A-35 
of the CFD and discuss the complications that arise from these properties when the 
CFD is used as an assessment tool. After defining the population which determines 
the CFD. we go on to discuss the currently proposed sampling and estimation 
scheme, sources of error in the estimation scheme, and problems that result from 
these. The goal is to succinctly define these problems and elucidate possible solu¬ 
tions. This section will cover: the behavior of the CFD as a function of temporal and 
spatial variance, methods for construction CFD reference curves, the influence of 
sampling and estimation variance on the CFD shape, and feasible methods for devel¬ 
oping statistical inference tools. 
5.1 REVIEW OF CFD PROPERTIES 
With any statistical application, it is important to distinguish between the true 
descriptive model underlying the population being sampled and the estimate of this 
model derived from the data collected in a sample. As described above, the CFD has 
a data driven definition where the CFD is constructed based on a sample from a 
population for some water quality parameter. This population is a continuous 
random process over space and time. 
In order to quantify the statistical properties of the CFD, the CFD is defined in terms 
of a population of experimental units. This approach is a discrete approximation of 
the continuous random process in both time and space. However, the estimation 
scheme involves interpolation to discrete units in a spatial dimension and discrete 
days in the temporal dimension. To facilitate an understanding of the relation of the 
estimator to the true population, it seems reasonable to use a discrete approximation 
as the model for the true population. 
5.2 DEFINING THE CFD IDEAL 
The population will be defined as having different sizes of experimental units in 
much the way we think of a population that gives rise to a nested design or repeated 
measures design. The Chesapeake Bay will be partitioned into segments. Assessment 
will be done for each segment based on a three year record of the segment. Thus a 
three year period for the segment defines the entire population that will be parti¬ 
tioned into experimental units. The continuous time dimension is partitioned into 
days to form the primary units which are the state of a segment for a day. Call this a 
Segment-Day. Let there be M segment-days in the assessment period (typically 3 x 
365). The continuous spatial dimension is partitioned into N 3-dimensional cells 
(may range from hundreds to thousands). The state of each cell for a day will be a 
unit nested within the segment-day. The attribute of interest will be a measure of 
water quality for each cell for a day. Examples might be the mean level of Chloro- 
phyll-a in the cell for one day or the minimum of dissolved oxygen in the cell during 
the day. Let Y be a random variable for the attribute of interest and consider the 
following model 
Yj(sj) =n + +/?j(Sj) Eqn 5.1.1.1 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
