Stratosphere-Troposphere Coupling: Vertical Wave Coupling

Last update: 2023-03-10

This POD assesses the seasonality and extremes of vertical planetary wave coupling between the extratropical troposphere and stratosphere. It makes four kinds of figures from provided model data:

  1. Climatological time series of planetary wave amplitudes in the troposphere (500 hPa) and stratosphere (10 hPa)

  2. NH winter and SH spring distributions of 50 hPa polar cap eddy heat fluxes (Shaw et al., 2014; Dunn-Sigouin and Shaw, 2015; England et al., 2016)

  3. Composite maps of eddy geopotential heights and anomalies during extreme heat flux days (Shaw et al., 2014; England et al., 2016)

  4. Correlation coherence of planetary waves between 10 and 500 hPa (Randel 1987; Shaw et al., 2014)

All figures are made for both hemispheres. The plots from (2) and (3) focus primarily on the JFM and SON periods for the NH and SH, respectively, as these are generally the seasons with the greatest variability/extremes in heat fluxes. The plots from (1) and (4) show full-season perspectives.

The figures from (1) and (2) together evaluate statistical characteristics of the planetary waves as a function of day of year and season. The figures from (3) show composite maps during extreme heat flux events relative to climatological stationary wave patterns, which help to assess the vertically-deep wave patterns associated with upward/downward propagation. The figures from (4) demonstrate the lag times at which planetary waves in the stratosphere and troposphere are most coherent, with positive lag times indicative of upward propagation and negative lag times indicative of downward propagation.

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 Fourier decomposition, and sends the digested data to the plotting functions. The POD computes Fourier coefficients of 10 and 500 hPa geopotential heights for the 60 degrees N/S latitudes and 45-80 degree latitude bands for zonal waves 1-3. It also computes zonal wave decomposed polar cap (60-90 degrees lat) eddy heat fluxes at 50 hPa.

The observational data this POD uses is based on ERA5 reanalysis (Hersbach, et al., 2020), and includes the same diagnostics described above. The observational data also includes eddy geoopotential height fields for the NH JFM seasons, and SH SON seasons, which are used to plot composite maps during extreme heat flux events.

Required programming language and libraries

This POD requires Python 3, with the following packages:

  • numpy

  • scipy

  • xarray

  • pandas

  • matplotlib

Required model output variables

The following daily mean fields are required:

  • Temperature at 50 hPa, ta50 as (time,lat,lon) (units: K)

  • Meridional wind at 50 hPa, va50 as (time,lat,lon) (units: m/s)

  • Geopotential Height at 10 hPa, zg10 as (time,lat,lon) (units: m)

  • Geopotential Height at 500 hPa, zg500 as (time,lat,lon) (units: m)

Scientific background

Wave motions in the polar stratosphere are primarily dominated by vertically propagating Rossby waves from the troposphere. Because of so-called “Charney-Drazin filtering”, only the largest planetary scale waves are able to propagate into the stratosphere when there are westerly mean winds (Charney & Drazin, 1961; Andrews et al., 1987). As a result, vertical wave coupling between the troposphere and stratosphere follows a distinct seasonal cycle organized around the formation of the westerly stratospheric polar vortex in autumn (when waves can enter the stratosphere), and its breakdown in spring/early summer (when easterly winds prevent propagation).

The propagation characteristics of planetary waves are strongly dependent on the background mean flow, which can influence where/how these waves propagate. In some cases these can lead to events in which waves are reflected from the stratosphere back into the troposphere, which tend to occur most often in late winter in the NH and spring in the SH (Shaw et al., 2010). These reflected waves can directly influence the tropospheric circulation.

Wave events in the stratosphere are associated with meridional fluxes of heat that can be characterized by “eddy heat fluxes” (v’T’, where v is the meridional wind, and T is the temperature, and primes denote deviations from the zonal mean), which are proportional to the wave vertical group velocity under linear wave theory (Andrews et al., 1987). Statistically extreme heat flux events thus represent extremes in wave propagation with vertically deep planetary wave structures (Dunn-Sigouin and Shaw, 2015); extraordinarily high heat fluxes weaken and warm the polar vortex, whereas negative heat fluxes are generally associated with wave reflection that can dynamically cool and strengthen the vortex.

Improper representation of the wave coupling between the troposphere and stratosphere can significantly influence the tropospheric stationary wave pattern, and be tied to climatological biases in the positions of the tropospheric jets (Shaw et al., 2014b, England et al., 2016). Biases in the stratospheric circulation that can arise from, e.g., too little parameterized gravity wave drag can also affect how planetary waves propagate in the stratosphere and affect the occurrence of extreme heat flux events. Model characteristics such as the height of the model top, and the implementation (or lack of) sponge layers near the model top can additionally lead to unphysical excessive damping or reflection of waves, which can subsequently influence biases in the tropospheric stationary wave patterns, blocking frequencies, and annular mode timescales (Shaw & Perlwitz, 2010).

More about this POD

Sign of eddy heat fluxes in NH vs SH

In the Northern Hemisphere (NH), positive eddy heat fluxes represent poleward and upward wave fluxes. However, in the Southern Hemisphere (SH), the sign is flipped such that negative eddy heat fluxes represent the poleward and upward wave fluxes. This means that the SH polar cap eddy heat flux distributions will appear “flipped” compared to those for the NH. This also means that the extreme positive/negative heat flux events are in the opposite sense of those in the NH (i.e., extreme negative SH heat flux events are akin to extreme positive NH heat flux events).

Tip about horizontal resolution of data

Since this POD is primarily concerned with planetary scale waves, data with high horizontal resolution can be usefully downsampled without affecting results too much. This can speed up the MDTF data preprocessing and POD operation, while also decreasing the memory footprint.


Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics, Academic press, No. 40.

Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary‐scale disturbances from the lower into the upper atmosphere. Journal of Geophysical Research, 66(1), 83-109.

Dunn-Sigouin, E., and T. A. Shaw, 2015: Comparing and contrasting extreme stratospheric events, including their coupling to the tropospheric circulation. J. Geophys. Res. Atmos., 120: 1374– 1390.

England, M. R., T. A. Shaw, and L. M. Polvani, 2016: Troposphere-stratosphere dynamical coupling in the southern high latitudes and its linkage to the Amundsen Sea. Journal of Geophysical Research: Atmospheres, 121, 3776–3789,

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

Randel, W. J., 1987: A Study of Planetary Waves in the Southern Winter Troposphere and Stratosphere. Part I: Wave Structure and Vertical Propagation. J. Atmos. Sci., 44, 917–935,<0917:ASOPWI>2.0.CO;2.

Shaw, T. A., J. Perlwitz, and N. Harnik, 2010: Downward Wave Coupling between the Stratosphere and Troposphere: The Importance of Meridional Wave Guiding and Comparison with Zonal-Mean Coupling. J. Climate, 23, 6365–6381,

Shaw, T. A., and J. Perlwitz 2010: The Impact of Stratospheric Model Configuration on Planetary-Scale Waves in Northern Hemisphere Winter, J. Clim., 23(12), 3369-3389.

Shaw, T. A., J. Perlwitz, and O. Weiner, 2014: Troposphere-stratosphere coupling: Links to North Atlantic weather and climate, including their representation in CMIP5 models. J. Geophys. Res.: Atmospheres, 119, 5864–5880,