A fixed 4.425-year term gave no clear gain for average monthly high-water maxima at six US gauges in 1998-2025

We tested whether a fixed 4.425-year term improved forecasts of the annual average monthly highest-water height above mean sea level. This period has a prior link to lunar perigee. We used six NOAA tide gauges and 161 complete test gauge-years in 1998-2025. Each fit used earlier years only. The reference had a linear trend and an 18.61-year term. The added term reduced the equal-gauge mean squared error by 2.49%. Its conditional 95% five-year block interval was -4.88% to +6.69%. Error fell at two gauges and rose at four. Seattle had a 28.96% reduction; the mean for the other five gauges was a 2.80% increase. A two-year reporting-lag check gave a 2.56% mean reduction. The test does not establish a useful added forecast signal or the absence of lunar modulation. The target is an average of monthly maxima, not an annual maximum or flood count. Selected gauges, revised data, missing months, simple harmonic models and a 28-year test span limit inference. The package includes exact source bytes and hashes, forecasts, code, uncertainty draws, a figure, an arithmetic audit and an offline repeat.

tide gauges · lunar perigee · chronological forecast · monthly maxima · null result · NOAA CO-OPS