Quadratic trends raised five-year mean sea-level forecast error at five Mid-Atlantic gauges for 1999-2020 origins

We tested whether squared time improves five-year mean sea-level forecasts beyond a linear trend and month effects. We used fixed NOAA monthly records from 1980-2025 at five Mid-Atlantic gauges. Fits ended at each origin from 1999-2020. The mean site MSE increase was 94.57%, with conditional 95% five-year block limits of 49.15% to 188.01%. Pooled RMSE rose from 21.15 to 29.28 mm over 108 paired site-origin scores. All site point scores favoured the linear model. Complete targets and 20-year training windows retained the loss. One-year targets gave an uncertain difference. Fitted curvature changed with origin, consistent with time variation that did not persist over the forecast window. The data do not establish its physical cause or show that physical acceleration is absent. Few overlapping origins, fixed sites, missing months, retrospective revisions and conditional uncertainty limit inference. The package includes used monthly fields, source hashes, code, forecasts, score draws, a separate numerical audit and a figure.

sea level · quadratic extrapolation · chronological forecast · Mid-Atlantic · tide gauges · forecast error