GULF OF MEXICO 



113 



CHARACTERISTICS FROM HARMONIC 

 CONSTANTS 



From the hannonic constants formulae may be 

 developed not only for determining the type of 

 tide but also various characteristics of the tide. 

 For precise results the formulae are rather involved 

 and require other of the harmonic constants thaa 

 those listed in table 3. For general purposes, 

 however, simplified formulae are convenient for 

 determining such characteristics approximately. 



In the semidaily type of tide M2 and S2 are the 

 principal components. Spring tides come when 

 they conspire, and neap tides, when they are 

 opposed. Hence, the formula 2.0 (M0 + S2) gives 

 an approximate value of the spring range, and 

 2.0 (M2 — S2) gives an approximate value of the 

 neap range. The mean range is given approxi- 

 mately by 2.2M2. 



In the daily type of tide Ki and Oi are the 

 principal constituents. Wlien Ki and d con- 

 spire, tropic tides occur, and the formula for the 

 tropic range, 2.0 (Ki + O,), gives an approximation 

 to the tropic range. The mean range for a daily 

 type will be given approximately by 1.5 (Ki+d). 



In the mixed types of tide things are more 

 complicated, but the formulae for the ranges of 

 the semidaily type may be used for the mixed 

 semidaily, and the formulae for the daily tides 

 may be used for the mixed diurnal. 



In the discussion of the combination of com- 

 ponent tides (p. 106), it was found that the phase 

 relations between the daily and semidaily com- 

 ponents determined whether the inequality would 

 be featured principally in the high or low waters 

 or equally in both. The following rule applies: 

 If the difference between M2° and (K,° + Oi°) is 

 zero, the inequality is wholly in the high waters; 

 if the difference is 90°, the inequality is exhibited 

 in equal degrees in both high and low waters; if 

 the difference is 180°, the inequality is wholly in 

 the low waters. In the application of this rule, 

 the difference between M2° and (Ki°-FO,°) is 

 taken without reference to the sign of the result, 

 and when this difference is greater than 180°, it is 

 to be subtracted from 360°. 



To exemplify the use of this rule, we may apply 

 it to the harmonic constants in table 3 for Key 

 West, Cedar Keys, Galveston, and Habana. 

 From table 3, the values of M2°-(Ki° + 0,°) 

 are, disregarding the sign of the result: Key West, 



641°, or after subtracting from 2 X 360° gives 

 79°; Cedar Keys, 122°; Galveston 152°; Habana 

 32°. In accordance with the above rule. Key 

 West with a value of 79° should exhibit inequality 

 in both the high and low waters with the high 

 water inequality somewhat the higher; Cedar 

 Keys, with 122° should likewise exhibit inequality 

 in both the high and low waters but with the 

 greater inequality in the low waters; Galveston, 

 with 152° should exhibit the inequality principally 

 in the low waters; Habana, with 21° should have 

 its inequality principally in the high waters. 

 Looking back to figures 23, 24, and 26, it is found 

 that the tide curves at these places conform to the 

 findings from the harmonic constants. 



In the discussion of the different types of tide, 

 spring tides were defined as those coming "near 

 the times of new and full moon" and tropic tides 

 were defined as those coming "when the moon is 

 near its maximum semimonthly declination." 

 This somewhat indefinite phraseology is necessary 

 because between any astronomical occurrence and 

 the resulting maximum effect upon the tide there 

 is usually a lag. In the spring or neap tides this 

 lag is known as the phase age, and for the tropic 

 or equatorial tides it is known as the diurnal 

 age. These ages vary from place to place but can 

 very readily be computed from the harmonic 

 constants. In hours, the phase age is given by 

 the formula 0.98 (S2°-M2°) and the diurnal age 

 by 0.91 (K,°-0,°). Thus, from table 3 we find 

 that at Key West, spring tides come 0.98 (101 — 77) 

 = 23.5 hours, or a day after full or new moon; 

 and at Pensacola, tropic tides come 0.91 (56 — 47) = 

 8 hours, or a third of a day after the moon's 

 maximum semimonthly declination. 



The harmonic constants lend themselves to the 

 derivation of various other features of the tides, 

 but the necessary formulae and calculations are 

 rather involved and would be out of place here. 

 The interested reader is referred to U. S. Coast 

 and Geodetic Survey Sp. Pub. 260, Manual of 

 Harmonic Constant Reductions. 



DISTURBING EFFECTS OF WIND AND 

 WEATHER 



The regularity in the periodic rise and fall of 

 the tide and in its cyclic variation is subject to 

 the disturbing effects of changing meteorological 

 conditions. These disturbances arise primarily 



