Forecasts Probabilities, not certainties, and their score on past data

Frequency, from 1994 to 2020, of alert days two days after a day with the same solar wind speed (4 classes) and the same electron level (below or above the threshold). The link and the two-day delay are established by the correspondence “Solar wind and radiation-belt electrons” (Reeves et al., 2011). Today’s measurements come from the real-time solar wind (DSCOVR or ACE) and GOES-16 or later, whose instrument differs from the archive’s (GOES-8 to 15): a calibration difference of a factor 2–3 is possible near the threshold.

Frequency, on the GFZ Kp index since 1932, of a storm (Kp ≥ 5) within the next three days, given three indicators known on the day: a storm one solar rotation earlier (coronal holes and their fast wind come back every 27 days), a storm in the last 24 hours (persistence) and the sunspot number of the last 28 days (under 50, 50 to 120, over 120). The 12 cells of the table are counted over the whole record; the score is measured with frequencies from 1932–1989 evaluated on 1990–2026. Coronal mass ejections, unpredictable more than three days ahead without images of the Sun, limit the gain: NOAA, which sees the Sun, does better one or two days ahead.

The attribution regression of global temperature (El Niño three months earlier, volcanic aerosols, the Sun and the CO₂ forcing, after Foster and Rahmstorf, 2011), fitted on 1959–2012 and extended to the coming months: the three-month delay of El Niño makes the next three months predictable from values already measured. CO₂ is extended along its last 24 months, the Sun kept at its last value. The forecast relaxes towards the mean residual of the last 36 months (the regression underestimates the warming since 2013) and keeps part of the last month’s departure (persistence φ^h). Hindcasts made every month since October 2012, with only the data available at their date, give the errors, the gain over persistence and the record probabilities.

Model of Reasenberg and Jones (1989): the aftershock rate decays as the Omori law, (t + c)^−p, grows with the mainshock magnitude and follows the Gutenberg–Richter law. Its parameters are fitted on the global USGS catalogue since 1973 (as Page et al., 2016), with a separate productivity for deep earthquakes (70 km or more), seven times less productive, and a negative binomial law, because sequences are far more variable than a Poisson process. The zone is a circle whose radius is the rupture length of Wells and Coppersmith (1994). The generic California model overestimated global aftershocks by a factor of 2 to 5: hence the refit.

The NOAA OVATION Prime model (Newell et al., 2014) estimates every few minutes, from the solar wind measured at L1, the probability of visible aurora on a 1° grid, valid 30 to 90 minutes later. For each city: the value of the nearest cell (aurora overhead) and the highest value within 600 km (an aurora whose lower edge is at 110 km altitude is then at least 8° above the horizon). The elevation of the Sun, from approximate formulas (± 1°), tells whether it is dark enough (Sun below −12°). It is a NOAA model: the Observatory neither scores nor logs it.