A-14 
with varying degrees of success to estimate the total spatial (to the limit of interpo¬ 
lator pixel size) distribution of a water quality constituent. As noted above, one could 
construct this process by reversing the roles of time and space. That is, first interpo¬ 
late over time and then build a cumulative distribution in space. In theory it is an 
abitrary choice to first standardize the data over space by interpolation and then 
construct the cumulative distribution in time. However, in practice, there is a greater 
diversity of sampling designs over space and therefore it is the sampling in the 
spatial dimension more than the temporal that creates many types of data that must 
be forced to a common currency. 
Step 2 - Interpolation. Interpolation is the step that puts data collected at various 
spatial intensities on a common footing. On the one hand, this is advantageous 
because data collected at many spatial intensities are available for the assessment 
process. On the other hand, it can be misleading to accept interpolated surfaces from 
different data sources as equivalent without qualifying each interpolation with a 
measure of the estimation error that is associated with each type of data. Clearly an 
interpolation based on hundreds of points per segment (such as cruise track data) will 
more accurately reflect the true noncompliance percent when compared to an inter¬ 
polation based on two or three points per segment (such a fixed station data). Of the 
various types of interpolation algorithms available, the method proposed for this 
assessment is kriging. Kriging offers the best available approach for the estimation 
error associated with interpolation. 
Step 3 - Pointwise Compliance. Determining the percent of compliance of each cell 
from each interpolation would seem to be a simple step. If the estimated value for a 
cell exceeds the criterion then that cell is out of compliance. 
While interpolation allows for a standardization of many types of data, pointwise 
compliance allows for standardization of many criteria. Because compliance is 
determined at points in time and space, it is possible to vary the compliance criteria 
in time and space. If different levels of a water quality constituent are acceptable in 
different seasons, then the criterion can vary by season. It is possible to implement 
different criteria over space for a segment that bridges oligohaline and mesohaline 
salinity regimes. It would even be possible to let the criterion be a continuous func¬ 
tion of some ancillary variable such as temperature or salinity. All that is required is 
that the final determination be yes or no for each interpolator cell. 
Even the simplicity of this concept becomes diminished when issues of interpolation 
error are considered. Consider the assessment of two interpolator cells from an inter¬ 
polation based on cruise track data. One cell near the cruise track has an estimated 
value is 4 and a standard error of 0.1. A second cell far from the cruise track has an 
estimated value of 4 and a standard error of 1.0. If the criterion were 3.0, it is fairly 
certain that the first cell represents exceedance. It is much less certain that the second 
cell represents exceedance. In the simple assessment of non-compliance, they count 
the same. 
Step 4 - Percent Non-compliance in Space. Computing a percentage should also 
be a simple step. The estimate is simply 100 times the number of cells out of compli¬ 
ance divided by the total number of cells. As a rule, the uncertainty of a binary 
process can be modeled using a binomial distribution. However, the issue of uncer- 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
