A quadratic ENSO term lowered eastern Pacific winter rain test error in 1980-2025, with wide uncertainty

We tested whether a squared Nino 3.4 term improves a model of concurrent winter rain in years excluded from fitting. We used fixed GPCP V2.3 and CPC ERSSTv5 data for 46 winters in 1980-2025. Both models had an intercept, a time trend, and a linear index term. We excluded five-year test blocks and one adjacent winter on each side from training. The squared term reduced mean squared error by 36.6% in the eastern Pacific, 2.8% in the central Pacific, and -2.3% over the Maritime Continent. The respective 98.33% paired three-winter block intervals were -18.2% to 63.1%, -15.2% to 19.1%, and -25.5% to 11.2%. All include zero under this nominal three-comparison interval rule. The eastern point gain remained 29.3% after three major El Nino winters were removed from fitting and testing. A local Nino 3 index gave a 69.3% eastern gain. These point estimates support a useful regional model check, but do not establish a clear gain after the wider uncertainty rule. The intervals condition on fitted models and omit training and product uncertainty. This is a concurrent response test, not a forecast or a causal test. The package includes code, source hashes, fixed regional evidence, every test prediction, bootstrap draws, figures, and an independent numerical audit.

ENSO · rainfall · GPCP · nonlinear response · blocked validation · uncertainty · eastern Pacific