SECKEL and YONG: SEA-SURFACE TEMPERATURES AND SALINITIES 



tions again during 1965-68. These modulations 

 are of a long-term nature but do not appear to 

 be related with the variations shown in panel B 

 of Figures 1, 2, and 3. 



On the Separation of Variability 

 Into Various Time Scales 



Although there are a number of curve-fitting 

 procedures such as were reviewed by Holloway 

 (1958), we have found Fourier analysis to be a 

 convenient method for the Koko Head and Christ- 

 mas Island time series. The filtering described 

 above is a byproduct of this method and serves 

 interpretive and descriptive purposes. 



Although the moving average method is not 

 recommended for climatological time series, 4 it 

 is commonly used. For this reason, curves ob- 

 tained by the moving average and the harmonic 

 analysis methods are compared in Figures 7 and 8. 

 The long-term as well as the residual curves of 

 the two procedures are similar though not identi- 

 cal. The amplitudes of the long-term variations 

 are larger in the curves derived by harmonic 

 analysis than in those derived by the moving 

 average method. This difference is to be expected 

 because, in contrast to the harmonic method, 

 input values in the moving average method are 

 weighted equally. 



The examples in Figures 7 and 8 were chosen 

 because they illustrate limitations, in terms of 

 physical interpretations, of the filtering tech- 

 niques. A time series of the sea-surface tempera- 

 ture (salinity) is the signature of processes that 

 govern the observed changes. What information 

 about the governing processes, then, can be 

 inferred from the time series? For example, is 

 the observed change of temperature the result 

 of an anomaly in the local heat exchange across 

 the sea surface and advection produced by the 

 local wind driven current, or is this temperature 

 change a part of a larger scale change with the 

 local processes remaining normal? The examples 

 in panel B of Figures 7 and 8 exhibit variations 

 with an annual periodicity during 1957 in the 

 Koko Head salinity and during 1963, 1964, and 

 1965 in the Christmas Island temperature al- 

 though this periodicity is not apparent in panel 

 A of Figures 2 and 3. In these cases were annual 



variations, such as produced by annually varying 

 processes, present or were they absent? 



In the case of the moving average method, 2 yr 

 of data are required to provide the smoothed curve 

 for a single year. At Koko Head the normal mid- 

 year declines in salinity occurred during 1956 

 and 1958, affecting the shape of the smoothed 

 1957 curve. Consequently the residual curve 

 showed an annual variation during 1957 (Fig- 

 ure 7B). At Christmas Island (Figure 8B), the 

 residual temperature curve during 1964 also 

 exhibits an annual variation, a maximum in 

 spring and a minimum in fall, although no sea- 

 sonal trends were indicated during the adjacent 

 years (Figure 3A). In this case, was the normal 

 annual variation in temperature present but 

 obscured by the long-term trend? 



In the harmonic analysis procedure the dom- 

 inant signal in the annual variation is produced 

 by the annual sinusoid. The amplitude of this 

 period is determined by all the data in the series 

 and contributes the same amount to the short- 

 term variations of every year shown in panel C 

 of Figures 1, 2, and 3. For example, a time series 

 could be synthesized by combining a long-term 

 variation with one that has an annual periodicity 



1956 



1957 



1958 



1959 



"Climate change. Tech. Note 79, WMO-No. 195, Tp. 100. 

 Seer. World Meteorol. Organ., Geneva, Switz., 1966, 79 p. 



FIGURE 7.— Koko Head salinity, 1956-59: A. Long-term varia- 

 tion produced by 12-mo moving average and by harmonic func- 

 tion (n = 1-17). B. Short-term variation (monthly input values 

 minus long-term values). Solid line — 12-mo moving average; 

 dashed line — harmonic function (/i = 1-17). 



775 



