OCS Study 

•

MMS 2004-008 

Low Frequency Waves in the Santa 

Barbara Channel Observed by High 

Frequency Radar 

Final Technical Summary 

Final Study Report 

U.S. Department of the Interior 

Minerals Management Service

Pacific OCS Region 

OCS Study 

MMS 2004-008 

Low Frequency Waves in the Santa 

Barbara Channel Observed by High 

Frequency Radar 

Final Technical Summary 

Final Study Report 

Authors 

Edwin Beckenbach 

Libe Washburn 

Principal Investigators 

Libe Washburn 

Steven Gaines 

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 

U.S. Department of the Interior 

Minerals Management Service Camarillo

Pacific OCS Region January 2004
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: 

Beckenbach, Edwin and Washburn, Libe. Low frequency waves in the Santa Barbara Channel 

observed by high frequency radar. MMS OCS Study 2004-008. Coastal Research Center, Marine 

Science Institute, University of California, Santa Barbara, California. MMS Cooperative Agreement 

Number 1435-01-00-CA-31063. 43 pages. 
Table of Contents 

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

An array of high frequency radars ................................................................. 1 

Low frequency waves in the Santa Barbara Channel .................................... 4 

Wind driven circulation in the Santa Barbara Channel.................................. 5 

Circulation patterns around point conception ................................................ 7 

Surface circulation ......................................................................................... 9 

Marine ecology ............................................................................................ 10 

FINAL STUDY REPORT:................................................................................. 13 

Summary ...................................................................................................... 13 

1. Background .............................................................................................. 14 

2. Observations............................................................................................. 15 

3. Methods.................................................................................................... 17 

 3.1 Missing Data ................................................................................ 17 

 3.2 Frequency band selection and filtering ........................................ 18 

 3.3 Complex empirical orthogonal function analysis ........................ 18 

 3.4 Stream function estimation .......................................................... 18 

4. Results...................................................................................................... 19 

 4.1 Propagating rotary flows.............................................................. 19 

 4.2 Modes of variance over the Santa Barbara basin......................... 25 

 4.3 Larger-scale current patterns........................................................ 30 

 4.4 Comparison with model results.................................................... 30 

5. Conclusions.............................................................................................. 33 

References.................................................................................................... 34 
List of Tables and Figures

Technical Summary 

Figure 1. High frequency radar array in the Santa Barbara Channel....................3 

Figure 2. Contours of mean relative vorticity and divergence..............................6 

Figure 3. Current vectors at shelf locations ..........................................................7 

Figure 4. Wind speed at NDBC buoy ...................................................................8 

Final Study Report 

Figure 1. Study area showing the Santa Barbara Channel and basin..................16 

Figure 2. Two counter rotating eddies in the coverage area...............................19 

Figure 3. Time-longitude contours of ζ/f from hourly HF radar ........................20 

Figure 4. Squared coherence γ

2

...........................................................................21 

Figure 5. Longitude-time contours of ζ/f for 21 June to 21 July 1999 ...............22 

Figure 6. Longitude-time contours of ζ/f for 1 June to 1 September 1998........23 

Figure 7. Conditionally averaged velocity patterns ............................................24 

Figure 8. Mean radial distributions.....................................................................25 

Figure 9. Velocity patterns of CEOF mode 1 .....................................................26 

Figure 10. Stream function for CEOF mode 1......................................................28 

Figure 11. Time-longitude contours for 1998-2000 of ζ/f....................................29 

Figure 12. Time series for 1998-2000 of frequency difference magnitude |∆f|....28 

Figure 13. Observed stream function pattern........................................................32 

 

 

 
Low Frequency Waves Observed 

1

FINAL TECHNICAL SUMMARY 

STUDY TITLE: Observing the surface circulation along the South-Central California 

Coast using high frequency radar: consequences for larval and pollutant dispersal

REPORT TITLE: Low frequency waves in the Santa Barbara Channel observed by high 

frequency radar 

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: December 2003 

COSTS: FY 01 - $108,017; FY 02 - $115,983; FY 03 - no cost 

CUMULATIVE PROJECT COST: $224,000 

PROJECT MANAGERS: Russell J. Schmitt

AFFILIATION: University of California, Santa Barbara 

ADDRESS: Coastal Research Center, Marine Science Insitute, University of California, 

Santa Barbara, CA 93106 

PRINCIPAL INVESTIGATORS: Libe Washburn1, and Steven Gaines2 

ADDRESS: 1Professor, Institute for Computational Earth System Science, Dept. of 

Geography, University of California, Santa Barbara, CA 93106-3060; 2Professor, Dept. of 

Ecology, Evolution, and Marine Biology, Biology, California, Santa Barbara, CA 93106 

KEY WORDS: Central and Southern California, coastal, Point Conception, Santa 

Barbara Channel, coastal circulation, high frequency radar, coastal trapped waves, 

topographic Rossby modes, rock fishes 
Final Technical Summary - Beckenbach and Washburn 

2

BACKGROUND: 

An array of high frequency radars along the South-Central California coast for 

oceanographic studies 

High frequency (HF) radars are becoming more common in studies of ocean circulation 

around the coasts of the United States. It is anticipated that HF radars will be key 

components of evolving coastal ocean observing systems (e.g. oceans.us web site: 

http://www.ocean.us/) since they are the only technology now available which can produce 

time series maps of surface currents round the clock. Other technologies such as arrays of 

moorings are prohibitively expensive for this purpose, although mooring arrays complement 

HF radars by supply critical sub-surface velocity and water property data. 

An array of HF radars has been operating in the Santa Barbara Channel since 1998 with 

observations being made from up to five sites. The current configuration of the array with 

three HF radar systems is shown in Fig. 1. Radar hardware was obtained through grants from 

the W.M. Keck Foundation and the University of California Marine Council. Two systems 

were borrowed from NOAA’s Environment Technology laboratory in Boulder Colorado. 

Operational support for the radar array has come from a number of agencies: Minerals 

Management Service, Partnership for Interdisciplinary Studies of Coastal Oceans (PISCO), 

University of California Marine Council, and NASA. 

 

Throughout most of this study, each radar system produced time series of radial current 

components (hereafter referred to as “radials”) out to a maximum range of 40 km off shore. 

More recently, software advances in the systems have allowed radials to be obtained out to a 

maximum range of 60 km. As discussed by Emery et al. (2004), the actual range and overall 

coverage area of the radars varies over a wide range of time scales with a prominent diurnal 

component. For the 12-13 MHz systems used in this study, radials are obtained as spatial 

averages over sectors of the sea surface measuring 5 degrees in azimuth by 1.5 km in range. 

Radials in each sector are computed over 10 minute intervals. Total current velocity vectors 

are estimated by averaging all radials each hour observed over circular areas of the sea 

surface with 3 km radii. The circles are centered on points on a square grid with two km 

spacing between points. The least square technique described by Gurgel (1994) is used to 

combine radials within the circular areas to estimate the eastward and northward current 

components at each grid point. Figure 1 shows examples of surface current vectors computed 

on the 2 km grid on 23 June 2003 at 1200 GMT. 
Low Frequency Waves Observed 

3

Figure 1. High frequency radar array in the Santa Barbara Channel as of December 2003. Diagram shows 

surface current vectors on 23 June 2003 at 1200 GMT. Radar systems are indicated by triangles at Refugio State 

Beach, Coal Oil Point, and the Mandalay Generating Plant near Oxnard California. Scale for surface current 

vectors is shown at left along with size of circles used in estimating surface current vectors. Box on map of 

California (upper right) shows study area. CES-SIO current meters SMIN, SMOF, and AMNI are indicated with 

circles. Current vectors are placed on a 2 km grid. 

Emery et al. (2004) describe the performance of the array by comparing surface currents 

obtained from the HF radars with an extensive array of moored current meters. The current 

meters were deployed by the Center for Coastal Studies at the Scripps Institution of 

Oceanography (CES-SIO). Four of these current meters are still in operation and three of 

them are shown with circles in Fig. 1. Data from the current meters were kindly made 

available to this project by CES-SIO personnel. Emery et al. (2004) found that the HF radarderived and current meter-derived radial time series were significantly coherent for time 

scales of about 11 hours and longer. Hourly radial measurements were significantly 

correlated for all radar-current meter pairs with r2 ranging from 0.5 – 0.7. Results of this 

study focus on current variability on sub-tidal time scales (36 hours and longer) since 

correlation between the radars and current meters was greatest for these time scales. 

OBJECTIVES: 

Our research examined various aspects of the surface circulation in the western Santa Barbara 

Channel and Santa Maria Basin with a particular focus on the following questions related to 

physical oceanography: 

1. What are the spatial and temporal scales of eddy variability? 

2. How is local wind forcing related to the surface circulation? 

3. How stable is the cyclonic circulation in the Santa Barbara Channel? 
Final Technical Summary - Beckenbach and Washburn 

4

4. How does the offshore flow influence flow on the inner shelf? 

The following questions related to marine ecology were also addressed in the research: 

1. Are dominant spatial patterns of recruitment linked to transient surface circulation 

features or to the time-averaged, “mean” flow? 

2. Is offshore flow at Pt. Conception important in maintaining the bio-geographic 

boundary there? 

3. Do poleward flow events lead to recruitment north of Pt. Arguello? 

4. Is local retention or remote supply more important in maintaining various marine 

populations on the south-central California coast. 

An operational goal of this research was to provide near-real time observations of surface 

currents in support of scientific research, management decision making, and other operations 

such as search and rescue. 

DESCRIPTION: 

Low frequency waves in the Santa Barbara Channel 

Previous observations in the western Santa Barbara Channel (SBC) have show that a 

dominant feature of the circulation there is a persistent cyclonic pattern of rotating currents 

(e.g. Harms and Winant (1998), Dever (2004). These and other observations showed that this 

cyclonic circulation is highly variable on time scales of a few days and longer. An important 

research focus of this study was an examination of propagating eddy-like features reported by 

Nishimoto and Washburn (2002) which disrupted the cyclonic circulation on time scales of 

about two weeks. Initial analysis suggested that these features were some type of eddy which 

formed to the east and then propagated into the radar coverage area. A three-year time series 

of HF radar observations of surface currents in the western Santa Barbara Channel (SBC) was 

used to examine these propagating features. This analysis, as summarized in the Study 

Report following this Technical Summary, indicates that the motions are not freely 

propagating eddies as we initially hypothesized, but are a type of large scale wave motion. 

 

The features appear as sequences of alternating cyclonic (counter-clockwise) and anticyclonic (clockwise) vortices propagating westward with a period of about two weeks. The 

sequences often last up to a few months and occur intermittently throughout the year. No 

distinct seasonal trend was found. The surface velocity patterns of the cyclones, when 

reversed, are very similar to those of the anticyclones, which indicates a high degree of antisymmetry. (Antisymmetry is used here to indicate that the velocity patterns of the cyclones 

and anticyclones are nearly “mirror-images” of each other.) Both the cyclones and 

anticyclones have mean propagation speeds of ~5 km day-1 and relative vorticity magnitudes 

of order 0.1 f, where f is the local Coriolis parameter (The Coriolis parameter is a measure of 

the strength of the Coriolis force at a given latitude. It is zero at the equator and increases 

toward the North Pole). The anti-symmetry of the features was remarkable as described in the 

Study Report. These propagating vortices resemble the propagating cyclones with periods of 

10 - 25 days reported in the SBC by Harms and Winant (1998). 
Low Frequency Waves Observed 

5

 

The dominant propagating patterns were extracted using an objective analysis technique 

described by Wallace (1972) called complex empirical orthogonal function (CEOF) 

decomposition. The method was applied to surface velocity data which had been band-pass 

filtered to eliminate variance outside the 10-20 day pass band. Coherence analysis of the HF 

radar data had revealed that the propagating features dominated the velocity variance in this 

band. The CEOF analysis separated the variance into two dominant modes. The first mode 

with an average period of 14.4 days explains 45% of the velocity variance and represents the 

alternating cyclones and anticyclones that are evident in the band-pass filtered record. The 

second mode, with an average period of 13.3 days, explains 25% of the velocity variance and 

mainly represents alongshore current fluctuations. Amplitude functions of the two modes 

correlate with in situ current time series at 5 and 45 m depths obtained from the CES-SIO 

moorings at the east and west channel entrances. This suggests coupling between the modes 

and the larger-scale circulation of the northern Southern California Bight. 

 

These results are consistent with previous observations in the SBC. Auad and Henderschott 

(1997), Auad et al. (1999) investigated the relationship between low-frequency flow in the 6 

to 18 day band and forcing by wind stress and remote adjusted sea level. The remotely-forced 

flow was explained as a coastal trapped, low-mode hybrid-wave with characteristics of both 

Rossby and Kelvin waves. The higher spatial resolution HF radar observations of this study 

support this interpretation since the period and along-shore flow of mode 2 are consistent with 

coastal trapped waves. 

 

We hypothesize that mode 1 observed in this study is a resonant response of the Santa 

Barbara Basin in the form of a trapped topographic Rossby mode (TRM). A stream function 

representation of the mode 1 resembles the predicted pattern based on a simplified analytical 

model of a fundamental TRM in a closed basin. Peak relative vorticity over the basin is about 

a factor of four higher than over the edges, indicating topographic control by the basin. The 

amplitude of mode 1 is consistently large when the frequency difference between modes 1 

and 2 is small. This suggests that the propagating vortices of mode 1 are a basin-scale 

resonant response to the coastal trapped wave represented by mode 2. A more complete 

discussion of this analysis is given in the Study Report and also by Beckenbach and 

Washburn (2002), Beckenbach and Washburn (2004). 

Wind driven circulation in the Santa Barbara Channel

As discussed by Beckenbach (2004), the wind patterns over the SBC are well described by 

the first two modes of an empirical orthogonal function (EOF) decomposition. Together they 

explain 80-90% of the variance in the wind field for National Data Buoy Center (NDBC) 

buoys in and around the channel and are consistent with previous studies such as Dorman and 

Winant (2000). 

Conditional averaging of the HF radar derived current fields for times when the modes 1 and 

2 exceed ± 1 standard deviation reproduce the upwelling, relaxation, and convergent states 

such as described by Harms and Winant (1998), Dever (2004). The new information 

compared with previous studies is an improved description of circulation patterns in the 

interior of the SBC. The interior flow patterns agree with those inferred from surface drifters 
Final Technical Summary - Beckenbach and Washburn 

6

(e.g. Dever et al., 1998). The flow patterns of the upwelling and convergent states are also 

consistent with the dynamical model of Oey et al. (2001): the upwelling flow state prevails 

when the along-channel wind stress gradient is small over the channel (even though the wind 

stress itself is large); cyclonic flow prevails when the wind stress gradient is large. 

A principal advantage of HF radar for observing surface circulation patterns is its ability to 

produce two-dimensional current maps which allows computation of the important quantities 

of relative vorticity ζ and divergence. The average ζ pattern computed from a 4-year record 

shows the strong cyclonic flow, characteristic of the western SBC and consistent with 

previous studies showing cyclonic circulation (Fig. 2a). Mean values of ζ/f are as large as 

~0.4 which means that secondary flow effects, such as localized upwelling or downwelling, 

are important (e.g. the so-called geostrophic balance does not strictly apply). Closely spaced 

streamlines in Fig. 2a (solid and dotted lines) indicate a strong westward current along the 

mainland coast which turns to the south on the western side of the Santa Barbara Basin. 

Figure 2. a) Contours of mean relative vorticity ζ normalized by the Coriolis parameter f. Red shades indicate 

positive ζ/f and a counter-clockwise turning of velocity vectors. Blue shades indicate negative ζ/f and a 

clockwise turning of velocity vectors. Streamlines are indicated by lines, solid for positive, dotted for negative. 

These also correspond to lines of constant sea surface elevation with solid lines indicating elevated sea surface 

and dotted lines indicating lowered sea surface elevation. Means are computed from a 4-year record 1998-2001. 

b) Contours of the mean divergence of surface currents, div u. Blue shades are negative indicating convergence 

and downwelling; red shades are positive indicating divergence and upwelling. Contours of velocity potential 

are indicated by lines, solid for positive, dotted for negative.

The pattern of divergence of horizontal velocity (div u) indicates a broad region of 

convergence consistent with downwelling in the channel interior (Fig. 2b). This is an 

unexpected result since the mean wind patterns generally favor upwelling and divergence. 

This pattern is currently being explored in collaboration with meteorologists Clive Dorman of 

SIO and Darko Koracin of the University of Nevada, Reno. An alternating pattern of positive 

and negative divergence on scales of ~10 km is prominent along the mainland coast. This 

pattern is consistent with a simple model of the advection of ζ as described in more detail by 

Beckenbach (2004). Lines in Fig. 2b show velocity potential contours which indicate the 
Low Frequency Waves Observed 

7

strength of the divergent part of the surface current field. Solid and dotted lines indicate flow 

direction such that the local velocity vectors are perpendicular to them and point from high to 

low contour levels. 

Circulation patterns around Point Conception

A combination of these HF radar observations and inner shelf moorings (funded by the 

Packard foundation as part of PISCO) are being used to explain circulation patterns around Pt. 

Conception. Knowing the circulation patterns around the point is important for understanding 

the movement of pollutants like oil and for describing the bio-geographic species range 

boundary found there. 

Figure 3. a) Current vectors at mid-shelf locations conditionally averaged by flow state: red for the relaxation 

state, blue for the upwelling state, and green for the convergent state. Circles indicate moorings SAMI, SMIN, 

and AMNI deployed by CES-SIO (see Harms and Winant, 1998). HF1, HF2, and HF3 indicate surface current 

vectors from the HF radars at selected locations. b) Current vectors at inner shelf locations conditionally 

averaged by flow state as in panel a). Circles indicate moorings deployed at 10-15 m depths as part of the 

Partnership for Interdisciplinary Studies of Coastal Oceans (PISCO). Square shows location of NDBC buoy 

46023.

Cudaback et al. (2004) find that flow patterns on the inner shelf (10-15 m water depths) 

generally mimic those over the mid-shelf when conditionally averaged by the flow states of 

relaxation, upwelling, and convergence using the classification scheme of Dever (2004). 

However, flow speeds over the inner shelf are usually smaller by factors of three to five. 

Figure 3a shows current vectors conditionally averaged by flow state at points over the midshelf (100 m water depth for SMIN and SAMI; 200 m for AMNI). Data were obtained at the 

CES-SIO moorings of SAMI, AMNI, and SMIN (naming scheme described by Harms and 

Winant, 1998) and at HF radar grid points labeled HF1, HF2, and HF3. Vectors are color 

coded as: red for relaxation, blue for upwelling, and green for convergence. Overall, 

conditionally averaged current vectors over the inner shelf (Fig. 3b) are generally similar to 

those over the mid-shelf. 

North of Pt. Conception the relaxation state produces poleward flow at all locations over the 

mid and inner shelf. At SMIN, HF1, HF2 and AMNI, the relaxation state forces generally 

westward flow. In contrast, the upwelling state produces flow with strong equatorward 
Final Technical Summary - Beckenbach and Washburn 

8

components over the mid and inner shelf, except for HF2 and Ellwood which are poleward. 

At Boathouse the upwelling state produces strong equatorward flow consistent with the 

upwelling center found at Pt. Conception. The convergent state produces larger differences in 

current direction between the mid and inner shelf north of Pt. Conception. At mid-shelf 

locations SAMI and HF3 the convergent state produces equatorward flow while on the inner 

shelf at Pt. Sal and Pt. Purisima, the flow is mostly offshore. In the channel, flow on the mid 

and inner shelf is poleward for the convergent state. 

Other important differences between mid and inner shelf also exist. One of the greatest 

differences is that for many wind relaxation events, warm waters flow poleward over the 

inner shelf while equatorward flow prevails over the mid-shelf. This means that relaxation 

events over the inner shelf are often not accurately predicted using mid-shelf circulation 

patterns. 

Figure 4. a) Wind speed at NDBC buoy 46023. b) Time series of principal axis current speed at inner shelf 

mooring Pt. Purisima (green) and mid-shelf mooring SAMI (black) for June – October, 2000. Positive currents 

are poleward. Vertical dashed lines indicate three relaxation events of weak or poleward winds. Poleward flow 

occurs at Pt. Purisima for wind relaxation events 1 and 2, but not at SAMI. Poleward flow occurs at both Pt. 

Purisima and SAMI for Event 3. c) Position-time contours of sea surface temperature for inner shelf moorings 

Ellwood, Alegria, Jalama, Boathouse, Pt. Purisima, and Pt. Sal. Locations of moorings and NDBC buoy 46023 

are shown in Fig. 3a. Arrow shows poleward propagation of warm water around Pt. Conception at ~13 km day-1

in June 2000. 

An example of the response of the inner shelf to wind relaxation is shown in Figure 4 as event 

1 when winds were almost zero (Fig. 4a). At this time currents flowed poleward at Pt. 

Purisima, but equatorward at SAMI (Fig. 4b). This event was accompanied by warm water 

reaching Pt. Purisima (Fig. 4c). A similar situation occurs during event 2, but in this case the 

winds reversed producing poleward flow at Pt. Purisima and nearly zero flow at SAMI. 

During event 3 flow was poleward at both Pt. Purisima and SAMI as warm water advected 

northward at ~13 km day-1 (arrow, Fig. 4c). 
Low Frequency Waves Observed 

9

Cudaback et al. (2004) find that poleward flow over the inner shelf is quite common year 

round as suggested by Fig. 4. This indicates that northward flow pathways for pollutants and 

larvae are fairly common year round. Furthermore, it suggests that the bio-geographic 

boundary at Pt. Conception is not simply due to flow since flow pathways around the point 

are frequent. We are currently exploring the effects that these warm flow events might have 

on organisms in inter-tidal habitats north of Pt. Conception. 

SIGNIFICANT CONCLUSIONS:

Surface circulation 

This study supports the following conclusions about the surface circulation in the western 

Santa Barbara Channel: 

1. Variability in the persistent cyclonic eddy-like circulation is controlled by a 

combination of local wind forcing and remote forcing by coastal trapped waves. 

An important conclusion of this study is that topographic Rossby modes exist in the 

channel over the Santa Barbara Basin and dominate the circulation in the 10-20 day 

band. 

2. Topographic Rossby modes appear as sequences of propagating eddy-like features 

with horizontal scales of about 30 km. The sequences last up to a few months and 

occur intermittently throughout the year. The surface velocity distribution of 

cyclones and anticyclones are anti-symmetric with a mean propagation speed of ~5 

km day-1 and relative vorticity magnitudes of order 0.1 f, where f is the local 

Coriolis parameter. 

3. The topographic Rossby modes appear to be forced by propagating coastal trapped 

waves which have been described in previous studies (e.g. Auad and Henderschott 

(1997), Auad et al. (1998) 

4. Conditional averaging based on the wind field shows that two-dimensional surface 

flow patterns over the inner shelf (10-15 m water depths) are strongly coupled to 

the wind field in the western Channel. Strong along-channel wind gradients 

coincide with cyclonic circulation and the so-called convergent flow state (e.g. 

Dever, 2004). Weak along channel wind gradients coincide with broad equatorward 

flow on the inner shelf and the upwelling state. Weakening or reversals of the wind 

patterns coincide with strong cyclonic circulation and strong poleward flow along 

the inner shelf of the mainland coast. 

5. Flow over the mid-shelf as observed by HF radar and an array of moorings shows 

that inner shelf flow patterns (10 - 15 m water depths) is often qualitatively similar 

to flow patterns over the mid-shelf (100 m water depths) for the upwelling state 

and, to a lesser extent, for the convergent state. 

6. Flow over the inner shelf appears to respond more strongly to relaxation events and 

reversals in the wind field than does the mid-shelf. Events frequently occur in 

which poleward advection of warm waters frequently occurs on the inner shelf, but 

not on the mid-shelf. 
Final Technical Summary - Beckenbach and Washburn 

10

Marine Ecology 

This study supports the following conclusions related marine ecology and pollution transport: 

the research: 

1. The predominant circulation pattern in the vicinity of Point Conception, CA 

probably cannot account for the bio-geographic boundary there because of the 

frequent occurrence of flow reversals on the inner shelf associated with wind 

relaxation events. 

2. Northward transport around Point Conception, CA of pollutants and larvae of 

marine organisms, is more likely near shore during wind relaxation events than in 

deeper waters offshore. Such events on the inner shelf are not consistently 

predictable using current observations farther offshore over the mid-shelf (100-200 

m water depths). 

3. Residence times of pollutants and passive larvae in the upper waters of the western 

Santa Barbara Channel are shorter when topographic Rossby modes are present. 

The modes are an important factor in controlling the stability of the cyclonic 

circulation in the channel; when present they disrupt this circulation. 

 The operational goal of putting real-time data from the HF radar network onto the 

internet was accomplished. Near real-time current observations from the array shown in Fig. 

1 are available at http://www.icess.ucsb.edu/iog/codar_realtime.htm. 

STUDY PRODUCTS: 

Publications: 

Beckenbach, E. H. (2004). "Surface circulation in the Santa Barbara Channel: An application 

of high frequency radar for descriptive physical oceanography of the coastal ocean". 

Ph.D. Dissertation, Interdepartmental Program in Marine Science. University of 

California, Santa Barbara, pp 126. 

Beckenbach, E. H. and L. Washburn (2004) "Low frequency waves in the Santa Barbara 

Channel observed using high frequency radar", in press, Journal of Geophysical 

Research. 

Cudaback, C. N., L. Washburn and E. P. Dever (2004) "Inner shelf circulation near Point 

Conception, California", Continental Shelf Research, submitted. 

Emery, B. M., L. Washburn and J. Harlan (2004) "Evaluating CODAR high frequency radars 

for measuring surface currents: observations in the Santa Barbara Channel", Journal of 

Atmospheric and Oceanic Technology, submitted. 

Nishimoto, M. M. and L. Washburn (2002) "Patterns of coastal eddy circulation and 

abundance of pelagic juvenile fish in the Santa Barbara Channel, California, USA", 

Marine Ecological Progress Series, 241, 183-199. 
Low Frequency Waves Observed 

11

Research Presentations: 

2001 "Surface circulation on the South-central coast: Mechanisms for larval transport and 

retention", seminar in the Dept. of Atmospheric Science, UCLA, 24 January. 

2001 "Variability in mesoscale oceanographic processes corresponds to variability in the 

distribution and abundance of rockfish (sebastes spp.) juveniles", Schroeder, D M , 

M.M. Nishimoto, and L. Washburn, American Society of Limnology and 

Oceanography, Albuquerque2001, Albuquerque, NM, 12-16 February. 

2001 "The physical environment of the Santa Barbara Channel", seminar presented to 

volunteers of the Channel Islands National Marine Sanctuary", Chase Palm Park, 1 

March. 

2002 “Observations of Wavelike Phenomena in the Santa Barbara Channel Using HF Radar”, 

Beckenbach, E.H. and L. Washburn, Ocean Sciences Meeting, Honolulu, HI, 11-15 

Feb. 

2002 “An Observational Network for Multidisciplinary Time Series on the Central California 

Coast”, Washburn, L., S. Gaines, E. P. Dever, and D. Reed, Ocean Sciences Meeting 

February, Honolulu, HI, 11-15 Feb. 

2002 “Observations of Wavelike Phenomena in the Santa Barbara Channel Using HF Radar”, 

Beckenbach, E.H., and L. Washburn, Eastern Pacific Ocean Conference, Stanford 

Sierra Camp, Fallen Leaf Lake 23-26 Sept. 

2002 “How Accurate are Total Vector Surface Currents from a Single HF Radar Site?”, 

Emery, B. M., L. Washburn, J.A. Harlan, Ocean Sciences Meeting February, Honolulu, 

HI, 11-15 Feb. 

2002 “Circulation near Pt. Conception California”, Cudaback, C., and L. Washburn, PISCO 

Symposium, Monterey, CA, 10 March. 

2002 “An Examination of Small-Scale Coastal Eddies and Pollution Hazards off California 

Using an Integrated Multi-Sensor/In-Situ Approach”, by P. M. DiGiacomo, B. Holt, and 

L. Washburn, AIRSAR Workshop, Jet Propulsion Laboratory, Pasadena, CA, 5 March. 

2002 “High frequency sampling of nearshore coastal circulation and invertebrate settlement 

near Santa Barbara California”, C. Cudaback, L. Washburn, J. Caselle, C. Blanchette, B. 

Gaylord, Eastern Pacific Ocean Conference, Timberline Lodge, OR, 25-28 Sept. 

2002 “A coastal observing system on the South-Central Coast for understanding links between 

the regional circulation, pollutant transport, and dispersion, L. Washburn, D. Reed, C. 

Ohlmann, C. Cudaback, E. Dever, California and the World Ocean, Santa Barbara, CA, 

27-30 Oct. 

2002 “Inner-Shelf Circulation Near Point Conception, California”, Cudaback, C., L. 

Washburn, E..P. DeverOcean Sciences Meeting February, Honolulu, HI, 11-15 Feb. 

2002 “How does the ocean flow in the Santa Barbara Channel?”, Geography Awareness Week 

presentation to Sue Bupperts and 2 other 5th class, Adams School, 18 November. 

2002 “How does the ocean flow in the Santa Barbara Channel?”, Geography Awareness Week 

presentation to 5th classes of Steve Bergdahl and Jennifer Edmonston, Adams School, 26 

November. 

2002 “Pollution Hazards Off the Southern California Coast: Satellite and In Situ Observations 

of Naturally Occurring Oil Seepage, Storm Water Runoff and Wastewater Plumes. 

Water Quality: Ocean Modeling, Observations and Remote Sensing”, P. M. DiGiacomo, 
Final Technical Summary - Beckenbach and Washburn 

12

B. Holt, and L. Washburn, California and the World Ocean, Santa Barbara, CA, 27-30 

Oct. 

2003 “Vorticity, divergence, and flow states in the western Santa Barbara Channel”, 

Beckenbach, E.H., and L. Washburn, Eastern Pacific Ocean Conference, Wrigley 

Institute, Catalina Island, 24-27 Sept. 

2003 “Low-frequency dynamics and nutrient flux to the inner shelf of the Santa Barbara 

Channel”, E. McPhee-Shaw, L. Washburn, and D. Siegel,Eastern Pacific Ocean 

Conference, Wrigley Institute, Catalina Island, 24-27 Sept. 

2003 “Sub-mesoscale eddies along the northern Santa Barbara Channel: A possible 

mechanism for nutrient delivery to the inner shelf”, Bassin, C.J., L. Washburn, and E.E. 

McPhee-Shaw, Eastern Pacific Ocean Conference, Wrigley Institute, Catalina Island, 

24-27 Sept. 

2003 “An Update on the Regional Ocean Observing Systems along the US West Coast”, 

Barth, J., A. Baptista, M. Kosro, D. Martin and J. Newton, L. Rosenfeld, F. Chavez, 

M. McManus and M. McNutt, E. Terrill and L. Washburn , T. Garfield, J. Hunter, 

Eastern Pacific Ocean Conference, Wrigley Institute, Catalina Island, 24-27 Sept. 
Low Frequency Waves Observed 

13 

FINAL STUDY REPORT 

Summary 

A three-year record of high frequency (HF) radar observations of surface currents in the 

western Santa Barbara Channel (SBC) reveals sequences of alternating cyclonic and 

anticyclonic vortices propagating westward with a period of about two weeks. The sequences 

last up to a few months and occur intermittently throughout the year. The surface velocity 

distribution of cyclones and anticyclones are anti-symmetric with a mean propagation speed 

of ~5 km day-1 and relative vorticity magnitudes |ζ| of order 0.1 f, where f is the local Coriolis 

parameter. The Coriolis parameter quantifies the effect of the earth’s rotation with latitude. 

The value of |ζ|/f = 0.1 indicates that the earth’s rotation is important the dynamics of the 

vortices. These propagating vortices resemble the propagating cyclones in the 10-25 day 

pass-band reported in the SBC by Harms and Winant (1998). 

Complex empirical orthogonal function (CEOF) decomposition in the 10-20 day pass-band, 

following the method of Wallace (1972) for detecting propagating features, partitions 

variance into two dominant modes. The first mode with an average period of 14.4 days 

explains 45% of the velocity variance and represents the alternating cyclones and 

anticyclones that are evident in the band-pass filtered record. The second mode, with an 

average period of 13.3 days, explains 25% of the velocity variance and mainly represents 

alongshore fluctuations. Amplitude functions of the two modes correlate with in situ current 

time series at 5 and 45 m depths obtained from moorings at the east and west channel 

entrances suggesting coupling between the modes and the larger-scale circulation of the 

northern Southern California Bight. 

Auad and Henderschott (1997), Auad et al. (1999) investigated the relationship between lowfrequency flow in the 6 - 18 day band and forcing by wind stress and remote adjusted sea 

level. The remotely-forced flow was explained as a coastal trapped, low-mode hybrid-wave 

with characteristics of both Rossby and Kelvin waves. The higher spatial resolution HF radar 

observations support this interpretation since the period and along-shore flow of mode 2 are 

consistent with a coastal trapped wave. 

We hypothesize that mode 1 is a resonant response of the Santa Barbara Basin in the form of 

a trapped topographic Rossby mode (TRM). A harmonic stream function representation of 

the spatial mode resembles the predicted pattern based on a simplified analytical model of a 

fundamental TRM in a closed basin. Peak relative vorticities over the basin are about a factor 

of four higher than over the edges, indicating topographic control. The amplitude of mode 1 is 

consistently large when the frequency difference between modes 1 and 2 is small. This 

suggests that the propagating vortices of mode 1 are a basin-scale resonant response to the 

coastal trapped wave represented by mode 2. 
Final Study Report - Beckenbach and Washburn 

14

1. Background 

The coastal ocean supports diverse circulation patterns due to the imposition of the coastal 

boundary and sloping topography. Along straight coastlines, coastal upwelling Sverdrup 

(1938) and coastally trapped-waves (CTWs) including barotropic Kelvin and topographicRossby modes are well known examples with straight-forward analytical descriptions Brink 

(1991). Real coastlines can be irregular with complex offshore topography and, in the 

presence of stratification, 3-dimensional fluid structures are common including jets, eddies, 

fronts and a series of baroclinic Kelvin and Rossby waves. The Santa Barbara Channel (SBC) 

is an example of a coastal region with variable bottom slope, offshore islands, and a deep 

basin, the Santa Barbara Basin (SBB). The SBC, located at the northern end of the Southern 

California Bight (SCB), runs east to west approximately 100 km between Pt. Mugu and Pt. 

Conception. The Northern Channel Islands of Anacapa, Santa Cruz, Santa Rosa and San 

Miguel form the Channel’s southern boundary. The 40 km wide channel is a region where 

coastal circulation patterns are complicated by irregular topography, interacting water masses 

and strong wind stress forcing. 

Circulation patterns in the SBC were first assessed by Kolpack (1971) based on hydrographic 

surveys conducted during 1969 and 1970 in response to the Santa Barbara Channel oil spill of 

1969. Drifter cards released during these surveys revealed that a complex field of eddies 

prevailed in the eastern channel, positioned between a large persistent cyclonic cell in the 

western channel and northwest flow at the eastern entrance. Later research conducted during 

the Organization of Persistent Upwelling Systems (OPUS) project and the Santa Barbara 

Channel Circulation Study (1983-1984) examined local flow patterns in response to the 

frequent, vigorous wind forcing common in the western channel. Brink (1983), Huyer 

(1983), Winant et al. (1987) found that near Pt. Conception and to the north flow responds to 

alongshore wind stress following classical Ekman dynamics and the thermal wind 

relationship. In contrast, Atkinson et al. (1986), Brink and Muench (1986), Barth and Brink 

(1987) described flow within the SBC as a complex system of eddies, jets, and fronts with 

poor correlation to local wind forcing. More recently, several studies have described flow in 

the SBC as a sequence of synoptic states consisting of upwelling/relaxation and cyclonic 

regimes regulated through a momentum balance including significant contributions from wind 

stress, wind stress curl, sea level tilt and Coriolis terms Auad and Henderschott (1997), Harms 

and Winant (1998), Oey (1999), Winant et al. (1999), Oey et al. (2001). 

An additional circulation pattern observed by Harms and Winant (1998) within the SBC is 

that of “propagating cyclones”. They observed that AVHRR satellite images often indicate 

cyclonic eddies drifting westward with a period of approximately 14 days. As one cyclonic 

eddy approached the western entrance, another appeared north of the western tip of Santa 

Cruz Island. These features extended below the thermocline based on observation from an 

array of vector measuring current meters (VMCMs) at depths of 5 and 45 meters placed 

around the SBB. Within the 10 to 25 day band, maximum lagged correlations of longitudinal 

velocities between neighboring stations indicated a translation rate of 0.06 m s-1. 

Auad and Henderschott (1997), Auad et al. (1999) investigated mechanisms of current 

generation and volume transport at the eastern entrance of the SBC in the 6 to 18 day band. 
Low Frequency Waves Observed 

15 

They found significant linear relationships between transport and both local wind stress and 

remote adjusted sea level (ASL). Regional-scale ASL behavior was consistent with 

theoretical predictions of a poleward propagating hybrid Kelvin-topographic Rossby wave 

Brink and Chapman (1985). Their mass-transport time series for the east and west entrances 

and the inter-island passages of the SBC also exhibited energy peaks at periods near 14 days 

In this study, propagating flow features in the 10-20 day band, comparable to the bands 

identified by Auad and Henderschott (1997), Harms and Winant (1998), are further explored. 

Using high frequency (HF) radar with coverage over SBB, we have isolated the surface 

expression of what we hypothesize is a low frequency resonant response of the basin to 

forcing by CTWs propagating poleward along coast of the Southern California Bight (SCB). 

The resonant response resembles a barotropic trapped Rossby mode (TRM) similar to the 

TRMs identified in the Straits of Sicily Pierini (1996) and on the Iceland-Faeroe Ridge Miller 

et al. (1996). 

The propagating eddy patterns within the 10-20 day band do not dominate circulation within 

the channel, but represent ~15% of the subtidal velocity variance. However these patterns are 

a curious aspect of the local circulation which may affect other flow regimes. For example, 

the propagating eddy patterns appear to constructively and destructively interfere with a 

persistent cyclonic circulation found over the SBB that can retain juvenile fishes Nishimoto 

and Washburn (2002). In addition, the regions between eddy centers are alternating crosschannel jets which propagate westward along with the vortices and may significantly 

influence cross-channel advection between the mainland coast and the offshore islands. 

2. Observations 

Hourly surface current observations from an array of three HF radars from 1 January 1998 

through 31 December 2000 are the primary data used in this study. Observations for the 

period 2001-2003 are consistent with the three year period of this study. The HF radars were 

direction-finding systems (Coastal Ocean Dynamics Applications Radar or CODAR, 

manufactured by CODAR Ocean Sensors, Ltd. of Los Altos, CA) operating at ~12 MHz over 

a range of 42 km with resolution of 1.5 km and azimuthal resolution of 5o

. Radial current 

vectors were available from three radars on the mainland coast (from east to west) at Coal Oil 

Point (COP), Refugio State Beach (RFG), and Pt. Conception (PTC) (Fig. 1). 

Figure 1. Study area showing the Santa Barbara Channel and Santa Barbara Basin. Inset shows study area 

(shaded box) on California Coast. Color contours show percent coverage from the HF radar array over the 
Final Study Report - Beckenbach and Washburn 

16

three year study period. HF radar locations at Point Conception (PTC), Refugio (RFG), and Coal Oil Point 

(COP) are indicated by dots in circles. SAMI, SMIN, SMOF, and AMNI are current meters deployed by the 

CCS. SMI, SRI, SCI, AMNI and Pt. M. identify San Miguel, Santa Rosa, Santa Cruz, Anacapa Islands, and Pt. 

Mugu respectively.

Following Paduan and Rosenfeld (1996), eastward and northward velocity components were 

computed at points over a 2 km square grid. The grid consists of 360 contiguous points 

covering 1440 km2 centered over the SBB. Surface current vectors are calculated from all 

radial vectors within 3 km of each grid point using the least-squares method of Gurgel (1994). 

 

We subjectively determined the coverage area by attempting to maximize the size of the longterm foot print of the HF radar array while minimizing data gaps. Grid points were excluded 

within 3 km of the coastline to avoid contamination from overland signal returns and avoid 

the radar baselines. As described in Emery et al. (2004), spatial coverage from each site 

within the radar footprint varied over a range of time scales due to several factors including 

failure of the radar algorithms to determine radial currents, broadcast interference, 

ionospheric propagation, and equipment failures. Surface current vectors are available for a 

minimum of 50% and maximum of 95% of the three-year record at individual grid points 

(color contours, Fig. 1). Averaged over all grid points, the velocity time-series over the 

coverage area is 80% populated. Because our analysis focused on time scales greater than 10 

days, only the longer-lasting gaps were a major concern in the analysis. Fortunately, these 

were infrequent in the record, particularly in 1998 and 1999. 

Data from long-term moorings, maintained by the Center for Coastal Studies (CCS) at the 

Scripps Institution of Oceanography, place the higher spatial resolution HF radar observations 

in a larger spatial context and provide sub-surface observations. Four moorings (Anacapa 

Middle, ANMI; San Miguel Inshore, SMIN; San Miguel Offshore, SMOF; and Point Sal 

Middle, SAMI) with vector measuring current meters (VMCMs) at 5m and 45m depths 

provided velocity measurements every 4 minutes at the east and west entrances and north of 

Pt. Conception (Fig. 1). Hourly, quality-controlled data were made available to us by CCS. 

Data concurrent with the HF radar time series were available through 19 November 1999 and 
Low Frequency Waves Observed 

17 

13 August 2000 for the 45 meter and 5 meter VMCMs, respectively. Harms and Winant 

(1998), Hendershott and Winant (1996), and Chen and Wang (1999) describe the mooring 

data in detail. 

3. Methods 

We used several data processing steps to characterize narrowband wave-like circulation 

patterns. Data gaps were filled, the frequency band containing the wave-like motions was 

identified, and the time series were filtered to isolate the relevant frequency band. The time 

series were then decimated to one observation per day. Relative vorticity ζ proved useful in 

quantifying the propagating vortices because of their strong rotation. We computed hourly 

estimates of ζ at grid points using centered first differences at points inside the coverage 

footprint (i.e. only at points where total velocity vectors were available at the four adjacent 

points). ζ estimates were normalized relative to planetary vorticity f (8.2x10-5s

-1 at 34.25o N). 

Some basic characteristics of the propagating vortices, such as length scales and period, were 

determined by examining the filtered time series. Then complex empirical orthogonal 

function (CEOF) decomposition was used to quantify the strength of the dominant flow 

patterns. Stream function estimates of the dominant modes were used for flow visualization 

and for comparison of the propagating vortices with an analytical TRM model. 

3.1 Missing Data 

Gaps occurred in all of the time series: 19.5% were missing over the 3-year record of HF 

radar data; 12.6% were missing for the 5 m moored current data records; and 13.2% were 

missing for the 45m moored records. Because some of the time series analysis methods 

employed, such as digital filtering and CEOF decomposition, required complete time series, it 

was necessary to estimate missing portions of the data records. We assumed (and verified) 

that the velocity observations were sampled from a multivariate normal distribution. Missing 

observations were optimally estimated using maximum likelihood principles as described by 

Orchard and Woodbury (1972) and Beale and Little (1975). 

This method is a two-step, iterative multiple linear regression procedure. One step is 

parameter estimation of the data’s underlying probability distribution conditioned on the 

observed data and the prior estimates of the missing data. The other step updates estimates of 

missing values by regression on the observed values using the estimated distribution 

parameters, in this case the mean vector and covariance matrix. The procedure starts on 

either step with some sensible initial estimates of the missing values or the distribution 

parameters and continues until convergence within a chosen tolerance is met. More details on 

the procedure are provided by Beckenbach (2004), Beckenbach and Washburn (2004). 

3.2 Frequency band selection and filtering 
Final Study Report - Beckenbach and Washburn 

18

Previous studies of low-frequency flow in the SBC have focused on the 10-25 day band 

Harms and Winant (1998) and the 6-18 day band Auad and Henderschott (1997). We 

identified westward propagating features within the overlapping 10-20 day band by 

computing the squared coherence γ

2

 for time series of ζ along the SBC axis as discussed 

below in section 4. To further examine the flow in this band, we digitally filtered the surface 

current time series in two steps using MATLAB numerical routines. The two-step filtering 

process was necessary because the pass-band frequency range (0.05-0.1 cycles per day, cpd) 

was a small fraction (1/600th) of the total bandwidth (0-12 cpd). First, a fifth order 

Butterworth low-pass filter with a half-power cutoff corresponding to a 36 hr period was 

applied to the hourly velocity time series and the data were decimated to one point per day. 

Second, the decimated data were band-pass filtered to retain periods between 10 and 20 days 

using a ninth order Type II Chebyshev filter with ripple peaks of –40 db relative to the 

passband. Both filters were applied in the forward and reverse directions to eliminate phase 

shifts. 

3.3 Complex empirical orthogonal function analysis 

 

Once the current time series were filtered to eliminate variance outside of the 10-20 day band, 

we computed complex empirical orthogonal functions (CEOFs) following the method of 

Wallace (1972) to evaluate the spatial patterns and temporal evolution of the dominant modes 

of variability. Auad and Henderschott (1997) used the technique to examine low frequency 

coastal waves propagating through the SBC based on moored current and bottom pressure 

time series. They also present a succinct description of the method. In the CEOF procedure 

each time series (u and v are treated independently as scalars) is augmented with an imaginary 

component to provide phase information to enable detection of variance propagation through 

the array. 

CEOFs differ from the more conventional real-EOFs because the associated eigenvalue 

problem is based on the band-averaged cross-spectrum matrix rather than the standard data 

covariance matrix. With real-EOFs propagating features can be spread across several modes, 

obscuring their detection. With narrow-banded CEOFs, propagating modes are distinct and 

uncorrelated across a finite frequency band. We argue that the two dominant CEOFs found in 

the 10-20 day band represent distinct propagating waves, although no such dynamical 

interpretation is implied by the CEOF method which is purely statistical. 

3.4 Stream Function Estimation 

The stream functions Ψ was used to estimate dynamic topography associated with surface 

flow patterns and to compare these results with a simple theoretical model. An estimate of the 

nondivergent flow field, recovered by differentiation of the streamfunction, is a useful firstorder characterization of the circulation patterns. The residual velocity fields contain the 

corresponding divergent component of circulation. Ψ was computed using harmonic 

expansions as described by Auad et al. (1998), Dever et al. (1998). The expansions were 

estimated by minimization of the square of the difference in the u (eastward) and v 

(northward) velocity components between velocity observations and non-divergent velocities 

based on the derivatives of Ψ. A similar method was used by Vastano and Reid (1985) with 
Low Frequency Waves Observed 

19 

two-dimensional (2-D) half-range sine expansions with constant Ψ on the domain boundaries. 

Auad et al. (1998), Dever et al. (1998) used the approach on a boundary-fitted orthogonal 

coordinate system for arbitrary Ψ along open lateral boundaries with explicit boundary 

conditions imposed for the alongshore boundaries. When open boundaries circumscribe the 

domain, as in this analysis, 2-D Fourier basis functions with arbitrary phase can be used to 

avoid edge constraints. Stream function contours are scaled as η = Ψf/g to approximate 

changes in sea surface elevation. 

4. Results 

4.1 Propagating Rotary Flows 

 

Preliminary analysis of raw hourly surface current patterns from the HF radars revealed 

westward propagating rotary flow patterns such as those shown in Fig. 2. The example shows 

two oppositely rotating eddy-like patterns over the Santa Barbara Basin on 26 May 1999. 

Figure 2. Two counter rotating eddies in the coverage area over the Santa Barbara Basin on 16 May 1999 at 

0300 GMT. Color contours give ζ/f according to the color scale to the right. The white line identifies the 

transect used to examine along channel variability of propagation.

The cyclonic flow pattern on the western boundary of the basin is intensified on its western, 

southward flowing side with maximum flow speeds of ~0.5 m s-1 and ζ/f of order 1. The anticyclonic pattern on the northeast side of the basin has lower flow speeds, is more symmetric, 

and has ζ/f of order -0.6. Both patterns span the north-south extent of the basin with 

horizontal length scales on the order of the basin width or about 25 km. Sequences of images 

suggested a westward propagation speed of about 4.7 km d-1. Similar propagating flow 

patterns at comparable speeds have been found in other circulation studies of the SBC. For 

example, Harms and Winant (1998) (their Plate 1a) show a westward propagating cyclonic 

eddy visualized by a sequence of satellite sea surface (SST) images in August 1994. 

 
Final Study Report - Beckenbach and Washburn 

20

Typically, energetic flow patterns in the SBC obscure propagating rotary structures like those 

of Fig. 2. One such pattern is the mean tendency for cyclonic flow in the western SBC as 

discussed by Harms and Winant (1998), Hendershott and Winant (1996), and Atkinson et al. 

(1986), Brink and Muench (1986), Auad et al. (1999). 

 

From these HF radar observations we estimate a mean ζ for the three-year record of 0.18f

over the radar coverage area shown in Fig. 1; maximum observed values averaged over the 

coverage area are on the order of 0.5f. Local values exceeding f are observed occasionally as 

in Fig. 3. Often propagating eddies appear as modulations of the larger cyclonic flow pattern: 

propagating cyclones temporarily intensify the pattern, propagating anti-cyclones weaken it. 

 

Time-longitude contours for 1999 (Fig. 3a) show the evolution of ζ/f along an east-west 

transect down the channel axis (transect shown in Fig. 2) calculated using the filled-in hourly 

time series with no filtering. Coherent rotational features, mostly cyclonic, at scales 

approaching the basin width appear as continuous, nearly vertical bands. The dashed vertical 

line of Fig. 3 identifies the time of the vortex pattern of Fig. 2. The flow varies on timescales 

of days to weeks over the basin, but a tendency for cyclonic flow (red-biased contours) is 

evident. 

Figure 3. a) Time-longitude contours of ζ/f computed from hourly HF radar observations along transect shown 

in Fig. 3 for 1999. b) as in panel a) but with ζ/f low-pass filtered with a cutoff frequency of 1/36 hours-1. c) as 

in panel a) but with ζ/f band-pass filtered with cutoff frequencies (1/10) days-1 to (1/20) days-1. Dashed vertical 

line indicates time of velocity pattern of Fig. 3. Color scales at right in each panel indicate values of ζ/f. 

Periods of negative vorticity (blue-biased contours) lasting up to a few weeks also occur, 

particularly along the transect’s eastern portion. A general negative sloping of the contours 

indicates persistent westward propagation of cyclonic and anti-cyclonic vorticity features 

along the SBC axis. Low pass filtering of the time series (cutoff frequency of 1/36 hr-1) more 

clearly shows the westward propagation by removing variance at tidal and higher frequencies 

(Fig 3b) It also clarifies the occurrence of negative vorticity, particularly on the eastern 

portion of the transect. 
Low Frequency Waves Observed 

21 

 

To identify the dominant time scales associated with westward propagation, we computed the 

squared coherence, γ

2

, and phase difference, φ, between vorticity time series at the transect 

endpoints. A peak in γ

2

 between 0.05-0.1 cpd indicates significant coherence (95% 

confidence threshold) for periods of 10-20 days (Fig. 4). The γ

2

 peak of 0.5 corresponds to a 

period of approximately 15 days. φ in the 10-20 day band ranges from 195-240o with the peak 

corresponding to 210o. The positive φ of 210° indicates that vorticity at the east end of the 

transect leads the west end by about nine days, consistent with the westward propagation 

inferred from Fig. 3. The distance between the ends is 42 km so the implied westward 

propagation speed is ~ 4.7 km d-1. 

Figure 4. a) Squared coherence γ

2

 and b) phase φ of ζ between the ends of the transect shown in Fig. 2. 

Dashed lines indicate the frequency band 1/10 day-1 to 1/20 day-1 over which γ

2

 is significant. Dotted lines 

shows 95% significance threshold. 

Based on the γ

2

 peak, velocity data were band-pass filtered to remove variance outside the 10-

20 day pass band. Contours of ζ f in the pass band show distinct alternating stripes which 

represent trains of counter-rotating features (Fig. 2c). This banding suggests a channel-scale 

instability or wave phenomenon. 
Final Study Report - Beckenbach and Washburn 

22

Figure 5. a) Longitude-time contours of ζ/f for 21 June to 21 July 1999. Color scale for the contours is given at 

the bottom. b) Surface velocity patterns at times indicated by horizontal lines in panel a). Sloping red (blue) line 

connects centers of cyclones (anti-cyclones) every three days. Arrow at lower left in each velocity pattern 

indicates 10 cm s-1. All data have been band pass filtered to retain frequencies from 1/10 day-1 to 1/20 day-1. 

The correspondence between the red and blue stripes and propagating cyclonic and anticyclonic vortices is apparent when the stripes are compared with patterns of band-pass filtered 

velocity vectors (Fig. 5). During the period 21 June – 21 July 1999 alternating anti-cyclonic 

and cyclonic vortices move through the coverage area. The propagating pattern varies 

strongly but recurs over the 3-year record with vortex trains lasting up to a few months. 

 

Vorticity time series along the transect reveals that the radar footprint is often too small for 

observing the complete evolution of the propagating features. Some of the stripes in Fig. 3c 

are cut off at both ends, although this occurs more frequently at the west end of the transect. 

There are no periods during which the HF radar coverage extended farther east so 

investigation into an eastward origin is precluded. During May - October 1998 coverage 

extended an additional 12 km to 120.4o W, over the western sill of the basin. We used data 

from this area to examine the evolution of the vortices as they propagate over the sill. Other 

periods of continuous coverage over this area were too short for analysis at periods of 10-20 

days. 

 

ζ/f contours over the extended coverage area show a marked decrease in relative vorticity as 

the vortices propagate westward over the western sill (Fig. 6a). Some propagating variance in 

the 10-20 day band persists over the sill such as in late June and early July 1998. 
Low Frequency Waves Observed 

23 

Figure 6. a) Longitude-time contours of ζ/f for 1 June – 1 September 1998 along extended transect (see text). 

Color scale for ζ/f is given at right. b) Solid line (left scale) shows average of envelope of amplitude ζ/f profile 

between 15 June – 15 August 1998. This time period is shown by dotted lines, panel a). Dashed line (right 

scale) shows bottom contour along transect of Fig. 2.

Shading of the contours indicates that the largest values of ζ/f are found near 120.2o W, above 

the slope leading to the western sill. Then the amplitude of ζ/f fluctuations decreases rapidly 

over the upper slope and remains small over the sill. This is confirmed in a comparison of the 

average envelope of ζ/f and the bathymetric profile along 34.27o N (dashed line, Fig. 6b). 

The amplitude envelope of ζ/f averaged over the 15 June – 15 August 1998 interval, shown 

by the dotted bars in Fig. 6a, increases from 0.11 on the eastern end of coverage area to a 

peak of 0.55 at 120.17o W. West of the peak it decreases rapidly to about 0.15 over the sill 

itself. A similar reduction in ζ/f amplitude at the ends of the transect were indicated for the 

entire 3-year record but the trend was not as well resolved due to the limited westward extent 

of the transect. 

 

The pattern of striped contours in Fig.6a and the eddy velocity patterns of Fig. 5b suggest 

symmetry between the cyclonic and anticyclonic features. We quantified this symmetry by 

conditionally averaging numerous cyclones together and numerous anti-cyclones together at 

similar phases during their propagation. To estimate the velocity field of the propagating 

cyclones, all times over the 3-year band-pass filtered record were identified which had 

maxima of ζ/f > 0.2 at a point near the center of the SBB (circle, Fig. 7a). A total of 32 

maxima satisfied this condition. At these times fully developed cyclones occupied the central 

portion of the basin. Then for each grid point at these times the velocity components, u and v, 

were individually averaged. The resulting pattern is shown as black arrows in Fig. 7a. A 

similar procedure for anti-cyclones found 35 peaks with ζ/f < -0.2. Velocity components -u 

and -v for the anti-cyclones are shown as gray arrows in Fig. 7a. Together these cyclones and 

anticyclones account for the upper 45% of |ζ/f |for the 3-year record. Strong spatial 

correlation among the vectors (ρ =-0.998; r2

=0.995) indicates the high degree of antisymmetry between the mean velocity fields of the cyclones and anti-cyclones over most of the 
Final Study Report - Beckenbach and Washburn 

24

coverage area. Large differences in current direction only occur over the western sill where 

velocity vectors are small. 

 

Because of the symmetry between the cyclones and anti-cyclones and their radial similarity, 

we computed representative radial profiles of tangential velocity, vt(r), and radial velocity, 

vt(r), where r is the distance from the center of the velocity patterns (plus signs (+) in Fig. 7a 

and 7b). 

Figure 7. a) Black arrows show conditionally averaged cyclonic velocity pattern and gray arrows show 

conditionally averaged anti-cyclonic velocity pattern. Velocity components of anti-cyclonic pattern have been 

multiplied by -1 for comparison. Patterns are formed by averaging velocity fields together subject to the 

conditions: (1) local maxima (for cyclones) and minima (for anti-cyclones) occur at the location indicated by the 

black circle; and (2) these maxima and minima satisfy |ζ|/f > 0.2. Velocity scale at lower left. b) Cyclonic 

velocity from CEOF mode 1 for phase φA1= 221o. In both panels, dotted circle indicates area, with center at plus 

(+) sign, used to produce the radial distributions of Fig. 8.

We used the mean velocity patterns of Fig. 7a with cyclones combined with Stoke’s theorem 

and the divergence theorem applied to a circular area were used to calculate the tangential 

velocity component vt(r) and the radial component vr(r) as functions of radius from the center 

of the eddies. The circular area was centered on the mean eddy center (plus sign (+), Fig. 7a). 

Also computed were the radial distributions of ζ(r) and the horizontal divergence, div v(r). 

Tangential and radial velocities at the eddy center were assumed to be zero. Profiles of vt(r) 

and vr(r) are linearly related (r2

=0.97), increasing from zero at the eddy center (extrapolating) 

to maximal values at ~10 km (Figures 8a and 8b). Signs are opposite with positive vt(r), 

representing cyclonic circulation, associated with negative vr(r), representing convergent flow 

towards the eddy center. The profile of vt(r) increases from ~2 cm s-1 at 2 km radius to a 
Low Frequency Waves Observed 

25 

maximum of ~7 cm s-1 at 10 km before decreasing to 5-6 cm s-1 at 16 km (Fig. 8a). The vr(r) 

profile is negative everywhere, lying in the range -0.5 to -1.5 cm s-1 (Fig. 8b). Radial profiles 

of ζ(r)/f and div v(r) are similarly related (Figures 8c and 8d). Extreme values of opposite 

sign, 0.28 for ζ(r)/f and -4.1x10-6 s-1 for div v(r), occur at the cyclone center and transition 

monotonically towards zero at 16 km, on the outer edge. Anti-cyclonic flow (negative vt(r) 

and ζ(r)/f) is associated with divergence (positive vr(r) and div v(r)) and is represented by 

scaling the radial profiles of Fig. 8 by a factor of -1.

Figure 8. Mean radial distributions of a) tangential velocity, vt(r), b) radial velocity, vr(r), c) normalized 

vorticity, ζ(r)/f, and d) divergence, div v. Solid lines are averages based on conditionally averaged patterns of 

Fig. 7a and dashed lines are based on CEOF mode 1 pattern of Fig. 7b. Scatter about the profiles are point 

calculations based on the CEOF mode 1 pattern. The scatter represents variability arising due to departure of the 

mean distribution from radial symmetry. 

4.2 Modes of variance over the Santa Barbara Basin 

Time-longitude contours of ζ/f (Fig. 3) and the time series of velocity distributions (Fig. 5) 

suggest that trains of westward propagating cyclones and anti-cyclones are common over the 

SBB. We employed CEOFs to isolate two modes of propagating variance associated with the 

time-scales of these motions and then explored the relationship between the modes. 

 

The first two CEOF modes account for 45% and 20% the velocity variance in the 10-20 day 

band, respectively. The spatial structure of mode 1 is similar to the trains of cyclones and 

anti-cyclones as is seen by comparing the mean velocity field of the cyclones (Fig. 7a) with 

the velocity field of mode 1 at phase angle φA1= 221o

 (Fig. 8b). 

 

Westward propagation of cyclones and anti-cyclones over the SBB is evident over one 

complete cycle of mode 1 as shown in Fig. 9a. As φA1 progresses from 0 through π/2, an anticyclonic eddy translates westward and a cyclonic eddy enters the eastern edge of the 

coverage. At π the cyclonic eddy occupies the center of the basin; only a hint of the original 

anti-cyclonic eddy remains to the west. This sequence resembles the time series of velocity 
Final Study Report - Beckenbach and Washburn 

26

patterns of Fig. 5b. Stream function distributions scaled as η (Fig. 9a) indicate that the 

propagating eddies span the basin. Accompanying sea surface elevation differences between 

centers of the cyclones and anti-cyclones are on the order of 5 mm over separation distances 

of approximately 30 km. 

 

A strong correspondence exists between ζ/f in the 10-20 day band (Fig. 11a) and the 

amplitude of the first mode |A1(t)| (black line, Fig. 11b) over the 3-year record. Gaps in 

coverage appear as white vertical bands in Fig. 11a. Curves of the first and second mode 

amplitude functions |A1(t)| and |A2(t)| are continuous in Fig. 11b because data were filled 

using the technique described in Section 3. Large peaks in |A1(t)| occur from June 1998 

through January 1999 and from June through August 1999 (Fig. 3c) when striped vorticity 

contours are prominent. Mode 1 is relatively weak in winter and early spring 1998 and 1999 

and throughout 2000. φA1 increases steadily over the record with an average frequency <f1>= 

0.069±0.010 cpd corresponding to an average period of T1 = 14.3 d (Fig. 11c) with the given 

frequency envelope defined as ±1 standard deviation of the instantaneous frequency. Angle 

brackets < > denote a time average. 

Figure 9. a) Velocity patterns of CEOF mode 1 at values of phase φA1 shown at left of each panel. Sloping 

solid (dashed) lines connect centers of cyclones (anticyclones). Velocity scale is at lower left in bottom panel. 

b) As in a), but for CEOF mode 2. 

Mode 2, accounting for 20% of variance, exhibits a broad pattern of along-channel velocity 

fluctuations with much lower ζ than mode 1 (Fig. 9b). The amplitude of mode 2 |A2(t)| does 

not show any distinct seasonal trend and is typically smaller than |A1(t)| (Fig. 11b). Flow for 

mode 2 is generally eastward and northeastward when φA1 = 0, westward and southwestward 

when φA1 = π. Mode 2 has a slightly higher frequency than mode 1 with <f2>= 0.075±0.015 

cpd and mean period T2 = 13.3 d. The mode 2 stream function is a broad pattern of tilting 
Low Frequency Waves Observed 

27 

ηcontours which run diagonally across the channel from southwest to northeast (Fig. 10b). 

Along the shelf on the northern boundary of the basin they run approximately parallel to 

isobaths. Further south they cross isobaths. The maximum change in η across the center of 

the basin is ~ 5 mm. Crowding of η contours indicate highest flow speeds over the 

northeastern portion of the basin. Spreading η contours over the southwestern region 

indicates a broadening and weakening flow. Turning of contours near Santa Cruz Island 

when φA1 = 0 and π suggests that flow along the island coast is opposite that along the 

mainland. 

 

Although modes 1 and 2 explain 45% and 20% of the total velocity variance in the 10 – 20 

day band, respectively, their spatial distributions are biased such that the modes contribute 

over 60% of total variance in the regions where each dominates. The spatial distribution of 

variance indicates that mode 1 explains most of the variance over the basin and the steep 

slope on the northern edge of the basin while mode 2 explains most of the variance in the 

northeastern portion of the basin. Combined, the modes explain the most variance, 60 - 80%, 

over the northern slope of the basin and the least, 20 - 40%, along the southern slope. 

 

Frequency variability based on standard deviations is large compared with differences 

between the average values of f1and f2 such that the individual frequency envelopes overlap. 

Coupling between modes 1 and 2 is suggested by time series of |A1(t)| and the absolute value 

of the frequency difference |∆f(t)| = |f2(t) - <f1>| (Fig. 12). When |∆f(t)| is small and exhibits 

local minima, such as in early December 1998, late March and early July 1999, |A1(t)| is large 

and exhibits local maxima. Conversely, when |∆f(t)| exhibits local maxima, such as in midNovember 1998, the end of March and mid-June 1999, |A1(t)| exhibits local minima. 
Final Study Report - Beckenbach and Washburn 

28

Figure 10. a) Stream function for CEOF mode 1 corresponding to velocity patterns of Fig. 9a). b) As in a) but 

for CEOF mode 2. Contours indicate sea surface height differences with a contour interval of 0.5 mm. Dashed 

contours are negative. Black and gray vectors show correlated velocities (see text) at 5m and 45m, respectively, 

from CCS moorings. Velocity scales are shown on bottom panels. Current vectors at western-most current 

meter shown (SAMI) are displaced south of the actual mooring location. Fig. 1 shows all mooring locations. 

This temporal pattern occurs consistently over the 3-year record, although the amplitudes of 

maxima and minima in |A1(t)| are not related to |∆f(t)| in a simple linear way. For example, 

the peak in |A1(t)| at the beginning of December 1998 is higher than the peak of early January 

1999, even though its |∆f(t)| is larger. Similarly, the trough in |A1(t)| in late March 1999 is 

slightly deeper than the trough of mid June 1999, even though its |∆f(t)| is much smaller. 

 

The mean velocity distribution for the cyclonic eddy in Fig. 8a is similar to the first CEOF 

mode at A1 φ = 221o

 as shown in Fig. 8b. This CEOF distribution was used as the basis for 

recalculating radial profiles for comparison with those derived from conditional averages. A 

strength of the CEOF decomposition is the implicit incorporation within each complex mode 

of the entire time series. Averaging at a single phase angle depends on the continuity of the 

propagating pattern at all phase angles over all times. In addition, no arbitrary constraints on 

vorticity magnitude, such as the vorticity threshold used in the conditional averages of Fig. 7, 

are required to extract the dominant velocity distributions. 

Radial distributions of vt(r), vr(r), ζ( r)/f , and div v computed from mode 1 are similar to 

those computed from the mean flow patterns of (Fig. 7a). 
Low Frequency Waves Observed 

29 

Figure 11. a) Time-longitude contours for 1998-2000 of ζ/f band pass filtered with cutoff frequencies (1/10) 

days-1 to (1/20) days-1. Color scale as in Fig. 3c. b) Time series of CEOF amplitude functions |A1| (black line) 

and |A2| (gray line). c) As in b), but for CEOF phase functions φA1 (black line) and φA2 (gray line). 

Profiles from mode 1 (solid lines, Fig. 8) correspond to a phase angle of 221o where the 

correlation with the mean pattern of Fig. 7 was greatest (r2 = 0.96). To produce mean 

profiles from mode 1, its (non-dimensional) spatial pattern was multiplied by the average 

magnitude of the upper 45% of values of its temporally-varying amplitude function. The 

threshold of 45% was chosen to match the upper 45% of ζ/f values used in calculating the 

mean velocity distribution. 

Figure 12. Time series for 1998-2000 of frequency difference magnitude |∆f| (black line) and magnitude |A1| of 

CEOF mode 1 (gray line). 
Final Study Report - Beckenbach and Washburn 

30

To show variability about the mean radial distributions due to departures from radial 

symmetry, panels of Fig. 8 include values of each variable at individual grid points as a 

function of radius based on the CEOF distribution scaling as described above. Scatter in the 

radial distributions is large, particularly for vr(r) and div v, although even with the wide range 

most vr(r) and div v values are negative. 

4.3 Larger-scale current patterns

To explore possible connections between surface flow patterns over the SBB and larger-scale 

coastal flows we examined the correlation between the CEOF modes and velocity time series 

from the CCS moorings at the east and west channel entrances. The mooring data were not 

incorporated into the CEOF analysis because they only overlapped with the HF radar time 

series for 23 to 32 months. Instead the mooring data were related to the CEOF modes using 

complex linear regression of the mooring data on the amplitude functions A1 and A2. 

Consistent with the HF radar data, the mooring data were band-pass filtered and augmented 

with their Hilbert transforms. Complex regression coefficients and associated r2 values were 

then calculated. 

The resulting moored current patterns are included with the CEOF stream functions in Fig. 

10. Currents at SAMI are displaced from their actual position for comparison with the HF 

radar-derived stream functions. Correspondence between the CEOF modes and correlated 

mooring patterns is seen for the most widely spaced currents at ANMI and SAMI suggesting 

that both spatial modes 1 and 2 are related to oscillations of the large-scale alongshore coastal 

flow, especially to the south but also to the north of Pt. Conception. 

The sense of the correlated moored currents agrees with the CEOF spatial distributions. The 

portion of the currents at ANMI correlated with mode 1 are out of phase with those at SMIN; 

maximum currents at ANMI occur simultaneously with minimum currents at SMIN and vicea-versa (Fig. 10a). In contrast, the second mode agrees with ANMI and SMIN in direction 

and magnitude as may be seen by comparing Figures 9b and 10b. These characteristics 

suggest that the mode 1 circulation pattern is smaller than the mooring array for mode 1 while 

the mode 2 pattern is larger. At SMIN and SMOF the alongshore velocity components are 

approximately opposite in direction with comparable magnitudes. Their phase is consistent 

with propagation of the weakening (mode 1) eddy patterns over the western sill. With respect 

to mode 2 (Fig. 10b), flow at SMOF is opposite but reduced in magnitude compared with 

SMIN. This corresponds well with the reversing of flow seen just north of the Channel 

Islands, at the southern edge of the HF radar coverage and the expected offshore attenuation 

in amplitude associated with CTWs. Overall, these results agree with the interpretation of the 

first mode as a basin response and the second as a coastally-trapped wave. 

4.4 Comparison with model results 

Evolving patterns of surface currents in the SBC in the 10-20 day band suggests a basin-scale 

(~30 km) modification of the larger-scale coastal flow associated with poleward-propagating 

CTWs with wavelengths much larger than the channel scale. Previous studies have shown 

that CTWs commonly occur along the west-coast of North America, including the SCB and 
Low Frequency Waves Observed 

31 

around Pt. Conception Battisti and Hickey (1984), Davis and Bogden (1989), Hickey (1992), 

Auad and Henderschott (1997). Auad and Henderschott (1997) observed propagating features 

in the SBC in the 6-18 day band at longer-than-channel scales which they concluded were 

hybrid Kelvin-Rossby waves. The second CEOF mode in this study resembles a CTW with 

surface currents approximately parallel to isobaths along the mainland coast and with an 

indication of current direction reversal along the slope north of the Northern Channel Islands 

(Fig. 11b). Auad and Henderschott (1997) found good agreement between a theoretical 

frequency of 0.073 cpd and an observed period of 0.075 cpd. We found a period for CEOF 

mode 2 of 0.075 ± 0.005 cpd consistent with these values. The combination of mode 2 and 

correlated portion of the mooring data (Fig. 11) is also consistent with a broad longwavelength oscillating flow along the mainland coastal slope. 

Mode 1, representing the propagating vortices, is limited horizontally by the basin dimensions 

(Fig. 7 and 10a). A Rossby wave-like flow is suggested by the symmetry of the cyclonic and 

anti-cyclonic patterns (Fig. 7a), their frequency, and their westward propagation. The centers 

of the propagating vortices move westward over the basin at 4.7 km day-1 along the channel 

centerline. This is consistent with topographic control in the north-south direction since the 

bottom shoals to the north. Topographic control is also indicated by the increase in vorticity 

over the center of the basin compared with the eastern and western sections of the basin (Fig. 

6). In addition, the spatial distribution of variance explained by mode 1 is most significant 

where the bottom shoals to the north and is much lower over the southern edge of the SBB 

where the bottom shoals to the south. Over this region the bottom slope does not allow 

westward propagation of topographic waves. 
Final Study Report - Beckenbach and Washburn 

32

Figure 13. a) Observed stream function pattern as described by CEOF mode 1 for values of phase φA1 shown at 

left. b) Predicted stream function pattern for the topographic Rossby mode model described by Pedlosky (1987). 

The similarity of the patterns suggests that the observed propagating eddy patterns are the response of the Santa 

Barbara Basin to the lowest frequency TRM. The patterns of stream function shown here are similar to those of 

sea surface elevation with solid lines indicating elevated sea surface and dashed lines indicating lowered sea 

surface. The darkest contours are zero sea surface elevation. 

We hypothesize that the mode 1 flow pattern is the lowest frequency topographic Rossby 

mode (TRM) of the SBB. Observations of TRMs are rare, although they have been observed 

near Iceland by Miller et al. (1996) and in numerical model outputs of the Mediterranean by 

Pierini (1996). The conclusion that the mode 1 flow pattern is a TRM follows from the 

similarity between observed mode 1 velocity patterns and those predicted by an analytical 

model described by Pedlosky (1987), page 148. Details of the analytical model and its 

comparison with observations are described in detail by Beckenbach and Washburn (2004). 

Here just the main results are summarized. 

The analytical model assumes that the basin containing a TRM is rectangular with a sloping 

bottom. The downward slope of the SBB is consistent with the westward propagation of the 

velocity pattern of mode 1. The dimensions of the SBB and the magnitude of its bottom slope 

reasonably predict the propagation speed of the eddies along with their dimensions and 

frequency. This may be seen by comparing the observed streamline patterns of Fig. 13a with 

the model predictions of Fig. 13. Differences in the patterns may result from the fact that the 

SBB is circular while the model assumes a rectangular basin. Nevertheless the similarity in 

the patterns is striking. 
Low Frequency Waves Observed 

33 

5. Conclusions 

This study supports the following conclusions: 

1. The stability of the predominant cyclonic circulation in the Santa Barbara Channel is 

strongly affected by the presence of trains of propagating eddy-like features. These features 

dominate the variability in the 10-20 day band. They have not been described in previous 

studies. Their discovery was made possible by the use of high frequency radar which can 

observe evolving patterns of surface currents. 

2. The propagating eddy-like patterns consist of two dominant components: (1) Mode 1, 

explaining 45% of the variance, is a pattern of westward-propagating counter-rotating 

vortices similar to the propagating cyclones reported by Harms and Winant (1998). (2) Mode 

2, explaining 20% of the variance, is a pattern of alongshore fluctuations on the mainland 

coast similar to the coastal trapped waves described by Auad and Henderschott (1997). The 

pattern of fluctuating along-shelf currents described by mode 2 with a period of 13.3 days 

extends from the eastern entrance, through the radar coverage area, and beyond Pt. 

Conception indicating a long wavelength. 

3. The propagating vortices described by mode 1 are consistent with the analytical model of 

topographic Rossby modes described by Pedlosky (1987). The observed stream function 

distribution (Fig. 13), propagation speed (4.7 km day-1) and period (14.3 days) are similar to 

those predicted by the model. 

4. Frequency coupling between modes 1 and 2 suggests that the propagating vortices are a 

resonant interaction between the basin and the coastal trapped waves. The amplitude of mode 

1 consistently increases when the frequency of mode 2 and the mean frequency of mode 1 

converge. The amplitude of mode 1 consistently decreases as these frequencies diverge. The 

relationship only exists between the frequency of mode 2 and the mean frequency of mode 1, 

not the instantaneous frequency, suggesting that the interaction is regulated by shape of the 

Santa Barbara Basin. 

These observations indicate that coastal trapped waves can interact with topographic features 

to produce strong secondary flows. In this case, the strong rotary flows are amplified in the 

basin and interact with the persistent cyclonic flow in the western Santa Barbara Channel. 

Similar interactions may occur more generally where basins are close enough to shore to be 

exposed to oscillatory flows from coastal trapped waves. 
Final Study Report - Beckenbach and Washburn 

34

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Low Frequency Waves Observed 

37 

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As the Nation's principal conservation agency, the Department of the Interior has responsibility for most 

of our nationally owned public lands and natural resources. This includes fostering sound use of our 

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