tide-producing forces. However, the actual tide does not conform to this theoretical value because of friction

and inertia as well as differences in the depth and distribution of land masses of the earth.

(b) Because of the above complexities, it is impossible to exactly predict the tide at any place on the earth

based on a purely theoretical approach. However, the tide-producing forces (and their expansion component

terms) are harmonic; i.e., they can be expressed as a cosine function whose argument increases linearly with

time according to known speed criteria. If the expansion terms of the tide-producing forces are combined

according to terms of identical period (speed), then the tide can be represented as a sum of a relatively small

number of harmonic constituents. Each set of constituents of common period are in the form of a product of

an amplitude coefficient and the cosine of an argument of known period with phase adjustments based on

time of observation and location. Observational data at a specific time and location are then used to

determine the coefficient multipliers and phase arguments for each constituent, the sum of which are used to

reconstruct the tide at that location for any time. This concept represents the basis of the harmonic analysis,

i.e., to use observational data to develop site-specific coefficients that can be used to reconstruct a tidal series

as a linear sum of individual terms of known speed. The following presentation briefly describes the use of

harmonic constants to predict tides.

(c) Tidal height at any location and time can be written as a function of harmonic constituents according

the following general relationship

(II-5-16)

where

(d) In the above formula, tide is represented as the sum of a coefficient multiplied by the cosine of its

respective arguments. A finite number of constituents are used in the reconstruction of a tidal signal. Values

for the site-specific arguments (*H*0, Hn, and *κ*n) are computed from observed tidal time series data, usually

from a least squares analysis. The National Oceanic and Atmospheric Administration's (NOAA) National

Ocean Survey (NOS) generally provides 37 constituents in their published harmonic analyses (generally

based on an analysis of a minimum of 1 year of prototype data). The NOS constituents, along with the

corresponding period and speed of each, are listed in Table II-5-3. The time-specific arguments (*f*n and

II-5-14

Water Levels and Long Waves

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