How TideTurtle predicts tides

What harmonic prediction is

Harmonic prediction is the method NOAA uses for US tide stations and that almost every national tide authority uses for its primary harbour gauges. The input is decades of measured water level at a specific gauge — typically hourly or sub-hourly readings going back to at least the 1970s, sometimes back into the 19th century. The Battery in New York has a continuous record dating to 1856.

The analyst fits a sum of sine waves to that record. Each sine wave matches a known gravitational forcing — the principal lunar semidiurnal constituent M2, the principal solar S2, the larger lunar elliptic N2, the diurnal lunar K1, the diurnal solar principal O1, plus dozens of smaller harmonics for shallow-water and seasonal effects. The frequencies are fixed by celestial mechanics; only the amplitudes and phases at this specific gauge are unknowns to fit.

To predict a future tide at the same gauge, you sum the fitted constituents forward in time. Done well, the result is accurate to within a few minutes and a few centimetres under normal weather. It works because the tide-generating forces are the same now as they were when the gauge record was being built. What the method cannot capture is anything not in the original record: storm surge, river discharge, secular sea-level rise beyond the calibration window. TideTurtle's NOAA-sourced US pages use this stream. UK Environment Agency pages show real-time gauge observations, not a harmonic forecast; their accuracy characteristics are listed in the table below.

What gridded modelling is

Gridded ocean modelling is the method behind every TideTurtle page outside the NOAA + UK EA coverage areas. Open-Meteo Marine, the source TideTurtle uses, ingests output from the MeteoFrance SMOC global ocean forecast — a numerical hydrodynamic model running on roughly a 0.08 degree grid (about 9 km at the equator, narrower toward the poles). The model solves the shallow-water equations for the whole ocean simultaneously, forced by the same astronomical inputs as harmonic prediction and additionally by the atmospheric forecast.

The trade-off compared to harmonic is twofold. Gridded data is consistent globally — every coast on Earth has a prediction, not just the ones with a gauge — and it includes wind and pressure effects in real time, which a pure-harmonic prediction misses. The cost is resolution. A 0.08 degree cell over a wide open coast like Costa da Caparica or Fistral Beach captures the tide well. The same cell across a narrow estuary, a fjord, a bar-mouthed harbour, or any feature smaller than the cell sees an averaged version of the bathymetry, which can offset the timing or compress the height of the predicted swing. The accuracy table below quantifies this.

Datum

A tide height is meaningless without naming the surface it is measured from. That surface is called the datum. TideTurtle shows the datum on every tide page, but the value differs by source. NOAA harmonic predictions in the US are referenced to mean lower low water (MLLW) — the average of the lower of each day's two low tides over the standard 19-year tidal epoch. That is also the datum on US nautical charts, so a NOAA tide and a NOAA chart speak the same language.

Open-Meteo Marine output is referenced to mean sea level (MSL) — the long-term average sea surface, with no daily tidal component. UK Environment Agency gauges report against Ordnance Datum Newlyn (ODN), the geodetic surface used for British land surveying, anchored to the long-term sea-level mean at Newlyn in Cornwall. None of these is the same as the chart datum used on a paper navigation chart, which is usually lowest astronomical tide (LAT). A height of 1.0 metre against MLLW is not a height of 1.0 metre against MSL or LAT — the same physical water level reads as different numbers under each datum. See the datum glossary entry for the full conversion picture.

Accuracy in practice

What to expect from each source on a normal-weather day.

Sub-grid features that degrade gridded accuracy include narrow estuaries, river-mouth bars, fjord heads, ria coastlines, and any inlet narrower than roughly 9 km. On those pages, expect the upper end of the error range or worse, and treat the numbers as planning information rather than navigational data.

Limitations

Three weather mechanisms shift actual water levels beyond what astronomical or model prediction captures. Storm surge — the inverse-barometer rise driven by low atmospheric pressure plus the pile-up driven by onshore wind — can lift water levels by half a metre to several metres during a major event. The Sandy peak at The Battery in 2012 was 2.8 metres above predicted. Wind setup, even on a fair-weather day, can shift the gauge by 20–30 centimetres against a steady onshore breeze. River discharge raises water levels in the inner reaches of an estuary independently of tide, which is why river-mouth gauges in the Tagus, the Thames, the Charleston Cooper, and the Boston Charles all behave differently from open-coast pages for the same region.

None of the predictions on this site are intended for navigation. For piloting, mooring, anchoring, or any decision where accuracy matters for safety, use the official tide tables and chart products from your national hydrographic authority — NOAA CO-OPS in the US, UKHO Admiralty TotalTide in the UK, BSH in Germany, Instituto Hidrográfico in Portugal, and equivalents elsewhere. Not for navigation.