A four-month cycle gave no clear seasonal sea-level error gain at 257 gauges in 2010-2024

We tested whether a four-month cycle reduced later monthly sea-level shape error beyond annual and six-month cycles. We used a fixed PSMSL RLR snapshot, with training in 1980-2009 and testing in 2010-2024. Data rules retained 257 gauges and 3,664 complete test station-years. Each year had its observed annual mean removed. This is a seasonal-shape test, not an absolute sea-level forecast. The added cycle reduced mean squared error by 0.48%. The conditional 95% common-calendar three-year block interval was -0.97% to +2.17%. Error fell at 127 gauges. Equal geographic cell weights, strict daily completeness, and shorter training also left the gain uncertain. A Fourier identity separates transferred alignment from the amplitude penalty and checks all station error differences. The result does not establish a reliable added gain or the absence of a four-month signal. One revised archive, uneven sites, short testing, and conditional uncertainty limit inference. Code, monthly inputs, source hashes, predictions, audits, and a figure are included.

sea level · seasonal shape · four-month cycle · harmonic transfer · PSMSL · null result