A-5 
estimation, kriging is designed to permit inferences from sampled data in the pres¬ 
ence of uncertainty. Thus the quantity and distribution of the sample data are 
reflected in those inferences. Indeed, the panel’s initial trials on the role of spatial 
sources of error in the CFD have depended upon the ability to propagate kriging 
interpolation uncertainty through the CFD process in generating confidence inter¬ 
vals of attainment. 
In comparison to IDW, kriging is more sophisticated but requires greater expertise 
in implementation. Kriging is available in commercial statistical software and 
also in the free open source R Statistical Computing Environment, and requires 
geostatistical expertise and programming skills for those software packages. 
Segment by segment variogram estimation and subsequent procedures would 
require substantial expert supervision and decision-making. Thus, this approach is 
not conducive to automation. On the other hand, there may be CBP applications 
where the decision on attainment is clearly not influenced to any substantial 
degree by the method of spatial interpolation. One 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). 
5. More intensive spatial and temporal monitoring of water quality will 
improve the CFD approach but will require further investigations on the 
influence of spatial and temporal covariance structures on the shape of the 
CFD curve. This issue is relevant in bringing 3-dimensional interpolations 
and continuous monitoring streams into the CFD approach. 
In the near future, the panel sees that the CFD approach is particularly powerful 
when linked to continuous spatial data streams made available through the cruise- 
track monitoring program, and the promise of continuous temporal data through 
further deployment of remote sensing platforms in the Chesapeake Bay (Chesa¬ 
peake Bay Observing System: http://www.cbos.org/). These data sets will support 
greater precision and accuracy in both threshold and attainment determinations 
made through the CFD approach but will require directed investigations into how 
data covary over different intervals of time and space. Further, there may be 
important space-time interactions that confound the CFD attainment procedure. 
Some of the assessments for the Bay such as that for dissolved oxygen require 
three dimensional interpolation, but the field of three dimensional interpolation is 
not as highly developed as that of two dimensional interpolation. Kriging can be 
advantageously applied in that it can use information from the data to develop 
direction dependent weighted interpolations (anisotropy). Kriging can include 
covariates like depth. Options for implementing 3-D interpolation include: 
custom IDW software, custom kriging software using GMS routines, or custom 
kriging software using the R-package. 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
