BOTSFORD and WICKHAM: UPWELLING INDEX AND DUNGENESS CRAB CATCH 







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3 



Aoo r 



300 



200 



100 



-100 



-200 



-300 



California 

 Oregon 



Washington 



Figure 2.-Bakun's upwelling index for Washington, Oregon, and California (mean removed). Units are cubic meters of water upwelled 



per second per 100 m of coastline. 



where .v{j) = the value of process .r at time j 



(mean removed) 

 ^0) = the value of process y at time j 



(mean removed) 

 S^ = the sample standard deviation of 



process .r 

 Sy = the sample standard deviation of 



process y 

 n = the total number of samples. 



The result of this formula is the product- 

 moment correlation coefficient for each value of 

 lag I. A graph of Rj.y (i) along the ordinate and i 

 along the abscissa is termed the correlogram 

 (Kendall and Stuart 1968). Assuming that the 

 processes are stationary and ergodic, Rj.y is an es- 

 timate of the expected value of the product of the 

 two variables at each lag time. If x and y are 

 different processes, it is termed the cross-correla- 

 tion coefficient. If .r and y are the same process, it is 

 termed the auto-correlation coefficient. 



Because R^y is a sample statistic, the sig- 

 nificance of its value must be considered. Although 

 the technique is commonly used in time series 

 analyses, the sampling theory of serial correla- 



tions has been developed only for restricted types 

 of data (e.g., normally distributed data). Because 

 the significance decreases as n increases, the serial 

 correlation coefficient is usually only calculated for 

 lags up to 30% of the total length of the data. The 

 interpretation of our results depends only on lags 

 of this length. However, the results are presented 

 for lags beyond this length because they are of 

 interest. 



Another consideration in the computation of 

 serial correlations is that of trend removal (Ken- 

 dall and Stuart 1968; Ontes and Enochson 1972). 

 Trends in the data (linear or higher order) which 

 are not pertinent to the analysis are subtracted 

 from the data before the correlation coefficients 

 are computed. The trend is usually a deterministic 

 artifact of known origin which is not present in 

 the actual data of interest. Although upwelling, 

 and to some extent catch data, seemed to increase 

 over the 24 yr considered, this effect was not 

 irrelevant to the purpose of the analysis. The 

 results presented, therefore, include no trend 

 removal. However, computation of the correlation 

 coefficients was performed after trend removal 

 and the results were similar. 



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