Note On Correlation Coefficients Derived from Cumulative Distributions with Reference to Glaciological Studies

In many areas of glaciology, cumulative degree days, either positive or negative, are regressed against another cumulative value, such as ablation or lake-ice growth. Very strong functional relationships are frequently found with high correlation coefficients. This note shows that, if pairs of random numbers are cumulated, the resulting correlation coefficients are extremely high with a Fisher transformed mean of r = 0.986 and standard error of ±0.001 (based on 50 individual computations of r which in turn were based on 20 cumulated pairs of random numbers between 0 and 99). These results indicate that caution must be exercised in the physical interpretation of data of this kind.