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For tidal harmonic analysis of sea level data, there are various packages which may be available free of charge:
The University of Hawaii and the NOC software packages are based on different mathematical engines. TASK is based on software developed by NOC (previously known as the Proudman Oceanographic Laboratory) over many years whereas the core of the University of Hawaii software is based on the work of Michael Foreman (Institute of Ocean Sciences in Canada). There are some subtle differences in the definitions of harmonic constants, which make the two slightly incompatible. These differences are documented in the TASK User Guide. Note that the UK Hydrographic Office’s internal analysis software uses the same mathematical definitions for harmonics as the NOC software. Therefore any users that obtain harmonic constants from the UKHO should check that their choice of prediction software is compatible. Questions should be directed to the NOC Marine Data Products Team.
There are various software packages (and even mobile apps) available for predicting tidal levels. Many use fixed databases of tidal harmonics, although some may allow you to include your own harmonic data. Most harmonic analysis software will also include a tidal prediction module.
Use your favourite search engine and search for “tidal predictions” to find suitable sources of tide tables or tidal software.
NOTE: The PSMSL does not endorse any of the software listed on this page, and it is far from being a complete list of the products available.