A probabilistic forecast of Singapore's 24-hour PSI for the next 15 days. Lagrangian transport over two weather ensembles, a 100,000-member Monte Carlo over the parts nobody measures, a Bayesian update on NEA's latest readings, and calibration against four replayed haze seasons.

1. Inputs

• Weather ensembles: NOAA GEFS (31 members, 16 days) plus 25 members of ECMWF's machine-learned ensemble AIFS ENS when the download succeeds. Winds and precipitation at 6-hourly steps.
• Fires: NASA FIRMS VIIRS active-fire detections (375 m) with fire radiative power (FRP), grouped into 14 source regions across Sumatra, Kalimantan and Peninsular Malaysia.
• Observations: NEA 24-hour PSI and 1-hour PM2.5 for five areas (data.gov.sg), re-ingested hourly. Rain over the fire areas (Open-Meteo), airport visibility (METAR), regional PM2.5 (OpenAQ).
• Second opinion: Copernicus CAMS PM2.5 forecast, used for comparison and, once the daily scoring supports it, as a learned weight on the middle of the distribution.

2. Transport

For every ensemble member and every arrival time (6-hourly to day 6, then 12-hourly to day 15), 300 particles are released at Singapore and integrated backwards 96 hours through that member's wind field, with a 2 m/s random-walk term for sub-grid turbulence. Where a particle passes over a fire cell it accumulates sensitivity to that cell's emissions, discounted by wet removal (8% per mm of rain along the path) and age (e-folding 96 h). The result is a source–receptor footprint S[member, arrival, region, emission-day].

3. Monte Carlo

Each of 100,000 futures draws an ensemble member and the quantities that are not observed:

• Smoke yield per unit FRP (log-normal, σ 0.6, plus per-island factors σ 0.35)
• Fire persistence: half-life 4–40 days without rain (peat smoulders), and suppression of 2–8% per mm of rain above about 6 mm/day
• New ignitions (growth rate, σ 0.04/day), background PM2.5 (18 ± 5 µg/m³)
• Regional reservoir share ρ 0.2–0.8 (aged haze not tied to today's winds) and a saturation scale 150–350 µg/m³ for direct plumes

PM2.5 at each arrival is bg + d·(1 − e−(1−ρ)·K·ΣS·E/d) + ρ·D₀·a(t), then converted to PSI with NEA's breakpoints over a time-weighted 24-hour window.

4. Bayesian update

Each future is weighted by the likelihood of what NEA measured: the latest 24-hour PM2.5 at its actual reading time (log-normal, σ 0.25) and the past day's hourly readings (σ 0.35·√n, since they are correlated). Futures are then resampled systematically. If the effective sample size falls below 30, or an input is missing, the run is marked degraded and not published.

5. Calibration and long range

• Spread is widened in log-PSI space by lead (×2.15, ×1.45, ×1.05 below the median for days 1–3, 4–6, 7–15), fitted on replays of the 2014 (held out), 2015, 2019 and 2023 seasons. One distribution drives every number on the page.
• Days 7–15 blend in analogues from NEA's record since 2014, more with lead time.
• End of season: monsoon onset over the fire areas from the ensemble while it reaches, beyond that a climatological onset shifted by the Relative Oceanic Niño Index and the Indian Ocean Dipole. In a strong El Niño year the shift grows faster than linearly, heavier rain is needed to count as the end, and a one-sided late tail is added: ending the season too early is the costlier mistake.

6. Outputs

Storylines partition the 100,000 futures (clears early, clears later, stays above 100, gets worse: a peak into a higher band, above 200 and at least 30% and 40 points above now). Yes/no odds are evaluated on every simulated time step. Best and worst case are the lowest and highest 10% by 6-day mean PSI.

7. Schedule, scoring and learning

• Full run every 6 hours; odds re-anchored to NEA's newest reading every hour. Rerun executes the same engine in a Web Worker on your device.
• Every issuance is archived as issued and scored against NEA two days later (range coverage, typical miss, Brier score).
• A daily review by Claude Opus 5.5 reads the scores and applies small, capped bias and spread corrections by lead.
• The short column under the skyline is written by Claude Opus 5.5 from the same numbers after each run. Any number it uses must appear in the model's output, or the text is rejected and a plain template is shown instead.
• Replays so far: 85% of readings inside the 90% range for days 1–6 (82% for days 7–15). Typical miss 19 PSI for days 1–6 (no better than persistence) and 20 for days 7–15 (persistence 25). Yes/no odds are about as good as base rates.

Limits: smoke amounts are scaled to match NEA's readings, not measured at the fires. Odds for extreme haze (PSI above 300) have not been validated, and in replays of past seasons they ran too high. This is an independent project, not an official forecast. For health advice, follow NEA.