SECKEL and YONG: HARMONIC FUNCTIONS 



Quality control of the data was achieved by 

 two passes of the data through the computer. 

 First, the fitted graphs and plots of the observed 

 values as well as listed deviations of observed 

 values from the functions that resulted from the 

 first computer analysis were used to reject ob- 

 viously erroneous observations. The analysis 

 was then repeated without the rejected obser- 

 vations. The tabulations in appendix A and 

 figures in appendix B are the result of the second 

 pass through the computer. The rejected val- 

 ues are plotted and identified in the figures of 

 appendix B. 



APPLICATION TO CHRISTMAS ISLAND 

 SEA-SURFACE TEMPERATURES 



The Christmas Island sea-surface tempera- 

 tures are measured with a bucket thermometer 

 each morning (about 0900 local time) in the 

 channel leading from the open sea to the lagoon. 

 The diff'erences between open sea and lagoon 

 water temperatures have not been determined. 

 It is reasonable to assume that these tempera- 

 tures diff'er, and so introduce variability in the 

 observed temperature as tidal currents in the 

 channel change from day to day. The tide- 

 induced variability will, however, not be reflected 

 by a harmonic function where the resolution of 

 the highest harmonic is longer than 1 month. 

 Although the sampling site is not ideal, the ob- 

 served temperatures are believed to reflect, with 

 some bias induced by lagoon temperatures, the 

 changes of sea-water temperature from month 

 to month. 



The procedure to obtain functions of the 

 Christmas Island temperatures was the same 

 as that used for the Koko Head temperatures 

 and salinities with the exception that a difl'erent 

 fundamental period was chosen. In contrast to 

 Koko Head where an annual cycle dominates the 

 sea-surface temperature, longer term changes 

 dominate the temperature at Christmas Island. 

 The basic temperature pattern at Christmas 

 Island also changes from year to year. For these 

 reasons a duration of 120 days was chosen as 

 fundamental period and Fourier analysis was 

 performed, as before, on the residuals of the 

 observed values from a linear fit. 



For each year, the 120-day periods followed 

 in sequence with an overlap of 30 days. The 

 periods ran from the first day of the year to 

 day 120, from day 91 to day 210, from day 181 

 to day 300, and from day 271 to day 390, ex- 

 tending 25 days into the following year. In 

 this manner rapid convergence of the harmonic 

 function to the best fit was obtained. 



With daily sampling and a fundamental per- 

 iod of 120 days, harmonic analysis could be car- 

 ried to the harmonic n — 30, but to do so would 

 introduce variability that we wish to smooth out. 

 Although a resolution of 1 month requires har- 

 monic analysis to w = 4 only, the analysis was 

 arbitrarily carried out to n ~ 7, resolving a 

 period of 16 days. 



The resulting phase angles and coefficients for 

 1954-69 of the sea-surface temperature are listed 

 in appendix C. The functions for each year 

 together with the observed values have been 

 drawn by automatic plotter and are presented 

 in appendix D. 



Quality control procedures were identical to 

 those for the Koko Head analyses. Relatively 

 large data gaps occurred at Christmas Island 

 in 1964, 1967, and 1968. Because some obser- 

 vations were available during each of the 120- 

 day periods in question, harmonic analysis pro- 

 duced coefficients that enabled drawing of curves 

 in appendix D although there were no data. 

 These curves were not erased since it is in- 

 structive to see what harmonic analysis will do 

 when faced with insufficient data. 



DISCUSSION OF RESULTS 



In this paper we are concerned with the deri- 

 vation and presentation of harmonic functions 

 of regularly observed sea-surface temperatures 

 and salinities at fixed stations rather than with 

 oceanographic interpretations. In the discussion 

 of the results we will, therefore, concern our- 

 selves primarily with the quality of fit of the 

 functions. We will also briefly discuss some 

 properties of the temperature and salinity dis- 

 tributions that are reflected by the functions and, 

 finally, show functions spanning the entire time 

 of observations. 



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