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 fast solar wind drives waves (ULF, chorus) and substorm injections in the magnetosphere that accelerate electrons to relativistic energies within one to three days (Paulikas and Blake, 1979; Baker et al., 1990). Reeves et al. (2011) showed the relation is “triangular”: fast wind makes a high flux likely, not certain.

Pearson correlation r (lag 2 days)

0.61

95% interval [0.58; 0.63] (block bootstrap)

Aligned points

9,341

effective n ≈ 1,755 (autocorrelation)

p-value

0.00000

two-sided, Fisher z transform, effective n

Alert days, all conditions

25 %

climatological probability, target day

Forecast gain (Brier, out of sample)

0.44

speed and today’s level; speed alone 0.28, persistence alone 0.29; 3,708 days from 2010 to 2020

Period analysed

1993-12-30 → 2020-03-02

computed on Oct 25, 2026 · engine v1.0

Aligned series (standard deviations, after preprocessing)

Show the data as a table

Solar wind speed on day D and electrons on day D + 2 (the chosen lag), in standard deviations (z), with no other filtering; the original values are in the table and the CSV export.

Correlation by lag (days)

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.

Probability of an alert day two days later

Condition on day D	Days	Alert day at D + 2
Slow wind (< 400 km/s)	286 / 4,319	7 % [6 ; 7]
Moderate wind (400–500 km/s)	709 / 3,009	24 % [22 ; 25]
Fast wind (500–600 km/s)	697 / 1,297	54 % [51 ; 56]
Very fast wind (≥ 600 km/s)	608 / 716	85 % [82 ; 87]
Electrons below the threshold on D	809 / 7,004	12 % [11 ; 12]
Electrons above the threshold on D	1,469 / 2,277	64 % [62 ; 66]

Alert day: fluence ≥ 8.64 × 10⁷ cm⁻² sr⁻¹ per day (mean flux of 1,000 pfu, the NOAA threshold). Wilson 95 % intervals. These frequencies are the basis of the forecast published in the Forecasts section.

Aligned series (CSV)

Method and sources

Daily mean solar wind speed (OMNI, NASA); decimal logarithm of the daily fluence of electrons > 2 MeV at geostationary orbit (NOAA “Daily Particle Data” archive, GOES-7 to GOES-15, 1994–2020). Lags of −3 to +7 days paired on the calendar (missing days left out, never interpolated); the expected sign is positive, the strongest positive correlation is kept. Bretherton et al. effective size, block bootstrap with 27-day blocks (one solar rotation). Conditional probabilities of an alert day at the chosen lag, by speed class and by the level of the day (persistence), Wilson intervals. Brier score: tables fitted on 1994–2009, scored on 2010–2020 only, against the climatological frequency.

Computation parameters

{
    "x": "daily mean solar wind speed, OMNI (km/s)",
    "y": "log10 of the daily fluence of electrons > 2 MeV at geostationary orbit, SWPC DPD (GOES-7 to GOES-15)",
    "alert": "fluence ≥ 8.64e7 cm⁻² sr⁻¹ day⁻¹ = mean flux 1 000 pfu (SWPC electron alert level)",
    "skill": "Brier skill score against climatology; probabilities fitted on days before 2010-01-01, scored on later days",
    "pairing": "calendar days (gaps left out, never interpolated)",
    "bootstrap": {
        "seed": 20261023,
        "block": 27,
        "draws": 1000
    },
    "intervals": "Wilson 95 %",
    "lags_days": [
        -3,
        7
    ],
    "lag_choice": "largest positive r (sign expected a priori)",
    "speed_classes_kms": [
        [
            0,
            400
        ],
        [
            400,
            500
        ],
        [
            500,
            600
        ],
        [
            600,
            3000
        ]
    ]
}

Inputs : omni.speed.hourly (430,563 pts, run #133) · swpc.dpd.electrons_2mev.daily (9,458 pts, run #3740)

Reading this result

The link is strong and expected; its interest is predictive. Speed alone and persistence each bring about 30 % of gain over climatology; together, more than 40 %, on years the tables never saw. The gain is partial: at equal speed, the direction of the interplanetary magnetic field (southward Bz), the wind density and losses to the atmosphere decide whether electrons are accelerated or swept away. Satellite changes hardly affect the result, which rests on day-to-day variations. 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

OMNI2 hourly near-Earth solar wind and geomagnetic indices: King, J. H., & Papitashvili, N. E. (2005). Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res., 110, A02104. OMNI2 data from NASA/GSFC SPDF OMNIWeb; Kp/ap from GFZ Potsdam, Dst from WDC Kyoto, F10.7 from NRC Canada (Penticton). · doi:10.1029/2004JA010649 · source page ↗
Licence : NASA data, public domain; acknowledge SPDF/OMNIWeb and the index providers · retrieved on Oct 23, 2026 · SHA-256 6de9b217bd4b…
Daily Particle Data archive, GOES proton and electron fluences 1994–2020 (NOAA SWPC): NOAA SWPC, Daily Particle Data (DPD), GOES-7 to GOES-15 integral particle fluences, old_indices archive. · source page ↗
Licence : U.S. Government work, public domain; credit NOAA SWPC · retrieved on Oct 25, 2026 · SHA-256 7d8ba231a162…
Paulikas et al. (1979): Paulikas, G. A., & Blake, J. B. (1979). Effects of the solar wind on magnetospheric dynamics: energetic electrons at the synchronous orbit. In W. P. Olson (Ed.), Quantitative Modeling of Magnetospheric Processes, Geophysical Monograph 21 (pp. 180–202). AGU. · doi:10.1029/GM021p0180
Licence : Published literature; cited
Baker et al. (1990): Baker, D. N., McPherron, R. L., Cayton, T. E., & Klebesadel, R. W. (1990). Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research, 95(A9), 15133–15140. · doi:10.1029/JA095iA09p15133
Licence : Published literature; cited
Reeves et al. (2011): Reeves, G. D., Morley, S. K., Friedel, R. H. W., Henderson, M. G., Cayton, T. E., et al. (2011). On the relationship between relativistic electron flux and solar wind velocity: Paulikas and Blake revisited. Journal of Geophysical Research, 116, A02213. · doi:10.1029/2010JA015735
Licence : Published literature; cited
Lam et al. (2012): Lam, H.-L., Boteler, D. H., Burlton, B., & Evans, J. (2012). Anik-E1 and E2 satellite failures of January 1994 revisited. Space Weather, 10, S10003. · doi:10.1029/2012SW000811
Licence : Published literature; cited

Solar wind and radiation-belt electrons Two days after a fast wind, the belts flare up

What is linked, what is not

Probability of an alert day two days later