Oceanic control of multidecadal variability in an idealized coupled GCM

Abstract

Idealized ocean models are known to develop intrinsic multidecadal oscillations of the meridional overturning circulation (MOC). Here we explore the role of ocean–atmosphere interactions on this low-frequency variability. We use a coupled ocean–atmosphere model set up in a flat-bottom aquaplanet geometry with two meridional boundaries. The model is run at three different horizontal resolutions (4°, 2° and 1°) in both the ocean and atmosphere. At all resolutions, the MOC exhibits spontaneous variability on multidecadal timescales in the range 30–40 years, associated with the propagation of large-scale baroclinic Rossby waves across the Atlantic-like basin. The unstable region of growth of these waves through the long wave limit of baroclinic instability shifts from the eastern boundary at coarse resolution to the western boundary at higher resolution. Increasing the horizontal resolution enhances both intrinsic atmospheric variability and ocean–atmosphere interactions. In particular, the simulated atmospheric annular mode becomes significantly correlated to the MOC variability at 1° resolution. An ocean-only simulation conducted for this specific case underscores the disruptive but not essential influence of air–sea interactions on the low-frequency variability. This study demonstrates that an atmospheric annular mode leading MOC changes by about 2 years (as found at 1° resolution) does not imply that the low-frequency variability originates from air–sea interactions.

Appendices

Appendix 1: Statistical significance test using Monte Carlo approach

The significance of a regression or a correlation is computed with a Monte Carlo approach. It consists in comparing the regression/correlation being tested to the regression/correlation of a randomly scrambled ensemble. Say we want to estimate the significance of the regression of a field $\lambda (x,y,t)$ onto a time series (usually the Meridional Overturning Circulation) MOC(t), t being the time in years, x and y the zonal and meridional coordinates. We first compute the initial regression maps, denoted as $reg_{{\rm init}}(x,y)$.

At each grid point $(x_i,y_j)$, the time series $\lambda (x_i,y_j,t)$ is randomly permuted by blocks of 3 years to reduce the influence of serial autocorrelation. The regression $reg_{k1}(x_i,y_j)$ between the resulting time series $\lambda_{{\rm permut}}(x_i,y_j,t)$ and MOC(t) is performed. This analysis is repeated N times, resulting in N different randomly permuted regression $reg_k(x_i,y_j),\,k=(k_1, k_2, \ldots, k_N)$. The estimated significance level is the percentage of randomized regression that exceeds the regression being tested:

$$signif(x_i,y_j) = \frac{\sum_{k=1}^N{reg_k(x_i,y_j) > reg_{init}(x_i,y_j)}}{N}$$

(2)

A smaller significance level indicates the presence of stronger evidence against the null hypothesis. In this paper, we fix the threshold of significance to 5 %. This statistical significant test is applied for all regression/correlation analyses performed.

Appendix 2: MOC anomalies reconstruction from the difference between density/temperature anomalies along the western and eastern boundaries

Hirschi and Marotzke (2007) show that the MOC variability can be reconstructed through the thermal wind relationship by considering boundary density anomalies. This reconstruction does include neither the Ekman shear mode nor the barotropic velocities. In flat bottom configuration, the latter is strictly zero, which facilitates the reconstruction in our case.

The thermal wind relationship

$$f\partial_z v = -\frac{g}{\rho_0} \partial_x\rho,$$

(3)

is used as the starting point, with f the Coriolis parameter, v the meridional velocity, g the earth’s acceleration, $\rho$ the density and $\rho_0$ its reference value. Integrating zonally and vertically the perturbation part of Eq. (3), with the condition $v^{\prime}(z=-H)=0$, leads to

$$\overline{v^{\prime}(z^{\prime})}^x = \int_{x_w}^{x_e}v^{\prime}dx = -\frac{g}{\rho_0f} \int_{-H}^{z^{\prime}}(\rho ^{\prime}_e - \rho ^{\prime}_w)dz$$

(4)

We reconstruct a geostrophic MOC anomaly $\psi_{\rho }^*$ as the vertical integration of $\overline{v^{\prime}(z^{\prime})}^x$:

$$\psi_{\rho }^*(z^{\prime}) = \int_{-H} ^{z^{\prime}} \left[ \overline{v^{\prime}}^x - \frac{1}{H} \int_{-H} ^0 \overline{v^{\prime}}^xdz \right] dz,$$

(5)

where $\frac{1}{H}\int_{-H}^0\overline{v^{\prime}}^xdz$ has been substracted in order to ensure that $\psi_{\rho }^*(z^{\prime}=0)=\psi_{\rho }^*(z^{\prime}=-H)=0$.

We can go a step further in the approximation by only considering the temperature contribution. The thermal wind relationship reduces to

$$f\partial_z v = g\alpha \partial_xT$$

(6)

with $\alpha =2.10^{-4}~K^{-1}$, the thermal expansion coefficient. Performing a similar integration, we obtain a reconstructed MOC anomaly $\psi_T^*$ computed with a zonally integrated meridional velocities anomalies of the form

$$\overline{v^{\prime}(z^{\prime})}^x = \int_{x_w}^{x_e}v^{\prime}dx = \frac{g\alpha }{f} \int_{-H}^{z^{\prime}}\left( T^{\prime}_e - T^{\prime}_w\right) dz,$$

(7)

with $T^{\prime}_e$ and $T^{\prime}_w$ the temperature anomalies along the eastern and western boundaries, respectively. We can also compute the contribution from the western boundary temperature anomalies only, $\psi_{T_w}^*$.

Note that this method misses one half grid point at the eastern and western boundaries. Both temperature and density anomalies that are used to reconstruct the MOC variability are located at the centre of the cell, rather than right along boundaries. This error is dependent on the horizontal resolution, and partially explains why the reconstructions are more accurate at higher resolution.

The geostrophic MOC indices are computed in the same way as for the model. The skill for the geostrophic MOC index $(I_{\psi ^*})$ accounting for the variance of the model MOC index $(I_{MOC})$ is defined as

$$S = 1-\frac{\left\langle(I_{MOC} - I_{\psi ^*})^2\right\rangle}{\left\langle(I_{MOC})^2\right\rangle}$$

(8)

with $<.>$ a time average operator. $S \in [-\infty ; 1]$, and $S \rightarrow 1$ indicates that the geostrophic MOC index and the model MOC index vary in phase and are of the same magnitude. Negative values denote a low or negative correlation and/or that the amplitude of $I_{\psi ^*}$ is larger than $I_{MOC}$.