Figure 1. Causal ``chain'' for a coupled oscillation in the midlatitudes.
A variety of null hypotheses for decadal variability in the atmosphere and ocean have been presented in previous lectures. These mechanisms produce red spectra of oceanic variability, and may redden the spectra of atmospheric variability. The phrase `exotic mechanisms' refers to coupled ocean-atmosphere mechanisms that produce variability in addition to these null hypotheses. Two mechanisms are discussed in the current lecture: interactions involving mid-latitude coupling between the ocean and atmosphere, and spatial or advective resonance. The implications for predictability are also presented.
A diagram describing coupled ocean atmosphere interactions is presented in Figure 1. For periods longer than a few weeks, internally generated atmospheric variability has no preferred time scale, and thus forces the sea surface with a white spectrum of momentum and heat fluxes (1). The ocean integrates the atmospheric forcing, producing a red spectrum in the upper ocean to first order (2). Due to its large thermal inertia and long adjustment time scale, the ocean response to atmospheric forcing is delayed, producing a time scale of months to centuries (3). Provided the ocean response involves changes in the sea surface temperature (SST), the ocean may force the atmosphere (4). The atmosphere responds to the ocean forcing (5), with a delay time on the order of days to weeks (6) before repeating the cycle in some new, unspecified manner.
The two most limiting branches of the diagram in Figure 1 involve details of the ocean delay (3) and of the atmospheric response to ocean forcing (5). The first, the ocean delay (3), involves ocean dynamics, which, in the mid-latitudes, tend to spatially confine and attenuate the oceanic response to atmospheric forcing. Theories for mid-latitude coupled mechanisms must account for this spatial confinement and signal attenuation. The second limiting branch, the atmospheric response (5), is very sensitive to the structure, location, and amplitude of the ocean forcing. The atmosphere responds more readily to large-scale spatial forcing. For spatially confined forcing, the atmosphere tends to simply laterally spread ocean temperature anomalies. Furthermore, the atmospheric response to ocean forcing is very sensitive to the location and amplitude of the forcing. In the mid-latitudes, the atmosphere is not sensitive to SST anomalies less than about 1C. Thus, the atmospheric response to ocean forcing is very weak. However, in the tropics, the atmosphere is quite sensitive to SST anomalies, implying a stronger response to a given temperature anomaly. Without any atmospheric response to ocean forcing, there can be no decadal atmospheric variability, due to the short time scale of intrinsic atmospheric variability.
Coupled mechanisms may be classified as unstable, or stable. An example of unstable mid-latitude atmosphere-ocean interaction is presented in Latif et al. (1994,1996). In these studies, a periodic mode of variability is modeled in the North Pacific (Figure 2). Changes in the circulation of the subtropical ocean gyre induce SST changes in mid-latitudes. The atmospheric heat flux response to these SST anomalies reinforces the SST anomalies, providing an unstable positive feedback. The SST anomalies also force wind stress curl anomalies which counter the positive feedback and produce a decadal cycle by reversing the anomalous gyre circulation. To test their mechanism, Latif et al. (1994,1996) force the atmospheric model with the coupled model's SST anomalies. The atmospheric response is very large, and the net heat flux tends to reinforce the SST anomalies. It is noted that the sensitivity of the model atmosphere used in Latif et al. (1994) is much larger than the sensitivity of other atmospheric models, and that the resulting atmospheric anomalies are much larger than should be expected for the modest forcing applied.
Unstable mid-latitude coupled mechanisms are also found by Xu et al. (1998), in a hybrid coupled ocean-atmosphere model. In this model, the atmosphere is replaced by a statistical atmosphere, generated from the same coupled model simulation as used in Latif et al. (1994). Xu et al. (1998) find unstable, growing oscillations as a solution to their coupled model (Figure 3). This instability is likely due to an inconsistency associated with using a statistical atmospheric model in mid-latitudes. In general, the use of a statistical atmospheric model implies that atmospheric variability covariant with a given SST anomaly is purely a response to the SST anomaly (branch 5 of Figure 1). For this to be true, the upward heat fluxes associated with a given SST anomaly should positively correlate with the SST anomaly (positive SST anomaly upward heat fluxes). In reality, the dominant patterns of mid-latitude SST variability are a response to atmospheric forcing (branch 2 of Figure 1), verified by a negative correlation between upward heat fluxes and SST anomalies. Thus, the statistical model incorrectly aliases atmospheric forcing as an atmospheric response. In the tropics, where the atmosphere is more sensitive to SST anomalies, the use of a statistical model can be justified under some circumstances.
Weng and Neelin (1999) analytically investigate the effect of mid-latitude coupling using a different hybrid coupled model. They use a linearized perturbation shallow-water system to represent the upper ocean, and couple it to a statistical atmosphere through a SST equation. From this construction, one can solve for the eigenvalues of the uncoupled and coupled systems (Figure 4). Both systems have in common a spectrum of ocean modes, and one decaying, non-oscillatory eigenvalue, with a damping time scale near the linear decay rate of the SST equation (the SST mode). When the model parameters are adjusted to mimic the model parameters used in Latif et al. (1994,1996), the SST mode is destabilized, resulting in a large positive eigenvalue (hence an exponentially growing mode). The coupled system has two unique eigenvalues from the uncoupled system, that have interdecadal frequencies, and are very weakly damped. The damping can be traced to Rayleigh friction and horizontal viscosity within the ocean. This damping is akin to the attenuation of a signal by the ocean delay (branch 3 of Figure 1). It is noted that the damped oscillatory inter-decadal modes should still produce dominant periodicities when forced stochastically.
Saravanan and McWilliams (1998) discuss a mechanism of decadal variability in the mid-latitude ocean atmosphere system that produces a defined time scale, based only on a spatial structure of atmospheric forcing, and on a constant ocean advective velocity. Schematics of the mechanism are shown in Figure 5. For long time scales (greater than intraseasonal), mid-latitude atmospheric variability tends to be dominated by fixed spatial patterns that vary with no preferred time scale. The atmospheric forcing is represented by the dashed dipole in Figure 5. The ocean currents advect temperature anomalies along a path outlined by the dark arrow in Figure 5. The model equations may be found in Saravanan and McWilliams (1998). The model solution can be separated into two different regimes, based on a non-dimensional parameter G = 2*Pi/Tadv, where Tadv is a characteristic time scale for advection, and is an effective damping rate for the ocean. The two regimes are: a slow-shallow regime (G << 1) where ocean thermal damping dominates advection, and a fast-deep regime (G >> 1) where ocean advection dominates thermal damping. For the slow-shallow case, the oceanic and atmospheric power spectra are slightly reddened, but do not show any preferred periodicities (Figures 6 and 7, dash-dot and thin solid line). In the fast-deep case, the overall variance in the atmosphere and ocean decreases, but a well defined periodicity corresponding to the timescale emerges (Figure 6 and Figure 7, dashed and dotted lines), where is a characteristic length scale of the atmospheric forcing and is the speed of the advecting ocean current. In a coupled model simulation, Haarsma et al. (2000) find advective resonance responsible for the existence and periodicity of the Antarctic Circumpolar Wave.
It is natural to ask whether periodic behavior implies some predictive skill. Two studies are presented, that use long coupled model simulations to answer this question. In the first, Grotzner et al. (1999) investigate the predictability of a 30-40 year periodicity in the North Atlantic, manifest in the thermohaline circulation, SST, and an annular mode-like atmospheric circulation. Predictability of this periodicity is tested by determining if the model is able to predict itself. Predictions are made by initializing an ensemble of coupled simulations with identical ocean conditions, and differing atmospheric initial conditions. The results of these predictions are shown in Figure 8, where each light line represents an individual ensemble member prediction, the dark sold line represents the ensemble mean, and the dark dashed line represents a best fit AR(1) process. Figure 8 shows the deep ocean is predictable with a time scale of one-quarter to one-third of the oscillation period (about a decade). However, the SST and atmospheric circulations are no more predictable than the AR(1) process used as a null hypothesis.
In the second study, Saravanan et al. (2000) use a long simulation of a coupled model with idealized geometry to assess the predictability of variability with a periodicity of about 20 years. Figure 9 shows the spatial structure and power spectrum of changes in the meridional overturning streamfunction associated with this variability. The authors define an AR(1) and AR(2) process using the first half of the data record, and use the autoregressive formulas to predict variability in the second half of the data. Plotted in Figure 10 is the forecast skill F for each autoregressive process, at given lead times. A forecast skill of 1 implies a perfect forecast and a zero value implies no skill. Figure 10 shows that with a one year lead, the AR(1) and AR(2) processes predict about 90% of the variance of the first principal component (PC) of the meridional overturning streamfunction and SST. With a five year lead, the ability of the AR(2) process (and not the AR(1) process) to predict the meridional overturning streamfunction implies that the periodicity does enhance the predictive skill of the variability. The atmosphere is predicted using a different method. Due to the short decorrelation time scale of the atmosphere (on the order of a couple of weeks), the first PC of SST is used to predict atmospheric variability. This SST mode explains about 20% of the simultaneous variability, but is unable to predict the atmospheric variability one year in advance. So, the periodicity only improves the forecast for the zonally averaged meridional overturning in this model.
Haarsma, R.J., F.M. Selten, and J.D. Opsteegh, 2000: On the mechanism of the Antarctic Circumpolar Wave, Journal of Climate, 13, 1461-1480.
Latif, M., Barnett, T.P., 1994: Causes of decadal climate variability over the North Pacific and North America. Science, 266, 634-637.
Latif, M., Barnett, T.P., 1996: Decadal climate variability over the North Pacific and North America: dynamics and predictability, Journal of Climate, 9, 2407-2423.
Saravanan, R., G. Danabasoglu, S.C. Doney and J.C. McWilliams, 2000: Decadal variability and predictability in the midlatitude ocean--atmosphere system. Journal of Climate, 13, 1073-1097.
Saravanan, R., and J.C. McWilliams, 1998: Advective ocean--atmosphere interaction: an analytical stochastic model with implications for decadal variability. Journal of Climate, 11, 165-188.
Weng, W. and Neelin, D., 1999: Analytical prototypes for ocean-atmosphere interaction at midlatitudes. Part II: Mechanisms for coupled gyre modes, Journal of Climate, 12, 2757-2774.
Xu, W., T.P. Barnett, and M. Latif, 1998: Decadal variability in the North Pacific as simulated by a hybrid coupled model, Journal of Climate, 11, 297-312.
Figure 1. Causal ``chain'' for a coupled oscillation in the
midlatitudes.
Figure 2. Results from the ECHO GCM (Latif et al. (1994,1996)). (A) Time series of SST anomalies in the western Pacific,
near the Kuroshio extension (C). (B) SST regressed onto the time series in
(A) (C). (C) Response of the atmospheric model to the SST anomalies shown
in (B): 500-hPa height anomalies (m) (top), net heat flux (W m)
(middle), and wind stress curl (Pa m).
Figure 3. Results from the coupled model of Xu et al. (1998).
SST averaged over the same region as in Figure 1a (averaged from
150E-180, 25N-35N). The solid line represents
the control simulation, and the remaining curves represent sensitivity
studies in which different forcing components are turned off.
Figure 4. Eigenvalues for the uncoupled (left) and coupled
(right) model of
Weng and Neelin (1999). For the uncoupled case, the eigenvalues represent
a set of ocean modes (n = 1, 3, 5, ...), as well as a separated
eigenvalue that represents the SST mode. For the
coupled case, the ocean and SST modes still exist.
Additionally, two
distinct interdecadal eigenvalues exist, produced by the effects of
coupling. Frequency is in yr.
Figure 5. Schematic diagrams illustrating the advective
resonance mechanism of Saravanan and McWilliams (1998). (A) Schematic of
interaction between an atmospheric standing wave dipole pattern
(dashed line) and an advective ocean circulation (thick solid line) in
the horizontal plane. (B) As in (A), but for the
zonally averaged vertical plane.
Figure 6. From Saravanan and McWilliams (1998). Frequency spectrum of
ocean temperature variance
associated with the direct (a) and orthogonal (b) modes of response, for
different values of G. Dot-dash, thin,
solid, thick solid,
dashed, and dotted lines denote G = 1/16, 1/4, 1, 4,
and 16 cases, respectively. That is, dot-dash and thin solid lines
correspond to the slow-shallow regime; dashed and dotted lines
correspond to the fast-deep regime; the thick solid line corresponds to
the intermediate value G = 1.
Figure 7. Frequency spectrum of atmospheric temperature
variance associated with the direct mode for weak (a) and strong (b)
coupling, for different values of G. Lines as in Figure 6.
Figure 8. Ensemble predictions from Grotzner et al. (1999).
Thin lines represent the projection of an individual ensemble onto the
first EOF of the respective field, solid lines represent the ensemble
mean, and the thin dashed line represents the temporal behavior of a
fitted first order autoregressive process. (Top) Projections onto the
first EOF of the North Atlantic meridional overturning. (Middle)
Projections onto the first EOF of Northern Atlantic SST. (Bottom)
Projections onto the first EOF of Northern Hemispheric 500-hPa
geopotential height.
Figure 9. (A) First EOF of the
meridional overturning streamfunction for the coupled simulation of
Saravanan et al. (2000). Units are in Sv per standard deviation of the
expansion coefficients of EOF1. (B) Frequency-variance spectrum of
the normalized expansion coefficients associated with EOF1 of the
meridional overturning streamfunction. The dotted lines indicate the
5% and 95% a posteriori confidence intervals of a reference red
noise spectrum. The spectral estimates were smoothed using a bin size
of 10.
Figure 10. Forecast skill F at different lead times as
shown, for the
last 500 years of the coupled integration of Saravanan et al. (2000).
Assuming conservatively that there are at least 30 degrees of freedom
in the data, a correlation of 0.35 would be significant at the 95%
level. This means that values of F > 0.12 may be considered to be
significant.