FISHERY BULLETIN: VOL. 69. NO. I 



1st and 16th of each month from the harmonic 

 functions whose phase angles and coefficients 

 are tabulated in appendixes A and C. Harmonic 

 analysis was carried to w = 42 for the Koko 

 Head temperature and salinity, and n = 48 for 

 the Christmas Island temperature, giving in 

 each case a 4 months' resolution. The fitted 

 curves resulting from this analysis are shown 

 in Figure 3, together with the values that were 

 used as input data. Clearly the annual cycle 

 forms the dominant signal in the Koko Head 

 temperature curve. In the Koko Head salinity 

 and Christmas Island temperature curves longer 

 term changes are more pronounced than the an- 

 nual cycle. 



The relatively large deviations of the input 

 data from the long-term function are to be ex- 

 pected. The figures of appendixes B and D show 

 that variations with a duration of less than 4 

 months can be relatively large and are not re- 

 solved by the long-term analyses made. 



The spectra of the long-term harmonic func- 

 tions for the Koko Head temperatures and sa- 

 linities and the Christmas Island temperatures 

 are shown in Figure 4. 



As is also apparent from Figure 3, the spec- 

 trum of the Koko Head temperature function is 

 distinct fi'om those of the Koko Head salinity 

 and Christmas Island temperature functions. 

 In the former the 12-month period has the most 

 pronounced amplitude, but in the latter two, al- 

 though the annual period has a large amplitude, 

 the amplitudes of longer period changes are 

 large and for some periods exceed those of the 

 annual period. 



CONCLUSION 



The results of this paper show that sea-surface 

 temperatures and salinities regularly monitored 

 at island sampling stations can be expressed by 

 harmonic functions of time. Advantages of an- 

 alytic expressions for the temperature and salin- 

 ity were cited in the introduction. Important 

 applications will be in climatic oceanography 

 where one may wish to filter out undesired "back- 

 ground noise." At Christmas Island, for ex- 

 ample, the short-term variability with a dura- 

 tion of 1 month or less can be filtered out by 



using only the harmonic terms to n = 3 in the 

 quarterly functions. At Koko Head, the vari- 

 ability with duration of less than 50 days, that 

 may be due to large geostrophic or island-in- 

 duced eddies, can be filtered out by using only 

 the harmonic terms to w = 7 in the annual 

 functions. 



We mentioned in the introduction that the 

 rates of change of temperature reflect the cli- 

 matic processes of change and that distortions 

 or aliasing may occur when monthly mean 

 temperatures are used to compute the change 

 of a property. Consider, for example, the Christ- 

 mas Island temperatures from March to May 

 1968 (appendix D, days 61 to 152). In Table 5 

 are listed the monthly mean observed temper- 

 atures, the month-to-month changes of mean 

 temperature, the expected temperatures from the 

 harmonic functions for the 16th of each month 

 (computed with harmonic terms up to w = 4), 

 and the month-to-month changes of expected 

 temperatures. It is clear from this illustration 

 that the use of mean values would result in an 

 underestimate of the rise in temperature from 

 March to April, and would obscure the decline 

 in temperature from April to May. The ex- 

 ample is not isolated and other instances can 

 be found in both the Koko Head and the Christ- 

 mas Island data. 



Table 5. — Month-to-month temperature differences using 

 mean observed temperatures and expected tempera- 

 tures from the harmonic function, Christmas Island, 

 March to May 1968. 



Mean 

 temperature 



Change of 



mean 

 temperature 



Expected 

 temperature 



Change of 



expected 



temperature 



March 1968 

 April 1968 

 May 1968 



° C 



25.1 



26.0 

 26.2 



' C 

 09 

 0.2 



° C 



25.1 



26.3 

 26.0 



' c 



1.2 



-0.3 



The results also aid in the choice of an opti- 

 mum sampling frequency. Both the desired 

 confidence limit and the desired resolution must 

 be considered. If the harmonic functions are 

 to be used in monitoring the oceanographic 

 climate as is the case of those presented in this 

 paper, then the limits of about ±0.1° C for the 

 expected temperature value and ±0.02%<! for 

 the expected salinity value are adequate. As- 



192 



