TailWeather: from tail to extremes, a global climatological dataset for machine-learning weather forecasting

1 Introduction

• Average forecast scores do not establish whether models identify rare conditions at a particular place and time.The section notes that models with low temperature error can still have limited heatwave-tail detection skill.Source: §1 · p. 1
• Disaster records reflect exposure, vulnerability, and reporting practice as well as weather, and their sparse, uneven coverage limits evaluation across the globe.The records therefore complement rather than replace a consistently defined physical target.Source: §1 · p. 1
• Climatological tails measure rarity relative to local climate, but rarity alone does not imply harm, so the paper keeps physical tails and recorded impacts separate.The paper measures their relationship rather than treating either as a substitute for the other.Source: §1 · p. 2
• TailWeather provides a consistent global target for five hazards, with daily labels for four and monthly labels for meteorological drought.The dataset covers land from 1981 through 2022 and part of January 2023.Source: §1 · p. 2
• The paper reports that higher tail intensity is more often associated with recorded impacts, but useful thresholds differ by hazard and catalogs cannot assess much of the world.Compound tails do not consistently improve that association; the dataset also reveals AI extreme-prediction weaknesses and may serve as a training signal.Source: §1 · p. 2

2 TailWeather: a dense tail-event benchmark

• The dataset uses a regular 0.25° grid and a 1991–2020 reference climate, spanning 1981 through part of January 2023.The terminal year is incomplete; its land mask selects 351,848 cells, including ice sheets.Source: §2 · p. 2
• The heat-impact illustration marks cells with fewer than five recorded impact days and contrasts selected heat events, including records without matched EM-DAT entries.The examples illustrate catalog-coverage differences but do not establish either source's completeness.Source: §2 · p. 3, Figure 1 · p. 3
• Severity tiers run from 0 to 3, while intensity scores increase toward the relevant tail and need not represent the same rarity across hazards at a common threshold.Daily hazards use discretized percentile-rank scores; drought uses a scaled SPI score that is missing outside drought events.Source: §2 · p. 3
• Temperature, precipitation, and wind thresholds are estimated empirically, whereas drought uses a gamma-based SPI transformation for three-month precipitation totals.Both approaches retain uncertainty from the finite reference record.Source: §2 · pp. 3–4
• Temperature RMSE rises from about 1 K at day 1 to 3 K at day 10, while heatwave CSI peaks below 0.5 near day 3.The contrasting metrics illustrate that regular-weather field error and extreme-event detection describe different forecast performance regimes.Source: §2 · p. 4, Figure 2 · p. 4

3 Example application: TailWeather reveals an extreme-skill gap

• Temperature error is about 1 K at day 1, yet heatwave CSI stays below 0.5 even at its day-3 peak.Average grid-point errors are dominated by ordinary weather and do not reveal this difference.Source: 803 Example application: TailWeather… · p. 4, Figure 3 · p. 5
• Models tend to miss temperature tails but over-predict extreme-wind tails, and tail-label detection and recorded-impact capture rank extreme-wind systems differently.The two evaluations address different targets.Source: 803 Example application: TailWeather… · p. 6
• Across six forecast systems, CSI is highest for temperature and lowest for extreme wind, with wind skill decaying fastest with lead time.The comparison uses day-resolved temperature and wind labels; heavy precipitation is excluded because comparable forecast archives are unavailable, and drought is monthly.Source: 803 Example application: TailWeather… · pp. 5–6

4.1 Design

• The study matches 1996–2023 EM-DAT records to like-named labels on the 0.25° ERA5 grid, with a ±2-day allowance; flood records are matched to heavy precipitation, a less direct pairing.Catalog precision measures tail cell-days overlapping records, while recall measures recorded-impact cell-days that are tails.Source: 1004.1 Design · p. 7

4.2 Documented disaster records cover only part of the world

• Only 4.7% of land supports local comparison for all five hazards, and 39.1% falls below the coverage screen for all five.The gaps generally do not indicate quieter weather; for four hazards, excluded areas have similar or higher tail-event rates.Source: §4.2 · p. 8, Figure 5 · p. 8

4.3 Tail labels overlap documented disasters

• All six well-documented European heatwaves matched TailWeather at maximum intensity with durations matching reported event lengths; event-level capture ranged from 55% for heat to about 93% for heavy precipitation and drought.These raw capture rates do not measure detection skill, and heat capture is sensitive to catalog date precision.Source: §4.3 · pp. 8–9, Figure 6 · p. 9

4.4 Stricter tails are more often linked to recorded impacts

• As q increases, enrichment rises for all five hazards while recall falls and precision rises; at q = 0.90, recall is 15% for heat, 9.8% for cold, and 13% for wind.These diagnostic thresholds do not replace the released hazard definitions.Source: §4.4 · pp. 9–10, Figure 7 · p. 10

4.5 One threshold does not fit all hazards

• The F1-maximizing threshold ranges from 0.99 for heat to 0.40 for drought, but these values summarize this catalog comparison rather than define universal hazard thresholds.Threshold choice depends on the target and the relative importance of missed events and unmatched detections.Source: §4.5 · p. 10

Appendix F.

• Table 3’s q* applies to Precision, Recall, and Lift, while Tail(%) and Impact(%) use conventional label thresholds, so the columns mix threshold conventions.Drought q is a scaled SPI score and should not be read on a common percentile scale.Source: Appendix F · p. 11, Table 3 · p. 11

4.6 The relationship differs by hazard and place

• Impact associations are generally positive where estimable, but sparse records leave much of Africa and South America unassessed; wind association is weakest, plausibly because ERA5 does not resolve short-lived gust maxima.The 0.25° six-hourly fields create a scale mismatch with gust maxima, making the wind label an imperfect proxy for wind impacts.Source: §4.6 · p. 12, Appendix F · p. 12

5 Compound tail events

• Across 13 comparisons, compounding weakened association with recorded impacts in nine, strengthened it in three, and made no difference in one; fitted thresholds prevent isolating compounding alone.Compound intensity uses the lower constituent score, and labels should be chosen for the process of interest.Source: §5 · pp. 12–13

6 Example application: AI model training with TailWeather

• The sharpening head reduced 10 m wind RMSE by 30–55% at day 7, yet extreme-event detection worsened at every lead time, hazard, and test year.The largest SEDI decline was 0.45 for extreme wind at day 1; the experiment does not establish the mechanism.Source: §6 · p. 13
• Five of nine compound labels diluted enrichment against a constituent’s EM-DAT record, three strengthened it, and one was unchanged.Compounding therefore did not systematically sharpen tail–impact correspondence.Source: §6 · p. 14, Figure 11 · p. 14

7 Discussion

• Thresholds and compound labels should be chosen for the hazard and question; ERA5’s 0.25°, 6 h inputs do not resolve convective gusts, tornadoes, hail, or downbursts.Thresholds use a fixed 1991–2020 reference climate, and source uncertainty, threshold estimation, and incomplete impact reporting limit interpretation.Source: §7 · pp. 14, 16

11 Conclusions

• TailWeather provides 0.25° global land labels for five hazards, and stricter tails are more often associated with recorded impacts, though rarity is not harm and disaster records cannot evaluate much of the world.Strong average forecast skill can conceal weak extreme-event detection; tail-aware correction can improve RMSE while worsening detection.Source: §11 · p. 16

Appendix A: Event definitions

• Heatwaves use local 90th-percentile exceedances persisting at least three days, while cold waves use the local 10th-percentile lower tail with the same minimum duration.Both use a centered ±15-day seasonal window and severity bins at 0.90/0.95/0.99.Source: A1 Heatwave · pp. 16–17, A2 Cold wave · p. 17

A3 Heavy precipitation

• Heavy precipitation uses the 95th percentile of wet-day precipitation, but the released label does not require a multi-day wet spell and has no moderate tier by construction.The separate long-spell field is not a condition for a heavy-precipitation label in the inspected release.Source: A3 Heavy precipitation · pp. 17–18

A4 Extreme wind

• Extreme-wind labels use sustained 10 m wind speed because no gust field was present in the released ERA5 archive; this proxy does not represent peak gusts.The local 98th percentile sets the flag, with severe and extreme tiers beginning at 20.8 and 28.5 ms−1.Source: A4 Extreme wind · p. 18

A5 Meteorological drought (SPI-3) 275

• Drought uses monthly SPI-3, with drought at SPI ≤−1.0 and tiers at −1.0/−1.5/−2.0; daily broadcast adds no temporal information and is not a contemporaneous predictor.The drought score is missing outside drought events, so lower thresholds cannot be reconstructed from that score alone; the stored spi3 field is needed.Source: A5 Meteorological drought (SPI-3) · pp. 18–19

Appendix B: Dataset characteristics

• Against the fixed 1991–2020 reference, heatwave frequency rose from 3.7% (1981–1990) to 5.9% (2014–2023), while cold-wave frequency fell from 6.4% to 3.1%.Source: Appendix B · pp. 19–20
• The severity-tier profile places almost all flagged extreme-wind days in the moderate band, while heavy precipitation has no moderate tier by construction.The wind tiers are Beaufort-anchored, with an absolute 20.8 ms−1 escalation threshold.Source: Figure B2 · p. 20
• The supplied drought frequency of 33.8% for 2023 reflects one January record, not a full-year rate, and its precipitation accumulation needs checking.The reported value is reproduced from 118,968 drought cells among 351,848 cells with finite SPI.Source: Appendix B · p. 20
• A fixed reference baseline alone cannot explain an anomalous terminal value; a moving-reference analysis would require refitting the climatology from underlying weather fields.Checking input completeness, precipitation accumulation, fitting, and spatial contributions is needed to assess an anomalous endpoint.Source: Appendix B · p. 20

Appendix C: Processing details

• The 2023 labels cover only partial January periods, and incomplete terminal precipitation or SPI accumulation windows should be excluded.Heat, cold, and wind cover January 1–10; precipitation covers January 1–9; monthly drought has one January coordinate.Source: Appendix C · pp. 20–21
• Drought is prevalent, long-duration, and coarse in time, whereas extreme wind is rare, short, and concentrated in its lowest severity tier.The comparative profile normalizes six dataset properties to their cross-hazard maxima.Source: Appendix C · p. 21, Figure B3 · p. 21
• Temperature and wind reference samples pool values within a circular ±15-day window, while precipitation pools reference-period wet days and SPI is fitted by calendar month.Leap-day handling shifts nominal day-of-year alignment after March in leap years, and the effect of that offset has not been quantified.Source: Appendix C · p. 21
• Threshold percentiles use linear interpolation between neighboring order statistics rather than a nearest-rank rule.The physical threshold difference depends on the spacing of those order statistics.Source: Appendix C · p. 21
• Across pooled 43-year percentile tables, all sixteen reported percentile scores for four daily hazards are exact multiples of 0.0005, not near multiples of 1/99, confirming the stored score grid.Increasing numerical storage precision alone would not resolve the far tail, which is a property of the empirical rank rather than storage.Source: Appendix C · pp. 21–22
• Drought scores equal min(1,−SPI/3) on drought cells and are missing elsewhere, so thresholds 0.1, 0.2, and 0.3 select the same finite-score set.The threshold plateau follows from the minimum finite score near 1/3, not from temporal broadcasting.Source: Appendix C · p. 22

Appendix D: Tail–impact comparison details

• The comparison defines precision, recall, F1, and lift from a shared valid mask and weights, with log odds ratios computed where defined.Zero counts require an explicitly stated correction or masking convention.Source: Appendix D · p. 22
• Missing disaster-catalog records cannot be treated as verified absence of impact, and the stated 15-day-block bootstrap omits several sources of uncertainty.The bootstrap may not represent uncertainty for monthly SPI, overlapping three-month accumulations, or long disaster records; intervals also omit reanalysis, threshold, geolocation, and catalog-inclusion uncertainty.Source: Appendix D · p. 22

Appendix E: Sharpening-head implementation

• The experiment freezes FourCastNet’s backbone and trains a shallow residual head to correct forecasts and predict TailWeather intensity, using progressively longer rollouts.The corrected forecast is not fed back into the autoregressive state, and the experiment is not a comparison of training methods.Source: Appendix E · p. 22

Appendix F: Limits of the tail–impact comparison

• Larger administrative footprints raise opportunities for any-overlap matches, but their effects on pooled precision, recall, and odds ratios are not universal bounds.The comparison should be stratified by geometry, event period, and date precision.Source: Appendix F · pp. 22–23
• The EM-DAT comparison concerns recorded disasters, and 1.79% heat cell-day recall is not the share of heat disasters captured.Event-level capture is defined separately from cell-day recall.Source: Appendix F · p. 23
• Daily empirical ranks tie many of the most extreme days near 1, so thresholds from about 0.99 to 1 select nearly the same top set.Drought scores instead begin near 1/3 on drought cells and are capped at 1 for SPI ≤ −3; a common numeric threshold is therefore not a common climatological percentile.Source: Appendix F · p. 23
• The selected q∗ describes the comparison sample, and generalization requires independent evaluation.Partial precision–recall areas cover different attained recall ranges across hazards and should not rank hazards or be compared directly with the full-curve no-skill baseline.Source: Appendix F · p. 23
• Recall is non-increasing under nested threshold masks when persistence and validity rules preserve nesting, while the observed precision rise is empirical.Source: Appendix F · p. 23

Appendix G: Event-level capture rates

• Precision-aware date windows yield event capture rates of 55.3% heat, 76.7% cold, 81.8% wind, 93.3% heavy precipitation, and 92.5% drought.The rates use ±2 days for day-precise records, ±15 for month-precise, and ±182 for year-precise records.Source: Appendix G · p. 23
• Precision-aware matching raises heat and cold capture from 46.6% and 63.2%, respectively, showing sensitivity to the matching window.This does not identify the cause of every unmatched event.Source: Appendix G · p. 23
• Capture rises with footprint area for all five hazards; severity-stratified capture rises for wind, heavy precipitation, and drought, but not heat or cold.Heat capture ranges from 31% to 86% across area quartiles, and wind from 60% to 88%.Source: Appendix G · pp. 23–24
• For localized footprints, observed capture exceeds the illustrative chance baseline for heat, wind, and heavy precipitation, while drought capture is at or below it.For large footprints, chance capture approaches 100%, illustrating strong footprint-size sensitivity.Source: Figure G1 · p. 24, Appendix G · p. 24
• The independent-cell chance calculation is not calibrated for spatially coherent, persistent weather, and its constant area-per-cell conversion is invalid across a latitude–longitude grid.Large-footprint capture can be inflated because more cells and days create more opportunities for overlap, irrespective of coincidence with damage.Source: Appendix G · p. 24
• The simplified independent-cell calculation reports observed-minus-null differences of 22, 51, and 61 percentage points for heat, wind, and precipitation in the smallest area quartile.These differences do not establish statistical significance or causal agreement.Source: Appendix G · p. 24

• Every per-hazard precision–recall curve sits above its impact base rate, indicating positive association in the reported sample.Source: Appendix H · p. 24, Figure H1 · p. 25
• F1-optimal tail thresholds differ across hazards, ranging from q∗ = 0.40 for drought to 0.99.The figures show that no single percentile is optimal across hazards.Source: Appendix H · p. 24, Figure H1 · p. 25
• Per-cell log-odds ratios complete the spatial comparison for cold wave, heavy precipitation, and drought.Source: Appendix H · p. 24

Appendix I: Severity-tier composition through time

• Heatwave increases span moderate, severe, and extreme tiers, with the extreme tier roughly doubling between 1981 and 2020.Source: Appendix I · p. 25, Figure I1 · p. 27
• The plotted 2023 drought rate has large severe and extreme contributions, but one January field does not establish an annual drying signal.Source: Appendix I · pp. 25, 27
• Heavy precipitation has no moderate tier by construction, while extreme wind events are almost entirely moderate because Beaufort escalation thresholds are seldom met.Source: Appendix I · p. 25
• Figure I1 breaks each hazard’s event-day rate into moderate, severe, and extreme contributions over time, with independent vertical scales and a shaded 1991–2020 reference period.Its 2023 endpoint is partial—a single month or ten days—not a full year.Source: Appendix I · p. 27, Figure I1 · p. 27