A temperature term gave no clear six-month ENSO uncertainty forecast gain at 2000-2024 origins

We tested whether current Nino 3.4 temperature improves six-month ENSO uncertainty forecasts beyond season. We used frozen NOAA GODAS volume and ERSSTv5 temperature inputs. Earlier-only mean forecasts supplied errors for annual variance fits. Across 300 monthly origins in 2000-2024, adding signed temperature raised mean Gaussian negative log density from 0.94223 to 0.94680 nats. Reference-minus-test gain was -0.00457 nats, with a conditional 95% three-year block interval of -0.02264 to +0.01269. Five-year blocks and an absolute-temperature term also gave no clear gain. The result is a negative benchmark for these variance rules. It does not establish equal physical noise in warm and cold states. Few ENSO cycles, revised data, normal distributions, one mean model and conditional uncertainty limit inference. Code, source hashes, aggregate scores, all variance fits, bootstrap draws, an audit and a figure are included.

ENSO · forecast uncertainty · warm water volume · variance model · null result