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: A positive NAO strengthens the westerlies: mild ocean air reaches far over northern Europe, which has a mild winter, while southern Europe stays away from that flow (Hurrell, 1995).

Pearson correlation r (lag 0 year(s))

0.70

95% interval [0.54; 0.78] (block bootstrap)

Aligned points

effective n ≈ 39 (autocorrelation)

p-value

0.00000

two-sided, Fisher z transform, effective n

r after a 21-year high-pass filter

0.63

p = 0.000, effective N ≈ 50: year-to-year variations only

r with Madrid and Rome

0.02

37 complete winters; south of the storm track

Period analysed

1963 → 2026

computed on Oct 25, 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

For each city, December–February mean of (Tmax + Tmin) / 2 (GHCN-Daily, months at least 90 % complete), standardised (departure from the mean divided by the standard deviation); mean of the three cities. Monthly NAO from CPC, same season. Lag fixed at zero a priori; Pearson correlation, effective size after Bretherton et al., 3-year block bootstrap. The test is repeated after removing variations slower than 21 years (warming). Contrast: same computation for Madrid and Rome.

Computation parameters

{
    "x": "mean NAO of December–February (NOAA CPC)",
    "y": "mean of the standardised December–February (Tmax + Tmin)/2 of London, Paris and Berlin (GHCN-Daily, months ≥ 90 % complete)",
    "lag": "fixed at 0",
    "contrast": "same for Madrid and Rome",
    "bootstrap": {
        "seed": 20261023,
        "block": 3,
        "draws": 1000
    },
    "high_pass_years": 21
}

Inputs : cpc.nao.monthly (921 pts, run #12) · ghcn.london.tmax.daily (23,626 pts, run #3700) · ghcn.london.tmin.daily (23,613 pts, run #3700) · ghcn.paris.tmax.daily (23,843 pts, run #3700) · ghcn.paris.tmin.daily (23,843 pts, run #3700) · ghcn.berlin.tmax.daily (23,998 pts, run #3700) · ghcn.berlin.tmin.daily (23,998 pts, run #3700) · ghcn.madrid.tmax.daily (23,918 pts, run #3700) · ghcn.madrid.tmin.daily (23,919 pts, run #3700) · ghcn.rome.tmax.daily (20,737 pts, run #3700) · ghcn.rome.tmin.daily (20,990 pts, run #3700)

Reading this result

This is one of the most robust links of European climatology: the NAO explains about half of the winter-to-winter departures in northern Europe, and the link holds without the trend. In the south, the NAO acts mostly on rain (dry winters with a positive NAO), not on temperature. Three cities are not a region: the page illustrates the mechanism without mapping it. 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

North Atlantic Oscillation index (NOAA CPC): NOAA CPC, monthly North Atlantic Oscillation index (rotated PCA of 500 hPa height anomalies, 1950–). · source page ↗
Licence : U.S. Government work, public domain · retrieved on Oct 23, 2026 · SHA-256 1d4c1cdcc5d0…
GHCN-Daily stations of the reference places (NOAA NCEI): Menne, M. J., Durre, I., Vose, R. S., Gleason, B. E. and Houston, T. G. (2012). An overview of the Global Historical Climatology Network-Daily database. J. Atmos. Oceanic Technol., 29, 897–910. Menne, M. J., et al. (2012). Global Historical Climatology Network - Daily (GHCN-Daily), Version 3. NOAA NCEI. · doi:10.7289/V5D21VHZ · source page ↗
Licence : U.S. Government work, public domain (data from national services under WMO Resolution 40); cite Menne et al. (2012) · retrieved on Oct 25, 2026 · SHA-256 fb525098ce40…
Hurrell (1995): Hurrell, J. W. (1995). Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science, 269(5224), 676–679. · doi:10.1126/science.269.5224.676
Licence : Published literature; cited

NAO and European winters Positive NAO, mild winter in northern Europe

What is linked, what is not