A-31 
variability. The reference and attainment curves follow the same general approach in 
derivation—water quality data collection, spatial interpolation, comparison to 
biologically-based water quality criteria, and combination of space-time attainment 
data through a CFD. Therefore, the biological reference curve allows for implemen¬ 
tation of threshold uncertainty as long as the reference curve is sampled similarly to 
the attainment curve. Bias and uncertainty are driven in CFD curves by sample 
densities in time and space. Therefore, we advise that similar sample densities are 
used in the derivation of attainment and reference curves. As this is not always 
feasible, analytical methods are needed in the future to equally weight sampling 
densities between attainment and reference curves. 
4.2. CBP DEFAULT REFERENCE CURVE 
In some cases, the development of biologically-based reference curve is not possible 
due to lack of data describing the health of the relevant species. In such cases, a more 
arbitrary approach is required since better information is not available. EPA recom¬ 
mends the use of a default curve in cases where a biologically-based one is not 
available. That default curve is defined by these properties: 
1. symmetric about the 1:1 line, 
2. hyperbolic, 
3. total area = 0.1, and 
4. pass through (1,0) and (0,1) 
(see EPA, 2003; page 174). The equation that describes this figure is defined by the 
equation: 
(x+b) * (y+b) = a 
Where: b = 0.0429945 
a = b : + b 
This reference curve is illustrated in Figure 4.1 by curve 1. 
An alternative default reference curve might be formulated by extending the arbi¬ 
trary allowance of 10% exceedance into the two dimensional framework of the CFD. 
The criterion threshold is a value that should be rarely exceeded by a population at 
healthy levels. When the population is unidimensional, say concentration in a point 
source effluent, then one can obtain this upper threshold based on the simple distri¬ 
bution of values in a healthy population (Figure 4.2). The ninetieth percentile of this 
distribution might be chosen as the criterion threshold. Thus in this example, 10% 
noncompliance is allowed because this level of noncompliance is expected in a 
healthy population. A standard technique for estimating distribution percentiles is to 
assume a mathematical form for the distribution, e.g., the normal distribution, and to 
estimate the percentile as some number of standard deviations above the mean. The 
90th percentile of the normal distribution is 1.2815 standard deviations above the 
mean. 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
