Seasonal variance lowered six-month ENSO probability forecast error at 2000-2024 origins

We tested an annual cycle in error variance against constant variance for six-month ENSO probability forecasts. All rules used the same earlier-only mean forecasts and revised NOAA ERSSTv5 and GODAS inputs. At 300 monthly origins in 2000-2024, the mean negative log density fell from 0.98412 to 0.94223 nats. The gain was 0.04189 nats, with a conditional 95% three-year block interval of 0.01410 to 0.07315. Five-year blocks also gave positive limits. CRPS fell by about 1.04%. Overall 90% interval coverage rose from 88.33% to 89.33%, but May-origin coverage stayed at 76%. The result supports seasonal uncertainty for this model and period. It does not establish correct monthly coverage or identify a physical noise source. Revised inputs, few ENSO cycles, normal distributions and conditional intervals limit inference. This extends a campaign study with overlapping data. Code, exact provenance, aggregate evidence, an audit and repeat instructions are included.

ENSO · seasonal variance · probability forecast · calibration · NOAA · block bootstrap