Seasonal cycle terms raised monthly high-water offset forecast error at six US gauges in 1998-2025

We tested whether a seasonal change in the effect of a fixed 18.61-year cycle improves monthly mean high water above mean sea level. We used 4,652 accepted NOAA station-months at six selected US gauges in 1960-2025. Both models used only earlier years. The reference had month means, a time trend, and cycle sine and cosine terms. The test model added four products of annual and cycle terms. In 1,995 scored station-months in 1998-2025, the equal-site mean squared error reduction was -1.71%. Its conditional 95% five-year block interval was -2.57% to -0.88%. Thus the added terms raised error. Absolute root mean squared error increases were 0.058 to 0.195 mm. Other block lengths, an added reporting lag, and separate month cycle effects also gave negative mean gains. This result gives no support for adding these terms to this reference. It does not show that physical seasonal modulation is absent. Revised source records, six selected sites, reused campaign data, model form, and only about 1.5 test cycles limit inference. The package supplies fixed input fields, exact source paths and hashes, code, all forecasts, resampling indices, a figure, audits, and offline repeat instructions.

tide gauges · lunar nodal cycle · seasonal modulation · chronological forecast · NOAA CO-OPS · negative result