VOL. 80, NO. 24
JOURNAL
OF GEOPHYSICAL
RESEARCH
AUGUST
20, 1975
Alongshore Coherenceat Low Frequenciesin Currents Observed Over the
Continental Shelf off Oregon and Washington
ADRIANA
HUYER
Oceanand Aquatic Affairs, EnvironmentCanada, Ottawa, Canada
BARBARA M.
HICKEY
AND J. DUNGAN
SMITH
Departmentof Oceanography,Universityof Washington,Seattle, Washington 98195
ROBERT L. SMITH AND R. DALE PILLSBURY
Schoolof Oceanography,OregonState University,Corvallis, Oregon 97331
Current observationsover the continental shelf at locationsoff central Oregon and southernWashington had the period from July 18to September18, 1972,in common.Low-frequencyfluctuations(lessthan
one cycleper day) in the currentsare comparedby meansof visualdisplay,linear regression,and spectral
analysis.The currentsare found to be highly coherentover an alongshoreseparationof 200 km. Coherent
signalsoccurat 0.16, 0.3, and 0.44 cpd. The signalat 0.16 cpd occurswith highmutual coherencein wind,
current, and sealevel and may be a forcedshelfwave driven by the wind. The signalat 0.3 cpd has high
coherencebetweencurrent and sealevel and may be a free shelf wavegeneratedby the wind. Correlation
betweenobservationsis higherfor separationsin the alongshoredirectionthan in the offshoredirectionin
spite of greater separations.
southern Washington arrays. The array at NH-10 was first
moored
on July 6, 1972, servicedon August 3 and 31, and
There is considerableenergy at periods of severaldays in
recovered
on September 18, 1972; the 20-m current meter
current observations over the continental shelf off Oregon
[Cutchinand Smith, 1973;Smith, 1974]. During the summerof did not function on the last installation. The array at NH-20
1972, direct current measurementsover the continental shelf was deployed on July 3, 1972, servicedon August 3, and
were made off southernWashington and central Oregon. The recoveredon August 30, 1972. Both arraysincludeda current
meter at 20 m and one near the bottom (at 60 and 120 m,
arrayswere separatedby about 200 km, and the observations
respectively).
are suitable for determining the coherenceof low-frequency
INTRODUCTION
current
Both
fluctuations.
sets of
current
meter
data
were
obtained
with
The coherence between current records separated in the Aanderaa current meterswith a samplinginterval of 5 or 10
alongshore distance is emphasized in this paper. The min. The data were initially filtered to provide hourly values.
Gaps due to the servicingof the arrays(all shorterthan a day)
coherence between current meters at the same location but at
were
filled by a time serieswhosespectralcharacteristics
were
different depthsand betweencurrent metersseparatedin the
determined
from
the
end
of
the
previous
record
and
the
beginoffshore direction is also briefly examined. Although we interpret the resultsin terms of wind and sealevel observations, ning of the following one. This procedure resulted in continuous data records for each of the current meters, of which
the main purposeof the paper is to demonstratethat current
observationsseparatedby 200 km in the alongshoredirection five overlappedfor the period from July 18 to September18,
and all eight overlappedfrom July 18 to August 30.
exhibit significantcoherenceat periods of severaldays.
Hourly wind observationswere available from both areas,
OBSERVATIONS
at Westport, Washington,and Newport, Oregon. Sealevelwas
Two current meter arrays were moored off southern obtained from tide gagesat Depoe Bay, Oregon, by Oregon
Washington, one near the shelf edgein about 160 m of water State University with a precisionof +0.3 cm; at Toke Point,
(UWOFF) at 46ø50'N, 124ø50'W and one nearer shorein 73 Washington, by the U.S. Army Corps of Engineerswith a
m of water (UWIN) at 46ø25'N, 124ø20'W(Figure 1). Moor- precisionof + 1 cm; and at Torino, B.C. (49ø10'N, 125ø55'W),
ings were deployedJuly 17, 1972, servicedAugust 17, 1972, by the Canadian HydrographicServicewith a precisionof + 1
and recoveredSeptember25, 1972.Both arraysincludeda cur- cm. Hourly valueswereobtainedfrom eachlocation.Sealevel
rent meter at about 20 m and a deep current meter (at 66 m at
UWIN and 110m at UWOFF) that appearedto be abovethe
bottom boundary layer.
The observationsoff central Oregon were made as part of
the 1972Coastal Upwelling Experiment.(CUE-1) [Pillsburyet
al., 1974a]. Two of the CUE arrays, NH-10 at 44ø39'N,
124ø17'W and NH-20 at 44ø39'N, 124ø32'W (Figure 1), were
exhibits
an 'inverted
barometer
effect'
due to variations
in
atmosphericpressure:sealevel changes1 cm for every 1 mbar
changein atmosphericpressure.Sea level was adjustedfor this
effectusingatmosphericpressureobservationsfrom Newport,
Oregon; Hoaquiam, Washington;and Torino, B.C.
The hourly current, wind, and adjustedsealevel data were
filtered by means of a symmetricalcosinefilter spanning121
deployedin waterdepths(80 and 142m) similarto thoseat the hours to suppresstidal and inertial oscillations.The halfpower point of the filter is 40 hours, and about 95% of the
energyis passedat 50 hours.The filtering resultsin truncating
Copyright¸ 1975 by the AmericanGeophysicalUnion.
the time seriesby 21/5days at each end.
3495
3496
HUYERET AL.' ALONGSHORE
CURRENTS
47 • N
Hoaquiam
Someof the currentrecords,e.g., 60 m at NH-10, havea mean
alongshorecomponent that is nearly zero. Others have
northward(e.g., 120m at NH-20) or southward(20 m at NH10)meanflows.All recordsshowhighvariability,a periodof
about6 daysbeingmostapparent.The fluctuations
at all eight
current meters appear to be somewhatsimilar, the greatest
similarityoccurringbetweenthe inshorecurrentmeters.
Simplestatisticsof the currentsand their components
in
/Oo
o
both the east-northand the local(natural) referenceframesare
shownin Table 1 for both the 56-dayand the 37-daycommon
period.Almostall statistics
are verysimilarfor the two time
periods.Standarddeviationsof both speedand the alongshorecomponentare greaterfor the nearshorethan for the
offshorecurrent meters.The standarddeviation of the along46eN
shore
component
isgreater
thanthaiof theonshore
component;in mostcasesthe differenceis greaterthan a factorof 2.
At all four locationsthe meandeepflow wasnorthwardrelative to the surfaceflow; this is consistentwith previousobservations over the Oregon continentalshelf in late summer
[Huyer et al., 1975].
Simplelinearregression.
We computed
thelinearregression
and correlation coefficientsbetween the alongshorecompo-
nentsof eachpair of currentmetersfor both periods.Results
are shown(Table 2) for the local isobathcoordinatesystem;
theydifferonlyslightlyfor thenorthwardcomponent.
Coefficientswerecomputedfrom 37 (56) daily valuestakenat 1200
UT. From analysisof variance[Panofsky
andBrier, 1963]the
probabilityof uncorrelated
populations
havinga correlation
coefficient
greaterthan0.42 (0.34)is lessthan 1%for a sample
45•,N
Depoe Bay
ß
ß
o
o
ß
ß
size of 37 (56).
Vertical correlationcoefficients
are greatestat UWIN and
NH-10 and least,but still significant,at UWOFF. The regressioncoefficientB is near unity at UWIN, NH-10, and NH-20,
suggesting
that the currentfluctuations
may be barotropic
there, but at UWOFF, fluctuationsat the deep current meter
NH
-20•_•$
ø
ß
125'•W
o
124'•W
havelessthan half the amplitudeof thoseat the shallowcurrent meter.The meanverticalshearA appearsto begreateroff
centralOregonthan off southernWashington.Correlation
coefficients
are higherbetweenthe deepcurrentmetersthan
between shallow current meters. This could be due to the
gradients
betweentheshalFig. 1. Locations
of currentmeterarraysandcoastallocations
of highervariabilityin lateraldensity
supplementary
observations
of sealevel,wind,and/oratmospheric low currentmeters(e.g.,dueto variationsin the positionof the
pressure.
ColumbiaRiver plume)than betweenthe deepcurrentmeters.
Current fluctuationshave smalleramplitudesat the offshore
locations(B < 1), suggesting
that the fluctuations
are trapped
COMPARISONS BETWEEN CURRENT OBSERVATIONS
along the coast.The correlationbetweenthe deep current
We comparethe currentobservations
by meansof visual metersisgreaterfor theinshorepairthanfor theoffshorepair,
display,simplestatistics,
simplelinearregression,
andspectral but the correlation between UWIN and NH-20 is also very
analysis.
The spectralanalysis
is restricted
to the fivecurrent high.
If the current fluctuation field were isotropic and
meterrecordswhichoverlappedfor 56 days,whileothercomhomogeneous,
the correlationcoefficientbetweena pair of
parisonsare alsomadefor the 37-dayperiodcommonto all
current meters would be a function only of the distance
eight current meters.
Comparisonsbetweencurrent meters were made in a
'natural'coordinatesystembecause
of significant
variationsin
betweenthem. Instead, the correlation coefficientswith lateral
isobath orientation. Natural coordinates could be taken to be
meters.Also the correlationcoefficientsfor alongshoresepara-
separationare greater for deeperthan for shallowcurrent
in spiteof
parallelto the localisobathor to betheaxesin whichtheoff- tionsare higherthanthosefor offshoreseparations
diagonalelementof the Reynoldsstress
is zero,i.e., theprin- much greater alongshoreseparations.
Alongshorecorrelationcoefficients
are lower for UWOFF
cipalaxes.At thedeepest
currentmeterin eachof thearraysin
thisstudytheprincipalaxeswerefoundto bewithin5%of the than for UWIN. This could be due to the greateralongshore
local isobath orientation. We therefore chose to use natural
coordinatesparallelto the local isobath:330øT at UWOFF,
347øT at UWIN, and 15øT at both NH-10 and NH-20.
separationbetweenUWOFF andthe southerncurrentmeters,
but it is more likely due either to its proximityto the shelf
break,to greateroffshoreseparation,or to somelocaleffectat
The time seriesof 6-hourlycurrentvectorsare shownin UWOFF. These effects would cause underestimates of the
Figure2 with the wind and adjustedsealevel observations. alongshorecorrelationcoefficient.In any casewe conclude
HUYER ET AL.' ALONGSHORE
CURRENTS
3497
TOKE
POINT
[
SEA LEVEL o
-2o
20 m
UWIN
N
lllllllllllllllllllll,,..,,,,,v&//l,,.,lx
,
lll[1111111111111111
.... ....
,111111111/
............
66 rn
UWIN
60m
NH-IO
N
20m
NH-IO
21
25
$0
I
5
I0
JULY
15
20
25
AUGUST
30
I
5
I0
15
SE PTE MBE R
WESTPORT
WIND
NEWPORT
WIND
20m
UWOFF
N
IlOm
UWOFF
120m
NH-20
N
20 m
NH-20
2,
25
•0
•UL•
,
5
,0
,5
AUGUST
•0
•5
S•
Fig. 2. Time seriesof 6-hourlyvectorsof low-passed
deepand shallowcurrent,wind andsealevelobservations,
July21
to September16. Current vectorsare shownin the local isobathcoordinatesystem.Directionof arrow at right indicates
true north; its magnitudecorresponds
to a currentspeedof 30 cm s-• and a wind speedof l0 m s-•.
3498
HUYER ET AL.: ALONGSHORE CURRENTS
TABLE 1. Vector Mean Currents, Principal Axis Angles, and Means and Standard Deviations of Speedand Componentsin the East-North
(u, v) and Local Isobath (u', v') Coordinates,1800 UT July 21 to 1800 UT August 27, 1972, and (in Parentheses)1800 UT July 21 to 0000 UT
September 16, 1972
UWOFF
20 m
Vector
UWIN
110 m
20 m
NH-10
66 m
20 m
14.0
NH-20
60 m
20 m
120 m
2.7
4.0
9.6
mean
Speed,cm s-1
Direction, øT
Principalaxisangle,deg
8.9
5.1
1.3
6.7
(8.7)
(5.6)
(0.8)
(6.2)
141
333
224
343
(136)
(333)
(265)
(348)
16.5
15.2
0.0
8.0
(33.4)
(20.2)
(0.1)
(9.7)
10.0
10.6
(9.5)
(9.7)
(2.4)
200
287
213
359
- 36.1
-6.9
(272)
- 17.0
-21.6
(-20.5)
Means
Speed
11.3
6.8
(11.1)
(7.1)
5.7
- 2.3
-0.9
- 1.9
(6.0)
(-2.6)
(-0.8)
(- 1.3)
-6.9
4.6
-1.0
6.4
(-6.3)
(5.0)
(-0.1)
(6.1)
1.5
0.3
-0.7
(2.0)
(0.3)
(-0.7)
-8.5
(- 8.5)
Standard
Speed
-0.4
16.5
-4.9
5.1
1.1
6.6
(0.1)
(6.2)
9.5
12.5
- 2.6
- 2.2
-0.2
(-2.4)
-13.1
0.8
-3.3
9.6
(0.1)
- 1.4
(0.1)
(5.6)
10.6
(10.2)
-2.7
- 1.3
-2.3
(-2.4)
-14.0
0.1
-3.8
9.4
(-0.5)
deviations
4.8
3.9
5.2
4.5
(5.1)
(4.0)
(4.8)
(4.7)
4.7
2.4
2.8
2.1
(4.4)
(2.4)
(3.3)
(2.4)
7.0
5.4
10.9
9.2
(7.4)
(5.4)
(10.1)
(8.5)
4.6
2.4
3.7
1.9
(4.7)
(2.7)
(3.9)
(2.1)
7.1
5.4
(7.2)
(5.2)
10.6
(9.9)
9.2
(8.5)
8.5
6.3
6.1
4.7
8.1
2.7
8.1
9.0
5.9
2.4
8.0
9.5
(5.6)
6.0
5.0
(4.6)
10.8
11.1
(10.4)
4.3
2.5
(3.0)
11.2
11.7
(10.9)
that the alongshorecorrelation length over the continental Figure 4. At UWIN the vertical coherenceis high over a wide
shelf is at least 300 km for the low-frequencycurrent fluctua- band (-0.55, 0.3 cpd), and it exceeds the coherence at
tions.
UWOFF at all frequencies.Vertical phasedifferencesare esSpectral analysis. We use the rotary spectral method sentially zero wherever the coherenceis high and phaseesdescribedin detail by Gonella [1972] and Mooers [1973]. In timates are most reliable. This is consistent with the idea that
effect,the method decomposes
the vector time seriesinto cir- the coherent current fluctuations are approximately
cularly polarized componentsrotating clockwiseand counter- barotropic.
clockwiseat each frequency.Spectra are then computedfor
Coherencesquaredand phasespectrafor the pairs of deep
clockwise (negative) and counterclockwise (positive) fre- current meters are shown in Figure 5. Between UWlN and
quencies.The time serieswere linearly detrendedbefore the NH-10 there is high coherenceover a wide frequencyband
spectra were computed.
(-0.5, 0.3 cpd), with a gap in the coherenceat -0.35 cpd.
and UWOFF
and between UWlN
and
The autospectrafor the five current recordsfor the period Between NH-10
1800 UT July 21, 1972, to 0000 UT September16, 1972, are UWOFF, coherence is lower and restricted to narrower freshown in Figure 3. The rotary autospectrashow not only at quency bands. The overall coherence(the integral of the
which frequencypeaksoccur but also whetherthe current at a coherencesquaredspectrum)appearsto be about the samefor
particular frequencyis more nearly circular or linear and two of the pairs, (UWIN, UWOFF) and (UWlN, NH-10), as
whether it rotates clockwise or counterclockwise.
All five
we might expectfrom the similar valuesof the linear correlaspectra show some similarity in that highest energy is ob- tion coefficient(0.65 and 0.62).
served at lowest frequenciesand in that energy tends to
We investigatefurther the signalsassociatedwith peaksin
decrease as frequency increases. The high-energy low- the autospectra
at frequencies
of 0.'15,0.3, and0.45 cpd.Table
frequencyband is narrowestat UWOFF. Apparent peaksoc- 3 showsthe valuesof somecurrentellipseparametersfor each
cur at -t-0.05 cpd, but sincethe valley betweenthem is due to of thesefrequencies:
kineticenergyof the rotary components
the linear detrending of the time series, this should be in- (S_ and S+) and ellipsestability, orientation [Gonella,1972],
terpretedsimply as a peak at the lowestfrequencies.All of the andeccentricity[Mooers,1973].The total kineticenergy(S+ +
spectrashow a peak or shoulderat 0.15 cpd, and three of the S_) at 0.16 cpd is larger than that at 0.3 and 0.44 cpd; the
spectra(from NH-10 and UWlN) showpeaksat 0.3 and 0.45 kinetic energyat 0.16 cpd is approximatelyindependentof
cpd. Of thesethreepeaks,greatestenergyoccursat the lowest depthat a givenlocation;at both 0.3 and0.44 cpd the kinetic
energyis greaterat the shallowercurrent meters;and the kinetic
frequencyand least energyat the highestfrequency.
Cross spectra were computed in local isobath coordinates energyis lessat UWOFF than at UWIN or NH-10 for all three
(coherencesquaredis independentof coordinaterotation, but signals.The senseof rotation (clockwiseor counterclockwise)
phaseis not). Coherencesquaredand phasebetweenvertically is givenby the signof the difference
in kineticenergyof the
separatedcurrent metersat UWIN and UWOFF are shownin two components(S+ - S_); when the signal is nearly rec-
HUYER ET AL..' ALONGSHORE CURRENTS
3499
TABLE 2. CorrelationCoefficient(CC) and Regression
Coefficients
(A and B) BetweenPairsof
Current
Depth, m
Station
Depth, m
Meters
Station
CC
A
B
VerticalSeparation
20
UWIN
66
UWIN
20
20
NH-10
UWOFF
60
110
NH-10
UWOFF
20
NH-20
120
NH-20
20
UWIN
20
20
60
NH-t0
UWIN
20
110
60
NH- 10
120
20
20
UWIN
UWOFF
20
20
20
20
UWIN
UWOFF
66
UWIN
0.96
5.7
0.83
(0.95)
(6.1)
(0.82)
0.83
0.57
(0.61)
0.73
NH-20
0.88
0.43
(9.3)
(0.44)
12.5
OffshoreSeparation
UWOFF
0.40
(O.48)
NH-20
UWOFF
12.4
8.9
0.86
-9.3
0.27
(-8.6)
(0.35)
0.50
0.70
1.5
2.4
0.38
0.41
(0.65)
(3.1)
(0.40)
0.87
9.3
0.72
-15.0
1.4
0.69
0.60
Alongshore
Separation
NH-10
NH-20
0.68
0.52
20
20
NH-20
NH-10
0.56
-4.4
0.43
0.53
-7.1
0.80
60
NH-10
1i0
UWOFF
120
NH-20
66
110
UWIN
UWOFF
120
60
NH-20
NH-10
0.9,0
-7.5
1.12
(0.87)
(-7.5)
(1.10)
0.79
0.95
0.68
1.9
2.7
-7.6
1.41
0.99
1.46
(0.62)
(-7.7)
(1.28)
Regression
equation
is V: = A + BV•.ValuesaregivenfortheperiodJuly21to August27, 1972,and
(in parentheses)
for July 21 to September15, 1972.
tilinearthisdifference
becomes
verysmallanditssignindeter- Ellipse
orientation
isshown
when
stability
exceeds
the95%
minate.We observe
clockwise
rotation(S_) S+) in all cases significance
level(0.53).Ellipseeccentricity,
2(S_ S+)•/•' (S_
except
at0.16cpdatuwIN, where
thesignal
isstrong
andap- + S+)-• [Mooers,1973],is equalto onefor rectilinearmotion
and to zero for circular motion.
proximatelylinear.
Ellipsestability[Gonella,
1972]islowfor nearlycircularmoWe interpretthe valuesof theseellipseparametersto
tionor if theorientation
of the majoraxisvariesappreciably.describe
theproperties
of thethreesignals.
Thesignalat 0.16
I000
iooo
-
I •
I
,oo
•oo
,,,. t •
I•
•/I
60m [
t•
•
..
I ..'-'.... .
NH-IO
/ I i-
"•.
zorn
,• [ it \j /UWOFF
io
it
I
I
-04
I
I
-02
I
0
I
I
02
I
I
04
I
016
IlOm,
UWOFF
•oi
I'"'i"""
•""
I •i
-0 6
-0 4
-0 2
0
cpo'
Fig.3. Autospectra
ofthecurrent
records,
July21to September
16,1972,withthe80%confidence
interval
andtheband
width.
3500
HUYER ET AL.: ALONGSHORE
CURRENTS
•.-
20m vs IlOm, UWOFF
-- -- 20 m vs 66 m, UWIN
I
\
It
fl
04-
I •
I
I
-
0
-06
iI
several pairs of current meters. Figure 6 showsvalues of the
coherence squared between each pair of current meters,
including vertical, offshore, and alongshore separations.
Relatively low valuesare observedfor the counterclockwise
components at 0.3 and 0.44 cpd (which have low kinetic
energy);the maximumvalue is 0.52 at +0.3 cpd and 0.57 at
0.44 cpd. Alongshore coherencevalues are high at -1-0.16,
-0.3, and -0.44 cpd for the inshorecurrent meters,and some
offshorecoherenceis observedfor each of thesesignals.
COMPARISON
02
04
WITH
WIND
AND SEA LEVEL OBSERVATIONS
O6
cpd
From the resultsof earlier studies,e.g., Huyer and Pattullo
[1972], Cutchinand Smith [1973], and Smith [1974] we expect
the current
61o
fluctuations
to be related to fluctuations
in wind
and sealevel. Figure 2 showssomesimilaritybetweenthe wind
and offshorecurrentsbut greatersimilarity betweenthe wind
and the inshorecurrents.Sea level fluctuationscloselyresem-
%
ble the fluctuations
in the alon•shorecomponent
of the cur-
%
rent, high sealevelbeingassociatedwith polewardflow. Cor-90
I
-0.6
I
I
I
-04
I
I
-0.2
I
0
I
I
02
04
6
relation coefficients between current and sea level and between
wind and current (Table 4) are higher for the deep current
½pd
Fig. 4. Coherencesquared and phase spectrafor vertically
meters than for shallow current meters. Current
fluctuations
geparated
currentmeters.
Coherence
squared
valueslessthanthe95% are more highly correlatedwith sealevelthan with wind. A sea
significancelevel (0.28) are not shown. Phase is shown only when level changeof 1 cm at Depoe Bay is associatedwith a change
coherencesquared exceedsthe 99% significancelevel (0.4). When in current velocity of 1.6 cm s-• at NH-10 and 1.5 cm s-• at
phase is positive, the secondseriesleads the first.
NH-20; a sealevel changeof 1 cm at Toke Point is associated
with current changesof 1 cm •-• at U.WIN and 0.5 cm s-1 at
haveabout4% of
cpd is the strongestof the three. Its eccentricityappearsto UWOFF. At UWIN, currentflucttlii{Ibns
decrease
aswaterdepth(or distance
offshore)
increases;
i.e.,it the amplitude of wind fluctuationsobservedat Westport; at
is morecircularfurtherfrom shore,andit is approximatelyNH-10 current changesare 2% of Newport wind changes.
The alongshorecorrelation and regressioncoefficientsfor
barotropic.Both the kineticenergyat a givendepthand its integral over the water columnappearto decreaseaswater depth the wind and sea level observations are shown in Table 5. The
(distanceoffshore)increases;
i.e., thesignalat 0.16 cpdappears high linear correlationcoefficientsindicate not only that the
to be trappedalongthe coast.The signalsat 0.3 and0.44 cpd dominant signals are coherent but also that the phase
are much weaker. Both appear to have higher energy at the differencein the dominantsignalsmust be relativelysmall.
shallowercurrent meters,and they may be baroclinic.The Fluctuationsin the wind at Westport have lessthan half the
signalat 0.3 cpd Seemsto be nearly rectilinearat UWOFF and amplitudeof thoseat Newport; this accountsfor the difference
more elliptical at NH-10 and UWIN. The signalat 0.44 cpd in the ratio betweencurrent and wind amplitudes,sincecurrent fluctuations at UWIN
and NH-10 have about the same
may be circular everywhere.
Each of these signals showed high coherence between amplitude(Table2). Alongshore
correlation
coefficients
are
about the samefor sealevel and the deepcurrents,lower for
the wind, and least for the shallow currentsfor comparable
1.0
I
......UWIN
vsUWOFF
separationbetweenobservations.
•
_[,• • UWlN
vs
NH-IO
Rotary autospectraof the low-passedwind observationsat
Newport and Westportand the coherencesquaredand phase
spectrabetweenthem are shownin Figure 7. Sincethe coastis
alignednearly north-southat both locations,east-northcoor-
/
-- vs-,o
..
/',
0.6
- 0.4
o •
dinates were used. The wind is more to the left and weaker at
:1
- 0 2
••
0
• • •._:'
I
- 0.6
ß
•'•
- 0.4
I
I
I
- 0.2
0.•
0.4
0.6
•f'..
I,
I
0
I
0.2
I
I
0.4
o16
cp•f
Fig. 5. Coherencesquaredand phasespectrafor the pairsof deep
current
meters.
Westport than at Newport (Figures 2 and 7, Table 5). The
decreasein speedand the changein direction are consistent
with the general northward decreasein zonal wind stressin
summer [Bakun, 1973] associatedwith the mean position of
the North Pacifichigh pressuresystem.
Autospectra of the wind (Figure 7) and current (Figure 3)
are somewhatsimilar, but the decreasein kinetic energywith
frequencyis more gradual for the wind. The wind showsrelatively low kineticenergyat 0.3 cpd, while the shallowcurrents
show fairly high energy at this frequency.The alongshore
coherenceat 0.3 cpd is very low for the wind but significantfor
the inshorecurrents(seeFigure 6). At other frequencies,including0.16 and 0.44 cpd, the alongshorecoherenceof the
wind is high.
Autospectraand the coherencesquaredand phasespectraof
sea level observationsare shown in Figure 8. The sea level
HUYER ET AL.' ALONGSHORECURRENTS
3501
TABLE 3. Kinetic Energy(cm:/s:/cpd) of Clockwise(S_) and Counterclockwise
(S+) Componentsand EllipseStability (s), Orientation
(½) in DegreesTrue, and Eccentricity(e) At SelectedFrequencies
Depth,
m
20
110
60
66
20
0.16 cpd
Station
UWOFF
UWOFF
NH-10
UWIN
UWIN
0.3 cpd
S_
S+
s
•b
81
82
232
142
216
28
32
140
190
189
0.02
0.78
0.93
0.99
0.88
356
26
359
4
e
0.873
0.898
0.968
0.989
0.998
S_
S+
10
5
38
17
77
6
5
29
10
13
autospectracloselyresemblethoseof the deepcurrents(Figure
3). Coherencesquaredfor sea level is high at 0.16 cpd both
betweenToke Point and Depoe Bay and betweenTorino and
Depoe Bay. At 0.33 cpd the coherenceis significant,although
at 0.3 cpd it is very low betweenTorino and Depoe Bay. The
bandwidthof the spectralestimatesis about 0.08 cpd, and we
assume that the coherencepeak at 0.33 cpd in sea level
s
0.02
0.29
0.77
0.47
0.30
0.44 cpd
•
e
S_
S+
s
14
0.97
1.00
0.99
0.96
0.70
12
4
25
14
35
7
3
12
1
5
0.05
0.01
0.79
0.35
0.06
357
' Figure9 showsthe coherence
squaredspectrabetweenthe
observations.
Sealevelis high!ycoherentwith the inshorecur-
rentmgtersovera widerangeof frequencies,
but c9herence
UWIN
JWlN
.204
.404
.•z•
-. NH-IO
ß$55
.87'4
NH-IO
.538
UWOFF
•(•:•"• UW•N
I
O..3 cpd
.37.2
\
"•,.•2'•.
/'l
'" -,
"./o.•"'-..
I / •.01•%•-'"'
J ß
0.44 cpd
Clockwise
Counterc Io,ckwise
Fig. 6. Valuesof coherence
squaredbetweenall pairsof currentmetersat selectedfrequencies.
A heavysolidline indicatesthat coherencesquaredexceedsthe 99% significancelevel,a thin line indicatesthat is is betweenthe 95% and 99%
levels,and a dashedlineindicatesthat thecoherence
squaredbetweena pair of currentmetersis not significantly
different
from zero at the 95% level.
0.96
0.99
0.94
0.50
0.66
deepcurrentsand the nearbywind and adjusted
sealevel
UWOFF
.•o/
e
is associatedwith the peak at 0.3 in currents. At 0.44 cpd
there is significantcoherencebetweenToke Point and Depoe
Bay but not betweenTorino and Depoe Bay.
UWOFF
O.16 cpd
•b
3502
HUYER ET AL.' ALONGSHORE CURRENTS
TABLE4.
Correlation
Coefficients
andSlopeof theRegression
LinesBetween
theAlongshore
Componentof the Currentand AdjustedSea Level and BetweenCurrentand the Northward
Component
of Wind•'
Location
of Observations
Current
Sea Level, Current
SeaLevel
Wind
Depth, m
Station
Toke Point
Westport
20
UWIN
20
UWOFF
'
66
UWIN
110
Depoe Bay
Newport
Wind, Current
CC
B, s-•
CC
B, cm/m
0.81
(0.79)
1.13
(1.12)
0,67
(0.62)
3.6
(2.95)
0.29
0.28
0.15
0.52
(0.36)
(0.37)
(0.41)
(1.41)
0.89
1.06
0.72
3.33
(0.87)
(1.06)
(0.67)
(2.77)
UWOFF
0.74
0.51
0.43
1.16
20
NH-10
(0.68)
0.65
(0.50)
1.16
(0.47)
0.40
(1.15)
1.07
20
60
NH-20
NH-10
0.72
0.87
0.95
1.64
0.44
0.68
0.91
1.99
120
NH-20
(0.82)
(1.71)
0.94
1.46
(0.68)
0.66
(1.84)
1.60
Values are givenfor the periodsJuly 21 to August27, 1972,and (in parentheses)for July 21 to September 15, 1972.
betweenthe offshoredeepcurrentand sealevelis low at most
frequencies.Coherencebetweenthe inshoredeepcurrentsand
the wind is high at low frequencies.
The offshoredeepcurrent
meter showslittle coherencewith the wind at any frequency.
The coherencesquaredspectrabetweenwind and sealevel are
quite differentfor the two locations.At 0.16 cpd thereis high
nearlyequallycoherent,but in the counterclockwise
componentsthe currentshowsgreateralongshorecoherence
than the
wind: this is likely becausethe current is constrainedto be
nearlylinearby thecoast,whilethewindis not.At 0.3 cpd
thereis significant.alongshore
coherence
in both currentand
coherencebetweeninshorecurrentsand sealevel and between
I00-
inshorecurrentsand win• at both locations;coheren,ce
NEWPORT
WIND
-- -- WTPT
WIND
between
windandsealevelishighonlyoffcentral
Oregon.
At
0.3cpd,thereishighcoherence
between
inshore
current
and
sealevelat bothlocations;
coherence
betweeninshorecurrent
andwindis highoffcentral
Oregon
butlowoffsouthern
Washington.Off Oregon,coherence
is high in both rotary
components between wind and inshore current and also
betweencurrent and sea levol. For a pure continentalshelf
wave we expecthigh coherenceonly in the clockwisecomponent, asis observedoff southernWashington.It seemspossible
'b
thatthesignalisgenerated
bythewindoffOregonandthatit
propagated northward as a wave. At 0.45 cpd, coherence
betweenwind and current is very low, although coherence
between sea level and current and between wind and sea level
is significantat both locatio,ns.
The a!ongshorecoherenceis higher for the deep current
than for wind and sea level at each of these frequencies
(Figures 5, 7, 8). At 0.16 cpd the clockwisecomponentsare
io
•
i
I
i
i
io-
TABLE 5. Correlation Coefficientand Slope of RegressionLines
Between
WindObservations
and Between
Adjusted
SeaLevelat
Different Locationsfor the PeriodsJuly 21 to August27, 1972,and {in
Parentheses)for July 21 to September15, 1972
CC
• 04
-- --
99%
B
i
Wind
Newport, Westport
0.80
•0.•
0.40
•0.4:•
9
•_.
NE
P.A
Sea level
Depoe Bay, Toke Point
0.92
1.17
(0.89)
(1.21)
Depoe Bay, Torino
0.86
(0.75)
0.74
(0.68)
Toke Point, Torino
0.84
0.57
(0.66)
(0.44)
-3-06
•
I
-04
I
-02
0
cpo•
•"
02
I
I
04
I
016
Fig. 7. Autospectraof the wind observationsat Newport and
W•stport and theircoherence
squaredand phasespectra(in principal
axesand east-northcoordinates).Positiv• phaseindicatesthat Newport leadsWestpOrt.
HUYER ET AL.' ALONGSHORECURRENTS
sealevelbut not in the wind. This supportsthe earliersuggestion that this signal may propagatenorthward like a wave.
Earlier we showedthat the kinetic energyat this signalwas
greaterat shallowthan at deepcurrent metersand hencethat
the wave is not strictly barotropic. The signal at 0.44 cpd
shows high alongshorecoherencein both wind and current
and lower but still significantalongshorecoherencein sea
level. This signalis also strongerat the shallowcurrentmeters
and hence also has a barocliniccomponent.
Phase spectra of pairs of vector componentsmeasuredat
different locations were used to estimate the time lags and
hencewavelengthand phasespeedand direction.The uncertainty in phaseand hencein wavelengthand phasespeeddependson the number of degreesof freedom(10, in our case)of
the spectralestimatesand on the value of coherencesquared
[Jenkinsand Watts, 1968].Table 6 showsvaluesof the alongshore coherencesquaredand phasewith its 95% confidence
limits for the three signalsat 0.16, 0.3, and 0.44 cpd as computed from the wind, adjustedsealevel,and deepinshorecurrent observations.The phasedifferencein the current observations is not highly sensitive to the choice of coordinate
systems.At each frequencyand for eachparameterthe observations off central Oregon lead those off southern
Washington;i.e., the signalsappearto propagatenorthward.
At 0.16 cpd the 95% confidencelimits for phaseresult in a
large range of possiblewavelengths:from a minimum of 1680
km (from the sealevelsat Torino and Toke Point) to infinite
wavelength(from sea levelsat Toke Point and Depoe Bay).
There is, however,a wavelengthintervalthat is commonfor all
current, wind, and sealevel pairs: from 3390 to 3790 km. The
correspondingphasespeedsare between540 and 610 km/day.
We tentatively concludethat the signal at 0.16 cpd has the
same wavelengthand phasespeedin wind, current, and sea
level. Its wavelengthappearsto be about 3500 km, and it
seemsto propagatenorthwardwith a phasespeedof about 575
km/day.
At 0.3 cpd both current and sealevelshowsignificantalongshore coherencebetween southern Washington and central
Oregon, but wind does not. Although coherenceis significantly different from zero at the 99% level, the valuesare not
high, and uncertaintyin the phaseestimatesis large. The 95%
confidenceintervals of phaseyield a common wavelengthinterval from 1360 to 14,400 km with a correspondingphase
speedinterval from 630 to 4320 km/day. The signal is not
sufficientlycoherentto enableus to determineits wavelength
and speedwithin reasonablelimits from the presentdata set.
Perhapslonger recordswould yield improved resolution.
The signalat 0.44 cpd showshigh alongshorecoherencein
currentsand hencemore reliablephaseestimates.Wavelength
estimatesfrom current and sea level data range from 790 to
1890km. The wavelengthinterval common to current and sea
level (1110, 1240 km) has a phasespeedinterval from 480 to
550 km/day. The wind has a longer wavelength(1270, 2900
km) with higherphasespeeds(560, 1280km/day). Thereis no
singlecommon interval for the wind, sealevel, and currentestimates.
3503
IO0•/'x\ 7'0#0
Point
Depoe
,•"
'-,,
•..11
90 ø
• oo <.p.'k
\/
_ GOo/
o
I
I
I
I
02
0.4
I
i
0.6
cpd
1.0
•
o
•
•
:•"
o.2
"t
0.4
o.6
cow
Fig. 8. Autospectra,coherencesquared,and phasespectrafor sea
level observationsat Depoe Bay, Oregon' Toke Point, Washington;
and Torino, B.C.
shore than for offshoreseparations,that the fluctuationsare
coastallytrapped, and that they are correlatedwith wind and
sea level. The spectral analysis showed that the coherent
energyoccursmainly at 0.16 cpd,with a lesserpeak at 0.3 cpd
and an even smaller one at 0.44 cpd.
io
CURRENT
vs WIND
•
66m, UWlN vs Westport
-- -- 60 m, NH-IO vs Newport
..... IlOm, UWOFF vs Westport
it
^
1, ,
• i
ß
:;,I
V Ill
I I I /1!t; .--99%
-06
02
•0
04
06
WIND vs SEA LEVEL
•
:•.
•
DISCVSSION
:
•
Westport
....
Newport vs Depoe Boy
ß
vs Toke Pt
:.:
:'
.
. ß
Both linbar regressionand the spectralanalysissupported •
.--: • . . --99%
what seemed obvious from the visual presentation of the
observations(Figure 2): that low-frequencyfluctuationsin the
current over the continentalshelfare coherentover an along-06
-04
-02
•d
02
04
06
shore separation of 200 km. In addition, the regression Fig. 9. Coherencesquaredspectrabetweensealevel, current, and
wind, central Oregon and southernWashington.
analysisshowedthat correlationlengthsare greater for along-
04
,:
I I
I
3504
HUYER ET AL.: ALONGSHORECURRENTS
TABLE 6. Values of AlongshoreCoherenceSquared(coh•') and Phase½ With Its 95% Confidence
Limits for Signalsat 0.16,0.3, and 0.44 cpd From Observations
of the DeepInshoreCurrent,Wind, and
Sea •vel at Locations Separatedby a DistanceL
0.16cpd
L, km
coh•'
200
200
0.92
0.92
23 4- 4
21 4- 4
M•ajoraxiscomponent 200
0.89
194-4
Current (66 m, UWIN;
60 m, NH-10)
Northward component
Alongshorecomponent
½,deg
0.3 cpd
0.44cpd
coha
½,deg
coha
½,deg
0.51
0.58
32 4- 28
29 4- 24
0.85
0.84
67 4- 9
56 4- 9
12 4- 24
Sea level
Toke Point, Depoe Bay
210
0.80
7 4- 16
0.59
490
280
0.76
0.60
36 4- 16
36 4- 24'
0.27
0.24
0.50
0.03
0.12
68 4- 28
Torino,DepoeBay
Torino,Toke Point
250
0.77
29 4- 16
0.22
0.66
51 4- 20
Wind (Westport, Newport)
Northward component
Positivephaseindicatesthat the southernobservationleadsthe northernone.
At 0.16 cpd the high mutual coherencebetweenwind, cur- the wind off Oregonand that it propagatesnorthwardwith a
rent, and sea level and the similar values of the alongshore phasespeedexceeding630 km/day, much like a continental
coherenceof eachparametersuggestthat the currentfluctua- shelf wave, althoughit is not strictly barotropic.
The signalat 0.44 cpd may be similarto the oneobservedat
tions at this frequencymay be directly forced by the wind.
it mightbe
Mooersand Smith [1968] in a studyof sealevel data obtained 0.4 cpd by CutchinandSmith [1973],who suggested
in 1933 and 1934 found couplingbetweenatmosphericpres- a second-modebarotropic continentalshelf wave. We found
sure and sea level at about 0.1 cpd with a predominating its phasespeedto be at least340 km/day and probablyabout
periodof 6-8 days;they foundthat the disturbances
traveled 500 km/day, which is higher than expected (about 150
continentalshelfwave.The signal
from north to southbetweenNewport and Brookings,Oregon km/day) for a second-mode
(at 42ø05'N). They concludedthat the sealevelmight simply appearsto be somewhatbaroclinic:kineticenergyis higherat
be reflectingthe passageof atmosphericsystems.Gill and the shallowercurrentmeter(Table 3), and thereforephasespeeds
Schumann[1974] suggestthat Mooers and Smith [1968] basedon barotropicshelf wave theory may not be relevant.
observed a forced shelf wave which moves with the wind
Values of correlation and coherencesquaredbetweencursystem.Smith [1974] comparedwind, sealevel, and currents rent metersare higherfor alongshoreseparationsthan for offobservedat a singlelocation off Oregon in July and August shore separations,although the alongshoreseparationsare
1972 and found high mutual coherencebetweenwind current much greater than the offshoreseparations.Also, the alongand sea level at 0.15 cpd. In a subsequentstudy of the same shorecorrelationmay dependon the locationof both observaobservations,Kundu et al. [1974] found that this signal has tions;e.g., the alongshorecorrelationis higherfor the inshore
propertiesconsistentwith the theoreticalresultsfor the reso- pair (UWlN and NH-10) than for the offshorepair (UWOFF
experiments
to
nant responseof longbarotropiccontinentalshelfwavesto an and NH-20). Hence care is requiredin designing
alongshore component of the wind stress propagating determinethe alongshorecorrelationlengthscalesin currents.
northward along the coast as a wave. Our results,indicating Alongshorearrayswith mooringson the sameisobathdo not
similar phasespeedsfor wind, current,and sealevel fluctua- necessarilyyield highestestimatesof the alongshoreseparation: we obtained slightly higher linear correlationbetween
tions, support their conclusion.
The signalwe observedat 0.3 cpd wasalsofoundto be pres- UWlN and NH-20 than betweenUWIN and NH-10, although
ent in the 1933-1934 sealevel data. Ma [1970], usingtwo 100- UWIN is the shallowestand NH-20 the deepestof the three.
day data segments,showedit to be strongerin winterthan in Perhapscurrent metersin even shallowerwater would yield
summer at Coos Bay, Oregon (43ø10'N), and Torino, B.C., evenhighervaluesof alongshorecorrelationand coherence.It
and hardlypresentat SanFranciscoin eitherseason.He found may be that our observationswere at an optimum location.
significantalongshorecoherencebetweenTorino and Coos Our resultsindicatethat alongshorecoherenceis a functionof
Bay, separatedby 720 km, and interpretedit as a continental the distance offshore or of the water depth at the mooring
shelf wave propagatingnorthward at 700 km/day in winter sites. Since this function is as yet undetermined,we recomand 270 km/day in summer. Mooers and Smith [1968] also mend that any experimentto measurealongshorecoherences
foundnorthwardpropallation
between
Brookings,
CoosBay, have an array with two offshorelines of currentmetermoorand Newport with phasedifferencesindicatinga phasespeed ings,with at leastthreemooringsin eachoffshoreline,sothat
of about 350 km/day. Cutchinand Smith [1973] found no the likelihood of severe underestimates of coherence and corevidenceof a continental shelf wave at 0.3 cpd in the 1968 relation coefficientswill be greatly reduced.
observationsbut apparentlyobservedone at 0.22 and perhaps
Acknowledgments.We have benefitedgreatly from the assistance
one at 0.4 cpd. Smith [1974] found that his sealevel and cur- of JosephBottero,William E. Gilbert, and Henry Pittock.The current
rent spectrasuggested
the presenceof a shelfwaveat 0.3 cpdin observationswere made under National ScienceFoundation grant
Analysis
his 1972 data. Kundu et al. [1974] found a signal with a ID071-04211 as part of the Coastal Upwelling Ecosystems
barotropiccomponentat 0.28 cpd in someof the 1973obser- (CUEA) program of the U.S. Office of the International Decadeof
Ocean Exploration (IDOE) and Atomic Energy Commissiongrant
vations [Pillsburyet al., 1974b].They indicatethat the results AT (45-1)-2225 (Columbia River PhysicalOceanography).Contribuare consistentwith local driving of the currentsby the wind tion 844 from the Departmentof Oceanography,Universityof Washstress.Our resultsindicatethat the signalmay be generatedby ington, Seattle.
HUYER ET AL.: ALONGSHORE CURRENTS
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