Stepwise monthly mean removal raised mean squared boundary jumps by 19% to 61% at six US gauges in 1960-2024

We tested how monthly mean removal changes daily water-level jumps at six US tide gauges. We used fixed NOAA hourly daily extrema and monthly means for retained days in 1960-2024. We compared subtraction of a constant monthly mean with subtraction of a line between adjacent monthly center values. On month boundaries, the equal-site mean increase in mean squared daily midpoint change was 38.85%, with a conditional 95% three-year block interval of 31.84% to 46.55%. Site estimates ranged from 19.48% to 60.83%. All six simultaneous site intervals were above zero. On other days, the equal-site mean increase was 0.051%. The boundary rate of jumps above a fixed interior 95th-percentile threshold rose by 2.90 percentage points on average. One- and five-year block checks retained the mean increase. This is a method comparison, not a measure of error against a known ocean signal. Smooth interpolation need not be the true mean level. Daily midpoints retain tides; monthly means include weather. Selected sites, missing days, fixed source products, and conditional block assumptions limit inference. The package preserves daily evidence, exact source paths and hashes, code, uncertainty draws, a figure, and numerical audits.

sea level · monthly mean removal · daily changes · month boundaries · NOAA CO-OPS · method audit