Stratosphere-Troposphere Coupling: Eddy Heat Fluxes

Last update: 2022-09-26

This POD assesses the interaction of vertically propagating planetary-scale stationary waves on the polar winter/spring stratosphere. The vertical component of the Eliassen-Palm Flux is approximately proportional to the zonal mean eddy heat flux, v’T’, where v is the meridional wind, and T is the temperature (see Andrews et al., 1987). Thus, this POD uses the eddy heat flux at 100 hPa as a proxy for the vertical flux of waves entering the stratosphere.

In general, when the time-integrated eddy heat flux in the lowermost stratosphere is above normal, the polar stratospheric circulation should be weaker than normal with warmer temperatures; similarly, when the eddy heat flux is below normal, the circulation should be stronger than normal with colder temperatures (see Newman, et al., 2001). The eddy heat fluxes entering the stratosphere are primarily driven by vertically propagating planetary-scale Rossby waves which have both stationary and transient components. This POD calculates eddy heat fluxes using monthly mean fields, and thus it primarily measures these relationships for stationary waves (since in the monthly mean the transient waves will be averaged out).

This POD makes two kinds of figures from provided model data:

  • Scatterplots of early-season eddy heat fluxes with late-season polar cap temperatures

  • Lag-correlation plots of polar cap geopotential heights at different pressure levels and months with early-season eddy heat fluxes at 100 hPa

These plots are made for both hemispheres; for the Northern Hemisphere (NH), they focus on the early (DJF or Dec) and late winter (JFM). For the Southern Hemisphere (SH), they focus on the early (ASO or Sep) and late spring (SON). These months are when coupling between the stratosphere and troposphere are most active in the respective hemispheres.

Polar stratospheric circulation variability is known to influence tropospheric weather and climate (see Kidston et al., 2015). Different teleconnections, like those related to ENSO, are sometimes considered to have stratospheric pathways through which they act. These stratospheric teleconnection pathways are generally related to how a given phenomenon influences stratospheric circulation variability, and the subsequent coupling of the stratospheric state with the troposphere.

In a simple sense, this POD evaluates the “first step” of stratosphere-troposphere coupling – that is, the tropospheric influence on driving stratospheric circulation anomalies. If a model underestimates or misrepresents this “upward coupling”, they can further miss or underestimate the impact of “downward coupling” related to the stratosphere. Issues in modeling these processes can be related to model characteristics such as vertical resolution, the height of the model lid, and the representation of parameterized processes.

Version & Contact info

  • Version/revision information: v1.0 (Jun 2022)

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

  • Developer/point of contact: Zachary Lawrence (


The entirety of this POD is contained in the file This script reads in the model fields, calculates zonal mean eddy heat fluxes and polar cap temperatures and geopotential heights, and generates the plots.

The observational data this POD uses is based on ERA5 reanalysis (Hersbach, et al., 2020), and includes pre-computed zonal mean eddy heat fluxes, temperatures, and geopotential heights (i.e., they have dimensions of (time,level,lat)) calculated from monthly mean fields.

Required programming language and libraries

This POD requires Python 3, with the following packages:

  • numpy

  • scipy

  • xarray

  • xesmf

  • matplotlib

Required model output variables

The following monthly mean fields are required:

  • Temperature at 50 hPa, t50 as (time,lat,lon) (units: K)

  • Temperature at 100 hPa, t100 as (time,lat,lon) (units: K)

  • Meridional Winds at 100 hPa, v100 as (time,lat,lon) (units: m/s)

  • Geopotential Height, zg as (time,level,lat,lon) (units: m)


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

Furtado, J. C., J. L. Cohen, A. H. Butler, E. E. Riddle, and A. Kumar, 2015: Eurasian snow cover variability and links to winter climate in the CMIP5 models. Clim Dyn, 45, 2591–2605,

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

Kidston, J., A. Scaife, S. C. Hardiman, D. M. Mitchell, N. Butchart, M. P. Baldwin, and L. J. Gray, 2015: Stratospheric influence on tropospheric jet streams, storm tracks and surface weather. Nature Geosci 8, 433–440.

Newman, P. A., E. R. Nash, and J. E. Rosenfield, 2001: What controls the temperature of the Arctic stratosphere during the spring? JGR: A, 106, 19999–20010,

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 statistical relationships evaluated in this POD will generally be opposite-signed for the SH figures.

Use of bootstrapping

The scatterplots provided by this POD show the correlations between the 100 hPa eddy heat flux and 50 hPa polar carp temperatures. In these figures, the parentheses next to the correlations contain the 95% bootstrap confidence interval on the correlations from resampling the available years 1000 times. These confidence intervals help to determine whether the correlations are significant; if 0 does not fall within the range of the confidence interval, the correlation can be said to be statistically significant. Furthermore, the bootstrap confidence interval in the observation plots give a sense of the sampling variability in the historical record; if the model correlation falls outside the observed bootstrap confidence interval, it is fair to say the model has a too strong or too weak relationship.