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Canonical sources on the NOS tide prediction methodology (including a mathematical explanation from first principles in SP98):
Manual of Harmonic Analysis and Prediction of Tides. Special Publication No. 98, Revised (1940) Edition (reprinted 1958 with corrections; reprinted again 1994). United States Government Printing Office, 1994. Downloaded from NOAA Central Library via NOAA's Historical Map & Chart Collection, 2015-04-27.
Computer Applications to Tides in the National Ocean Survey. Supplement to Manual of Harmonic Analysis and Prediction of Tides (Special Publication No. 98). National Ocean Service, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, January 1982. Downloaded from NOS, 2016-12-18.
Miscellaneous publications available from http://www.flaterco.com/xtide/files.html#pubs:
Tide and Current Glossary. National Ocean Service, January 2000. Downloaded from NOS, 2003-12-19.
Tidal Datums and their Applications. NOAA Special Publication NOS CO-OPS 1, June 2000. Downloaded from NOS, 2004-08-27.
Nathaniel Bowditch, LL.D. The American Practical Navigator: An Epitome of Navigation. NIMA Pub. No. 9, Bicentennial Edition, 2002. Downloaded from NGA, 2004-09-28. 42 MB. Chapter 9 is a tutorial on tides and currents.
My sources for X-windows programming reference:
Kimball, Paul E. The X Toolkit Cookbook. Prentice Hall P T R, New Jersey, 1995.
Nye, Adrian. Xlib Programming Manual. O'Reilly & Associates, Inc., Volume 1, Third Edition, July 1993.
A catalog of information on the ISO 8601 standard date and time notation can be found at http://dmoz.org/Science/Reference/Standards/Individual_Standards/ISO_8601/.
iCalendar format and usage is according to RFC 2445 and RFC 2446, with some hints taken from RFC 2447 (November 1998).
Harmgen uses ordinary least squares for harmonic analysis of tides. An improved method that is more robust to outliers in the data is described in
Keith E. Leffler and David A. Jay, "Enhancing tidal harmonic analysis: Robust (hybrid L1∕L2) solutions," Continental Shelf Research, 2008. Available at http://web.cecs.pdx.edu/~jaylab/group/leffler/publications/Leffler_Jay_2009.pdf.
An article about a model-based approach to tide prediction, which is completely different from what XTide does, is
Derek Goring, "Computer Models Define Tide Variability," The Industrial Physicist, v. 7, n. 5, October/November 2001, pp. 14-17.
Michael Foreman's publications are a good read if you are interested in the Doodson approach to tide prediction.
Foreman, M.G.G., 1977. Manual for Tidal Heights Analysis and Prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 58 pp. (2004 revision).
Foreman, M.G.G., 1978. Manual for Tidal Currents Analysis and Predition. Pacific Marine Science Report 78-6, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 57 pp. (2004 revision).
Foreman, M.G.G., and R.F. Henry, 1979. Tidal Analysis Based on High and Low Water Observations. Pacific Marine Science Report 79-15, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 36 pp. (2004 revision).
Miscellaneous publications mentioned by Hugh Casement that I haven't read:
On the response method of tide prediction, which is completely different and allegedly better than what XTide does: Munk, Walter H.; Cartwright, David E.: Tidal spectroscopy and prediction. Philosophical Transactions of the Royal Society, A 259 (1966).
An interesting-sounding publication that Hugh Casement hasn't read either: Horn, Walter: Some recent approaches to tidal problems (Centre Belge d'Océans, Brussels, year unknown).
Horn, Walter: Tafeln der Astronomischen Argumente V0 und der Korrektionen j, v (Deutsches Hydrographisches Institut, Hamburg, 1967).
Doodson, in Proceedings of the Royal Society A.100 (London, 1921).
Cartwright and Tayler, in Geophysical Journal of the Royal Astronomical Society 23 (1971).
Jean Meeus, Astronomical Algorithms, Willmann-Bell.
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