Accepted, J. Climate, Nov. 5, 2006

Coupled Decadal Variability in the North Pacific:

An Observationally-Constrained Idealized Model

Bo Qiu∗, Niklas Schneider, and Shuiming Chen

Department of Oceanography, University of Hawaii at Manoa, Honolulu, Hawaii

Abstract

Air-sea coupled variability is investigated in this study by focusing on the observed sea surface temper-ature signals in the Kuroshio Extension (KE) region of 32◦–38◦N and 142◦E–180◦. In this region, both theoceanic circulation variability and the heat exchange variability across the air-sea interface are the largestin the midlatitude North Pacific. SST variability in the KE region has a dominant timescale of ∼ 10 yrand this decadal variation is caused largely by the regional, wind-induced sea surface height changes thatrepresent the lateral migration and strengthening/weakening of the KE jet. The importance of the air-seacoupling in influencing KE jet is explored by dividing the large-scale wind forcing into those associated withthe intrinsic atmospheric variability and those induced by the SST changes in the KE region. The lattersignals are extracted from the NCEP-NCAR reanalysis data using the lagged correlation analysis. In theabsence of the SST feedback, the intrinsic atmospheric forcing enhances the decadal and longer timescaleSST variance through oceanic advection, but fails to capture the observed decadal spectral peak. Whenthe SST feedback is present, a warm (cold) KE SST anomaly works to generate a positive (negative) windstress curl in the eastern North Pacific basin, resulting in negative (positive) local SSH anomalies throughEkman divergence (convergence). As these wind-forced SSH anomalies propagate into the KE region in thewest, they shift the KE jet and alter the sign of the pre-existing SST anomalies. Given the spatial patternof the SST-induced wind stress curl forcing, the optimal coupling in the midlatitude North Pacific occursat the period of ∼ 10 yr, slightly longer than the basin crossing time of the baroclinic Rossby waves alongthe KE latitude.

1 Introduction

Decadal variability in the midlatitude North Pacifichas received considerable attention in recent years be-cause of its impact upon the Pacific marine ecosys-tems and long-term weather fluctuations over theNorth America continent. Comprehensive reviews onthe North Pacific decadal variability can be found inrecent articles by Pierce et al. (2001), Mantua andHare (2002), Miller et al. (2004), and the referenceslisted therein. Analyses of the sea surface tempera-ture (SST) data have revealed that the low-frequencySST changes in the North Pacific consist of two dom-inant modes: one that is remotely forced by telecon-nected ENSO signals, and the other associated withthe processes intrinsic to the midlatitude North Pa-cific (e.g., Deser and Blackmon 1995; Nakamura etal. 1997; Zhang et al. 1997). The former mode, alsoknown as the ENSO mode, has a center of action inthe central, eastern North Pacific, whereas the latter

∗E-mail: bo@soest.hawaii.edu

mode (the North Pacific mode) has its center of ac-tion confined to the western half of the midlatitudeNorth Pacific basin. Compared to the ENSO mode,the North Pacific mode has been observed to havemore power in the SST spectrum on the decadal-to-multidecadal timescales. It is on the North Pacificmode that the present study will focus.

Decadal-to-multidecadal timescale SST variabilityin a midlatitude ocean can be generated through 3different scenarios. The first is the climate noisescenario (a.k.a. the null hypothesis) in which thelow-frequency SST variability simply reflects low-frequency changes in the short timescale statistics ofthe atmospheric forcing (Hasselmann 1976; Frankig-noul and Hasselmann 1977). The second scenario em-phasizes the ocean circulation and its slow responsein contributing to the reddening of the SST signals.While the ocean dynamics is active in this scenario, itis assumed to have no dynamically important impactupon the overlying atmosphere through the resultingSST changes. Under this “uncoupled” scenario, sev-

1

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 2

eral mechanisms have been proposed that can giverise to preferred timescales in SST, including advec-tion of the mean upper ocean circulation (Saravananand McWilliams 1998), spatial pattern of the atmo-spheric forcing (Jin 1997; Frankignoul et al. 1997;Weng and Neelin 1998; Saravanan and McWilliams1998; Neelin and Weng 1999), latitude-dependentRossby wave adjustment (Qiu 2003; Schneider andCornuelle 2005), and inertial recirculation gyre dy-namics (e.g., Dewar 2001; Hogg et al. 2005; Taguchiet al. 2005; Pierini 2006).

The third scenario regards the midlatitude oceanand atmosphere as a coupled system, in which thestrength and frequency of the low-frequency variabil-ity are determined by both the ocean dynamics andits feedback to the atmospheric circulation (Bjerknes1964). Latif and Barnett (1994, 1996) explored thisscenario and identified a 20-yr coupled mode in themidlatitude North Pacific by using a coupled generalcirculation model (CGCM). The existence of the cou-pled modes in the North Pacific have also been exam-ined by Pierce et al. (2001), Schneider et al. (2002),Wu et al. (2003), and Kwon and Deser (2006), us-ing various long-term CGCM runs. While the ocean-to-atmosphere feedback processes vary subtly frommodel to model, all CGCM studies point to the im-portance of the Kuroshio Extension (KE) variabilityin controlling the regional SST signals and to the roleplayed by the baroclinic Rossby waves in the KE’s re-sponse to the time-varying surface wind stress forcing(see also Miller et al. 1998; Deser et al. 1999; Xie etal. 2000; Seager et al. 2001).

It is worth emphasizing that clarifying the natureand the mechanism of the decadal-to-multidecadalSST variability is important from the prediction per-spective (Pierce et al. 2001). While the climate noisescenario would suggest very limited predictive skill,the deterministic ocean dynamics in scenario 2 canpotentially improve the predictive skill significantly(Schneider and Miller 2001; Scott 2003; Scott and Qiu2003). In the coupled scenario, predictability may befurther enhanced by taking into account the feedbackpart of the atmospheric forcing. In the past, an ef-fective method of distinguishing the 3 scenarios listedabove has been through numerical modeling, in whichone tests various hypotheses by altering the complex-ity of the ocean dynamics or by conducting partialcoupling experiments (e.g., Barnett et al. 1999; Pierceet al. 2001; Schneider et al. 2002; Dommengnet andLatif 2002; Wu et al. 2003; Solomon et al. 2003). Inthe present study, we attempt to explore the relevanceof the above 3 scenarios by analysis of available obser-vational data and adoption of idealized models with

different dynamic complexities.

We begin the study by describing the SST, sea sur-face height, and surface wind stress data in section 2.With our interest in the coupling between the midlat-itude ocean and atmosphere, we introduce in section3 an SST index taken along the KE band centeredalong 35◦N. This section provides the rationale forselecting this band and discusses the result under theclimate noise scenario. In section 4, we explore theuncoupled scenario by looking into how surface windvariability affects the SSH changes in the KE band,and to what extent the changing SSH signals, in turn,modify the regional SST anomalies. The influence ofthe SST changes in the KE band upon the basin-scale surface wind stress field is examined in section5. Section 6 explores the differences between the cou-pled and uncoupled scenarios and the results are usedto better understand the KE SST anomalies. Discus-sions and summary of the present study are providedin section 7.

2 Data

Several observational data sets are used in this studyto construct an idealized midlatitude air-sea coupledmodel and to explore underlying causes for the ob-served decadal signals in the sea surface temperature(SST) field of the North Pacific Ocean. For the SSTdata, we utilize the Extended Reconstruction SSTversion 2 (ERSST.v2) product compiled by Smithand Reynolds (2004). The monthly ERSST.v2 dataset has a 2◦ spatial resolution and covers the periodfrom 1948 to 2005.

Monthly surface wind stress and net heat fluxdata from the National Centers for Environmen-tal Prediction–National Center for AtmosphericResearch (NCEP–NCAR) reanalysis (Kistler etal. 2001) are used in this study to represent the at-mospheric forcing field. The reanalysis data set has aspatial resolution of 1.9◦ lat.× 1.875◦ long. and coversthe same 1948–2005 period as the SST data set. Forboth the atmospheric and SST data, we derive theirmonthly anomalies by removing their respective, cli-matological monthly values.

With the advent of satellite altimetry measure-ments of sea surface height (SSH), our ability to mon-itor the global surface ocean circulation has improvedsignificantly after 1992. The satellite altimetry dataare used in this study to capture the large-scale sig-nals of the time-varying surface ocean circulation. Weuse the global SSH anomaly data set compiled bythe CLS Space Oceanographic Division of Toulouse,France. The data set merges the Ocean Topography

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 3

Mea

n SS

H [c

m]

−80

−60

−40

−20

0

20

40

60

80

120°E 140°E 160°E 180° 160°W 140°W 120°W10°N

20°N

30°N

40°N

50°N

60°N

Figure 1. Mean sea surface height topography of theNorth Pacific (adapted from Niiler et al. 2003). Contourintervals are 10 cm. Dashed line indicates the KuroshioExtension band of 142◦–180◦E and 32◦–38◦N.

Experiment (TOPEX)/Poseidon, Jason-1, and Euro-pean Remote Sensing Satellite (ERS)-1/2 along-trackSSH measurements and has the improved capabilityof detecting mesoscale SSH signals (Le Traon andDibarboure 1999; Ducet et al. 2000). The CLS SSHanomaly data set has a 7-day temporal resolution, a1/3◦ × 1/3◦ Mercator spatial resolution, and coversthe period from October 1992 to December 2005.

3 The KE SST index

As the interest of our investigation is in the air-seacoupled mode in the midlatitude North Pacific, wewill focus on a band centered along 35◦N in the west-ern North Pacific. As shown in Fig. 1 (dashed line),the band has a width of 6◦ latitudes (32◦–38◦N) andextends from 141◦E to the dateline. Because it en-compasses the eastward-flowing KE jet, the band willbe referred to hereafter as the KE band. Notice thatmany of the previous studies of the Pacific decadalvariability have focused on the Subarctic Front bandcentered along 40◦N (e.g., Miller et al. 1994; Deserand Blackmon 1995; Nakamura et al. 1997; Pierce etal. 2001; Wu et al. 2003; Kwon and Deser 2006). Theselection was commonly based on EOF analysis of thewintertime SST signals. Because the SST gradient isgreater across the Subarctic Front than across theKE front, the variance-based analysis of EOF tendsto emphasize the variability of the Subarctic Front(Nakamura and Kazmin 2003; Nonaka et al. 2006).

There are two reasons for our study to choose thesoutherly KE band. From the atmospheric point ofview, if the oceanic variability is to influence the over-lying atmosphere, it would be through the anoma-lous air-sea surface heat flux forcing. A look at theanomalous wintertime surface heat flux data from theNCEP–NCAR reanalysis reveals that its largest vari-

Qne

t [W

m−2

]

0102030405060708090100110120

(a) RMS amplitude of JFM net heat flux

120°E 140°E 160°E 180° 160°W 140°W 120°W10°N

20°N

30°N

40°N

50°N

60°N

SSH

rms

[cm

]

0

2

4

6

8

10(b) RMS amplitude of SSH variability (10/92−12/05)

120°E 140°E 160°E 180° 160°W 140°W 120°W10°N

20°N

30°N

40°N

50°N

60°N

Figure 2. Root-mean squared (rms) amplitudes of (a)the wintertime (JFM) net surface heat flux anomaliesand (b) the low-passed filtered (with a 2-yr cutoff) SSHvariability in the North Pacific. Based on the NCEP–NCAR reanalysis of 1948–2005 for (a) and the satellitealtimetric data of 10/1992–12/2005 for (b). In both pan-els the dashed line indicates the Kuroshio Extension bandof 142◦–180◦E and 32◦–38◦N.

ations over the open North Pacific Ocean follow thepath of the KE jet from the coast of Japan to thedateline (see Fig. 2a).

Oceanographically, the KE band is where the sur-face geostrophic circulation has the largest varianceon interannual-to-decadal timescales. To corroboratethis point, we plot in Fig. 2b the rms amplitude ofthe SSH anomalies from the satellite altimeter mea-surements that are low-pass filtered to retain signalslonger than 18 months. From the map, it is obviousthat the low-frequency changes in the oceanic circu-lation are concentrated along the KE band of our in-terest. This second point is important because we areinterested in the mode in which the ocean circulationchanges are expected to play an active role.

Figure 3a shows the time series of the monthly SSTanomalies in the KE band from 1948 to 2005. A vi-sual inspection of the time series reveals that in addi-tion to the existence of a very low-frequency, warm-cold-warm signal over the 58-yr record, warm SST

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 4

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−2

−1

0

1

2SS

TA [o

C]

(a)

10−1 100 10110−4

10−2

100

Frequency [cpy]

Powe

r Spe

ctru

m [C

2 /cpy

]

ω−2 (b)

ObservedAR−1

Figure 3. (a) Time series of the monthly sea surfacetemperature anomalies averaged in the KE band. (b)Power spectrum of the SST anomaly time series. Red lineindicates the best fit based on a first-order autoregressiveprocess, climate noise model.

anomalies dominated in years around 1951, 1956,1961–62, 1969–72, 1978–82, 1989–91, and 1999–2001.The dominance of this quasi-decadal signal is con-firmed by the power spectrum of the time seriesshown in Fig. 3b.

Given the SST time series presented in Fig. 3a, itis helpful to start by exploring the “climate noise hy-pothesis” of Hasselmann (1976) and Frankignoul andHasselmann (1977). Under this hypothesis, the redspectrum of SST (Fig. 3b) simply reflects year-to-yearor decade-to-decade changes in the white noise atmo-spheric forcing:

∂T

∂t= −λT + q(t), (1)

where λ denotes the thermal damping rate and q(t),the white noise atmospheric forcing. By least-squaresfitting the observed SST time series of Fig. 3a toEq. (1), we find λ−1 = 138 days (∼ 4.5 months) andthat the variance for q(t) is equal to 1.83 × 10−14

K2 s−2. The red curve in Fig. 3b shows the SST spec-trum based on the climate noise model with the abovebest-fit λ and q values. There is an overall agreementin spectral shape between the two SST spectra, in-dicating the usefulness of Eq. (1) in understandingthe SST signals in midlatitude oceans. In the intra-annual frequency band (ω > 1 cpy), the observed SSTvariance appears to exceed consistently the fitting

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−4

−2

0

2

4

PDO

Inde

x

(a)

10−1 100 101

10−2

100

102

Powe

r Spe

ctru

m

Frequency [cpy]

ω−2 (b)

ObservedAR−1

Figure 4. Same as Fig. 3 except for the monthly PDOindex (available athttp:// jisao.washington.edu/pdo/PDO.latest).

based on the simple noise model. This discrepancy islikely due to the deficiency of Eq. (1) in capturing theseasonal re-emergence process (see Dommengnet andLatif 2002; Deser et al. 2003; Schneider and Cornuelle2005). The largest difference in spectral level occursnear ω = 0.1 cpy in Fig. 3b where the climate noisemodel fails to capture the observed decadal spectralpeak.

A widely used index for the long-term climate vari-ability in the North Pacific is the “Pacific decadaloscillation (PDO)” index defined as the leading com-ponent of the North Pacific monthly SST anomaliesnorth of 20◦N (Mantua et al. 1997; see Fig. 4a). Whilethe KE SST index given in Fig. 3a shares some simi-larities with the PDO index (the two time series arelinearly correlated at −0.63), the PDO index lacks thedecadal spectral peak detected in the KE SST index.In fact, the climate noise model provides a better ex-planation for the PDO time series than it does for theKE SST time series (Fig. 4b; see also Pierce 2001).It is worth emphasizing that the PDO-related SSTanomalies have their center of action located along40◦N, where the oceanic circulation variability is lessactive than along the KE band (recall Fig. 2b). Inthe following sections, we examine how inclusion ofthe oceanic variability modifies the SST spectrum inthe KE band on the decadal and longer timescales.

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 5

(a) Altimetry SSH anomaly

140°E 160°E 180° 160°W 140°W 120°W93

94

95

96

97

98

99

00

01

02

03

04

05

06

−20−16−12 −8 −4 0 4 8 12 16 20

(b) Model SSH anomaly

SSH Anomaly [cm]

140°E 160°E 180° 160°W 140°W 120°W93

94

95

96

97

98

99

00

01

02

03

04

05

06

Figure 5. SSH anomalies along the zonal band of 32◦–34◦N from (a) the satellite altimeter data and (b) thewind-forced baroclinic Rossby wave model, Eq. (2).

4 Climate noise model for SST with

the advective effect

In order to understand how oceanic circulation vari-ability can change the SST signals in the KE band,we explore two dynamic processes in this section: (1)upper ocean’s adjustment to the time-varying atmo-spheric forcing, and (2) SST’s change in the KE bandresulting from the changing SSH field.

a. Oceanic adjustment to the changing wind stressfield:

It is well established that the large-scale SSH (or,equivalently, the upper ocean thermocline) variabil-ity is controlled by baroclinic Rossby wave dynamics.Specifically, the linear vorticity equation under thelongwave approximation states:

∂h

∂t− cR

∂h

∂x= −

g′ curl τ

ρogf, (2)

where h is the SSH anomaly, cR the speed of the long

baroclinic Rossby waves, g the gravitational constant,g′ the reduced gravity, ρo the reference density, f theCoriolis parameter, and τ the anomalous wind stressvector. Given the wind stress curl data, Eq. (2) canbe easily solved by integration along the baroclinicRossby wave characteristic:

h(x, t) =g′

cRρogf

∫ x

0

curl τ

(x′, t +

x − x′

cR

)dx′.

(3)In (3), we have ignored the solution due to the east-ern boundary forcing at x = 0. As detailed in Fu andQiu (2002), contributions from the eastern boundaryforcing in the midlatitude North Pacific is largely con-fined to the area a few Rossby radii away from theboundary.

The importance of the Rossby wave dynamics inhindcasting the SSH changes has been pointed outin several OGCM and CGCM studies focusing onthe KE variability (e.g., Xie et al. 2000; Seager etal. 2001; Schneider et al. 2002). Indeed, the relevance

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 6

2 4 6 8 100

20

40

60

80

100

Mode Number

Perc

enta

ge

(a)

ετ Var

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.2

−0.1

0

0.1

0.2 (b)

totalmode 2

Figure 6. (a) Dashed line shows the percentage of thecumulative variance over the total wind stress curl vari-ance as a function of spatial modes s defined in Eq. (4).Solid line shows the ratio of the SSH variance explainedby the Rossby wave model driven by the wind forcingwith spatial modes lower than s. (b) SSH time series inthe KE band driven by the full wind forcing (solid line)versus the wind forcing with the 2 lowest spatial modes(dashed line).

of Eq. (2) is favorably supported by observations.Figure 5a shows the time-longitude plot of the SSHanomalies along 32◦–34◦N across the North Pa-cific Ocean from the satellite altimeter measure-ments. Using the monthly wind stress curl data fromthe NCEP-NCAR reanalysis, we plot in Fig. 5b theh(x, t) field in the same latitudinal band based onEq. (3). Although the observed SSH field in the KEregion contains mesoscale eddy signals that are miss-ing in Fig. 5b, the large-scale decadal SSH changes(e.g., positive SSH anomalies in 1992–1995 and 2001–2004, and negative SSH anomalies in 1996–2000 and2005, in the KE region west of 160◦E) are capturedwell by Eq. (2). The linear correlation coefficient be-tween the observed and modeled h(x, t) fields is r =0.54 and this coefficient increases to 0.62 when onlythe interannual SSH signals are retained in Fig. 5a.

The dominance of the long baroclinic Rossby wavedynamics in determining the SSH changes in the KEregion points to the importance of the wind stress curlforcing in the KE’s latitudinal band. With the windstress curl variability being weak at the ocean’s east-ern and western boundaries, this forcing field (i.e.,the RHS of Eq. 2) can be mathematically decomposedusing

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−1

−0.5

0

0.5

1

w1 [1

0−8 m

s−1 ]

(a) w1(t)

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−1

−0.5

0

0.5

1

w2 [1

0−8 m

s−1 ]

(b) w2(t)

10−1 100 10110−20

10−19

10−18

10−17

10−16

Powe

r Spe

ctru

m [(

ms−

1 )2 /c

py]

Frequency [cpy]

(c)

n=1n=2

Figure 7. Time series of wind stress curl along the KElatitude band with the spatial patterns of (a) sin(πx/W )and (b) sin(2πx/W ). (c) Power spectra of the wind stresscurl time series shown in (a) and (b).

the basis function of sine:

−g′ curlτ (x, t)

ρogf=

N∑

n=1

sin(nπx

W

)wn(t), (4)

where x = −W denotes the western boundary of thebasin, wn(t) the temporal coefficient for the n-th spa-tial mode, and N the highest spatial mode resolvedby the NCEP–NCAR reanalysis data. Notice thatwhile a large number of modes is needed to repre-sent the wind stress curl variability, a significantlysmaller number of modes is required to simulate thetime-varying SSH signals in the KE band.

In order to quantify this point, we form themonthly curlτ (x, t) field averaged between 32◦N and38◦N. The dashed line in Fig. 6a shows the percentageof the cumulative variance over the total wind stresscurl variance when the number of spatial modes inEq. (4) is increased. To capture 90% of the total vari-ance, the 10 lowest spatial modes are required. Thewind stress curl field defined in Eq. (4) can be usedto calculate the SSH signals averaged in the KE band

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 7

(recall Eq. 3):

hs(t) ≡1L

∫−W+L

−W[− 1

cR

∫ x0

∑sn=1

sin(

nπx′

W

)wn

(t + x−x

′

cR

)dx′

]dx,

(5)

where L is the zonal length of the KE band and hsdenotes the SSH signals induced by the wind forc-ing with spatial modes ≤ s. (Thus defined, hN givesthe SSH signals induced by the full wind forcing.) InFig. 6a, we plot in solid line the ratio of the variancefor hs over that for hN . In contrast to the wind vari-ance (the dashed line), only the 2 lowest modes of thewind forcing are needed to capture 90% of the totalSSH variance [ see Fig. 6b for comparison between thetime series hN (t) and h2(t) ]. Physically, wind forc-ing with high spatial modes is unimportant for h(t)because the integration along the Rossby wave char-acteristic in Eq. (5) works as an effective spatial filter.In addition, we are interested in the SSH signals av-eraged in the KE band, which further filters out thesmall-scale wind forcing effect.

Given the importance of the 2 lowest modes ofwind forcing, we plot in Figs. 7a and 7b the time se-ries of w1(t) and w2(t), respectively. Unlike the SSTsignals shown in Fig. 3, both modes have a largely“white” spectrum and this is particularly true forw1(t). These “white” spectra reflect the dominanceof the intrinsic atmospheric variability in the mid-latitude North Pacific. Averaged over the frequencyband, the magnitudes of spectral power for w1(t) andw2(t) are |ŵ1(ω)|

2 = 1.127× 10−18 (m s−1)2/cpy and|ŵ2(ω)|

2 = 6.429× 10−19 (m s−1)2/cpy, respectively.

b. SSH-induced SST changes in the KE band:

As the wind-induced positive (negative) SSHanomalies propagate from the central North Pacific,previous studies based on the satellite altimetry dataanalysis indicate that they tend to enhance (weaken)the zonal KE jet and shift the path of the KE jetnorthward (southward) (Qiu 2000; Vivier et al. 2002;Kelly 2004; Qiu and Chen 2005). Both of these pro-cesses work to increase (decrease) the SST value inthe KE band. To include the time-varying SSH effecton the SST signals in the KE band, we extend theclimate noise model, Eq. (1), to:

∂T (t)

∂t= ahN(t) − λT (t) + q(t), (6)

where hN (t) is defined in Eq. (5) and a is a coefficientrelating the SSH changes to those of SST in the KEband. In their respective analyses of coupled modeloutputs, Schneider et al. (2002) and Kwon and Deser(2006) have found that the low-frequency SSH

10−1 100 10110−8

10−6

10−4

10−2

100

ω [cpy]

SSH

Powe

r Spe

ctru

m [(

m2 /c

py]

(a)

10−1 100 10110−3

10−2

10−1

100

ω [cpy]

SSTA

Pow

er S

pect

rum

[C2 /c

py]

(b)

ObservedAR−1AR−1,adv

Figure 8. (a) Power spectrum of the SSH time seriesforced by the full wind stress curl field (see the solid line inFig. 6b). (b) Power spectrum of the SST anomalies in theKE band (grey line) and the best fit based on the climatenoise model with and without the SSH effect (solid versusdashed lines).

signals in the model’s KE band represented well theheat convergence associated with the geostrophic sur-face ocean circulation. In other words, the ahN(t)term in Eq. (6) can be interpreted physically as rep-resenting geostrophic advection associated with thetime-varying KE jet.

By least-squares fitting the SST and hN (t) timeseries to Eq. (6), we find a = 2.73 × 10−7 K m−1s−1,λ−1 = 129.2 days and that the variance for q(t) isequal to 1.734 ×10−14 K2s−2. With q(t) in Eq. (6)representing the white noise forcing and assuming itis uncorrelated to the hN (t) time series at all frequen-cies, the power spectrum for T (t) in this case is givenby:

| T̂ (ω) |2 =a2 | ĥN(ω) |

2 + | q̂(ω) |2

λ2 + ω2. (7)

where ω is the frequency and ̂ denotes the Fouriertransform. Figure 8a shows the power spectrum

| ĥN(ω) |2 based on the hN (t) time series shown in

Fig. 6b. Using this result and the values for a, λ, and| q̂(ω) |2 = 0.289× 10−14 (K s−1)2/cpy derived above,

we plot | T̂ (ω) |2 in Fig. 8b by the solid line. Com-

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 8

pared to the SST spectrum from the climate noisemodel without the oceanic effect (the dashed line inFig. 8b; same as in Fig. 4), the SST spectrum has50% more variance in the 9–16 yr band. Reflectingthe dominance of the SSH variations on the decadaltimescales, inclusion of the SSH effect has little im-pact upon the SST signals with frequencies higherthan 2 cpy.

A stringent method for testing the significance ofthe SSH’s impact upon the SST signals is to comparethe observed SST signals with those hindcast usingthe hN (t) time series alone, namely:

∂TSSH(t)

∂t= ahN (t) − λTSSH(t) (8)

(Schneider and Cornuelle 2005). Because of the ther-mal damping timescale, λ−1, is much shorter thanthe decadal timescale dominating the hN time series,TSSH derived from Eq. (8) is temporally very similarto the hN time series (cf. the thin line in Fig. 9 and thesolid line in Fig. 6b). The correlation between hN andthe observed SST time series (Fig. 3a) is r = 0.297.To test the significance of this correlation, we com-pare it to the null hypothesis, namely, a selection ofrandom red-noise h(t) time series are able to performas well as the hN time series based on the baroclinicRossby wave dynamics. To do so, we first generate1,000 time series of h(t) that have the same AR-1characteristics as that for hN (Fig. 8a). For each h(t)time series generated, we derive TSSH(t) from Eqs. 6and 8 and calculate its correlation with the observedSST time series. The 95% highest correlation levelfrom these 1,000 trials is 0.258, indicating that theinfluence of hN upon the SST signals in the KE bandis significant above the 95% confidence level. It isworth noting that while it only explains 9.3% of theobserved, monthly SST variance, the TSSH(t) timeseries accounts for 27.4% of the SST variance withtimescales longer than 10 yr (see Fig. 9 for the com-parison between TSSH and the low-pass filtered SSTtime series).

5 Surface wind response to the KE

SST anomalies

In the preceding section, we showed that inclusion ofthe oceanic SSH signals in the climate noise modelincreases the decadal SST variance in the KE band.While this inclusion helps to model the observed spec-trum of SST, it does not answer the crucial ques-tion of whether this decadal enhancement is due to apurely forced ocean response, or a result of the air-seacoupling. To answer this question requires an

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−1

−0.5

0

0.5

1

T SSH

[oC]

HindcastedObserved

Figure 9. Thick line: Low-pass filtered SST anomalytime series observed in the KE band (see Fig. 3a for theoriginal time series). Thin line: The SST time series hind-cast by the SSH times series hN (t); see Eq. (8) for details.

in-depth examination of the surface wind stress curlfield and its connection to the SST anomalies in theKE band.

Because of its strong intrinsic variability, the ex-tent to which the atmosphere responds to midlati-tude SST anomalies has been a focus of many ob-servational and modeling studies (e.g., Peng et al.1997; Barnett et al. 1999; Pierce et al. 2001; Kush-nir et al. 2002; Tanimoto et al. 2003). In this study,we adopt the statistical approach proposed by Czajaand Frankignoul (1999, 2002) and examine the tem-poral covariance between the SST anomalies in theKE band and the basin-wide wind stress curl anoma-lies. Although Czaja and Frankignoul’s studies havefocused on the North Atlantic basin, their approachhas been applied recently by Liu and Wu (2004) andFrankignoul and Sennéchael (2006) to the North Pa-cific basin. Our present analysis complements theseexisting studies and of particular interest to us is howthe SST anomalies detected in the KE band impactthe wind stress curl field that subsequently drives theSSH changes in the KE band1.

The essence of Czaja and Frankignoul’s approachis to examine the covariability of an atmospheric vari-able (here, the surface wind stress curl) and the SSTwith a lag that is longer than the intrinsic atmo-spheric timescale (∼ 1 month), but shorter than thepersistence timescale of SST, λ−1. Before applyingthis approach, we follow Frankignoul and Sennéchael(2006) and remove by linear regression the Niño-3.4SST signals from the monthly τ (x,y,t) time series atall midlatitude grid points. The regression is done ona seasonal basis and works to remove the low-

1Both Liu and Wu (2004) and Frankignoul and Sennéchael(2006) have investigated the ocean-atmosphere covariability byfocusing on the SST signals centered along 40◦N in the west-ern North Pacific Ocean. As we argued in section 3, despitehaving less variance, the SST anomalies in the KE band (cen-tered along 35◦N) are likely to be more relevant for the air-seacoupled mode in the North Pacific.

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 9

(a) m=−1: SST(DJF) vs. curl (NDJ)

20°N

30°N

40°N

50°N

60°N

Correlation Coefficients: SST vs. curl−0.6 −0.4 −0.2 0 0.2 0.4 0.6

(b) m=3: SST(DJF) vs. curl (MAM)

20°N

30°N

40°N

50°N

60°N

Figure 10. Lagged correlation between the wintertime(DJF) SST anomalies in the KE band and the North Pa-cific wind stress curl field: (a) the wind stress curl leadsthe DJF SST by one month, and (b) the wind stress curllags the DJF SST by three months. Contour intervals are0.1, with the white contours indicate r = 0. The dashedbox indicates the latitudinal band of the KE.

frequency, surface wind signals that are teleconnectedfrom the tropics (Alexander et al. 2002). Figure10 shows the spatial patterns of lagged correlationr(x, y, m) between the wind stress curl anomalies andthe wintertime (DJF) SST anomalies in the KE re-gion:

r(x, y, m) =〈T (t) curl τ (x, y, t + m) 〉√〈T 2(t) 〉 〈 curl τ 2(x, y, t + m) 〉

,

where angle brackets denote the ensemble averageand m (> 0) denotes the SST lead time in months.Here, we focus on the wintertime SST signals becauseDJF are the months when both the SST and air-seaheat flux anomalies have the largest seasonal ampli-tude. To better understand the SST’s impact on theoverlying surface wind field, it is instructive to firstexamine the spatial pattern when the wind stress curlsignal leads the SST signal. Figure 10a shows ther(x, y, m) pattern when m = −1 month. The dipo-lar structure shown in the figure reflects that warmSST anomalies in the KE region are associated withthe weakening of the surface westerlies, resulting ina negative (positive) wind stress curl anomaly in thesubpolar (subtropical) North Pacific. This dipolar

140°E 160°E 180° 160°W 140°W 120°W−0.4

−0.2

0

0.2

0.4

Lag

Corre

latio

n

(a)

10−1 10010−19

10−18

10−17

Powe

r Spe

ctru

m

Frequency [cpy]

(b)

ObsIntrinsic

Figure 11. (a) Correlation along the 32◦ − 38◦N bandwhen the wind stress curl lags the DJF KE SST bythree months (see the dashed box in Fig. 10b). Solidcurve shows the best fit to the sin(2πx/W ) function.(b) Power spectra of the observed wind stress curl forc-ing −g′curl τ/ρogf (black line) versus the intrinsic windstress curl forcing −g′curl τ/ρogf−b T sin (2πx/W ) (greyline). The forcing values have been averaged in the east-ern half of the 32◦ − 38◦N band.

pattern bears a resemblance to those of the leadingEOF modes of the decadal sea level pressure anoma-lies identified by several previous investigators (e.g.,Trenberth and Hurrell 1994; Deser and Blackmon1995; Nakamura et al. 1997). Notice that the valuesof the correlation coefficient in Fig. 10a are generallyhigh ( | r | > 0.6), reflecting the dominance over themidlatitude SST forcing by the overlying atmosphericvariability.

The spatial pattern of r(x, y, m) becomes very dif-ferent when the surface wind signal lags that ofSST. Figure 10b shows the r(x, y, m) pattern whenm = 3 months2. Along the KE band of our interest,warm KE SST anomalies tend to generate an over-lying, negative wind stress curl anomaly (i.e., a highpressure anomaly), and a downstream positive windstress curl anomaly (see Fig. 11 a). This warm SST–downstream low pressure anomaly structure is consis-tent with the AGCM results that are forced by local-

2Spatial patterns similar to Fig. 10b are found for m = 1and 2 months, but they are generally less well-organized spa-tially. As stressed in Czaja and Frankignoul (2002), m = 3here should not be interpreted as a delayed response of theatmosphere to SST by 3 months. Rather, it indicates that thewind stress curl variability over the North Pacific Ocean hasa KE SST induced component that has the persistence of theSST anomalies.

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 10

ized, midlatitude heat flux anomalies (Yulaeva et al.2001; Sutton and Mathieu 2002). Compared to them = −1 case, the correlation coefficient in Fig. 10bgenerally has smaller values, suggesting that the dy-namical feedback of SST to the overlying atmosphereis relatively weak. Indeed, with each year providingan independent sample (i.e., the number of degreesof freedom at 57), most of the estimated correlationcoefficients in the 32◦–38◦N band of our interest fallin the confidence level between 90% (r = 0.22) and95% (r = 0.26).

The spatial pattern presented in Fig. 11 a sug-gests that the SST induced wind stress curl vari-ability along the KE band has a spatial structure ofsin(2πx/W ). By adding this feedback component ofthe wind forcing to the intrinsic atmospheric forcing,we can express the total wind stress curl signal by(recall Eq. 4):

−g′ curlτ (x, t)

ρogf=

N∑

n=1

sin

(nπx

W

)wn(t) + b sin

(2πx

W

)T (t),

(9)

where b is a coefficient relating the SST anomaliesin the KE band to those in the wind stress curl fieldalong the 32◦–38◦N band. For a 1◦C SST change,a linear regression between the monthly SST andwind stress curl anomalies with the spatial struc-ture of sin(2πx/W ) reveals that the curlτ change is1.35 × 10−8 N m−3. Using g′ = 0.04 m s−2, g = 9.8m s−2, ρo = 10

3 kgm−3, and f = 8.34 × 10−5 s−1,this leads to b = 6.64× 10−10 m s−1 K−1.

It is worth commenting on the size of the feed-back term b T sin(2πx/W ) in Eq. (9). While mod-erate, this feedback term is not negligible and thisis particularly true for the wind stress curl signalswith a decadal timescale. Averaged over the easternhalf of the 32◦–38◦N band, the power of the observeddecadal wind stress curl forcing −g′curl τ/ρogf is1.44 × 10−18 (m s−1)2/cpy (see Fig. 11b, solid line).The power for the “feedback” wind stress curl forc-ing averaged in the same region can be estimated by2b2|T̂ (ω)|2/π. Using b = 6.64 × 10−10 m s−1 K−1

and |T̂ (ω)|2 = 1 K2/cpy based on Fig. 3b, we have

2b2|T̂ (ω)|2/π = 0.28×10−18 (m s−1)2/cpy, indicatingthat the SST-induced wind stress curl forcing can ex-plain close to 20% of the observed decadal variance.A calculation of the area-averaged spectrum showsthat −g′curl τ/ρogf − b T sin (2πx/W ) has a decadalpower at 1.23×10−18 (m s−1)2/cpy (Fig. 11b, dashedline). This reduction in the decadal spectral powerconfirms that the observed wind stress curl data in-deed contains a decadal feedback component that can

be traced back to the KE SST anomalies.

6 Coupled versus uncoupled

variability

By relating the SST variability to that of the surfacewind stress curl field in the previous section, we ob-tain the following set of equations governing the SSTchanges in the KE band:

∂h(x, t)

∂t− cR

∂h(x, t)

∂x= −

g′ curlτ

ρogf, (10)

∂T (t)

∂t= a h(t) − λT (t) + q(t), (11)

−g′ curlτ

ρogf=

2∑

n=1

sin(nπx

W

)wn(t) + b sin

(2πx

W

)T (t).

(12)Notice that in Eq. (12), we have replaced the orig-inal N in Eq. (9) by 2, because the higher spatialmodes, as we discussed in section 4a, exert little im-pact upon the SSH signals averaged in the KE band.For brevity, we have also replaced h2 (i.e., the SSHsignal induced by the 2 leading spatial modes of thewind forcing) by h. By explicitly separating the windstress forcing into the intrinsic and feedback compo-nents in Eq. (12), we will assume in this section thatboth w1(t) and w2(t) have white spectra and focuson the coupling effect of the SST-induced wind stresscurl forcing.

It is worth commenting that Eqs. (10)–(12) resem-ble the set of equations put forth previously by Jin(1997) in his theoretical study of the North Pacificdecadal variability. While similar in form, the physi-cal processes assumed by Jin (1997), especially thoseof Eqs. (11) and (12), are different from the ones de-rived in this study. Given a warm SST anomalyin the KE, Jin (1997) assumes that it generates adownstream high pressure anomaly and, hence, anenhanced Ekman pumping. As the positive SSHanomalies generated by the enhanced Ekman pump-ing reach the western boundary, Jin (1997) arguesthat they generate a southward interior geostrophicflow (v′ < 0), that will change the sign of the KE SSTanomaly through interior geostrophic heat advection(i.e., −v′∂Tm/∂y < 0, where Tm is the mean sur-face ocean temperature). From the statistical analy-sis conducted in section 5, we find that a warm SSTanomaly in the KE band works to generate a down-stream low pressure anomaly and, hence, an enhancedEkman suction. The latter lowers the SSH in theeastern North Pacific and tends to weaken the KEjet as the SSH anomalies propagate westward. By

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 11

10−1 100 1011010

1012

1014

1016

1018|P

n(ω

)|2

(a)

n=1n=2

10−1 100 10110−3

10−2

10−1

100

ω [cpy]

SSTA

Pow

er S

pect

rum

[C2 /c

py]

(b)

ObservedUncoupled

Figure 12. (a) Squared amplitudes of P1(ω) and P2(ω)as a function of frequency. (b) Grey line: power spec-trum of the observed SST anomalies in the KE band.Black line: power spectrum of SST forced by the “white-noise” surface wind and thermal forcing under the air-seauncoupled scenario, Eq. (17).

weakening the KE jet and shifting it southward, theEkman suction-induced negative SSH anomalies re-sult in cold SST anomalies in the KE region, therebyswitching the phase of the coupled oscillation.

a. Air-sea uncoupled case ( b = 0 ):

Before exploring the coupled case, it is instructiveto examine the case where there is no SST feedbackto the atmosphere. In this case, b = 0 and, uponsubstituting Eq. (12) into Eq. (3), we have:

h(x, t) = −1

cR

∫ x

0

2∑

n=1

sin

(nπx′

W

)wn

(t +

x − x′

cR

)dx′.

(13)

Taking its Fourier transform:

ĥ(x, ω) = −

2∑

n=1

ŵn(ω)

cR

∫ x

0

sin

(nπx′

W

)eiω(x−x

′)/cR dx′,

we can express the Fourier transform for the SSHanomaly averaged in the KE band by:

ĥ(ω) ≡1

L

∫ −W+L

−W

ĥ(x, ω) dx =

2∑

n=1

Pn(ω) ŵn(ω),

(14)

where Pn(ω) is given by

Pn(ω) =1

2LcR

[W

nπαn+

(einπL/W − 1

)e−inπ

+W

nπαn−

(e−inπL/W − 1

)einπ

−

(1

αn+−

1

αn−

)cR

ω

(eiωL/cR − 1

)e−iωW/cR

],

(15)

and αn± = i(−ω/cR ± nπ/W ). For ĥ(ω) inEq. (14), Pn(ω) serves as a frequency-dependent fil-ter to the wind forcing that has the spatial structuresin(nπx/W ). Figure 12a shows the squared ampli-tude of P1(ω) and P2(ω) as a function of frequency.Reflecting the integrating nature of the forced Rossbywave dynamics, both terms are highly effective low-pass filters.

Taking the Fourier transform of Eq. (11) and usingEq. (14), we have:

(λ + iω)T̂ (ω) = a

2∑

n=1

Pn(ω) ŵn(ω) + q̂(ω). (16)

With the assumption of wn(t) and q(t) being inde-pendent white-noise forcing, the power spectrum forthe SST anomalies in this uncoupled case can be cal-culated by:

| T̂ (ω) |2uncoupled =1

λ2+ω2

[a2

∑2n=1

|Pn(ω) |2 | ŵn(ω) |2 + | q̂(ω) |2]

.(17)

Using the parameter values derived in the previoussections (Table 1), we plot | T̂ (ω) |2uncoupled by thesolid line in Fig. 12b and compare it to the observedSST spectrum in the KE band. From the figure,it is clear that the uncoupled model is inadequateto explain the decadal spectral peak of our interest.It is worth noting that Eq. (17) contains the “spa-tial resonance” mechanism proposed by several previ-ous investigators (e.g., Frankignoul et al. 1997; Sara-vanan and McWilliams 1998; Neelin and Weng 1999).For example, |P2(ω) |

2 has a spectral peak around8 yr (Fig. 12a) and this peak would have shown up

in | T̂ (ω) |2uncoupled if the n = 2 wind forcing haddominated the n = 1 wind and heat flux forcingsin Eq. (17). In other words, given the physical pa-rameters appropriate for the midlatitude North Pa-cific, the spatial resonance mechanism alone, withoutthe SST feedback to the atmosphere, is insufficient togenerate the preferred decadal timescale detected inthe KE’s SST field.

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 12

10−1 100 1010.6

1

1.4

1.8G

(ω)

(a)

10−1 100 10110−3

10−2

10−1

100

ω [cpy]

SSTA

Pow

er S

pect

rum

[C2 /c

py]

(b)

ObservedUncoupledCoupled

Figure 13. (a) Amplitude of the amplification factorG(ω) as a function of frequency. (b) Grey line: powerspectrum of the observed SST anomalies in the KE band.Solid line: power spectrum of SST under the air-sea cou-pled scenario, Eq. (20). Dashed line: power spectrum ofSST under the air-sea uncoupled scenario, Eq. (17).

b. Air-sea coupled case ( b 6= 0 ):

The analysis pursued above can be easily extendedto include the SST feedback (i.e., b 6= 0). In this case,Eq. (14) is replaced by:

ĥ(ω) =2∑

n=1

Pn(ω) ŵn(ω) + b P2(ω) T̂ (ω), (18)

and Eq. (16) by:

[ λ + iω − abP2(ω) ] T̂ (ω) = a

2∑

n=1

Pn(ω) ŵn(ω)+q̂(ω).

(19)From Eq. (19), it is easy to derive:

| T̂ (ω) |2coupled =

∣∣∣∣λ + iω

λ + iω − abP2(ω)

∣∣∣∣2

| T̂ (ω) |2uncoupled.

(20)Equation (20) indicates that the SST spectrum inthe coupled case is equal to the spectrum of theuncoupled case (i.e., Eq. 17) amplified by G(ω) =| (λ + iω)/(λ + iω − abP2) |

2. In Fig. 13a, we plot theamplification factor G(ω) as a function of frequency.For parameter values relevant to the North Pacific, itis shown in the Appendix that the largest amplifica-tion occurs when the period of the coupled mode isat:

Table 1. Parameter values appropriate for themidltitude North Pacific Ocean.

Parameter Value

cR 0.033 m s−1

f 8.34× 10−5 s−1

W 95◦ longitude

L 40◦ longitude

λ 1/129.2 days

a 2.73× 10−7 K m−1 s−1

|ŵ1(ω)|2 1.127× 10−18 (m s−1)2/cpy

|ŵ2(ω)|2 0.643× 10−18 (m s−1)2/cpy

|q̂(ω)|2 2.89× 10−15 (K s−1)2/cpy

b 6.64× 10−10 m s−1 K−1

Toptimal 'W

cR

1

(1 − �), (21)

where � is a small correction term defined in (A5) inthe Appendix. Using the parameter values listed inTable 1, we have � = 0.21 and Toptimal ' 10.4 yr, inagreement with the peak in G(ω).

Aside from the correction term �, the physical inter-pretation of Toptimal = W/cr (= 8.23 yr) in Eq. (21)is straightforward. With the spatial structure of theSST-induced wind forcing being sin(2πx/W ), the op-timal coupling occurs when the time required for thewind induced SSH anomaly to travel from the centerof the maximum forcing (at x = −W/4) to the centerof the KE band (at x ' −3W/4) is equal to half ofthe wave period. In such a case, an initial warm SSTanomaly, for example, would induce a positive curlτanomaly in the eastern half of the basin, generatingnegative SSH anomalies through Ekman divergence.As the negative SSH anomalies reach the center of theKE band in the west half of a wave period later, theycause the regional SST to decrease, which, in turn,switches the sign of the curlτ anomaly in the east.The correction term � in Eq. (21) accounts for devia-tions from this simple physical picture due to the factthat the SST-induced wind forcing is spatially a sinefunction (instead of a δ-function) and that the

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 13

10−2 10−1 100 1010.6

1

1.4

1.8G

(ω)

(a) L=50L=40L=30

10−2 10−1 100 1010.6

1

1.4

1.8

ω [cpy]

G(ω

)

(b) ab=1.5ab=1ab=0.5

Figure 14. Amplitudes for the amplification factor G(ω)when (a) the length of the KE band L and (b) the coupledparameter ab are changed parametrically. In (b), ab = 1denotes the case in which ab is given by the values listedin Table 1 and ab = 1.5 (0.5) the case in which ab isenhanced (reduced) by 50%.

KE band does not occupy the exact western half ofthe North Pacific basin.

In Fig. 13b, we compare the spectra of |T̂ (ω)|2coupled(the black line) versus | T̂ (ω) |2uncoupled (the dashedline). In contrast to the “red” spectrum found in

the uncoupled case, | T̂ (ω) |2coupled now has a decadalspectral peak due to the amplification through G(ω).Over the decadal frequency band, the spectral shapeof | T̂ (ω) |2coupled agrees closely with the full forcing

case (the case in which | ĥ(ω) |2 was calculated basedon the observed wind forcing; cf. the black line inFig. 8b), indicating the air-sea coupling described inthis subsection is a likely explanation for the en-hanced decadal SST variability observed in the KEband. Like Fig. 8b, the modeled decadal spectralpeak in Fig. 13b still underestimates the observedspectral peak. A possible reason for this underes-timation is discussed in section 7.

c. Parameter sensitivity:

Given the importance of G(ω) for the coupled SST

variability, it is useful to comment on its sensitivityto the relevant parameters. Once the basin size Wand the Rossby wave speed cR are fixed, the peak inG(ω), or Toptimal, is dependent only on the chosenlength of the KE band, L. Because L only changes�, a small correction term in Eq. (21), its impact onToptimal is rather limited. To quantify this statement,we compare in Fig. 14a the G(ω) values when L islengthened/shortened by 10◦ from its nominal valueof 40◦ in longitude. Despite the 25% change in L,the change in Toptimal is less than 9% (Toptimal =12.1 yr, 11.2 yr, and 10.5 yr, for L = 30◦, 40◦, and50◦, respectively, in Fig. 14a). In other words, thedominance of the 10-yr signals found in Fig. 13b is arobust feature insensitive to our choice of L.

While having no influence on Toptimal, parametersa and b affect the amplitude of G(ω) through theirproduct, ab. For the decadal frequency band of ourinterest, the amplitude of G(ω) increases with in-creasing ab (see Fig. 14b). Recall that a is the param-eter coupling the SSH anomalies to the SST anoma-lies in the KE band, and b is the parameter couplingthe SST anomalies to the wind stress curl anoma-lies. So, strengthening either of the coupling pa-rameters would enhance the decadal spectral peakin | T̂ (ω) |2coupled.

7 Discussions and summary

The objective of the present study is to clarify thenature underlying the observed decadal variability inthe midlatitude North Pacific. To achieve this objec-tive, we examined in detail the long-term SST sig-nals in the Kuroshio Extension (KE) region of 32◦–38◦N and 142◦E–180◦. In addition to being the re-gion where the ocean circulation is most variable inthe North Pacific, the KE is also where the largestheat/moisture exchanges take place across the air-seainterface. Over the past 58 years covered in this anal-ysis, SST signals in the KE region are dominated bychanges with periods of ∼ 10 and ∼ 50 yr. Given thelength of the available data, only the decadal signalsare explored in this study (for pentadecadal signals,see Minobe 1997).

Two issues are of particular interest to this study:(1) what role does the ocean dynamics play in con-tributing to the observed decadal SST signals, and (2)to what extent is the observed decadal SST variabil-ity a consequence of coupling between the midlatitudeocean and atmosphere. To answer these questions, webegan by testing the climate noise scenario, in whichno ocean dynamics was considered. While providinga reasonable overall spectral shape of the observed

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 14

SST spectrum, the simple climate noise model failsto capture the decadal spectral peak of our interest.

To examine the advective effect of the ocean cir-culation, we extended the climate noise model to in-clude the sea surface height (SSH) signals averaged inthe KE region. Satellite altimeter measurements ofthe past decade have shown that the low-frequencyKE variability is dominated by concurrent changesin the strength and path of the KE jet. A strength-ened (weakened) KE jet tends to be accompanied bya northerly (southerly) path, giving rise to a positive(negative) regional SSH anomaly. By adopting a lin-ear vorticity model with the baroclinic Rossby wavedynamics, we hindcast the SSH changes forced by thewind stress data from the NCEP–NCAR reanalysis.Due to the integrating nature of the wave dynamics,we found that the wind-induced SSH signals in theKE region have a broad spectral peak in the decadal-to-interdecadal frequency band, in agreement withmany of the previous studies of the low-frequency KEvariability (e.g., Miller et al. 1998; Deser et al. 1999;Seager et al. 2001; Schneider et al. 2002; Qiu 2003).Much of the modeled SSH variability was found tobe induced by the basin-scale wind stress curl forcingwith the lowest 2 spatial modes.

Inclusion of the SSH signals in the climate noisemodel helps to explain the observed decadal spec-tral peak in the SST spectrum, although the levelof power is still underestimated. One possibility forthis underestimation is that the linear Rossby wavedynamics does not account for the SSH signals. Ourrecent analysis of satellite altimetry data revealedthat while the linear Rossby wave dynamics mod-eled adequately the phases of the SSH changes inthe KE, it underestimated the amplitude by ∼ 40%(Qiu and Chen 2005). As the wind-induced, neg-ative SSH anomalies propagated from the east, al-timetry measurements show that they tend to weakenthe stability of the KE jet, enhancing the regionalmesoscale eddy variability and further lowering theregional SSH signals. This rectified effect of eddy-mean flow interaction is also emphasized in the re-cent study by Taguchi et al. (2006). By analyzingthe output from the high-resolution Ocean model forthe Earth Simulator (OfES), Taguchi et al. founda covariability between the large-scale KE changesthat are wind driven, and the “frontal-scale” intrin-sic changes of the recirculation gyre that enhancesthe wind-driven SSH signals. Notice that if such arectified effect of the intrinsic ocean variability couldbe “parameterized” through increasing the value forthe coupling parameter a in Eq. (6), the magnitudeof the modeled decadal spectral peak would be en-

hanced and the comparison between the modeled andobserved SST spectra improved.

The presence of a localized spectral peak per sedoes not imply the existence of an air-sea coupledmode. To clarify the mechanism responsible for theobserved decadal spectral peak, we adopted the sta-tistical approach of Czaja and Frankignoul (1999,2002) and examined the lagged correlation betweenthe wintertime SST anomalies in the KE band andthe basin-scale wind stress curl anomalies. Whenthe SST signals lead by 3 months (a timescale longerthan the intrinsic atmospheric variability and shorterthan the SST decorrelation timescale), the respond-ing wind stress curl field has a negative anomaly (i.e.,a positive pressure anomaly) over the KE band anda positive anomaly (a negative pressure anomaly) inthe eastern half of the basin. This response patternof the wind stress curl field is very different from thewind stress curl pattern that forces the KE SST sig-nals.

The importance of the air-sea coupling is exploredin this study by dividing the wind stress curl forcinginto those associated with the intrinsic atmosphericvariability and those induced by the SST signals inthe KE band. In the absence of the SST feedback, theintrinsic atmospheric forcing generates low-frequencychanges in the SSH signals in the KE band. Whilethis forced oceanic variability enhances the SST spec-tral level in the decadal and longer frequency band,it fails to capture the decadal SST peak detected inthe observations. When the SST feedback is present,a warm SST anomaly would generate positive windstress curl in the eastern part of the basin, resultingin negative local SSH anomalies through Ekman di-vergence. As these wind-forced SSH anomalies propa-gate into the KE region in the west, they shift the KEjet southward and alter the sign of the pre-existingSST anomalies. In this coupled scenario, it is theadjustment of the upper ocean through baroclinicRossby waves that provides the memory for the sys-tem. Given the spatial pattern of the SST-inducedwind stress curl forcing, the optimal coupling in themidlatitude North Pacific occurs at a period slightlylonger than the basin crossing time of the baroclinicRossby waves along the KE latitude (∼ 8.23 yr).We believe that it is this coupled mechanism thatcontributes to the increase in variance around thedecadal timescale in the SST field observed along theKE band.

It is worth noting that several coupled GCM stud-ies of the midlatitude North Pacific have identifiedair-sea coupled modes involving the KE system witha period ranging from 16 to 20 yr (e.g., Latif and

Qiu et al.: Decadal Variability in NP: An Observationally-Constrained Model 15

Barnett 1994, 1996; Barnett et al. 1999; Pierce etal. 2001; Kwon and Deser 2006). The period of thesecoupled modes is clearly longer than the 10-yr periodidentified in the present study. Due to the model res-olution, the KE jet in these climate models tends tocommonly separate from the Japan coast at ∼ 40◦N,which is 5◦ farther north than the observed KE sep-aration latitude (Hurlburt et al. 1996). Given thatthe baroclinic Rossby wave speed depends sensitivelyon latitude (e.g., cR = 0.033 m s

−1 along 35◦N ver-sus 0.020 m s−1 along 40◦N; see Fig. 7 in Qiu 2003),it is possible that a mechanism similar to that de-scribed in this study may be at work for the coupledvariability in the existing CGCM runs.

Finally, we note that although the variance of thecoupled SST mode is modest in comparison to thetotal SST variance in the KE region, the fact thatthe SSH signals constitute a deterministic forcingcan have a large impact upon the predictability ofthe western North Pacific SST signals (Schneider andMiller 2001; Scott and Qiu 2003). It will be interest-ing for future studies to explore whether the SST pre-dictability could benefit from incorporating the SSTfeedback onto the basin-scale wind stress forcing.

Acknowledgments

This study benefited from the discussions withClaude Frankignoul, Rob Scott, and Michael Alexan-der. Detailed comments made by the anonymousreviewers helped improve an early version of themanuscript. The surface wind stress and heat fluxdata were provided by the National Centers for Envi-ronmental Prediction, and the merged T/P, Jason-1 and ERS-1/2 altimeter data by the CLS SpaceOceanography Division as part of the Environmentand Climate EU ENACT project. We acknowledgesupport from NSF (OCE-0220680) and NASA (Con-tract 1207881) for BQ and SC, and NSF (OCE-0550233), NOAA (NA17RJ1231), and DOE (DE-FG02-04ER63862) for NS.

Appendix

Optimal amplification period for coupling

As we derived in Eq. (20), amplification of the SSTspectrum in the air-sea coupled case is determined bythe factor:

G(ω) =

∣∣∣∣λ + iω

λ + iω − abP2(ω)

∣∣∣∣2

. (A1)

With λ dominating over ω and | abP2(ω) | in thelow-frequency band of our interest, finding maximum

G(ω) becomes equivalent to finding the maximum inthe real part of P2(ω): Re [ P2(ω) ]. From Eq. (15),we have:

Re [ P2(ω) ] =1

ωL

[(ω

cR

)2

−( 2πW )2

]{

2πW

sin(

ωW

cR

)

− 2πW

sin[

ω(W−L)cR

]− ω

cRsin

(2πLW

)}.

(A2)

Let Re [ P2(ω) ] ≡ A(ω)/B(ω), the maximum inRe [ P2(ω) ] can be found by solving:

B(ω)∂

∂ωA(ω) − A(ω)

∂

∂ωB(ω) = 0. (A3)

With ω = 2πcR/W being a regular singular point, itis useful to rewrite ω as ω ≡ 2πcR/W + ω

′ and solve(A3) using the Taylor expansion with regard to ω′.By truncating high order terms in ω′ and ignoringterms of small values, we derive the following expres-sion for ω′:

ω′ '

− 9cR4πW

[1 −

(W−L

W

)cos

(2πLW

)+ 2π

3

(W−L

W

)2sin

(2πLW

) ].

(A4)

Using (A4), we find the optimal amplification forcoupling occurs at the period:

Toptimal =2π

2πcR/W + ω′≡

W

cR

1

(1 − �),

where

� '

98π2

[1 −

(W−L

W

)cos

(2πLW

)+ 2π

3

(W−L

W

)2sin

(2πLW

)].

(A5)

Notice that ω′ is positive definite, indicating that theoptimal amplification for coupling always occurs at aperiod longer than W/cR. Also, when W/4 < L <W/2 (as is the case for the KE band), � decreaseswith increasing L. In other words, Toptimal tends toshorten as L increases (see Fig. 13a).

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