Surrogates with fixed month distributions did not reproduce six-month Nino 3.4 change asymmetry in 1950-2025

We tested whether calendar-month distributions can reproduce a previously reported six-month temperature change asymmetry. We used 912 NOAA CPC ERSSTv5 Nino 3.4 monthly anomalies for 1950-2025. The normalized cubic change statistic was -0.5066. None of 999 surrogate records with fixed calendar-month distributions had a larger absolute statistic. The nominal tail fraction was 0.001. A pooled comparison also gave 0.001. However, the month constraints increased median Fourier amplitude error from 0.44% to 5.84%. The 1950-1987 test gave 0.182; the 1988-2025 test gave 0.002. This supplies a seasonal distribution benchmark for a pattern selected on the same data. It does not test all seasonal linear models or establish a physical cause. The method does not preserve month-specific transition covariance, and its tail fractions are not calibrated probabilities. Source error, nonstationarity, approximate spectral fit and prior selection limit inference. The package includes original code, source hashes, scalar simulations, checks and a figure. External monthly data stay outside the bundle.

ENSO · Nino 3.4 · seasonal distributions · surrogate data · time asymmetry · spectral fit