14 
No specific theoretical basis underlies this definition of the default reference curve, 
but the definition does provide equal weight to exceedances occurring in either space 
or time. This approach is appropriate since no information exists to indicate that 
either time or space should take precedence. Selection of the 10 percent value is 
based on its consistency with past national EPA guidance (U.S. EPA 1997). The 
default reference curve is hyperbolic, making it similar in shape to biologically 
based reference curves. In fact, the shape of the default reference curve is quite 
similar to some of the established biologically based reference curves, such as the 
30-day mean open-water dissolved oxygen reference curve (Figure 11-5). 
Figure 11-5. Biological reference curve for 30-day mean open-water dissolved oxygen 
criterion applied for assessment during the summer months (June-September) only. 
A default reference curve, defined as a hyperbolic curve encompassing no more than 
10 percent frequency exceedances, was also considered. Such a curve is based on a 
simple model: 
Xjj = u + aj + bj Equation 2 
where a is temporal term with variance <F 2 a and b is spatial term with d> 2 b . The vari¬ 
ance of x^ is <t> 2 . d + <I> 2 b = d> 2 . The standard deviation of x,j is sqrt(<5> 2 ) = <t>. Ten 
percent of the Xy should fall above u + 1.2815 * where 1.2815 is the 90th 
percentile of the standard normal distribution. Thus, assuming normality, a popula¬ 
tion with equal spatial and temporal variance and a mean that is 1.2815 * below 
the threshold criterion should have an exceedance rate of 10 percent over space and 
time. Figure II-6 shows the CFD for the 10 percent frequency exceedance default 
reference curve in black. 
chapter ii 
Refinements to the Chesapeake Bay Water Quality Criteria Assessment Methodology 
