A-45 
iments will be discussed first. Conditional simulation will then be evaluated in its 
efficacy in obtaining confidence intervals. 
This section first outlines the basic concept of conditional simulation and provides 
an algorithm that employs conditional simulation to estimate confidence bounds for 
the CFD. The results of this experiment support the potential of conditional simula¬ 
tion for correcting the sample size bias. A heuristic discussion of the mechanism 
underlying this adjustment for sample size effect is presented with the hope of moti¬ 
vating additional analytical investigation of this effect. 
Conditional simulation (Journel, 1974; Gotway, 1994) is a geostastical term for 
simulating a population conditional on information observed in a sample. In the case 
of kriging, a sample from a spatial population is used to estimate the variogram and 
mean for the population. The conditional simulation procedure generates a field of 
simulated values conditioned on the estimated mean and variogram from the sample. 
To the extent that the estimated mean and variogram approximate the true mean and 
variogram and the assumed distribution is a reasonable model for the true distribu¬ 
tion, repeated simulations of this virtual population will represent the variability 
typical of the true population. It follows that statistics computed from the condition¬ 
ally simulated fields will represent the expected variability of statistics from the true 
distribution. The CFD is a graphical representation of ordered statistics of percent 
compliance over time and it is a reasonable to assume that repeated conditional 
simulations will lead to effective confidence bounds for the CFD. 
Conditional Simulation Methods 
In the computation of the CFD, conditional simulation is implemented at the inter¬ 
polation step for each month. Interpolation produces an estimate of the spatial 
surface of the target parameter. From that estimate of the surface is obtained an esti¬ 
mate of the percent of noncompliance. Using conditional simulation, the surface can 
be reconstructed 1000 times. From the 1000 simulated surfaces are computed 1000 
estimates of the proportion of noncompliance. When this is repeated for each month 
for say 36 months, the result is an array of 1000 sets of 36 values of the proportion 
of noncompliance. Each of the 1000 sets of 36 can then be ranked from largest to 
smallest to compute a CFD in the usual way which results in 1000 CFD estimates. 
The variability among these 1000 CFDs can be used to estimate confidence intervals. 
To evaluate this concept, the following simulation experiment was conducted 
1. The first step is to simulate a population that will be considered the “true” 
population for this exercise. A grid of dimensions 5x60 is populated using an 
exponential spatial variance model with variogram parameters set to 
(0.00625026, 2.67393446). These variogram parameters were estimated from 
Patuxent cruise track chlorophyll data. This grid is populated 36 times to repre¬ 
sent 36 months. The mean and variogram are held constant for the 36 
simulations to create a simplistic case with no seasonal or spatial trend. Using 
this set of data, the CFD is computed in the usual way and this is considered 
the “true” CFD. 
appendix a 
The Cumulative Frequency Diagram Method tor Determining Water Quality Attainment 
