Decadal Variability of the Midlatitude Climate System Driven by the Ocean Circulation

Andrew Mc C. Hogg Australian National University, Canberra, Australia

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William K. Dewar The Florida State University, Tallahassee, Florida

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Peter D. Killworth Southampton Oceanography Centre, Southampton, United Kingdom

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Jeffrey R. Blundell Southampton Oceanography Centre, Southampton, United Kingdom

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Abstract

A midlatitude coupled ocean–atmosphere model is used to investigate interactions between the atmosphere and the wind-driven ocean circulation. This model uses idealized geometry, yet rich and complicated dynamic flow regimes arise in the ocean due to the explicit simulation of geostrophic turbulence. An interdecadal mode of intrinsic ocean variability is found, and this mode projects onto existing atmospheric modes of variability, thereby controlling the time scale of the atmospheric modes. It is also shown that ocean circulation controls the time scale of the SST response to wind forcing, and that coupled feedback mechanisms thus modify variability of the atmospheric circulation. It is concluded that ocean–atmosphere coupling in the midlatitudes is unlikely to produce new modes of variability but may control the temporal behavior of modes that exist in uncoupled systems.

Corresponding author address: Dr. Andrew McC. Hogg, Geophysical Fluid Dynamics Group, Research School of Earth Sciences, Australian National University, Acton, ACT, 0200, Australia. Email: Andy.Hogg@anu.edu.au

Abstract

A midlatitude coupled ocean–atmosphere model is used to investigate interactions between the atmosphere and the wind-driven ocean circulation. This model uses idealized geometry, yet rich and complicated dynamic flow regimes arise in the ocean due to the explicit simulation of geostrophic turbulence. An interdecadal mode of intrinsic ocean variability is found, and this mode projects onto existing atmospheric modes of variability, thereby controlling the time scale of the atmospheric modes. It is also shown that ocean circulation controls the time scale of the SST response to wind forcing, and that coupled feedback mechanisms thus modify variability of the atmospheric circulation. It is concluded that ocean–atmosphere coupling in the midlatitudes is unlikely to produce new modes of variability but may control the temporal behavior of modes that exist in uncoupled systems.

Corresponding author address: Dr. Andrew McC. Hogg, Geophysical Fluid Dynamics Group, Research School of Earth Sciences, Australian National University, Acton, ACT, 0200, Australia. Email: Andy.Hogg@anu.edu.au

1. Introduction

Climate variability in the midlatitudes is a topic of considerable recent interest, which proves to be both difficult to diagnose and a complex problem to model accurately. Some of these difficulties are due to the high short-term variability in both ocean and atmosphere in these regions. The atmospheric storm track is responsible for synoptic-scale and seasonal variability, and it is generally positioned above the most variable part of the ocean circulation where (in the Northern Hemisphere) western boundary currents separate from the coast, meandering and shedding eddies into the ocean interior. With such a strong high-frequency variability it is difficult to investigate sources of lower frequency (interannual and decadal) variability. The problem is not so much in diagnosing the low-frequency variability; after all, climate oscillations such as the North Atlantic Oscillation (NAO; Deser and Blackmon 1993; Kushnir 1994), the Pacific decadal oscillation (PDO; Mantua et al. 1997; Qiu 2003), and the possibility of an Antarctic Circumpolar Wave (ACW; White and Peterson 1996; Jacobs and Mitchell 1996) are found in observations. However, the short-term variability masks lower-frequency interactions between the ocean and atmosphere, so that it is difficult to attribute low-frequency variability to a single cause.

It is for this reason that coupled climate models are used to investigate these phenomena. The modeling approach has the advantage that long records (subject to available computing resources) and higher-resolution data can be obtained. However, to undertake such extended runs, coupled global climate models (CGCMs) necessarily use low spatial resolution in the ocean component of the model. For example, the Third Hadley Centre Coupled Ocean–Atmosphere GCM (HadCM3; Gordon et al. 2000) uses a 1.25° × 1.25° ocean grid with a 3.75° × 2.5° atmosphere grid as its standard configuration. With these parameters, HadCM3 marginally resolves the first Rossby radius in the atmosphere [the ratio of Rossby radius to grid length is (rdx) ≈ 2], but not the midlatitude ocean [where (rdx) ≈ 0.2]. Even the high-resolution simulation of Roberts et al. (2004) barely resolves midlatitude ocean eddies. As such, these models obscure the synoptic-scale circulation in the ocean.

The poor resolution of some oceanic processes is not a problem per se; there are many processes in both the atmosphere and ocean that cannot be resolved by climate models. In such cases, processes are parameterized. Ocean eddies are usually parameterized by horizontal viscosity in such a way that the mean oceanic circulation is of the right order of magnitude. However, there is an emerging body of evidence that indicates that ocean eddies not only contribute to the high-frequency variability, but that they play a role in governing low-frequency oscillations in the oceanic circulation. This evidence comes from a hierarchy of idealized wind-driven ocean models (e.g., Berloff and McWilliams 1999; Primeau 2002; Nauw et al. 2004; Hogg et al. 2005) as well as some regional high-resolution models (Spall 1996). However, there are several aspects of this low-frequency variability that remain unresolved. First, there are significant arguments regarding the physical mechanisms underpinning the ocean variability, and second, it is not clear how, or if, such variability will affect the midlatitude climate system.

The physical mechanisms that lead to intrinsic variability of the wind-driven ocean circulation are complicated. One path to variability can be illustrated using a simple model (barotropic or baroclinic) in which there is a steady wind-driven circulation. Then, by changing parameters (either decreasing viscosity, increasing wind stress, or altering bottom drag), one is able to generate variability. For example, multiple stable states (e.g., Cessi and Ierley 1995; Primeau 1998), bifurcations resulting in periodic orbits (e.g., Nauw and Dijkstra 2001), and homoclinic bifurcations (Simonnet and Dijkstra 2002) have been shown to occur in different parts of parameter space: all of these factors may lead to variability in the circulation. Such mechanistic studies can be grouped under the banner of nonlinear dynamical systems theory, and they provide a method to evaluate the different proposed causes of variability. These mechanisms do not rely explicitly upon the presence of eddies, but upon nonlinearity of the ocean circulation.

The addition of eddies complicates the picture enormously—eddy-resolving models exhibit low-frequency variability that is dependent upon both viscosity and bottom drag. It is possible that the low-frequency variability in these simulations (e.g., Dewar 2001; Hogg et al. 2005) is due simply to the generation of nonlinear mean flow, and thus can be explained in terms of dynamical systems theory (Simonnet 2005, hereafter SIM). Another plausible hypothesis is that eddies play an active role in governing variability, as observed by Spall (1996) and Qiu and Miao (2000). However, in the absence of firm evidence to distinguish between these options, we elect to use an ocean model that includes both an active eddy field and nonlinear ocean circulation. We focus on resolving the second relevant question: how does intrinsic ocean variability alter the midlatitude climate system?

In this paper, we present results from an idealized coupled model that emphasizes ocean dynamics. The ocean component is a high-resolution three-layer quasigeostrophic (QG) box ocean, while the atmospheric component uses the same dynamical core in a channel configuration. The model is called the Quasi-Geostrophic Coupled Model (Q-GCM; Hogg et al. 2003b), and is summarized in the next section. The manuscript is then organized as follows. Sections 3 and 4 show the atmospheric and oceanic climate and variability, respectively, and place both of these in the context of other recent investigations. The variability of the coupled system is presented in section 5, and this is compared with a suite of partially coupled experiments in section 6. These results are discussed in section 7.

2. Q-GCM

We use Q-GCM version 1.2 with three atmosphere and three ocean layers. The basic architecture and dynamics of Q-GCM are now outlined; see Hogg et al. (2003a, b) for a detailed account.

Figure 1 shows the layout of Q-GCM. The three QG layers in both the ocean and atmosphere are indicated in Fig. 1 by the interfaces between layers. We use three layers to enable realistic simulation of baroclinic instability in both domains (we have observed, as have other workers in this field, that two-layer models tend to suppress baroclinic instability). These layers are of constant potential temperature, and so we require surface boundary layers to be embedded in layer 1 of both the atmosphere and ocean, to enable coupling. The embedded boundary layers also allow for absorption of incoming solar radiation, which varies with latitude and is the only driving force in the model. In addition, these boundary layers are used to calculate stress, which gives rise to ageostrophic velocity in the boundary layer, and Ekman pumping. A linear radiation and convection scheme allows for vertical transport of heat in the atmosphere; diabatic heating in the ocean is due to Ekman pumping, which exchanges heat between the surface mixed layer and QG layer 1. The equations for the QG layers and surface mixed layers are shown separately below.

a. QG layers

The QG equations in both the atmosphere and ocean are written in terms of the time rate of change of potential vorticity q:
i1520-0442-19-7-1149-e1
where p is a three-element pressure vector (one element for each layer), f0 is the Coriolis parameter, and A4 is the biharmonic diffusion coefficient. Thus, the evolution of the system depends upon advection of potential vorticity anomalies described by the Jacobian term,
i1520-0442-19-7-1149-eq1
the forcing term 𝗕e and the dissipation. The potential vorticity is written as
i1520-0442-19-7-1149-e2
where β is the (assumed constant) meridional gradient of the Coriolis parameter. In (2) the second term on the left describes the planetary vorticity, while the terms on the right represent relative vorticity and vortex stretching, respectively. For both ocean and atmosphere, the matrix 𝗔, which defines the relation between interface displacement and layer pressures, is
i1520-0442-19-7-1149-e3
where Hi is the unperturbed thickness of layer i and gi is the reduced gravity between layers i and i + 1.
The forcing term in (1) is governed by 𝗕, a 3 × 4 matrix that defines the forcing on the top and bottom of each layer. In the ocean it is written as
i1520-0442-19-7-1149-e4
while the atmospheric version is simply the opposite sign; aB = −oB. In addition, there are forcing vectors e that, for the ocean and atmosphere, respectively, are given by
i1520-0442-19-7-1149-e5
i1520-0442-19-7-1149-e6
Here wek is the Ekman velocity (proportional to the wind stress curl) calculated from the surface boundary layers (see below), and the second element in each forcing vector is the diabatic heating term, dominated by vertical advection due to Ekman pumping in the ocean and by parameterized radiation terms in the atmosphere [see Hogg et al. (2003a) for full details]. The atmospheric instantaneous diabatic heating term is labeled F, while the mean diabatic heating term () is calculated from the time average of a coupled simulation. It is only activated when the coupling parameter XC (described in section 2d below) is not unity. The ocean forcing also includes a linear bottom drag on the bottom layer.
The boundary conditions in the model are mixed conditions following Haidvogel et al. (1992). The conditions are applied to the pressure field, and are written as
i1520-0442-19-7-1149-e7
i1520-0442-19-7-1149-e8
i1520-0442-19-7-1149-e9
where the nondimensional coefficient αbc is zero for free-slip and infinite for no-slip boundary conditions (although, in practice, αbc > 2 is a good approximation to no slip), Δx is the horizontal grid spacing, and subscript n denotes the outward normal derivative. In the ocean the value of fk(t) is constrained by mass conservation and is the same for all boundaries; in the atmosphere the north and south boundaries use different values of fk(t), with the relationship between them constrained by momentum (McWilliams 1977). The east and west atmospheric boundaries are periodic.

b. Ocean surface mixed layer

The temperature evolution of the ocean mixed layer is given by
i1520-0442-19-7-1149-e10
where
i1520-0442-19-7-1149-e11
and oF is the total heat forcing of the ocean mixed layer, including the contribution transferred from the atmosphere. The second to last term in (10) explicitly shows the direct influence of Ekman pumping on the mixed layer temperature evolution through diabatic exchange of heat with QG layer 1. We include both Laplacian and biharmonic diffusion of temperature (coefficients oK2 and oK4, respectively), as well as advection by ageostrophic mixed layer velocity (oum, oυm) rather than the geostrophic velocity used in (1). The coupling parameter YC is described in section 2d below.

c. Atmosphere surface boundary layer

The atmospheric surface boundary layer differs in several respects from the ocean. First, the height of the layer is allowed to vary according to the equation
i1520-0442-19-7-1149-e12
where aem is a damping term and contributes to the diabatic heating term F in the QG layers. Temperature evolution is given by
i1520-0442-19-7-1149-e13
The forcing term aF is calculated from radiation, sensible and latent heat transfer from the ocean, Ekman pumping, and convection.
At the start of each ocean time step we find the atmospheric dynamic stress (aτ) from a quadratic drag formula that depends upon a dimensionless drag coefficient CD:
i1520-0442-19-7-1149-e14
where the geostrophic velocities are
i1520-0442-19-7-1149-e15
i1520-0442-19-7-1149-e16
and
i1520-0442-19-7-1149-e17
Ocean dynamic stress is then simply
i1520-0442-19-7-1149-e18
which requires interpolating stress onto the oceanic grid, and multiplication by the density ratio aρ/oρ.

d. Framework for partially coupled experiments

This paper includes a suite of numerical simulations in which the atmosphere and ocean domains are decoupled. The simplest way to do this is to run uncoupled experiments, with forcing from the temporal mean of a coupled run. However, it is more informative to partially couple the two domains using the parameters XC and YC defined in (6) and (11) above (both of which are constrained to the range [0, 1]). For example, when XC = YC = 1 the two domains are fully coupled, but with XC = 0 the atmosphere is forced by the mean forcing , rather than the time-varying forcing. Under this scenario, the ocean is still forced by the atmosphere in the usual way (driven by wind stress curl, and exchanging heat with the atmospheric boundary layer), but variability in the atmospheric boundary layer does not force the atmospheric circulation. As such, any modes of variability that are completely coupled or are driven by the ocean will be damped; any variability driven entirely from the atmospheric circulation will remain.

Likewise, the parameter YC controls the link between ocean advection and sea surface temperature (SST). When YC = 1, (10) describes the evolution of a temperature field that is advected by the oceanic circulation. But when YC = 0, this effect is eliminated—in such cases the SST variability is driven only by the wind-driven ageostrophic component of (11), Ekman pumping, and ocean–atmosphere heat flux. This parameter setting does allow limited coupled interactions, in the same way as a swamp ocean, but does not allow ocean dynamics to play any role in such interactions. The methodology used here produces a mean SST field that differs substantially from the mean of the fully coupled system. One therefore needs to be cautious about interpreting changes in the mean atmospheric circulation; however, results pertaining to the variability of the model climate are still relevant. Both of these coupling coefficients are used in the simulations described in section 6 to investigate the sources of variability in the coupled system.

3. Review of atmospheric variability

The dynamics of the Q-GCM atmosphere can be demonstrated from a rudimentary analysis of a coupled simulation, using the default parameter set shown in Table 1. We use a standard run length of 200 model years (following a 20-yr spinup phase) and save atmospheric data every 5 days. These data are then analyzed using empirical orthogonal functions (EOFs) that separate the data into a number of statistical modes. EOFs involve an eigenvalue analysis of the covariance matrix of the data. The result is that the data are decomposed into eigenvectors (spatial patterns that maximize variance) and their principal components (PCs) that describe the amplitude of the pattern as a function of time. In many cases the bulk of the variance can be attributed to only a few spatial modes [see von Storch and Zwiers (1999) for a full treatment of EOFs]. In this case, the data are separated into a number of modes, shown in Fig. 2.

The mean field (Fig. 2a) shows that the lower interface height (denoted HA1 hereafter) is sloping down to the south, consistent with heating in the southern latitudes and cooling in the north, and is very nearly zonally symmetric. The slope is greatest at the midlatitudes, indicating the position of the atmospheric storm track. The patterns of the five primary EOFs are shown in the subsequent panels. The behavior of the system is dominated by waves traveling from the west. In standard EOFs, traveling waves are shown as a pair of EOFs, 90° out of phase; when this occurs we elect to show only one of these pairs. Wavenumbers 3 (EOFs 1–2), 4 (EOFs 3–4), and 5 (EOFs 6–7) are shown, in descending order of significance. In addition, a standing annular mode (EOF 5) and a traveling mode with meridional and zonal wavenumbers both equal to one (EOFs 8–9) are found. The temporal variability of the modes is indicated by the spectra of the PCs (Fig. 2g). Here we see that highest wavenumbers (EOFs 3 and 6) dominate the high-frequency (monthly) spectrum. Wavenumber 3 (EOF 1) is greatest at all other frequencies, with a peak at 3 months, and the standing annular mode has a 6-month peak.

The EOFs shown here compare well with the atmospheric EOFs from previous baroclinic β-channel experiments (Vautard et al. 1988; Kravtsov and Robertson 2002; Kravtsov et al. 2003). Our model differs principally in that we include an atmospheric boundary layer, we use three atmospheric layers, and we eliminate artificial damping terms on the lowest planetary modes.

The difficulty with the EOF analysis is that it selects patterns from the total variance, which, in the atmosphere, is dominated by the high frequencies, while we are primarily interested in low-frequency variability. Thus, we temporally filter the data with a Fourier low-pass filter at every point in space (eliminating variance with a period less than 2 yr). The filtered data can then be reevaluated with the EOF analysis, yielding the filtered EOFs shown in Fig. 3.

The filtered data show few differences from the raw data. The primary mode of variability is still the traveling wavenumber-3 mode, which takes up EOFs 1 and 2, now totaling 59% of the variance of the filtered dataset. Note that wavenumbers 4 and 5, which had a considerable high-frequency component (see Fig. 2g) are not important at low frequency. Instead the annular mode (now EOF 3) is more prominent, and the traveling mode is now the fourth EOF (formerly EOF 8; mode 1 in both meridional and zonal directions). The spectra in the filtered dataset are essentially flat, with no significant tendency toward domination by either low or high frequencies, except for a decadal peak in the EOF 1 spectra, which is statistically significant.

Finally, we can compare the HA1 data with EOFs of the temporally filtered atmospheric boundary layer temperature (ABLT) as shown in Fig. 4. The ABLT is controlled principally by the atmospheric circulation. As such, we see that the primary modes of variability are, once again, the wavenumber-3 traveling mode (EOFs 1 and 2; total 59%) and the annular mode seen in the HA1 EOFs (now EOF 3). EOF 5 reflects the wavenumber-4 mode, which was important at high frequencies. However, EOF 4 shows a pattern that does not relate to HA1 modes. It has a strong maximum in amplitude over the ocean, and a “red” spectrum, with variance greatest at low frequencies. It will be shown below that this mode is the product of intrinsic ocean variability.

4. Review of ocean variability

There is a long history of ocean-only studies that demonstrate that variability emerges in high-resolution, low-viscosity models. Most recently Hogg et al. (2005) used the ocean component of Q-GCM to demonstrate that decadal modes of variability arise when geostrophic ocean turbulence is adequately resolved, and viscosity is sufficiently small. The ocean circulation that ensues is shown in Fig. 5. Here we see the rich eddy activity in the instantaneous snapshots of the first ocean interface height (HO1) and SST, and the strong front that develops in the central latitudes of the ocean. This front is part of the general double-gyre circulation of the upper layer that can be seen in the mean data. The front develops in the region of a jet near the separation of the western boundary currents. The gradient at the front is weaker in the mean field, purely because of the temporal averaging of the moving front, but is still discernible in both HO1 and SST.

Ocean data are saved at 15-day intervals and again filtered with a 2-yr Fourier filter. In Fig. 6 we show the first three Hilbert EOF modes of the filtered HO1 data. Hilbert (or complexified) EOFs (von Storch and Zwiers 1999) reveal modes that have different patterns according to the phase of the oscillation. They can be calculated by taking the Hilbert transform of the data to produce a complex dataset. One then determines EOFs in the usual way, producing a complex eigenvector (the spatial pattern of the mode) and complex PCs. We therefore show a real and imaginary pattern for each mode. We specifically use Hilbert EOFs for the ocean data because standard EOFs separate the imaginary and real phases of the oscillation into two orthogonal components. If these components contribute equally to the variance (as occurs with the propagating modes in the atmospheric analysis above), then it is a simple matter to correlate pairs of standard EOFs in the results. However, in the ocean we find oscillating modes in which two orthogonal components have unequal magnitudes and differing patterns; thus we are forced to use Hilbert EOFs to ensure we fully capture the correct modes.

In the case shown in Fig. 6 the first mode is centered on the ocean jet that divides the subtropical and subpolar gyres. The real part of the mode (left-hand panel) describes a phase where the jet is shifted either northward or southward, while the imaginary component (right-hand panel) indicates that the jet is either stronger or weaker. The mode is identical to Fig. 6a in Hogg et al. (2005), which is driven by steady atmospheric forcing, demonstrating that this is an intrinsic ocean mode of variability. It can be shown that this mode emerges at low Reynolds number but is strongly modified at high Reynolds number (Hogg et al. 2005). The low Reynolds number oscillation has been dubbed the gyre mode (see Fig. 6 of Dijkstra and Katsman 1997; Fig. 3 of Simonnet and Dijkstra 2002). Similar patterns are seen in barotropic low Reynolds number simulations that include strong bottom drag and high wind stress, implying that it may be possible to trace such oscillations to their dynamical roots without explicit resolution of eddies (SIM).

At the Reynolds number used here, Fig. 6d shows that the mode has a strong spectral peak at about 15 yr. This peak is significant compared with EOF modes 2 and 3, and the mode explains 43% of the total variance of the filtered dataset. Modes 2 and 3 have spatial patterns that are more widely distributed across the basin and have weaker amplitude (11% and 5.5%, respectively), particularly at low frequency. Mode 2 shows a statistically significant peak at 10 yr, while mode 3 shows a generally red spectrum.

Advection of SST by the layer-1 ocean circulation [the geostrophic term in (11)] is the primary mechanism producing SST variability. Thus the first HO1 mode dominates the SST EOFs at low frequencies. The first filtered Hilbert EOF for SST (Fig. 7a) has a maximum amplitude near the ocean jet and has a spectral peak at 15 yr (Fig. 7d). The temporal correlation between the first SST and HO1 modes is very strong (correlation coefficient: 0.7). However, the SST mode has an additional feature: SST variations of finite amplitude are seen over the whole ocean basin. In short, this is due to intermittent exchange of heat between the two gyres at a particular phase of the oscillation. This temperature anomaly is mixed throughout the two gyres relatively rapidly. In this way, the ocean mode creates SST anomalies that can be seen over a wide spatial scale, and thus has a greater capacity to force atmospheric changes than if the SST mode were confined to the ocean jet region.

The origin of SST modes 2 and 3 is not clear. For example, mode 2, which has a statistically significant decadal peak, shows a basinwide spatial signature that suggests forcing by Ekman pumping or Ekman transport due to the first atmospheric mode (Fig. 3a). In addition, the signals are intensified around the inertial recirculations, resembling HO1 mode 2 (Fig. 6b). It follows that this mode may be either atmospheric or oceanic in origin, and this is discussed further in the following section.

5. Variability of the coupled system

a. Evidence for coupled interactions using EOFs

In the previous sections we used EOFs to extract the primary modes of variability of each part of the system. A number of those modes selected by the EOF routines can be identified as interactions between different parts of the system. For example, the dominant ocean HO1 mode directly contributes to SST mode 1. In addition Fig. 4d shows that EOF 4 in ABLT (which accounts for only 2.6% of the total variance but is the strongest mode in the interdecadal range) has a spatial pattern that is consistent with the dominant mode in SST. This implies that the interdecadal ocean mode in this model influences the atmospheric temperature variability. Furthermore, we look in the HA1 field for evidence that this mode can alter the atmospheric circulation. However, the first five EOFs show no spectral signal, nor a pattern that suggests oceanic control of low-frequency variability. Thus, we conclude that this technique is unable to find signals of the ocean mode in the troposphere.

Another possible avenue for coupled interaction involves the influence of variability in the wind stress curl upon ocean temperature and circulation. For example, in Fig. 7b, SST EOF 2 has some similarities to the pattern of ABLT EOF 1 in the ocean region (and therefore HA1 EOF 1). This may be direct forcing of the SST through Ekman pumping or Ekman transport. The oceanic response is modification of the inertial recirculations (see the mode-2 HO1 EOFs; Fig. 6b). The dominant time scale for all of these four modes is approximately 10 yr and is likely to be a product of internal ocean adjustment. We therefore postulate that a weak coupled feedback is operating between the primary atmospheric mode, its influence on SST, and the nonlinear adjustment of the ocean (similar to that proposed by Kravtsov et al. 2005a, b, manuscripts submitted to J. Climate).

Thus, the EOF analysis yields some information about modes of variability that are common to both atmosphere and ocean domains, but quantification of relationships between such modes is difficult. We might attempt to calculate quantitative relationships using lagged correlation of the PCs; however, these results also prove inconclusive, except for the clear examples such as those detailed in the above paragraphs. Instead, we turn to canonical correlation analysis (CCA) to select coupled modes of variability.

b. Evidence for coupled interactions using CCA

CCA is a technique that determines patterns from two distinct datasets that are temporally correlated (Bretherton et al. 1992). We use a version of CCA proposed by Barnett and Preisendorfer (1987) in which the dataset is first reduced to a small number of EOFs (the first 12 EOFs in our case), thereby ensuring that the number of temporal samples exceeds the spatial dimension so that the covariance matrix obtained is full rank. One then finds the cross-covariance matrix of two fields (we use HA1 and SST). The singular value decomposition (SVD) of this cross-covariance matrix generates pairs of spatial patterns that maximize the correlation between the two fields. Thus, subsequent pairs of patterns are temporally uncorrelated, but not necessarily spatially orthogonal (Bretherton et al. 1992). The results from CCA are presented in a similar fashion to the EOF results, except that in each case we show patterns from the two fields that are optimized for the maximum correlation. In addition, we also show the temporal spectrum from each pattern, which delineates whether the correlation is at low or high frequencies. The correlation coefficient (CC) between the two patterns indicates the strength of the relationship between the two fields.

The first few modes from CCA applied to the standard coupled run show some key features (see Fig. 8). Patterns 1 (and 2; not shown) have high correlation coefficients (0.53) and spatial patterns that are consistent with the hypothesis of a weakly coupled decadal oscillation involving the HA1 mode 1 and SST mode 2 extracted from the direct EOF analysis (section 5a). As stated above, it is proposed that this correlation is due to the direct Ekman forcing of SST by the atmospheric wavenumber-3 mode; however, the time scale and the spatial pattern of SST are modified by the nonlinear component of the ocean circulation.

Figure 8 also shows two further modes (3 and 5) that are candidates for processes where SST influences HA1 via the atmospheric boundary layer. Both of these modes show SST patterns that are similar to the double-gyre SST EOF 1 pattern shown in Fig. 7a, and SST spectra with interdecadal peaks. The correlation coefficients in these cases are 0.34 and 0.24, respectively. The HA1 patterns are a composite of standing wavenumber 3 and the annular mode, and their associated spectra also show maximum variance at low frequencies.

The patterns shown here suggest the following hypothesis: that the intrinsic interdecadal ocean mode drives SST variability with a dipole pattern, in which the temperature difference between the two ocean gyres is reduced or increased. When the temperature difference between the gyres is larger (smaller), this influences the ABLT, which exerts a greater (lesser) driving force on the atmosphere above via radiation. The atmospheric response is dominated by a standing wave downstream from the perturbation, which projects onto the wavenumber-3 and annular mode patterns and has a strong low-frequency component. This intrinsic ocean mode hypothesis can be tested using partially coupled simulations.

6. Variability of partially coupled systems

Partially coupled simulations are now used to test the intrinsic ocean mode hypothesis. In addition, we further examine the way in which the atmosphere directly forces the ocean and search for coupled feedbacks. This is achieved using both CCA and the spectra of the PCs derived from EOF analysis.

a. Testing the intrinsic ocean mode hypothesis

We begin with a partially coupled simulation in which the parameter XC = 0. In this simulation the radiative link between ABLT variability and HA1 is nonexistent; thus, the intrinsic ocean mode can still exist in HO1, SST, and ABLT, but the above hypothesis, which depends upon radiative communication between ABLT and HA1, is excluded. However, variations in HA1 are able to influence SST via direct Ekman pumping and transport. Therefore, if the intrinsic ocean hypothesis is correct, then the same patterns may form in both SST and HA1, but they will have a weak low-frequency signal, and weak temporal correlation.

Figure 9 shows modes 1, 3, and 8 of the CCA results from this simulation. Mode 1, once again, reflects the Ekman forcing of SST by the atmospheric circulation. The correlation coefficient is almost unchanged from the fully coupled case shown in Fig. 8; however, the decadal spectral peak in both SST and HA1 has disappeared. In other words, the ocean adjustment no longer influences the time scale, so that this mode is purely driven by atmospheric variability.

Mode 3 shows the same HA1 pattern as the fully coupled case (a mix of the annular mode and standing wavenumber 3); however, there are two key differences. First, while the SST spectra show a low-frequency peak (similar to Fig. 8; mode 3), the HA1 variance is reduced at low frequencies. Second, the associated SST pattern does not resemble the dipole structure of the ocean mode. The HA1 mode is likely to be a natural atmospheric mode of variability. The SST mode is partly forced by the HA1 mode but can also lock onto the low-frequency forcing of the ocean circulation mode. In the fully coupled simulation (Fig. 8) this feeds back to the atmosphere, increasing HA1 mode-3 variance in the interdecadal band. But this possibility is excluded in the partially coupled case (Fig. 9) so that the time scale of the atmospheric mode is biased toward higher frequencies.

The dipole SST pattern is seen in mode 8. It is correlated to an annular atmospheric mode; however, there is a very low correlation coefficient (0.08), and the HA1 spectra shows no interdecadal peak.

This simulation clarifies the origin of the interdecadal standing mode 3 in the HA1 field: the same pattern is seen in the HA1 field in both simulations; however, when the model is coupled, this mode is controlled at low frequencies by variations in SST. In other words, the ocean variability projects onto an existing mode of atmospheric variability, thereby increasing the variance of that mode at low frequencies. This is consistent with the intrinsic ocean mode hypothesis.

b. Coupled feedback effects

We now show a partially coupled simulation in which the advection of SST by ocean circulation is eliminated (XC = 1 and YC = 0). CCA modes 1, 3, and 4 from this simulation are shown in Fig. 10. Once again, the correlations are dominated by the HA1 traveling wavenumber-3 mode; however, on this occasion the lack of influence of ocean circulation on SST is self-evident. The SST mode-1 patterns are broadly similar to the CCA mode 1 from the coupled simulation (where XC = 1 and YC = 1) in that the Ekman response is of opposite sign to the HA1 pattern; however, the pattern is smooth and omits the contribution from the gyre advection. Thus, there can be no modification of the time scales by oceanic adjustment, so that the decadal peak is not present. We argue that this result, in combination with mode 1 in Fig. 9, provides strong support for the coupled feedback mechanism in which the time scale is controlled by ocean adjustment.

The next most important CCA modes show similar HA1 patterns to the coupled case, but the correlated SST patterns are very different. The SST spectra show no peaks at a 20-yr time scale. However, broad spectral peaks at 30–50 yr can be seen for modes 3 and 4. These peaks suggest another mode of variability at longer time scales, but our simulations are not long enough to adequately sample 40-yr variability, so these effects are not investigated here.

This simulation shows how the atmosphere plays a strong role in shaping SST patterns, but when ocean advection is active the actual patterns of SST are strongly modified. In fact the total variance in SST is greater in this partially coupled case. This is best seen by comparing spectra of the first SST CCA mode in Figs. 8 and 10. Therefore, ocean advection of SST not only enables generation of low-frequency climate variability, but also acts to damp variability forced by the atmosphere.

The data shown above indicate that coupling in this system does not produce any “new” modes of variability—instead we observe that the effect of coupling is to project onto existing modes. This allows for either damping or amplification of these existing modes in different parts of frequency space. One ramification of this process is that positive feedback effects may occur in the coupled system. We evaluate this possibility by comparing spectra of the PCs from the coupled and partially coupled simulations. For this analysis we again use standard EOFs for the atmospheric fields and Hilbert EOFs for the ocean.

Figure 11 shows spectra for the wavenumber-3 PCs in the atmosphere, the weak coupled mode in SST (e.g., Fig. 7b), and the HO1 EOF 2 that is most closely correlated with that SST mode (see Fig. 6b). The two spectra shown in each panel are from the fully coupled (solid line) and partially coupled (dashed line) simulation that excludes ocean advection of SST (YC = 0). Recall that it was shown in the previous section that ocean advection damps variability in the Ekman-driven SST mode—this is confirmed in Fig. 11d by the large variance in the SST spectra when YC = 0. In addition, the two cases show different maxima, with a decadal peak in the coupled case and peaks at 5 and 14 yr in the partially coupled system. These peaks are also present in the HO1 spectra, but there is no significant difference in the total variability.

Spectra for the ABLT field (Fig. 11b) show that the variability of the wavenumber-3 mode is greater in the partially coupled simulation at all frequencies except for the decadal peak that arises in the coupled system. The same is true for the HA1 spectra (Fig. 11a), but the decadal peak is more significant.

Therefore, we find that ocean advection helps to reduce the component of SST variability due to Ekman transport and that this acts to decrease variability over the whole system at periods shorter than decadal. At decadal frequencies, variability is enhanced by ocean advection, consistent with our hypothesis of a weak coupled feedback through nonlinear oceanic adjustment, resulting in time scales that are controlled by the ocean rather than the atmosphere. These spectral signals are seen in both the ocean and atmosphere, implying that there is feedback between SST advection and atmospheric variability in this model.

We now turn our attention to the diagnosis of coupled feedback, which may act to intensify the dominant mode of ocean variability. To do this we compare spectra from the coupled and partially coupled (XC = 0) simulations. Spectra are selected from the first EOFs in HO1 and SST, and the fourth EOF (the double-gyre pattern shown in Fig. 4d) in ABLT and the annular mode in HA1 (Fig. 3b). Recall that the difference between the coupled and partially coupled experiments here is that the radiative communication between ABLT variability and HA1 is eliminated. We know from the CCA results that the interdecadal ocean mode projects onto a mix of the annular and standing wavenumber-3 modes, and for this reason we see in Fig. 12a that the low-frequency HA1 variability in the coupled simulation exceeds the partially coupled case. The question of coupled feedback can be resolved here by the relative spectra in the other three fields. Low-frequency variability is enhanced by coupling in all three fields. This is particularly clear for ABLT; however, the enhancement in the ocean fields is small, especially at the primary 15-yr peak. We conclude from these results that there may be a positive coupling feedback for the interdecadal ocean mode but that feedback is so weak (compared with the magnitude of the dynamical oscillation) as to be insignificant.

7. Conclusions

The numerical experiments conducted for this study use a coupled ocean–atmosphere model in which the ocean dynamics is emphasized by high resolution and low viscosity in an idealized box ocean. When geostrophic turbulence is strong, this model demonstrates the emergence of a strong mode of natural ocean variability, which peaks in the interdecadal band. The coupled experiments show that this mode is intrinsic to ocean circulation, and that it forces a strong signal in the SST field and thereby alters the atmospheric temperature. Accordingly, there is a component of this variability that projects onto existing modes of atmospheric variability (an annular mode and a standing wavenumber-3 mode) and enhances the low-frequency components of these existing modes.

The effect of the ocean in this model is not limited to the interdecadal mode. The ocean circulation can control SST variability; when this occurs, Ekman-driven SST variability is, in general, reduced. The exception is that in the decadal frequency band variability is highest when the model is coupled, implying that nonlinear ocean adjustment modifies the SST response to Ekman transport and Ekman pumping in this frequency band. This signal is seen throughout both oceanic and atmospheric domains, from which we infer that weak coupled feedback is operating. In addition, it can be noted that models that do not fully model ocean advection will incorrectly estimate variability of SST. It is not clear from these experiments whether a fully turbulent ocean simulation is required for this; however, it is unlikely that the same results would be found in models with viscous, relatively stable ocean circulation.

In our model, the spatial patterns of low-frequency atmospheric variability are set by modes that are intrinsic to the atmosphere. However, when ocean dynamics is fully incorporated into the simulations, the variance of these modes at low frequency is modified by oceanic heat flux that projects onto the existing atmospheric modes. This idea has been previously explored using both idealized (Saravanan and McWilliams 1997) and comprehensive (Saravanan 1998) coupled climate models where the concept of free modes (which are intrinsic to the atmosphere and occur in uncoupled simulations) and forced atmospheric modes (which are the atmospheric response to ocean coupling) are used. It is found (using both coupled and partially coupled simulations) that the forced modes are simply linear combinations of existing free modes. This is precisely what is observed in the results shown here—the (forced) atmospheric response to the primary interdecadal ocean mode is found in a linear combination of two free modes: the annular and standing wavenumber-3 modes. Saravanan (1998) infers from this that midlatitude coupling is very limited. The results presented here suggest that, while the correct spatial patterns of variability can be produced in coupled, uncoupled, and partially coupled experiments, the time scale of variability can be controlled by coupling. It follows that truly coupled modes are difficult to diagnose from observations, or even from CGCMs that do not vary coupling as an experimental parameter.

It is tempting to compare these results with observations of midlatitude variability in the Pacific and Atlantic Oceans. For example, recent data linking variations in the Kuroshio Extension strength to the PDO (Qiu 2003) raise the possibility of a coupled mode in the Pacific Ocean. This theoretical coupled mode has similar properties to the interdecadal ocean mode described here: large variance in the ocean jet region that is correlated with basinwide variability in wind stress curl. However, there is a limited amount of high-quality observational data available (11 yr of satellite data), which complicates quantitative comparisons of the model with observations.

Acknowledgments

Sergey Kravtsov and two anonymous reviewers provided valuable feedback on the first draft of this manuscript. This work was funded by NERC, COAPEC Grant NER/T/S/2000/00319. AMH was supported by an Australian Research Council Postdoctoral Fellowship (DP0449851) during the latter stages of this work. Numerical computations were supported by an award under the Merit Allocation Scheme on the National Facility of the Australian Partnership for Advanced Computing. WKD is supported by NSF Grants OCE-020884 and OCE-020700. This is a contribution of the Climate Institute, a Center of Excellence supported by the Research Foundation of the Florida State University.

REFERENCES

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    • Search Google Scholar
    • Export Citation
  • Berloff, P. S., and J. C. McWilliams, 1999: Large-scale, low-frequency variability in wind-driven ocean gyres. J. Phys. Oceanogr, 29 , 19251949.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Cessi, P., and G. Ierley, 1995: Symmetry-breaking multiple equilibria in quasigeostrophic, wind-driven flows. J. Phys. Oceanogr, 25 , 11961205.

    • Search Google Scholar
    • Export Citation
  • Deser, C., and M. Blackmon, 1993: Surface climate variations over the North Atlantic Ocean during winter: 1900–1989. J. Climate, 16 , 17431753.

    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., 2001: On ocean dynamics in midlatitude climate. J. Climate, 14 , 43804397.

  • Dijkstra, H. A., and C. A. Katsman, 1997: Temporal variability of the wind-driven quasigeostrophic double gyre ocean circulation: Basic bifurcation diagrams. Geophys. Astrophys. Fluid Dyn, 85 , 195232.

    • Search Google Scholar
    • Export Citation
  • Gordon, C., C. Cooper, C. A. Senior, H. Banks, J. M. Gregory, T. C. Johns, J. F. B. Mitchell, and R. A. Wood, 2000: The simulation of SST, sea ice extents and ocean heat transport in a version of the Hadley Centre coupled model without flux adjustments. Climate Dyn, 16 , 147168.

    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., J. C. McWilliams, and P. R. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J. Phys. Oceanogr, 22 , 882902.

    • Search Google Scholar
    • Export Citation
  • Hogg, A. M., J. R. Blundell, W. K. Dewar, and P. D. Killworth, 2003a: , Formulation and users' guide for Q-GCM (version 1.0). Southampton Oceanography Centre, Internal Doc. 88, 44 pp. [Available online at http://www.soc.soton.ac.uk/JRD/PROC/Q-GCM/.].

  • Hogg, A. M., W. K. Dewar, P. D. Killworth, and J. R. Blundell, 2003b: A Quasi-Geostrophic Coupled Model (Q-GCM). Mon. Wea. Rev, 131 , 22612278.

    • Search Google Scholar
    • Export Citation
  • Hogg, A. M., P. D. Killworth, W. K. Dewar, and J. R. Blundell, 2005: Mechanisms of decadal variability of the wind-driven ocean circulation. J. Phys. Oceanogr, 35 , 512531.

    • Search Google Scholar
    • Export Citation
  • Jacobs, G. A., and J. L. Mitchell, 1996: Ocean circulation variations associated with the Antarctic circumpolar wave. Geophys. Res. Lett, 23 , 29472950.

    • Search Google Scholar
    • Export Citation
  • Kravtsov, S., and A. W. Robertson, 2002: Midlatitude ocean-atmosphere interaction in an idealized coupled model. Climate Dyn, 19 , 693711.

    • Search Google Scholar
    • Export Citation
  • Kravtsov, S., A. W. Robertson, and M. Ghil, 2003: Low-frequency variability in a baroclinic β channel with land–sea contrast. J. Atmos. Sci, 60 , 22672293.

    • Search Google Scholar
    • Export Citation
  • Kushnir, Y., 1994: Interdecadal variations in North Atlantic sea surface temperature and associated atmospheric conditions. J. Climate, 7 , 141157.

    • Search Google Scholar
    • Export Citation
  • Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, 1997: A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Amer. Meteor. Soc, 78 , 10691079.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1977: A note on a consistent quasigeostrophic model in a multiply connected domain. Dyn. Atmos. Oceans, 1 , 427441.

    • Search Google Scholar
    • Export Citation
  • Nauw, J. J., and H. A. Dijkstra, 2001: The origin of low-frequency variability of double-gyre wind-driven flows. J. Mar. Res, 59 , 567597.

    • Search Google Scholar
    • Export Citation
  • Nauw, J. J., H. A. Dijkstra, and E. Simonnet, 2004: Regimes of low-frequency variability in a three-layer quasi-geostrophic ocean model. J. Mar. Res, 62 , 684719.

    • Search Google Scholar
    • Export Citation
  • Primeau, F. W., 1998: Multiple equilibria of a double-gyre ocean model with super-slip boundary conditions. J. Phys. Oceanogr, 28 , 21302147.

    • Search Google Scholar
    • Export Citation
  • Primeau, F. W., 2002: Multiple equilibria and low-frequency variability of the wind-driven ocean circulation. J. Phys. Oceanogr, 32 , 22362252.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., 2003: Kuroshio Extension variability and forcing of the Pacific decadal oscillations: Responses and potential feedback. J. Phys. Oceanogr, 33 , 24652482.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., and W. Miao, 2000: Kuroshio path variations south of Japan: Bimodality as a self-sustained internal oscillation. J. Phys. Oceanogr, 30 , 21242137.

    • Search Google Scholar
    • Export Citation
  • Roberts, M. J., and Coauthors, 2004: Impact of eddy-permitting ocean resolution on control and climate change simulations with a global coupled GCM. J. Climate, 17 , 320.

    • Search Google Scholar
    • Export Citation
  • Saravanan, R., 1998: Atmospheric low-frequency variability and its relationship to midlatitude SST variability: Studies using the NCAR climate system model. J. Climate, 11 , 13861404.

    • Search Google Scholar
    • Export Citation
  • Saravanan, R., and J. C. McWilliams, 1997: Stochastic and spatial resonance in interdecadal climate fluctuations. J. Climate, 10 , 22992320.

    • Search Google Scholar
    • Export Citation
  • Simonnet, E., 2005: Quantization of the low-frequency variability of the double-gyre circulation. J. Phys. Oceanogr, 35 , 22682290.

  • Simonnet, E., and H. A. Dijkstra, 2002: Spontaneous generation of low-frequency modes of variability in the wind-driven ocean circulation. J. Phys. Oceanogr, 32 , 17471762.

    • Search Google Scholar
    • Export Citation
  • Spall, M. A., 1996: Dynamics of the Gulf Stream/Deep Western Boundary Current crossover. Part II: Low-frequency internal oscillations. J. Phys. Oceanogr, 26 , 21692182.

    • Search Google Scholar
    • Export Citation
  • Vautard, R., B. Legras, and M. Déqué, 1988: On the source of midlatitude low-frequency variability. Part I: A statistical approach to persistence. J. Atmos. Sci, 45 , 28112843.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • White, W. B., and R. G. Peterson, 1996: An Antarctic circumpolar wave in surface pressure, wind, temperature and sea ice extent. Nature, 380 , 699702.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Schematic of Q-GCM. The mesh surfaces show the interface positions in the atmosphere, with the lower interface sloping down to the south (indicating atmospheric heating there). The atmospheric boundary layer temperature is shown by the gray shading, although the southeast corner and the area over the ocean have been cut away to reveal the (much smaller) ocean region. The SST can also be seen in the grayscale, while the two QG interfaces in the ocean are shown by black surfaces, illuminated from the southwest. The upper-ocean interface is elevated (depressed) in the north (south), where an anticlockwise (clockwise) subpolar (subtropical) gyre exists.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 2.
Fig. 2.

EOFs of the unfiltered first atmospheric interface height data: (a) mean HA1 (contour interval: 400 m), (b) mode 1 (paired with mode 2) traveling wavenumber 3 (accounting for a total of 38% of the variance), (c) mode 3 (paired with mode 4%–13%), (d) mode 5 (annular mode: 3.8%), (e) mode 6 (paired with mode 7: 4.8%), (f) mode 8 (paired with mode 9: 4.6%), and (g) spectra of the PCs of the five modes shown. In this figure and in all subsequent contour plots, negative contours are drawn with a dashed line, and zero contours with a heavy line. The dashed box shows the position of the ocean.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 3.
Fig. 3.

EOFs of the filtered HA1 data: (a) mode 1 (paired with mode 2) traveling wavenumber 3 (accounting for a total of 59% of the variance in this band), (b) mode 3 (7.9%), (c) mode 4 (paired with mode 5: 5.2%), and (d) spectra of the PCs of the three modes shown.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 4.
Fig. 4.

EOFs of the filtered ABLT data: (a) mean (contour interval: 4°C), (b) mode 1 (paired with mode 2: totaling 59% of the variance) traveling wavenumber 3, (c) mode 3 (7.9%), (d) mode 4 (2.6%), (e) mode 5 (2.5%), and (f) spectra of the PCs of the four modes shown.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 5.
Fig. 5.

Instantaneous (a) HO1 field and (b) SST. (c) Mean HO1 and (d) mean SST. Contour intervals are 20 m and 1.5°C.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 6.
Fig. 6.

Hilbert EOFs of HO1, with (left) real and (right) imaginary components. (a) EOF 1, (b) EOF 2, (c) EOF 3, and (d) spectra of the PCs for the first three Hilbert EOFs.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 7.
Fig. 7.

Same as in Fig. 6, but for Hilbert EOFs of SST.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 8.
Fig. 8.

Results of CCA for SST against HA1 for the standard coupled simulation: (a) mode 1, with the SST pattern on the left and HA1 pattern on the right, and a correlation coefficient of 0.53; (b) mode 3, with a correlation coefficient of 0.34; (c) mode 5, with a correlation coefficient of 0.26; (d) spectra for the SST patterns; and (e) spectra for the HA1 patterns.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 9.
Fig. 9.

Same as in Fig. 8, but for SST against HA1 for the XC = 0 decoupled simulation (i.e., ABLT cannot force variability in HA1). (a),(b),(d),(e) Same as in Figs. 8a,b,d,e, but with correlation coefficients of (a) 0.50 and (b) 0.31. (c) Mode 8, with correlation coefficient of 0.08.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 10.
Fig. 10.

Same as in Fig. 8, but for SST against HA1 for the YC = 0 decoupled simulation (i.e., HO1 cannot drive SST). (a),(b),(d),(e) Same as in Figs. 8a,b,d,e, but with correlation coefficients of (a) 0.49 and (b) 0.36. (c) Mode 4, correlation coefficient of 0.29.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 11.
Fig. 11.

Spectra of (a) the HA1 wavenumber-3 EOF; (b) the ABLT wavenumber-3 EOF; (c) the corresponding HO1 EOF 2, which correlates best with the atmospheric modes; and (d) the Ekman-driven SST EOF 2. Data shown from the coupled and partially coupled (YC = 0) simulations.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Fig. 12.
Fig. 12.

Spectra of (a) the HA1 annular mode, (b) the ABLT mode corresponding to the SST double-gyre pattern, (c) the primary HO1 mode, and (d) the double-gyre SST mode. Data shown from the coupled and partially coupled (XC = 0) simulations.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3651.1

Table 1.

Default parameter list for Q-GCM. The table is divided into atmospheric, oceanic, and global parameters.

Table 1.
Save
  • Barnett, T. P., and R. Preisendorfer, 1987: Origins and levels of monthly and seasonal forecast skill for United States surface air temperatures determined by canonical correlation analysis. Mon. Wea. Rev, 115 , 18251850.

    • Search Google Scholar
    • Export Citation
  • Berloff, P. S., and J. C. McWilliams, 1999: Large-scale, low-frequency variability in wind-driven ocean gyres. J. Phys. Oceanogr, 29 , 19251949.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Cessi, P., and G. Ierley, 1995: Symmetry-breaking multiple equilibria in quasigeostrophic, wind-driven flows. J. Phys. Oceanogr, 25 , 11961205.

    • Search Google Scholar
    • Export Citation
  • Deser, C., and M. Blackmon, 1993: Surface climate variations over the North Atlantic Ocean during winter: 1900–1989. J. Climate, 16 , 17431753.

    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., 2001: On ocean dynamics in midlatitude climate. J. Climate, 14 , 43804397.

  • Dijkstra, H. A., and C. A. Katsman, 1997: Temporal variability of the wind-driven quasigeostrophic double gyre ocean circulation: Basic bifurcation diagrams. Geophys. Astrophys. Fluid Dyn, 85 , 195232.

    • Search Google Scholar
    • Export Citation
  • Gordon, C., C. Cooper, C. A. Senior, H. Banks, J. M. Gregory, T. C. Johns, J. F. B. Mitchell, and R. A. Wood, 2000: The simulation of SST, sea ice extents and ocean heat transport in a version of the Hadley Centre coupled model without flux adjustments. Climate Dyn, 16 , 147168.

    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., J. C. McWilliams, and P. R. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J. Phys. Oceanogr, 22 , 882902.

    • Search Google Scholar
    • Export Citation
  • Hogg, A. M., J. R. Blundell, W. K. Dewar, and P. D. Killworth, 2003a: , Formulation and users' guide for Q-GCM (version 1.0). Southampton Oceanography Centre, Internal Doc. 88, 44 pp. [Available online at http://www.soc.soton.ac.uk/JRD/PROC/Q-GCM/.].

  • Hogg, A. M., W. K. Dewar, P. D. Killworth, and J. R. Blundell, 2003b: A Quasi-Geostrophic Coupled Model (Q-GCM). Mon. Wea. Rev, 131 , 22612278.

    • Search Google Scholar
    • Export Citation
  • Hogg, A. M., P. D. Killworth, W. K. Dewar, and J. R. Blundell, 2005: Mechanisms of decadal variability of the wind-driven ocean circulation. J. Phys. Oceanogr, 35 , 512531.

    • Search Google Scholar
    • Export Citation
  • Jacobs, G. A., and J. L. Mitchell, 1996: Ocean circulation variations associated with the Antarctic circumpolar wave. Geophys. Res. Lett, 23 , 29472950.

    • Search Google Scholar
    • Export Citation
  • Kravtsov, S., and A. W. Robertson, 2002: Midlatitude ocean-atmosphere interaction in an idealized coupled model. Climate Dyn, 19 , 693711.

    • Search Google Scholar
    • Export Citation
  • Kravtsov, S., A. W. Robertson, and M. Ghil, 2003: Low-frequency variability in a baroclinic β channel with land–sea contrast. J. Atmos. Sci, 60 , 22672293.

    • Search Google Scholar
    • Export Citation
  • Kushnir, Y., 1994: Interdecadal variations in North Atlantic sea surface temperature and associated atmospheric conditions. J. Climate, 7 , 141157.

    • Search Google Scholar
    • Export Citation
  • Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, 1997: A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Amer. Meteor. Soc, 78 , 10691079.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1977: A note on a consistent quasigeostrophic model in a multiply connected domain. Dyn. Atmos. Oceans, 1 , 427441.

    • Search Google Scholar
    • Export Citation
  • Nauw, J. J., and H. A. Dijkstra, 2001: The origin of low-frequency variability of double-gyre wind-driven flows. J. Mar. Res, 59 , 567597.

    • Search Google Scholar
    • Export Citation
  • Nauw, J. J., H. A. Dijkstra, and E. Simonnet, 2004: Regimes of low-frequency variability in a three-layer quasi-geostrophic ocean model. J. Mar. Res, 62 , 684719.

    • Search Google Scholar
    • Export Citation
  • Primeau, F. W., 1998: Multiple equilibria of a double-gyre ocean model with super-slip boundary conditions. J. Phys. Oceanogr, 28 , 21302147.

    • Search Google Scholar
    • Export Citation
  • Primeau, F. W., 2002: Multiple equilibria and low-frequency variability of the wind-driven ocean circulation. J. Phys. Oceanogr, 32 , 22362252.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., 2003: Kuroshio Extension variability and forcing of the Pacific decadal oscillations: Responses and potential feedback. J. Phys. Oceanogr, 33 , 24652482.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., and W. Miao, 2000: Kuroshio path variations south of Japan: Bimodality as a self-sustained internal oscillation. J. Phys. Oceanogr, 30 , 21242137.

    • Search Google Scholar
    • Export Citation
  • Roberts, M. J., and Coauthors, 2004: Impact of eddy-permitting ocean resolution on control and climate change simulations with a global coupled GCM. J. Climate, 17 , 320.

    • Search Google Scholar
    • Export Citation
  • Saravanan, R., 1998: Atmospheric low-frequency variability and its relationship to midlatitude SST variability: Studies using the NCAR climate system model. J. Climate, 11 , 13861404.

    • Search Google Scholar
    • Export Citation
  • Saravanan, R., and J. C. McWilliams, 1997: Stochastic and spatial resonance in interdecadal climate fluctuations. J. Climate, 10 , 22992320.

    • Search Google Scholar
    • Export Citation
  • Simonnet, E., 2005: Quantization of the low-frequency variability of the double-gyre circulation. J. Phys. Oceanogr, 35 , 22682290.

  • Simonnet, E., and H. A. Dijkstra, 2002: Spontaneous generation of low-frequency modes of variability in the wind-driven ocean circulation. J. Phys. Oceanogr, 32 , 17471762.

    • Search Google Scholar
    • Export Citation
  • Spall, M. A., 1996: Dynamics of the Gulf Stream/Deep Western Boundary Current crossover. Part II: Low-frequency internal oscillations. J. Phys. Oceanogr, 26 , 21692182.

    • Search Google Scholar
    • Export Citation
  • Vautard, R., B. Legras, and M. Déqué, 1988: On the source of midlatitude low-frequency variability. Part I: A statistical approach to persistence. J. Atmos. Sci, 45 , 28112843.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • White, W. B., and R. G. Peterson, 1996: An Antarctic circumpolar wave in surface pressure, wind, temperature and sea ice extent. Nature, 380 , 699702.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Schematic of Q-GCM. The mesh surfaces show the interface positions in the atmosphere, with the lower interface sloping down to the south (indicating atmospheric heating there). The atmospheric boundary layer temperature is shown by the gray shading, although the southeast corner and the area over the ocean have been cut away to reveal the (much smaller) ocean region. The SST can also be seen in the grayscale, while the two QG interfaces in the ocean are shown by black surfaces, illuminated from the southwest. The upper-ocean interface is elevated (depressed) in the north (south), where an anticlockwise (clockwise) subpolar (subtropical) gyre exists.

  • Fig. 2.

    EOFs of the unfiltered first atmospheric interface height data: (a) mean HA1 (contour interval: 400 m), (b) mode 1 (paired with mode 2) traveling wavenumber 3 (accounting for a total of 38% of the variance), (c) mode 3 (paired with mode 4%–13%), (d) mode 5 (annular mode: 3.8%), (e) mode 6 (paired with mode 7: 4.8%), (f) mode 8 (paired with mode 9: 4.6%), and (g) spectra of the PCs of the five modes shown. In this figure and in all subsequent contour plots, negative contours are drawn with a dashed line, and zero contours with a heavy line. The dashed box shows the position of the ocean.

  • Fig. 3.

    EOFs of the filtered HA1 data: (a) mode 1 (paired with mode 2) traveling wavenumber 3 (accounting for a total of 59% of the variance in this band), (b) mode 3 (7.9%), (c) mode 4 (paired with mode 5: 5.2%), and (d) spectra of the PCs of the three modes shown.

  • Fig. 4.

    EOFs of the filtered ABLT data: (a) mean (contour interval: 4°C), (b) mode 1 (paired with mode 2: totaling 59% of the variance) traveling wavenumber 3, (c) mode 3 (7.9%), (d) mode 4 (2.6%), (e) mode 5 (2.5%), and (f) spectra of the PCs of the four modes shown.

  • Fig. 5.

    Instantaneous (a) HO1 field and (b) SST. (c) Mean HO1 and (d) mean SST. Contour intervals are 20 m and 1.5°C.

  • Fig. 6.

    Hilbert EOFs of HO1, with (left) real and (right) imaginary components. (a) EOF 1, (b) EOF 2, (c) EOF 3, and (d) spectra of the PCs for the first three Hilbert EOFs.

  • Fig. 7.

    Same as in Fig. 6, but for Hilbert EOFs of SST.

  • Fig. 8.

    Results of CCA for SST against HA1 for the standard coupled simulation: (a) mode 1, with the SST pattern on the left and HA1 pattern on the right, and a correlation coefficient of 0.53; (b) mode 3, with a correlation coefficient of 0.34; (c) mode 5, with a correlation coefficient of 0.26; (d) spectra for the SST patterns; and (e) spectra for the HA1 patterns.

  • Fig. 9.

    Same as in Fig. 8, but for SST against HA1 for the XC = 0 decoupled simulation (i.e., ABLT cannot force variability in HA1). (a),(b),(d),(e) Same as in Figs. 8a,b,d,e, but with correlation coefficients of (a) 0.50 and (b) 0.31. (c) Mode 8, with correlation coefficient of 0.08.

  • Fig. 10.

    Same as in Fig. 8, but for SST against HA1 for the YC = 0 decoupled simulation (i.e., HO1 cannot drive SST). (a),(b),(d),(e) Same as in Figs. 8a,b,d,e, but with correlation coefficients of (a) 0.49 and (b) 0.36. (c) Mode 4, correlation coefficient of 0.29.

  • Fig. 11.

    Spectra of (a) the HA1 wavenumber-3 EOF; (b) the ABLT wavenumber-3 EOF; (c) the corresponding HO1 EOF 2, which correlates best with the atmospheric modes; and (d) the Ekman-driven SST EOF 2. Data shown from the coupled and partially coupled (YC = 0) simulations.

  • Fig. 12.

    Spectra of (a) the HA1 annular mode, (b) the ABLT mode corresponding to the SST double-gyre pattern, (c) the primary HO1 mode, and (d) the double-gyre SST mode. Data shown from the coupled and partially coupled (XC = 0) simulations.

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