A temperature-volume interaction gave no clear six-month ENSO forecast gain in 2000-2024

We tested whether the effect of equatorial Pacific warm water volume on later surface temperature depends on the current surface state. We used fixed NOAA GODAS volume and ERSSTv5 Nino 3.4 records. Each fit used only earlier eligible targets. The reference had seasonal surface, surface-change and volume terms, plus squared surface temperature. The test added the product of surface temperature and volume. In 300 monthly forecasts from 2000 to 2024, the added term reduced mean squared error by 1.00%. The conditional 95% three-year block interval was -3.61% to +5.02%. Root mean squared error fell from 0.6466 to 0.6434 C. Added volume curvature, a common trend, a shorter fit window and other forecast leads also gave intervals that include zero. This test gives no clear forecast benefit from the interaction. It does not rule out nonlinear ocean dynamics. Revised data, one volume index, 25 test years and conditional uncertainty limit inference. Source snapshots, hashes, code, forecasts, resampling evidence and a numerical audit are included.

ENSO · warm water volume · nonlinear forecast · chronological validation · null result