where D is time measured in days from some arbitrary origin, and T' is the 

 fitted value of the surface temperature. Fitting equation (IB) to the ob- 

 served surface temperature, T, using the method of least squares yields 

 estimates of the regression coefficients, /S, and an estimate of the variance 

 of f . The amplitude a and phase Q can be obtained from the /3's. The quantity 

 t is the random error of residual term. 



TABLE 1. LOCATION OF SEA-SURFACE TEMPERATURE TIME-SERIES 



Location 



Time Period 



Weather Ship PAPA 



1/56-8/62 



50°N 145°W 



6 yr 7 mo 



North Pacific 





Weather Ship ECHO 



9/49-9/56 



35°N 48°W 



7yr 



North Atlantic 





Cape St. James 



1/35-1/61 



52°N 131°W 



21 yr (5 yr 



North Pacific 



missing) 



Triple Island 



1/40-1/61 



54°N 131°W 



21 yr 



North Pacific 





Langara Island 



1/41-1/61 



54°N 133°W 



20 yr 



North Pacific 





Scripps Pier 



1/21-1/61 



33°N 117°W 



40 yr 



North Pacific 





An integral part of any estimation problem is the determination of the 

 reliability of the estimate as measured by the variability of observed data about 

 the estimated values. As a measure of this variability consider the statistic R 2 , 

 the fraction of variability explained by a statistical fit. Equation (IB) was fitted 

 to the Scripps Pier data using samples within the 40 years of lengths 1, 5, 8, 10, 

 20, and 40 years. This resulted in the following samples: forty 1-year, eight 5- 

 year, five 8-year, four 10-year, two 20-year, and one 40-year. 



Figure 1 summarizes the R 2 statistic for records of various lengths for 

 the Scripps Pier data. In general, a single year's data are expected to yield a 

 higher R 2 than would several years of data, where year-to-year variations would 



