FISHERY BULLETIN: VOL. 69. NO, 1 



ing to Tabata's table the standard error of the 

 mean for July 1959 is for twice daily sampling 

 every day 0.086° C, and for twice daily sampling 

 every seventh day 0.253° C. For the same 

 sampling frequencies in May 1961 the standard 

 errors of the mean are 0.053° and 0.15° C, re- 

 spectively. For the May 1961 Koko Head tem- 

 peratures the standard error of the mean is 

 0.055° C with 25 samples and 0.16° C with 

 sampling every fifth day. The standard error 

 of the mean for the May 1961 Koko Head sa- 

 linities is 0.010'/,, with 25 samples and 0.024',, 

 with sampling every fifth day. On the basis 

 of these considerations, the expected values ob- 

 tained from the temperature functions have an 

 uncertainty of ±0.10° C, and those from the sa- 

 linity functions have an uncertainty of ±0.015'/(c 

 when samples are obtained twice weekly. 



At Christmas Island temperatures are sampled 

 daily rather than twice weekly as at Koko Head. 

 In consequence, despite the larger variability, 

 expected values obtained from the harmonic 

 functions have approximately the same uncer- 

 tainty as those obtained from the Koko Head 



harmonic functions. This statement is con- 

 firmed by considering the error terms that can 

 be obtained by taking the difference of the ex- 

 pected values at the midpoint of the 30-day over- 

 lap portion of the Christmas Island temperature 

 functions (see appendix D). On average this er- 

 ror term is 0.07° C and ranges from to 0.26° C. 



SOME PROPERTIES OF THE TEMPERATURE 

 AND SALINITY DISTRIBUTIONS 



Although the harmonic functions are merely 

 analytic expressions of the temperature and sa- 

 linity as a function of time, they do provide, to 

 some extent, insight into the nature of the dis- 

 tributions. For instance, the monthly standard 

 error of estimate, mentioned in the previous 

 section, provides a measure of the month-to- 

 month changes in variability. At Koko Head 

 there is no seasonal pattern in this variability 

 of the temperature; however, there is a seasonal 

 pattern in the variability of the salinity. The 

 monthly standard errors of estimate of the sa- 

 linity function with harmonic analysis carried 

 out to n = l;i, are listed in Table 4. 



Table 4. — Standard error of estimate (/(c) for each month, 1956-68, of the Koko Head salinity. Harmonic 



analysis is carried out to n = 13. 



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