18 
Currently, limited pointwise attainment determination compliance has been im¬ 
plemented. For example, the open-water 30-day mean dissolved oxygen criterion is 
5 mgxliter' 1 , except when the ambient salinity drops below 0.5 psu and the criterion 
becomes 5.5 mgxliter' 1 (U.S. EPA 2003a). During the summer months, the open- 
water designated use boundaries are selected based on local density conditions 
reflecting stratification of the water column. 
Even the simplicity of this concept diminishes when examining interpolation error. 
Consider the assessment of two interpolator cells from an interpolation based on 
cruise track data. While both interpolations could have the same value, each could 
have a different level of error. Such different levels of error could mean that these 
were different probabilities that the criteria were actually exceeded. For the simple 
assessment of non-attainment, however, they count the same. Thus, one advantage of 
a statistical framework is that it accounts for different levels of error throughout the 
interpolation grid and these error levels could be incorporated into a single overall 
assessment of attainment. 
Step 5—Percent Non-Attainment in Space 
Computing a percentage should also be simple. The estimate is simply 100 times the 
number of cells not in attainment divided by the total number of cells. As a rule, the 
uncertainty of a binary process can be modeled using a binomial distribution. The 
issue of uncertainty described in step 3 propagates into computing the percent of 
attainment for a segment. In addition, estimated values for interpolator cells have a 
complex dependence structure, ruling out a simple binomial model. The rules 
governing the uncertainty of this step are also complex. The mathematics for 
modeling this propagation of error are feasible, but have not yet been developed. 
Step 6—Percent of Time 
While the CFD’s percent-of-space coordinate provides a simple interpretation of the 
percent of the spatial assessment unit that is out of attainment on a given date, the 
percent-of-time coordinate is not simply the percent of time out of attainment at a 
given point. Instead this coordinate is interpreted similarly to that of a cumulative 
distribution function; it represents the percent of time that the associated spatial 
percent of non-attainment is exceeded. For example, if the (percent space, percent 
time) coordinates for a point on the CFD are (90, 10), the spatial percent of non¬ 
attainment is greater than or equal to 90 percent about 10 percent of the time. 
This step is very similar to computing an empirical distribution function, which is an 
estimator of a cumulative distribution function. This similarity brings to mind 
statistical inference tools associated with empirical distribution functions—the 
Kolmogorov-Smimov, Shapiro-Wilk, Anderson-Darling, or Cramer-von Mises — as 
candidates for inference about the CFD (STAC 2006). These procedures model 
uncertainty as a function of sample size only (in this case, the number of sample 
dates). Since they do not account for uncertainty associated with the number of 
chapter ii 
Refinements to the Chesapeake Bay Water Quality Criteria Assessment Methodology 
