A statistical attribute of the connection 

 between concentration (or temperature) 

 and time that constitutes a trend is the 

 Spearman rank correlation coefficient. 

 In the case of carbon dioxide in Figure 

 5a, the Spearman correlation coeffi- 

 cient is 1 .0, as high a value as possible. 

 The annual changes are small, but they 

 occur invariably in the same direction. 

 The temperature record is not so clear, 

 because temperature in any one year is 

 not always higher than the year before. 

 Nevertheless, there is a trend in the 

 temperature data. The Spearman corre- 

 lation coefficient between temperature 

 and year in Figure 5b is 0.57, and for a 

 record with 1 34 observations the coeffi- 

 cient need equal only 0. 14 for a statisti- 

 cally significant indication of a trend (at 

 the 0.05 level) . The temperature record 



is "noisy" because many natural factors 

 determine temperature in any given year, 

 and extracting long-term trends requires 

 data over many years. The carbon-diox- 

 ide record, on the other hand, is abso- 

 lutely clear. The increase in carbon 

 dioxide is attributable to the human ac- 

 tivities of fossil-fuel burning and defor- 

 estation, and no natural factors are strong 

 enough to complicate the record of those 

 activities. 



If all the Mussel Watch concentration 

 time plots were shown, the vast major- 

 ity would look like the temperature 

 record in Figure 5b except they would 

 only be for four or five years. With only 

 five years of data, a trend cannot be 

 identified unless the Spearman correla- 

 tion is as high as 0.9. So to find a trend, 



31 5 



I 



_L 



I 



I 



1955 1960 1965 1970 1975 1980 1985 1990 



Year 



Figure 5a. Annual average atmospheric carbon dioxide concentration (Keeling and 

 Boden, 1986). 



21 



