A-33 
Figure 4.2. Hypothetical lognormal distribution that might be typical of Chlorophyll. 
The figure illustrates the relation of the geometric mean and the criterion threshold 
set at the 90th percentile. 
where 1.2815 is the 90th percentile of the standard normal distribution. Thus (assum¬ 
ing normality) a population with spatial and temporal variance characterized by o 2 a 
and o 2 ^ that has a mean that is 1.2815*a below the threshold criterion should have 
an exceedance rate of 10% over space and time. Note that the reference curve is 
determined by the ratio o 2 Jo 2 ^ and the distance in standard deviations of the mean 
from the threshold. The actual values of the variance components, the mean, and the 
threshold, are not important as long as the relationships hold. Thus as long as the 
variance ratio is consistent, and mean to threshold distance is a fixed number of stan¬ 
dard deviations, the same reference curve will serve for all seasons and regions. 
Letting chlorophyll observed in the decade of the 1960s serve as a reference popu¬ 
lation, the parameters in Table 4.1 can be used to construct this reference curve based 
on the variance ratio and the mean to threshold distance given in the table. The ratio 
° 2 a /° 2 ti * s computed as the ratio of the temporal variance term and the spatial vari¬ 
ance term. The mean to threshold distance is computed to be 1.2815a for all regions 
and seasons. Based on there parameters, a reference curve for chlorophyll can be 
derived (curve 3 , Figure 4.1). For comparison a reference curve based on a variance 
ratio of 1.0 (curve 2, Figure 4.1) and the standard CBP reference curve (curve 1, 
Figure 4.1) are also shown. 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
