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Armed with as few as nine of the major tidal constituents (see tide analysis module), you can make a quite respectable tide prediction using the HAMELS method (Harmonic Analysis, Method of Least Squares). One model that HAMELS can use is simply the sum of nine tidal constituents symbolized as follows:
Each symbol shown above represents a cosine wave with a frequency or “speed” that uniquely identifies the tidal constituent – M2, for example, is the major lunar semidiurnal constituent with a speed of 28.984 degrees per mean solar hour. The amplitude and phase of the wave vary from place to place, however, and must be found through tide analysis. The amplitude and phase values are known as the tidal harmonic constants for the place in question.
If NOS harmonic constants are sometimes difficult to use, the tidal datum elevations available at most NOS tide stations are very simple and straightforward. They come in handy when you want your tidal predictions to refer to a specific datum such as Mean Lower Low Water (MLLW). Tidal height predictions initially refer to the base elevation in the absence of a tide – Mean Sea Level (MSL). If you want them to refer to MLLW instead, add the amount of offset (MSL-MLLW) between the two datums to the tide model.
NOS normally use thirty-eight tidal constituents in their official predictions at stations in North and South America, part of a broader effort consistent with their legal responsibilities for vessel navigation and marine safety. The additional constituents can improve the final prediction of, say, the time and height of a certain high tide by a few minutes or a few centimeters – but generally no more than that. The lion’s share of the difference between a prediction and an observation of a given tide, as tide analysis repeatedly shows, rests with the so-called meteorological tide caused by winds and barometric pressure changes. A purely astronomical tide model is incapable of accounting for this part of the daily change in water level but hydrodynamic models using data assimilation techniques are beginning to fill the void.
While a HAMELS analysis by definition fits each water level data set with the least error possible for a given mix of tidal constituents, the question remains - how well does it agree with a different, or independent, data set? Verification of the harmonic model is still somewhat subjective (how well is well enough?) but employing independent plots such as the following provide a partial answer to this question. As often happens in January, a northeaster occurred in lower Chesapeake Bay on the first day of 2003, causing observed water levels to rise well above predicted levels at the Chesapeake Bay Bridge Tunnel lying at the entrance to the bay. Although the water levels are different, the phase of the observed and predicted tides remain in close agreement throughout the weather event.