A-42 
Increasing the spatial and temporal variance together has the opposite effect of 
decreasing the population mean. The CFD tends to move in a direction of noncom¬ 
pliance. Thus compliance as measured by the CFD depends on the relative values of 
the population mean, the temporal and spatial variance, and the criterion threshold. 
Increasing the population mean has the same effect as decreasing the criterion 
threshold. Increasing population variance has the same effect as increasing the mean 
or decreasing the criterion threshold. In a sense, the CFD is measuring the distance 
between the population mean and the criterion threshold in units of variance analo¬ 
gous to a simple t-test. A nuance introduced here that has no analogy in the t-test is 
that the ratio of spatial to temporal variance controls the symmetry of the curve. 
5.4 UNCERTAINTY AND BIAS 
In Section 5.1., it was shown that the shape of the CFD is a critical element to deter¬ 
mining compliance. Thus it is important that this shape be primarily determined by 
the state of compliance of a segment and not be influenced by factors not relating to 
the status of compliance. Because the CFD is constructed based on data that are a 
sample from the whole, it is clear that some uncertainty in the CFD will result. In 
addition, the CFD is a function of the empirical distribution function (EDF) of frac¬ 
tion of space in compliance. The shape of this EDF is determined by the mean and 
variance of the sample. Thus any factor, such as sample size, that affects the preci¬ 
sion of the fraction of space estimate, will affect the shape of the CFD. In this section 
we review the effect of noncompliance factors on the shape of the CFD. 
Sample Size and Shape 
As noted, because the CFD is a function of the EDF of estimates of “fraction of 
space”, any factor affecting the precision of the estimate of fraction of space in 
exceedance will affect the shape of the CFD. In particular, the number of samples 
used for each p-hat (% exceedence) will affect precision. For a given segment, this 
fraction will be estimated more accurately if twelve samples are used to form the 
interpolated surface rather than six. Because of unknown spatial dependence in the 
data, it is difficult to analytically quantify the magnitude of this sample size effect. 
Therefore simulation analysis was employed to address this issue. 
Numerous simulation tests were performed. These begin with a simulation of struc¬ 
turally simple data that have no temporal or seasonal trend and progress to simulated 
data that mimic the temporal and spatial structure of observed data. Because the 
results from this latter simulation are most relevant, these are the results that are 
presented and discussed. 
Simulation Experiment 
Simulated data were created to mimic the properties of surface chlorophyll in the 
Patuxent estuary. Data were created to fill a 5 by 60 cell grid which approximates 
the long and thin nature of an estuary. These data have mean zero and a spatial 
variance-covariance structure chosen to approximate the spatial variance-covariance 
structure of cruise-track chlorophyll observed in the Patuxent estuary. Thirty-six 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
