A-57 
1. Effects of Sampling Design on CFD Results. The CFD is a special case of an 
unbiased estimator for a cumulative distribution function of a population. Like 
the cumulative distribution function, the CFD is a function of the mean and the 
variance of the population being assessed. And the better the mean and vari¬ 
ance are characterized with sample data, the more accurate the shape of the 
CFD will be. As the sampling density increases, the estimated CFD begins to 
approach the true CFD. However, if the sampling density is low, then sampling 
error could become important and there is potential that it could affect the 
shape of the CFD and ultimately the accuracy of the compliance assessment. 
Furthermore the potential for the sample size to affect the shape could create a 
compliance assessment bias if the reference curve and assessment curve are 
based on different sampling densities. Conditional simulation methods devel¬ 
oped by STAC panel members showed promise toward resolving these issues 
and mitigating potential biases caused by differences in sample size. 
2. Statistical inference framework for the CFD. It is important in a regulatory 
process to differentiate an exceedance that is small and might have resulted 
from chance variability from those that are large and indicative of an inherent 
problem. This differentiation will require mathematical tools to quantify the 
variability in the CFD that occurs as a result of sampling. The STAC panel 
made progress on this issue by demonstrating a confidence interval procedure 
based on conditional simulation associated with kriging. It remains to be 
assessed whether or not confidence intervals produced by this algorithm 
perform at the nominal level of coverage, fore example, does a nominally 95% 
CFD confidence interval cover the true CFD 95% of the time. 
3. Choice of Interpolation Method. The STAC panel considered several inter¬ 
polation methods and outlined the features of each. Those features illustrate 
tradeoffs between ease of implementation and maximizing the information 
garnered from the data. Further work is needed to compare the features to the 
requirements of wide-scale implementation of assessment procedures and 
formulate a plan for tractable implementation that results in credible assess¬ 
ments. One strategy is to implement easily performed analysis (e.g. IDW) as a 
screening tool to identify cases where compliance / non-compliance is clear, 
and then implement more labor intensive methods (e.g. kriging) for cases 
where compliance is more difficult to resolve. One difficulty with imple¬ 
menting a full comparison of methods is that implementation of each method 
requires considerable work in terms of setting up file systems, interfacing soft¬ 
ware and data, and coupling the considerable bathymetry data of the bay. Thus 
it would be prudent to narrow the choices based on theoretical considerations 
where possible. 
4. Three-Dimensional Interpolation. Assessments of the dissolved oxygen 
criteria require three-dimensional interpolation. However, the field of three- 
dimensional interpolation is not as highly developed as that of two-dimensional 
interpolation. While the mathematics of each method extend easily to three 
dimensions, there are relatively few examples of 3-D interpolation available in 
the literature and issues such as data density requirements for reliable results 
are not well studied. Efforts are needed to further evaluate research in three- 
dimensional interpolation and seek additional outside scientific input and 
appendix a • The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
