available through the Automated Coastal Engineering System (ACES) (Leenknecht, Szuwalski, and Sherlock

1992).

(e) Most of the constituents listed in Table II-5-3 are associated with a subscript indicating the

approximate number of cycles per solar day (24 hr). Constituents with subscripts of 2 are semidiurnal

constituents and produce a tidal contribution of approximately two high tides per day. Diurnal constituents

occur approximately once a day and have a subscript of 1. Symbols with no subscript are termed long-period

constituents and have periods greater than a day; for example, the Solar Annual constituent Sa has a period

of approximately 1 year.

(f) In most harmonic analyses of tidal data in the continental United States, the majority of constituents

shown above have amplitude contributions that are negligible with respect to the magnitude of the full tide.

For example, in the Gulf of Mexico and east coast of the United States, well over 90 percent of the tidal

energy can be represented by the amplitudes of the *M*2, S2, N2, and *K*2 semidiurnal and *K*1, O1, P1, and *Q*1

diurnal constituents. In other locations, many more tidal constituents are needed to adequately represent the

tide. For example, over 100 constituents are needed for Anchorage, AK.

(g) Two categories of tidal constituents are necessary to reconstruct a tidal signal:

! Those that represent the elevation of the water surface.

! Those that specify a time and the phase shift associated with that time.

For example, the value for *H*n in Equation II-5-16 is the mean constituent amplitude and is a function of both

location and variations arising from changes in the latitude of the moon's node. The nodal effect of the moon

is reflected by the introduction of the node factor *f*n, which modifies each constituent amplitude to correspond

to a specific time period. Mid-year values are usually specified for reconstructed time series because node

factors vary slowly in time. Mid-year values for each constituent listed in Table II-5-3 are presented in

Shureman (1924) for the years 1850 through 1999. An example is shown in Table II-5-4 for the years 1970

through 1999. Equations for computing *f*n are given by Schureman.

(h) The second category of arguments specifies the phasing of high water for each constituent with

respect to both time and location. These arguments are based on the fact that phases of the constituents of

the observed tide do not coincide with the phases of the corresponding constituents of the equilibrium tide.

For example, a high tide does not occur directly beneath the moon. There is a lag between the location of the

tide-producing force (i.e., location of the moon) and the observed time of high water. This lag, due to

frictional and inertial forces acting on the propagating tide, is referred to as the epoch of the constituent and

is denoted by κn in Equation II-5-16.

(i) The relationship between the constituent arguments and high tide is shown in the schematic

Figure II-5-10. In this figure, the cosine curve represents the surface elevation in the y-direction as a function

of time or degrees of phase (maximum at 0 and 360 deg). For the *M*2 tidal constituent, the cosine curve has

a period of 12.42 hr (other constituent periods are indicated in Table II-5-3). Therefore, in Figure II-5-10,

the horizontal axis represents either time or phase, both increasing to the right. The value of κ represents the

actual phase lag required for the water surface to reach high water (HW) following the passing of the tide-

producing force. In the case of the semidiurnal constituents, this force is the crossing of the moon.

Water Levels and Long Waves

II-5-15

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