JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 98, NO. C12, PAGES 22,589-22,602, DECEMBER
15, 1993
Wind-Forced Variability of the Deep Eastern North Pacific'
Observations of Seafloor Pressure and Abyssal Currents
P. P. NIILER, • J. FILLOUX, • W. T. LIU, 2 R. M. SAMELSON,3 J. D. PADUAN,• AND C. A. PAULSON4
Data from an array of bottom pressuregaugesand a string of current meters in the vicinity of 47øN,
139øW, are used to examine the deep-ocean variability forced by ocean surface wind stress curl from
August 1987 to June 1988. Bottom geostrophic currents are computed from the pressure gauge array,
and these correspond well to the long-period directly measured currents at 3000 m. The supratidalperiod bottom pressure variations are coherent at 95% confidence with the wind stress curl in period
bands of 3-4 days and 15-60 days but removed in distancesof 400 and 700 km to the northwest and
the southeast,respectively. A linear, two-layer hydrodynamic model is used to examine the theoretical
forcing produced by random-phasedsurface wind fields for the conditions of the eastern north Pacific
and the 15- to 60-day-period observed response is reproduced credibly. To model 3- to 15-day
variations, more realistic models are required.
1.
INTRODUCTION
tions in velocity at this site were shown to dynamically
follow the steady state Sverdrup relationship, expressed as,
The first observations that time-dependent, deep-ocean
currents
are related
to surface
winds
were
derived
H2v V - (f/H) = z. V - x(r/p),
from
yearlong current meter records in a cluster of moorings north
and east of Barbados. Koblinsky and Niiler [1982] showed
that significantcoherences existed between the 4- to 40-dayperiod east-west pulsations of the trade winds r x above
Barbados and the north-south currents v at all depths in the
ocean at 15øN, 54øW. The responseamplitude of v to r x was
depth- and period-dependent. It decreased by a factor of 3
from 150- to 4000-m depths and increased by a factor of 5
from 8- to 40-day periods. The interpretation of these data
was that the deep-ocean forcing was produced by large
horizontal scale wind stress curl (hereinafter referred to
simply as "curl") due to westward propagatingpulses in the
trade winds with larger east-west than north-south scale.
The amplitude of the deep wind-related currents was 1-3
cm/s. Thus deep-oceanforcing shouldbe observable in many
places where the mesoscaleeddy energy is low.
Theoretically, wind-forced deep-ocean motions should
depend upon wind stress curl. Mt;iller and Frankignoul
[1981], using a model of randomly forced linear motions in a
stratified, infinite, flat-bottom, beta-plane ocean, computed
local coherencesand showed that motions across the planetary vorticity gradient should exhibit the strongest coherence with the local wind stress curl. Niiler and Koblinsky
[1985], using current meter data, demonstrated that such a
dynamical link does in fact exist locally at 42øN, 152øW,
although at a shorter period than was predicted by Milller
and Frankignoul. Both the amplitude and the phase of the
currents that were forced across the planetary potential
vorticity field (orf/H contours) on a 150-km horizontal scale
were predicted from the local surface wind stress computed
(1)
where H is the ocean depth, v is the horizontal velocity, f is
the Coriolis parameter, r is the surface wind stress, p is the
density of seawater, and z is the unit vector in the vertical
direction.
That deep-ocean motions that are perpendicular to the
planetary vorticity gradient should show a wind-forced component has also been suggestedby measurements of currents
along the continental rise in the northeastern Atlantic. Dickson et al. [1982] analyzed current meter data from six sites in
the eastern
North
Atlantic
between
41 ø and 59øN.
Record
lengths ranged from 5 to 25 months, and depths ranged from
200 to 4700 m. They showed that the eddy kinetic energy of
motions with periodicities between 3 and 80 days along
topographic contours increased in winter by a factor of 5.
Because mesoscale wind forcing at these latitudes has a
strong seasonal cycle, they suggested that the increased
current variability in winter was caused by the concurrent
increase of atmospheric variability. In the analysis of 3 years
of deep-ocean currents from 42øN, 152øW, Koblinsky et al.
[1989] showed that in the direction of the planetary vorticity
gradient, variable currents of annual and interannual time
scale followed the variability of the mesoscale curl at that
location. Thus the seasonally forced local response was
established. However, in a survey of 31 sites in the Pacific
for which an excess of 1 year of current meter data exists,
they found only three locations where a local relationship of
wind curl and currents could be established. Cummins [1991]
used a barotropic, variable-depth model of the northeast
Pacific and forced it with random, white-spectrum wind
stress curl. He found that local planetary vorticity balance
from a similar 150-km-scale wind field. The 4000-m oscillawas establishedonly for large (4ø x 4ø) area averages of the
velocity and at periods larger than 40 days. In models,
1Scripps
Institution
of Oceanography,
La Jolla,California.
bottom topography produces many small-scale, incoherent
2jet Propulsion
Laboratory,
Pasadena,
California.
3WoodsHole Oceanographic
Institution,WoodsHole, Massa- waves. Cummins's [1991] calculations with a three-layer
chusetts.
baroclinic model, but now forced with European Center for
4College
of OceanicandAtmospheric
Sciences,
OregonState Medium-Range Weather Forecasts (ECMWF) winds, also
University, Corvallis.
demonstrated that the wintertime increase of kinetic energy
Copyright 1993 by the American Geophysical Union.
at the lowest level is not necessarily a consequence of local
planetary
vorticity tendency but is most likely a consePaper number 93JC01288.
0148-0227/93/93JC-01288505.00
quence of increased wintertime, barotropic wave activity.
22,589
22,590
NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
The theoretical framework of how both componentsof
motion are forced by curl and how, in a more generalsense,
coherence analyses can be used to examine deep-ocean
forcing by curl was extendedin an importantway by BAnk
[1989]. He noted that since the wind responseshould be
quasi-geostrophic,Rossby waves (or topographicRossby
waves) that are excited by the curl shouldtransportinformation, or coherence,along the direction that wave groups
travel. Both eastwardand westward propagationof information in the deep ocean is possible. His inclusion of wave
dynamicsin the searchfor deep-oceanresponsewas motivated by the work of Allen and Denbo [1984],who observed
in the analysis of wind-forced continental shelf motions,
where the continental shelf waveguide is very strongly
oriented alongshore,that motions alongf/H contours are
most coherent with wind forcing removed some distance
from the measurementsite, oppositethe direction of wave
group propagation.B•ink [1989] showed theoretically that
the strongestcoherencein a randomly forced ocean should
be nonlocal because of Rossby wave propagation and,
indeed, discoveredthat deep currents at 28øN, 70øWwere
more stronglycoherentwith curl to the east of this site than
with the local curl, althoughpredicted and observedenergy
levels differed by 2 orders of magnitude.Samelson [1990]
compared a similar model with observationsfrom current
meters at 32øN, 24øW and found reasonable agreement in
deep energy levels and in coherence patterns for 3.7- to
8.0-day-period motions, especiallywhen a reflectingmidoceanridgewas includedalongwith the absorbingeasternand
western boundaries. These results suggestedthe possible
existenceof wind-forced,standingplanetarywaves at 3.7- to
8.0-dayperiodsin the easternNorth Atlantic basin,although
only one reflection,rather than the two neededfor a standing
ally, it is found that motions alongf/H contourson continentalshelvesand margins,where trappedwaves are possible, exhibitsignificantremotecoherences
with wind forcing.
In the openocean,barotropiccomponentsshouldbe present
at all latitudesand observations,andtheory showsthat both
velocity componentsare coherent.Both eastwardand westward propagationof informationfrom a forcingarea should
be expected.In mid to highlatitudes,the motionsshouldnot
exhibit significantbaroclinic forced componentsfor 2- to
40-day periodicities.
In August 1987, as part of the Ocean Stormsexperiment,
we placeda coherentarray of sevenbottompressuregauges
and a string of deep current meters in the vicinity of 47øN,
139øW,to observethe deep-oceanresponseto surfaceforcingin a detailedfashion,whichhadnot beenpossiblebefore.
The array of instrumentswas recoveredin June 1988. This is
a report of an observationaland theoretical synthesisof the
relationshipbetweenwind forcingand deepresponsein the
easternNorth Pacific. In section2 the array of instruments
and the data series are discussed, in section 3 the relation-
shipsbetweenwind stresscurl and deep-ocean
variability
are analyzed, in section4 a theoreticalmodel is compared
with the observations,and the conclusionsare presentedin
section
5.
2.
THE DATA
The array of sensorswas deployedfrom R/V Melville in
the period August 22-27, 1987, and recovered during the
periodJune 18-25, 1988. Figure la showsthe array location
and configurationsuperimposedon a 2ø spatial averagefield
of f/H contours. Figure lb shows the detailed locations,
within the topographicfeatures, of the array of bottom
wave, was allowed in the model.
pressuresensorsand the current meter mooringfrom which
The theoriesof Brink and Samelsonpredict that typically good data were obtained. A discussionof the pressure
the strongestcoherenceshouldbe between bottom pressure sensorprinciples,performance,drift correctionprocedures,
and curl. Luther et al. [1990] demonstrated,with a yearlong and data reduction is given by Filloux [1980, 1983]. The
bottom pressure and barotropic velocity determined from current meters were deployed on a taut-wire, subsurface
electric field measurementsat 41øN, 169øW,that significant mooringwith an Aanderaa acousticcurrent meter at 3000 m.
nonlocal
coherences
can be found between
the bottom
The detailed instrumentperformance,methods of data repressure,"electromagnetic" barotropicvelocity, and curl in duction,and raw statisticsare givenby Levine et al. [1990].
the period band between 2 and 25 days. The observed Here we use bottom pressure records which were low
coherencewas considerablylarger than that predicted. The passedwith a 38-hourDoodsonfilter to remove tidal signals
large-periodcoherencewas strongestwith the forcing to the andthe currentmeter recordfrom 3000-mdepth,which was
southeast of the bottom record location and was 180 ø out of
averaged daily. All records were decimated to 0.2-day
phase, while the small-periodresponseexhibiteda coher- intervals.
The wind stress data were obtained from the ECMWF
encemaximumdirectly over the pressuresensor,with phase
decreasingto the west. In our paper we find several quali- 6-hourlysurfaceanalysison a 2.5ø x 2.5ø stereographicgrid
tative aspectsof agreementof Samelson'stheory with both (a separateanalysiswith the National MeteorologicalCenter
our observationsand those of Luther et al. [1990].
dataproducedno significantdifferences).The surfacewinds
In summary, we now know that wind-forced deep-ocean and other boundarylayer parameterswere used to produce
motions are observable and that strong, wintertime wind a wind stressaccordingto the schemeof Liu et al. [1979]
stressvariability producesthe strongestdeep currents. The- under neutral conditions.Curls were computedon a central
ory suggeststhat in the open ocean, the field most coherent finite-difference scheme.
with the surface forcing should be bottom pressure. The
There was sucha high degreeof similaritybetweenthe six
motions acrossf/H contour should also have an observable recoveredpressurerecords (Figure 2) that we restrict our
coherent responseto the curl at distancesremoved from the analysisandinterpretationto datafrom the centralsite (P7).
observationsite which dependupon the period of the forc- However, there are also small but significantdifferencesin
ing. For small periods (few days or strictly to < f), the the amplitudesof the pressuresignalswhich we used to
highestcoherencesare expectedto be local, while for large compute the pressure gradients. The 300-day record of
periods(but smallerthan the values for which the Sverdrup utility to us containsthe infratidal pressurevariations with
balance is established), the remote forcing will play an periodicitiesof up to about 50 days. At longer periods the
increasinglyimportant role. Theoretically and observation- signalsbecome severely contaminatedby the inelastic re-
NIILERETAL.' WIND-FORCED
VARIABILITY
OFTHEDEEPEASTERN
NORTHPACIFIC
22,591
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Fig. 1. •cations(top)oftheinstrumented
arrayon2øspatial
averagef/H
contours
(inunitsof 10-•2 cm-• s-•) and
(bottom)
of bottompressure
gauge(squares)
anddeepcurrentmeter(square
labeledC1)in OceanSto•s.
120
22,592
NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERN NORTH PACIFIC
P8
5O
v+4
P?
4O
•
3o
P6
'•
2o
P4
P3
P2
0
-10
230
270
310
350
390
430
470
510
550
Yearday (1987)
Fig. 2. The long-periodrecordsof bottom pressurefrom Ocean
Storms,which have been passedthrougha 38-hour-cutoffDoodson
filter.
-2
sponse,or creep, of the sensorunder the stressof a 4200-m
water pressurehead. This longer-periodlimitation is discussedby Filloux et al. [1991]. It is alsoillustratedin Figure
3, which displaysthe pressuredifferencebetween the two
closest sites (P3 and P8), and discussedfurther in the
appendix,which describesthe insightsinto pressuresensor b
behavior gainedfrom the presentstudy.
To provide a realistic, independent,quantitative assessment of the creep-correcteddata and their significance,we
computedthe horizontal pressuregradientwithin the array
by fitting, in a least squaressense, a quadratic function of
longitudeandlatitudeto the pressuresignalsandevaluatedit
0.0
at the location of the current meter mooring. Since the
180 currentswith periods longer than 10 times 17.4 hours (the
inertial period) shouldbe within 10% of geostrophicequilib90rium, a comparisonof the geostrophiccurrents computed
from this pressure gradient with the measured currents N•:• 0should further define the useful frequency range of the
-90
pressure records. Figure 4 shows the comparisonof the
directly measuredcurrent componentswith the geostrophi-180
_
N
D
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F
M
1987
A
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1988
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cpd
Fig. 4. (a) Directly measuredcurrentsat 3000-mdepth (dotted
line) and geostrophicallycomputedcurrentsfrom the bottom pressure array (solid line); (b) rotary coherence and phase of the
measuredand computedcurrents. Positive phase meanscomputed
currents lead the measured
confidence level.
230
270
310
350
390
430
470
510
550
Yearday (1987)
Fig. 3.
Pressure differences between P3 and P8, which were
separatedby 0.5 kin.
currents.
The dotted
line is the 95%
cally determinedcomponentsfrom the pressurearray. The
trends in pressuredifference (Figure 4a) which are not
reproducedin the correspondingdirectly measuredcurrents
further demonstratethat these pressuredata must be used
with appropriate care, particularly at longer periods. It is
expected, however, that the coherencebetween currents
measured at a single point at 3000-m depth and those
averaged over the separation distancesbetween pressure
sensorsat 4200-mdepthwould be lessthan unity. We do not
have informationon the spatialscaleof currentsin this area,
so we cannot
estimate
what
the true coherence
should be
NIILER ET AL.' WIND-FORCED VARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
TABLE 1. Parametersof the Two-Layer, StochasticallyForced
22,593
lengthof instrumentP7 (Figure 2) is 300 days; averagedraw
estimates of the cospectra and quadspectrawere used to
produce
band-averagedcoherenceand phaseestimatesas a
Description
Definition and/or Value Used
function of period. Coherence estimates above 95% confiD1 = 700m
Layer depths
dence limits were found in the 3- to 4-day-period band and
D2 = 3500 m
the 15- to 60-day-periodband. The 3- to 4-day-periodvarigAp/p= 1 cms-2
Reducedgravity
ability of the bottom pressureis most coherentwith the curl
f = 1.1 x 10-4 s-1
Coriolis parameters
400 km to the northwest;the phaseincreasesacrossthis area
/3 = 1.6 x 10-•3 cm-• s-•
Effective/3 magnitude
from east to west (Plate 1). The 15- to 60-day-periodbottom
/3 = HIVf/H[ = 3.2 x 10-•3 cm-1 s-•
18 ø T
Effective/3 direction
pressure was most coherent with curl 400-700 km to the
Fraction parameter
R = (180days)-•
southeast, which follows remarkably the direction from
Eastern boundary
X = 1250 km from site in lower layer
which
energy of the large-scaletopographicRossby waves
Autocorrelation
for curl
t(x, y) = exp (-lxl - s
would propagateto the bottom pressuresite along (f/H)
*For3-dayperiod,$r-• = 750kmandg-• = 250km,andfor 25 contours(Figure 1); the phase is nearly constantat 180ø
dayperiod,$r-1 = 1200kmandg-• = 500km.
(Plate 1). These results are quantitatively similar, both in
amplitudeof the coherenceand in phase, to those of Luther
et al. [1990], who used similar-length bottom pressure
compared with that computed from the pressure array as records from 1986-1987 at 40.7øN, 169.3øW. Thus the northshown in Figure 1. Because a significant coherence was ward location of the small-periodcoherenceand the southcomputedbetween these two time seriesin the period band eastward location of the large-period coherence maxima
3 to 40 days (Figure 4b), we felt it was legitimateto use the between bottom pressureand curl are firmly establishedat
pressuredata in this period interval to relate bottom pressure the two sites for which yearlong bottom pressuremeasureto surfaceforcing.Note that in the 3-day-periodmotions,the ments exist.
The 3000-m-depthnorthward velocity has significantcocurrent meter record leads the bottom pressure record,
herence with the curl located 200 km to the north of the
implying a vertical-phase propagationin the 3-day-period
signal.This is the first time we are aware of that a pressure mooringin the 3- to 4-day band and 600 km to the northeast
gradient has been measured with sufficient precision and in the 9- to 33-day band (Plate 2). We also computedthe
proper spatial scale to be used to derive an absolute two- geostrophicallyderived northward current coherence with
dimensionalcurrent from the geostrophicmomentum bal- the curl, and no essential differences were found. The
ance.
coherencebetweeneastwardcurrentand the curl (Plate 3)
was lower than with bottom pressureand northward velocity; at a few locations,95% significantcoherencesappeared
3.
THE OBSERVED DEEP RESPONSE TO SURFACE FORCING
at period bandsof 4.5 and 15-60 days,which appearto be at
As we have pointed out, the atmosphericforcing of ocean longer periods than the significantcoherencesobservedfor
bottomcurrentsandpressurein time periodsof a few daysto the northwardcomponent(Plate 2). Since bottom pressure
a few monthsis causedprimarilyby the curl (seeworks cited variationsare causedby the deep currents,it is not surprisin the introduction). Measurable forcing by atmospheric ing that the bottom pressurecoherencespansthe bands of
surfacepressuredistributionsis not expected, becausethe the combinedvelocity coherences.
surface pressuredistributionsover our site have horizontal
Because surface winds are proportional to geostrophic
scalesof less than 1250 km in periodsof less than 25 days winds, the curl is a twice-differentiated function of the
(Table 1), and theseare smallerthan the barotropicradiusof atmosphericsurfacepressure,being nearly proportional to
deformation. If H is a constantwater depth and the atmo- Laplacian of pressure. In the atmospheric systems that
sphericpressurehas a horizontal scaleL, then isostasywill travel throughour observationalsite, Laplacian pressureis
occurif (L/R)2 << 1, whereR 2 = (gH)/f2 isthesquare
of proportionalto pressureitself (with a negativesign)because
the barotropic deformationradius of 2000 km. An isostatic, the time-dependentpressure systemsare "bowl-shaped."
or inversebarometer, responseof the sea level is expected. Thus the coherencepattern expectedbetween the curl and
We computedthe correlationsof the bottom pressurewith surfacepressureis similar to that observedbetween the cud
the local atmosphericpressure,and they were not significant and bottompressure(with a 180øphaseshift). This relationin any period band between 3 and 50 days, which is consis- ship is not, however, a dynamical one but rather is caused
tent with local isostasy(this can alsobe seenfrom the phase purelyby the natureof the self-coherence
of the atmospheric
and coherencestructuresin Plate 4). Of course, significant variables (for similar reasons,we expect to have coherence
correlationsare found between bottom pressureand atmo- of the deep measurementswith the surfacewinds). Differsphericpressure(or winds) removedin spaceor laggedin entiationintroducesnoise.Therefore the coherencepatterns
time, but those are producedby the features in the sea level obtainedusingatmosphericpressureare expectedto be at a
pressure (and winds) which produce a curl of the wind higher significancelevel than those obtainedusingthe curl.
stress.So, we go directly to the analysisof bottom response This is dramaticallydemonstratedin the coherencepatterns
in termsof the curl. Someof the most dramaticrelationships of bottom pressureand velocity with atmosphericpressure
of the associatedatmosphericpressuredistributionsto the (Plates 4-6). The atmosphericpressurecoherencesmirror
bottom pressure and velocities at 3000 m are also demon- the curl coherencesbut at a largerlevel of significance.Note
strated.
that over the bottom pressurearray, there is no correlation
We computed the spatial distribution of coherence and (coherenceat 0ø or 180ø phase) of bottom pressure and
phase between bottom pressure and curl as a function of atmosphericpressure.
period over the area 35ø-60øN, 120ø-160øW. The record
A computationof the stericlevel determinedfrom temperModel
22,594
NIILER ET AL.' WIND-FORCED VARIABILITY OF THE DEEP EASTERN NORTH PACIFIC
NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERN NORTH PACIFIC
22,595
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¸
22,596
NIILER ET AL.: WIND-FORCEDVARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
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NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERN NORTH PACIFIC
22,597
22,598
NIILER ET AL.' WIND-FORCED VARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
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NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
22,599
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22,600
NIILER ET AL.: WIND-FORCEDVARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
ature and salinity observations in the upper 200 m and
temperatureand water massobservationsfrom 200-3000 m
revealed no significantamplitude of wind coherent steric
level changesin the periodicitiesconsideredhere (but see
Tahara et al. [1986] for steric level coherencewith curl in
interannualperiods). Thus the sea level locally is consistent
with the inverse barometer behavior. By virtue of their
mutual coherenceto sea level pressure,we are able to better
separatethe patternsof bottom pressurethat are associated
with the northward (3- to 4- and 9- to 33-day) and the
eastward (4- to 5- and 15- to 60-day) componentsof the
motion in the analysis of atmosphericpressure.We make
this latter computationboth to demonstratethe robustness
of the observed forcing of the deep ocean by atmospheric
variability and to provide a more comprehensiveforum for
ocean model and observationintercomparisons.
3day
55
45
,,
50
40
Phase
I
55
I
I
I
•
,
I
I
•
,
I
I
,
•
45
35
•
180
4.
I
25 day
,
,
170
COMPARISONS WITH A STOCHASTICALLY FORCED MODEL
160
150
140
130
--X
It is of considerableinterest to ascertainwhether simple
models of ocean circulation can reproducethe more robust
results of the observations described in this paper. One
simple model is that of Satnelson [1989], in which the
responseof a two-layer quasi-geostrophicocean to a statistically homogeneousstochasticcurl may be obtained in an
analytically closed form, and the coherencescan be rapidly
evaluated numerically. This model is an extensionof those
initiated by Miiller and Frankignoul [1981] and is similar to
that of Brink [1989]but allowsthe introductionof a reflecting
meridional barrier and can also include a gentle, uniform
bottom slope. The spaceand time scalesof the curl are not
related, so a separablefunction of the frequencyand wavenumber spectrumis assumed.Its chief virtue is that a large
number of parameter studies can be done with great efficiency. We are aware that more realistic modelingefforts,
observingsite for northward velocity. The phase was uniform at 180ø. The computedcoherencemaxima were 0.8-0.9
(Figure 6).
3. Removingthe reflectingbarrier at the easternboundary reduced the coherence.Satnelsonand Shrayer [1991]
have have modified the model to allow a meridionally
varying curl amplitude (at the expense of removing the
meridionalboundariesandbarrier), and their resultsindicate
with
that the coherence
the observed
winds
and more
realistic
bottom
varia-
Fig. 5. Model-computedspatialdistributionof (top) coherence
and (middle) phase between curl, bottom pressure,and bottom
currentsat a periodof 3 days,and(bottom)coherencebetweencurl
andbottompressureat a periodof 25 days(the phaseis uniformat
180ø).The model parametersare listed in Table 1. The x andy axes
are in units of degreeswest and degreesnorth, respectively.
maxima
shift to the north when
the curl
amplitudeincreasesto the north, as it does in the eastern
North Pacific [Evensonand Veronis, 1975].
The major observedfeatureswhich agreewith the model
computations are the general locations of the small- and
large-period maxima of the coherencesand, surprisingly,
To use this model, estimates of the horizontal coherence also the phases(recall the differenceof the phase of the
scalesof the curl as a functionof periodare requiredas input small-periodcurrents measuredat 3000 m and those deterto the model. We computedthe spatial distributionsfor the minedfrom the bottom pressurearray at 4200-mdepth).The
autocorrelationfunctionof the curl for the periodbandslisted phasesof randomly forced motions and those forced by the
in Table 1. We estimated the horizontal coherence scales from
real curl patternsare expectedto be differentbecauseof the
an exponentialfunctionrepresentationof theseobservations. travelingwave trains in the real atmosphere.An inclusionof
Other parametersused in the model are alsolisted in Table 1. a northward increasing curl could move the site of the
As has been discussedby Satnelson [1990], this model computed coherence maxima northward and closer to the
reproducesobserveddeep energylevels and severalfeatures observed location (not done here because of the added
of the spatial patterns of observed coherencebetween curl complexity,which seemednot to be warranted). The major
and deep currents in the eastern North Atlantic for 3.7- to discrepanciesare the very low levels of theoretical coher8.0-day-period motions. For our calculations,with the pa- ences at 3-5 days comparedwith the observations,though
rametersappropriateto the easternNorth Pacific,the robust this may in part be corrected by increasing the bottom
model results were as follows.
friction as a function of frequency.The observedlow coher1. The locations of the coherence maxima for a 3-day enceswith the eastwardcomponentof flow are not reproperiodwere very near the observationsitefor bottompressure duced in the model. The observationssuggestthat either a
and northwardvelocity and to the north of the observingsite strongly phase-lockedand resonantbasin mode of motion
for the eastwardvelocity. The phase decreasedto the west. mustbe excitedin the ocean(for PacificOceanbasinmodes,
see Miller [1989]), or, as Luther et al. [1990] have pointed
The computedcoherencemaximawere 0.2-0.3 (Figure5).
2. The locations of the coherencemaxima for a 25-day out, the 2- to 4-day-periodcurl is very ineffectiveat generperiodwere to the southeast,alongthe lines of constantf/H,
atingtopographicRossbywaves becauseit tendsto travel to
of the observing site for pressure and to the south of the the east. This latter effect is not included in the simple
tions and coastlines,are under way. We presentthe simplest
model resultshere, becausenot only is it a first logical step
to any theoreticalinterpretation,but alsowe were curiousto
learn which, if any, of the observedfeaturesof the responses
could be replicatedwith the simplestideas.
NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERN NORTH PACIFIC
retain
35
25 day
45 0
35
,
180
,
170
,
of the curl
for a distance
from
the
locationwhere they were generatedby simple constructive
reinforcement of waves generated from that source. This
striking similarity between these two sets of measurements
over several period bands is an indication that at both sites
there were similar wind-forced motions (but also note that
Luther et al. [1990] did not find the 7- to 15-day-period
coherencegap we found). Such a robust observation, be-
45
55
the coherence
22,601
,
cause it was taken
,
160
150
140
130
at different
latitudes
over
different
de-
tailed bottom topographiesand in different years, implies
that several of its features should also be apparent in very
simplemodelsof wind-forcedvariability in the easternNorth
Pacific.The observedcoherencewith bottompressurein the
15- to 60-day-period band is very similar indeed in both
location and phase to that which is computed from the
simpleststochasticallyforced model.
The 2- to 5-day-period oscillations were not as well
modeledin the northeasternPacific.This mightbe due to the
fact that the stochasticmodels of the wind are not a good
representationof the real curl in this period band, or it might
be due to the latitudinal variations of the curl, which we did
>,
5525
day
not model here in detail.
35 , , , , , ,
180
170
160
150
The theoretical
coherence
estimate
due to random forcing would be an underestimateof the
expected, more realistic case in which the small-period
winds propagate to the east and do not generate Rossby
45
140
130
waves, which reduce the coherences. The random forced
--X
curlshave equal componentspropagatingto the east and the
west. Also, a theoretical explanation as to why the 5- to
15-day-periodvariabilities near the bottom are not expected
to be coherent with the surface forcing is missing. Our
theory in simple basinswould have the coherencesin this
bandbe simply halfway betweenthoseof the 2- to 5- and 15to 60-day bands. Neither spectra of the curl nor bottom
pressureshowsa lack of energyat 5- to 15-dayperiodicities.
The absenceof a 7- to 15-day coherenceat our location is a
modelswe used of the wavenumberand frequency structure strong indication that in this period band, topographic
of the curl.
Rossbywaves from distant locations arrive at the site and
interfere with the more local forcing. The qualitative reason
5.
DISCUSSION
is perhapsfound in the computationsby Luther et al. [1990]
The understandingof the responseof the deep ocean to which show that in this period band, atmosphericdistursurfacewind forcingin periodsof 2-60 dayshas dramatically bances over the northeastern Pacific travel increasingly to
improved in the last few years owing to the deploymentof the northeast, a feature which is not modeled in the wavearrays of deep pressuresensorsand velocity sensors,from number and frequency spectrum used in our theoretical
which robust deep responsescan be estimated, and to the calculation. Finally, these simple models do not represent
use of simple models, from which nonlocal forcing can be the smaller subbasinsin topography which can exhibit
calculated with relative ease. Our measurements
of bottom
semiresonancesat this incoherentperiod band.
The overall result of modeling bottom pressure with
pressureand near-bottomcurrents demonstratethat wind
curl forces deep-oceanmotions, and the associateddeep stochastic models appears more realistic than modeling
pressuresignalscausedby thesemotionsreveal the clearest, currents, and this is to be expected, because currents are
most coherentpatterns:(1) 2- to 5-day-periodbottom pres- more sensitive to the details of local bottom variations than
sure variations
are coherent with curl to the north of the
is bottom pressure.The least well modeled feature, as well
observing site; (2) 15- to 60-day-periodbottom pressure as the least coherentfeature, is the eastwardcomponent(or
variations are coherent with curl to the south and east of the
the motion alongthef/H contours).This is to be contrasted
observingsite; (3) the northwardcomponentof current is with the result from the continental shelf, where the best
more coherentthan the eastwardcomponent,and the former observedcoherencyand best modeledcurrent are alongthe
exhibitsstrongerrelative coherencesat shorterperiodsthan f/H contours.The principal differencesbetween deep ocean
the latter; and (4) the phase of the coherenceis such that and the shelf are that discrete, resonant modes (the shelf
there is no local correlationbetweenoceanbottom pressure waves) can occur on the shelf and the local stratificationis
and atmosphericpressure, a picture consistentwith the crucial to their structure, while in the deep ocean the
expectedtheoreticalisostasyof sealevel fluctuationswhose responseis barotropicto a very high degreeand resonances
scale is less than 2000 kin.
are very difficult to excite.
As we have seen from Chave et al. [1991], the frequency
Our data also corroborate the evidence presented by
Luther et al. [1990]that 15- to 60-day-periodmotionstend to and wavenumberspectraof wind stresscurl computedover
Fig. 6. Model-computedspatial distributionof squaredcoherence between curl and bottom currentsat periods of 3 and 2!; days
for (a) northward componentand (b) eastward component.The
phaseof both 3- and 25-day-periodbandsfor v is similar to that of
the bottompressure(Figure5). The modelparametersare listed in
Table 1. The x andy axes are in units of degreeswest and degrees
north, respectively.
22,602
NIILER ET AL.: WIND-FORCED VARIABILITY OF THE DEEP EASTERNNORTH PACIFIC
a few years of time seriesare not stationary.This calls into
questionthe utility of comparingstatisticallystationarymodels
of wind forcingwith severalyears of in situ oceanobservations. Perhapsnow is a propitioustime to do more model
computationswhich are forced with observed(assimilated)
winds and which have realistic topographies,orographies,
and stratifications[Willebrand et al., 1980]. An excellent
data set and an analysisframework now existsfor interpreting and testingthe verity of basin-widecomputationsof the
time-dependent,wind-forced motions in the deep ocean.
APPENDIX.' CORRECTIONS FOR PLASTIC FLOW
OF PRESSURE SENSORS
From our drift-modelingexercise, we have learned that
the selectedsemideterministicapproachto plastic flow rejection did not use all informationavailableand, in particular, that it did not perform aswell as it ultimatelycouldin the
presenceof a signal other than plastic deformation.This
conclusion is evident from the discrepancyillustrated in
Figure 3 between the drift-correctedrecordsfrom two identical instrumentsthat were closelyspacedat the samewater
depth. The generalshapeof the error curve is that of a steep
quadratic initial slope followed by a long period of small
offset and ending in a sustained, nearly linear trend. The
plasticflow expressionis [Filloux, 1980]
,4 + B(T + C)D
The resultsin Figure 3 suggestthat an optimumD was not
used. Choosinga D for either sensorin lessthan an optimum
way would producepreciselythe shapeof the difference(or
error) curve that we see in Figure 3. The difficultyof better
determining the D parameters results from that portion of
the deformationwhich is nonplasticin nature, which in turn
producesan apparent couplingbetween parametersD and
B. This couplingis manifestedas a rangeof D (andB) values
over which the misfit does not changerapidly.
On the basisof our experiencesin this study, we recommend that for an array of pressuresensors,the final step in
the selectionof creep parametersshouldbe a joint optimization that minimizes
overall misfit of the ensemble of differ-
oceanic responsemeasurements,J. Geophys. Res., 96(C10),
18,361-18,396, 1991.
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Pacificto stochastic
wind forcing,J. Geophys.
Res.,•96(C5),
8869-8880, 1991.
Dickson, R. R., W. J. Gould, P. A. Gurbutt, and P. P. Kilworth, A
seasonalsignalin the oceancurrentsto abyssaldepths,Nature,
295, 193-198, 1982.
Evenson,A. J., and G. Veronis, Continuousrepresentationof wind
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Acknowledgments. The authorswould like to acknowledgethe
assistanceof Russ Davis in the field operations of setting the
barometer array. P. P. Niiler and W. T. Liu were supportedby
NASA's TOPEX and NSCAT projects at the Jet PropulsionLaboratory. NASA funded J. Filloux at ScrippsInstitution of Oceanography. J. D. Paduan, R. M. Samelson, and C. A. Paulsonwere
supportedby the Office of Naval Research.
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(ReceivedFebruary 4, 1992;
revised March 25, 1993;
acceptedMarch 25, 1993.)