A-32 
Figure 4.1. Illustrations of three reference curves: 1) the standard CBP reference curve 
derived to cover 10% of the percent space by percent time plane (curve 1); 2) a reference 
curve based on 10% exceedance frequency and a temporal-spatial variance ratio of 1.0 
(curve 2); and 3) a reference curve based on 10% exceedance frequency and a temporal- 
spatial variance derived from chlorophyll data (curve 3). 
When regulating populations that are distributed in both space and time, this simple 
concept for regulating noncompliance must be extended to account for the variability 
in each dimension. While there is some added complexity in the mathematics, the 
fundamental concept remains the same: That is, to set the criterion threshold at a 
certain distance above the mean so that exceedance of that threshold will be rare in 
a healthy population. In this case, the distance by which the threshold must exceed 
the mean is a function of both the spatial and temporal variance components as 
described below. 
To establish these criteria thresholds for populations with two components of vari¬ 
ance, assume the simple model: 
Yj(Sj) + a x + PiiSj) 
where: 
H is the desired mean level of chlorophyll (in log space) 
a, is a random term for variation over time with variance a 2 , 
is a random term for variation over space with variance o 2 p 
Yj(Sj) is a water quality constituent measured at time i and location Sy 
The variance of Xy is u 2 a + a 2 ^ = a 2 . The standard dev of x is is sqrt(er) = o. It is 
common to allow an overall 10% exceedance rate without declaring an assessment 
unit out of compliance. We would expect 10% of the x is to fall above /u + 1.2815*a 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
