give a poorer fit, although in the forty single-year fits there are some years with 

 poorer fits than those for longer periods. To compensate for the few years of 

 poor fits there are many years of excellent fits. The fact that for 33 years R 2 was 

 greater than 0.81 and for 23 years was greater than 0.86 substantiates this con- 

 clusion. 



To compare R 2 's for the various record lengths, L, the mean R 2 's for the 

 available runs of each length have been computed and 100R 2 's have been plotted 

 on figure 2. As expected the mean R 2 is a decreasing function of the length of 

 record, L. More unexpected is the actual shape of the curve. From L = 1 the 

 curve drops off sharply to somewhere between L = 5 and L = 10, from which point 

 on there is a negligible decrease in R 2 . 



The mean R 2 is plotted in preference to the mean R or to the mean of 



Fisher's Z = -^ log — — , since R 2 is easiest to interpret. In addition, the rela- 

 2 1 — R 



tionship of R to R 2 in the range of consideration of R 2 is so nearly linear that a 

 plot of mean R with appropriate scale changes cannot be distinguished from that 

 of mean R 2 . The relationship of Z to R 2 is such that the curvature of figure 2 

 would be even more emphasized if Fisher's statistic were plotted. The distri- 

 bution of R 2 is asymptotically normal for R ^ 0. 4 



Because of the dependence of the average R 2 among the samples from 

 which they were computed, and because of the autocorrelated residuals, the 

 development of confidence limits for these average R 2 's seems intractable. How- 

 ever, as a rough estimate of their variability, one standard deviation of the mean 

 R 2 is plotted as a vertical bar in figure 2. These standard deviations are given 

 by the formula: 4 



a (R')= 2RQ-R 2 ) (2) 



N 1/2 (365) 1/2 



They are computed under the assumption that repeated sampling over the same 

 N = 40 year period at Scripps Pier is possible. In this conceptually possible but 

 practically impossible situation, the deviations about the same mathematical 

 model of regression are assumed to be independent among the repeated samples. 



Under these assumptions the confidence limits for the plotted points are 

 narrow, and it is concluded that the sharp change in slope of the curve in the 

 region 5 < L < 10 is real. 



Attention is called to the systematic change in the absolute magnitude of 

 the average R 2 's, for the data for PAPA, ECHO, Langara Island, Cape St. James, 

 and Triple Island. This change appears to be associated with the exposure, or 

 "continentality," of the station — thus, PAPA and ECHO are typical of open- 

 ocean locations; Triple Island is much like an open-ocean location, being a very 

 small coastal island; and Scripps Pier is least like an open-ocean location with 

 the observations being made at the end of a 1000-foot pier. Cape St. James and 

 Langara Island have a "continentality" between Scripps Pier and Triple Island. 



