Monthly iteration gave no clear six-month ENSO forecast gain over direct fits at 2000-2024 origins

We tested whether a monthly temperature-volume model improves six-month ENSO forecasts when it is stepped forward six times instead of fitted directly for that lead. We used NOAA ERSSTv5 and GODAS records, expanding fits from 1981, and 300 monthly origins in 2000-2024. Both methods had equal training target months and equal coefficient counts. With seasonal slopes, iteration increased temperature mean squared error by 3.60%. RMSE was 0.6577 C for iteration and 0.6461 C for direct fitting. The conditional 95% three-year block interval for error reduction was -7.21% to +1.02%. Five-year blocks and two simpler model forms also gave no clear temperature gain. All full-period temperature intervals at 3, 6, 9 and 12 months included zero. This is a null method benchmark, not a test against the physical recharge process. Revised data, few ENSO cycles, a small state and conditional uncertainty limit inference. Code, exact source hashes, aggregate scores, a numerical audit and a figure are included.

ENSO · warm water volume · direct forecast · iterated forecast · recharge model · null result