Correspondences

What is linked, what is not

Each arc joins two phenomena tested on this site. Green and animated: clear link (correlation significant at 5 % after correcting for autocorrelation, or a response outside chance in an event study). Grey: inconclusive test. A statistical link alone does not establish causation.

Clear link
Inconclusive

Hypotheses tested

Clear links

correlation p < 0.05 or epochs outside chance

Causation demonstrated

a correlation demonstrates none

Arc width from |r| of the stored result; several tests between the same phenomena are drawn as stacked arcs.

Hypothesis tested: Planetary waves rising from the troposphere carry heat towards the pole: the v′T′ flux at 100 hPa measures their activity. As they break in the stratosphere they decelerate the vortex and warm the polar cap. Strong, lasting flux precedes weak vortices and sudden warmings (Newman et al., 2001; Polvani and Waugh, 2004).

Pearson correlation r (lag 0 year(s))

-0.27

95% interval [-0.48; -0.09] (block bootstrap)

Aligned points

effective n ≈ 47 (autocorrelation)

p-value

0.067

two-sided, Fisher z transform, effective n

r after a 21-year high-pass filter

-0.29

p = 0.053, effective N ≈ 47: year-to-year variations only

Period analysed

1980 → 2026

computed on Nov 6, 2026 · engine v1.0

Aligned series (standard deviations, after preprocessing)

Show the data as a table

Both series are drawn in standard-deviation units (z) after removing the seasonal cycle and slow variations, to compare their fluctuations; original values are in the table and the CSV export.

Correlation by lag (year(s))

Show the data as a table

Pearson coefficient for each lag; a positive lag means the second series follows the first. The table gives n, effective n and p for each lag.

Aligned series (CSV)

Method and sources

Flux: covariance of meridional wind and temperature (v′T′) at 100 hPa, averaged from 45° N to 75° N, from NASA’s MERRA-2/GEOS analyses; mean of December and January. Vortex: zonal-mean zonal wind at 60° N and 10 hPa, same analyses, mean of February and March, after the flux window so that the two do not overlap. One point per winter since 1978/79; Pearson, effective sample size of Bretherton et al., 3-year block bootstrap; test repeated after removing variations longer than 21 years. The lag is fixed in advance.

Computation parameters

{
    "x": "eddy heat flux v′T′ at 100 hPa, 45–75° N, December–January mean (NASA MERRA-2/GEOS)",
    "y": "zonal-mean zonal wind at 60° N, 10 hPa, February–March mean (NASA MERRA-2/GEOS)",
    "lag": "fixed at 0 (the response window starts after the driver window)",
    "terciles": "mean vortex after the winters of the lowest and highest thirds of the heat flux",
    "bootstrap": {
        "block": 3,
        "draws": 1000
    },
    "high_pass_years": 21
}

Inputs : nasa.vt4575n.100.daily (17,462 pts, run #30467) · nasa.u60n.10.daily (17,462 pts, run #30467)

Reading this result

The expected sign shows, but not clearly enough to conclude: r ≈ −0.27 (p ≈ 0.07), −0.29 after removing slow variations (p ≈ 0.05). After the third of winters with the weakest flux, the February–March vortex averages 20 m/s, against 16 m/s after the third with the strongest. The literature finds a much stronger link when flux and vortex are taken over the same period (Newman et al., 2001): here the vortex is measured after the flux window, a more demanding forecast test, and the February waves, not counted, matter too. Correlation is not causation: common factors (seasons, cycles, trends) or coincidence can produce it. The p-values account for autocorrelation (effective n) but not for preprocessing choices; the confidence interval comes from a block bootstrap. The limits of the source data apply.

SOURCES OF THIS PAGE

Northern stratosphere: polar vortex, polar-cap temperature and wave heat flux, daily (NASA GSFC, MERRA-2 and GEOS FP): NASA GSFC Atmospheric Chemistry and Dynamics Laboratory, Annual Meteorological Statistics (Northern Hemisphere), from MERRA-2 (Gelaro, R., et al., 2017, Journal of Climate, 30, 5419–5454) and GEOS FP. · doi:10.1175/JCLI-D-16-0758.1 · source page ↗
Licence : NASA data, no restriction on use (NASA Earth science data policy); cite MERRA-2 (Gelaro et al., 2017). The GEOS forecasts are experimental and given for research · retrieved on Nov 5, 2026 · SHA-256 c25a0547fd3f…
Newman et al. (2001): Newman, P. A., Nash, E. R., & Rosenfield, J. E. (2001). What controls the temperature of the Arctic stratosphere during the spring? Journal of Geophysical Research: Atmospheres, 106(D17), 19999–20010. · doi:10.1029/2000JD000061
Licence : Published literature; cited
Polvani et al. (2004): Polvani, L. M., & Waugh, D. W. (2004). Upward wave activity flux as a precursor to extreme stratospheric events and subsequent anomalous surface weather regimes. Journal of Climate, 17(18), 3548–3554. · doi:10.1175/1520-0442(2004)017<3548:UWAFAA>2.0.CO;2
Licence : Published literature; cited

Planetary waves and polar vortex When planetary waves rise strongly into the stratosphere in early winter, is the polar vortex weaker afterwards?

What is linked, what is not