A-4 
or other tests of spatial and temporal compliance. Work remains to be done in 
understanding fundamental properties of how the CFD represents likely covari¬ 
ances of attainment in time and space and how temporal and spatial correlations 
interact with sample size effects. Further, more work is needed in analyzing biases 
across different types of designated use segments. The panel expects that a two- 
three year time frame of directed research and development will be required to 
identify and measure these sources of bias and imprecision in support of attain¬ 
ment determinations. 
3. The success of the CFD-based assessment will be dependent upon decision 
rules related to CFD reference curves. For valid comparisons, both reference 
and attainment CFDs should be underlain by similar sampling densities and 
spatial covariance structures. 
CFD reference curves represent desired segment-designated use water quality 
outcomes and reflect sources of acceptable natural variability. The reference and 
attainment curves follow the same general approach in derivation: water quality 
data collection, spatial interpolation, comparison to biologically-based water 
quality criteria, and combination of space-time attainment data through a CFD. 
Therefore, the biological reference curve allows for implementation of threshold 
uncertainty as long as the reference curve is sampled similarly to the attainment 
curve. Therefore, we advise that similar sample densities are used in the deriva¬ 
tion of attainment and reference curves. As this is not always feasible, analytical 
methods are needed in the future to equally weight sampling densities between 
attainment and reference curves. 
4. In comparison with the current IDW spatial interpolation method, kriging 
represents a more robust method and was needed in our investigations on 
how spatial covariance affects CFD statistical inferences. Still, the IDW 
approach may sufficiently represent water quality data in many instances 
and lead to accurate estimation of attainment. A suggested strategy is to use 
a mix of IDW and kriging dependent upon situations where attainment was 
grossly exceeded or clearly met (IDW) versus more-or-less “borderline” 
cases (kriging). 
The current modeling approach for obtaining predicted attainment values in space 
is Inverse Distance Weighting (IDW), a non-statistical spatial interpolator that uses 
the observed data to calculate a weighted average as a predicted value for each loca¬ 
tion on the prediction grid. IDW has several advantages. It is a spatial interpolator 
and in general such methods have been shown to provide good prediction maps. In 
addition, it is easy to implement and automate because it does not require any deci¬ 
sion points during an interpolation session. IDW also has a major disadvantage - it 
is not a statistical method that can account for sampling error. 
Kriging is also a weighted average but first uses the data to estimate the weights 
to provide statistically optimal spatial predictions. As a recognized class of statis¬ 
tical methods with many years of dedicated research into model selection and 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
