u′ x t +τ j is the velocity residual at time t +τ for the j

th track that passes 

through x0 at time t0, and T is the total integration time. Lagrangian integral time (Ti

L

) and length 

(Li

L

) scales for a single track i are then 

∫ =

t

0

T R ( ) dt ii

L

i τ (2) 

∫ = < ′ >

t

0

2 1/ 2 L u R ( ) dt i ii

L

i τ (3) 

where< ′ >2

i u is the velocity variance for track i, and integration is to the first zero crossing 

following Poulain and Niiler (1989). 

Mean Lagrangian autocovariance curves computed from all tracks with lengths greater than 180 

minutes show along-shore velocity observations decorrelate smoothly reaching zero between 90 

and 100 minutes (Figure 7a). The along-shore curve continues to decrease until it reaches a 

value of -0.19 at 160 minutes, and then increases back toward zero. The region of negative 

correlation may be suggestive of eddy motions where along-shore flow in one direction occurs 

for roughly two hours followed by return flow in the opposite direction during the next (roughly) 

two hours (~120 to 250 minutes). After a period of near 4 hours the drifter has moved out of the 

eddy into a different (and uncorrelated) transient feature. Across-shore velocity observations 

decorrelate smoothly over a slightly longer time, reaching zero at a lag between 130 and 140 
Transport over the Inner-Shelf 

15

minutes (Figure 7b). Across-shore autocovariance values do not display negative values beyond 

-0.03. If the along-shore autocovariance curves indeed point to return flows associated with 

eddies, then the across-shore curves indicate the eddies are oriented mainly in the along-shore 

direction. 

Figure 7. Mean autocovariance carves for the a) along-shore, and b) across-shore velocity components. 

Decorrelation time scales for the along- and across-shore components are 42 and 43 minutes, 

respectively. Corresponding decorrelation length scales are 0.10 and 0.08 km, respectively. 

These scales are significantly shorter than those reported by Dever et al. (1998) for the basin 

scale circulation (1 day and 10 km). This is partly attributable to the enhanced velocity 

fluctuations that occur nearer the shore, but also to the higher frequency sampling rates and much 

shorter overall track lengths in the present study. It is possible that significant correlations exist 

on scales beyond the reported range, but they are not discernable with the existing data. 

 

4.4 Dispersion Statistics 

Mean squared dispersion has been computed by selecting all inner-shelf drifter pairs that come 

within 250 m and computing their subsequent separation (squared) in both the along- and across-
Final Study Report – Ohlmann 

16

shore directions (Figure 8). The 250 m threshold was arbitrarily selected to give close proximity 

while also allowing sufficient leeway so that at least 25 drifter pairs are used in the computation. 

Since initial spacing is greater than 250 m, pairs included in the analysis originally converged. 

Mean squared dispersion in both the along- and across-shore directions is surprisingly similar. 

Separation grows to ~0.02 km2

 after 40 minutes, and to 0.20 km2 after 240 minutes. Dispersion 

follows a power law during the first 40 minutes and then grows as a linear function of time 

between 40 and 240 minutes. The sharp increase after 240 minutes is an artifact of a limited 

number of pairs extending that far in time, and the fact that once drifters are sufficiently 

separated they can be in extremely different flow regimes. After 240 minutes, one drifter has 

typically moved near the shore and is moving at a few cm s-1, and the other (in the pair) is still 

offshore moving at > 10 cm s-1. At first glance, the inner-shelf dispersion on such small scales 

does not closely follow Taylor (1921). This will be investigated in a more complete analysis of 

dispersion which is forthcoming. 

Figure 8. Mean squared dispersion in both the along-shore and across-shore directions. Error bars show standard 

deviations. 

4.5 Comparison with HF radar derived velocities 

High frequency radar systems have become a popular means of obtaining surface current data 

near the coast. HF radars use a Doppler technique to measure currents in the radial direction 
Transport over the Inner-Shelf 

17

from each instrument. Radials must then be smoothed by averaging. Typical HF radar data are 

presented as hourly average velocities on a spatial grid near 1 to 2 km square, depending on radar 

frequency and radial averaging radii. HF radar coverage typically begins somewhere on the 

shelf and reaches the horizon. 

HF radar results have a demonstrated accuracy of near 10 cm/s (Paduan and Rosenfeld 1996, 

Chapman and Graber 1997, Emery et al. 2004). Validation has occurred through comparison of 

HF radar data that are space and time averages against data from a single current meter that is 

only a time average. Existing comparisons with drifter derived velocities use few tracks so 

averaging is over the limited locations and times of drifter sampling, and not the same space and 

time domains used to compute average HF radar values. Meaningful validation of HF radar 

velocities requires comparison with measurements made on commensurate time and space 

scales. 

The HF radar grid sampling gives up to 41 velocity observations distributed throughout a 2 km 

square HF radar grid cell in an hour. This space-time resolution can offer a much improved 

validation of 2 km, hourly average, HF radar velocities. Comparison of drifter and HF radar 

derived velocities when there is at least 1 drifter velocity observation in the HF radar 

(time/space) bin gives root mean square (rms) errors of 9.8 and 9.9 cm s-1 for the east-west (u; 

mainly alongshore) and north-south (v; mainly across-shore) velocity components, respectively 

(Figure 9a). As the number of drifter velocity observations within each 2 km bin for a given 

hour increases, the rms velocity error decreases. For time and space bins when there are at least 

34 drifter derived velocity observations, the rms velocity error decreases to 6.7 and 6.1 cm s-1 for 

the u and v velocity components, respectively. 
Final Study Report – Ohlmann 

18

Figure 9. Root mean squared error (RMSE) between HF radar and drifter derived average velocity components 

(top). Average velocities are over 2 km square bins and 1 hour. RMSE is computed using average velocities where 

at least x drifter observations are used to calculate the average. The u velocity component is east-west and mostly 

along-shore in the study region. The v component is north-south and mostly across-shore. Associated eddy kinetic 

energy (EKE) on from drifter data (bottom). EKE is computed as 0.5 ∗ ( u′u′ + v′v′ ) where u′ and v′ give 

deviations from the average u and v velocities, respectively, and the angle brackets denote mean quantities. EKE is 

computed separately for each time (1 hour) and space (2 km grid) bin. Data for two days that give a relatively large 

contribution to a single space bin were removed to avoid spatial biasing. 
Transport over the Inner-Shelf 

19

This simple performance analysis suggests that previous validations may have overstated HF 

radar error near 50%, or ~3 to 4 cm s-1, by failing to resolve the same time-space motions which 

are included in typical 2 km square and 1 hour HF radar averages. More importantly, the 

analysis indicates that coastal flows are highly variable on (time and space) scales shorter than 

typically resolved with HF radar data. Eddy kinetic energy (EKE), computed as 

2 2 0.5∗ u′ + v′ , where u’ and v’ are the fluctuating components of the east-west and north-south 

velocity components, respectively, and the brackets denote a mean, is 15.1 cm-2 s-2 when 

computed on spatial scales less than 2 km, and hour time scales, with all the HF radar grid data 

(Figure 9b). EKE increases 67%, to 25 cm-2 s-2 when computed for times when there are at least 

25 drifter observations within the grid. The number of observations within a grid cell needs to 

be increased in future experiments to determine the asymptotic value of EKE. Such a value is of 

interest for tuning models to produce realistic values of eddy energy. 

4.6 Comparison with HF radar derived trajectories 

Tracks computed from 2 km hourly average Eulerian HF radar fields, using a fourth order 

Runge-Kutta integration scheme, are compared with observed drifter tracks. Mean separation 

distances for the east-west (mainly alongshore) and north-south (mainly across-shore) directions, 

are computed every 10 minutes (Figure 10). Mean east-west separation grows to -65 m after 60 

minutes, to -273 m after 120 minutes and to -673 m after 240 minutes. The negative values 

indicate that trajectories computed from HF radar derived trajectories are moving faster in the 

westward direction than the drifters. Mean north-south separation grows at almost the same rate 

out to 90 minutes and then begins to grow faster. The mean north-south separations at 120 and 

240 minutes are -358 m and -1260 m, respectively, indicating the HF radar derived trajectories 

move slower in the onshore direction. 
Final Study Report – Ohlmann 

20

Figure 10. Average separation distance (with standard error) between observed drifter tracks and tracks computed 

with HF radar derived velocities as a function of time. The HF radar tracks are computed from hourly average 

velocities on a 2 km grid using fourth order Runge-Kutta integration. The number of track pairs used to compute a 

mean varies from 88 (at 10 minutes) to 9 (at 280 minutes), and decreases fairly linearly. 

Although comparisons between HF radar and drifter derived velocities show improved 

agreement, there are still significant discrepancies in trajectories. Significant directional biases 

and a larger difference in the across-shore component exist. Such results indicate that an 

optimum sub-grid-scale-model for rectifying trajectory discrepancies should not simply be 

isotropic. If an HF radar derived trajectory were to be used to assist an at-sea search, results 

suggest that the lost object would most likely be located to the east, and onshore of the position 

given by the computed trajectory. Additional comparisons, and more thorough quantitative 

analyses, are necessary to develop sub-grid-scale parameterizations in terms of location, flow 

properties, and HF radar sampling characteristics. This will ultimately increase the accuracy of 

trajectories computed with HF radar data. 
21

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23

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