Collect the observation series
Each station reports at six-minute intervals. A year of clean observation is the minimum for a first analysis; stations with less are marked provisional and are excluded from the network summary.
Fit the harmonic constituents
We solve for 62 constituents by least squares. The four principal ones account for most of the range at every station in this network; the remainder matter chiefly in shallow water where the curve is distorted.
Predict forward
The fitted constituents are evaluated forward to produce height at any instant. This step is deterministic and contains no weather information at all, which is the single most misunderstood fact about tide prediction.
Compare against observation
The difference between observed and predicted height is the surge. It is a residual, not a measurement, and it carries everything the harmonic model does not know about — chiefly wind and atmospheric pressure.
What the published uncertainty covers
The quoted ±0.05 m is the residual standard deviation of the harmonic fit over the analysis period. It does not include gauge error, datum error, or any allowance for weather. A day with a 0.40 m surge is not a day on which the prediction was wrong by 0.40 m; it is a day on which the weather added 0.40 m to a correct prediction.