Periodic Variability in the Large-Scale Southern Hemisphere Atmospheric Circulation

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The SAM and southern BAM are defined as the leading empirical orthogonal functions (EOF)/principal components (PC) time series of the zonal-mean kinetic and eddy kinetic energies, respectively. If X is a two-dimensional data matrix that samples space and time, then the leading EOF of X is the spatial function that explains the largest possible fraction of the variance in X. The leading PC of X is the expansion coefficient time series associated with the leading EOF. The leading EOF is found as the eigenvector associated with the largest eigenvalue of the covariance matrix of X.

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All observational results except the red curve in Fig. 1F are based on the interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) data from 1 January 1979 to 31 December 2010. The red curve in Fig. 1F is based on Version 7 of the Advanced Microwave Scanning Radiometer (AMSR)-E precipitation data, obtained from Remote Sensing Systems. For details of ERA-Interim, see (32).

The results in the left panel of Fig. 1 and in Table 1 are based on standardized values of the BAM index, defined here as the leading PC of zonal-mean eddy kinetic energy computed over all levels and latitudes within the domain from 1000 to 200 hPa and 20° to 70°S. The data are weighted by the area represented by each grid box and the mass represented by each vertical level in the ERA-Interim before calculating the PC time series.

The zonal-mean eddy fluxes of heat and eddy kinetic energy are defined as [v^*T^*] and $\frac{1}{2}[v^{*2}+u^{*2}]$, respectively, where asterisks denote departures from the zonal mean and brackets denote the zonal mean. Eddy fluxes and eddy kinetic energy are calculated from 4x daily data before computing daily averages.

The eddy fluxes of heat are proportional to the vertical flux of wave activity. Thus, the vertical divergence of the eddy fluxes of heat in the lower troposphere is proportional to the generation of wave activity there.

The ERA-Interim precipitation is based on the 12-hour forecast of 12 Greenwich mean time total precipitation. The ERA-Interim precipitation is a model-derived quantity but is calculated using physically consistent parameterizations that link atmospheric motions to precipitation.

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All spectra are found by (i) Calculating the spectra for subsets of the time series that are 500 days in length. A Hanning window is applied to each subset, and the overlap between adjacent subsets is 250 days. (ii) Averaging the power spectra over all subsets and then applying a three-point running mean to the resulting mean power spectra. Every 10 years of data yield ~40 degrees of freedom per spectral estimate. The spectral estimates in Fig. 1, B, D, and F (black curve) have ~120 degrees of freedom; the spectral estimates for AMSR-E precipitation shown in Fig. 1F (red curve) have ~40 degrees of freedom.

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The Geophysical Fluid Dynamics Laboratory (GFDL) CM3 is a coupled chemistry climate model. The analyses shown here are based on a simulation performed for the Coupled Model Intercomparison Project (CMIP5), phase 5. See (33). We analyzed one ensemble of the historical simulation over years 1970–2004. The aquaplanet simulation is identical to that used in (34). The model is integrated at T85 resolution for 21 years, with the first 2 years discarded for spin-up. All model parameters are set to the values from the control experiment of Frierson et al. (34). The idealized dry GCM is the GFDL spectral dry dynamical core of (35). The model does not include radiation or moisture and uses Newtonian relaxation to a zonally symmetric equilibrium temperature profile and Rayleigh damping of the low-level winds to simulate boundary layer friction. The model is integrated at T42 (42-wave triangular truncation) resolution for 6000 days with 2000 days for spin-up. Both the aquaplanet and the dry dynamical core do not have topography and are run under perpetual equinoctial conditions with no diurnal cycle.

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