VARIATION IN SOIL PLUTONIUM CONCENTRATIONS 169 



TABLE 2 Distances from the Source of Plutonium Release, Mean Plutonium 

 Concentrations in Soil, and Estimates of the Variance Components for the Model 



,5)* 



oj =0m,/ 



+ ol j for Each Transect (/ = 1 ,2, . 



*Each CT^ j-has df = 2, and each a^ ■ has df = 3. Mean concentrations are computed from all six 

 samples at each transect. 



of freedom associated with the a^ ^ and olj. The olj for 2 39 ,240 p^^ concentrations also 

 differed significantly among transects (Fmax. = 519,3; df= 5,3; P < 0,01) and tended to 

 decrease as the mean 2 3 9,2 4 op^^ concentrations decreased. 



Although the a^ ^ did not differ significantly among transects, there appeared to be a 

 positive correlation between a^ ,• and mean concentration for both ^^*Pu and 

 2 39,240py concentrations. The apparent correlations of a^,- and blj with mean 

 concentration suggested that o^ ^ and Qg / were proportional to mean concentration. 

 Proportional relationships between means and variances can be expected because 

 concentrations varied over a broad range and analytical error was controlled to plus or 

 minus a percentage of the measured value. The components a^ ,- and olj may also vary 

 because the statistical model was inappropriate (e.g., a linear model for a nonlinear 

 process) or failed to contain important causes of variation, such as soil type or 

 disturbance. The variation in a^ y and olj recorded in Table 2 probably resulted from a 

 combination of factors, including the proportionality between analytical error and 

 concentration, the nonlinear relationship between concentration and distance from the 

 point of release, a change in soil type between transects 3 and 4, and soil disturbances. 

 The impacts of the first three of these factors on our interpretations of the relative 

 importance of microtopographical heterogeneity and sampling error were evaluated by 

 comparing the interpretations resulting from applying more-complex statistical models to 

 the original arithmetic data as well as logarithmic transformations of the data. None of 

 the results for these alternative models affected our conclusions that sampling error was a 

 small fraction of the total variation or that microtopographical heterogeneity was more 

 important for 2 3 9,2 4 Op^^ ^.j^j^ ^^j. 2 3 8p^ Because some readers may be interested in 

 specific alternate interpretations, we have added the raw data as Table 3. 



