Response of the southwestern Japan/East Sea to atmospheric pressure

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Deep-Sea Research II 52 (2005) 1671–1683

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Response of the southwestern Japan/East Seato atmospheric pressure

Jae-Hun Park, D. Randolph Watts�

Graduate School of Oceanography, University of Rhode Island, 215 South Ferry Road, Narragansett, RI 02882-1197, USA

Received 18 July 2002; received in revised form 5 August 2003; accepted 11 August 2003

Available online 21 July 2005

Abstract

The response of the southwestern Japan/East Sea (JES) to atmospheric pressure ðPatmÞ and wind-stress ð~tÞ forcing isinvestigated by analyzing 2-year bottom pressure ðPbotÞ data and coastal tide-gauge records. Coherence analyses

between Pbot data reveal that the response of the southwestern JES is nearly uniform at frequencies lower than 0.6 cycles

per day (cpd). The Ulleung Basin (UB) average Pbot ðPbotÞ departs significantly from inverted-barometer (IB) response

to the basin average Patm ðPatmÞ at frequency bands from 0.2 to 0.7 cpd. The coherence between Patm and Pbot has

maximum value at 0.2 cpd. Multiple coherence analysis, applied with Patm and UB average~t ð~tÞ as inputs and Pbot as

output, reveals that Patm is the most significant forcing, with a peak at frequencies between 0.2 and 0.3 cpd. A simple

model [Garrett, 1983. Variable sea level and strait flows in the Mediterranean: a theoretical study of the response to

meteorological forcing. Oceanologica Acta 6, 79–87; Lyu et al., 2002. Atmospheric pressure-forced subinertial

variations in the transport through the Korea Strait. Geophysical Research Letters 29, 10.1029/2001GL014366] is used

to investigate the limiting role of the three straits on the JES response to Patm. Coastal sea-level ðZÞ data inside the JESas well as outside the straits demonstrate that the JES responds with a damped Helmholtz-like resonance. The

resonance frequency predicted by this simple model is near the frequency of maximum coherence between Patm and Zd,estimated from Pbot by the hydrostatic approximation. Phase relations and response function gain between these

variables confirm the applicability of this simple model to the JES for low-frequency bands below the Helmholtz-like

resonance frequency. At higher frequencies, the response relaxes back toward IB, which suggests the mass field adjusts

internally within the JES.

r 2005 Elsevier Ltd. All rights reserved.

e front matter r 2005 Elsevier Ltd. All rights reserve

r2.2003.08.007

ng author. Tel.: +1401 874 6507;

6728.

ss: [email protected] (D.R. Watts).

1. Introduction

The response to atmospheric pressure ðPatmÞ

differs between the open ocean and a semi-enclosed sea. The former has nearly an isostaticresponse called the inverted-barometer (IB) effect(Brown et al., 1975). The latter depends on the

d.

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J.-H. Park, D.R. Watts / Deep-Sea Research II 52 (2005) 1671–16831672

frequency of Patm because the interior massadjustment is restricted by the channels thatconnect the semi-enclosed sea to the open ocean.In general, at sufficiently low-frequency Patm

forcing, water has enough time to exchangethrough the channels and the interior exhibitsisostatic response. However, higher than someparticular frequency, the sea-level response differsfrom the IB effect because the rate of massexchange through the channels is insufficient.Moreover, wind stress ð~tÞ can redistribute masswithin the basin on a broad range of frequencies.The Japan/East Sea (JES) is a semi-enclosed sea

that has four straits, among which the KoreaStrait is the widest and longest (Fig. 1). As themass exchange through the Tatarsky Strait isnegligible, we expect the Korea, Tsugaru, andSoya Straits in combination to govern the responseof the JES to Patm.Several studies have investigated the sea-level ðZÞ

response in the JES at seasonal or interannualperiods (e.g., Kang and Lee, 1985; Oh et al., 1993;Kim et al., 2002). Kim et al. (2002) showed, usingmonthly mean Z data, that seasonal time-scalechanges of adjusted Z at Ulleung Island in the JESare closely associated with the seasonal change ofsteric height. Fewer studies have investigated thehigh-frequency response of Z in the JES. High-frequency variability on periods of several days toseveral weeks might be associated with atmo-spheric forcing from Patm or ~t. Sokolova et al.(1992) investigated atmosphere-induced Z varia-tions along the Korean and Russian coasts of theJES with 3-month-long hourly series of Z, Patm and~t. They showed that Patm produced the largestcontribution to the Z variance along eastern Koreafor all examined frequencies by applying multipleand partial coherence analyses. However, theywere unable to reveal the generally dominantresponse of the JES, because coastal tidal stationstend to be affected by other local driving forces,producing qualitatively different structures ofcoherence for each station. Oh et al. (1997)investigated the response to Patm of daily mean Zalong the coasts of the northwestern Pacific Ocean.They found that Z exhibited an abrupt decrease incoherence with Patm at periods shorter than2–4 days. This nonisostatic response occurred only

at stations within the JES. They applied Garrett’ssingle-basin, single-strait theory (Garrett, 1983) toexplain that this high-frequency nonisostatic re-sponse is caused by the limiting role of the KoreaStrait. However, high coherence alone between Zand Patm does not mean isostatic response unlessin addition they are out of phase with correspond-ing amplitudes. Recently, a thorough study by Lyuet al. (2002) demonstrated 3–5 day transportvariations through the Korea Strait by cross-straitcable voltage fluctuations and direct measurementsof the current. They also found an abrupt drop ofcoherence between Z and Patm at periods of3–4 days. They interpreted these as atmosphericpressure-forced variations using a simple single-basin, three-strait model, with which they calcu-lated a Helmholtz-like resonant period of3.12 days. However, they noted that both ~t andPatm affect the strait transport and Z. They ignoredvariations higher than the Helmholtz-like resonantperiod.The relation between Z, Patm and bottom

pressure ðPbotÞ is accurately expressed from thehydrostatic relation, with the mean water densitytaken to be r0,

Z ¼ ðP0bot � PatmÞ=r0g, (1)

where P0bot ¼ Pbot � r0gH, g gravitational accel-

eration, H the depth of water column in a steadystate. All subsequent variables P0

bot drop the primein this paper. Hence in the open ocean Pbot

represents Z if Patm is known at the Pbot site (weassume changes in r0 are negligible). The advan-tage of using Pbot data is that unlike coastal Z data,they are free from localized contaminating effects.The aim of this study is to investigate the

response of the JES to atmospheric forcing usingPbot data. Our focus is upon the variation of Pbot

at time scales ranging from 1 day to several weeks.We will use 2-year-long records of 12 h Pbot data inthe southwestern JES plus some coastal Z data.The response of the JES is investigated byconducting spectral analyses of Pbot, Patm, and Z.The dominant effect of Patm on the response isdemonstrated with a multiple coherence analysis.The results are then compared with a simple modelsuggested by Lyu et al. (2002), which takes intoaccount the role of three straits of the JES. Lastly,

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JAPAN

Japan/East Sea

Korea

Stra

it

Ulleung Basin

Tsugaru Strait

Soya Strait

P11 P16

P55P32

P51

Fig. 1. The Japan/East Sea. Solid diamonds indicate PIESs and solid circles coastal sea level stations used in this study. Bathymetry

contours are in meters.

J.-H. Park, D.R. Watts / Deep-Sea Research II 52 (2005) 1671–1683 1673

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we will show that the dominant response of Pbot

and Z in the JES occurs at a damped Helmholtz-like resonance period of 5 days.

2. Data

During 1999–2001, an array of pressure-sensor-equipped inverted echo sounders (PIESs) wasdeployed in the southwestern JES for about 2 years(Fig. 1). The array was designed to have 55–60 kmspacing between mooring sites and to cover all ofthe Ulleung Basin (UB). The Paroscientific Digi-quartz pressure sensors recorded hourly Pbot withbetter than 1mm resolution and 0.1–0.3 dbaraccuracy. Twenty-three PIESs were recoveredsuccessfully and used in this study. Diurnal andsemi-diurnal tidal signals were eliminated from allof the Pbot records by the response analysismethod (Munk and Cartwright, 1966). Details ofthe moorings are given in the companion paper byMitchell et al. (2005).We also use hourly values of Z at Maizuru,

Sasebo, Urakawa and Monbetsu, Japan, from thesame time interval. The data, collected from tide-gauge observations along the Japan coast, wereobtained from the Japan Oceanographic DataCenter (JODC) website. The Maizuru station islocated inside the JES, and the others are justoutside of the Korea, Tsugaru and Soya Straits(Fig. 1). The diurnal and semi-diurnal tidal signalsalso were filtered from these records.The reanalyzed Patm and ~t data come from

Navy Operational Global Atmospheric PredictionSystem (NOGAPS). They are on a degree gridwith time interval 12 h.As our interest is in periods longer than 24 h, the

Pbot and coastal Z data were subsampled every12 h, corresponding to the atmospheric data.Every data set we used has 1477 values from00:00GMT, June 16, 1999 to 00:00GMT, June 23,2001.Time series of Pbot, coastal Z at Maizuru and

Sasebo and UB average atmospheric pressureðPatmÞ are shown in Figs. 2(a), (b) and (c),respectively. Patm was calculated by averagingvalues at nine grid points between 130–1321Eand 36–381N chosen to span the UB. The means

have been removed from all of the time series inFig. 2. Strikingly, all the Pbot records showednearly identical variations through two years, eventhough the mooring sites span the four corners ofthe UB with separations as large as 350 kmbetween P11 and P55. Although the coastal Zand Patm records have noticeable seasonal signals,it is absent from the Pbot records. Of course thesteric warming that affects Z does not change themass nor Pbot. Furthermore we infer from thisfigure that at seasonal periods, the mass field insidethe JES adjusts with an IB response.High-frequency variations at time scales of

several days are shown in all of the time series inFig. 2. As will be shown by the spectral analyses innext section, these variations of Pbot are mainlycaused by those of Patm, but with phase shifts andgains that differ from an isostatic response. Anextraordinary maximum of Pbot occurred on aboutthe end of October 1999. The coastal Z at Maizurualso shows a peak at the same time. This extremepeak is likely to be caused by the maximumvolume transport through the Korea Strait inOctober, 1999, which was reported by Teagueet al. (2002).

3. Results

3.1. Spectral analysis of bottom pressure data

All time series had their mean and a linear trendremoved prior to spectral analysis. The techniqueof block averaging in the frequency domain wasused to smooth the spectra (Emery and Thomson,2001). The time series were divided into 50%overlapped equal-length blocks each having 128data points, and final results ensemble-average thespectra of all blocks. The Nyquist frequency is1 cycle per day (cpd) and the maximum observableperiod is 64 days because of the time step (12 h)and length of block, respectively. All spectralanalyses in this study use this same procedure.Variance-preserving power spectra of Pbot for

three representative sites (P11, P16 and P55) arenearly identical, in accord with the time series ofthe Pbot records (Fig. 3). All show the same peaksat 0.2 cpd. The coherences between pairs of Pbot

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dbar

Bolaven (11W) Saomai (22W)

Maizuru

Sasebo

P16 P11

P32 P51 P55

1999 2000 2001

Fig. 2. Time series of bottom pressure ðPbotÞ at P11, P16, P32, P51 and P55 (a), coastal sea level ðZÞ at Maizuru and Sasebo (b), and UBaverage atmospheric pressure ðPatmÞ (c), from 00:00GMT, June 16, 1999 to 00:00GMT, June 23, 2001.


data (not shown here) are almost unity from lowfrequency to 0.6 cpd, while at higher frequenciesthey drop to approximately 0.8 but remain farabove the significance level. The phases (notshown here) remain near 0� through all analyzedfrequencies. This indicates that the depicted Pbot

signal is nearly uniform throughout the UB. Thisis compatible with the relatively short adjustmenttime scale set by long gravity waves (barotropicKelvin waves) travelling in the JES. For example,if we take the length and depth scale of the JESas 1:4� 106 m and 1350m, respectively, thetime scale of gravity wave propagation isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9:8� 1350

p=ð1:4� 106Þ ’ 3:4 h. Within just the

UB, this time scale is about 1 h. Because of this, in

analyzing data at 12-hour intervals we averagetogether our 23 time series of bottom pressureðPbotÞ in our following analyses. To aid the reader,we summarize the variables used for this study inTable 1.

3.2. Spectral analysis of Ulleung Basin average

atmospheric pressure and bottom pressure

The variance-preserving power spectrum of Patm

has high values at atmospheric synoptic time scalesbetween 14–3.5 d, or 0.07–0.3 cpd (Fig. 4(a)).Theoretically, if the UB were to respond to Patm

with an IB effect, there should be no coherenceand zero response function gain (m/dbar) between

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Fig. 3. Variance-preserving power spectra of P11 (solid), P16

(dash) and P55 (dash-dot). The 95% confidence factors are

(0.69, 1.60).

Table 1

Definition of variables

Variables Description

Patm UB average atmospheric pressure

Patm0 JES average atmospheric pressure

Pbot UB average bottom pressure

Pbot0 JES average bottom pressure

Zd UB average sea level obtained from bottom pressure

Zb Sea level in the JES

~t UB average wind stress

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(db)

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0.6

0.8

1

Coherence

0

0.5

1

1.5

2Gain

0

100

Coherence phase (°)

Patm

Patm

& Pbot

(A)

(B)

(C)

(D)


Patm and Pbot. This is exhibited for low frequenciesbelow 0.1 cpd (Fig. 4(b), (c)). However, thecoherence and gain abruptly increase above 0.5at 0.2 cpd and remain high until 0.7 cpd. Thismeans that the UB response to Patm differs from

10-2 10-1 100

-100

Frequency (cpd)

Fig. 4. (a) Variance-preserving power spectra of Patm. The 95%

confidence factors are (0.69, 1.60). Coherence (b), gain (c) and

phase (d) between Patm and Pbot. The horizontal thin line in (b)

indicates the 95% significance level. Phase is omitted if

coherence is lower than the significance level. The dotted lines

in (c) and (d) represent the theoretically computed gain and

phase, respectively. In (d) positive phase represents Patm leading

Pbot.

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Multiple

Patm

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τxτy

(A)

(B)

Fig. 5. (a) Multiple and partial coherences between three inputs

ðPatm, tx and tyÞ and one output ðPbotÞ. (b) Phases for the same

pairs. Two horizontal thin lines in (a) indicate 95% significance

level for multiple (upper line) and partial (lower line)

coherences. Phase is omitted if coherence is lower than the

significance level.


IB qualitatively between 0.2 and 0.7 cpd. Thephase has no meaning when the coherence is low,but within the coherent band it decreases withincreasing frequency from about 80� to 0, withPatm leading Pbot (Fig. 4(d)). The phase relationbetween Patm and Pbot will be interpreted in thenext section.The low coherence (and gain) at yet higher

frequencies above 0.7 cpd arises partly because lessforcing-variance is present in Patm, but this alsosuggests that other processes may be active. The Zvalues inside the JES and outside the connectingstraits have insufficient time to equilibrate throughwater exchange for those high-frequency motions,in contrast to the low frequencies. So it might atfirst seem surprising for the response to returntoward IB at high frequencies. However, internaladjustments within the basin (rather than theentire JES being ‘‘compact’’ with Z the sameeverywhere) could reenable the IB response if thespatial scale of the Patm is less than the basin scale.Garrett and Majaess (1984) reported on internalbasin adjustments in the Mediterranean Sea atfrequencies higher than about 0.5 cpd.The response of the JES to typhoons might

provide examples of these internal basin adjust-ments. Two typhoons, Bolaven (11W) and Saomai(22W), passed through the PIES mooring arrayduring 2000 (2000 Annual Tropical CycloneReport in website of Naval Pacific Meteorologyand Oceanography Center/Joint Typhoon Warn-ing Center). During the two storm passages, Zmeasurements at Maizuru and Sasebo show highpeaks (Fig. 2). However, Pbot records reveal nodistinctive response to the typhoon passages—providing an example in which IB response returnsat high frequencies.

3.3. Multiple coherence analysis

In general, mutual coherences between Patm and~t are high. Because of this significant coherence,the ordinary single coherence analysis, betweenPbot (or Z) as an output and any one of theseatmospheric forcings as a single input, would bephysically incorrect. A way to account for mutualcorrelations between inputs is multiple coherenceanalysis. Furthermore, using partial coherence

analysis, we can separately identify the contribu-tion of each input to the output as a function offrequency (Bendat and Piersol, 2000).The partial and multiple coherence are esti-

mated between three inputs, Patm and x and y

components of UB average wind stress (tx and ty),and one output Pbot (Fig. 5(a)). They reveal thatthe high coherence obtained by single coherencebetween 0.2 and 0.7 cpd has some contributionsfrom ~t. Generally, low-frequency motions areinfluenced by ty and high-frequency motions bytx. Insignificantly low coherence between Patm andPbot at the lowest analyzed frequencies, which wasshown by the single coherence analyses, isconfirmed by the partial coherence. While thePatm forcing remains dominant in the 0.2–0.3 cpdfrequency band, and the multiple coherenceremains high to at least 0.7 cpd, the partialcoherences are individually strikingly smaller thanobtained from the single coherence analysis. Themaximum coherence peak is close to 0.7 at a periodof 5 days for both the Patm partial coherence andthe multiple coherence. The phases between Patm

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and Pbot remain almost the same as those from thesingle coherence analysis (Fig. 5(b)).

4. Theory and comparisons with observations

We interpret these results in terms of barotropicresponse of the semi-enclosed JES having threestraits. Our analysis is closely guided by studies ofGarrett (1983) and Lyu et al. (2002), but we extendthe results to examine additional variables. Thebasin is treated as compact, and the strait(s)constrain the water-volume transport (Q), withthe adjustment time to equilibrate pressuresbetween inside and outside the basin restrictedprimarily by gravity waves, but importantlymodified by Coriolis effects and friction.Garrett (1983) introduced a simple theoretical

model of rotationally influenced flow through astrait, connected to a single basin. He considered astrait, having uniform depth H, width W andlength L, and a basin of area A (Fig. 6). Byusing a sea-level difference between Zm themouth of the strait and Zb inside the basinRe½DZe�iot� ¼ Re½ðZm � ZbÞe

�iot�, the average sur-face current Re½ue�iot� through the strait is derived

Tsugaru

Soya

Korea Strait

Fig. 6. Schematic of a basin connected to the ocean by three

straits. L is the strait length, W the strait width and A the area

of basin. Strait flow u is caused by the Z difference ðZm � ZbÞ. Inthe extended model, each strait has its own values for L, W, An,

u, H and Zm.

as follows:

u ¼ gL�1DZ½�ioþ ðlþ 1=2fWL�1Þ��1, (2)

where l is the linear friction coefficient for thestrait and f Coriolis frequency. Note that to let Zbbe spatially uniform is valid as discussed in theprevious section since long gravity waves requireonly 3–4 h to traverse a basin such as the JES. Theearth’s rotation effect fWL�1, called geostrophiccontrol, in Eq. (2) is modified by the factor 1

2, based

on the correction of Wright (1987) applicable toone compact basin connected to a semi-infinitereservoir. An estimate for the friction coefficient isl ¼ CDU0=H with a bottom drag coefficient CD,average speed U0 and average channel depth H. Iff ¼ 0 the flow through the strait is dominated byacceleration ðoÞ and friction ðlÞ. If 1

2fWL�1

bo; l,the flow is dominated by geostrophic control. Forthe Korea, Tsugaru and Soya Straits, U0 is 0.1,0.7, 0:4m s�1, respectively, and the estimated lþ12

fWL�1 are obtained as ð0:3þ 1:4Þ � 10�5 s�1,ð1:8þ 0:9Þ � 10�5 s�1 and ð3:0þ 2:2Þ � 10�5 s�1,respectively, when the values used by Lyu et al.(2002) are applied (Table 2). For the Korea Strait,geostrophic control is about four times as im-portant as friction and about the same magnitudeas o at 5.2 day period. Therefore, the flow throughthe Korea Strait is geostrophically controlled atfrequencies lower than about 5 day periods. On theother hand, Tsugaru and Soya Straits are stronglyconstrained by bottom friction.

Table 2

Summary of the values used for the three channel basin model

Values Description

A ¼ 1:3� 1012 m2 Surface area of the JES

A1 ¼ 1:2� 105 � 100m2 Cross-sectional area of Korea Strait

A2 ¼ 1:9� 104 � 120m2 Cross-sectional area of Tsugaru Strait

A3 ¼ 4:8� 104 � 40m2 Cross-sectional area of Soya Strait

L1 ¼ 4:0� 105 m Along-strait length of Korea Strait

L2 ¼ 1:0� 105 m Along-strait length of Tsugaru Strait

L3 ¼ 1:0� 105 m Along-strait length of Soya Strait

CD ¼ 3� 10�3 Bottom drag coefficient

f ¼ 9� 10�5 s�1 Coriolis frequency

g ¼ 9:8m s�2 Gravitational acceleration

r0 ¼ 1027kgm�3 Mean seawater density

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Let Patm0 denote the average Patm all over thebasin, which we treat as the forcing to the basin,and let Z0m be any departure from an IB response atthe mouth outside of the strait. Then the followingrelation between Zb and Patm0 arises by combiningthe momentum equations and the mass conserva-tion relation (Garrett, 1983):

Zb ¼ ½Z0m � ðr0gÞ�1Patm0� 1�

o2

o2r

�

�i lþfW

2L

� �oo2r

��1. ð3Þ

This relation indicates that Zb and Patm0 are out ofphase/in phase at low/high frequencies and have90� phase difference, with Patm0 in the lead, at aHelmholtz-like resonance frequency or defined as

o2r ¼

gHW

AL. (4)

When o5or and Z0m ¼ 0, Zb and Patm0 have an IBresponse relation.To extend Garrett’s model to a multi-channel

model is straightforward. Lyu et al. (2002) used athree-channel model applicable to the JES. Therelation between Zb and Patm0 in the multi-channelmodel can be obtained as follows if we approx-imate Z0m as zero (exact IB response in the externalreservoirs):

Zb ¼�1

r0gð1� 1=SÞPatm0, (5)

where

X¼

Xn

o2

o2n

þ i ln þfW n

2Ln

� �oo2

n

� ��1

(6)

and on is the Helmholtz-like resonance frequencyfor the nth channel (see Appendix).Spectral analyses between the coastal Z at

Sasebo, Urakawa and Monbetsu stations outsideeach respective strait and local Patm inform usabout the neglected Z0m (Fig. 7). The coastal Zrecord at Maizuru is also analyzed to exhibit thedifferent response of Z inside versus outside ofthe JES.At Sasebo the variance-preserving power spec-

trum of Z shows a peak at 0.07 cpd (14 d), which is

longer than the atmospheric synoptic forcing.Hence, this is likely caused by other physicalprocesses such as Kuroshio variation, since thecoherence at this frequency is relatively low (butstill far above the significance level). The strongestspectral density near 1 cpd represents tidal signals.The maximum coherence peak close to 0.9 isshown at 0.2 cpd. The gain is close to unity fromvery low frequency to 0.4 cpd. The phase is steadyand close to 180� (Fig. 7(g)).At Urakawa the variance-preserving power

spectrum of Z reveals high values at a frequencylower than 0.1 cpd. However, the coherence showshigh values between 0.1 and 0.5 cpd. This indicatesthat the Z variations at Urakawa longer than 10-day period arise mainly from another physicalprocess. However, within the band 0.1–0.7 cpd, ofmain interest to the response of the JES, theobserved high coherence, unity gain, and 180�

phase correspond to IB response, as was assumedfor the above model.The coherence of Z at Monbetsu with local Patm

shows low values at most frequencies, indicatinginfluence by other processes, either non-IB re-sponse within the Okhotsk or because Monbetsu ison the left side of the channel looking in, whichdiffers from Garrett’s assumption of Kelvin waveadjusted height. (We have no access yet to Russiantide station data on the right side, which isKamchatka Peninsula.) Nevertheless the gain andphase at Monbetsu reveal IB response-like rela-tions from very low frequency to 0.5 cpd.Overall, these results indicate that the outside

regions of the three straits connecting the JES tothe East China Sea and northwestern PacificOcean exhibit some differences from IB responseto Patm. Neglecting Z0m in Eq. (3) might cause someerrors in the theoretical interpretation, but thiswould be a subject for future study requiring amore complete atmosphere–ocean coupled model.At Maizuru the variance-preserving power

spectrum of Z exhibits a peak at 0.2 cpd(Fig. 7(a)). The gain and phase results differ fromthose outside the straits. The gain peaks are at 0.2and 0.4 cpd, and the phase decreases from 180� to20� at frequencies lower than 0.5 cpd. These resultsagree well with those of Lyu et al. (2002). The gainpeak at 0.4 cpd is likely indirectly affected by ~t,

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Coherence phase (° )

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(A) (B)

(C) (D)

(H) (G)

(F) (E)

Fig. 7. Variance-preserving power spectra of coastal Z at (a) Maizuru, Sasebo, (b) Urakawa and Monbetsu. The 95% confidence

factors are (0.69, 1.60). (c, d) Coherence, (e, f) gain and (g, h) phase between local Patm and Z at each of the four coastal locations. Thehorizontal thin line in (c) and (d) indicates the 95% significance level. Phase is omitted if coherence is lower than the significance level.

The dotted lines in (e) and (g) represent the theoretically computed gain and phase, respectively.


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analogous to our results displayed in Fig. 5for Pbot.To compare the simple model expressed by

Eq. (5) to our observational data inside the JES,we also conducted multiple coherence analysisbetween atmospheric forcings and Zd. We approx-imate Zd ¼ ðr0gÞ

�1ðPbot � PatmÞ from Eq. (1). The

atmospheric forcing variables are Patm0, tx and ty,where Patm0 is estimated by averaging Patm

spatially over the JES. The multiple and partialcoherence results in Fig. 8 reveal that Patm is thedominant forcing for Z as well as for Pbot.Reminiscent of Fig. 5, the maximum partialcoherence between Patm0 and Zd is also shown at0.2 cpd. The phase is observed to follow strikinglywell the theoretically calculated decrease from 180�

to 100� at frequencies lower than 0.3 cpd, using thevalues in Table 2. This decreasing trend is alsosimilar to the result of Lyu et al. (2002), which theyobtained by averaging coastal Z inside the JES.However, the phase increases again (returning to180� IB response) at frequencies higher than0.5 cpd. This increasing trend of phase forfrequencies higher than 0.33 cpd, becoming out

10-2

10-1

100

0

0.2

0.4

0.6

0.8

1

Multiple & Partial Coherence of ηd

Multipleτx

τy

Patm0

10-2

10-1

100

0

100

200

300

Coherence Phase (° )

Frequency (cpd)

(A)

(B)

Fig. 8. (a) Multiple and partial coherences between three inputs

ðPatm0, tx and tyÞ and one output ðZdÞ. (b) Phases for the samepairs. Two horizontal thin lines in (a) indicate 95% significance

level for multiple (upper line) and partial (lower line)

coherences. Phase is omitted if coherence is lower than the

confidence level. The dotted line in (b) represents the

theoretically computed phase.

of phase again around 0.7 cpd, might be caused byinternal (IB) adjustments as explained in theprevious section.The partial coherences between ~t and Zd show

that the contributions of ty are significant atfrequencies lower than 0.4 cpd. The decreasingtrend of phase from in-phase to out-of-phasebetween ty and Zd demonstrates the response ofthe JES to the ty forcing. At very low frequencies,the water mass forced by ty blowing southward,for example, has enough time to exit the JESthrough the Korea Strait. Otherwise, at highfrequencies, it accumulates in the southern JES,which makes the response out-of-phase.A relation between Patm0 and average Pbot over

the JES ðPbot0Þ may be obtained by substitutingRe½Zbe

�iot� ¼ ðr0gÞ�1 Re½ðPbot0 � Patm0Þe

�iot� intoEq. (5)

Pbot0 ¼1

1� SPatm0. (7)

The computed gain and phase between Patm0 andPbot0 are shown as dotted lines in Fig. 4(c) and (d),respectively. Our bottom pressure observationscover only the southwestern JES, so we haveavailable only an approximation to Pbot0 forestimating Pbot. However, the computed gain andphase relations for Pbot0 are consistent with theobserved values between 0.1 and 0.5 cpd (Fig. 4)where coherence is above the significance level,except that the observed Pbot gain peak is lesspronounced than the theoretically predicted.Without frictional and geostrophic constraints,

lþ 12

fWL�1, in the channels, both Eqs. (5) and (7)would reveal the same Helmholtz-like resonancefrequency of 0.32 cpd using the channel sizes inTable 2. However, due to these constraints, thetwo damped Helmholtz-like resonance frequencies(i.e. gain maxima) are at 0.2 and 0.35 cpd for Z andPbot, respectively (Figs. 7(e) and 4(c)). Thisprediction is inconsistent with the observed Pbot

coherence curve, which shows the same resonancefrequency of 0.2 cpd (Fig. 5(a)) as for Z (Fig. 8(a)).This discrepancy might be caused by inadequateassumptions for the simple model, such asneglecting Z0m and assuming compactness (uniformZ all over the JES). The corresponding reduction

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of the high-frequency response would shift theobserved Pbot peak to a lower frequency.

5. Summary

The response of the southwestern JES to Patm

shows a significant departure from the IB responseat frequencies between 0.2 and 0.7 cpd, at which thecoherences between Patm and Pbot show high values.At low ðo0:2 cpdÞ and high frequencies ð40:7 cpdÞ,IB responses are observed. Multiple and partialcoherence analyses enable us to distinguish thecontributions of the atmospheric forcings. Theyshow that Pbot variations around 0.2–0.3 cpd arepredominantly induced by Patm, with maximumcoherence at 0.2 cpd. The coherence curves are closeto the theoretically computed damped Helmholtz-like behavior predicted by a simple model. The phaserelations between Patm and Pbot also agree well withthose predicted from the model.The Zd, estimated hydrostatically in mid-basin,

shows respectively decreasing and increasingtrends in the phase relation with Patm0 at lowðo0:3 cpdÞ and high ð40:5 cpdÞ frequencies. Thedecreasing trend is consistent with a theoreticallycalculated phase relation from the simple model.We suggest the increasing trend is caused byinternal adjustments, which are not taken intoaccount in the simple model. The additionalresponse of the JES to wind stress is exemplifiedby the phase relation of Zd with ty. At lowfrequencies, water-mass exchange through theKorea Strait induced by ty forcing is enough tochange Z inside the JES; whereas at high frequen-cies the water mass accumulates or depletes in thesouthern JES, and hence raises or lowers Z.This study demonstrates that the JES responds

to atmospheric pressure as an IB effect at thelowest ðo0:2 cpdÞ frequencies. The Korea, Tsu-garu and Soya Straits modify this IB response ofthe JES to the atmospheric forcing. At mid-frequencies (0.2–0.7 cpd), the JES has a dampedHelmholtz-like resonance response that departssubstantially from the IB response. As this bandalso contains the greatest variance in Patm, theSSH ðZÞ inside the JES departs significantly fromIB—a fact to bear in mind when interpreting

satellite altimeter observations there. At frequen-cies higher than 0.7 cpd, Patm spatial scales aresmaller and internal adjustments restore theresponse back toward an IB response. The simplethree-channel model has clearly identified theprocesses, and a numerical model would berequired to achieve substantially improved predic-tion of the response of the JES to atmosphericforcing. The roles of the neighboring Yellow Sea,East China Sea, the northeastern Pacific Ocean,and Okhotsk Sea should probably be included insuch a model.

Acknowledgments

We thank Douglas Mitchell and Karen Traceyfor their help in processing the bottom pressuredata. Thanks also to Mark Wimbush and Sang JinLyu for their useful comments and advice on thiswork. William J. Teague kindly provided usNOGAPS atmospheric data. Comments fromanonymous reviewers were helpful for the im-provement of this paper. This work was supportedby the Office of Naval Research ‘‘Japan/East SeaDRI’’. Basic Research Programs include theJapan/East Sea initiative under GrantN000149810246 and the Naval Research Labora-tory’s ‘‘Linkages of Asian Marginal Seas’’ underProgram Element 0601153N.

Appendix A

To extend Garrett’s model to a multi-channelmodel, having a single compact basin and n

channels to separate reservoirs, the governingequations are mass conservation and momentumbalance, as follows:

AqZbqt

¼X

n

Qn, (A1)

qQn

qt¼ � An

Patm0 þ r0gðZb � Z0mnÞ

r0Ln

� ln þfW n

2Ln

� �Qn; n ¼ 1; 2; 3; . . . ðA2Þ

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where Qn is the volume transport through the nthchannel, An ¼ W nHn the cross-sectional area ofthe nth channel, ln the linear friction coefficient forthe nth channel, and Ln the length of the nthchannel. We set Z0mn

equal to zero on theassumption that the response at the outside ofthe channels to Patm is the IB response. If we let Zb,Qn and Patm0 be Re½Zbe

�iot�, Re½Qne�iot� and

Re½Patm0e�iot�, we obtain Eq. (5). The Helmholtz-

like resonance frequency for the nth channel is

on ¼gHnW n

ALn

. (A3)

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http://dx.doi.org/10.1016/j.dsr2.2003.09.005

http://dx.doi.org/10.1016/j.dsr2.2003.09.005

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Response of the southwestern Japan/East Sea to atmospheric pressure

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