Stratosphere-Troposphere Coupling: Annular Modes

Last update: 2023-03-28

This POD assesses characteristics of the annular modes as a function of day of year. It makes four kinds of figures from provided model data:

  1. EOF1 pattern plots on standard pressure levels, representing the annular mode structures throughout the troposphere and stratosphere. (cf., Gerber et al. 2010, Fig. 4; Simpson et al., 2011, Fig. 1)

  2. Annular mode interannual standard deviation (cf., Gerber et al., 2010, Fig. 7)

  3. Annular mode e-folding timescales (or “persistence”; cf., Gerber et al. 2010, Fig. 8; Kidston et al., 2015, Fig. 1)

  4. Annular mode predictability (cf., Gerber et al., 2010, Fig. 9)

All figures are made for both hemispheres. This POD also outputs the computed annular mode indices and EOF structures as netcdf files.

The figure from (1) should always be viewed to verify the spatial structure of the annular modes; if the spatial patterns for model data do not match the observations (or the figures in the papers referenced above), then the 1st EOF may not represent an “annular mode”-like pattern, which means caution is warranted for interpreting the other figures and the digested output data.

The figures from (2) highlight the seasonal cycle in annular mode variability. The figures from (3) show estimates of the seasonally varying persistence of the annular modes. Lastly, the figures from (4) demonstrate what fraction of the variance of the annular mode at a given pressure level (default 850 hPa) can be “predicted” using a persistence forecast of the annular mode at other levels (see Gerber et al., 2010 for full details).

Version & Contact info

  • Version/revision information: v1.0 (Mar 2023)

  • Project PIs: Amy H. Butler (NOAA CSL) and Zachary D. Lawrence (CIRES / NOAA PSL)

  • Developer/point of contact: Zachary Lawrence (


This POD is composed of three files, including the main driver script, the functions that perform the diagnostic computations in, and the functions that compile the specific POD plots in The driver script reads in the necessary data, calls the computation functions to perform the anomaly calculations, the EOF analysis, and annular mode diagnostics.

The observational data this POD uses is based on ERA5 reanalysis (Hersbach, et al., 2020) zonal mean geopotential heights.

By default, the annular modes are computed for input model data as described in Gerber et al., 2010; in short, for every timestep, the global mean geopotential height is removed, and then a 60 day low-pass filter is applied across the daily data before a 30 year low-pass filter is applied across the days of year. This process is intended to remove a slowly varying climatology that helps to remove trends, such that the anomalies represent “true” variations. The annular modes are then assumed to be the 1st EOF of these daily anomalies between 20-90 degrees latitude (for the Northern and Southern hemispheres).

Note: Users can opt to adjust this POD’s settings.jsonc file to instead compute the annular modes using a “simple” method, which computes anomalies by removing the global mean heights, removing a standard climatology, and linearly detrending the anomalies across the days of year. However, the pre-digested observational data provided with this POD are computed using the “gerber” method.

Required programming language and libraries

This POD requires Python 3, with the following packages:

  • numpy

  • scipy

  • xarray

  • pandas

  • eofs

  • matplotlib

Required model output variables

Only one daily mean field on pressure levels is required:

  • Zonal Mean Geopotential Height, zg as (time,lev,lat) (units: m)

Ideally, this data should span pressure levels between 1000 and 1 hPa. Results will be plotted for this range of levels. However, absent/missing data will properly have blanks in the output figures.

Scientific background

The Northern and Southern Annular Modes (NAM/SAM) are the dominant large-scale circulation variability patterns of the extratropics (Thompson and Wallace, 2000). They represent fluctuations of mass into or out of the polar cap regions, manifesting as patterns of similarly signed height/pressure anomalies in the polar cap surrounded by an opposite signed ring of anomalies in the midlatitudes (hence their “annular” appearance).

The annular modes also characterize a coupled pattern of variability between the troposphere and stratosphere (Gerber et al., 2010; Kushnir 2010; Simpson et al., 2011). In the troposphere, the NAM/SAM roughly correspond to the strength and latitudinal position of the mid-latitude jets; in the wintertime stratosphere, they represent the strength of the stratospheric polar vortex. During these winter periods, the state of the stratosphere can have a “downward influence” on the tropospheric annular mode state, whereby anomalies in the strength of the stratospheric vortex can drive persistent same-signed tropospheric annular mode phases (Baldwin and Dunkerton 2001). The resultant influence on the position of the jets can further impact regional shifts in large-scale weather patterns. Thus, while the tropospheric annular modes can evolve year-round, the stratosphere-troposphere coupling that occurs during winter/spring drives a distinct seasonal cycle in tropospheric annular mode variance and persistence (Gerber et al., 2010; Simpson et al. 2011; Schenzinger & Osprey 2015).

In the Northern Hemisphere, the aforementioned sort of “downward influence” is generally organized around midwinter extreme vortex events such as sudden stratospheric warmings and vortex intensifications. However, in the Southern Hemisphere, stratosphere-troposphere annular mode coupling is typically organized around the seasonal breakdown of the polar vortex in late spring. As a result, the seasonal cycle in annular mode variability and persistence tends to occur close in time in both hemispheres, maximizing around December-February in the Northern Hemisphere, and October-December in the Southern Hemisphere (Kidston et al., 2015).

A misrepresentation of stratospheric variability in models can lead to biases in annular mode coupling (Gerber et al., 2010; Simpson et al., 2011). For instance, a lack of SSWs or too late final warmings can shift the seasonal cycle in annular mode variance/persistence too late in models relative to observations. Processes that affect stratospheric polar vortex variability in models (e.g., model lid height, gravity wave parameterizations, interactive chemistry, etc.), can thus potentially affect the representation of the tropospheric jets, regional weather, and the statistics of temperatures and precipitation through the annular mode “pathway”. However, it is also possible for model biases in the annular modes to arise separately from the stratosphere due to poorly represented processes such as low-level orographic drag (Pithan et al., 2016).


Thompson, D. W. J., and J. M. Wallace, 2000: Annular Modes in the Extratropical Circulation. Part I: Month-to-Month Variability. J. Climate, 13, 1000–1016,<1000:AMITEC>2.0.CO;2.

Baldwin, M. P., and T. J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294(5542), 581-584,

Baldwin, M.P. and D.W.J. Thompson, 2009: A critical comparison of stratosphere–troposphere coupling indices. Q.J.R. Meteorol. Soc., 135: 1661-1672,

Gerber, E. P., et al. 2010: Stratosphere-troposphere coupling and annular mode variability in chemistry-climate models, J. Geophys. Res., 115, D00M06,

Kushner, P. J., 2010: Annular modes of the troposphere and stratosphere. The Stratosphere: Dynamics, Transport, and Chemistry, 190, 59-91.,

Simpson, I. R., P. Hitchcock, T. G. Shepherd, and J. F. Scinocca, 2011: Stratospheric variability and tropospheric annular-mode timescales, Geophys. Res. Lett., 38, L20806,

Kidston, J., et al. 2015: Stratospheric influence on tropospheric jet streams, storm tracks and surface weather. Nature Geosci 8, 433–440,

Schenzinger, V., and S. M. Osprey, 2015: Interpreting the nature of Northern and Southern Annular Mode variability in CMIP5 Models, J. Geophys. Res. Atmos., 120, 11,203– 11,214,

Pithan, F., T. G. Shepherd, G. Zappa, and I. Sandu 2016: Climate model biases in jet streams, blocking and storm tracks resulting from missing orographic drag, Geophys. Res. Lett., 43, 7231–7240,

Hersbach, H. and coauthors, 2020: The ERA5 global reanalysis. Q J R Meteorol Soc., 146, 1999-2049,