The implications of figure 2 are: 



1. A record of daily surface temperatures of 10-year length is adequate 

 for fitting a regression curve to estimate long-term variability. 



2. The unexplained long-term variability, that is, variability unexplained 

 by the regression model, varies from about 23 percent at Scripps Pier, for a 

 sample longer than 10 years; to less than 5 percent at PAPA and ECHO, both 

 one-year samples taken at exposed open-ocean locations. Since R 2 is not de- 

 graded by extending a record beyond 10 years, the estimates of regression co- 

 efficients based on 10 years are as adequate as those that might be obtained from 

 a longer record. In the same light, records of 5 years or less reflect shorter-term 

 variability in temperature and thus give an improved fit as record length decreases. 



Additional information on the length of time-series necessary for obtain- 

 ing long-term estimates of sea-surface temperature may be obtained from an exam- 

 ination of the autocorrelation function available from the 40 years of Scripps Pier 

 record. 



For the various samples of Scripps Pier data, the autocorrelation func- 

 tions were determined for the time-series consisting of the differences of the ob- 

 served surface temperatures and the temperatures estimated by the fit of combined 

 annual and semiannual terms, equation (IB) (fe = 2). The functions were computed 

 for lags at intervals of 5 days up to 900 days in most cases. Consider first the 

 autocorrelation functions for the eight different 5-year samples of data plotted in 

 figure 3. There is considerable variability among the functions. It would be 

 desirable to compute some measure of this variability, and compare it with the 

 corresponding variability of the autocorrelation functions for the 8-, 10-, and 

 20-year records of figure 4. 



Before computing any such measure, we have to make a decision as to 

 the range of lags to use in the comparison. The value of the standard deviation 

 of the nonsignificant autocorrelations, a c for the 40 years of Scripps Pier data is 

 0.0293. 3 For a 10-year record a c = 0.0586, and the 95 percent significance values 

 are ±0.115. For reasons previously discussed, a 10-year record of sea-surface 

 temperature is needed in order to obtain reliable estimates of the long-term vari- 

 ability. Thus it is not necessary to consider 5- or 8-year records in selecting the 

 range of lags to use. If we assume the 40-year autocorrelation function is close 

 to the true function, lags out to 145 days yield autocorrelations greater than 0.115 

 and can be used to compare the sets of functions. 



For the set of autocorrelation functions based on samples of length L 

 years and for each lag r = 5(5)145 days, we determine the following sum of squares: 



40/L 



= y i 



.7=1 



4U/ p 



,L)= y [C,(r)-C(V)] 2 



11 



