VOL. 83, NO. C4
JOURNAL OF GEOPHYSICAL RESEARCH
APRIL 20, 1978
Variations in the AlongshoreCorrelation of Sea Level
Along the West Coast of North America
STEPHEN R. OSMER
USCG Researchand DevelopmentCenter, Groton, Connecticut06340
ADRIANA
HUYER
Schoolof Oceanography,OregonState University,Corvallis, Oregon97331
We investigatedsea level fluctuationsat seven locations from San Francisco to Torino, British
Columbia, during a 2-year period beginning in August 1973. Using overlapping 2-month periods, we
found the alongshorecorrelation to vary with time and with location along the coast. In winter the
flfiCtuations
arecorrelated
alongtheentirecoastfromSanFrancisco
toTorino;
at intermediate
locations
the correlation is higher with Torino than with San Francisco. In summer, sea level variations at San
Francisco and CrescentCity are not correlated with those farther north; there is still high alongshore
correlation among the stationsto the north and also betweenCrescentCity and San Francisco.In all
seasonstheesealevelfluctuationspropagatenorthward, althoughvariationsin the wind stresspropagate
southward.At each location the sealevel is usuallyalso correlatedwith the local wind stress,the wind
stressleading by about a day.
INTRODUCTION
filtered, but they were implicitly smoothedover both time and
spacein the computationprocess.
The 6-hour time seriesof atmosphericpressurewere usedto
Sea level fluctuations with periods of several days have
amplitudesof the order of 10 cm along the westcoastof North
America.
The fluctuations
correct
in sea level seem to be coherent with
fluctuationsin the wind and current [Cutchinand Smith, 1973;
Smith, 1974]. They are also highly coherent over alongshore
separations
of a fewhundred
kilometers
[Hu•Jer
etal., 1975].
There is someevidencethat the sea level fluctuationspropagate northward in summer [Clarke, 1977; Wang and Mooers,
1977] but southwardin winter [Mooersand Smith, 1968];Ma
[1970] found northward propagation in both summer and
winter but at different phase speeds.
Two years of sea level and wind stress data from seven
for the 'inverted
barometer
effect' on sea level. To
obtain the 'adjusted sea level' in centimetersfor each station,
we removed a 2-year mean (computed for the period from
August 1, 1973, to July 31, 1975) and added the atmospheric
pressure(in millibars minus 1000). The time seriesof adjusted
sealevel at the differentlocations(Figure 2) showthat the sea
level fluctuations are larger in winter than in summer. In
winter the fluctuationsare larger at the northern stations,but
in summerthey are somewhatlarger at the southernstations.
The time seriesof the northwardcomponentof the wind stress
(Figure 3) show similar patterns:fluctuationsare larger in
winter than in summer; in winter, they are largest at the
thatstudywecalculated
laggedandunlagged
correlation
coef- northernstations,and in summerthey are largestoff southern
locations between San Francisco and Torino, British Colum-
bia, were examinedin a recentpaper [Osmer, 1978].As part of
ficients between
Oregon and northern California.
wind and sea level data at the same location
and at different locationsand for different periods to determine if the correlation
between
sea level and wind
same at different locationsand at differenttimes of the year
and if the correlation
between
sea level at different
ANALYSIS
was the
locations
was independentof location and of season.
We computedlinear correlationcoefficientsamong the sea
level and wind stressrecords,both for the entire time period
and for overlapping2-month periods.The usual formulasfor
computing the significancelevels for correlation coefficients
assumethat all data pairs are independent.In our data, how-
OBSERVATIONS
Hourly tide gage data were available for San Francisco,
CrescentCity, Charleston,Newport, Toke Point, Neah Bay,
and Torino (Figure 1) for the period from August 1, 1973, to
September9, 1975. The hourly data were low passedto remove
tidal oscillationsby using a filter designedby Godin [1966,
1972], which has a half-power point of 95 hours. The lowpassedtime serieswere decimated to a &hour data interval
with 3080 points.
Estimates of the 6-hour atmospheric pressureand wind
stressat each tide gage location were supplied by Andrew
Bakun of the National Marine FisheriesService, Monterey;
theseestimateswere computedfrom the large-scalesynoptic
pressurecharts as describedby Bakun [1973, 1975]. These
times seriesof atmosphericpressureand wind stresswere not
ever, a singleevent lasts a few days, while our samplesare
separatedby only 6 hours; clearly, these pairs are not independent.To determinehow many independentsamplepairs
therewere (and hencethe significancelevel), we computedthe
integral time scale from the autocorrelationfunctionsand
divided our total record length by this integral time scale
[Allen and Kundu, 1978;Bendatand Piersol, 1971, p. 183].
Correlationcoefficients
for the entireperiod. We computed
both laggedand unlaggedalongshorecorrelation coefficients
for the adjusted sea level and the wind stressand also the
correlation
coefficients between sea level and wind stress at
each location. For sea level we found that the alongshore
correlationwasmaximumat zero lag for almosteverycase;in
no case did the maximum correlation exceed the zero lag
correlationcoefficientby more than 0.03. At intermediate
Copyright¸
1978 by the AmericanGeophysicalUnion.
Paper number 7C1089.
0148-0227/78/047C-
1089503.00
locationsthe sea level is more highly correlated with Torino
1921
1922
OSMER
ANDHUYER:
WESTCOAST
SEALEVEL
level at each location
relative
to Torino
and San Francisco.
During every period, the sea level at the southernlocations
leads the sea level at the northern locations;betweenCrescent
City and Torino the lag is about 1 day. The alongshorecorrelation variesa great deal during the 2-year period. In winter the
sealevelfluctuationsare correlatedalongthe entirecoastfrom
48øN
Torino to San Francisco, a distance of about 1260 km. In
TOKF
summerthe alongshorecoherenceis generallylower, and there
seemto be two domains: sealevel fluctuationsalong the coast
POI
between Charleston and Torino are correlated, and sea level
fluctuationsare also correlatedbetweenCrescentCity and San
Francisco. In summer there is no significantcorrelation between Charleston and San Francisco (620 km) or between
CrescentCity and Torino (820 km). The boundary between
thesetwo domains seemsto be quite sharp:Figure 5 shows
that in summer there is no significantcorrelation between
Charlestonand CrescentCity, althoughthey are only 180km
46 o
NEWPORT
44 o
-
Oregon
-
apart; at the sametime the sealevelat Charlestonis verywell
correlatedwith Newport, and CrescentCity is well correlated
CHARLESTON
_
with San Francisco. Poor correlation between Crescent City
and Torino occursin springand fall, just before and after the
--
period of very poor correlationbetweenCrescentCity and
42 o
CRESCENT
Charleston. We can think of a moving boundary betweentwo
domains:in winter it is south of San Francisco;in spring it
movesnorthward, between San Franciscoand CrescentCity;
in summerit liesbetweenCrescentCity and Charleston;and in
fall it againmovessouthwardbetweenCrescentCity and San
CITY
Coliforn/•
Franciscoto take up its winter positionsouth of San Fran-
40 o
cisco.
Table 2 showsthe alongshorecorrelation coefficientsfor
wind stress at each location relative to Torino and San Fran-
cisco.Wind stress,like sea level, has the highestalongshore
38 o
SAN
FRANCISCO
TOFINO
60 ÷
I
128øW
124 ø
40:
Fig. 1. Locations of the sea level observations.
20
0
than with San Francisco(Figure 4a), i.e., there is a definite
asymmetryin the alongshorecorrelationfunctionof sealevel.
For wind stress,too, the correlation coefficientwas maximum
0
at zero lag in almost every case, and in no case did the
maximum correlation exceedthe zero lag correlation by more
than 0.05. The wind stress at intermediate
locations
'' '
'v'•V •v,
60
is as well
correlated with San Francisco as with Torino (Figure 4b);
there is no asymmetryin the alongshorecorrelation function
•••ttTOKE
POINT
of the wind stress. At each location, sea level and wind stress
are significantlycorrelated(Figure 4c), and the correlationcoefficientis maximumat about5 lags(30 hours),thewind stress
leading the sea level.
Thesecorrelationcoefficients
werecomputedfrom the entire
records of 3080 points each. In this calculation we made no
attempt to remove the seasonalcyclesapparent in Figures2
and 3. Hence the correlationcoefficientsin Figure 4 reflectthe
coherenceof the seasonalcyclesaswell asthe coherenceof the
shorter-periodfluctuations.
Correlation coefficientsfor 2-month segments. We computed similar correlation coefficientsfor 24 overlapping2month periods,startingwith August-September1973 and extending through July-August 1975. Each 2-month data seg-
mentwaslinearlydetrended
beforecorrelation
coefficients
were computed;this detrendingeffectivelyremovesthe seasonal variation
from.the
data.
Table 1 showsthe alongshorecorrelationcoefficientsof sea
ol
i
i
i
i
•i i
JAN
1974
i
,
,
, i
JUL
i
,
,
JAN
i
,
,
••
•1
JIUL
1975
Fig. 2. Time seriesof the adjustedsealevel(in centimeters)at each
location, August 1, 1973, to September9, 1975.
OSMERANDHUYER:WESTCOASTSEALEVEL
1923
fluctuationsalong the North American west coastin terms of
coastallytrapped long waves.Thesemodelscan accountfor
the northward propagation of sea level and current fluctuations [MooersandSmith, 1968;CutchinandSmith, 1973;Wang
and Mooers, 1977]and alsofor the high alongshorecorrelation
[Huyer et al., 1975;KunduandAllen, 1976].Gill andSchumann
[1974] deviseda model for the generationof long shelfwaves
by the wind; Clarke [1977] used this model to compute sea
level at Newport from wind stressat severallocationssouthof
Newport and obtained reasonable agreement with the observedsealevel;he also obtainedreasonableagreementassuming purely local generation.
Our observationthat sealevelfluctuationspropagatenorthward, while wind stressfluctuations propagate southward,
strongly suggeststhat the response to the wind is predominantly in free, rather than forced, shelf waves. Forced
shelf waveswould propagatein the samedirection as that of
the forcing mechanism,i.e., the wind stress[Gill and Schumann, 1974].
We found that the sea level is almost always significantly
correlated
with the local wind stress. We also found that the
lag betweenwind stressand sea level at the same location is
about a day, regardlessof the location.Togethertheseobservations suggestthat at each location a significantportion of
thesealevelfluctuations
isgenerated
locallybythewindstress.
The properties of free barotropic continental shelf waves
SEA
A
LEVEL
rs. San
Francisco
rs. Torino
Fig. 3. Time seriesof the northward componentof the wind stress
(in dynesper squarecentimeter)at each location as computedfrom
the large-scalesynopticpressurecharts [Bakun, 1973],August 1, 1973,
to September9, 1975.
Sea
Sea Level
Level
0
o
$
o
0.4
correlation coefficients in late winter and the lowest values in
summer and fall. Unlike sea level the wind stress at the north-
o
i
•
i
i
1200
800
ALONGSHORE
ern locationstendsto lead(althoughonly by severalhours)the
i
i
400
o
SEPARATION (kin)
wind stress at the southern locations. In winter the wind stress
A
is correlated along the entire coast from San Franciscoto
Torino.
In summer
the wind stress at San Francisco
A
-
is not
significantlycorrelatedwith the wind stressat Torino, and the
wind stressat CrescentCity is more highlycorrelatedwith San
ß A
WIND
STRESS
_ v$ Son Francisco Wind Stress ß
vs Torino
Franciscothan with Torino.This againsuggests
the presence
W/nd Stress
IX
_
of two domains
in summer.
We were not able to establish
i
whetherthere really are two domainsin the wind stressor to
investigatethe boundary between them: the wind stressestimatesat neighboringstationsare not independent,sincethe
I
i
I
I
400
800
ALONGSHORE
SEPARATION (kin)
SEA
original atmosphericpressuredata are storedon a 3ø grid
LEVEL
[Bakun, 1973, 1975]. Becauseof this, correlation coefficients
betweenwind stressat locationslessthan 3ø (330 km) apart
are veryhigh,e.g., over0.95 for Newport and Charleston(140
km) andover0.8 for Charleston
andCrescent
City( 180km).
Table 3 shows the correlation coefficients between the north-
wardcomponent
of windstress
andthe sealevelat each
location. In general, wind stressleads sea level at the same
location by about 1 day. There is no o'bviousseasonalvariation in the correlation between wind stress and sea level. At the
threecentrallocations,Charleston,Newport,and Toke Point,
the wind stressand sealevel are almost alwayscorrelatedat
•
.
ß
ß
•0.4II•[]
•
o
o
ß
[]
•
vs. WIND
STRESS
Unlagged Corr
Coeff.
[]
Maximum
CoefL
ß
Corr.
ß
[] [] ß
[]
i
DISTANCE
/%•
i
40o
8oo
FROM
1200
TOFINO
Fig. 4. Correlationcoefficients
calculatedfor theentireperiod:(a)
Maximumcorrelationcoe•cientsas a functionof alongshore
separation for sea level at each location relative to Torino and San Francisco.
(b) Maximum correlationcoefficientsas a function of alongshore
separationfor the northward componentof wind stressat each loca-
the 1% level.
tion relativeto TorinoandSanFrancisco.(c) Unlaggedandmaximum
DISCUSSION
Beginningwith Mooers and Smith [1968] there have been
severalattemptsto accountfor the nature of the sea level
correlation coe•cients between the adjusted sea level and the north-
ward componentof the wind stressat each location,plotted as a
functionof distancefrom Torino.The dashedline in eachcaserepresentsthe 1% significancelevel.
1924
OSMER
ANDHUYER:WESTCOAST
SEALEVEL
+
++++
++++
+
+
+
+++
o
•
+++
.,..
•
,.•
Z
--.
o•,
+•
+++
+
--
+++
+++
+
o •
+++
+++++
o
._= o
.,-.
+++
++++
++
++
.,.. -'•
o
++
+
+
•o
+
o •
o
,_.
r,•
,,.
,--
OSMERANDHUYER:WESTCOASTSEALEVEL
c•
,.•
c•
o
o
._,
._,
o
o
._,
o
oooooo••
m
o
o
o
o
z
o
._,
o
o
._,
o
._,
•",,I
o
••ooooo
1925
1926
OSMERANDHUYER:WESTCOASTSEALEVEL
0 197,.•-1974
ß /974-1975
that the seasonalchangein stratificationmight be suitable,
alongpart of the coastline,for the presence
of internalKelvin
wavesduringpart of the year and of barotropiccontinental
shelfwavesduringthe remainderof theyear.Sucha changein
stratification
wouldresultin quitedifferentpropagationvelocitiesbut wouldprobablynot affectthe alongshore
correlation
0.8•,0""0
'0-0•
k,,
• NEWPORT
vs.
CHARLESTON
(140km)
I,•
0
I
of coastal sea level.
If localgenerationby the wind stressis importantin determining the characterof the shelf waves,we might expect
alongshoreand seasonalvariations in the wind stressfield to
affectthe sea level. We saw earlier that in winter, wind stress
•
0•
fluctuationsare correlatedalong the entirecoast.In summer
the windstressat SanFranciscois not significantly
correlated
0.4 - -- !
-- --
-
.
•
•
0
•
•
CHARLESTON
rs.CRESCENT
CITY(180km)
I I I I I I I I I ! I I
-GRESGEMT
CITY
rs.S•MER•MGISGO
(440kin)
0.8-
•0•
o- -/-
_ _,,
,,- /
7o
with the wind stress at Torino. We were unable to determine
whetherthereis a narrow boundarybetweentwo domainsin
the wind stressfield, as there appearsto be in the coastalsea
levelfluctuations.
Thereis a suggestion
thatsucha boundary
may indeedexist:the latitude of the centerof the North Pacific
high-pressure
cell variesfrom about30øN (well southof San
Francisco)
to about40øN(aboutthelatitudeof Crescent
City)
in summer.It may be that there is somefeaturein the atmosphereassociated
with this high that actsas a barrier to the
propagation of fluctuations in the wind stress.
CONCLUSIONS
o
Sealevelfluctuationsalongthe PacificNorthwestcoasttend
Fig. 5. S•asonalvariation
althoughfluctuationsin
th• adjusted
s•al•v•l for n•ighboring
stations:
N•wportandCharl•s- to propagatenorthwardin all seasons,
tendto propagate
southward.
Hencea signifiton,Charleston
andCrescent
City, andCrescent
City andSanFran- thewindstress
cisco.
cantportionof thesealevelfluctuations
isprobablyassociated
withfree,asopposedto forced,coastally
trappedlongwaves.
dependonly on the bathymetryof the continentalshelfand Sea level fluctuationsare significantlycorrelatedwith local
slope
region.
Hence
thealongshore
correlation
wouldnotvary variationsin thewindstressandlagthewindstress
by about1
seasonally.
Therearemorecomplex
theories
[e.g.,Allen,1975] day.
in whichthenatureof coastally
trapped
waves
depends
onthe
We have shownthat the alongshorecorrelationcoefficients
stratification
as well ason thebathymetry.
It is conceivableof sealevelalongthePacificNorthwestcoastvarywithseason
TABLE
3. Maximum
Lagged
Correlation
Coefficients
CCr•Between
theSeaLevel
andtheNorthward
Component
ofWindStress
atEach
Locationfor 24 Overlapping2-Month Periods
CCm
Period
Torino
Neah
Bay
TokePoint
Newport
CharlestonCrescent
City SanFrancisco
A73-S73
S73-O73
O73-N73
N73-D73
D73-J74
J74-F74
F74-M74
M74-A74
A74-M74
0.44(-2)
0.35(-1)
0.34(+4)
0.38(+4)
0.46(-2)
0.43(+3)
0.41
(+5)
0.41(+5)
0.31(+5)
0.46(+4)
0.33(+5)
0.45(+5)
0.50(+5)
0.51
(+6)
0.48(+5)
0.47(+6)
0.40(+8)
0.41(+4)
0.48(+4)
0.49(+4)
0.56(+4)
0.54(+4)
0.53(+4)
0.55(+4)
0.60(+4)
0.58(+5)
0.48(+4)
0.65(+5)
0.53(+4)
0.50(+5)
0.61
(+8)
0.64(+7)
0.54(+5)
0.53(+6)
0.53(+5)
0.50(+4)
0.62(+5)
0.52(+5)
0.54(+5)
0.67(+7)
0.70(+7)
0.60(+5)
0.61
(+6)
0.54(+6)
0.60(+4)
0.63(+4)
0.64(+4)
0.64(+4)
0.41(+4)
0.46(+4)
0.47(+8)
0.51(+6)
0.40(+8)
0.41(+8) . 0.37(+5)
0.33(+4)
0.32(+4)
0.36(+4)
0.41
(+4)
0.43(+4)
0.44(+4)
0.60(+5) 0.59(+4)
0.48(+5)
0.57(+6)
0.58(+4)
0.64(+5)
0.58(+3)
0.55(+4)
0.38(+4)
0.53(+6)
0.34(+6)
0.39(+5)
0.33(+5)
0.44(+6)
0.47(+6)
0.56(+6)
0.58(+5)
0.68(+5)
M74-J74
J74-J74
J74-A74
A74-S74
S74-O74
O74-N74
N74-D74
D74-J75
J75-F75
F75-M75
M75-A75
A75-M75
M75-J75
J75-J75
J75,A75
0.37(+4)
0.40(+5)
0.38(+1)
0.42(+4)
0.37(+5)
0.33(-2)
0.36(-1)
0.58(+4)
0.34
0.47(+5)
0.50(+5)
0.50(+5)
0.37(+8)
0.41(+8)
0.39(+6)
0.33(+5)
0.35(+9)
0.37(+7)
0.58(+7)
0.50(+12)
0.49(+5)
0.39(+4)
0.51(+4)
0.52(+5)
0.59(+4)
0.56(+2)
0.63(+5)
0.65(+4)
0.56
0.66(+6)
0.69(+4)
0.43(+4)
0.67(+4)
0.64(+4)
0.58(+5)
0.71
(+5)
0.69(+3)
0.61
(+4)
0.65(+6)
0.32(+4)
0.58(+4)
0.55(+6)
0.44(+5)
0.31(+5)
0.51
(+4)
0.47(+6)
0.55(+6)
0.56(+4)
0.38(+6)
0.3•(+4)
0.44(+4)
0.44(+4)
0.59(+4)
0.66(+4)
0.59(+6)
0.42(+4)
0.56(+4)
0.54(+4)
0.49(+1)
0.41(+4)
0.49(+4)
0.37
(+4)
0.55(+3)
0.48
0.67
(+4)
0.59(+4)
0.61
(+4)
0.38
0.45(+4)
0.32
0.37
ThelagL, inmultiples
of6 hours,
isshown
(inparentheses)
if it isdifferent
fromzero.
A positive
lagindicates
thatthewindstress
leads
thesealevel.
The5%,1%,and0.1%
significance
levels
are0.30,
0.38,and0.48,respectively.
Correlation
coefficients
less
than
0.30arenotshown.
OSMERAND HUYER:WESTCOASTSEALEVEL
1927
America, 1967-1973, Tech. Rep. Nat. Mar. Fish. Serv. SSRF-693,
and with location along the coast. In winter the alongshore
Nat. Oceanicand Atmos..Admin., Seattle,Wash., 1975.
correlationis highest,and sealevelfluctuationsare correlated
Bendat, J. S., and A. G. Piersol,RandomData.' Analysisand Measurealongtheentirestretchof coastfrom SanFranciscoto Torino.
ment Procedures,407 pp., John Wiley, New York, 1971.
In summerthereis pooralongshore
correlationbetween
Char-
Clarke, A. J., Observational and numerical evidencefor wind-forced
leston and CrescentCity, although there is high alongshore
coastaltrappedlong waves,J. Phys. Oceanogr.,7, 231-247, 1977.
correlationboth north and southof this apparentboundary. Cutchin, D. L., and R. L. Smith, Continental shelf waves: Lowfrequencyvariations in sea level and currentsover the Oregon
We suggest
that theremay be two domainsof coastalsealevel
continental shelf,J. Phys. Oceanogr.,3, 73-82, 1973.
fluctuationsyear-round:in winterthe boundarybetweenthem Gill,A. E.,andE. H. Schumann,
Thegeneration
of longshelfwaves
is southof San Francisco,in springit movesnorthwardto its
by the wind, J. Phys.Oceanogr.,4, 83-90, 1974.
summerpositionbetweenCrescentCity and Charleston,and Godin, G., Daily mean sea level and short period seiches,Int. Hydrogr. Rev., 43, 75-89, 1966.
in fall it returnsto itswinterpositionsouthof SanFrancisco.
We are unable to account in detail for the seasonal variation
Godin, G., The Analysisof Tides, 264 pp., University of Toronto
Press, Toronto, 1972.
in the alongshorecorrelationof sealevel fluctuations.How- H uyer, A., B. M. Hickey, J. D. Smith, R. L. Smith, and R. D.
ever,the alongshorecorrelationof wind stressshowsa similar
Pillsbury,Alongshorecoherenceat low frequenciesin currentsobserved over the continental shelf off Oregon and Washington,J.
seasonalvariation.There mightwell be a seasonallymigrating
Geophys.Res., 80, 3495-3505, 1975.
barrier to the alongshorepropagationof fluctuationsin the
wind stress.
Acknowledgments.This study was completed while the senior
author was completinghis M.S. degreeat Oregon State University.
National ScienceFoundation grant DES 74-22290 provided support
for the junior author and for the computer processing.We thank
Robert L. Smith and John S. Allen for helpful commentsand Andrew
Bakum for supplyingthe wind stressand atmosphericpressuredata.
Kundu, P. K., and J. S. Allen, Some three-dimensionalcharacteristics
of low frequencycurrent fluctuations near the Oregon coast, J.
Phys. Oceanogr.,6, 188-199, 1976.
Ma, H. S., Sea level responseto low-frequencyatmosphericpressure
fluctuationsalong the northwesternAmerican coast, M.S. thesis,
Oregon State Univ., Corvallis, 1970.
Mooers, C. N. K., and R. L. Smith, Continental shelf waves off
Oregon, J. Geophys.Res., 73, 549-557, 1968.
Osmer,
S.R.,A statistical
analysis
ofsealevelandWindstress
atseven
locationson the west coast of North America, M.S. thesis,Oregon
State Univ., Corvallis, 1978.
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Allen, J. S., Coastal trapped waves in a stratified ocean,J. Phys.
Oceanogr.,5, 300-325, 1975.
Allen, J. S., and P. K. Kundu, On the momentum,vorticity, and mass
balanceoff the Oregon coast,J. Phys. Oceanogr.,in press,1978.
Bakun, A., Coastalupwellingindices,westcoastof North America,
1947-1971,Tech.Rep. Nat. Mar. Fish.$erv. SSRF-671,Nat. Oceanic and Atmos. Admin., Seattle, Wash., 1973.
Bakun, A., Daily and weeklyupwellingindices,westcoastof North
Smith, R. L., A descriptionof current, wind, and sealevel variations
duringcoastalupwellingoff the Oregoncoast,July-August 1972,J.
Geophys.Res., 79, 435-443, 1974.
Wang, D.-P., and C. N. K. Mooers, Long coastaltrappedwavesoff
the west coast •f the United States, summer, 1973, J. Phys.
Oceanogr.,6, 856-864, 1977.
(Received September26, 1977;
revised November 18, 1977;
accepted
November
21, 1977.)